Mr Julien Aubril

ARRIVE, Mr. BIOTTEAU Mr Arnaud

Mr Gwenael

Fernandez-Pacheco Jorge

Armenteros

Keywords: Thermal energy storage (TES), packed bed, thermocline, packing configuration, storage media, multi-objective optimization

The thermocline packed-bed tank with sensible heat or latent heat fillers is a cost-effective option for thermal energy storage (TES). Its thermal performance is very dependent on the packing configurations to each fluid flow and temperature situation. The principal objective of this PhD dissertation is to study the influence factors for different configuration of fluid flow and tank design, and then to conduct multi-layered packing configuration optimization of the storage tank.

It starts by exploring the wall impact on thermocline and global thermal performance in dynamic conditions. Then, various influences, including the inlet configuration, the insulation, the filler size, and the operating parameters, on the thermocline in radial and axial direction based on a basic sensible heat filler tank are investigated. After that, the multi-layered configuration optimization of phase change material storage tank using a multi-objective genetic algorithm in multiple cycling is carried out by integrating the tank into an agriculture greenhouse application. The thermal performance of optimal tanks in seasonal operations is studied to find the potential for improvement of future work.

Résumé

III

Résumé

Un réservoir thermocline avec un garnissage constitué de matériaux pour du stockage thermique sensible et/ou latent est une solution prometteuse pour le stockage d'énergie thermique (TES).

Les performances d'un tel réservoir sont très dépendantes de la configuration physique, et des matériaux du garnissage. Ainsi, il existe un optimum pour chaque cas d'usage même si quelques règles générales sont conservées. L'objectif de cette thèse consiste à d'abord étudier l'effet de ces différents paramètres géométriques, physiques et thermo-hydrauliques sur l'efficacité du stockage. Une étude d'optimisation est réalisée afin de déterminer la meilleure configuration des paramètres pour un objectif donné. La première partie du manuscrit traite de l'impact des parois sur l'évolution de la thermocline et sur l'efficacité globale de la charge/décharge du réservoir, au moyen d'un modèle numérique simplifié prenant en compte ces effets tout en restant rapide à résoudre. Ensuite, les effets de la configuration du diffuseur d'entrée/sortie, de l'isolation thermique et des paramètres de charge/décharge sont étudiés expérimentalement sur un banc de tests dédié. Cette expérience a permi également de valider le modèle numérique. Ce modèle numérique est ensuite utilisé pour mener une optimisation avec une configuration multi-couches et multi-matériaux du garnissage grâce à un algorithme génétique multi-objectifs pour différents types de cycles de charge/décharge. Cette méthodologie est notamment mise en oeuvre pour une application de stockage thermique dédiée à une serre horticole. Le manuscrit décrit, enfin, des pistes à développer pour des travaux futurs. In coping with issues of the fluctuating and intermittent renewable energy sources in utilization, thermal energy storage (TES) technology is an effective way. It addresses the contradiction between energy supply and demand through smoothing production and shifting peak load [1]. Integrating TES system in various applications like buildings, agriculture, and industries is feasible to improve the system stability and efficiency by replacing the conventional carbon dioxide (CO2) emission energy backup.

Thermocline packed-bed TES tank (or dual-media thermocline) is a type of cost-effective and potential technology. As a type of one-tank system, it has tank volume investment reduction compared to the two-tank system, and also shows the filler advantages compared to another onetank system of single-media thermocline (by 45% than two-tank in total) [2]. In this kind of tank, cheap sensible heat fillers and latent heat fillers (or phase change material, PCM) with high energy density are good selections, or even mixing both as fillers through different packing configurations

to increase efficiency of system [3].

However, barriers still exist:

-Unstable temperature stratification or thermocline in one-tank system is leading to thermal performance degradation.

-The tradeoff between configurations (packing structure, filler types) and high efficiency under various operational parameters is difficult to be achieved, comparing to single-media thermocline system.

It's necessary to propose proper packing configuration in consideration of the influence factors (wall impact, inlet flow, heat loss, etc.) on thermocline in a packed-bed system.

Research foundation

This thesis work is part of a cooperation project of the 'OPTICLINE' supported by l'Agence Nationale de la Recherche (ANR): Optimization of high temperature thermal energy storage by the thermocline technology. Researchers in this project had conducted a lot of interesting and meaningful work in thermocline storage tank, including the single-media thermocline and the dual-media thermocline. Various parameters were investigated and optimized to stabilize the thermocline, as well as improve the thermal performance.

On one side, colleagues of PROMES laboratory focus on dual-media thermocline tank and design a large pilot-scale high-temperature experimental tank. Vannerem et al. [4] once investigated the operating parameters of the interstitial fluid velocity cause effect on thermocline performance. Finding that the impact of fluid velocity is too moderate to observe an optimal velocity, especially because of non-ideal inlet temperature conditions. Then, they tried to understand the effect of fluid distribution on the storage tank in experiment [5]. Later, latent heat PCMs were also attempted to be filled at top layer to enhance the thermal performance [START_REF] Keilany | Experimental and numerical study of combining encapsulated phase change material to sensible heat storage material in one-tank pilot scale thermal energy storage[END_REF].

On another side, works on laboratory LTEN begins from the single-media storage tank. Lou et al. [START_REF] Lou | Single-tank thermal energy storage systems for concentrated solar power: Flow distribution optimization for thermocline evolution management[END_REF][8] built a small lab-scale low-temperature experimental system and aimed at solving the flow distribution problem by designing the inlet/outlet manifold, to enhance the temperature stratification performance. In experimental validation, it was proved that the mixing behavior within the main fluid region doesn't represent obvious anymore after the optimized upper distributor equipping.

This thesis is a supplement of previous works and an extension to the dual-media thermocline (or packed-bed thermocline) tank investigation, focusing on influence factors and packing configuration optimization. Simulation is chosen as MATLAB and the experiment is based and modified on Lou's experimental set-up in LTEN.

Research objective

The main objective of this thesis is to propose the packing strategy for improving efficiency and utilization in cycles of thermocline packed-bed TES system. Initially, to understand the influence factors on thermocline system from the wall, insulation, inlet configuration, flow rate, etc. Subsequently, through optimizing packing configuration to obtain a stable and thinner thermocline for alleviating the influence of the unstable temperature input. Accessorily, the experimental methodology is used to clarify some phenomena that were insufficiently explained in the simulation and to validate the developed models for this study.

The present thesis is implemented to combine the scientific methodologies of the theoretical analysis, numerical simulation, and experimental validation to provide a case study for industrial applications.

Thesis outline

This thesis paper is introduced in several parts:

Chapter 2
This chapter presents a comprehensive review of the thermocline packed-bed TES system, covering the storage mechanisms, packing configurations, and the application temperature ranges.

A detailed description of storage media is presented. An introduction of influence factors i.e., operational, geometrical, and thermophysical parameters, on the thermal performance of storage systems, is exhibited. The state of the art of thermocline packed-bed system based on storage media and packing structure is presented in a series of studies. This chapter is objective to offer good guideline to design the initial packing structure, the selection of filler materials, or the operational conditions.

Chapter 3

This chapter systematically explores the wall impact on the thermocline behavior comparing with two typical configurations -a lab-scale low-temperature tank and a pilot-scale hightemperature tank. The amount of energy stored in wall and insulation is quantified to define the influence degree. The dynamic influence of wall stored energy in discharging on thermocline is

presented. An adapted transient model that accounting the wall impact and heat loss in governing equation is defined. After that, a wall parametric study is performed to propose an optimal wall design guideline to avoid thermocline degradation.

Chapter 4

This chapter experimental and numerical investigated influence factors on dynamic thermal behavior of thermocline packed-bed tank with sensible fillers. It studied the impact of diffuser and insulation on radial temperature distribution, and clarifies the impact of flow rate and operational temperature on axial heat transfer and diffusion based on parametric study. The developed threephases model was experimental validated for the temperature gradient inside and particle. At last, a parameter study of influence factors, including inlet temperature and mass flow rate, on thermocline thickness is performed to get a highest energy efficiency.

Chapter 5

This chapter provides an optimization method for packing configuration strategy on maximizing the overall energy efficiency and storage/utilization ability in multiple cycles by using

PCM. An initial tank is first designed according to meteorology data of a low-temperature application of the seasonal greenhouse. Adapting a multi-objective genetic algorithm (MOGA) to optimize the layer configuration under PCM property constraints (thermal conductivity, phase change temperature, and layer thickness) and operational constraints (mass flow rate). Based on optimal result, the steady and dynamic inlet temperature input were compared in real greenhouse application to find the influence for improvement.

Chapter 6

At last, this chapter summaries main results in former chapters of this thesis paper and give some prospective for future work.

Literature review on thermocline packed bed thermal energy storage system Abstract

The thermocline packed-bed thermal energy storage (TES) system acted as dual-media is an alternative to conventional two-tank storage system, exhibiting excellent cost and heat capacity advantages. This chapter is the literature review that provides an overview of thermocline packed-bed TES systems, covering the storage mechanism, packing configurations, application temperature ranges, etc. It is looking forward to presenting the research progress, identifying the existing challenges, and giving perspective for future work. The objectives of this chapter are as follows:

• Summarize the different storage materials that used in packed bed system and corresponding advantages/disadvantages.

• Analyze the influencing factors on thermal performance, i.e., operational, geometrical, and thermophysical parameters.

• Make a clarification of the state-of-art of various thermocline packed-bed TES system.

• Point out the interesting of improving the system through designing configuration.

Keywords: thermal energy storage, thermocline, packed bed, packing configuration, sensible heat, latent heat

This chapter is published as:

Introduction

Energy demand is in rapid growth especially for energy sources without environmental issues of global warming and air pollution. The International Energy Agency (IEA) pointed out in "Tracking Report 2020" that the renewable energy counted for about 27% of the global electricity production in 2019. However, the use of renewable power needs to be significantly increased to half of the production to meet the demand of sustainable development scenario by 2030 [START_REF]Renewable Power Tracking Report[END_REF]. Solar energy as a feasible alternative to fossil fuel is one of the promising options due to the large quantities of solar radiation on the surface of earth [START_REF] Prieto | Thermal energy storage (TES) with phase change materials (PCM) in solar power plants (CSP). Concept and plant performance[END_REF]. However, the solar power source and the power demand are both intermittent, and often in mismatch.

To address these problems, the TES system is integrated in solar energy system, like concentrated solar power (CSP) and domestic solar hot water supply, to promote the system reliability by replacing conventional fossil fuel backup systems [1][11] [START_REF] Pelay | Dynamic modeling and simulation of a concentrating solar power plant integrated with a thermochemical energy storage system[END_REF][13] [14][15]. This economic and CO2 emission free solution allows buffering transient weather conditions, increases the annual capacity factor and evens the electricity production. More than that, the TES has been applied in various energy systems in order to improve the system stability and efficiency, including building energy conservation, waste heat recovery, cooling system, and many others [START_REF] Merlin | Industrial waste heat recovery using an enhanced conductivity latent heat thermal energy storage[END_REF][17] [START_REF] Tatsidjodoung | A review of potential materials for thermal energy storage in building applications[END_REF][19] [START_REF] Mckenna | Geocooling with integrated PCM thermal energy storage in a commercial building[END_REF][21].

Storage mechanism

There are different ways to store heat: the sensible heat storage based on a change of temperature, the latent heat storage based on a physical status change, and the thermochemical storage based on endothermic/exothermic chemical reactions [START_REF] Wei | Selection principles and thermophysical properties of high temperature phase change materials for thermal energy storage: A review[END_REF] [START_REF] Sarbu | A comprehensive review of thermal energy storage[END_REF]. The latter can potentially store more energy per volume unit (nearly 10 6 kJ m -3 ) but suffers from high complexity and low technical maturity [START_REF] Chen | State of the art on the high-temperature thermochemical energy storage systems[END_REF] thus will not be involved in this chapter. In single-media systems, heat storage is achieved using the sensible heat transfer fluid (HTF) only, such as in domestic hot water tanks [START_REF] Chandra | Stratification analysis of domestic hot water storage tanks: A comprehensive review[END_REF]. However, in CSP, those require high temperatures and thus expensive and nonenvironmental friendly fluids, which usually shows poor thermal properties. The packed bed or dual-media is then preferred, with solid fillers in the tank acting as main storage media, exchanging heat with HTF through direct contact, decreasing thereby the total amount of HTF required. There are other considerations when conceptualizing a TES system, such as using active or passive, direct or indirect concept (Figure 2.1). Such aspect will not be detailed here and the following parts of the chapter will focus on the storage tanks themselves.

Thermocline packed bed technology

Typically, the integrated TES system is designed as a one-tank or a two-tank system [26][7].

In two-tank system, the HTF is stored in two isolated and insulated tanks with two extreme temperatures. One primary example of a two-tank system is a CSP plant, shown in Figure 2.1 a.

In daytime, the HTF collects solar heat energy from solar receiver and transfers heat to the steam generator for power generation, and extra heat energy is stored in a hot tank. During the night or insufficient sunlight day, the HTF from the hot tank is delivered and used to maintain the power production. The one-tank system (or single-tank) is a substitution of the conventional two-tank system that greatly cuts off investment costs by removing a tank, as shown in Adapted from figures that obtained the copyright permission of Elsevier [License No. 5207601058078, Dec 14, 2021].

In this system, the hot HTF is stored at the top, and the cold HTF stays at the bottom of tank.

Physical stratification between both HTFs is maintained by buoyancy forces due to the density difference [START_REF] Zhao | Thermal performance and cost analysis of a multi-layered solid-PCM thermocline thermal energy storage for CSP tower plants[END_REF]. The zone between the hot and cold HTF, characterized by a temperature gradient, is called thermocline, and is represented on Figure 2.2. With cheap fillers and smaller tank volume, the cost reduction of overall investment can be up to 35% for packed-bed TES tank in comparison to traditional two-tank TES system in CSP plant [START_REF] Brosseau | Testing of thermocline filler materials and molten-salt heat transfer fluids for thermal energy storage systems in parabolic trough power plants[END_REF]. For many packing materials used in industry, the energy density in theory is about 180-250 MJ m -3 (or 50-70 kWhth m -3 ) based on a temperature change of about 100 K [START_REF] Esence | A review on experience feedback and numerical modeling of packed-bed thermal energy storage systems[END_REF]. Due to these advantages, the thermocline packedbed TES system is considered to be a promising technology for solar energy application, embracing the low, middle, and high-temperature ranges [START_REF] Singh | A review on packed bed solar energy storage systems[END_REF].

(a) (b)

Challenges

However, the shortcoming of the present thermocline packed-bed TES system also exists: the useful zone called "dead zone" because the heat stored in this region is mostly at a temperature lower than the cutoff temperature, under which the charging/discharging process is hard to be operated (Figure 2.3). In theory, the thermocline quality evaluated by its stability and thickness reflects the system performance: higher level of thermal stratification in the thinner thermocline zone means higher energy and exergy efficiencies [START_REF] Roux | Thermocline thermal energy storage optimisation combining exergy and life cycle assessment[END_REF] [START_REF] Rosen | The exergy of stratified thermal energy storages[END_REF]. Nevertheless, the thermal stratification tends to become unstable and expanded over dynamic and cycling operations. This thermocline degradation (or decay) can be due to several reasons [34][35].

• Thermal diffusion in the solid fillers and the fluid.

• Heat losses through the walls.

• Heat convection of the HTF itself resulted from fluid flow regimes in porous bed.

• Limited heat convection between solid and fluid causing heat transfer delay.

• Variable operational conditions during charging and discharging.

• Non-uniform flow distribution at the inlet due to sudden fluid injection or near the wall region because of the different porosities.

In addition, this system faces challenges like conflict between high storage capacity per unit volume and low cost, the temperature dropping or heat loss at the end of heat storage/release cycles, pressure drop under high porosity bed, and stability under various operational parameters.

Therefore, investigations on the physical phenomena influencing the thermocline thickness and on the performance optimization under techno-economic constraints of the single tank parameters are required. Only through that, the development of the thermocline packed-bed system will become more attractive through designing optimization.

Figure 2.3:

Intermediate "dead zone" in conventional rock-filled thermocline tank [START_REF] Flueckiger | Latent heat augmentation of thermocline energy storage for concentrating solar power -A system-level assessment[END_REF].

Obtained copyright permission of Elsevier [License No. 5207601468200, Dec 14, 2021]

Storage media

This section presents the different storage materials and the properties considered for the appropriate design, considering the storage media or fillers are the core among other elements of a packed-bed thermocline TES system, including the (sensible heat and/or latent heat) fillers, the HTF, the wall and insulation [START_REF] Mohamed | A review on current status and challenges of inorganic phase change materials for thermal energy storage systems[END_REF], and the inlet/outlet manifolds or diffusers.

Sensible heat fillers

Sensible heat storage occurs when the temperature of material rises. When choosing the materials, the important thermal properties are the volumetric heat capacity (𝜌𝜌 • 𝐶𝐶 𝑝𝑝 ), which dictates the energy storage density capability, and the heat diffusivity (

𝜆𝜆 𝜌𝜌•𝐶𝐶 𝑝𝑝

), which reflects the rate of the heat released and absorbed [START_REF] Kuravi | Thermal energy storage technologies and systems for concentrating solar power plants[END_REF].

Table 2.1 lists some sensible material fillers for packed-bed TES system and corresponding thermophysical properties. For most of sensible heat storage materials, the volumetric heat capacity can vary between 900 and 3000 kJ m -3 K -1 [START_REF] Stutz | Storage of thermal solar energy[END_REF]. With favorable features of the proper volumetric heat capacity, low cost, and availability, sensible heat material is commonly used in industrial or lab thermocline tanks. Rocks are interesting fillers in packed-bed TES system since they have a high heat capacity and are cheap. Tiskatine et al. [START_REF] Tiskatine | Suitability and characteristics of rocks for sensible heat storage in CSP plants[END_REF] evaluated 52 sensible heat materials of a packed-bed system for high-temperature CSP application. Among those, four types of materials, the dolerite, granodiorite, hornfels, gabbro and quartzitic sandstone were found to be excellent in air-based solar.

The stored heat of material ( 𝑄𝑄 ) for a given temperature elevation of sensible fillers is calculated:

𝑄𝑄 = ∫ 𝑚𝑚 • 𝐶𝐶 𝑝𝑝,𝑠𝑠 • 𝑑𝑑𝑑𝑑 𝑇𝑇 2 𝑇𝑇 1 (2.1)
where -𝑑𝑑 1 and 𝑑𝑑 2 , the initial and final temperature, respectively.

-𝐶𝐶 𝑝𝑝 , the heat capacity.

-, the mass.

-λ , the thermal conductivity.

-, the density.

Sensible fillers

ρs (kg m -3 ) Cp,s ( J kg -1 K -1 ) 𝜆𝜆s (W m -1 K -

Latent heat fillers

Latent heat storage occurs when a material changes its phase from one physical state to another. When heating/cooling, a material that undergoes this phenomenon and releases/absorbs heat in a narrow temperature range is called phase change material (PCM). Four types of phase transition exist [START_REF] Herrmann | Survey of thermal energy storage for parabolic trough power plants[END_REF]: solid-solid (crystalline heat), solid-liquid (fusion heat), liquidgas (vaporization heat), and solid-gas (sublimation heat). Among them, PCM based on solid-liquid transition is widely used in TES for its simplicity and wide temperature availability The stored energy of PCM in different heating stages is calculated as:

[21][52][53][54].
𝑄𝑄 = ∫ 𝑚𝑚 • 𝐶𝐶 𝑝𝑝,𝑠𝑠 • 𝑑𝑑𝑑𝑑 𝑇𝑇 2 𝑇𝑇 1 (𝑑𝑑 2 < 𝑑𝑑 𝑚𝑚 ) (2.2) 𝑄𝑄 = ∫ 𝑚𝑚 • 𝐶𝐶 𝑝𝑝,𝑠𝑠 • 𝑑𝑑𝑑𝑑 𝑇𝑇 𝑚𝑚 𝑇𝑇 1 + 𝑚𝑚 • ∆𝐻𝐻 𝑚𝑚 (𝑑𝑑 2 = 𝑑𝑑 𝑚𝑚 ) (2.3) 𝑄𝑄 = ∫ 𝑚𝑚 • 𝐶𝐶 𝑝𝑝,𝑠𝑠 • 𝑑𝑑𝑑𝑑 𝑇𝑇 𝑚𝑚 𝑇𝑇 1 + 𝑚𝑚 • ∆𝐻𝐻 𝑚𝑚 + ∫ 𝑚𝑚 • 𝐶𝐶 𝑝𝑝,𝑙𝑙 • 𝑑𝑑𝑑𝑑 𝑇𝑇 2 𝑇𝑇 𝑚𝑚 (𝑑𝑑 𝑚𝑚 < 𝑑𝑑 2 ) (2.4)
where -𝑑𝑑 𝑚𝑚 , the phase change temperature.

-∆𝐻𝐻 𝑚𝑚 , the phase change enthalpy.

-𝐶𝐶 𝑝𝑝,𝑠𝑠 , the heat capacity of solid phase PCM.

-𝐶𝐶 𝑝𝑝,𝑙𝑙 , the heat capacity of liquid phase PCM. Table 2.2 Thermophysical properties of some candidate solid-liquid PCM fillers for thermocline packed-bed TES [START_REF] Mehling | Heat and cold storage with PCM[END_REF].

PCM Liquid Solid

Tm (°C)

ΔHm (J g -1 ) ρl (kg m -3 ) 𝜆𝜆l (W m -1 K -1 ) ρs (kg m -3 ) 𝜆𝜆s (W m -1 K -1 )

Organic (0-200°C)

Paraffins n-Tetradecane, C14H30 The phase change temperature of PCM commonly maintains at a relatively stable value, allowing a constant temperature heat exchange for process control. But in some real cases, the phase change does not happen in a such stable platform and there is a small temperature range in phase transition actually appears [START_REF] Mehling | Heat and cold storage with PCM[END_REF]. When calculating the apparent heat capacity, the latent heat depends on transient temperature due to this temperature range [START_REF] Galione | Numerical evaluation of multi-layered solid-PCM thermocline-like tanks as thermal energy storage systems for CSP applications[END_REF][58][59] [START_REF] Yang | Thermal performance of a solar storage packed bed using spherical capsules filled with PCM having different melting points[END_REF]."Subcooling" (or supercooling) is another phenomenon that when PCM begins to solidify and release heat, the initial freezing temperature is below the melting temperature, caused by the nucleation rate [61][62]. Decreasing subcooling degree and the difficulty to bed operated.

In TES system, the PCM is commonly encapsulated to obtain a packed bed. Using encapsulated PCM as fillers is helpful to improve the stability and the sharpness of the thermocline in a packed-bed tank owing to the features presented above. Putting the PCM near the ports of tank system can restrict the outlet temperature at a constant value [START_REF] Zanganeh | Experimental and numerical investigation of combined sensible-latent heat for thermal energy storage at 575°C and above[END_REF]. Ge et al. [START_REF] Ge | Low melting point liquid metal as a new class of phase change material: An emerging frontier in energy area[END_REF] summarized several types of PCMs that can be used in solar energy storage. Mix molten salt is a promising material for high-temperature CSP plant, showing large melting temperature ranges from 100 to above 600 °C depending on the mixing ratio [START_REF] Wu | Dynamic thermal performance analysis of a molten-salt packed-bed thermal energy storage system using PCM capsules[END_REF]. The organic PCM shows great volumetric latent heat storage capacity around 128-200 kJ m -3 ×10 3 , while that of inorganic PCM is even doubled (250-400 kJ m -3 ×10 3 ) [START_REF] Sharma | Review on thermal energy storage with phase change materials and applications[END_REF]. However, the high cost and low thermal conductivity (about 0.2-0.7 W m -1 K -1 [START_REF] Stutz | Storage of thermal solar energy[END_REF]) restrict its wide application. Hence, heat transfer enhancement techniques are widely proposed and implemented to improve the thermal conductivity.

In summary, Table 2.3 compares the cost of some sensible and PCM materials applied in thermocline packed-bed TES. Sensible materials show cost advantages while PCMs with high energy density and stable phase change temperature can store more energy. It is observed that there is natural connection inside capsules when the PCM is melting, so that the thermal conductivity of PCM capsules should be considered in to an effective value in some conditions [START_REF] Lee | Numerical analysis in a full-scale thermal energy storage tank with dual PCM capsules[END_REF]. While the density variation of PCM in phase change process can be negligible in the constant capsule volume [START_REF] He | Phase transition temperature ranges and storage density of paraffin wax phase change materials[END_REF]. Moreover, the geometric properties of solid media, including particle size, shape (spherical, cylindrical, or rectangular), shell types, porosity, packing arrangement (random or regular), etc., all have influence on the thermal performance of packedbed system, especially the level of thermal stratification. Those will be discussed in the later part of this chapter.

Influencing factors on thermal performance

System thermal performance is mainly affected by three aspect factors (in Figure 2.7):

operational parameters, geometrical parameters, and thermophysical parameters [START_REF] Li | Sensible heat thermal storage energy and exergy performance evaluations[END_REF].

The operational parameters are commonly decided by the requirements of certain application. The geometrical parameters include the tank and filler geometries and configurations.

The thermophysical parameters are mainly decided by the selected material themselves and are usually temperature and/or pressure dependent. These influences factors are introduced in this sub-section.

Figure 2.7:

Influencing parameters of thermocline packed-bed TES system.

Operational parameters

The HTF mass flow rate, the inlet temperature, the cutoff temperature, and the cycling number are main operational parameters.

Mass flow rate

The HTF mass flow rate mainly determines the flow conditions and heat transfer rate between different phases. Commonly, higher flow velocity is beneficial to reduce the charging/discharging time due to the increment of heat transfer rate between HTF and solid fillers [START_REF] Li | A review of performance investigation and enhancement of shell and tube thermal energy storage device containing molten salt based phase change materials for medium and high temperature applications[END_REF][34] [START_REF] Felix Regin | An analysis of a packed bed latent heat thermal energy storage system using PCM capsules: Numerical investigation[END_REF]. Nallusamy et al. [START_REF] Nallusamy | Study on performance of a packed bed latent heat thermal energy storage unit integrated with solar water heating system[END_REF] proved that when the flow rate increased from 2 to 6 kg min -1 , the time required for the complete charging decreased by 24% in a PCM thermocline packed-bed system. However, some works found that the total stored energy in the tank [START_REF] Khor | Application of granular materials for void space reduction within packed bed thermal energy storage system filled with macro-encapsulated phase change materials[END_REF] and the thermocline development [82][34] were less influenced by the HTF flow rate. In fact, the impacts of the high velocity on uneven flow temperature distribution and stratification cannot be neglected in actual cases. The mass flow rate should be determined by comprehensively considering various factors such as the ending time, the efficiency and the flow distribution uniformity. More discussion on the influence of this parameter can be found in reference [1].

Inlet temperature

The inlet temperature is usually decided by application specifications. It determines the temperature difference thus the driving force for the heat transfer between HTF and solid fillers, but also responsible for the heat loss from the storage tank to the ambient. The inlet temperature impacts on heat transfer rate, heat loss, and total stored/released energy should be firstly investigated before system optimization [START_REF] Li | A review of performance investigation and enhancement of shell and tube thermal energy storage device containing molten salt based phase change materials for medium and high temperature applications[END_REF]. More information about the influence of this parameter is presented in [1].

Cutoff temperature

Likewise, the cutoff temperature referring to the termination condition of operation which is usually decided by application specifications, defined in Chapter 3. It is often set as 0.8-0.95 times to working temperature range in discharging process, and 0.05-0.2 times in charging process [START_REF] Zhao | System-level performance optimization of molten-salt packed-bed thermal energy storage for concentrating solar power[END_REF][84] [START_REF] Fasquelle | A temperature threshold evaluation for thermocline energy storage in concentrated solar power plants[END_REF]. With lower cutoff temperature, the storage tank cannot be fully charged. In discharging, a lower cutoff outlet temperature will cause more heat loss because of longer operation time, and may be insufficient to drive the power generation or energy supply.

Cycling operation

Efficient thermal cycling is closely related to the level of thermal stratification inside the tank [START_REF] Mahmood | Thermal energy storage for CSP hybrid gas turbine systems: Dynamic modelling and experimental validation[END_REF]. Firstly, the thermocline zone is expanding and stratification degrading after several charging/discharging cycles, causing the declined efficiency [START_REF] Xu | Sensitivity analysis of the numerical study on the thermal performance of a packed-bed molten salt thermocline thermal storage system[END_REF]. In the end, the thermocline region could occupy the whole tank volume. Secondly, the heat loss and pumping loss increase as time increase in the cycles [START_REF] Zanganeh | Design of packed bed thermal energy storage systems for high-temperature industrial process heat[END_REF]. There is no choice on this parameter it is ignored by the application. But of course, the thermocline will change in function of the number of cycles.

As a result, the cycling numbers should be decided when the outlet temperature at the cutoff time seems stable in cycling. Thus, it can be used to optimize the capacity and efficiency of system for long-term operation.

Geometrical parameters

Tank wall and insulation

Wall is the main support component of the tank. The selection of wall material is mainly depending on the temperature ranges and tank size. Metals like carbon steel serve as the wall material owing to their high strength and resistance to high pressure in high-temperature applications [START_REF] Zhao | System-level performance optimization of molten-salt packed-bed thermal energy storage for concentrating solar power[END_REF]. But, using this material may result in more heat loss to the ambient because of the high thermal conductivity. Meanwhile, it has a higher volumetric heat capacity than HTF.

Therefore, the wall may as the storage media to store/release heat in charging/discharging, leads to a thermocline radial temperature difference between the center and near-wall region.

Therefore, the wall impacts should be well considered in designing the thermocline packed-bed tank [START_REF] Xie | Wall impact on efficiency of packed-bed thermocline thermal energy storage system[END_REF].

Good insulation avoids heat loss and improve system stability. Whereas the energy variation of thick insulation is negligible for different temperature applications. Commonly, insulation is not worth to be considered as storage media.

Flow diffuser and buffer and inlet position

The flow distribution and thermocline stability are greatly affected by the injection of the HTF at the inlet. The sudden entering of HTF from the inlet tube will cause high fluid local velocity on the part region inside the bed. Because the inflow jet temperature is comparatively hotter/colder than the surrounding bed. The streamflow leads to the center temperature differing from the temperature in the radial direction of the same high height and may disturb the stratification [START_REF] Chandra | Stratification analysis of domestic hot water storage tanks: A comprehensive review[END_REF].

Through installing the flow diffuser and buffer at the inlet/outlet position will alleviate this phenonmen to achieve homongenous flow distribution. In packed-bed system, the porous media can serve as the diffuser to a certain extent to eliminate the flow fluctuation. Thus, it may be unnesessary to add a diffuser inside packed-bed tank, especially with the tank diameter to particle size ratio (

𝐷𝐷 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝐷𝐷 𝑝𝑝

) larger than 10. Moreover, the inlet/outlet position and numbers can also affect the stratification in non packed-bed TES system [START_REF] Zurigat | Influence of inlet geometry on mixing in thermocline thermal energy storage[END_REF].

Tank diameter-to-height ratio (aspect ratio)

In general, the increasing aspect ratio of tank ( 𝐷𝐷 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝐻𝐻 ) leads to the decreased heat loss because of the smaller lateral wall surface area for the same bed volume. Zanganeh et al. [START_REF] Zanganeh | Design of packed bed thermal energy storage systems for high-temperature industrial process heat[END_REF] reported that when the ratio increase from 0.5 to 2, the fraction of the pumping energy strongly decreased from 6.75% to 0.75% due to the shorter bed length. Oppositely, the overall efficiency decreased due to the weaker heat transfer rate caused by the decreased fluid velocity at constant inlet mass flow rate.

Particle size

Sensible fillers have a wide range of average particle size, usually varying between 1×10 -3 m to 0.05 m. Bruch et al. [START_REF] Bruch | Experimental and numerical investigation of a pilot-scale thermal oil packed bed thermal storage system for CSP power plant[END_REF] once investigated the fluid flow through a 3 mm sand bed and a 3 cm rock bed in pilot-scale thermal oil bed system. Smaller particle diameter facilitates the flow distribution for better thermal stratification and can increase heat transfer surface area [START_REF] Yang | Thermal analysis of solar thermal energy storage in a molten-salt thermocline[END_REF], but in the meantime it will cause higher pressure drops. Sometimes, the influence of boundary effect of mass transfer may be alleviated when the bed-to-particle diameter ratio is large [START_REF] Agalit | Numerical investigations of high temperature packed bed TES systems used in hybrid solar tower power plants[END_REF] [START_REF] Meier | Experiment for modelling high temperature rock bed storage[END_REF].

Larger particles (with low thermal conductivity) may have a larger temperature difference between solid and fluid, causing the faster expansion of the thermocline [START_REF] Xu | Effects of solid particle properties on the thermal performance of a packed-bed molten-salt thermocline thermal storage system[END_REF]. Sorour [START_REF] Sorour | Performance of a small sensible heat energy storage unit[END_REF] suggested to use intermediate particle size of 18 mm with low mass velocity instead of small particle size of 12 mm with high mass velocity to increase the storage efficiency. PCMs use the "capsules" to seal the material to avoid leakage. The encapsulated PCM capsules may be classified based on the diameter into: macro (>1 mm); micro (1-1000 µm); nano (< 1 µm).

Macro-encapsulation PCM is a good choice to be applied to packed-bed system. In fact, in actual thermocline packed bed tanks, the particle size is generally above 10 mm considering both the preparation technique and application requirements [START_REF] Li | Experimental and numerical study on the performance of a new hightemperature packed-bed thermal energy storage system with macroencapsulation of molten salt phase change material[END_REF]. However, the phase change time is mostly influenced by the relatively large capsule size of PCM [START_REF] Regin | Latent heat thermal energy storage using cylindrical capsule: Numerical and experimental investigations[END_REF]. Gao et al. [START_REF] Gao | Multi-objective optimization of thermal performance of packed bed latent heat thermal storage system based on response surface method[END_REF] used the PCM spherical particle with a small size of 40 mm instead of 100 mm to achieve a higher heat transfer rate with a shorter phase change time. Wu et al. [START_REF] Wu | Dynamic thermal performance analysis of a molten-salt packed-bed thermal energy storage system using PCM capsules[END_REF] decreased capsule diameter from 0.1 m to 0.02 m achieving the effective discharging efficiency from 73.78% to 98.33%.

Particle shape

Sensible fillers have including cylinder, sphere, cubic, rectangle or irregular shape, as shown in Figure 2.8. For the encapsulated PCM, the basic shapes are nearly the same, like spherical or cylindrical capsules [START_REF] Regin | Latent heat thermal energy storage using cylindrical capsule: Numerical and experimental investigations[END_REF]. The sphere shape shows highest the surface area than other regular shapes, facilitating heat exchange with the HTF. Moreover, increasing the surface roughness can increase the pressure drop [START_REF] Allen | Packed bed pressure drop dependence on particle shape, size distribution, packing arrangement and roughness[END_REF]. The flow condition inside the tank correspondingly changes when using particles with different shapes, resulting in different heat transfer behaviors between

Porosity and packing structure

Lower porosity means more packed bed region occupied by the solid fillers, usually resulting in a higher pressure drop [START_REF] Lew | Analysis of heat storage and delivery of a thermocline tank having solid filler material[END_REF][100] [START_REF] Anderson | Packed bed thermal energy storage: A simplified experimentally validated model[END_REF]. Typically, the porosity is about 0.3-0.4 using uniform spheres [START_REF] Nellis | Heat Transfer[END_REF] and about 0.22 by mixing two size particles [START_REF] Bruch | Experimental and numerical investigation of a pilot-scale thermal oil packed bed thermal storage system for CSP power plant[END_REF][103] [START_REF] Pacheco | Development of a molten-salt thermocline thermal storage system for parabolic trough plants[END_REF]. Nevertheless, the porosity depending on arrangement is hard to be controlled in reality. Cárdenas et al. [START_REF] Cárdenas | Techno-economic optimization of a packed-bed for utility-scale energy storage[END_REF] tested the porosity for the regular sphere particles ranging from 0.660 to 0.259. It was found that the porosity was 0.395 for a hexagonal packing, higher than that of random packing (0.36). Thoenes

and Kramers [START_REF] Thoenes | Mass transfer from spheres in various regular packings to a flowing fluid[END_REF] tested the relationship between porosity and regular packing structure. Each cross section is exhibited in sphere center in one layer (Figure 2.9). The dense cubic packing in Figure 2.9 a b are identical but distinguish in orientation. The body-centered cubic particle packing in Figure 2.9 f is in structure but to random packing of spheres, spheres do not attach to each other and only single sphere in the next layer lies in a "pit" formed by four spheres. It was obtained the cubic particle packing structure that nine particles located in body-centered cubic position shows the highest porosity of 0.48 than other packing at the same particle diameter. But, Allen et al. [START_REF] Allen | Packed bed pressure drop dependence on particle shape, size distribution, packing arrangement and roughness[END_REF] reported that the simple cubic packing was extremely unstable and shifted very easily while random arrangement of irregular-shaped particles was almost not isotropic.

Capsule shell thickness

PCMs can be well sealed in macro capsules using metal or plastic shell, as it shown in Figure 2.5. However, the thermal resistance of the shell may hinder the heat transfer process, resulting in slow PCM melting and solidification rate. Bellan et al. [START_REF] Bellan | Numerical and experimental studies on heat transfer characteristics of thermal energy storage system packed with molten salt PCM capsules[END_REF][108] found when the polymer shell thickness of PCM capsule increases around 66% from 1 to 3 mm, the charging time of storage tank is increased nearly by 15%. Zhang and Wang [START_REF] Zhang | Synthesis and properties of microencapsulated n-octadecane with polyurea shells containing different soft segments for heat energy storage and thermal regulation[END_REF] proposed an optimal core-to-coating weight ratio (wt./wt.) of 75/30 rather than 75/25 for capsulated PCM to avoid the spillage. Therefore, decreasing shell thickness as soon as possible can achieve high heat transfer efficiency for PCM capsule designing, but the mechanical strength should also be considered.

Types of thermocline packed bed system

The classification of thermocline packed-bed TES system based on different criteria is exhibited Figure 2.10.

• According to the storage mechanism of fillers, thermocline packed-bed system can be divided into sensible-heat thermocline packed-bed (SHTPB), latent-heat thermocline packed-bed (LHTPB), and heterogeneous-heat thermocline packed-bed (HHTPB)

combining sensible and latent.

• From system temperature range, it covers the low-temperature, e.g., domestic hot water heater, to the high-temperature application, e.g., CSP plant, reflected by the HTF and fillers.

• The layer packing structure is an optimization objective to achieve high performance in recent years.

Sensible-heat thermocline packed bed (SHTPB)

Packing sensible heat material in full bed is a simple, mature, and cost-effective way for TES with a lot of commercialized applications.

Single-layered sensible-heat thermocline

Comparing to the commercial two-tank system, the single-layered dual-media thermocline system is cheaper. Mostafavi Tehrani et al. [START_REF] Tehrani | Shell-and-tube or packed bed thermal energy storage systems integrated with a concentrated solar power: A techno-economic comparison of sensible and latent heat systems[END_REF][70] reported that when integrating thermocline systems into a validated 19.9 MWe Gemasolar CSP plant, there is a 62% reduction of specific storage cost for a dual-media thermocline with sensible concrete media of 9.38 US$ kWhth -1 compared to the two-tank molten salt system of around 24.5 US$ kWhth -1 (Figure 2.11). In addition, Strasser and Selvam [START_REF] Strasser | A cost and performance comparison of packed bed and structured thermocline thermal energy storage systems[END_REF] conducted cost analysis on two thermocline systems of 2165

MWh storage capacity, including a packed bed and a non-packed bed thermocline system. It obtained the thermocline packed-bed system of around 30 US$ kWh -1 is 12.5% costly lower than the structured-concrete thermocline system with axisymmetric and parallel-plate of around 34 Obtained copyright permission of Elsevier [License No. 5207680114050, Dec 14, 2021] For this type of single tank, designing the tank geometrical parameters, like tank height, tank shape, and inside fillers, to improve thermal performance is the main strategy once the solid filler material is determined.

US$ kWh -1 . (a) (b)
For example, Yang and Garimella [START_REF] Yang | Thermal analysis of solar thermal energy storage in a molten-salt thermocline[END_REF][112] studied the quartzite rocks (5 cm diameter)molten-salt thermocline system with small particle Reynolds number (𝑅𝑅𝑅𝑅) from 1 to 50 and where the ratio of the tank height to the particle diameter was 10 to 800. They found the discharging efficiency that is the output energy to the total energy initially stored energy was enhanced with decreasing tank height and increasing 𝑅𝑅𝑅𝑅.

Some works focus tank shapes, such as designing the truncated cone shape Moreover, the special packing structure that mixes different fillers in one tank as the one-tank system was also investigated. Like, Yin et al. [START_REF] Yin | Experimental research on thermal characteristics of a hybrid thermocline heat storage system[END_REF] used two representative porous fillers of zirconium ball and silicon carbide (SiC) foam in an experimental cylindrical tank. However, the mixed-filler thermocline system showed a declined effective heat storage capacity than singlephase molten salt thermocline tank due to the conflicts between the low volumetric heat storage capacity and the improved impact of porous structure on thermal performance (Figure 2.12 b).

(a) (b) The mixed-filler thermocline system with SiC foam and zirconium ball [START_REF] Yin | Experimental research on thermal characteristics of a hybrid thermocline heat storage system[END_REF].

Multi-layered sensible-heat thermocline

For the multi-layered particle bed, it actually aims to the improvement on the thermal energy storage capacity and the stratification through filling materials into different layers. Relatively few studies have been devoted to multi-layered SHTPB tanks [START_REF] Türkakar | Performance analysis and optimal charging time investigation of solar air heater with packed bed sensible heat storage device[END_REF]. Some inspiring works still exist.

Crandall and Thacher [START_REF] Crandall | Segmented thermal storage[END_REF] filled three layers of tank by the cast iron, copper, and rock to provide highest outlet temperature in discharging and the lowest outlet temperature in charging through the good stratification. The study showed that the cast iron with highest volumetric heat capacity at the inlet side in charging can maintain its temperature at low levels for an extended period. Li et al. [START_REF] Li | Cyclic thermal performance analysis of a traditional Single-Layered and of a novel Multi-Layered Packed-Bed molten salt Thermocline Tank[END_REF] also put five sensible-heat storage materials in TES tank (Figure 2.13).

Authors proposed a concept of the interface effect on thermocline, which refers to the enlarging or shortening effect at the interface between two types of filler on thermocline thickness. Once HTF flows from one layer with slow thermocline expanding velocity to another one with fast expanding velocity, the thermocline thickness increases. Thus, the thermocline thickness can be controlled by filling different materials orderly with different volumetric heat capacities, vice versa.

Latent-heat thermocline packed bed (LHTPB)

Using PCM capsules as filler in TES system, the LHTPB can obtain much higher energy density than SHTPB and two-tank system [START_REF] Zhao | Thermal performance and cost analysis of a multi-layered solid-PCM thermocline thermal energy storage for CSP tower plants[END_REF]. In this sub-section, a summary of the "pure" TES verses "combined" TES in terms of material types, or single-layer thermocline versus multi-layer PCM thermocline system are presented. Various investigations carried out on LHTPB system for different temperature applications are listed in Table 2.4.

Single-layered latent-heat thermocline

There is a lot of works on basic thermal behavior investigation and efficiency enhancement for tank systems. Chen and Yue [START_REF] Chen | Thermal performance of cool storage in packed capsules for air conditioning[END_REF] developed a 1D model validated by experimental data to characterize the thermal performance of PCM capsules packed-bed system with air HTF. Their results presented that the lump model is a convenient and simple method to determine the thermal performance of cool storage systems. Another interesting attempt was conducted by Rady [START_REF] Rady | Thermal performance of packed bed thermal energy storage units using multiple granular phase change composites[END_REF] through the mixing of two or three kinds of PCMs and placing them in a packed bed to improve performance. Experiments on packed-bed column system were performed to obtain basic understanding of dynamic thermal behavior of the composite bed with different ratio of mixing materials. Authors found through determining the proper mixing ratio, the overall unit performance with multiple granular phase change composites could be enhanced by about 15%

compared to the single material unit. An optimization strategy of the mixing ratio was determined according to the overall charging and discharging times and the exergy efficiency.

Many studies integrated this system into applications in different temperature ranges.

For low-temperature ranges, a single-layered LHTPB system has been applied and shown advantages of high security and easy operation for hot water or air condition system. Arkar et al.

[74] interagrated the low-temperature LHTPB system in a ventilation system of a building, which is able to cut down the volume of the mechanical ventilation system with a better thermal comfort. For high-temperature ranges, Flueckiger and Garimella [START_REF] Flueckiger | Latent heat augmentation of thermocline energy storage for concentrating solar power -A system-level assessment[END_REF] replaced the single-layered LHTPB system the conventional rock filler inside the tank in CSP. It found that the annual storage yield or plant output of the thermocline system could not be increased compared to a conventional rock-filled tank of equal size. A multiple filler structure consisting of cascaded PCMs with adjusted melting temperatures along the tank height should be designed, which will be introduced later.

In another study, the cost of this tank type was investigated. Li et al. [START_REF] Li | Comparisons of thermal performance and cost for three thermal energy storage systems utilized in supercritical CO2 Brayton cycle[END_REF] compared the twotank, sensible-, and latent-heat packed-bed systems coupled with a supercritical carbon dioxide (S-CO2) Brayton cycle. It was found that the sensible packed-bed tank had the smallest stored thermal energy due to the influence of the expanded thermocline thickness. The latent heat storage system showed the highest stored energy and effective discharging time. Moreover, the power cycle performance by integrating the latent packed-bed had the largest total work output with the lowest capital cost (37 US$ kWhth -1 ) compared to two tank (54 US$ kWhth -1 ) and sensible filler (52 US$ kWhth -1 ) concepts. That is because the vessel cost of tank were reduced a lot accoding to the definition of capital cost including thermal storage materials cost, vessel cost, and other costs.

Multi-layered latent-heat thermocline

The intention of multi-layered (or cascaded) LHTPB system is cascading PCMs in sequence of increasing phase change temperature in axial direction from bottom to top of packed bed, to harvest more heat by taking advantage of the temperature difference under the same flow velocity condition. In more detail, in single-layered system (charging for example), the hot HTF flows from the top to the packed-bed bottom and with decrease temperature due to the extracted heat from PCM storage media. The heat transfer rate near the bottom region of the tank would therefore be low since it is directly proportional to the temperature gap between HTF and PCM media, conversely in discharging.

To further enhance the heat transfer, it is a possible way to pack the tank by selecting the PCMs with different phase change temperature according to the HTF temperature distribution along the tank in axial direction [START_REF] Aldoss | Comparison between the single-PCM and multi-PCM thermal energy storage design[END_REF]. More importantly, the PCM phase change process should be constrained within the require temperature of charging/discharging to stablize the outlet temperature. Commonly, the PCM with high melting temperature should be placed at the top of the tank, while the PCM with low melting temperature can be at the bottom to form a temperature gradient along tank height. Felix et al. [START_REF] Felix Regin | An analysis of a packed bed latent heat thermal energy storage system using PCM capsules: Numerical investigation[END_REF] proposed that the complete melting time for the PCM bed system with a phase change temperature range, is faster than the system with a fixed phase change temperature.

Better thermal performance of this multi-stage concept has been proved in some packed-bed systems [START_REF] Watanabe | Second law optimization of a latent heat storage system with PCMS having different melting points[END_REF], no packed-bed systems with PCM modules [START_REF] Domański | Exergy analysis for the evaluation of a thermal storage system employing PCMS with different melting temperatures[END_REF][128] [START_REF] Gong | Enhancement of energy charge-discharge rates in composite slabs of different phase change materials[END_REF], or multi-layered shell-tube filled systems [10][130]. Table 2.5 lists the studied multi-layered LHTPB systems in the literature and their corresponding design parameters.

Yang et al. [START_REF] Yang | Thermal performance of a solar storage packed bed using spherical capsules filled with PCM having different melting points[END_REF] developed a multi-stage LHTPB system evenly filled by three layers of PCMs.

In contrast to the conventional single-layered PCM packed bed, the multi-layered system shows higher energy and exergy efficiencies. Elfeky et al. Chirino et al. [START_REF] Chirino | Parametric study of cascade latent heat thermal energy storage (CLHTES) system in Concentrated Solar Power (CSP) plants[END_REF] conducted parametric study and sensitivity analysis under different operational parameters on a three-stage LHTPB system for a 60 MWe CSP. It is obtained under the same tank volume condition, the sensitivity as a function of the thermal energy storage efficiency by changing tank diameter alone is double than that from changing tank height. Their results also revealed that the thermocline thickness could be increased and the efficiency decreased due to the natural convection in the tank.

The number of PCM layers is also a parameter of optimization analyzed in some investigations. For example, Wu et al. [START_REF] Wu | Cyclic behaviors of the molten-salt packed-bed thermal storage system filled with cascaded phase change material capsules[END_REF] investigated the influence of cascaded number (3 or 5 layers of PCM) on this type of system (Figure 2.15 b). Their results showed that a higher cascade number could result in faster charging and discharging rates. The actual store capacity of this type of system relays deeply on the threshold (or cutoff ) temperatures for charging or discharging process.

Heterogeneous-heat thermocline packed bed (HHTPB)

The features and limitations of SHTPB and LHTPB systems have been comprehensively

compared in the literature [START_REF] Nithyanandam | Analysis of a latent thermocline storage system with encapsulated phase change materials for concentrating solar power[END_REF][30] [START_REF] Gautam | A review on technical, applications and economic aspect of packed bed solar thermal energy storage system[END_REF]. SHTPB is commercially available by using cheap raw materials and well-studied by researchers. The main shortcomings are the low volumetric storage capacity and the temperature degradation at the end of dis-/charging cycles [136][137]. LHTPB is regarded as more promising owning to its high energy storage density and the unique characteristic of PCM, such as the relatively constant phase change temperature, but with a much higher cost [138][135].

The concept of HHTPB is proposed in order to reduce the amount of PCM fillers as well as to achieve the stable thermal behavior. This type of system, also called "combined" or "hybrid" sensible-latent TES system, can incorporate the advantages and cope with the techno-economic issues experienced by the LHTPB and SHTPB systems [START_REF] Ahmed | Thermal and economic evaluation of thermocline combined sensible-latent heat thermal energy storage system for medium temperature applications[END_REF][140] [141][142]. Table 2.6 lists the present multi-layered HHTPB systems and their corresponding design parameters.

There are several works focusing on stabilizing the outlet HTF temperature. Galione et al. For example, Zanganeh et al. [START_REF] Zanganeh | Experimental and numerical investigation of combined sensible-latent heat for thermal energy storage at 575°C and above[END_REF] designed and developed a 42 kWhth pilot-scale TES for CSP application by placing the PCM section on top of the rocks. AlSi12 with a phase change temperature of 575 °C was encapsulated in stainless steel tubes. Experimental and numerical analysis proved this "rocks+PCM" system could stabilize the outflow air temperature around the melting temperature of the PCM [START_REF] Zavattoni | High-temperature thermocline TES combining sensible and latent heat -CFD modeling and experimental validation[END_REF].

Zhao et al. [START_REF] Zhao | Thermal performance and cost analysis of a multi-layered solid-PCM thermocline thermal energy storage for CSP tower plants[END_REF][145] [START_REF] Zhao | An efficient tank size estimation strategy for packed-bed thermocline thermal energy storage systems for concentrated solar power[END_REF] had performed a series of works on the designed thermocline TES system for CSP plants. Two different PCMs (high-and low-phase change temperature) were installed at the top and bottom position of the tank, respectively, cheaper solid being put in the middle. Their results highlighted the advantage of this concept, in term of cost, to meet various cyclic operating time durations than other systems, especially with a smaller packing thickness of PCM layer [START_REF] Zhao | Thermal performance and cost analysis of a multi-layered solid-PCM thermocline thermal energy storage for CSP tower plants[END_REF]. The corresponding performance has been optimized by selecting less lower cutoff temperatures to enhance the utilization rate from economic and operational aspects [START_REF] Zhao | System-level performance optimization of molten-salt packed-bed thermal energy storage for concentrating solar power[END_REF]. Its application has also been extended to a 200 MWe hybrid nuclear-solar power system for ondemand power supply [START_REF] Zhao B Chen | Conceptual design and preliminary performance analysis of a hybrid nuclear-solar power system with molten-salt packed-bed thermal energy storage for on-demand power supply[END_REF] .

Abdulla and Reddy [START_REF] Abdulla | Comparative study of single and multi-layered packed-bed thermal energy storage systems for CSP plants[END_REF] compared the multi-layered HHTPB (PCM-rock-PCM) system with the single-layered rock media system. The improved HHTPB concept with PCM on the top and bottom 10% height of the tank showed longer discharge time for storing more energy. When the PCM width increases from 0 to 50%, the tank height decreases by around 50%. Thus, the cost associated with tank material, installation, maintenance, and operating could be significantly saved. However, the study of Liao et al. [START_REF] Liao | Efficiency analyses of high temperature thermal energy storage systems of rocks only and rock-PCM capsule combination[END_REF] showed that with extra PCM capsule layer, the capacity ratio and the charging/ discharging time of the storage tank could be increased only when a special cutoff temperatures for the cycling processes were chosen.

In addition, Ahmed et al. [START_REF] Ahmed | Thermal and economic evaluation of thermocline combined sensible-latent heat thermal energy storage system for medium temperature applications[END_REF] developed and compared three concepts of thermocline packed-bed storage tanks for mixing configuration: sensible rod structure (Figure 2.17 a), and spherical PCM capsules (Figure 2.17 b) and combined sensible-latent in radial direction (Figure 2.17 c). The effective discharging efficiency and capacity costs were estimated to be 95%, 87%,

The interests of packing configuration

Low economic investment and high system efficiency are two goals for system. Given those, the interest in designing configuration is to achieve higher system efficiency despite using the same amount of fillers and HTF. It should be noted that, the optimal configuration does not always get the highest thermal performance when operational changes.

Thus, this thesis is intended to design or optimize the packing configuration of thermocline packed system by using sensible heat or latent heat filler in layer structure.

Chapter conclusion

This chapter summarizes the development of the thermocline packed-bed tank for TES system. The storage material types, the influencing factors, and the state-of-art of tank concepts are overviewed. Main conclusions could be listed as follows.

• Good quality of thermocline reflects good thermal performance of packed-bed TES system. The objective is to maintain a stable and sharp stratification zone for high energy capacity ratio, thermodynamic efficiency, and proper operational time. High thermal performance of thermocline packed-bed tank with stable thermal stratification can be achieved by careful selection and determination of geometrical (packing), operational and thermophysical parameters.

• Based on storage materials, there are generally three types of thermocline packed-bed tanks, sensible-heat, latent-heat, heterogeneous-heat, with different packing structure and operating parameters. Sensible-heat system is cost-effective and commercial mature but has the problem of outlet temperature "decay" in cycling. Latent-heat system shows high energy density and stabilize outflow temperature but the PCM cost is also relatively higher than sensible fillers. The heterogeneous-heat system can combine characterizations and advantages of the former types, thus will have a bright foreground.

• Influence factors of operational, geometrical, and thermophysical parameters shows positive or negative on thermocline packed-bed system due to the complicated heat diffusion, heat convection, and hear transfer in charging/discharging cycling process. The useful/harmful impacts are need to be accounted and clarified and the trade-off between parameters still needs to be optimized.

• Packing configuration is a solution for efficiency improvement the thermal performance.

Multi-layered structure (single-layered, multi-layered) and storage media are designed elements for configuration. Among them, packing PCMs in a multiple layer manner with different melting temperature along the axial direction of the tank can cause a large temperature gap between solid and fluid in charging/discharging process.

Some scientific and technological barriers remain to be overcome for the widespread industrial application of thermocline packed-bed storage systems, which are also the key issues and challenges of the current research and development.

1) improving stratification quality and stability of thermocline for high thermal performance in the operational process.

2) achieving benefits maximization of thermal efficiency, loading capacity, and economic cost of system under various parameters.

3) splitting the technology as a commercial one into wide applications like the lowtemperature built environment. Num.

-- Chapter 3

Thermocline packed-bed thermal energy storage system under wall impact

Abstract

As introduced in last chapter, tank wall and the insulation layer may affect the thermal stratification and cause thereby the thermocline degradation, which issue has not yet been fully addressed in the literature. This chapter tried to fill this research gap by exploring the effect of wall thermal properties and heat loss on thermocline thermodynamic behavior of packed-bed tanks with the aim of their efficiency improvement. Meanwhile, this is the premise of accurate optimization simulation for next work. The contents of this chapter contains:

• Develop and fully exploit a transient numerical model considering wall impact.

• Compare two tank configurations: a high-temperature pilot-scale tank with a steel wall and a low-temperature lab-scale tank with a polycarbonate wall, to find the wall impact applicability.

• Quantify the stored energy in wall and insulation at steady condition, and evaluate wall impact on thermocline evolution and system efficiency under dynamic condition.

• Propose an optimal wall design guideline for different industrial applications.

Keywords

Introduction

Wall heat impact is a heat transfer phenomenon that the heat transfer fluid (HTF) in nearwall region appears to be overheated/overcooled than that in central tank region due to various factors, including the heat loss from storage tank to ambient, the stored/released wall energy in charging/discharging and the different void fraction in near-wall region compared to the center.

It is regarded to be responsible, to some extent, for the thermocline decay or instability and thus the reduced efficiency of the thermal energy storage (TES) system.

Wall impact on thermocline packed bed: the state-of-art

Various studies have been done to investigate the wall impact or boundary conditions in packed-bed TES tanks [START_REF] Díaz-Heras | Effective thermal conductivities in packed beds: Review of correlations and its influence on system performance[END_REF]. Argo and Smith [START_REF] Argo | Heat transfer in packed beds-prediction of radial rates in gas-solid beds[END_REF] conducted fundamental research on the effect of convective boundary layer in wall region on the temperature distribution of packed beds. By testing and comparing the temperature profiles in core region and near-wall region of a packedbed tank with gas flow, their results showed that a temperature drop in near-wall region occurred.

Chang et al. [START_REF] Chang | The effect of the physical boundary conditions on the thermal performance of molten salt thermocline tank[END_REF] further investigated the effect of physical boundary conditions including insert liner and sloped wall on the thermal performance of thermocline storage system by analyzing the entropy generation. It was observed that the thermocline thickness was larger and much more fluctuated in the near-wall region along the tank height than that in the center of the tank under the insert liner boundary condition. De Beer et al. [START_REF] Beer | Experimental study of the effective thermal conductivity in the near-wall region of a packed pebble bed[END_REF] studied the influence of wall effects on the effective thermal conductivity in the near-wall region at different temperature levels and with different packing structures. A notable reduction of the thermal effective conductivity of the bed that separated into the inner and outer regions was found and the influence was more significant at high temperature. In summary, such wall effects are mainly caused by unevenly distributed fluid flow in the near-wall region, which can though be ignored/alleviated at low Reynolds numbers (𝑅𝑅𝑅𝑅) or using the effective bed thermal conductivity [START_REF] Yagi | Heat and mass transfer from wall to fluid in packed beds[END_REF].

Another class of studies in the literature has focused on the heat loss and the stored/released heat in tank wall as well as in the insulation layer. Commonly three boundary types with increasing complexity have been used: (1) adiabatic boundary; (2) non-adiabatic boundary with heat loss and (3) non-adiabatic boundary with heat loss and with stored heat. The adiabatic/non-adiabatic boundary condition was usually adopted to simplify the model when heat loss to ambient was negligible or could be calculated using an overall wall heat transfer coefficient. For example, Yang

and Garimella [START_REF] Yang | Molten-salt thermal energy storage in thermoclines under different environmental boundary conditions[END_REF] compared the adiabatic and non-adiabatic boundary on the thermocline performance. It was found that the heat loss under non-adiabatic boundary distorted the flow temperature distributions, but such influence became insignificant at large flow 𝑅𝑅𝑅𝑅. The discharge efficiency of the thermocline tank was found to increase with the increasing 𝑅𝑅𝑅𝑅, opposite to the trend under adiabatic condition. Mira-Hernández et al. [START_REF] Flueckiger | Comparative analysis of single-and dual-media thermocline tanks for thermal energy storage in concentrating solar power plants[END_REF] reported that the heat loss under non-adiabatic condition could cause inhomogeneous internal flow for the whole tank due to the cooling of molten salt near the tank wall. But the total heat lost during charge/discharge the cycle was estimated to be negligible compared to the heat storage capacity.

Nevertheless, when the wall volume (or mass) constitutes a large proportion of the whole storage system, the heat capacity of tank walls (including the insulation) has to be taken into account by adding the energy equation. In this regard, Beasley and Clark [START_REF] Beasley | Transient response of a packed bed for thermal energy storage[END_REF] have developed a the effect of insulation on the thermocline behavior in a hypothetical high temperature utilityscale tank (14 m in height). Their results showed that the increased insulation thickness could form a uniform temperature in the cross-section even through the temperature of HTF (molten salt) near the wall could be slightly influenced by the wall temperature. Hoffmann et al. [START_REF] Hoffmann | A thermocline thermal energy storage system with filler materials for concentrated solar power plants: Experimental data and numerical model sensitivity to different experimental tank scales[END_REF] further proposed a model with three governing equations considering the wall as a third component in addition to solid and fluid phases. Their model, validated in different size tanks with liquid HTF, showed that the tank walls and the heat loss had a direct influence on the HTF outlet temperature for a pilot-scale tank. However, the radiative loss from the outer tank surface and the thermal resistance of the wall was not considered in their modeling. Table 3.1 summarizes main features of previous studies on the issues of wall impacts in thermocline packed-bed TES systems. • Wall impact on thermocline behavior.

• Wall parametric studies to provide wall design guideline.

Aim and scope

The above literature survey indicates that even though previous works investigated the influence of non-adiabatic boundary on the thermal performance of thermocline packed-bed tank, the research gap still exists in the following points. Firstly, the effects of wall thermal properties on the dynamic thermocline behavior are not fully addressed. The total amount of stored heat in the wall (and insulation) phase and its influence on the efficiency of the storage tank need to be further evaluated as well. Secondly, besides the large-scale thermocline tanks applied to concentrated solar power (CSP) plants at high temperature, thermocline tanks are also frequently used for waste heat recovery at medium temperature or for buildings at low temperature. For these applications, the size of the storage tanks is relatively small thus the tank wall and the insulation could occupy a relatively large volume ratio compared to the packed-bed region. It is thereby essential and necessary to explore wall impact on different size tanks to acquire a better understanding of system operation, especially the wall parameters. Thirdly, the trade-off between conflicting requirements that models correspond to different levels of detail and different calculation times has been rarely reported in the literature. Choosing a proper model to do such wall parametric study is equally important towards an optimal wall design for packed-bed TES tank.

In order to fill the above-mentioned research gap, the present study aims at developing adapted transient model(s) with balanced complex physical phenomena description and computation time to systematically explore the wall impact on the dynamic thermocline behavior of the packed-bed storage tanks. Main objectives of this study are as follows:

--to comprehend the impact of the wall thermal properties on the heat loss and on the thermal performance of thermocline packed-bed storage tank with different sizes and under different working temperatures;

--to identify the most influencing factors through the parametric and sensitivity analyses in order to provide design guidelines for thermocline packed-bed tank.

Methodology

Geometrical model

• ) of packed-bed [START_REF] Wu | Dynamic thermal performance analysis of a molten-salt packed-bed thermal energy storage system using PCM capsules[END_REF]. The packed-bed cylindrical tank has an inner wall to form the tank and an outer insulation to prevent heat loss. These two layers constitute a composite wall called 'tank walls' in the following text. Furthermore, the inlet and outlet ports are openings at the top and bottom of the tank, allowing HTF to flow in and out the tank.

• Charging/discharging operation

In charging or thermal storage stage, the hot HTF at 𝑑𝑑 𝐻𝐻 flows into the TES tank from the top port to transfer heat to low-temperature solid medium, and then flows out from the bottom port.

Conversely, in discharging or energy on loading, the cold HTF with 𝑑𝑑 𝐶𝐶 enters from the tank bottom to absorb heat from high-temperature solid media and flows out of tank from the top port. where -𝐻𝐻, the tank height in packed bed region.

-𝜀𝜀, the porosity of packed bed.

-𝑅𝑅 𝑖𝑖𝑖𝑖𝑖𝑖 , 𝑅𝑅 𝑚𝑚𝑖𝑖𝑚𝑚 , 𝑅𝑅 𝑒𝑒𝑒𝑒𝑖𝑖 , the internal bed, middle wall, external insulation radius of tank, respectively.

-𝑉𝑉 𝑠𝑠 , the total volume of solid particles.

-𝑉𝑉 𝑏𝑏 , the whole tank volume based on 𝑅𝑅 𝑖𝑖𝑖𝑖𝑖𝑖 and 𝐻𝐻.

-𝑑𝑑 𝐻𝐻 , the hottest operational temperature.

-𝑑𝑑 𝐶𝐶 , the coldest operational temperature.

-𝑧𝑧, 𝑟𝑟, the axial and radial coordinate of tank, respectively.

Three numerical models

In To simplify the model formulation and analysis, following assumptions have been employed:

(1) Inlet temperature and inlet/outlet mass flow rate of HTF are constant in charging and discharging.

(2) Bottom and top surfaces of the tank are adiabatic and there is no internal heat generation in the bed. The contact thermal resistance between wall and insulation is neglected.

(3) Thermal conduction and radiation between solid fillers are neglected as well as the heat transfer between solid particles and wall, due to the point contact.

(4) The thermo-physical properties of HTF and solid fillers are considered as constant and determined by an average operating temperature:

𝑑𝑑 𝑎𝑎𝑎𝑎𝑒𝑒 = � 𝑇𝑇 𝐻𝐻 +𝑇𝑇 𝐶𝐶 2 �.
(5) HTF is assumed as incompressible fluid and plug flow (in z-axis direction). Solid fillers are identical and isotropic spherical particles with homogeneous temperature.

When the temperature inside a particle varies significantly in space coordinate, the internal heat conduction resistance cannot be ignored. This assumption is named as a lumped capacitance that is valid when the value of the solid Biot number (𝐵𝐵𝐵𝐵 𝑠𝑠 =

ℎ 𝑠𝑠𝑠𝑠 •𝐷𝐷 𝑝𝑝 6•𝜆𝜆 𝑠𝑠
) is smaller than 0.1 [START_REF] Çengel | Heat and mass transfer: fundamentals and applications[END_REF][START_REF] Ranmode | Analytical formulation of effective heat transfer coefficient and extension of lumped capacitance method to simplify the analysis of packed bed storage systems[END_REF].

Even the 𝐵𝐵𝐵𝐵 𝑠𝑠 in this work ranges between 0.2 and 0.28, the temperature gradient inside particle is neglected by introducing an effective heat transfer coefficient (HTC) between solid and fluid [START_REF] Bradshaw | Heat transfer between air and nitrogen and packed beds of non-reacting solids[END_REF][START_REF] Xu | Extending the validity of lumped capacitance method for large Biot number in thermal storage application[END_REF].

One-dimensional two-phase model (1D-2P)

A 1D-2P model, or Schumann's model, is introduced to perform fast simulation. In this model, only fluid and solid filler material are modeled using an averaged porous model while the walls are not included. Governing equations of the control volume for two phases and corresponding correlations can be written as follows.

• Governing equations Fluid (1D):

𝜀𝜀 • 𝜌𝜌 𝑓𝑓 • 𝐶𝐶 𝑝𝑝, 𝑠𝑠 • � 𝜕𝜕𝑇𝑇 𝑠𝑠 𝜕𝜕𝑖𝑖 + 𝑁𝑁 𝑓𝑓 • 𝜕𝜕𝑇𝑇 𝑠𝑠 𝜕𝜕𝜕𝜕 � = 𝜕𝜕 𝜕𝜕𝜕𝜕 • �𝜆𝜆 𝑓𝑓,𝑒𝑒𝑓𝑓𝑓𝑓 • 𝜕𝜕𝑇𝑇 𝑠𝑠 𝜕𝜕𝜕𝜕 � + ℎ 𝑠𝑠𝑓𝑓,𝑒𝑒𝑓𝑓𝑓𝑓 • 𝐴𝐴 𝑠𝑠 𝑉𝑉 𝑠𝑠 • �𝑑𝑑 𝑠𝑠 -𝑑𝑑 𝑓𝑓 � + ℎ 𝑜𝑜 • 𝐴𝐴 𝑏𝑏 𝑉𝑉 𝑏𝑏 • �𝑑𝑑 𝑎𝑎𝑚𝑚𝑏𝑏 -𝑑𝑑 𝑓𝑓 � (3.1)
Solid (1D):

(1 -𝜀𝜀) • 𝜌𝜌 𝑠𝑠 • 𝐶𝐶 𝑝𝑝 ,𝑠𝑠 • 𝜕𝜕𝑇𝑇 𝑠𝑠 𝜕𝜕𝑖𝑖 = 𝜕𝜕 𝜕𝜕𝜕𝜕 • �𝜆𝜆 𝑠𝑠,𝑒𝑒𝑓𝑓𝑓𝑓 • 𝜕𝜕𝑇𝑇 𝑠𝑠 𝜕𝜕𝜕𝜕 � + ℎ 𝑠𝑠𝑓𝑓,𝑒𝑒𝑓𝑓𝑓𝑓 • 𝐴𝐴 𝑠𝑠 𝑉𝑉 𝑠𝑠 • �𝑑𝑑 𝑓𝑓 -𝑑𝑑 𝑠𝑠 � (3.2)
where -𝑡𝑡, the time.

-𝐷𝐷 𝑝𝑝 , the particle diameter.

-ℎ, the heat transfer coefficient.

-f, s, w, o, eff, amb (subscripts), the fluid, solid, wall, overall value, effective value, and ambient, respectively.

-𝑁𝑁 𝑓𝑓 , the interstitial fluid velocity, calculated by the mass flow rate

𝑚𝑚̇𝑓𝑓 = 𝑁𝑁 𝑓𝑓 • 𝜌𝜌 𝑓𝑓 • 𝜀𝜀 • 𝜋𝜋 • 𝑅𝑅 𝑖𝑖𝑖𝑖𝑖𝑖 2 .
-

𝐴𝐴 𝑠𝑠 𝑉𝑉 𝑠𝑠 = 6•(1-𝜀𝜀) 𝐷𝐷 𝑝𝑝
, the shape ratio for solid particles diameter.

-

𝐴𝐴 𝑏𝑏 𝑉𝑉 𝑏𝑏 = 2 𝑅𝑅 𝑖𝑖𝑡𝑡𝑡𝑡
, the shape ratio for cylindrical bed.

On the left side of Eq. 3.1, the first term is the accumulative term of heat transfer for fluid and second term represents the heat convection of fluid. On the right side, the first term is the axial heat conduction, the second term is the heat exchange between solid and fluid, and the third term refers to heat losses to the ambient.

For solid phase in Eq. 3.2, the difference is that there is no heat conduction between solid and wall, thus only two terms are on the right side.

• Effective HTC between solid and fluid

The forced convection and natural convection contribute dissimilarly to the heat transfer between fluid and solid [START_REF] Yang | Study on standby process of an air-based solid packed bed for flexible high-temperature heat storage: Experimental results and modelling[END_REF]. The solid-to-fluid HTC (ℎ 𝑠𝑠𝑓𝑓 ) from Pfeffer is given as [START_REF] Pfeffer | Heat and mass transport in multiparticle systems[END_REF]:

ℎ 𝑠𝑠𝑓𝑓 = � 𝜆𝜆 𝑠𝑠 𝐷𝐷 𝑝𝑝 � • �1.26 • � 1-(1-𝜀𝜀) 5 3 2-3•(1-𝜀𝜀) 1 3+3•(1-𝜀𝜀) 5 3-2•(1-𝜀𝜀) 2 • 𝑅𝑅𝑅𝑅 • 𝑃𝑃𝑟𝑟� 1 3 � (Re<74) (3.3)
Moreover, in order to approach the assumption of uniform temperature inside the solid particle, or to extend the applicability of lumped capacitance method when 𝐵𝐵𝐵𝐵 𝑠𝑠 >0.1, the solid-tofluid effective HTC (ℎ 𝑠𝑠𝑓𝑓,𝑒𝑒𝑓𝑓𝑓𝑓 ) through the method of weight average time (or the effective average time [START_REF] Stuke | Berechnung des Wärmeaustausches in Regeneratoren mit zylindrischem und kugelförmigem Füllmaterial[END_REF]) is used [START_REF] Ranmode | Analytical formulation of effective heat transfer coefficient and extension of lumped capacitance method to simplify the analysis of packed bed storage systems[END_REF]:

ℎ 𝑠𝑠𝑓𝑓,𝑒𝑒𝑓𝑓𝑓𝑓 = 1 1/ℎ 𝑠𝑠𝑠𝑠 +3•𝐵𝐵𝑖𝑖 𝑠𝑠 /𝑚𝑚 ( 3 . 4 )
where the value of m equal to 5, 4, and 3 for different shapes of sphere, cylinder and slab (cube), respectively. m=5 is used in this study.

• Overall HTC through tank walls

The overall HTC through tank walls (ℎ 𝑜𝑜 ) based on the inner surface area is calculated by:

1 ℎ 𝑜𝑜 = 1 ℎ 𝑖𝑖𝑡𝑡𝑡𝑡 + � 1 𝜆𝜆 𝑤𝑤 𝑙𝑙𝑙𝑙 � 𝑅𝑅 𝑚𝑚𝑖𝑖𝑚𝑚 𝑅𝑅 𝑖𝑖𝑡𝑡𝑡𝑡 � + 1 𝜆𝜆 𝑖𝑖𝑡𝑡𝑠𝑠 𝑙𝑙𝑙𝑙 � 𝑅𝑅 𝑒𝑒𝑒𝑒𝑡𝑡 𝑅𝑅 𝑚𝑚𝑖𝑖𝑚𝑚 �� • 𝑅𝑅 𝑖𝑖𝑖𝑖𝑖𝑖 + 1 ℎ 𝑒𝑒𝑒𝑒𝑡𝑡 +ℎ 𝑟𝑟𝑡𝑡𝑚𝑚 • 𝑅𝑅 𝑖𝑖𝑡𝑡𝑡𝑡 𝑅𝑅 𝑒𝑒𝑒𝑒𝑡𝑡 ( 3.5)
where fluid-to-wall convective HTC (ℎ 𝑖𝑖𝑖𝑖𝑖𝑖 ) on internal or inner wall surface according to the empirical correlation of Yagi and Wakao [START_REF] Yagi | Heat and mass transfer from wall to fluid in packed beds[END_REF], the insulation-to-ambient air convective HTC (ℎ 𝑒𝑒𝑒𝑒𝑖𝑖 ) on external or outer surface based on a correlation of natural convection on vertical standing wall given by VDI-Wärmeatlas [START_REF] Staff | VDI-wärmeatlas[END_REF], and the radiative HTC (ℎ 𝑟𝑟𝑎𝑎𝑚𝑚 ) based on the Stefan-Boltzmann law can be written:

ℎ 𝑖𝑖𝑖𝑖𝑖𝑖 = � 𝜆𝜆 𝑠𝑠 𝐻𝐻 � • 0.6 • 𝑅𝑅𝑅𝑅 1/2
ℎ 𝑟𝑟𝑎𝑎𝑚𝑚 = 𝜖𝜖•𝜎𝜎•(𝑇𝑇 4 -𝑇𝑇 𝑡𝑡𝑚𝑚𝑏𝑏 4 ) 𝑇𝑇-𝑇𝑇 𝑡𝑡𝑚𝑚𝑏𝑏 (3.8)
where -𝑅𝑅𝑅𝑅, the Rayleigh number (𝑅𝑅𝑅𝑅 𝑎𝑎𝑖𝑖𝑟𝑟 = 𝐺𝐺𝑟𝑟 𝑎𝑎𝑖𝑖𝑟𝑟 • 𝑃𝑃𝑟𝑟 𝑎𝑎𝑖𝑖𝑟𝑟 ).

-𝐺𝐺𝑟𝑟, the Grashof number

(𝐺𝐺𝑟𝑟 𝑎𝑎𝑖𝑖𝑟𝑟 = 𝑔𝑔•𝛽𝛽•𝐻𝐻 3 •∆𝑇𝑇 𝑎𝑎 2
).

-∆𝑑𝑑, the temperature difference between the outer surface and the ambient of the HTF (refers to air here).

-ϵ, the emissivity factor is taken to 0.95, and 𝜎𝜎 =5.67×10 -8 W m -2 K -4 is the Stefan-Boltzmann constant.

-𝑔𝑔, 𝛽𝛽, and 𝑣𝑣, the acceleration of gravity, the thermal expansion coefficient of air, and the kinematic viscosity of the HTF (refers to air here), respectively.

-𝑑𝑑 in Eq. 3.8 is defined as the outer surface temperature of the insulation calculated at average operational temperature 𝑑𝑑 𝑎𝑎𝑎𝑎𝑒𝑒 , using the iterative method in advance.

• Effective thermal conductivity for fluid and solid

The heat transfer of the fluid phase takes into account the thermal diffusion in stagnant fluid and the turbulent thermal contribution in fluid mixing. Thus, the effective thermal conductivities for each fluid (𝜆𝜆 𝑓𝑓,𝑒𝑒𝑓𝑓𝑓𝑓 ) and solid phase (𝜆𝜆 𝑠𝑠,𝑒𝑒𝑓𝑓𝑓𝑓 ) are given as:

𝜆𝜆 𝑓𝑓,𝑒𝑒𝑓𝑓𝑓𝑓 ≅ (𝜀𝜀 • 𝜆𝜆 𝑓𝑓 + 𝑐𝑐 • 𝜆𝜆 𝑓𝑓 ) + 𝜆𝜆 𝑚𝑚𝑖𝑖𝑒𝑒 (3.9) 𝜆𝜆 𝑠𝑠,𝑒𝑒𝑓𝑓𝑓𝑓 ≅ [(1 -𝜀𝜀) • 𝜆𝜆 𝑠𝑠 -𝑐𝑐 • 𝜆𝜆 𝑠𝑠 ] (3.10)
where 𝜆𝜆 𝑚𝑚𝑖𝑖𝑒𝑒 = 0.

𝜆𝜆 𝑒𝑒𝑓𝑓𝑓𝑓 0 = � 1+2•𝛼𝛼•(1-𝜀𝜀)+�2•𝛼𝛼 3 -0.1•𝛼𝛼�•(1-𝜀𝜀) 2 +(1-𝜀𝜀) 3 •0.05•𝑒𝑒𝑒𝑒𝑝𝑝 (4.5•𝑒𝑒) 1-𝛼𝛼•(1-𝜀𝜀) � • 𝜆𝜆 𝑓𝑓 (3.12) 𝑥𝑥 = (𝜆𝜆 𝑠𝑠 -𝜆𝜆 𝑓𝑓 )/(𝜆𝜆 𝑠𝑠 + 2 • 𝜆𝜆 𝑓𝑓 ) (3.13)
where 𝜆𝜆 𝑒𝑒𝑓𝑓𝑓𝑓 0 is the thermal conductivity contribution of both phase in stagnant condition with the valid range of 0.15<𝜀𝜀<0.85, and 10 -3 <𝜆𝜆 𝑠𝑠 /𝜆𝜆 𝑓𝑓 <10 4 [START_REF] Gonzo | Estimating correlations for the effective thermal conductivity of granular materials[END_REF].

One-dimensional three-phase model (1D-3P)

A modified 1D-3P model was developed by considering the tank wall as a separate phase in addition to the fluid and solid phases. In this way, the energy balance and the heat capacity of the tank wall are considered in 1D (z-axis direction). The insulation is simplified by a thermal resistance while its heat capacity is neglected due to the small temperature variation.

• Governing equations Fluid (1D):

𝜀𝜀 • 𝜌𝜌 𝑓𝑓 • 𝐶𝐶 𝑝𝑝,𝑓𝑓 • � 𝜕𝜕𝑇𝑇 𝑠𝑠 𝜕𝜕𝑖𝑖 + 𝑁𝑁 𝑓𝑓 • 𝜕𝜕𝑇𝑇 𝑠𝑠 𝜕𝜕𝜕𝜕 � = 𝜕𝜕 𝜕𝜕𝜕𝜕 • �𝜆𝜆 𝑓𝑓,𝑒𝑒𝑓𝑓𝑓𝑓 • 𝜕𝜕𝑇𝑇 𝑠𝑠 𝜕𝜕𝜕𝜕 � + ℎ 𝑠𝑠𝑓𝑓,𝑒𝑒𝑓𝑓𝑓𝑓 • 𝐴𝐴 𝑠𝑠 𝑉𝑉 𝑠𝑠 • �𝑑𝑑 𝑠𝑠 -𝑑𝑑 𝑓𝑓 � + ℎ 𝑓𝑓-𝑤𝑤 • 𝐴𝐴 𝑠𝑠-𝑤𝑤 𝑉𝑉 𝑏𝑏 • �𝑑𝑑 𝑤𝑤 -𝑑𝑑 𝑓𝑓 � (3.14)
Solid (1D):

(1 -𝜀𝜀) • 𝜌𝜌 𝑠𝑠 • 𝐶𝐶 𝑝𝑝,𝑠𝑠 • 𝜕𝜕𝑇𝑇 𝑠𝑠 𝜕𝜕𝑖𝑖 = 𝜕𝜕 𝜕𝜕𝜕𝜕 • �𝜆𝜆 𝑠𝑠,𝑒𝑒𝑓𝑓𝑓𝑓 • 𝜕𝜕𝑇𝑇 𝑠𝑠 𝜕𝜕𝜕𝜕 � + ℎ 𝑠𝑠𝑓𝑓,𝑒𝑒𝑓𝑓𝑓𝑓 • 𝐴𝐴 𝑠𝑠 𝑉𝑉 𝑠𝑠 • �𝑑𝑑 𝑓𝑓 -𝑑𝑑 𝑠𝑠 � (3.15)
Wall (1D):

𝜌𝜌 𝑤𝑤 • 𝐶𝐶 𝑝𝑝,𝑤𝑤 • 𝜕𝜕𝑇𝑇 𝑤𝑤 𝜕𝜕𝑖𝑖 = 𝜕𝜕 𝜕𝜕𝜕𝜕 • �𝜆𝜆 𝑤𝑤 • 𝜕𝜕𝑇𝑇 𝑤𝑤 𝜕𝜕𝜕𝜕 � + ℎ 𝑓𝑓-𝑤𝑤 • 𝐴𝐴 𝑠𝑠-𝑤𝑤 𝑉𝑉 𝑤𝑤 • �𝑑𝑑 𝑓𝑓 -𝑑𝑑 𝑤𝑤 � + ℎ 𝑤𝑤-𝑎𝑎𝑚𝑚𝑏𝑏 • 𝐴𝐴 𝑠𝑠-𝑤𝑤 𝑉𝑉 𝑤𝑤 • (𝑑𝑑 𝑎𝑎𝑚𝑚𝑏𝑏 -𝑑𝑑 𝑤𝑤 ) (3.16)
where • Equivalent HTC of fluid-to-wall center, wall center-to-ambient

𝐴𝐴
The equivalent HTC of fluid-to-wall center (ℎ 𝑓𝑓-𝑤𝑤 ) and the equivalent HTC of wall center-toambient (ℎ 𝑤𝑤-𝑎𝑎𝑚𝑚𝑏𝑏 ) can be formulated as:

1 ℎ 𝑠𝑠-𝑤𝑤 = 1 ℎ 𝑖𝑖𝑡𝑡𝑡𝑡 + 1 𝜆𝜆 𝑤𝑤 • 𝑙𝑙𝑙𝑙 � 𝑅𝑅 𝑖𝑖𝑡𝑡𝑡𝑡 +𝑅𝑅 𝑚𝑚𝑖𝑖𝑚𝑚 2•𝑅𝑅 𝑖𝑖𝑡𝑡𝑡𝑡 � • 𝑅𝑅 𝑖𝑖𝑖𝑖𝑖𝑖 (3.17) 1 ℎ 𝑤𝑤-𝑡𝑡𝑚𝑚𝑏𝑏 = � 1 𝜆𝜆 𝑤𝑤 • 𝑙𝑙𝑙𝑙 � 2•𝑅𝑅 𝑚𝑚𝑖𝑖𝑚𝑚 𝑅𝑅 𝑖𝑖𝑡𝑡𝑡𝑡 +𝑅𝑅 𝑚𝑚𝑖𝑖𝑚𝑚 � + 1 𝜆𝜆 𝑖𝑖𝑡𝑡𝑠𝑠 • 𝑙𝑙𝑙𝑙 � 𝑅𝑅 𝑒𝑒𝑒𝑒𝑡𝑡 𝑅𝑅 𝑚𝑚𝑖𝑖𝑚𝑚 � + 1 ℎ 𝑒𝑒𝑒𝑒𝑡𝑡 +ℎ 𝑟𝑟𝑡𝑡𝑚𝑚 • 1 𝑅𝑅 𝑒𝑒𝑒𝑒𝑡𝑡 � • 𝑅𝑅 𝑖𝑖𝑖𝑖𝑖𝑖 (3.18)

One and half-dimensional four-phase model (1.5D-4P)

A 1.5D-4P model was used to explore the thermal behavior inside of the whole tank walls. In this model, the heat transfer in z-axis and r-axis for the wall and insulation occurs, and the different HTCs and effective thermal conductivities are calculated as defined before. It bases on full resolution and shows even more accuracy than the former two models.

• Governing equations Fluid (1D):

𝜀𝜀 • 𝜌𝜌 𝑓𝑓 • 𝐶𝐶 𝑝𝑝,𝑓𝑓 • � 𝜕𝜕𝑇𝑇 𝑠𝑠 𝜕𝜕𝑖𝑖 + 𝑁𝑁 𝑓𝑓 • 𝜕𝜕𝑇𝑇 𝑠𝑠 𝜕𝜕𝜕𝜕 � = 𝜕𝜕 𝜕𝜕𝜕𝜕 • �𝜆𝜆 𝑓𝑓,𝑒𝑒𝑓𝑓𝑓𝑓 • 𝜕𝜕𝑇𝑇 𝑠𝑠 𝜕𝜕𝜕𝜕 � + ℎ 𝑠𝑠𝑓𝑓,𝑒𝑒𝑓𝑓𝑓𝑓 • 𝐴𝐴 𝑠𝑠 𝑉𝑉 𝑠𝑠 • �𝑑𝑑 𝑠𝑠 -𝑑𝑑 𝑓𝑓 � + ℎ 𝑖𝑖𝑖𝑖𝑖𝑖 • 𝐴𝐴 𝑏𝑏 𝑉𝑉 𝑏𝑏 • �𝑑𝑑 𝑤𝑤,𝑖𝑖𝑖𝑖𝑖𝑖 -𝑑𝑑 𝑓𝑓 � (3.19)
Solid (1D):

(1 -𝜀𝜀) • 𝜌𝜌 𝑠𝑠 • 𝐶𝐶 𝑝𝑝,𝑠𝑠 • 𝜕𝜕𝑇𝑇 𝑠𝑠 𝜕𝜕𝑖𝑖 = 𝜕𝜕 𝜕𝜕𝜕𝜕 • �𝜆𝜆 𝑠𝑠,𝑒𝑒𝑓𝑓𝑓𝑓 • 𝜕𝜕𝑇𝑇 𝑠𝑠 𝜕𝜕𝜕𝜕 � + ℎ 𝑠𝑠𝑓𝑓,𝑒𝑒𝑓𝑓𝑓𝑓 • 𝐴𝐴 𝑠𝑠 𝑉𝑉 𝑠𝑠 • �𝑑𝑑 𝑓𝑓 -𝑑𝑑 𝑠𝑠 � (3.20)
Wall (2D):

𝜌𝜌 𝑤𝑤 • 𝐶𝐶 𝑝𝑝,𝑤𝑤 • 𝜕𝜕𝑇𝑇 𝑤𝑤 𝜕𝜕𝑖𝑖 = 𝜕𝜕 𝜕𝜕𝜕𝜕 • �𝜆𝜆 𝑤𝑤 • 𝜕𝜕𝑇𝑇 𝑤𝑤 𝜕𝜕𝜕𝜕 � + 𝜆𝜆 𝑤𝑤 𝑟𝑟 • 𝜕𝜕 𝜕𝜕𝑟𝑟 • �𝑟𝑟 • 𝜕𝜕𝑇𝑇 𝑤𝑤 𝜕𝜕𝑟𝑟 � (3.21)
Insulation (2D):

𝜌𝜌 𝑖𝑖𝑖𝑖𝑠𝑠 • 𝐶𝐶 𝑝𝑝,𝑖𝑖𝑖𝑖𝑠𝑠 • 𝜕𝜕𝑇𝑇 𝑖𝑖𝑡𝑡𝑠𝑠 𝜕𝜕𝑖𝑖 = 𝜕𝜕 𝜕𝜕𝜕𝜕 • �𝜆𝜆 𝑖𝑖𝑖𝑖𝑠𝑠 • 𝜕𝜕𝑇𝑇 𝑖𝑖𝑡𝑡𝑠𝑠 𝜕𝜕𝜕𝜕 � + 𝜆𝜆 𝑖𝑖𝑡𝑡𝑠𝑠 𝑟𝑟 • 𝜕𝜕 𝜕𝜕𝑟𝑟 • �𝑟𝑟 • 𝜕𝜕𝑇𝑇 𝑖𝑖𝑡𝑡𝑠𝑠 𝜕𝜕𝑟𝑟 � (3.22)
where the subscript "ins" represents the insulation phase.

Initial and boundary conditions

In this chapter, only the discharging process was simulated and discussed. The initial conditions are given as:

𝑑𝑑 𝑠𝑠 (𝑡𝑡 = 0) = 𝑑𝑑 𝑓𝑓 (𝑡𝑡 = 0) = 𝑑𝑑 𝐻𝐻 (3.23) 𝑑𝑑 𝑤𝑤,𝑖𝑖𝑖𝑖𝑖𝑖 (𝑡𝑡 = 0) = 𝑑𝑑 𝑤𝑤,𝑖𝑖𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖𝑖𝑖 ; 𝑑𝑑 𝑤𝑤,𝑚𝑚𝑖𝑖𝑚𝑚 (𝑡𝑡 = 0) = 𝑑𝑑 𝑤𝑤,𝑚𝑚𝑖𝑖𝑚𝑚,𝑖𝑖𝑖𝑖𝑖𝑖 ; 𝑑𝑑 𝑤𝑤,𝑒𝑒𝑒𝑒𝑖𝑖 (𝑡𝑡 = 0) = 𝑑𝑑 𝑤𝑤,𝑒𝑒𝑒𝑒𝑖𝑖,𝑖𝑖𝑖𝑖𝑖𝑖 (3.24)
The initial temperature of tank walls (𝑑𝑑 𝑤𝑤,𝑖𝑖𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖𝑖𝑖 ; 𝑑𝑑 𝑤𝑤,𝑚𝑚𝑖𝑖𝑚𝑚,𝑖𝑖𝑖𝑖𝑖𝑖 ; 𝑑𝑑 𝑤𝑤,𝑒𝑒𝑒𝑒𝑖𝑖,𝑖𝑖𝑖𝑖𝑖𝑖 ) as shown in

Performance indicators

In this chapter, several performance indicators for evaluating walls impact are presented, other definitions will be introduced in Chapter 4 and Chapter 5.

• Discharging energy efficiency considering walls

For a given time, the discharging energy efficiency considering walls (𝜂𝜂 𝑚𝑚𝑖𝑖𝑠𝑠 ′ ), is expressed as the ratio of the output energy by HTF in discharging (∆𝐸𝐸 𝑜𝑜𝑜𝑜𝑖𝑖 ) (or cumulatively released energy) to the stored energy considering walls (∆𝐸𝐸 𝑠𝑠𝑖𝑖𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 ′ ): where the reference temperature 𝑑𝑑 0 is selected as the coldest operational temperature (𝑑𝑑 𝐶𝐶 ) in this chapter.

𝜂𝜂 𝑚𝑚𝑖𝑖𝑠𝑠 ′ = ∆𝐸𝐸 𝑜𝑜𝑜𝑜𝑡𝑡 ∆𝐸𝐸 𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 ′ = ∫ �𝑚𝑚̇𝑠𝑠•𝐶𝐶

• Pumping energy

The consumed pumping energy (∆𝐸𝐸 𝑝𝑝𝑜𝑜𝑚𝑚𝑝𝑝 ) for a given time is expressed as:

∆𝐸𝐸 𝑝𝑝𝑜𝑜𝑚𝑚𝑝𝑝 = ∫ � 𝑚𝑚̇𝑠𝑠 𝜌𝜌 𝑠𝑠 • ∆𝑃𝑃� 𝑑𝑑𝑡𝑡 𝑖𝑖 0 ( 3 . 3 2 )
where ∆𝑃𝑃 of the packed-bed tank is calculated using the superficial fluid velocity (𝑁𝑁 𝑠𝑠𝑜𝑜𝑝𝑝 ) by Ergun equation [START_REF] Ergun | Fluid flow through packed columns[END_REF] that the values of A and B depend on the variation of porosity 𝜀𝜀 [START_REF] Du Plessis | Pore-scale derivation of the Ergun equation to enhance its adaptability and generalization[END_REF]:

∆𝑃𝑃 𝐻𝐻 = 𝐴𝐴 • (1-𝜀𝜀) 2 𝜀𝜀 3 • 𝜇𝜇 𝑠𝑠 •𝑜𝑜 𝑠𝑠𝑜𝑜𝑝𝑝 𝐷𝐷 𝑝𝑝 2 + 𝐵𝐵 • (1-𝜀𝜀) 𝜀𝜀 3 • 𝜌𝜌 𝑠𝑠 •𝑜𝑜 𝑠𝑠𝑜𝑜𝑝𝑝 2 𝐷𝐷 𝑝𝑝 ( 3 . 3 3 )

• Thermocline thickness

The dimensionless thermocline thickness ( 𝐿𝐿 𝑖𝑖ℎ𝑒𝑒𝑟𝑟𝑚𝑚𝑜𝑜𝑒𝑒𝑙𝑙𝑖𝑖𝑖𝑖𝑒𝑒 *

) is determined by the length of stratification region in bed [START_REF] Chang | The design and numerical study of a 2 MWh molten salt thermocline tank[END_REF], according to the physical boundary within a certain temperature range before reaching the top or bottom of the tank.

𝐿𝐿 𝑖𝑖ℎ𝑒𝑒𝑟𝑟𝑚𝑚𝑜𝑜𝑒𝑒𝑙𝑙𝑖𝑖𝑖𝑖𝑒𝑒 * = 𝜕𝜕{𝑇𝑇=𝑇𝑇 𝐶𝐶 +𝑖𝑖%•(𝑇𝑇 𝐻𝐻 -𝑇𝑇 𝐶𝐶 )}-𝜕𝜕{𝑇𝑇=𝑇𝑇 𝐻𝐻 -𝑖𝑖%•(𝑇𝑇 𝐻𝐻 -𝑇𝑇 𝐶𝐶 )} 𝐻𝐻 (3.34) -In charging, 𝑧𝑧{𝑑𝑑 = 𝑑𝑑 𝐶𝐶 + 𝑙𝑙% • (𝑑𝑑 𝐻𝐻 -𝑑𝑑 𝐶𝐶 )} > 0; -In discharging, 𝑧𝑧{𝑑𝑑 = 𝑑𝑑 𝐻𝐻 -𝑙𝑙% • (𝑑𝑑 𝐻𝐻 -𝑑𝑑 𝐶𝐶 )} < 𝐻𝐻;
where n is a threshold value that is defined as the hottest/coldest temperature differs 𝑙𝑙 % to the operational temperature range (𝑑𝑑 𝐻𝐻 -𝑑𝑑 𝐶𝐶 ), setting as 5% in this study. In experiment, the thermocline thickness is calculated by the fluid temperature variation at the axial centerline of the storage tank.

• Threshold temperature

In a cycling process, it assumes the initial condition of changing is fully discharged and with a homogenous coldest operating temperature, while the end of charging at the cutoff temperature is the beginning of discharging. In this study, the cutoff threshold temperature for charging/discharging changed by 20% of operational temperature [START_REF] Zhao | System-level performance optimization of molten-salt packed-bed thermal energy storage for concentrating solar power[END_REF][84] [START_REF] Fasquelle | A temperature threshold evaluation for thermocline energy storage in concentrated solar power plants[END_REF]:

𝑑𝑑 𝑒𝑒𝑜𝑜𝑖𝑖𝑜𝑜𝑓𝑓𝑓𝑓,𝑒𝑒ℎ = 𝑑𝑑 0.2 = 𝑑𝑑 𝐻𝐻 -20% • (𝑑𝑑 𝐻𝐻 -𝑑𝑑 𝐶𝐶 ) (3.

Model validation and comparison

The models were solved with the MATLAB function ode45 for the time derivatives. The explicit Runge Kutta (4.5) method was used with an adaptive time step. The advection term was discretized with a first order upwind finite difference, and the diffusion term was discretized with a second order central finite difference. The computational domain of numerical simulation was discretized into non-overlapping control volumes as illustrated in Figure 3.1. To obtain accurate simulation results and reduce the consumption of time, the height node number (𝑁𝑁) in z-axis and the time node number (M) were determined by using the cutoff time as an indicator of stable solution. When the cutoff time is in stable with increasing node numbers.

Cases description

Three cases with different scales, including two real tanks and a hypothetical lab-scale tank, are introduced. Table 3.2 shows the characteristics and parameters of those three packed-bed TES tanks. * It means the bulk density. but the predicted temperature of 1D-3P and 1.5P-4P models are higher than that of 1D-2P model at a certain height, which may be due to the release of the stored heat in the walls. The phenomenon will be discussed in detail in the following section. By examining the mean difference of different models shown in Table 3.4, it is found that three models show similar standard deviation of around 3 K and two detailed models which can characterize the physical phenomenon in walls show similar root mean square difference of about 5 K, close to that of 1D-2P simple model (4 K). All three models reflect good agreement with the experimental data with an acceptable average difference.

Validation results

Unification of different scale tanks

Two tanks listed in Table 3.2, the pilot-scale tank (Sandia's Lab) and the hypothetical labscale one, will then be fully studied to investigate the wall impact. Despite different sizes and operational temperatures, the influence levels of governing terms should be set similar for better comparison and exploitation. For this purpose, the dimensionless numbers (Πi) (in Eq.s A 3.4-A 3.11) are used to unify two tanks. The dimensionless governing equations of the 1D-3P model (in Eq.s A 3.1-A 3.3) and corresponding analysis are provided in FigureA 3.1 of the Appendix. ) is calculated to be 0.1 for pilot-scale tank and be 9 for lab-scale tank. Smaller 𝐵𝐵𝐵𝐵 𝑤𝑤 for the pilot-scale tank means that heat transfer is mainly governed by convection between the wall and the fluid. For the lab-scale tank, the insulation can be hotter than the small temperature gradient within the wall, the conduction thermal resistance can thereby be ignored. A heat transfer from the insulation layer to the wall is then occupying, which may lead to instability. Furthermore, the

Wall thermal behavior discussion

dimensionless

Wall heat flux

Wall heat transfer rate analysis

Heat transfer rate (𝑄𝑄 ̇) analysis of tank walls was conducted to investigate the rate of energy transfer in discharging process.

Stored heat in wall

Figure 3.11 a shows the percentage of stored energy in each phase at the beginning and of discharging. Before discharging (fully charged state), the solid phase has a dominant energy storage percentage of 65% for lab-scale tank and 55% for pilot-scale tank. The proportion of energy stored in the tank wall is also as high as 8% and 10%, respectively. This non-negligible part of energy remains no valorized. Nevertheless, the stored energy in the insulation can hardly be captured, implying that the insulation phase may be simplified in the modeling without affecting much the energy efficiency calculation of the packed-bed TES tank. The stored energy (∆𝐸𝐸 𝑠𝑠𝑖𝑖𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 ′ ) of pilot-scale tank at initial time is larger than that of lab-scale tank. At 𝑡𝑡 𝐸𝐸 * = 1, it decreases from 1×10 10 to 4×10 8 J (-96%) for the pilot-scale tank, and from 2×10 6 to 1×10 5 J (-95%) for the labscale tank. At the cutoff time, energy of each part still decreases and the pump energy due to packed bed pressure drop at cutoff time is 7.3 ×10 3 J and 0.24 J, respectively, which can be neglected safely (⩽1%). Nevertheless, the heat loss due to the radiation should be considered, accounting for about 5% of the total heat loss (lab-scale tank). Table 3. 5 shows that the lab-scale tank presents higher HTC ℎ 𝑜𝑜 (1.0 W m -2 K -1 ) through the tank walls than that of the pilot-scale tank (0.2 W m -2 K -1 ), exhibiting a higher possibility to lose heat to ambient despite a lower value of total heat loss. In summary, the impacts of wall stored energy and radiation heat loss must be considered in the performance evaluation while the insulation heat capacity and pump energy consumption can be neglected in Chapter 4 and Chapter 5. Types hint

(W m -2 K -1 ) hext (W m -2 K -1 ) hrad (W m -2 K -1 ) ho (W m -2 K -

Energy and exergy efficiency

Energy and exergy efficiency variation during discharging and comparison between models based on two indicators are presented in Figure 3.12. Exergy, as the work potential of energy, is defined as the maximum useful work that can be obtained from system before reaching the equilibrium state [START_REF] Bejan | Thermal design and optimization[END_REF]. The 100% exergy efficiency refers to completely reversible process and the higher efficiency can be achieved by forming a stable and thinner thermocline or enhanced thermal stratification [START_REF] Bindra | Thermal analysis and exergy evaluation of packed bed thermal storage systems[END_REF]. It can be observed that energy and exergy efficiencies are timedependent and show the same increasing tendency for discharging. The energy efficiency at the 𝑡𝑡 𝐸𝐸 * = 1 for lab-scale tank (86% using 1D-2P model) is lower than that of the pilot-scale tank (90%), as well as the exergy efficiency. This is because of the higher heat loss to ambient due to the higher ℎ 𝑜𝑜 and the more extended thermocline as discussed above. Moreover, it is observed that the difference on exergy efficiency between 1D-3P (1D wall domain) and 1.5D-4P (2D wall and 2D insulation domain) models is below 5% and both energies higher than 1D-2P (no wall, no

The effect of heat stored in wall and heat loss

In order to evaluate the influence of the wall thermal properties and the heat loss on the efficiency of different size tanks, the thermocline thickness over discharging time under different boundary conditions are investigated, including (1) adiabatic or non-adiabatic and (2) with or without wall and insulation. The ending time was set as when thermocline region reaches the tank top in discharging.

The effect of wall thickness and thermal conductivity

The walls parametric study was performed on the wall thermal conductivity and thickness by using the 1D-3P model according to sensitivity analysis in

Chapter conclusion

In this chapter, three models (1D-2P, 1D-3P, and 1.5D-4P) of thermocline packed-bed tank were first developed. After model validation by experimental data, the wall dynamic thermal behavior was fully investigated and the wall impact on the performance of packed-bed TES tanks has been evaluated. Finally, sensitivity and parametric analyses have been performed using the appropriate 1D-3P model to evaluate the influence of wall parameters. Main findings of this study may be summarized as follows.

(1) Before discharging, the maximum energy stored in wall at fully charged state can be up to 10% of the total stored energy. During discharging, the stored heat in wall can be released back to the fluid, increasing thereby the fluid temperature in contact as well as the thermocline thickness by up to 15%.

(2) The convective heat transfer between fluid and inner wall is dominant while the heat loss from the outer wall to the ambient is time-dependent and non-negligible. In contrast, the axial heat conduction in the walls and the pump power consumption can be ignored for these configurations.

(3) The stored energy in the insulation is small. As a result, the insulation phase may be simplified as a thermal resistance in the modeling. In this regard, the 1D-3P model could be a balanced choice between the complex physical phenomenon description and required computational time.

(4) The wall thermal conductivity and thickness have a great impact on wall energy balance, as well as a great interaction degree with other parameters. The optimal wall parameters for packed-bed TES tank are that a thinner wall has a smaller impact on the energy and exergy efficiencies at the discharging cutoff time.

The next chapter is focused on the thermocline packed-bed TES systems under influence factors in radial and axial direction including inlet configuration, insulation, flow rate, and inlet temperature, by comparing experimental and numerical results.

Appendix 3.I Definition of dimensionless numbers

In order to solve the model with different parameters, the governing equations of 1D-3P model are nondimensionalized into:

� 𝜕𝜕𝑇𝑇 𝑠𝑠 * 𝜕𝜕𝑖𝑖 * + 𝜕𝜕𝑇𝑇 𝑠𝑠 * 𝜕𝜕𝜕𝜕 * � = Π 1 • 𝜕𝜕 𝜕𝜕𝜕𝜕 • � 𝜕𝜕𝑇𝑇 𝑠𝑠 * 𝜕𝜕𝜕𝜕 * � + Π 2 • �𝑑𝑑 𝑠𝑠 * -𝑑𝑑 𝑓𝑓 * � + Π 3 • �𝑑𝑑 𝑤𝑤 * -𝑑𝑑 𝑓𝑓 * � (A 3.1) 𝜕𝜕𝑇𝑇 𝑠𝑠 * 𝜕𝜕𝑖𝑖 * = Π 4 • 𝜕𝜕 𝜕𝜕𝜕𝜕 * • � 𝜕𝜕𝑇𝑇 𝑠𝑠 * 𝜕𝜕𝜕𝜕 * � + Π 5 • �𝑑𝑑 𝑓𝑓 * -𝑑𝑑 𝑠𝑠 * � (A 3.2) 𝜕𝜕𝑇𝑇 𝑤𝑤 * 𝜕𝜕𝑖𝑖 * = Π 6 • 𝜕𝜕 𝜕𝜕𝜕𝜕 * • � 𝜕𝜕𝑇𝑇 𝑤𝑤 * 𝜕𝜕𝜕𝜕 * � + Π 7 • �𝑑𝑑 𝑓𝑓 * -𝑑𝑑 𝑤𝑤 * � + Π 8 • (𝑑𝑑 𝑎𝑎𝑚𝑚𝑏𝑏 * -𝑑𝑑 𝑤𝑤 * ) (A 3.3) Π 1 = 1 𝑃𝑃𝑒𝑒 • 𝜆𝜆 𝑠𝑠,𝑒𝑒𝑠𝑠𝑠𝑠 𝜆𝜆 𝑠𝑠 • 𝐷𝐷 𝑝𝑝 𝐻𝐻 (A 3.4) Π 2 = 𝑆𝑆𝑡𝑡 𝑠𝑠𝑓𝑓,𝑒𝑒𝑓𝑓𝑓𝑓 • 𝑅𝑅 𝑠𝑠 • 𝐻𝐻 (A 3.5) Π 3 = 𝑆𝑆𝑡𝑡 𝑓𝑓-𝑤𝑤 • 𝑅𝑅 𝑓𝑓 • 𝐻𝐻 (A 3.6) Π 4 = 1 𝑃𝑃𝑒𝑒 • 𝜀𝜀 (1-𝜀𝜀) • 𝛼𝛼 𝑠𝑠,𝑒𝑒𝑠𝑠𝑠𝑠 𝛼𝛼 𝑠𝑠 • 𝐷𝐷 𝑝𝑝 𝐻𝐻 (A 3.7) Π 5 = 𝑆𝑆𝑡𝑡 𝑠𝑠𝑓𝑓,𝑒𝑒𝑓𝑓𝑓𝑓 • 𝑅𝑅 𝑠𝑠 • 𝐻𝐻 𝜌𝜌 𝑠𝑠 •𝐶𝐶 𝑝𝑝 ,𝑠𝑠 𝜌𝜌 𝑠𝑠 •𝐶𝐶 𝑝𝑝 ,𝑠𝑠 • 𝜀𝜀 (1-𝜀𝜀) (A 3.8) Π 6 = 1 𝑃𝑃𝑒𝑒 • 𝜀𝜀 • 𝛼𝛼 𝑤𝑤 𝛼𝛼 𝑠𝑠 • 𝐷𝐷 𝑝𝑝 𝐻𝐻 (A 3.9) Π 7 = 𝑆𝑆𝑡𝑡 𝑠𝑠𝑓𝑓,𝑒𝑒𝑓𝑓𝑓𝑓 • 𝑅𝑅 𝑤𝑤 • 𝐻𝐻 • 𝜌𝜌 𝑠𝑠 •𝐶𝐶 𝑝𝑝 ,𝑠𝑠 •𝜀𝜀 𝜌𝜌 𝑤𝑤 •𝐶𝐶 𝑝𝑝, 𝑤𝑤 (A 3.10) Π 8 = 𝑆𝑆𝑡𝑡 𝑤𝑤-𝑎𝑎𝑚𝑚𝑏𝑏 • 𝑅𝑅 𝑤𝑤 • 𝐻𝐻 • 𝜌𝜌 𝑠𝑠 𝐶𝐶 𝑝𝑝 ,𝑠𝑠 𝜀𝜀 𝜌𝜌 𝑤𝑤 •𝐶𝐶 𝑝𝑝, 𝑤𝑤 (A 3.11)
where, In definition, Πi reflect the energy contribution to each phase. For example, Π1, Π4, and Π6 represent the influence of the ratio of heat diffusion to increment term on energy, while Π2, Π3, Π5, Π7, and Π8 represent the influence of ratio of the heat convection plus radiation to increment term on energy. In order to set two tanks at a similar resolution condition, the Πi were calculated and compared. Here, for the pilot-scale tank with a certain packing configuration, the Π2 and Π5 are dominant. Therefore, a comparison of both tanks can thus be conducted under the condition that the value of dominant Πi of two tanks is determined to be close to each other in FigureA 3.1.

Péclet number: 𝑃𝑃𝑅𝑅 = 𝑅𝑅𝑅𝑅 • 𝑃𝑃𝑟𝑟 = 𝐷𝐷 𝑝𝑝 •𝑜𝑜 𝑠𝑠𝑜𝑜𝑝𝑝 𝛼𝛼 𝑠𝑠 (A 3.

Appendix 3.III

Parametric sensitivity analysis

To better understand the effect of different parameters on the performance of the storage tank, especially the wall impact, global sensitivity analysis (GSA) was conducted by using the 1D-3P model. An adaptation algorithm named the Morris method, or Elementary Effect (EE) method, which gives rough quantitative estimations with a limited number of calculations, was used based on a MATLAB toolbox provided by Pianos [START_REF] Pianosi | A Matlab toolbox for Global Sensitivity Analysis[END_REF]. It computes two sensitivity indices for each input: one is the mean of EEs, measuring the effect of an input over output, and another is the standard deviation of EEs, representing the interaction degree with other factors. In this study, the main parameters (𝜀𝜀, 𝑁𝑁 𝑎𝑎,𝑓𝑓 , 𝐷𝐷 𝑝𝑝 , 𝜆𝜆 𝑠𝑠 , 𝐿𝐿 𝑤𝑤 , 𝜌𝜌 𝑠𝑠 • 𝐶𝐶 𝑝𝑝 𝑠𝑠 , 𝜆𝜆 𝑤𝑤 , 𝜌𝜌 𝑤𝑤 • 𝐶𝐶 𝑝𝑝 𝑤𝑤 ) were served as input after considering the determined tank geometry size and HTF type. The Πi in dimensionless energy equation were taken as outputs, which reflect the contribution of the heat convection, the convection, or the radiation on fluid, solid, and wall energy. The definition has been introduced in Eq.s A 3.4-A 3.11. and high value (like metals).

TableA 3.3Dimensionless number (Πi) variation within the value range of parameters.

Dimensionless number Pilot-scale tank Uncertainty Lab-scale tank Uncertainty

Π1 5×10 -4 ± 4×10 -4 8×10 -3 ± 5×10 -3 Π2 4000 ± 3×10 4 243 ± 1790 Π3 1 ± 1 1 ± 1 Π4 2×10 -4 ± 10×10 -4 4×10 -3 ± 10×10 -3 Π5 14000 ± 35000 120 ± 1380 Π6 10×10 -4 ± 8×10 -4 14×10 -3 ± 80×10 -3 Π7 2 ± 14 3 ± 15 Π8 22×10 -4 ± 0.2 14×10 -3 ± 70×10 -3
For different operational conditions or packing configurations, the parametric sensitivity analysis within the variable ranges of parameters was studied. The value range of parameters is indicated in TableA 3.2 and the corresponding dimensionless number variation is reported in TableA 3.3. For both tanks, the influence of heat convection (Π2, Π5) on the performance of storage tank is larger than heat loss (Π3, Π7, Π8), while the influence of axial conduction (Π1, Π4, Π6) can be largely ignored. This is in line with our findings reported above. Samples number is defined as 4000 according to the convergence result shown in FigureA 3.2 a b.

The dominant Πi (Π2, Π5, Π7, and Π8) for each phase all own to heat convection. Π7 have dominant influence on wall energy balance due to the wall impact on heat loss of lab-scale tank.

Thus, FigureA 3.2 c d displays the means and standard deviation of EEs of main parameters for Π7 of two tanks. It was demonstrated that wall volumetric heat capacity, wall thickness, and wall thermal conductivity have a great impact on wall energy balance, as well as a great interaction degree with other parameters. Considering the wall volumetric heat capacity is the inherent property of material, the wall parameters only containing wall thickness and wall thermal conductivity be studied in this study. The objective of this chapter includes:

• Improve the model of wall heat capacity for large size particles and determine the applicable ranges.

• Validate the thermal gradient inside sensible particle.

• Assess the influences of radial temperature non-uniformity due to the injecting flow and heat loss with experiments.

• Clarify the impact of solid and fluid heat transfer and the axial diffusion based on parametric study through comparison of numerical and experimental results.

• Propose an application of this configuration and model for latent heat packing.

Keywords: sensible fillers, flow diffuser, insulation, mass flow rate, experiment, DC-3P model

This chapter is under review by Renewable Energy.

Introduction

In theory, the thermocline quality evaluated by its stability and thickness reflects the SHTPB system's performance: higher level of thermal stratification in the thinner thermocline zone means higher energy and exergy efficiencies [32][33]. Nevertheless, the thermal stratification tends to become unstable and expanded over dynamic and cycling operations. This thermocline degradation (or decay) can be due to many factors [34][35]. On one hand, the low heat transfer rate between heat transfer fluid (HTF) and solid fillers or the strong heat diffusion inside HTF, solid media, or wall phases, would result in the expanded thermocline thickness in the axial direction [START_REF] Geissbühler | An assessment of thermocline-control methods for packed-bed thermal-energy storage in CSP plants, Part 2: Assessment strategy and results[END_REF]. On the other hand, the flow injection, the heat loss to the environment, and the wall impacts would cause the non-uniform radial temperature distribution inside the tank, lowering thereby the thermocline stability and increasing the thermocline thickness [START_REF] Cascetta | Experimental and numerical research activity on a packed bed TES system[END_REF][186].

Effect on radial temperature gradient

Uniform radial flow velocity and temperature profiles are usually assumed in onedimensional (1D) models (e.g., Schumann model) for modeling SHTPB systems due to the flow homogenizing effect of the porous fillers [START_REF] Nicolas | Flexibility and robustness of a high-temperature air/ceramic thermocline heat storage pilot[END_REF]. The necessity of additional flow diffuser instead of inlet port in packed bed storage tanks to guarantee the good and stable thermal stratification is controversy in early stages. There is study focusing on installing special types of flow diffuser in SHTPB tanks to effectively utilize the bed domain [START_REF] Sanderson | Performance and efficient design of packed bed thermal storage systems. Part 1[END_REF]. Later, Bruch et al. [START_REF] Bruch | Experimental and numerical investigation of a pilot-scale thermal oil packed bed thermal storage system for CSP power plant[END_REF] experimentally observed that there was no significant inhomogeneity of radial temperature in a SHTPB tank without diffuser (tank height to diameter aspect ratio 𝐻𝐻 𝐷𝐷 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 =3) and proposed that the 1D heat transfer model was adequate. Yin et al. [START_REF] Yin | Experimental research on thermal characteristics of a hybrid thermocline heat storage system[END_REF][189] also experimentally tested in a near-tube tank ( 𝐻𝐻 𝐷𝐷 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 =5) and showed that the porous fillers could help to maintain the HTF as an ideal plug flow pattern. However, up to different inside configurations and various heat transfer behavior, the real impact of the injecting flow on the thermal performance is different. For example, Reddy and Pradeep [START_REF] Reddy | Stability analysis of the thermocline thermal energy storage system during high flow rates for solar process heating applications[END_REF] numerically observed that the radial non-uniform temperature distribution of their SHTPB tank ( 𝐻𝐻 𝐷𝐷 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 =4) is negligible in laminar flow owing to the porous packed bed working as flow distributor, but not in turbulent condition. Wang et al. [START_REF] Wang | Influence of flow distribution on the thermal performance of dual-media thermocline energy storage systems[END_REF] simulated a flow annul diffuser (80% annular area) at the inlet of a SHTPB tank ( 𝐻𝐻 𝐷𝐷 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 =1/3) and found that the non-uniformly radial flow has a limited influence on output energy but it affects the interstitial heat transfer thus improving thermal performance. Recently, there is an interesting and systematic work conducted by Vannerem et al. [4] to analyze these problems by comparing three types of baffle-type flow diffusers, as well as considering different flow rates. They found that the solid filler acts as a natural distributor and fluid distribution at the inlet does not impact the global storage performance due to the flow being restricted to a small fraction of the packed bed in their SHTPB tank ( 𝐻𝐻 𝐷𝐷 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 =2). Low flow rate keeps this homogeneity. In brief, more investigations are still needed to show from what height (distance to the inlet) such radial temperature gradient can be eliminated by the porous bed with different packing properties (e.g., particle size, Biot number, etc.), and to further clarify the relation between the thermocline expansion due to the injecting flow and the global thermal performance reduction of the SHTPB tank.

The wall impact and associated heat losses are another influencing factor on the radial temperature distribution of SHTPB tank. Early studies [START_REF] Cascetta | Experimental investigation of a packed bed thermal energy storage system[END_REF] [START_REF] Cascetta | Comparison between experimental and numerical results of a packed-bed thermal energy storage system in continuous operation[END_REF] reported the existence of radial temperature gradient for about 30-40% of the tank radius due to the heat loss, leading to the higher centerline temperature than that in near-wall region. This radial temperature gradient cannot be reflected in the 1D model and will cause the smaller amount of energy stored in the SHTPB tank than predicted [START_REF] Cascetta | A study of a packed-bed thermal energy storage device: Test rig, experimental and numerical results[END_REF] [START_REF] Cascetta | Experimental and numerical research activity on a packed bed TES system[END_REF]. Hoffmann et al. [START_REF] Hoffmann | Experimental and numerical investigation of a thermocline thermal energy storage tank[END_REF] [START_REF] Hoffmann | A thermocline thermal energy storage system with filler materials for concentrated solar power plants: Experimental data and numerical model sensitivity to different experimental tank scales[END_REF] reported that the heat losses would lead to the unstable thermocline, reduced output power, and decreased outlet temperature.

Xie et al. [START_REF] Xie | Wall impact on efficiency of packed-bed thermocline thermal energy storage system[END_REF] have developed adapted transient models to systematically explore the wall impact on the dynamic thermocline behavior of the SHTPB tanks by including the wall and insulation heat capacity in the governing equations. The most influencing factors have also been identified to provide useful design guidelines. Nevertheless, systematic experimental investigation of a SHTPB tank under two extreme conditions (with or without insulation) is still needed in order to validate the developed numerical model. This topic will be discussed in detail in the current work.

Effect on axial heat diffusion and heat transfer

The thermal stratification in the axial direction of SHTPB tank is mainly determined by the heat transfer rate between the HTF and solid fillers as well as the thermal diffusion of the liquid and solid phases. One of the key operating parameters is the charging/discharging flow rate (or the superficial fluid velocity) which has been subjected to many parametric studies with the purpose of improving the overall efficiency of the storage tank [START_REF] Chandra | Stratification analysis of domestic hot water storage tanks: A comprehensive review[END_REF]. On the one hand, the increasing flow rate would enhance the solid-fluid heat transfer, decrease the thermal diffusion [4] [START_REF] Esence | A versatile one-dimensional numerical model for packedbed heat storage systems[END_REF], and reduce the heat loss to environment owing to the lower charging/discharging time (or residence time) [START_REF] Theade | Experimental study on the cyclic behavior of thermal energy storage in an air-alumina packed bed[END_REF]. These effects contribute to the increased overall efficiency of the SHTPB tank. In this regard, Al-Azawii et al. [START_REF] Theade | Experimental study on the cyclic behavior of thermal energy storage in an air-alumina packed bed[END_REF] experimentally tested a SHTPB tank with small particles size (Sphere Biot number, 𝐵𝐵𝐵𝐵 𝑠𝑠 <0.1, 𝐻𝐻 𝐷𝐷 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 =8) under 21.5-150 °C and found that the overall exergy efficiency could be increased from 35.7% to 55.4% by increasing the air flow rate from 120 to 366 L min -1 . On the other hand, the incoming flow at a high flow rate can penetrate deeper along the centerline of the SHTPB tank (radial temperature non-uniformity as mentioned above), leading consequently to the thermocline expansion and lowered efficiency. Kocak and Paksoy (2019) [START_REF] Koçak | Packed-bed sensible thermal energy storage system using demolition wastes for concentrated solar power plants[END_REF] numerically proved that when the Reynolds numbers (𝑅𝑅𝑅𝑅) increased from 22 to 135 the charging efficiency reduced by about 30% because of the local flow turbulences. As a result, efforts have been devoted to find the optimal operating flow rate (or velocity) that leads to the best performance of SHTPB tanks. For example, Hoffmann et al. (2017) [START_REF] Hoffmann | Experimental and numerical investigation of a thermocline thermal energy storage tank[END_REF][155] and Vannerem et al (2021) [4] both numerically proved the existance of an optimal HTF flow rate for a SHTPB tank (𝐵𝐵𝐵𝐵 𝑠𝑠 <0.1) operated under medium or high temperature (100-300 °C). Kocak and Paksoy (2020) [START_REF] Kocak | Performance of laboratory scale packed-bed thermal energy storage using new demolition waste based sensible heat materials for industrial solar applications[END_REF] experimentally obtained a maximum system energy efficiency of 67% at charging temperature of 150 °C under the optimum charging superficial fluid velocity of 1.9 mm s -1 (𝑅𝑅𝑅𝑅<10, 𝐵𝐵𝐵𝐵 𝑠𝑠 <0.1). Nevertheless, all the tested cases are with small particle fillers and a low Bis number, the combined impact of HTF flow rate and heat loss on the thermocline expansion of SHTPB tanks with larger particle size (𝐵𝐵𝐵𝐵 𝑠𝑠 >0.1) is still not enough clear thus should be further investigated experimentally.

Aim and scope

Numerical modeling and simulation tools have the advantage of testing the influences of various variables so to predict the thermal performance of the SHTPB tanks under different operational and geometrical conditions. Nevertheless, each numerical model for SHTPB tanks has its own accuracy due to different assumptions made, and at first, its applicable range needs to be tested and validated by experimental results. Table 4.1 lists main experimental investigations using sensible fillers reported in the open literature. Systematic investigations on the impacts of various influencing factors on the thermocline expansion are still needed, especially for SHTPB tanks operated under low temperature range (<100 °C).

For all these reasons, a lab-scale SHTPB tank has been fabricated, instrumented and experimentally tested under controlled conditions. The dynamic thermocline behaviors under charging and discharging operations have been systematically characterized by both the numerical and experimental approaches so as to evaluate the impacts of various influencing factors (inlet configuration, insulation, HTF flow rate, filler particle size, etc.) on the axial and radial thermocline expansion and on the overall performances of the SHTPB tank. The obtained experimental data-sets, especially under small flow rate (𝑅𝑅𝑅𝑅 <15), relatively large particle size (𝐵𝐵𝐵𝐵 𝑠𝑠 >0.1) and low temperature (<100 °C) operational conditions, could also be used to determine the applicable range of different numerical models in view of model validation. It is also expected that this work can provide useful design and operating guidelines for alleviating thermocline expansion in SHTPB tanks in practical applications. • Reduced energy efficiency with the increasing charging temperature.

• Thermocline expansion at higher flow rate due to the stratification disturbance.

• Thermocline expansion at lower flow rate due to heat loss.

Experimental setup and improved model 4.2.1. Test-rig description

This experimental set-up is first designed by Lou et al. [START_REF] Lou | Optimized flow distributor for stabilized thermal stratification in a single-medium thermocline storage tank: A numerical and experimental study[END_REF] in LTEN laboratory of a onetank system for flow diffuser optimization. It was then modified for the packed-bed one tank system in this thesis.

The laboratory-scale SHTPB tank tested has a cylindrical shape with a height of 398 mm and Both the charging and discharging operations were tested. In charging, hot water first entered from tank top port and transfers heat to solid fillers inside to store heat. In discharging, cold water entered from tank bottom port to drive the stored hot water from tank top to release heat. The charging or discharging stopped when each outlet temperature reached the corresponding set point according to the designed requirement.

an

Tested cases

To evaluate the various impacting factors (inlet configurations, mass flow rate, insulation, inlet temperature, etc.) on the thermocline, six SHTPB configurations were experimentally investigated in this work, including two sizes of glass fillers, three inlet diffuser configurations, and with/without insulation. Details of these configurations and the main operating parameters are listed in Table 4.2.

In order to verify the temperature gradient inside the glass sphere and to explore the influence of particle size on the thermocline behavior, two sizes of glass spheres (7 mm and 10 mm) with the same thermophysical properties (cf. In order to analyze the buffering effect of porous bed to alleviate the impact of inflowing HTF jet on the thermocline stability, 3 inlet configurations were tested for comparison as shown in works [START_REF] Lou | Optimized flow distributor for stabilized thermal stratification in a single-medium thermocline storage tank: A numerical and experimental study[END_REF]. In Case 5, the gap between the diffuser at z1=10 mm and the tank top/bottom cover was filled with one layer of glass spheres to make full use of the tank volume, both the porous bed and the plate diffuser acting as the inlet configuration. In comparative Case 6, no solid fillers were packed in this gap to eliminate the effect of porous fillers, and the height was set to be larger (z1=35 mm) to amplify the impact of inflowing jet and mitigating effect of the plate-type diffuser.

Moreover, in order to explore the impact of heat loss on thermocline expansion, both Case 2 and Case 4 without insulation layer were tested and compared with others.

Improved dispersion-concentric three-phase model

In order to consider the thermal gradient inside the ball (𝐵𝐵𝐵𝐵 𝑠𝑠 >>0.1), a dispersion-concentric three-phase (DC-3P) numerical model (Figure 4.5) is developed based on the 1D-3P model in Chapter 3. Assumptions and equations are follows:

(1) Solid sphere is modeled as dispersion concentric because of the possible non-ignorable temperature gradient inside (𝐵𝐵𝐵𝐵 𝑠𝑠 >0.1).

(2) Wall is modeled as a separate phase in 1D (axial direction).

(3) Insulation layer is simplified and represented by a thermal resistance in Chapter 3.

(4) Thermophysical properties of fluid and solid materials (Table 4.3) are set as constant due to relatively small operational temperature range.

• Governing equations

Fluid (1D):

𝜀𝜀 • 𝜌𝜌 𝑓𝑓 • 𝐶𝐶 𝑝𝑝, 𝑠𝑠 • � 𝜕𝜕𝑇𝑇 𝑠𝑠 (𝜕𝜕) 𝜕𝜕𝑖𝑖 + 𝑁𝑁 𝑓𝑓 • 𝜕𝜕𝑇𝑇 𝑠𝑠 (𝜕𝜕) 𝜕𝜕𝜕𝜕 � = 𝜕𝜕 𝜕𝜕𝜕𝜕 • �𝜆𝜆 𝑓𝑓,𝑒𝑒𝑓𝑓𝑓𝑓 • 𝜕𝜕𝑇𝑇 𝑠𝑠 (𝜕𝜕) 𝜕𝜕𝜕𝜕 � + ℎ 𝑠𝑠𝑓𝑓 • 𝐴𝐴 𝑠𝑠 𝑉𝑉 𝑠𝑠 • �𝑑𝑑 𝑠𝑠 ′ (𝑧𝑧, 𝑟𝑟 𝑝𝑝 = 𝐷𝐷 𝑝𝑝 2 ) -𝑑𝑑 𝑓𝑓 (𝑧𝑧)� + ℎ 𝑓𝑓-𝑤𝑤 • 𝐴𝐴 𝑠𝑠-𝑤𝑤 𝑉𝑉 𝑏𝑏 • �𝑑𝑑 𝑤𝑤 (z) -𝑑𝑑 𝑓𝑓 (𝑧𝑧)� (4.1)
Solid (2D spherical radius coordinate):

𝜌𝜌 𝑠𝑠 • 𝐶𝐶 𝑝𝑝,𝑠𝑠 • 𝜕𝜕𝑇𝑇 𝑠𝑠 (𝜕𝜕,𝑟𝑟 𝑝𝑝 ) 𝜕𝜕𝑖𝑖 = 1 𝑟𝑟 𝑝𝑝 2 • 𝜕𝜕 𝜕𝜕𝑟𝑟 𝑝𝑝 • �𝑟𝑟 𝑝𝑝 2 • 𝜆𝜆 𝑠𝑠 • 𝜕𝜕𝑇𝑇 𝑠𝑠 (𝜕𝜕,𝑟𝑟 𝑝𝑝 ) 𝜕𝜕𝑟𝑟 𝑝𝑝 � (4.2)
Wall (1D):

𝜌𝜌 𝑤𝑤 • 𝐶𝐶 𝑝𝑝,𝑤𝑤 • 𝜕𝜕𝑇𝑇 𝑤𝑤 (𝜕𝜕) 𝜕𝜕𝑖𝑖 = 𝜕𝜕 𝜕𝜕𝜕𝜕 • �𝜆𝜆 𝑤𝑤 • 𝜕𝜕𝑇𝑇 𝑤𝑤 (𝜕𝜕) 𝜕𝜕𝜕𝜕 � + ℎ 𝑓𝑓-𝑤𝑤 • 𝐴𝐴 𝑠𝑠-𝑤𝑤 𝑉𝑉 𝑤𝑤 • �𝑑𝑑 𝑓𝑓 (𝑧𝑧) -𝑑𝑑 𝑤𝑤 (𝑧𝑧)� + ℎ 𝑤𝑤-𝑎𝑎𝑚𝑚𝑏𝑏 • 𝐴𝐴 𝑠𝑠-𝑤𝑤 𝑉𝑉 𝑤𝑤 • [𝑑𝑑 𝑎𝑎𝑚𝑚𝑏𝑏 -𝑑𝑑 𝑤𝑤 (𝑧𝑧)] (4.3)
where 𝑟𝑟 𝑝𝑝 -axis is the spherical coordinate in the schematic used for the fillers, differ to the r-axis radial coordinate of tank. 𝑑𝑑 𝑠𝑠 ′ is the solid surface temperature.

• Boundary and initial conditions

In a charging/discharging cycling process, the boundary and initial condition are described in Table 4.4. It assumes the initial condition of changing is fully discharged and with a homogenous coldest operating temperature, while the cutoff temperature after charging is the beginning of discharging.

• Solving and steps

The solving of the model is the same to that one designed in Chapter 3. ) from 5 to 20. The particle nodes have a minor influence on the convergence of cutoff temperature. Thus, N=1000 and M=1000 are used for height and time node differential mesh, respectively, and F=20 is chosen to better capture the temperature gradient inside the particle.

Table 4.4

Initial and boundary condition in axial 𝑧𝑧-direction and spherical radius 𝑟𝑟 𝑝𝑝 -direction.

Key performance indicators

In this chapter, the energy efficiency indicators chosen are different compared to Chapter 3.

Still, they are uniform to Chapter 4 because it's not only focused on tank walls but more on the cycling process. Additional energy efficiency indicators are used in this Chapter.

• Energy efficiency (1 st law)

Charging energy efficiency (𝜂𝜂 𝑒𝑒ℎ ) is defined as the ratio of the stored energy (∆𝐸𝐸 𝑠𝑠𝑖𝑖𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 ) to the input energy by HTF (∆𝐸𝐸 𝑖𝑖𝑖𝑖 ). The stored energy of ∆𝐸𝐸 𝑠𝑠𝑖𝑖𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 is the amount of thermal energy stored in solid and fluid phases from beginning (t=0) to ending (t=tch) in charging. Discharging energy efficiency (𝜂𝜂 𝑚𝑚𝑖𝑖𝑠𝑠 ) is the ratio of the output energy by HTF (∆𝐸𝐸 𝑜𝑜𝑜𝑜𝑖𝑖 ) in discharging to the stored energy of ∆𝐸𝐸 𝑠𝑠𝑖𝑖𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 at the beginning of discharging. The heat loss ratio of charging (𝜂𝜂 𝑒𝑒ℎ,𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠 ) is defined as the ratio of the heat loss (∆𝐸𝐸 𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠 ) to the total input energy of ∆𝐸𝐸 𝑖𝑖𝑖𝑖 in charging.

𝜂𝜂 𝑒𝑒ℎ = ∆𝐸𝐸 𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 ∆𝐸𝐸 𝑖𝑖𝑡𝑡 = ∆𝐸𝐸 𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 (𝑖𝑖=𝑖𝑖 𝑐𝑐ℎ )-∆𝐸𝐸 𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 (𝑖𝑖=0) ∫ �𝑚𝑚̇𝑠𝑠•𝐶𝐶 𝑝𝑝,𝑠𝑠 •(𝑇𝑇 𝑖𝑖𝑡𝑡 -𝑇𝑇 0 )�𝑚𝑚𝑖𝑖 𝑡𝑡 𝑐𝑐ℎ 0 (4.4) 𝜂𝜂 𝑒𝑒ℎ,𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠 = ∆𝐸𝐸 𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠 ∆𝐸𝐸 𝑖𝑖𝑡𝑡 = ∫ �𝑚𝑚̇𝑠𝑠•𝐶𝐶 𝑝𝑝,𝑠𝑠 •(𝑇𝑇 𝑖𝑖𝑡𝑡 -𝑇𝑇 𝑜𝑜𝑜𝑜𝑡𝑡 )�𝑚𝑚𝑖𝑖 𝑡𝑡 𝑐𝑐ℎ 0 -∆𝐸𝐸 𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 (𝑖𝑖=𝑖𝑖 𝑐𝑐ℎ ) ∫ �𝑚𝑚̇𝑠𝑠•𝐶𝐶 𝑝𝑝,𝑠𝑠 •(𝑇𝑇 𝑖𝑖𝑡𝑡 -𝑇𝑇 0 )�𝑚𝑚𝑖𝑖 𝑡𝑡 𝑐𝑐ℎ 0 (4.5) 𝜂𝜂 𝑚𝑚𝑖𝑖𝑠𝑠 = ∆𝐸𝐸 𝑜𝑜𝑜𝑜𝑡𝑡 ∆𝐸𝐸 𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 = ∫ �𝑚𝑚̇𝑠𝑠•𝐶𝐶 𝑝𝑝,𝑠𝑠 •(𝑇𝑇 𝑜𝑜𝑜𝑜𝑡𝑡 -𝑇𝑇 0 )�𝑚𝑚𝑖𝑖 𝑡𝑡 𝑚𝑚𝑖𝑖𝑠𝑠 0 ∆𝐸𝐸 𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 (𝑖𝑖=𝑖𝑖 𝑐𝑐ℎ ) (4.6)
where -𝑑𝑑 𝑖𝑖𝑖𝑖 is the inlet temperature of HTF.

-Tout is the outlet temperature of the HTF.

-T0 is the reference coldest operational temperature 𝑑𝑑 𝐶𝐶 (20 °C).

In addition, the stored energy in the tank at a certain time for fluid and solid is calculated:

∆𝐸𝐸 𝑠𝑠𝑖𝑖𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 (𝑡𝑡) = 𝜋𝜋 • 𝑅𝑅 𝑖𝑖𝑖𝑖𝑖𝑖 2 • ∫ �𝜌𝜌 𝑓𝑓 • 𝐶𝐶 𝑝𝑝,𝑓𝑓 • 𝜀𝜀 • (𝑑𝑑 𝑓𝑓 -𝑑𝑑 0 ) + 𝜌𝜌 𝑠𝑠 • 𝐶𝐶 𝑝𝑝,𝑠𝑠 • (1 -𝜀𝜀) • (𝑑𝑑 � 𝑠𝑠 -𝑑𝑑 0 )�𝑑𝑑𝑧𝑧 𝐻𝐻 0 (4.7)
where 𝑑𝑑 � 𝑠𝑠 is the average temperature of single solid spheres at the same height. In experiment, the stored energy is calculated using the average temperatures of solid and fluid for a number of small unit volumes. More precisely, the tank volume is firstly divided into small cells by thermocouple points and the temperature of such single unit volume is considered as homogenous.

• Storage/utilization ability

Uncertainty analysis

The uncertainties of experimentally measured parameters and calculated parameters are listed in Table 4.5.

The measurement uncertainties were obtained by evaluating the standard deviation in repeated testing [START_REF] Taylor | Guidelines for evaluating and expressing the uncertainty of NIST measurement results[END_REF]. The thermocouples were calibrated with an oil FLUKE 6102 MICRO-BATH The analytical uncertainties for indirect parameters, such as energy efficiency, are determined by the components uncertainties, 𝜗𝜗, that are contributed by the measurement uncertainties based on error propagation [START_REF] He | Experiments on comparative performance of water thermocline storage tank with and without encapsulated paraffin wax packed bed[END_REF]. In experiment, the average temperature of small unit volume is used to calculate energy. Both measurement uncertainty and analytic interpolation integral uncertainty of the average temperature can influence the energy calculation (average temperature is actually a type of middle point integration method). Firstly, the temperature error (systematic error) is estimated to be ±0.37 K, the measurement uncertainty on average temperature is calculated to be ±0.15 K, and the numerical integration uncertainty is below that, as calculated in FigureA 4.2 a.

Especially due to the different radial thermocouples number, the uncertainty is different for radial thermocouples. Thus, among those, system error of ±0.

𝑆𝑆𝐷𝐷 = � 1 𝑖𝑖 ∑ (𝑥𝑥 𝑖𝑖 -𝑥𝑥̅ ) 2 𝑖𝑖 𝑖𝑖=1
, where 𝑥𝑥 is measured parameter and 𝑙𝑙 is the repeated measurement times [START_REF] Taylor | Guidelines for evaluating and expressing the uncertainty of NIST measurement results[END_REF].

Assess calculation error:

*2 The components uncertainty is defined as

:𝜗𝜗 = �∑ � 𝜕𝜕𝜕𝜕 𝜕𝜕𝑒𝑒 𝑗𝑗 𝑆𝑆𝐷𝐷 𝑒𝑒 ,𝑗𝑗 � 2 𝑚𝑚-1 𝑗𝑗=1
, where 𝑦𝑦 = 𝑐𝑐(𝑥𝑥 1 , 𝑥𝑥 2 … . . 𝑥𝑥 𝑚𝑚 ) is the in-directly parameter, and m is the number of components [START_REF] Stern | Summary of exerimental uncertainty assessmet methodology[END_REF].

Experimental study on the influence of diffuser and insulation

This work experimentally investigated the thermocline expansion of SHTPB TES system due to various factors, including the inlet diffuser configuration, the insulation, the filler diameter, the HTF flow rate and the working temperatures. The developed DC-3P was firstly validated by comparison with the experimental data and then was used to conduct numerical parametric study.

Model validation

The experimental data of Case 1 (Pećlet number 𝑃𝑃𝑅𝑅 =12, Particle Reynolds number 𝑅𝑅𝑅𝑅 =3, 𝐵𝐵𝐵𝐵 𝑠𝑠 =0.76, charging process) have firstly been used for the numerical model validation. and the corresponding standard deviation (𝑆𝑆𝐷𝐷). For most of thermocouples in the axial centerline of the tank, ∆𝑑𝑑< ±2.5 K and 𝑆𝑆𝐷𝐷< 0.7 K can be observed, indicating that the temperature evolution at these positions can be well predicated by the developed DC-3P model. However, for TC-7 near the top inlet, the discrepancy ( ∆𝑑𝑑 ≈10 K and 𝑆𝑆𝐷𝐷 ≈2 K) is still noticeable, implying that the assumption of plug flow used in this 1D model at this position is not validated. This is mainly due to the impact of inflowing HTF jet from the inlet port on the radial velocity distribution and consequently on the thermocline expansion and evolution, which will be further investigated in detail and discussed in later sub-sections.

During the charging process, the energy efficiency difference at the cutoff time between numerical and experimental results is around 2%, which is within the experimental uncertainty of 5% (cf.

Validity range of the DC-3P model

Numerical and experimental results are compared for the investigated Case 1 (7 mm glass ball) and Case 3 (10 mm glass ball) in order to determine the precision or applicable range of the developed DC-3P model. and the energy efficiency difference (∆𝜂𝜂 𝑒𝑒ℎ ) obtained under various operating conditions. It is found that, within the tested condition of 𝑅𝑅𝑅𝑅 <15 and 𝐵𝐵𝐵𝐵 𝑠𝑠 <1.3, the 𝑆𝑆𝐷𝐷 and ∆𝜂𝜂 𝑒𝑒ℎ can be kept below 2.5 K and 3%, respectively. The developed DC-3P model could thereby be safely used with good precision under this applicable range even though the inlet HTF penetration has a non-negligible effect on the thermocline expansion.

Evolution of temperature field

Figure 4.9 shows the evolution of the fluid temperature cartography inside the SHTPB tank experimentally measured for one fully charging and discharging cycle. Case 3 with porous bed inlet (𝐷𝐷 𝑝𝑝 =10 mm) has been tested at two flow rates, i.e., 𝑉𝑉 ̇𝑓𝑓=0.3 (𝑅𝑅𝑅𝑅=5) and 1.5 L min -1 (𝑅𝑅𝑅𝑅=15), to highlight the impact of inflowing jet on the thermocline expansion in SHTPB. The colormap is constructed from data interpolation of 17 thermocouples measurements (linear interpolation in axial direction). The dimensionless time equaling to 𝑡𝑡 * =1 (cf. in Chapter 3) means that the theoretical plug flow reaches the tank top or bottom. It can be observed that at the beginning of charging (𝑡𝑡 * =0), the tank has a quasi-homogeneous temperature of 𝑑𝑑 𝐶𝐶 (blue color). But for the beginning of discharging, the temperature distribution inside tank is a bit less homogeneous since the ending of fully charging (𝜃𝜃=0.01, for better observation) has been used as the initial condition for discharging.

By examining the temperature color maps, it can be observed that the thermocline region grows thicker over charging or discharging time. Moreover, the shape of thermocline region is not flat, indicating that temperature gradient exists in radial direction. The impact of penetrating flow inject on the thermocline expansion can be clearly seen, especially under high flow rate (𝑉𝑉 ̇𝑓𝑓=1.5 L min -1 ) with more important inertial force. It seems that the solid fillers alone are not totally capable of buffering the momentum-dominated injecting flow under this tested condition, resulting in the non-uniform fluid distribution which destabilizes much the temperature stratification. Note that the shape of thermocline is a little bit different in charging and discharging due the influence of gravity and the lowered temperature at near-wall region due to the heat loss.

Impact of inlet configuration

The testing results of Case 3 (packed bed), Case 5 (packed bed + diffuser) and Case 6 (diffuser) .10 a, the radial temperature difference (∆𝑑𝑑 ) at TC-7 level decreases after adding the plate-type diffuser. The corresponding value of 𝑐𝑐 𝑟𝑟 is 0.83 for basic case 3 (z1=0, only the packed bed), 0.66 for case 6 (z1=35 mm, only the diffuser), and 0.30 for case 5 (z1=10 mm, the combined diffuser and packed bed), respectively. As expected, the combined effect of diffuser and packed bed largely alleviates the influence of penetrating HTF jet on the thermocline stability in the entrance, better than that with only the diffuser or only the packed bed.

At TC-5 level near the middle tank height, the impact of penetrating HTF jet on the radial temperature distribution uniformity is shown to be rather limited even at high flow rate, reflected by the small radial temperature differences and low 𝑐𝑐 𝑟𝑟 values (<0.2) for all tested inlet configurations (Figure 4.10 b). The outer radial temperature of Case 6 (no packed bed in entrance region) is a little higher than the center temperature because of the double-hump shape of thermocline caused by higher velocity in near-wall region [START_REF] Lou | Single-tank thermal energy storage systems for concentrated solar power: Flow distribution optimization for thermocline evolution management[END_REF]. Without packed bed in the entrance, the double-hump phenomena being more obvious that the 𝑐𝑐 𝑟𝑟 value for case 6 is higher than other configurations. The influence of radial thermocline expansion or instability due to the penetrating jet on the global performance of the SHTPB tank needs further discussion. To this end, Figure 4.11 a shows the energy efficiency (𝜂𝜂 𝑒𝑒ℎ ) and capacity ratio (Cratio) or utilization at the cutoff time for different inlet configurations. For all studied inlet configurations, when 𝑑𝑑 𝐻𝐻 increases, the energy efficiency slightly decreases mainly due to the higher heat loss, while the capacity ratio slightly increases because of the higher heat transfer rate by larger temperature difference, which will be discussed in detail in the next sub-section.

Case 5 with the most uniform radial temperature distribution at the inlet region has the largest capacity ratio and the longest charging time. The near plug flow pattern and the flattened thermocline shape renders the better utilization of the storage capacity (around 3%) of the SHTPB tank. However, it presents the lowest energy efficiency (Figure 4 Moreover, thermal infrared imaging is used to observe the qualitative trend of thermocline behavior on the outer surface of the tank. The wall emissivity is 0.90, the acquisition frequency is 10 s by using the Fluke thermal image camera TiS75 with a verification range of -20 to 80°C. The impact of heat loss on the performance of the SHTPB tank has been evaluated by comparing the experimental results of Case 3 (with insulation) and Case 4 (without insulation) for the same testing condition. From Figure 4.13 a, it is found that due to the heat loss, the outlet fluid temperature of no-insulation tank is 5 K lower than that of the tank with insulation at the ending moment of charging (40 min, t*=2.5). Longer charging time by around 5% is also needed to reach the cutoff temperature (𝜃𝜃=0.2) when the tank is not insulated due to the serious tailing effect. and heat loss ratio (𝜂𝜂 𝑒𝑒ℎ,𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠 ) curve, not surprisingly both indicating that the SHTPB tank performs better when well-insulated. At the cutoff temperature set as 𝜃𝜃 =0.2, the SHTPB tank with an insulation can improve the energy efficiency by about 5-7%, increase total stored energy for 4-7%, and augment the capacity ratio by about 3-5%.

Impact of insulation

Impact of flow rates and inlet HTF temperature

The influence of HTF flow rate and inlet temperature on the thermocline evolution in axial direction is further investigated experimentally and reported in this sub-section.

Further comparison between numerical and experimental results

Further interpretation and comparison between numerical (DC-3P) and experimental results are performed with the intention of addressing some interesting issues such as the temperature gradient inside the solid particles, the existence of optimum flow rate for SHTPB and the applicable range of the DC-3P model. The temperature gradient inside sensible fillers, reflected by the existence of a temperature difference between the solid sphere center and the surrounding HTF, has been reported by numerical modeling but inadequately investigated nor validated in experiments. To addressee this question, Figure 4.17 presents the time and volume-averaged temperature gap between solid sphere center and fluid as defined in Eq. 4.11, obtained both by experimental measurements of all thermocouples and by DC-3P modeling. The solid Biot number 𝐵𝐵𝐵𝐵 𝑠𝑠 ranges from 0.6-1.1 for 7 mm sphere fillers (Case 1) and from 0.7-1.2 for 10 mm sphere fillers (Case 3) with the tested flow rates, implying that the dispersion-concentric model is necessary to be used [START_REF] Wang | Thermal performance analysis of packed-bed thermal energy storage with radial gradient arrangement for phase change materials[END_REF]. Both numerical and experimental results show that the ∆𝑑𝑑 � 𝑠𝑠𝑓𝑓 increases with the increasing flow rate and inlet fluid temperature ( 𝑑𝑑 𝐻𝐻 ). Comparing two sphere sizes, the difference between the numerical and experimental results is smaller than 0.3 K for 10 mm fillers and about 1 K for 7 mm fillers, respectively, showing good agreement. Contrary to theory, the temperature gap in experiments is larger for small size particles, may be due to heat transfer surface difference of the flow thermal front [START_REF] Hoffmann | Experimental and numerical investigation of a thermocline thermal energy storage tank[END_REF] as well as the measurement uncertainties and difficulties. But in general, the ∆𝑑𝑑 � 𝑠𝑠𝑓𝑓 value up to 1.7 K can be detected in experiments, confirming the existence of noticeable temperature gradient inside sphere under certain circumstances which is rarely reported in the open literature.

Temperature gradient inside sphere particles

Optimal flow velocity

Additional simulations using the DC-3P model have been performed and compared with the experimental data in order to exhibit the existence (or not) of an optimal HTF flow rate (𝑅𝑅𝑅𝑅) for SHTPB TES tanks.

Chapter conclusion

In this work, a laboratory-scale SHTPB has been systematically evaluated by experimentally measuring the temperature evolution of both the fluid phase and the solid phase at different axial and radial positions inside the tank. In parallel, a dispersion-concentric 3-phase (DC-3P) numerical model has been developed and simulations have been performed with various operating conditions to be compared with the experimental data for model validation. In particular, the impacts of penetrating inlet flow and heat loss on the thermocline expansion and on the global performances of the TES tank have been investigated and analyzed in detail. Other issues such as the temperature gradient inside the solid particles, the influences of flow rate and working temperature and the applicable range of the DC-3P model have also been discussed. Main conclusions of this study are summarized as follows.

(1) The developed DC-3P model considering the wall heat capacity and heat loss is proved to be capable of precisely predicting the global performance of the SHTPB TES tank. Compared to the experimental data, the temperature standard deviation and energy efficiency difference can be kept below 2.5 K and within 3%, respectively, under the applicable range of 𝑅𝑅𝑅𝑅 <15

and 𝐵𝐵𝐵𝐵 𝑠𝑠 <1.3.

(2) The inlet HTF penetration into the packed-bed will cause the non-uniform radial temperature distribution and thermocline expansion near the inlet region of the SHTPB tank, especially with higher flow rate (higher Re) condition. Nevertheless, the middle height of the tank is less affected due to the buffering effect of porous fillers. The combined effect of diffuser and packed bed as inlet configuration could better maintain the radial temperature uniformity as well as the thermocline stability, increasing the capacity ratio of the storage tank by about 3%

at the cutoff time. Nevertheless, slightly decreased energy efficiency could be registered for this inlet configuration due to the delayed cutoff time and the resulted higher amount of total heat loss.

(3) The heat loss without no insulation condition lead to a noticeable thermocline expansion (>20%), lowered charging energy efficiency (5-7%), increasing cutoff time (4-5%), and decreased capacity ratio (3-5%), even for low-temperature applications of the SHTPB TES tank.

(4) There is a temperature gradient inside sensible sphere particle due to the convection resistance between the solid and fluid and the conduction resistance of the solid particles. A temperature difference up to 1.7 K between the sphere particle center and surrounding fluid has been observed both by modeling and experimental measurement for our tested conditions.

(5) An optimal flow velocity corresponding to Reynolds number of 𝑅𝑅𝑅𝑅=3 has been determined in simulation for this tank geometry ( 𝐻𝐻 𝐷𝐷 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 =2, inlet port width/tank diameter=0.06) and tested temperature range (20/70°C). But this optimum is not enough significant to be confirmed in experiments.

This chapter contributes to exploring the influencing factors based on a packing configuration by sensible fillers, enabling the inclusion of thermocline expansion into the design and optimization of low-temperature thermocline packed-bed system. It used the optimized diffuser by Lou et al. [START_REF] Lou | Single-tank thermal energy storage systems for concentrated solar power: Flow distribution optimization for thermocline evolution management[END_REF] in the thermocline one-tank system and served as an improvement of the thermocline packed-bed system.

Next chapter will focus on optimization of multi-layered packing configuration, using diverse PCMs or mixtures of PCM-sensible material as fillers for different applications.

Introduction

Greenhouse energy consumption issues

A roadmap for the global energy sector by International Energy Agency (IEA)'s Net Zero by 2050 reported that, achieving transformation of the global energy system is critical to reaching carbon dioxide (CO2) emissions to net zero by 2050 [START_REF]Net Zero by 2050--A Roadmap for the Global Energy Sector[END_REF]. Rapidly boost clean or renewable energy technologies like solar energy is one solution to net zero emission. To sustain agriculture, greenhouse (GH) needs considerable energy consumption for heat, cool, light, and etc. to maintain the desired climate for plant growing. In north European region, the annual energy demand of greenhouse agriculture is up to 3,600 MJ m -2 [212] [START_REF] Gorjian | Recent advances in net-zero energy greenhouses and adapted thermal energy storage systems[END_REF]. Conventionally, GH integrates extra heater systems to supply heat, such as gas heater or steam from power plant, causing CO2 emission [START_REF] Gross | CUAES Greenhouses -Energy Consumption and Equivalents CUAES Greenhouses -Energy Consumption and Equivalents[END_REF].

Net-zero greenhouse

Agricultural net-zero energy greenhouse (net-zero GH) is a solution, that employ renewable energy-conservation techniques like solar photo-voltaic or solar thermal to address energy consumption or provide electric power. In terms of energy-saving strategies and overcoming global hunger and poverty, net-zero GH shows advantages [START_REF] Gorjian | Recent advances in net-zero energy greenhouses and adapted thermal energy storage systems[END_REF]. Integrating thermal energy storage (TES) in net-zero energy GH is one good way on solving the issues like overheating in daytime and excessive cold at night through providing stable energy supplies.

Employing latent heat material or PCM in TES is more useful for improvement of energy loading capacity and efficiency over sensible heat material due to the high energy density. Latent heat thermocline packed-bed (LHPTB) system is applied in reduction of investment comparing to conventional two tanks. Filling one type of PCM in the one tank is a common configuration strategy, but under the limitation of utilization ratio. Designing packing configuration is a method to enhance storage ability [START_REF] Nithyanandam | Analysis of a latent thermocline storage system with encapsulated phase change materials for concentrating solar power[END_REF].

Multi-layered PCM thermocline system

Multi-layered (or cascaded) PCM in thermocline storage tank is good at enhance thermal performance by filling different layer PCMs comparing to uniform filled PCM. Packing PCMs from top to bottom with a declining melting temperature configuration also improve charging/discharging rate due to the larger temperature difference along the flow direction.

Moreover, thermal buffering in cycling on PCM layer causes minor degradation of thermocline [2].

In early stages, the multi-layered PCM system using cylindrical PCM capsules were analyzed on longitudinal heat transfer fluid (HTF) [START_REF] Watanabe | Enhancement of charging and discharging rates in a latent heat storage system by use of PCM with different melting temperatures[END_REF] and transverse HTF [START_REF] Farid | Thermal performance of a heat storage module using PCM's with different melting temperature: Experimental[END_REF]. Later, in thermocline system, researchers [START_REF] Yang | Thermal performance of a solar storage packed bed using spherical capsules filled with PCM having different melting points[END_REF] [START_REF] Peng | Modeling on heat storage performance of compressed air in a packed bed system[END_REF][217] [START_REF] Elfeky | Numerical comparison between single PCM and multi-stage PCM based high temperature thermal energy storage for CSP tower plants[END_REF] proposed the two or three-staged tank configuration shows higher exergy and energy efficiency than single-stage tank. For example, Wu et al. [START_REF] Wu | Cyclic behaviors of the molten-salt packed-bed thermal storage system filled with cascaded phase change material capsules[END_REF] investigated the PCM packed-bed system with 1, 3, and 5 cascaded phase change temperatures with high-temperature molten salt HTF in cycles. It proved more number of PCM layers have a faster charging/discharging rate, higher accumulated efficiency, and even can reach a repeatable state after some cycling in the adiabatic boundary. Meanwhile, increasing threshold outlet temperature is good to enlarge storage capacity in the cascaded system.

However, uniform or proportional layer thickness is often adopted and the selection of cascaded phase change temperature configuration is hard to be determined according to cutoff temperature threshold [START_REF] Alptekin | A systematic assessment on a solar collector integrated packed-bed single / multi-layered latent heat thermal energy storage system[END_REF]. Parametric studies or optimization were carried out to explain the influence of those variables (including, layer thickness, phase change temperature) and give instruction of designing multi-layered PCM strategies. Cascetta et al. [2] compared a two-tank system with one-tank systems, including a packed-bed one-tank system filled with rock and another tank filled with PCM in 10% top layer to avoid substantial thermocline degradation.

Results show that the one-tank system increases annual thermal energy output than the two-tank direct system by 5% higher. Li et al. [START_REF] Li | Optimization of the packed-bed thermal energy storage with cascaded PCM capsules under the constraint of outlet threshold temperature[END_REF] studied the influence of melting temperature on the effective utilization rate of non-cascaded and cascaded PCM system. It was found that in two-and three-cascaded system, the top and bottom melting temperature can be chosen as slightly lower/higher than threshold temperature in charging/discharging, the maximum effective utilization rate reaches 84% which is higher than the non-cascaded system only about 40%.

Aim and scope

The optimization performed in literatures is almost on the basis of particular or few amount of configurations [START_REF] Wang | Analytic optimization of Joule-Brayton cycle-based pumped thermal electricity storage system[END_REF][96] [START_REF] Li | Optimization of the packed-bed thermal energy storage with cascaded PCM capsules under the constraint of outlet threshold temperature[END_REF]. In addition, PCM suffering from low thermal conductivity but can be improved by adding high thermal conductivity material like graphite [START_REF] Wu | Thermal conductivity enhancement on phase change materials for thermal energy storage: A review[END_REF]. As an influence factor, thermal conductivity is less considered in literatures for thermocline TES tank. This point has to be investigated more clearly.

Therefore, the goal of this chapter is to propose two-layered PCM configuration optimization method to improve the overall energy efficiency and the storage/utilization ability in multiple cycles. Design factors of PCM (phase change temperature, thermal conductivity, and layer thickness) are chosen as constraints for multi-objective optimization. The optimization is used for greenhouse application.

At first, built a multi-layered PCM system in a Lab-scale experimental set-up to validate the model. Then, an initial tank is designed according to the meteorology data and requirement of a greenhouse application. Later, a multi-objective optimization is used to optimize the layer packing and results were compared with real greenhouse to find the potential improvement work.

Model and experiment

In this chapter, the mathematical model of dispersion-concentric three-phase (DC-3P) used in Chapter 4 is validated by lab-scale experimental tank with multi-layered PCM-sensible packing configuration. This model is for optimization.

Numerical model: PCM capsule properties

Differently, this model taken into account the PCM capsule parameters, including the thermophysical properties of PCM in phase change process, the characteristic length of capsule, and capsule-fluid heat transfer coefficient.

• Equivalent thermophysical properties of PCM capsule

The apparent parameter method is used to define the thermophysical parameters of PCM, assuming the phase changes from solid to liquid in a narrow temperature ranges [START_REF] Felix Regin | An analysis of a packed bed latent heat thermal energy storage system using PCM capsules: Numerical investigation[END_REF] where -𝐶𝐶 𝑝𝑝,𝑃𝑃𝐶𝐶𝑃𝑃 , the equivalent specific heat capacity of PCM.

-𝜌𝜌 𝑃𝑃𝐶𝐶𝑃𝑃 , the equivalent density.

-𝜆𝜆 𝑃𝑃𝐶𝐶𝑃𝑃 , the equivalent thermal conductivity.

-𝑑𝑑 𝑚𝑚1 , 𝑑𝑑 𝑚𝑚2 , the initial and ending phase change temperature.

-𝐻𝐻 𝑚𝑚 (J kg -1 ), the enthalpy.

-Subscript of 's, l' represents the solid and liquid phases of PCM.

Once the volumetric heat capacity of shell is significantly higher than PCM (𝜌𝜌 𝑃𝑃𝐶𝐶𝑃𝑃 • 𝐶𝐶 𝑝𝑝,𝑃𝑃𝐶𝐶𝑃𝑃 ≪ 𝜌𝜌 𝑠𝑠ℎ𝑒𝑒𝑙𝑙𝑙𝑙 • 𝐶𝐶 𝑝𝑝,𝑠𝑠ℎ𝑒𝑒𝑙𝑙𝑙𝑙 ) or the volume difference for both is large (V 𝑃𝑃𝐶𝐶𝑃𝑃 ≫ V 𝑠𝑠ℎ𝑒𝑒𝑙𝑙𝑙𝑙 ), the stored heat in shell cannot be ignored. For example, metal shell or shell with considerable thickness. For simplification, the thermophysical properties of 𝐶𝐶 𝑝𝑝 , and 𝜌𝜌 for capsule shell should be equivalently considered.

𝐶𝐶 𝑝𝑝 = 𝑤𝑤 1 • 𝐶𝐶 𝑝𝑝,𝑠𝑠ℎ𝑒𝑒𝑙𝑙𝑙𝑙 + (1 -𝑤𝑤 1 ) • 𝐶𝐶 𝑝𝑝,𝑃𝑃𝐶𝐶𝑃𝑃 (5.5
)

𝜌𝜌 = 1/ � 𝑤𝑤 1 𝜌𝜌 𝑠𝑠ℎ𝑒𝑒𝑙𝑙𝑙𝑙 + 1-𝑤𝑤 1 𝜌𝜌 𝑃𝑃𝐶𝐶𝑃𝑃 � (5.6)
where 𝑤𝑤 1 is the mass fraction of capsule shell to PCM capsule.

• Stored energy of PCM capsule

The stored energy in PCM capsule (∆𝐸𝐸 𝑠𝑠𝑖𝑖𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚,𝑃𝑃𝐶𝐶𝑃𝑃 ) depends on temperature that is calculated based on liquid fraction [107] [206]. (5.7)

• Characteristic length of PCM capsule (𝑳𝑳 𝒄𝒄 )

When the capsule is cylinder or cubic shapes, the 𝐿𝐿 𝑒𝑒 or equivalent diameter (𝐷𝐷 𝑝𝑝 ) of capsule is defined according the ratio of the volume (𝑉𝑉 𝑒𝑒𝑎𝑎𝑝𝑝𝑠𝑠𝑜𝑜𝑙𝑙𝑒𝑒 , m 3 ) to outer surface area (𝐴𝐴 𝑒𝑒𝑎𝑎𝑝𝑝𝑠𝑠𝑜𝑜𝑙𝑙𝑒𝑒 , m 2 ) [START_REF] Khor | Application of granular materials for void space reduction within packed bed thermal energy storage system filled with macro-encapsulated phase change materials[END_REF]:

𝐷𝐷 𝑝𝑝 = 𝐿𝐿 𝑒𝑒 = 𝑉𝑉 𝑐𝑐𝑡𝑡𝑝𝑝𝑠𝑠𝑜𝑜𝑙𝑙𝑒𝑒 𝐴𝐴 𝑐𝑐𝑡𝑡𝑝𝑝𝑠𝑠𝑜𝑜𝑙𝑙𝑒𝑒
(5.8)

• Equivalent heat transfer coefficient between HTF and PCM capsule (𝒉𝒉 𝒇𝒇𝒇𝒇𝑪𝑪𝒇𝒇 )

When the capsule shell has high thermal conductivity and the 𝐵𝐵𝐵𝐵 𝑠𝑠ℎ𝑒𝑒𝑙𝑙𝑙𝑙 is less than 0.1, the temperature inside shell assumed spatially uniform based on the lump capacitance method. The total thermal resistance of shell and convection HTC between HTF and capsule surface (ℎ 𝑠𝑠𝑓𝑓 ) are both taken account into equivalent HTC (ℎ 𝑓𝑓𝑃𝑃𝐶𝐶𝑃𝑃 ) [START_REF] Khor | Application of granular materials for void space reduction within packed bed thermal energy storage system filled with macro-encapsulated phase change materials[END_REF].

1 ℎ 𝑠𝑠𝑃𝑃𝐶𝐶𝑃𝑃 = � 1 ℎ 𝑠𝑠𝑠𝑠 •𝐴𝐴 𝑐𝑐𝑡𝑡𝑝𝑝𝑠𝑠𝑜𝑜𝑙𝑙𝑒𝑒 + 𝑟𝑟 𝑝𝑝,2 -𝑟𝑟 𝑝𝑝,1 4𝜋𝜋•𝑟𝑟 𝑝𝑝,2 •𝑟𝑟 𝑝𝑝,1 •𝜆𝜆 𝑠𝑠ℎ𝑒𝑒𝑙𝑙𝑙𝑙 � • 𝐴𝐴 𝑒𝑒𝑎𝑎𝑝𝑝𝑠𝑠𝑜𝑜𝑙𝑙𝑒𝑒
(5.9)

ℎ 𝑠𝑠𝑓𝑓 = 𝑁𝑁𝑜𝑜 𝑠𝑠𝑠𝑠 •𝜆𝜆 𝑠𝑠 𝐿𝐿 𝑐𝑐 (5.10)
where -𝑁𝑁𝑁𝑁 𝑠𝑠𝑓𝑓 , the Nusselt number between solid phase and HTF, from the correlation [START_REF] Pfeffer | Heat and mass transport in multiparticle systems[END_REF].

-𝜆𝜆 𝑠𝑠ℎ𝑒𝑒𝑙𝑙𝑙𝑙 ,the capsule shell thermal conductivity.

-𝑟𝑟 𝑝𝑝,1 , the capsule internal radius.

-𝑟𝑟 𝑝𝑝,2 = 𝐿𝐿 𝑐𝑐 2 , the capsule external radius or shell radius.

Experimental validation: PCM capsule configuration

Two experimental cases were used to validate the model. The first is a single-layer latentheat thermocline packed-bed (LHTPB) tank integrated with solar water heating system in literature [START_REF] Nallusamy | Study on performance of a packed bed latent heat thermal energy storage unit integrated with solar water heating system[END_REF]. Another is the LTEN-designed experimental system in the lab in Chapter 4 with a heterogeneous thermocline packed-bed (HHTPB) tank.

The HHTPB tank is with good insulation and there are two layers. The upper layer is filled by PCM capsules with 1/3 volume ratio, while the remained bottom layer is filled by 7 mm glass sphere used in Figure 5.1. These PCM capsules are the same of the one used in SOTO et al. [START_REF] Soto | Thermal cycling aging of encapsulated phase change material -Compressed expanded natural graphite composite[END_REF].

The capsules are a cylindrical aluminum shells where the paraffin-compressed expanded natural graphite composite is encapsulated. All capsules were samples after the cycling test. Table 5.1 lists the main parameters of the two packed-bed experimental cases.

Multi-layered optimization methodology

In this chapter, a methodology for the design of multi-layered PCM packed-bed TES tank through the multi-objective optimization is proposed.

Step 1: Propose a single-layered packed-bed PCM tank.

Step 2: Design an initial tank based on the practical application of greenhouse (@Project SERRES+) [START_REF] Serres | Bilan énergétique global des besoins et des ressources, prédimensionnement des moyens de production et de stockage[END_REF]: first, to determine the initial tank volume according to the input (radiation intensity) and output (greenhouse consumption); then considering different charging/discharging time, to determine two mass flow rates for charging/discharging process; at last, taking into account the unstable weather, to obtain the dynamic inlet temperature input based on meteorological data.

Step 3: Evaluate the thermodynamic behavior of the initial tank: first, to explore the difference between steady and dynamic operation through the comparison the thermal performance of steady and dynamic inlet temperature; then to conduct sensitivity analysis of different phase change temperature to define key performance indicators' (KPI) influence; at last, through consecutive thermal cycling test, to discuss the cycling numbers influence.

Step 4: Conduct the multi-objective optimization: first, to define the best option between one or two layer packing filling; and then, to identify the parameter variables for a simplified irradiation boundary steady condition; at last, analyze results to a real greenhouse application from the optimized configuration defined in steady state, assess the stability of performance indicators of the TES to solar irradiation change: on steady case.

Initial tank design

The objective of this section is to design an initial tank size and define the initial operational condition for multi-objective optimization of the multi-layered PCM packed-bed tank based on a practical greenhouse application.

(1) It was first calculated the maximum energy demand of greenhouse to design a baseline tank storage capacity.

(2) Then, it was evaluated the energy need during a daily cycling process based on the meteorological data to determine a heat transfer rate. A mass flow rate-time profile for the charging/discharging was then calculated as a constant variable considering outlet temperature.

(3) Finally, considering the seasonal differences, it was defined two types of inlet temperature (steady and dynamic conditions) in charging process. Four typical seasonal days were selected to present the difference.

(4) Other parameters at a steady condition were finally decided and optimization was then performed for the steady condition.

System operation

The greenhouse internal temperature needs to be kept constant for plant growing. However, temperature drops sharp especially at night that needs to be avoided through the extra gas heating source.

The thermocline PCM packed-bed as alternative is designed to supply heat to keep the greenhouse night temperature at relatively constant level, while charge itself by absorbing free natural solar energy provided by solar panel in daytime. Moreover, comparing to the traditional single-media water or dual-media sensible thermocline storage system, PCM packed-bed TES system have more stable outlet temperature and significant higher energy density. In this chapter, a PCM thermocline packed-bed is thereby designed for daily greenhouse operation. The input solar energy is used to heat the water HTF with collectors, and then directly flows into the thermocline packed-bed tank to minimize the thermal losses to the environment. The output energy from TES is an indirect system that HTF flows out from top of thermocline tank and then transfers heat in heat exchanger unit to feed greenhouse. In real application, both output and input energy are dynamic in function of varying independently under the influence of changeable weather and climate. In this work, an assumption that the dynamic output for greenhouse heating can be achieved by controlling the operational condition of the exchanger was proposed for simplification. Thus, only the dynamic input is investigated under the fluctuation of solar radiation.

Defining tank volume

The preliminary tank volume (𝑉𝑉 𝐷𝐷𝐸𝐸𝐷𝐷 ) is estimated based on the maximum daily consumption of greenhouse in one year with a steady initial condition.

𝑉𝑉 𝐷𝐷𝐸𝐸𝐷𝐷 = 𝐸𝐸 𝐺𝐺𝐻𝐻,𝑚𝑚𝑡𝑡𝑒𝑒 �(1-𝜀𝜀)•𝜌𝜌 𝑃𝑃𝐶𝐶𝑃𝑃 •𝐶𝐶 𝑝𝑝,𝑃𝑃𝐶𝐶𝑃𝑃 +𝜀𝜀•𝜌𝜌 𝑠𝑠 •𝐶𝐶 𝑝𝑝,𝑠𝑠 �•∆𝑇𝑇 𝐷𝐷𝐸𝐸𝐷𝐷 •𝜂𝜂 𝑚𝑚𝑖𝑖𝑠𝑠,𝐷𝐷𝐸𝐸𝐷𝐷 (5.11)
► 𝐸𝐸 𝐺𝐺𝐻𝐻 [J] is the daily greenhouse consumption, calculated by integrating the required thermal power (𝑃𝑃 𝑜𝑜𝑜𝑜𝑖𝑖𝑝𝑝𝑜𝑜𝑖𝑖 , W) within the designed daily discharging time (𝑡𝑡 𝑚𝑚𝑖𝑖𝑠𝑠,𝐷𝐷𝐸𝐸𝐷𝐷 , s). Here, the maximum daily value, 𝐸𝐸 𝐺𝐺𝐻𝐻,𝑚𝑚𝑎𝑎𝑒𝑒 , is selected to amplify the operational flexibility for extreme weather when designing a tank.

► 𝜂𝜂 𝑚𝑚𝑖𝑖𝑠𝑠,𝐷𝐷𝐸𝐸𝐷𝐷 is the designed discharging efficiency of TES system, accounting heat loss and outlet temperature drop in discharging, which can be set as 0.85 based on different studies [START_REF] Trevisan | Packed bed thermal energy storage: A novel design methodology including quasi-dynamic boundary conditions and techno-economic optimization[END_REF][43] [START_REF] Zanganeh | Experimental and numerical investigation of combined sensible-latent heat for thermal energy storage at 575°C and above[END_REF].

► ∆𝑑𝑑 𝐷𝐷𝐸𝐸𝐷𝐷 [K]
is the designed maximum temperature difference on the tank, 𝑑𝑑 𝐻𝐻 -T 𝐶𝐶 .

Defining mass flow rates

Constant operational condition (mass flow rate or inlet temperature) is necessary for an ideal steady operational condition for thermocline packed-bed optimization. However, the output and input of greenhouse are changeable with the fluctuant solar radiation intensity and unstable heating requirement, respectively. In this system, in discharging process, the greenhouse consumption is assumed to be stable in steady condition.

A constant mass flow rate but changeable inlet temperature for real application was defined to simulate the dynamic process. Once the difference between steady and dynamic conditions are larger, the dynamic influence then need to be considered in optimization.

Designed mass flow rates in charging and discharging processes (𝑚𝑚̇𝑓𝑓 ,𝑒𝑒ℎ,𝐷𝐷𝐸𝐸𝐷𝐷 , 𝑚𝑚̇𝑓𝑓 ,𝑚𝑚𝑖𝑖𝑠𝑠,𝐷𝐷𝐸𝐸𝐷𝐷 ) are assumed to be constant value.

►𝜂𝜂 𝑜𝑜,𝐷𝐷𝐸𝐸𝐷𝐷 is the designed overall efficiency, accounting for the charging efficiency, standby heat loss, as well as charging efficiency. The designed mass flow rate allows to the keep the outlet temperature be higher than the hottest cutoff temperature in charging and lower than the coldest cutoff temperature in discharging to make full use of the tank.

Defining inlet temperature

Steady working temperature range is first designed into 20-70 °C depending on the water properties and practical condition, which is the maximum temperature difference (∆𝑑𝑑 𝐷𝐷𝐸𝐸𝐷𝐷,𝑚𝑚𝑎𝑎𝑒𝑒 ). ► 𝜂𝜂 𝑒𝑒𝑜𝑜𝑙𝑙𝑙𝑙𝑒𝑒𝑒𝑒𝑖𝑖𝑜𝑜𝑟𝑟 is the overall efficiency of thermal solar panel which is assumed as a constant value. Only solar thermal is taken into account. An efficiency of 50% is taken for solar collector system [START_REF] Chatelain | Récupéré sur quelleenergie[END_REF].

► 𝑆𝑆 𝑒𝑒𝑜𝑜𝑙𝑙𝑙𝑙𝑒𝑒𝑒𝑒𝑖𝑖𝑜𝑜𝑟𝑟 [m 2 ] is the effective surface area of solar collector, which is designed as the lowest value under the highest radiation day. On the one hand, for a whole year, the average daily heating consumption (𝐸𝐸 𝐺𝐺𝐻𝐻,𝑖𝑖𝑖𝑖𝑔𝑔ℎ𝑖𝑖 ) from night to morning (22:00-10:00) accounts for about 50% of the total daily heating energy (𝐸𝐸 𝐺𝐺𝐻𝐻,𝑖𝑖𝑜𝑜𝑖𝑖𝑎𝑎𝑙𝑙 ), including in winter (Dec.-Feb., 50%), in spring (Mar.-May, 53%), in summer (Jun.-Aug., 45%), and in autumn (Sep.-Nov., 53%).

Meteorological data

On another hand, the average daily radiation is different during the year but is nearly located at 10:00-18:00 which accounts for around 83% of total daily radiation, including in winter (Dec.-Feb., 94%), in spring (Mar.-May, 82%), in summer (Jun.-Aug., 78%), and in autumn (Sep.-Nov.,

87%).

Therefore, two different times for charging and discharging process are designed as 𝑡𝑡 𝑚𝑚𝑖𝑖𝑠𝑠,𝐷𝐷𝐸𝐸𝐷𝐷 =12 h (22:00-10:00), 𝑡𝑡 𝑒𝑒ℎ,𝐷𝐷𝐸𝐸𝐷𝐷 =8 h (10:00-18:00) finally. In daytime, solar collector absorbs thermal energy and then transfer to greenhouse for daily heating, as well as to the thermocline system for charging. At night, thermocline discharges thermal to greenhouse for heating. Thus, during the night, thermocline tank releases energy that drop into the minimum storage condition.

During the daytime, it stores excess energy that reaches the maximum condition. Table 5.2 is the annual energy consumption and solar energy supply of the greenhouse. The maximum energy demand of greenhouse of 𝐸𝐸 𝐺𝐺𝐻𝐻,𝑚𝑚𝑎𝑎𝑒𝑒 =1 kWh m -2 /day in Appendix FigureA 5.1 is used to determine the tank volume. The maximum solar thermal radiation of 𝐼𝐼 𝑚𝑚𝑎𝑎𝑒𝑒 =6 kWh m -2 /an in FigureA 5.2 is selected to calculate the dynamic inlet temperature in charging. This choice might be utilized as the maximum of energy demand is in winter and the maximum energy supply is in summer. We choose anyway to start with these conditions.

The output energy to greenhouse and input energy from solar are daily different, as well as seasonal changeable in Appendix FigureA 5.1-FigureA 5.2. To simplify the optimization process, the steady initial condition is set and the total daily consumption is assumed to be the same in different seasons. The assessment of the life cycle assessment and economic cost optimization will not be considered in this chapter. The pump energy is not considered. *6 The discharging is designed for the time (22:00-10:00), and charging is within the time of 10:00-18:00.

Final design results

Preliminary tank parameters and final designing results for greenhouse are listed in Table 5.3. The steady and dynamic inlet temperature in charging in Paraffin is a phase change material for thermal energy storage that was used because it has features of the wide commercial application, cost-economy, non-corrosion, low phase separation, chemical and thermal stability [68][225]. Most importantly, it shows various phase change temperatures below 100 °C and large with unreasonably high enthalpy around 150-250 J g -1 due to the different length of alkane chain [226][227]. The thermal conductivity of PCM can be improved by additive like graphite [START_REF] Qureshi | Recent advances on thermal conductivity enhancement of phase change materials for energy storage system: A review[END_REF].

Multi-objective optimization

The multi-objective genetic algorithm (MOGA) optimization based on the non-dominated sorted genetic algorithm-II (NSGA-II) that controls elitism selection strategy, is applied as tool.

The optimization of this work is to find the optimal layer thickness of PCM, phase change temperature, and thermal conductivity based one or several similar PCM materials through a multi-layered packing strategy for a given greenhouse application. The nonlinear optimization problem with bound constraints is studied.

Optimization process

A flow chart of designing tank and optimization process is shown in Figure 5.6. Based on the initial design of the single tank, optimizing the thermal performance of packed-bed tank by multilayered PCM packing.

Step 1: Determining the two layer numbers.

Step 2: Designing four configurations as optimization target to conduct MOGA in turns.

Step 3: MOGA optimization process: S1: determining the cycling times, cutoff temperature operational conditions of TES system for model simulation. Step 4: Defining a better configuration as the optimization result.

Variables and objectives

Variables constraints and objectives functions of MOGA optimization are in Table 5.4.

( (2) Two KPIs are considered as objective functions or fitness functions (Fi) to access the thermodynamic behavior in Eq.s 5.17-5.18: the overall energy efficiency (𝜂𝜂 𝑜𝑜 ), and the overall storage/utilization ratio ( γ 𝑜𝑜 ), considering the capacity ratio in charging (Cratio) and the utilization ratio in discharging (Uratio).

(3) The optimization algorithm is the elitist genetic algorithm by using the global optimization Toolbox in Matlab 2021a® [START_REF]Matlab. Global optimization Toolbox[END_REF], which is the variant of the non-dominant sorting genetic algorithm (NSGA-II) [START_REF] Justesen | Multi-objective Optimization using Evolutionary Algorithms Progress[END_REF]. This genetic algorithm is good at the continuity and differentiability of fitness function [START_REF] Arora | Chapter 16 -Genetic Algorithms for Optimum Design[END_REF] and is able to create a set of points on the Pareto front to minimize the objective functions [START_REF] Yusoff | Overview of NSGA-II for optimizing machining process parameters[END_REF]. The algorithm is completed when the average change in the spread of Pareto solutions is below a determined threshold or to the max setted generations.

Two KPIs in the objective functions are as follows:

Overall energy efficiency (𝜂𝜂 𝑜𝑜 ) physically means the comparison of the total energy released from the tank by HTF in discharging process and the total energy supplied to the tank by HTF in charging process. [START_REF] Hänchen | High-temperature thermal storage using a packed bed of rocks -Heat transfer analysis and experimental validation[END_REF] 𝜂𝜂

𝑜𝑜 = 𝜂𝜂 𝑒𝑒ℎ • 𝜂𝜂 𝑚𝑚𝑖𝑖𝑠𝑠𝑒𝑒ℎ = ∫ �𝑚𝑚̇𝑠𝑠•𝐶𝐶 𝑝𝑝,𝑠𝑠 •(𝑇𝑇 𝑜𝑜𝑜𝑜𝑡𝑡 -𝑇𝑇 0 )�𝑚𝑚𝑖𝑖 𝑡𝑡 𝑚𝑚𝑖𝑖𝑠𝑠 0 ∫ �𝑚𝑚̇𝑠𝑠•𝐶𝐶 𝑝𝑝,𝑠𝑠 •(𝑇𝑇 𝑖𝑖𝑡𝑡 -𝑇𝑇 0 )�𝑚𝑚𝑖𝑖 𝑡𝑡 𝑐𝑐ℎ 0 (5.17)
where 𝑑𝑑 𝑖𝑖𝑖𝑖 is the inlet temperature of HTF and T0 is the reference coldest operational temperature 𝑑𝑑 𝐶𝐶 (20 °C), respectively, Tout is the outlet temperature of the HTF.

Overall storage/utilization ratio (𝛶𝛶 𝑜𝑜 ) is used to evaluate the both effect of capacity ratio (𝐶𝐶 𝑟𝑟𝑎𝑎𝑖𝑖𝑖𝑖𝑜𝑜 ) in charging and the utilization ratio (𝑈𝑈 𝑟𝑟𝑎𝑎𝑖𝑖𝑖𝑖𝑜𝑜 ) in cycles, accessing by the weight-mass method [START_REF] Marler | Survey of multi-objective optimization methods for engineering[END_REF] in Chapter 4 in Section 4.2.4.

𝛶𝛶 𝑜𝑜 =

𝑪𝑪 𝒓𝒓𝒎𝒎𝒕𝒕𝒓𝒓𝒓𝒓 +𝑼𝑼 𝒓𝒓𝒎𝒎𝒕𝒕𝒓𝒓𝒓𝒓 𝟐𝟐

(5.18) In optimization process, four configurations presented in ) is 300×300×10. Therefore, they are adopted in the following simulation and optimization algorithm.

Grid and time step convergence study

One-layer TES tank design

Once defining an initial tank with single PCM, the second step of this study is to evaluate the thermal performance of this tank.

(1) Considering the real fluctuated weather, it is necessary to compare the dynamic operation of real greenhouse and the steady operation of simulation to explore the influence degree at first.

(2) Then, as the dominant factor, the phase change temperature cause influence on performance is meant to be discussed by sensitivity analysis.

(3) Later, the cycling performance should be evaluated to determine the cycling number to obtain stable condition.

Performance at steady and dynamic operational conditions

In real greenhouse, the input to TES tank is dynamic due to the fluctuated radiation of weather. PCM is characterized by absorbing energy during the phase transition and keep the phase change temperature at a constant value. It thus interesting to use PCM as a temperature buffer to alleviate the influence of fluctuated inlet temperature on thermocline and to achieve stable output.

Based on this premise, we selected two paraffin PCMs (PCM60 and PCM30 that phase change temperatures is 𝑑𝑑 𝑚𝑚 =30 °C and 𝑑𝑑 𝑚𝑚 =60 °C, respectively) and compare to both with the sensible rock fillers in packed-bed tank based on a representative day of 1 st January and 1 st July. The dynamic results of a sunny day in July are not so different from the steady results in the aspect of outlet temperature and capacity ratio. Therefore, in this study, the steady input will be used in optimization simulation and the realistic variable input will be evaluated based on the optimization result at the end.

Sensitivity of efficiency of the phase change temperature

Figure 5.10 is the evaluation results of the phase change temperature in the first charging and discharging cycling with a constant cutoff threshold temperature. 𝑑𝑑 20% is cutoff for discharging and 𝑑𝑑 80% is for charging. With the phase change temperature from 20 °C to 70 °C, the KPIs, including overall energy efficiency (𝜂𝜂 𝑜𝑜 ), capacity ratio (Cratio), utilization ratio (Uratio), and dimensionless cycling time (the average time for charging and discharging process), vary and exhibits obvious stages: below 𝑑𝑑 20% , between 𝑑𝑑 20% ~𝑑𝑑80% , above 𝑑𝑑 80% . Sensitivity analysis shows the selection of phase change temperature is influenced by cutoff threshold temperature.

In addition, in Figure 5.10 a, when the phase change temperature is between two cutoff temperature ranges ( 𝑑𝑑 20% < 𝑑𝑑 𝑚𝑚 < 𝑑𝑑 80% ), the overall efficiency is only around 60% and dimensionless time is all equal to 1. That means that PCM cannot be fully utilized within this designed time. This result suggested that the mass flow rate should be designed higher than the present value to fully store energy for design, and later optimization on the thermal conductivity increase to enhance the heat transfer with the PCM capacity ratio increase.

Cycling performance

Performance indicators in a stable condition are the principle of system evaluation. Stable thermocline behavior in cycling means a constant outlet temperature at the ending of each discharging and means with cycling numbers increase there is no degradation increase.

Two-layer optimized TES tank design

As mentioned in Section 5.3, the optimization process is designed to obtain an optimal PCM packed tank of two layers, that is subjected to the maximum 7 constraints. All parameters were calculated at the third cycle of steady conditions. But before that, to better understand why this case is optimal, it should begin from a basic case of Design A & B with fewer constraints, and then to the advanced Design A+ & B+.

The method is the following:

(1) Calculate and observe on the Pareto front of design cases to compare the difference of basic and advanced configuration.

(2) Select the optimal special case from Pareto front and comparing with the reference case.

An optimized design is determined.

(3) Based on the optimized design results, explain the influence of variables on MOGA result.

(4) Extend the analysis to a more general case in order to define a design guideline.

Optimization results

Pareto front is a set of optimal results that designer can select compromised results according to requirement of packed-bed system. It is proposed that once fixing the upper/lower layer phase change temperature according to the cutoff temperature, the storage and the utility of tank are not as high as enough within the designed variable ranges. Thus, Design A+ is a better case which is determined to be the optimization subject in this study and will be introduced later.

Advantages of optimal result • Energy storage density

In order to illustrate the advantages of the optimized tank of Design A+, as a reference, the single sensible ROCK tank is first compared. Table 5.6 and Table 5.7 lists three special results and corresponding variables of Design A+ and B+ in Pareto front (Figure 5.12): the maximum 𝜂𝜂 𝑜𝑜 , maximum 𝛶𝛶 𝑜𝑜 , and the tradeoff both objectives. Among those, a selected point at maximum 𝜂𝜂 𝑜𝑜 is used to compare with the reference tank considering the 𝛶𝛶 𝑜𝑜 is almost not changed. Noted that if filling sensible fillers with higher volumetric heat capacity material (like direct using water, 𝜌𝜌 • 𝐶𝐶 𝑝𝑝 = 4138 kJ m -3 K -1 is 2 times higher than rock 𝜌𝜌 • 𝐶𝐶 𝑝𝑝 = 2075 kJ m -3 K -1 ). The advantage of store energy of PCM is not so obvious. In the low-temperature application with adequate water, the cheaper rock cannot present great advantage in the improvement of heat storage capacity in industrial. Another important advantage of PCM is to keep stable temperature that will be discussed following.

• Evolution of outlet temperature

In order to exhibits the advantages on stabilizing outlet temperature, the outlet temperature of optimal Design cases is presented in Figure 5.14. Table 5.8 shows optimal cases with maximum 𝜂𝜂 𝑜𝑜 in Pareto front. The higher outlet temperature in charging process means less energy is stored, the more stable outlet temperature in longer time refers to released more energy.

In

• Evolution of fluid temperature profile

The thermocline behavior of optimal result is compared with sensible filler tank to show the advantage of PCM in keeping inside temperature stratification. temperature and thermocline (white dash line) are observed.

• In Design B of charging, there is a thin PCM80% in the upper layer with a thickness 𝐿𝐿 𝑜𝑜𝑝𝑝 * =0.1

(in Table 5.8). The thermocline increase and reaches 30% tank height at t*=1.

• In Design A+ ( 𝐿𝐿 𝑜𝑜𝑝𝑝 * =0.5, in Table 5.8) of charging, albeit the thermocline zone or thermocline thickness accounts for 32% of the tank height with a range of 20% to 80% of operational temperature ranges at t*=1, there is an "extreme" plateau temperature region in Design A+.

• Comparing both cases, the thermocline of Design A+ expanded higher than Design B. One reason is the thermal conductivity for Design A is larger, the thermocline expansion is avoidable. Another is that the heat capacity is higher the temperature of material is increased slower when heating. However, the thermocline thickness is interesting compressed when reaching to the second layer of Design A in charging, and stretched to keep longer outlet temperature constant in discharging.

Therefore, it should be necessary to take into account the thermocline using another definition in multi-layer configuration and considering the exergy efficiency optimization in future work. In this study, the volumetric heat capacity and phase change enthalpy are the same for all PCM. The inlet configuration of charging and discharging process is conversed, the influence of packing configuration parameters on objectives may opposite. when increasing the thermal conductivity of upper layer PCM and decreasing its value of the lower layer PCM, the 𝜂𝜂 𝑜𝑜 becomes higher. In fact, heat transfer rate is still the main reason and heat diffusion in HTF is negligible under the mass flow rate. Due to the higher thermal conductivity (higher heat transfer rate,) of upper layer, the upper layer temperature of HTF within same charging time will be higher and stable. When it comes to discharging process, this part of HTF in good quality will results in higher outlet temperature within same discharging time, which is beneficial to higher 𝜂𝜂 𝑜𝑜 .

• Figure 5.16 e presents the upper layer thickness variation. A smaller upper layer thickness is with higher 𝜂𝜂 𝑜𝑜 but it also has lower 𝜂𝜂 𝑜𝑜 simultaneously. It's unclear to explain the influence of upper layer thickness by physical phenomena. Because in this case, the optimized phase change temperature of upper layer is not always larger than upper layer temperature, as well as changeable thermal conductivity.

In general, to improve 𝜂𝜂 𝑜𝑜 , one could increase heat transfer rate or one could decrease phase change temperature of PCM fillers but is not beneficial to have a high outlet temperature. To improve the 𝛶𝛶 𝑜𝑜 , it is necessary to increase upper-layer temperature within designed variables range. In this range, the tank can be fully or near-fully charged/discharged within the designed cycling time (Figure 5.17). However, the optimal charging/discharging time is not total equal to the designed initial time and there is little bit higher for discharging time than that of charging process. In real case optimization, the designed time and the optimized time could be unified by using linear constraints of time in future work.

Secondly, it is interesting to find that the phase change temperature of upper and lower layers is in 0.35-0.39 and 0.20-0.49 respectively. Actually, if the outlet temperature is unnecessary to be equal to the cutoff temperature, the phase change temperature is suggested to set near to the average operational temperature (Tave). It can achieve a high energy efficiency in cycling, as well as higher utilization-capacity ratio. Moreover, the upper layer value is lower than the lower layer considering the influence of packing is converse in charging and discharging, that's why the upper layer thickness is not extrude half height of tank (0.50-0.67). Upper and lower layer configuration effect on charging and discharging process are different and sometimes opposite converse, causing the optimal PCM phase change temperature of two layer into average operational temperature in Design A+, instead of cut off temperature.

Thirdly, the 𝜆𝜆 𝑃𝑃𝐶𝐶𝑃𝑃 * of bottom is near the same, the thermal conductivity is in 0.6-0.8 for upper layers and 0.6-0.9 for lower layers. In actual definition, the PCM thermal conductivity should be selected many times higher than pure PCM.

These results are useful in selecting PCM with different thermal conductivities and proposes configuration strategies for filling 2-layer pure PCM packed-bed thermocline. Overall, the variable ranges can be determined and give a degree of optimization results that can be achieved.

Evaluation of dynamic performance based on optimization results

This section is to apply the optimal Design A+ in real application and try to find the problem for future improvement. On 1 st July, the inlet temperature during a day is smooth and looks like a Gaussian curve (Figure 5.5), increasing temperature in the morning and decreasing in the afternoon. Alleviating the fluctuated inlet to and achieving a stable outlet of thermocline tank is needed to better control the heat transfer process with greenhouse. Table 5.9 is KPIs results for four seasonal days. One aspect, the dynamic seasonal inlet condition in charging causes the reduction of capacity ratio by up to larger than 80% in winter and 4% in summer for both cases, and leads to reduction of charging energy efficiency by 50% in winter and 1% in summer.

Another aspect, the design A+ improves charging energy efficiency of dynamic condition by 34% than rock tank, but utilization ratio is negligible because the tank is designed according to the maximum load.

In winter, the tank cannot be fully used because the tank volume is designed according to the maximum heat load within one year. It is thus necessary to design an ideal tank for seasonal storage but the inlet temperature can be maintained by filling PCM. * The calculated standard according to the 𝑑𝑑 𝐻𝐻 and 𝑑𝑑 𝐶𝐶 , in July, the hottest inlet temperature is larger than TH in some times. That' why the efficiency is equal to 1.

Chapter conclusion

The multi-layered PCM packing configuration strategy of a thermocline PCM packed-bed TES tank for a 0.9 MWh agriculture greenhouse in Carquefou, France, was studied and optimized based on the multi-objective genetic algorithm using NSNA-Ⅱ. The steady and dynamic input were compared in the final optimal multi-layered tank.

Main results are as follows:

• Optimizing upper and lower configuration using PCMs is good for optimal energy efficiency and utilization ratio in charging/discharging process in Pareto front. An optimal Design A case and corresponding variable ranges are obtained through optimizing the thermal conductivity, phase change temperature, and layer thickness.

• Layer configuration effects on charging and discharging process are different leading to optimized phase change temperature of the two layers close to the average operational temperature in optimization. But fixing the upper phase change temperature of PCM equaling to or close to the charging cutoff temperature leads to high outlet temperature but low utilization ability. According to requirements, selecting appreciated optimization goal.

• According to influence investigation of variables, decreasing two-layer PCMs phase change temperature leads to larger overall energy efficiency but smaller storage/utilization ability. Increasing upper layer thermal conductivity and decreasing the lower layer thermal conductivity simultaneously, facilitating improvement of overall energy efficiency.

• Variable inlet temperature in charging influences the thermal performance, resulting in a capacity ratio reduction of 80% in winter 5% in summer and efficiency decreasing of 50% in winter and 1% in summer based on the optimal tank Design A+. Comparing to filling sensible rock tank, the optimal tank can alleviate the influence of fluctuated inlet temperature and compress themocline thickness around 20% and charging energy efficiency by 34% in a summer day.

In further work, it should take the dynamic input into account for configuration optimization strategy of thermocline packed-bed TES tank to understand how the efficiency and cost can be tradeoff by using different fillers under seasonal weather condition. Moreover, it is meaningful to combine the exergy efficiency (or thermocline thickness) in optimizing objectives to get better and thinner stratification zone and useful energy. In addition, it would be good to test the optimal tank design in real experiment case and to apply the optimization produce for designing of different size tank and different temperature applications.

Chapter 6

General conclusions and perspectives

Conclusions

This thesis focuses on the optimization of packing configuration strategies for the thermocline packed-bed TES system under different influence factors. The main conclusions of each chapter are concluded as below.

In chapter 1, the interests of the thermocline packed-bed TES system are presented. The objective and guideline are introduced.

In chapter 2, the literatures concluded that storage media is the core of the system. The influence factors of operational, geometrical, and thermophysical parameters showing positive or negative especially the impact degree on system is necessary to be considered in designing the system. The status of three types of systems including sensible-heat system, latent-heat system, heterogeneous-heat system, based on storage media presents the advantages of packing configuration on thermal performance improvment.

In chapter 3, the wall impact on the performance of packed-bed TES tanks was first evaluated by using three models through comparing two tank configurations: a high-temperature pilot-scale tank with a steel wall and a low-temperature lab-scale tank with a polycarbonate wall. The maximum energy stored in wall at fully charged state is up to 10% of the total, increasing the thermocline thickness by up to 15% during discharging, but negligible stored energy in the insulation. A transient model considering wall impact is thereby developed. At last, parametric studies show a thinner wall has a smaller impact on the energy and exergy efficiencies.

In chapter 4, various influencing factors including inlet configuration, insulation, mass flow rate, inlet temperature, etc., on thermocline behavior and on the overall performances of a labscale sensible-heat storage tank is then investigated through both experiment and modeling. The combined effect of diffuser and packed bed as inlet configuration maintains the radial temperature uniformity and the axial thermocline expansion, increasing the capacity ratio by about 3% but effect on the global performance is rather limited. Good insulation reduces the thermocline thickness by about 20%, and increase the energy efficiency by 5-7% and the capacity ratio by 3-5%. At last, validating a temperature difference up to 1.7 K between the fluid and the solid particle center, determining an optimal flow velocity of about 𝑅𝑅𝑅𝑅=3.

In chapter 5, the multi-layered packing configuration strategy of a thermocline packed-bed TES tank for a 0.9 MWh agriculture greenhouse application in Carquefou, France, was studied and optimized. Optimizing upper and lower layer configuration for PCMs is good choice for optimal energy efficiency of 88% and storage/utilization ability of 98% in multiple cycles. On the optimal tank, variable inlet temperature results in a capacity ratio reduction of 80% in winter 5% in summer and efficiency decreasing of 50% in winter and 1% in summer. Comparing to filling sensible rock tank, the optimal tank compress thermocline around 20% and charging energy efficiency by 34% in a summer day.

Perspectives

In fact, this thesis is the basic work in the packing configuration optimization of the thermocline packed-bed TES system. They are still a lot of work to do before being integrated into a real greenhouse application. Based on the results that obtained in this thesis, several perspectives were proposed for future work.

• Validation of the optimal tank

At first, it is looking forward to test the optimal tank design in real experiment case and to apply the optimization produce for designing of different size tank and different temperature applications.

• Optimization for the economic cost and efficiency

Investment reduction and efficiency improvement are mutual and necessary for a commercial mature application. This thesis doesn't extend to it. In future work based on this thesis, it should be taken into account: 1) Make a trade-off between cheaper sensible fillers and higher storage capacity; 2)The investment of storage media should account for the cost of storage media themselves, the investment in preparation of PCM capsules to avoid phase change leakage, and the cost of graphite additives for thermal conductivity improvement of capsules; 3) The investment in solar collectors should be considered in the optimization of operational parameters (the mass flow rate and inlet temperature) because those parameters depend on the solar collective (heat source input power).

• Topology optimization of packing configuration

The topology optimization is interesting to design the packing configuration according to the the fluid flow, or temperature distribution inside the tank.

• Optimization based on dynamic seasonal application

In the whole year, the climate changes a lot that the optimal tank under steady input is not suitable for application in variable input conditions. It should take the dynamic input into account for configuration optimization strategy of thermocline packed-bed TES tank to understand how the efficiency and cost can be tradeoff by using different fillers under seasonal weather condition.

• Life cycling assessment (LCA) after integration

The environmental impacts or potential impacts of this thermocline packed-bed greenhouse system need to be estimated compared to conventional system with fossil sources or CO2 emission sources, through a standardized, mature, systems-oriented analytical tool of LCA.

Mots clés :aFi 2 hṁTCλ 4 Υo

 clés24 AbbreviationsANR l'Agence Nationale de la Recherche CSP Concentrated Solar Power GH Greenhouse HDPE High-density Polyethylene HHTPB Heterogeneous Heat Thermocline Packed Bed HTC Heat Transfer Coefficient HTF Heat Transfer Fluid IEA International Energy Agency KPI Key Performance Indicators LCA Life Cycling Assessment LHTPB Latent Heat Thermocline Packed Bed MOGA Multi-objective Genetic Algorithm PCM Phase Change Material RMS Root Mean Square SD Standard Deviation SHTPB Sensible Heat Thermocline Packed Bed TC Thermocouple TES Thermal Energy Storage TR Thermal Resistance

2 . 1 . 2 . 2 .

 2122 Xie B, Baudin N, Soto J, Fan Y, Luo L. Chapter 10 -Thermocline packed bed thermal energy storage system: a review. In: Jeguirim MBT-REP and D, editor. Adv. Renew. Energy Technol., vol. 1, Academic Press 2022, p. 325-85. Chapter content Introduction ....................................................................................................................................... 2.1.1. Storage mechanism .................................................................................................................... 2.1.2. Thermocline packed bed technology .................................................................................. 2.1.3. Challenges ...................................................................................................................................... Storage media .................................................................................................................................

2. 4 . 2 . 5 .

 425 Types of thermocline packed bed system ........................................................................ 2.4.1. Sensible-heat thermocline packed bed (SHTPB) ......................................................... 2.4.2. Latent-heat thermocline packed bed (LHTPB) ............................................................ 2.4.3. Heterogeneous-heat thermocline packed bed (HHTPB) .......................................... 2.4.4. The interests of packing configuration ............................................................................ Chapter conclusion ......................................................................................................................

Figure 2 Figure 2 . 1 :

 221 Figure 2.1: CSP plant with Brayton gas cycle: (a) two-tank direct; (b) one-tank direct; (c) onetank packed-bed direct; (d) one-tank packed-bed indirect storage systems [27].

Figure 2 . 2 :

 22 Figure 2.2: Schematic of thermocline during (a) charging and (b) discharging.

Figure 2 . 4 :

 24 Figure 2.4: Phase change temperature profiles of solid-liquid transition [55][56].Adapted from the figure that obtained the copyright permission of Elsevier [License No. 5207611412736,Dec 14, 2021]

Figure 2 . 5

 25 shows some examples of sensible and PCM fillers used in real cases. Figure 2.6 is a typical encapsulated PCM.

Figure 2 . 5 :

 25 Figure 2.5: Example of sensible and latent heat fillers used for thermocline packed-bed TES tanks. Sensible heat fillers: (a) demolition wastes, 𝐷𝐷 𝑝𝑝 =10 mm, 120-180 °C [71]; (b) sandstone and limestone, 𝐷𝐷 𝑝𝑝 =6-50 mm, 25-587 °C [72]; (c) quartzite pebbles, -160-25 °C [73]. PCM capsules fillers: (d) paraffin RT20, 𝐷𝐷 𝑝𝑝 =50 mm, 19-28 °C [74][75]; (e) lab-designed PCM, 𝐷𝐷 𝑝𝑝 =50 mm, -160-25 °C [73]; (f) paraffin RT 70HC, =15 mm, <40-85 °C [76].

Figure 2 . 6

 26 Figure 2.6 PCM capsules melting process in experiment and simulation [77][78].Obtained copyright permission of Elsevier [License No. 5207630764534,Dec 14, 2021]

Figure 2 . 8 :

 28 Figure 2.8: Different shapes for sensible material fillers: (a) cylindrical; (b) spherical; (c) rectangular; (d) crushed [98][97].Obtained copyright permission of Elsevier [License No. 5207671070704,Dec 14, 2021]

Figure 2 . 9 :

 29 Figure 2.9: Cross section of sphere packing: (a) dense cubic, ε=0.260; (b) dense cubic, ε=0.260; (c) dense hexagonal, ε=0.260; (d) orthorhombic ε=0.395; (e) cubic, ε=0.476; (f) body-centred cubic, ε=0.320 [106].Obtained copyright permission of Elsevier [License No. 5207671403313,Dec 14, 2021]

Figure 2 . 10 :

 210 Figure 2.10: Classification of thermocline packed-bed TES system.

Figure 2 . 11 :

 211 Figure 2.11: Different packing strategies of thermocline systems integrated into a 19.9 MWe Gemasolar CSP: (a) two-tank with specific storage cost of 24.55 US$ kWhth -1 ; (b) dual-media thermocline tank filled concrete with specific storage cost of 9.38 US$ kWhth -1 [70].

[ 113 ]

 113 [START_REF] Chang | The effect of the physical boundary conditions on the thermal performance of molten salt thermocline tank[END_REF][START_REF] Singh | Investigation on transient performance of a large-scale packed-bed thermal energy storage[END_REF][START_REF] Marti | Constrained multi-objective optimization of thermocline packed-bed thermal-energy storage[END_REF]. Zanganeh et al. [87] studied a 7.2 GWhth rock tank with the varied cone angle. Increasing angle reduces effective storage volume but increases the final outlet temperature degradation in cycling during discharging, thus leading the overall storage efficiency above 95% (Figure 2.12 a).

Figure 2 . 12 :

 212 Figure 2.12: (a) Scheme of 7.2 GWhth single-layered truncated cone shape tank with 25 m tank height [87]. (b) The mixed-filler thermocline system with SiC foam and zirconium ball [117].

Figure 2 . 13 :

 213 Figure 2.13: The multi-layered SHTPB system by filling quartzite cork at top layer and cast iron at the bottom layer: the expanding effect on HTF temperature distribution in charging process (5.9 m tank height, 3.0 m tank diameter, 0.04 m wall, 0.2 m insulation) [120].Obtained copyright permission of Elsevier [License No. 5207680725306,Dec 14, 2021]

  Li et al. [123] demonstrated the optimal design of PCM storage tank for the outdoor open-air swimming pool during daytime operation in the City University of Hong Kong. This case can meet the enviroment temperautre comfort demand and achieve the economic operation (Figure 2.14).

Figure 2 . 14 :

 214 Figure 2.14: Schematic of the outdoor open-air swimming pooling system with PCM packed bed system in City University of Hong Kong [123].Obtained copyright permission of Elsevier [License No. 5207680984690,Dec 14, 2021]

[ 59 ]Figure 2 . 15 :

 59215 Figure 2.15: Multi-layered concept of LHTPB system: (a) 1-3 cascaded systems [59]; (b) 1-5 cascaded PCM systems (PCT: phase change temperature) [133].Obtained copyright permission of Elsevier[License No. 5207681128925, No. 5207681314417, Dec 14, 2021]

[ 143 ]

 143 [START_REF] Galione | Numerical evaluation of multi-layered solid-PCM thermocline-like tanks as thermal energy storage systems for CSP applications[END_REF][142] conducted a series works and designed the multi-layer solid-PCM thermocline tanks for CSP plants. Two PCM layers acted as thermal buffers were respectively put at the top and bottom of the tank, whose phase change temperature were selected to control the outlet temperature within an admissible interval. Compared to other concepts introduced above, the novel multi-layered solid-PCM system can achieve high overall energy storage capacity as well as excellent thermal efficiency. Such strategies for different given cases are shown in Figure2.16.

Figure 2 . 16 :

 216 Figure 2.16: Scheme of the multi-layered solid-PCM of three configuration cases, C1: KOH380-Quartzite and rock (Qu)-KOH300 (20-60-20 v%), D1: KOH380-Qu-KOH340-Qu-KOH300 (20-20-20-20-20 v%), F1: KOH380-KOH370-KOH340-KOH310-KOH300 (32-15-6-15-32 v%) [142].Obtained copyright permission of Elsevier [License No. 5207681466334,Dec 14, 2021]

76% and 42 ,Figure 2 . 17 :

 42217 Figure 2.17: Scheme of three kinds of TES packing configurations: (a) sensible rod structure configuration, SRS; (b) encapsulated PCM configuration; (c) hybrid sensible rod structure and encapsulated PCM configuration [139].Obtained copyright permission of Elsevier [License No. 5207690072229,Dec 14, 2021]

: 3 . 1 . 3 . 2 .

 3132 wall impact, thermocline thickness, heat loss, lab-scale tank, pilot-scale tank, 1D-3P model This chapter is published as: Xie B, Baudin N, Soto J, Fan Y, Luo L. Wall impact on efficiency of packed-bed thermocline thermal energy storage system. Energy 2022;247:123503. Chapter content Introduction .................................................................................................................................... 3.1.1. Wall impact on thermocline packed bed: the state-of-art ....................................... 3.1.2. Aim and scope ........................................................................................................................... Methodology .................................................................................................................................... 3.2.1. Geometrical model ..................................................................................................................

3. 3 . 3 . 3 . 1 . 3 . 3 . 2 . 3 . 3 . 4 . 3 . 3 . 5 . 3 . 4 . 3 . 5 .

 33313323343353435 Wall thermal behavior discussion ....................................................................................... General temperature profiles .............................................................................................. Wall heat flux ............................................................................................................................. 3.3.3. Wall heat transfer rate analysis ......................................................................................... Stored heat in wall ................................................................................................................... Energy and exergy efficiency .............................................................................................. Wall parametric study ................................................................................................................ 3.4.1. The effect of convection and radiation of external surface ..................................... 3.4.2. The effect of heat stored in wall and heat loss ............................................................. 3.4.3. The effect of wall thickness and thermal conductivity .............................................. Chapter conclusion ...................................................................................................................... Appendix 3.I ............................................................................................................................................. Appendix 3.II ............................................................................................................................................ Appendix 3.III .......................................................................................................................................... Appendix 3.IV ..........................................................................................................................................

2D transient response model

  of both solid and fluid phases that includes the effects of longitudinal conduction, the stored heat in walls and the heat loss, with air as the working fluid. But the solid internal heat conduction term was neglected in this model.Xu et al. [41] developed a 2 dimension-2 phase (2D-2P) model with energy equations for the insulations and tank steel wall, and studied

Figure 3 . 1 .

 31 Storage tank structureA typical structure of thermocline packed-bed TES tank and the computational domain are illustrated in It is a vertical cylindrical tank with solid particles as heat storage medium to form the packed-bed thermal storage region. The HTF flows in void space of the region, the void fraction or porosity (𝜀𝜀 = 𝑉𝑉 𝑏𝑏 -𝑉𝑉 𝑠𝑠 𝑉𝑉 𝑏𝑏

Figure 3 . 1 :

 31 Figure 3.1: Thermocline packed-bed TES tank: (a) schematic illustration; (b) computational domain in discharging process.

  this chapter, three transient numerical models with different dimensions and phases, fluid, solid fillers, wall, or insulation phase, are studied: a z-axis 1D-2P model (fluid-solid), a z-axis 1D-3P model (fluid-solid-wall), and a 1.5D-4P model (1D z-axis for fluid-solid, 2D z-axis and r-axis for wall-insulation) that 1.5D refers to the average of 1D and 2D. Figure3.2 shows the research process and the relationship between models. At first, models were compared and validated by experimental data sets. Further, the wall thermal behavior for two different scale tanks was investigated by using a numerical reduced CPU resource model (1.5D-4P). After that, an appropriate model (1D-3P) is selected to conduct parametric sensitivity analysis and wall parametric study.

Figure 3 . 2 :

 32 Figure 3.2: Diagram of the research process in this study.

  shape ratio for fluid-wall surface to packedbed volume and fluid-wall surface to wall volume, respectively. The wall temperature (𝑑𝑑 𝑤𝑤 ) is defined as the temperature at the average diameter [(𝑅𝑅 𝑖𝑖𝑖𝑖𝑖𝑖 + 𝑅𝑅 𝑚𝑚𝑖𝑖𝑚𝑚 )/2] of the tank wall.

Figure 3 . 3 before 3 . 4 .

 3334 discharging is calculated by the fully charged tank temperature at the standby process using the iteration method as explained in Figure The initial wall temperature (𝑑𝑑 𝑤𝑤,𝑖𝑖𝑖𝑖𝑖𝑖 ) in 1D-3P model is the average value of inner and middle surface temperature of wall.

Figure 3 . 3 :

 33 Figure 3.3: Initial and boundary conditions for the modeling of discharging operation: heat transfer through the wall and insulation at steady standby state (𝑑𝑑 𝑤𝑤,𝑖𝑖𝑖𝑖𝑖𝑖 , 𝑑𝑑 𝑤𝑤,𝑚𝑚𝑖𝑖𝑚𝑚 , and 𝑑𝑑 𝑤𝑤,𝑒𝑒𝑒𝑒𝑖𝑖 is the temperature on inner, middle, and outer surface of tank, respectively).

Figure 3 . 4 : 1 bBC5 for 1 .

 3411 Figure 3.4: Iterative calculation to determine the initial outer surface temperature of fully charged tank before discharging.

Figure 3 . 5

 35 Figure 3.5 shows the comparisons between numerical results and experimental data for axial temperature evolution curves of packed bed TES tanks in discharging. The measured experimental temperature profile at 0 h was used as the initial temperature profile in the modeling to have the same beginning. The standard deviation (SD) and root mean square (RMS) of temperature difference between experiment and simulation results were calculated to evaluate the agreement degree.

Figure 3 . 5 a

 35 Figure 3.5 a shows the validation results of 1D-2P model using the measured data from the solar thermal power plant tank (Bis=0.1). It is found that the simulated temperature profiles at 4h to 8h are generally consistent with the experimental data considering that the experimental temperatures are taken at one radial position in the tank while the computed data are average temperatures on a cross section. Only slight deviations exist at some time intervals, indicating that the basic 1D-2P model has enough accuracy in modeling large-scale thermocline packed-bed tanks.

Figure 3 . 5 b

 35 Figure 3.5 b is the comparison on the results of 1D-2P, 1D-3P, and 1.5D-4P models with Sandia pilot-scale packed-bed tank. These simulation curves are not far away from experimental values,

Figure 3 . 5 :

 35 Figure 3.5: Comparison of axial temperature evolution curves in discharging process between numerical results and experimental data: (a) solar power plant [176,177]; (b) Sandia pilot-scale tank [104].

3. 3 . 1 .

 31 General temperature profilesThe 1.5D-4P model was first used to analyze detailed thermal behaviors of fluid and tank walls in discharging. Figure 3.6 shows the fluid temperature profiles of two tanks along z-axis height at different times. Recall that 𝑡𝑡 𝐸𝐸 * is the dimensionless time based on energy flow through the tank, the thermocline zone is defined within the fluid temperature range of 0.05<𝑑𝑑 * <0.95, and the center position of thermocline refers to the height where 𝑑𝑑 * =0.5. At half discharging time (𝑡𝑡 𝐸𝐸 * =0.5), the thermocline center position of large pilot-scale tank is at around 𝑧𝑧 * =0.54, slightly lower than that of the small lab-scale tank at 𝑧𝑧 * =0.57. At the same time, in both cases, the thermocline zone is found to be nearly symmetrical. The thermocline thickness 𝐿𝐿 𝑖𝑖ℎ𝑒𝑒𝑟𝑟𝑚𝑚𝑜𝑜𝑒𝑒𝑙𝑙𝑖𝑖𝑖𝑖𝑒𝑒 * of pilot-scale tank (0.33) is smaller than that of the lab-scale tank (0.54). All these differences indicate that the pilot-scale tank may have a higher discharging (release) efficiency.

Figure 3 . 6 :

 36 Figure 3.6: Evolution of temperature profiles of two tanks for the discharging process using 1.5D-4P model: fluid temperature along z-axial height.

Figure 3 . 7 :

 37 Figure 3.7: Wall and insulation temperature along r-direction at the middle tank height (z*=0.5); (c)(d) temperature color map of fluid, wall, and insulation at 𝑡𝑡 𝐸𝐸 * =0, 0.5 and 1.

Figure 3 .

 3 Figure 3.7 a b show temperature distribution of tank walls along the radial direction at the middle tank height (𝑧𝑧 * =0.5).Figure 3.7 c d show the cross-sectional temperature color map of three phases. When discharging proceeds, the wall and insulation are cooled down from bottom to top as the cold fluid flows. Note that the insulation temperature 𝑑𝑑 𝑖𝑖𝑖𝑖𝑠𝑠 * near the outer surface of the pilot-scale tank shows a negative value due to the far greater cold fluid temperature than the ambient (𝑑𝑑 𝐶𝐶 ≫ 𝑑𝑑 𝑎𝑎𝑚𝑚𝑏𝑏 ). The variation of 𝑑𝑑 𝑤𝑤 * and 𝑑𝑑 𝑖𝑖𝑖𝑖𝑠𝑠 * as a function of 𝑡𝑡 𝐸𝐸 * in the pilot-scale tank shows the same tendency, while for lab-scale tank, the 𝑑𝑑 𝑤𝑤 * shows sharper decrease over the discharging time and there is a heat delay for 𝑑𝑑 𝑖𝑖𝑖𝑖𝑠𝑠 * . That is because the fluid-wall Biot number 𝐵𝐵𝐵𝐵 𝑤𝑤 (𝐵𝐵𝐵𝐵 𝑤𝑤 = ℎ 𝑖𝑖𝑡𝑡𝑡𝑡 •𝐿𝐿 𝑤𝑤 𝜆𝜆 𝑤𝑤

Figure 3 . 8

 38 Figure 3.8 exhibits the heat flux through the wall surfaces based on Fourier's law. At inner (fluid-wall) surface, the negative value of heat flux represents the radial heat transfer from wall to fluid. At outer (insulation-ambient) surface, the positive value indicates the heat flux (heat loss) from the storage tank to the ambient and it reduces with upward fluid flowing. At the beginning of discharging (𝑡𝑡 𝐸𝐸 * =0.1), the inner surface at the top portion of both tanks has a small positive heat flux while the bottom has a larger negative. This is due to the heat loss from the storage tank to the ambient through the top part of tank walls as long as the cold HTF does not reach it. After the arrival of cold fluid, the walls are cooled down and a large proportion of heat initially stored in the tank walls is released back to the fluid, indicated by the negative values of heat flux curves. A small proportion of heat stored in the walls is still dissipated to the ambient, indicated by the always positive values of heat flux through the outer surface of both tanks.

Figure 3 . 8 :

 38 Figure 3.8: Heat flux at the inner (fluid-wall) and outer (insulation-ambient) surface during the discharging process: (a) pilot-scale tank; (b) lab-scale tank.

Figure 3 . 9

 39 is the schematic of heat transfer rate balance through tank walls, including inner surface convection (𝑄𝑄 ̇𝑖𝑖𝑖𝑖𝑖𝑖 ), wall axial diffusion (𝑄𝑄 ̇𝑤𝑤,𝑚𝑚𝑖𝑖𝑓𝑓𝑓𝑓 ), insulation axial diffusion ( 𝑄𝑄 ̇𝑖𝑖𝑖𝑖𝑠𝑠,𝑚𝑚𝑖𝑖𝑓𝑓𝑓𝑓 ), inside increment ( 𝑄𝑄 ̇𝑤𝑤,𝑖𝑖𝑖𝑖𝑒𝑒𝑟𝑟𝑒𝑒𝑚𝑚𝑒𝑒𝑖𝑖𝑖𝑖 + 𝑄𝑄 ̇𝑖𝑖𝑖𝑖𝑠𝑠,𝑖𝑖𝑖𝑖𝑒𝑒𝑟𝑟𝑒𝑒𝑚𝑚𝑒𝑒𝑖𝑖𝑖𝑖 ), and outer surface convection and radiation (𝑄𝑄 ̇𝑒𝑒𝑒𝑒𝑖𝑖 ).

Figure 3 . 9 :

 39 Figure 3.9: Schematic of heat transfer rate balance in wall and insulation.

Figure 3 . 1 .

 31 Figure 3.10 shows the heat transfer ratio at the middle height of tank at different discharging times. In this chapter, each contribution was compared with inner surface input heat transfer rate (𝑄𝑄 ̇𝑖𝑖𝑖𝑖𝑖𝑖 ). The 𝑚𝑚𝑇𝑇 𝑠𝑠 𝑚𝑚𝑖𝑖 represents the rate of fluid temperature variation at the middle position. At the beginning (𝑡𝑡 𝐸𝐸 * = 0.1), cold flow enters from tank bottom showing a small value of 𝑚𝑚𝑇𝑇 𝑠𝑠 𝑚𝑚𝑖𝑖 . With time increases to 𝑡𝑡 𝐸𝐸 * = 0.5, the thermocline with temperature gradient zone moves to the middle height of tank showing a large 𝑚𝑚𝑇𝑇 𝑠𝑠 𝑚𝑚𝑖𝑖 . The cutoff time, 𝑡𝑡 𝐸𝐸 * = 𝑐𝑐𝑁𝑁𝑡𝑡𝑐𝑐𝑐𝑐𝑐𝑐 referring to the ending time, is a little longer than 𝑡𝑡 𝐸𝐸 * = 1. Near the ending time (𝑡𝑡 𝐸𝐸 * = 1), cold fluid fills the tank up showing again a small 𝑚𝑚𝑇𝑇 𝑠𝑠 𝑚𝑚𝑖𝑖 . A similar tendency can be found for the wall temperature variation rate 𝑚𝑚𝑇𝑇 𝑤𝑤 𝑚𝑚𝑖𝑖 . Through the results of heat transfer ratio, it can be found that the 𝑄𝑄 ̇𝑖𝑖𝑖𝑖𝑖𝑖 is close to the 𝑄𝑄 ̇𝑒𝑒𝑒𝑒𝑖𝑖 at the beginning. But with the increase of discharging time, 𝑄𝑄 ̇𝑖𝑖𝑖𝑖𝑖𝑖 becomes dominant over other parts. It should be specially noted that the wall and insulation axial diffusion (𝑄𝑄 ̇𝑤𝑤,𝑚𝑚𝑖𝑖𝑓𝑓𝑓𝑓 and 𝑄𝑄 ̇𝑖𝑖𝑖𝑖𝑠𝑠,𝑚𝑚𝑖𝑖𝑓𝑓𝑓𝑓 ) are all near 0,indicating that the influence of heat diffusion in axial direction of walls can even be ignored compared to the inner or outer surface heat transfer.

Figure 3 . 10 :

 310 Figure 3.10: The variation of heat transfer rate over discharging time at middle tank height (𝑧𝑧 * =0.5). (a), (b) pilot-scale tank; (c), (d) lab-scale tank.

Figure 3 .

 3 Figure 3.11 b shows the contribution of each factor to the total thermal resistance of each tank. The biggest proportion of the total thermal resistance is from the insulation layer.

Figure 3 . 11 :

 311 Figure 3.11: (a) Proportion of stored energy in different phases of packed-bed TES tank at the beginning 𝑡𝑡 𝐸𝐸 * = 0 and at the ending 𝑡𝑡 𝐸𝐸 * = 1 of discharging; (b) proportion of different thermal resistances at stable heat flux state.

  insulation domain) model due to the extra heat from wall. Because of complex physical phenomenon description than 1D-2P model and decreased computational time by a factor of 100 than 1.5D-4P model (cf. TableA 3.1), the 1D-3P model can be selected to conduct the wall parameter study. Therefore, taking into the wall has an impact on the energy and exergy efficiency close to 5%.

Figure 3 . 12 :

 312 Figure 3.12: Comparison of (a) energy efficiency and (b) exergy efficiency between 1D-2P, 1P-3P, and 1.5P-4P models for pilot-scale tank and lab-scale tank.

3. 4 . Wall parametric study 3 . 4 . 1 .Figure 3 .

 43413 Figure 3.13 a b show the influence of emissivity variation on the tank outer surface temperature, energy and exergy efficiencies. When emissivity changes from a low value of 0.65 to a high value of 0.95, the radiative HTC (hrad) increases from 3.8 to 5.6 W m -2 K -1 , causing outersurface temperature to decline and more radiative heat loss to ambient. However, the energy and exergy efficiencies at cutoff time are almost the same, indicating that the tiny influence of emissivity on the overall efficiency of the storage system efficiency when the insulation thickness is "sufficient".

Figure 3 .

 3 Figure 3.13 b is the comparison of natural convection and forced convection on the outer surfaces for two tanks, which were calculated by Eq. 3.8. When the effective outdoor HTC (including both convection and radiation) ranges from 17 to 50 W m -2 K -1 [181], the external HTC (hext) varies from 2 to 17 W m -2 K -1 . This value range considers the heat exchange between the outer surface and the ambient air in real practice [182][183]. The simulation results show the noticeable influence of the external heat transfer coefficient on the evolution of outer surface temperature. Nevertheless, the energy and exergy efficiencies of the storage tank at cutoff time vary slightly by about 0.01% and little influence on the thermocline thickness can be observed.

Figure 3 . 13 :

 313 Figure 3.13: (a) Outer surface temperature at cutoff with emissivity variation; (b) energy and exergy efficiency at cutoff with external heat transfer coefficient variation.

Figure 3 .

 3 [START_REF] Pelay | Integration of a thermochemical energy storage system in a Rankine cycle driven by concentrating solar power: Energy and exergy analyses[END_REF] shows that the thermocline thickness of other three conditions in discharging is always larger than the ideal condition (no wall, no insulation, and adiabatic state), proving that both the stored heat in walls and the heat loss would enlarge the thermocline thickness. Comparing adiabatic conditions of with/without wall and insulation, the degradation of thermocline in the lab-scale tank is more obvious than pilot-scale tank, due to more stored heat of wall returning to fluid in discharging as explained in earlier sub-sections. Without considering the stored heat in walls and the heat loss, the thermocline thickness might be underestimated by 10% and 15% for pilot-scale tank and for lab-scale tank, respectively.

Figure 3 . 14 :

 314 Figure 3.14: Thermocline thickness variation over discharging time under different boundary conditions of two tanks.

FigureA 3 . 2 3 . 15 . 3 . 30 .Figure 3 . 15 :

 32315330315 Figure 3.15: The effect of wall thickness and thermal conductivity on energy efficiency, exergy efficiency and discharging time. (a) pilot-scale tank; (b) lab-scale tank.

  Heat diffusivity: 𝛼𝛼 = 𝜆𝜆 𝜌𝜌•𝐶𝐶 𝑝𝑝(A 3.14)

FigureA 3 . 1

 31 FigureA 3.1 The dominant dimensionless number of Π2 and Π5 of the lab-scale tank at the certain fluid interfacial velocity and particle diameter is near to the pilot-scale tank (Π2=525, Π5=201).

FigureA 3 . 2 : 4

 324 FigureA 3.2: Sensitivity analysis: convergence results of dominant dimensionless number Π7 (a), (b); elementary effect method of Π7 (c), (d).

  inner diameter of 194 mm (Figure 4.1 a), the total useful volume being 11.8 L. It has a transparent polycarbonate wall (3 mm in thickness) enclosed by an insulation layer made of black nitrile rubber (25 mm thickness). Glass spheres as the sensible fillers are randomly filled inside the tank. Water is used as the HTF. During charging process, the hot water flows the top port and cold water flows out from the bottom port of the tank, and vice-versa for the discharging process. Note that top and bottom ports are simple tubes (Φ= 11.6 mm) located at the center of the top and bottom cover of the tank.

Figure 4 . 1 :

 41 Figure 4.1: Laboratory-scale SHTPB tank tested: (a) Geometry and dimensions; (b) axial and radial thermocouples locations inside the tank.

Figure 4

 4

Figure 4 . 2 :

 42 Figure 4.2: Schematic view (a) of the experimental test loop and photographic view and (b) for the laboratory-scale SHTPB tank (without insulation).

Figure 4 . 2

 42 Figure 4.2 shows the schematic and the photo view of the experimental setup used to study the SHTPB TES system. A hot and a cold water tank was used as hot and cold source for testing the SHTPB tank in charging or discharging, respectively. A PID-controlled electrical heater installed inside the hot water tank and a low-temperature thermostat with smart cool system (Lauda, RP 855) connected to the cold water tank were used to stabilize the water temperature in each tank.Stirring devices were installed in both water tanks, ensuring the homogenous water temperature inside. Two magnetic coupled external gear pumps (Tuthill D-series, 0.07 to 7.63 L min -1 ) with filters were used to deliver the HTF from the water tank to the top/bottom port of the storage tank.The flow rate of the HTF was controlled and measured by a flow meter (Kobold DPM-1550, 0.05 to 50 L min -1 ) A reservoir was used to collect the water flowing out from the SHTPB tank for recycling.

FigureA 4 . 1 a

 41 of the Appendix) were used as packing in Figure 4.3.

Figure 4 . 3 :

 43 Figure 4.3: Photograph of SHTPB tank configurations without insulation: (a) case 2, 7 mm glass ball (b) case 4, 10 mm glass ball.

Figure 4 . 4 .

 44 Figure 4.4. Case 3 is the fully packed tank without diffuser while top and bottom diffusers are introduced in Cases 5 and 6. The plate-type diffuser (6 mm in thickness) having three ring-shaped grooves has been optimized and tested for a single-media thermocline TES tank in our previous

Figure 4 . 4 :

 44 Figure 4.4: Different inlet diffuser configurations experimentally tested in this study: (a) only porous bed; (b) porous bed & plate diffuser; (c) only plate-type diffuser.

Figure 4 . 5 :

 45 Figure 4.5: Schematic of numerical resolution domain for the developed DC-3P model.

Figure 4 . 6

 46 shows the results of height mesh size and time step sensibility test with a variation of the particle mesh size.It calculated that the cutoff temperature variation is smaller than 1% when the height node number (𝑁𝑁 = 𝐻𝐻 ∆𝜕𝜕) and time node number (𝑀𝑀 = 𝑖𝑖 ∆𝑖𝑖) is larger than 1000, with an increase of particle radius node number (𝐹𝐹 = 𝐷𝐷 𝑝𝑝 ∆𝑟𝑟 𝑝𝑝

2 ]Figure 4 . 6 :

 246 Figure 4.6: Height, time, and particle radius node number independence tests in differential mesh.

  calibration device in the validation range of 35-200 °C and by the low-temperature thermostat below 35 °C. The specific heat capacity of glass sphere was measured by Differential Scanning Calorimetry (DSC Q200) with a heating/cooling rate of 5 K min -1 showing in FigureA 4.1 a of Appendix. The inlet flow rate was calibrated by the gravimetric method with testing curves shown in FigureA 4.1 b. The thermal conductivity of insulation was measured by Thermal Constants Analyser (Hot-Disk TPS1500) at different temperatures, with a small variation rate of 2.7×10 -3 W m -1 K -1 per 1 K shown in FigureA 4.1 c.

  37 K is used to calculate the in-direct parameters uncertainty. The corresponding uncertainty of stored energy, input energy, and efficiency of the validation case are exhibited in FigureA 4.2 b-d.

Figure 4 . 7 a

 47 shows the comparison of fluid temperature evolution at TC1-7 axial positions (cf. C in Figure 4.4 b; r=0). A good agreement between numerical and experimental results can be found at first sight.

Figure 4 . 7 b

 47 further shows the variation of temperature difference (∆𝑑𝑑) vs. charging time

FigureA 4 .

 4 2 d). At the final cutoff fluid outlet temperature of 43.8 °C (𝜃𝜃=0.2), the energy efficiency is calculated to be 𝜂𝜂 𝑒𝑒ℎ =83.3% by modeling and is 𝜂𝜂 𝑒𝑒ℎ =85.5% in experiment, showing a good agreement. In conclusion, the DC-3P model shows good accuracy in simulating the large size sphere (𝐵𝐵𝐵𝐵 𝑠𝑠 >0.1) and tank with large wall volume of SHTPB.

Figure 4 . 7 :

 47 Figure 4.7: Comparison between numerical results and experimental data: (a) Evolution of fluid temperature at different locations of axial centerline; (b) fluid temperature differences and corresponding standard deviations (Case 1: 𝑑𝑑 𝐶𝐶 /𝑑𝑑 𝐻𝐻 =20/50 °C, 𝐷𝐷 𝑝𝑝 =7 mm, 𝑉𝑉 ̇𝑓𝑓 =0.5 L min -1 , 𝑃𝑃𝑅𝑅=12, 𝑅𝑅𝑅𝑅=3, 𝐵𝐵𝐵𝐵 𝑠𝑠 =0.76, charging operation).

Figure 4 . 8

 48 reports the values of temperature standard deviation (SD)

Figure 4 . 8 :

 48 Figure 4.8: Comparison of numerical and experimental results on temperature standard deviation (SD) and energy efficiency difference (∆𝜂𝜂 𝑒𝑒ℎ ) in charging process: (a) Case 1 (𝐷𝐷 𝑝𝑝 =7 mm); (b) Case 3 (𝐷𝐷 𝑝𝑝 =10 mm).

Figure 4 . 9 :

 49 Figure 4.9: Evolution of fluid temperature distribution experimentally measured for one charging-discharging cycle (Case 3: 𝑑𝑑 𝐶𝐶 /𝑑𝑑 𝐻𝐻 =20/50 °C, 𝐷𝐷 𝑝𝑝 =10 mm): (a) 𝑉𝑉 ̇𝑓𝑓=0.3 L min -1 ; (b) 𝑉𝑉 ̇𝑓𝑓=1.5 L min -1 .

Figure 4 . 4

 44 are compared to assess the performance of different inlet configurations to mitigate the impact of penetrating flow inject.

Figure 4 .Figure 4 . 10 .

 4410 Figure 4.10. When the value of 𝑐𝑐 𝑟𝑟 approaches 0, there is almost no radial temperature gradient, indicating that the shape of thermocline is flattened as assumed in 1D numerical model. From

Figure 4

 4 Figure 4.10 a, the radial temperature difference (∆𝑑𝑑 ) at TC-7 level decreases after adding the

Figure 4 . 10 :

 410 Figure 4.10: Radial temperature difference inside the SHTPB tank with different tested inlet configurations: (a) TC-7 position; (b) TC-5 position (Case 3, 5 & 6: 𝐷𝐷 𝑝𝑝 =10 mm; 𝑉𝑉 ̇𝑓𝑓=1.5 L min -1 ; charging).

  .11 a) mainly due to the longest charging time before reaching the cutoff fluid outlet temperature thus additional amount of heat loss as shown in Figure 4.11 b. In reality, the 𝜂𝜂 𝑒𝑒ℎ curves for Case 3 with serious radial thermocline expansion and Case 5 are very close (<2%) during the charging operation (Figure 4.11 b). This implies that the radial temperature non-uniformity and the thermocline expansion near inlet region caused by the penetrating HTF inject may have negligible influence on the energy efficiency of the SHTPB tank. It actually depends largely on the cutoff temperature and the corresponding cutoff time. The energy efficiency and capacity ratio of Case 6 with full water HTF in entrance (thereby larger volumetric heat capacity than that of glass) are very close to those for Case 3. The near-entrance region of the tank is less utilized due to the strong mixing of hot and cold fluids, such like in single-medium thermocline tanks [7].

Figure 4 . 11 :

 411 Figure 4.11: Effect of inlet configuration on the global performance of the SHTPB tank: (a) energy efficiency and capacity ratio at cutoff time; (b) energy efficiency and heat loss ratio vs. charging time (Case 3, 5 & 6: 𝐷𝐷 𝑝𝑝 =10 mm, 𝑉𝑉 ̇𝑓𝑓=1.5 L min -1 , charging).

Figure 4 .

 4 Figure 4.12 shows the captured images for Case 5 but without insulation layer in charging and discharging operations. The thermocline region on the images is marked by dash line, showing that its thickness increases by 13 % from 2 min to 5 min in charging and discharging process. The flat shape of the thermocline region captured by infrared imager, though at the outer surface of the tank, may imply the good flow distribution behavior by the combined effect of porous bed and flow diffuser (Case 5).

Figure 4 . 12 :

 412 Figure 4.12: Experimental thermal infrared images of charging and discharging process (𝑑𝑑 𝐶𝐶 /𝑑𝑑 𝐻𝐻 =20/50 °C, 𝐷𝐷 𝑝𝑝 =10 mm, 1.5 L min -1 , diffuser 𝑧𝑧 1 =10 mm, no insulation, 𝜖𝜖=0.90, 𝑑𝑑 𝑎𝑎𝑚𝑚𝑏𝑏 =20.7 °C).

Figure 4 . 13 :& 4 :

 4134 Figure 4.13: Experimental results comparing the performance of SHTPB tank with/without insulation. (a) inlet and outlet temperature; (b) dimensionless thermocline thickness 𝐿𝐿 𝑖𝑖ℎ𝑒𝑒𝑟𝑟𝑚𝑚𝑜𝑜𝑒𝑒𝑙𝑙𝑖𝑖𝑖𝑖𝑒𝑒 *

Figure 4 .

 4 Figure 4.13 b shows the variation of the normalized thermocline thickness over charging time for the two cases. It may be observed that the 𝐿𝐿 𝑖𝑖ℎ𝑒𝑒𝑟𝑟𝑚𝑚𝑜𝑜𝑒𝑒𝑙𝑙𝑖𝑖𝑖𝑖𝑒𝑒 *

Figure 4 .

 4 9 a) thus the influence of heat loss on the thermocline expansion is negligible. But at the second half of the charging, there is an obvious discrepancy between the two 𝐿𝐿 𝑖𝑖ℎ𝑒𝑒𝑟𝑟𝑚𝑚𝑜𝑜𝑒𝑒𝑙𝑙𝑖𝑖𝑖𝑖𝑒𝑒 * curves, implying the noticeable influence of heat loss on the thermocline expansion. Comparing the insulation tank and no-insulation tank, the 𝐿𝐿 𝑖𝑖ℎ𝑒𝑒𝑟𝑟𝑚𝑚𝑜𝑜𝑒𝑒𝑙𝑙𝑖𝑖𝑖𝑖𝑒𝑒 * is calculated to be 0.59 and 0.76 at t*=1.38 (thermocline zone reaching the tank bottom).

Figure 4 .

 4 Figure 4.13 c shows the variation of input energy (∆𝐸𝐸 𝑖𝑖𝑖𝑖 ), stored energy (∆𝐸𝐸 𝑠𝑠𝑖𝑖𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 ), and outlet energy (∆𝐸𝐸 𝑜𝑜𝑜𝑜𝑖𝑖 ) as a function of charging time for the SHTPB tank with/without the insulation. It is observed that both 𝐸𝐸 𝑠𝑠𝑖𝑖𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 curves increase almost linearly until reaching a plateau. At the cutoff moment of charging, the 𝐸𝐸 𝑠𝑠𝑖𝑖𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 value of no-insulation tank is 4-7% lower than that of the tank with insulation, mainly due to the heat loss.Figure 4.13 c shows the energy efficiency (𝜂𝜂 𝑒𝑒ℎ ) curve

Figure 4 .

 4 13 c shows the energy efficiency (𝜂𝜂 𝑒𝑒ℎ ) curve

Figure 4 . 14 shows 5 L

 4145 the fluid temperature profile along the tank height (centerline) for various flow rates, particles size, and operating temperatures at charging time of 𝑡𝑡 𝐸𝐸 * =0.5 (input energy by HTF is equal to the half of ideal maximum stored energy of tank ). When HTF flow rate increases from 0.3 to 1.min -1 and the theoretical input energy by HTF is the same, the fluid temperature at the same z* becomes higher. That's because the shorter residence time at high flow rate causes insufficient heat exchange between solid and HTF.

Figure 4 .

 4 Figure 4.15 is the fluid temperature profiles for various inlet temperatures at a charging time of 𝑡𝑡 𝐸𝐸 * =0.75. The time is chosen in order to get the more obvious comparison results. When the inlet temperature increase from 50 to 70 °C, the fluid temperature at the same height under the same flow rate decreases. That's because the higher operational temperature causes more heat loss to decrease fluid temperature.

Figure 4 . 14 :

 414 Figure 4.14: Experimental fluid temperature profile at the axial centerline of the SHTPB tank for various flow rates, particles sizes, and working temperatures at charging time of 𝑡𝑡 𝐸𝐸 * =0.5.

Figure 4 . 15 :

 415 Figure 4.15: Experimental fluid temperature profile of different inlet temperature at charging time of 𝑡𝑡 𝐸𝐸 * =0.75.

Figure 4 .

 4 Figure 4.16 shows the variation of normalized thermocline thickness as a function of 𝑡𝑡 𝐸𝐸 * in charging. Curves are fitted linearly for a better comparison using the direct proportion formula, 𝐿𝐿 𝑖𝑖ℎ𝑒𝑒𝑟𝑟𝑚𝑚𝑜𝑜𝑒𝑒𝑙𝑙𝑖𝑖𝑖𝑖𝑒𝑒 *

Figure 4 . 16 :

 416 Figure 4.16: Evolution of thermocline thickness for various flow rates, particles sizes, and working temperatures in charging process.

Figure 4 . 17 :

 417 Figure 4.17: Average temperature difference between sphere center and fluid in charging process: comparison between experimental and numerical results: (a) Dp=7 mm; (b) Dp=10 mm

Figure 4 .

 4 [START_REF] Tatsidjodoung | A review of potential materials for thermal energy storage in building applications[END_REF] shows the numerical results of the energy efficiency and remained thermocline thickness at cutoff time with HTF flow rate ranging from 0.12 to 2.5 L min -1 (𝑅𝑅𝑅𝑅=0.8- 25). The inlet fluid temperature has negligible effect on the energy efficiency and the remained thermocline thickness. Numerically, the smaller filler particle size is more advantageous and an optimal inlet flow rate (about 𝑅𝑅𝑅𝑅 =3) in charging can be identified for this SHTPB under low temperature operation. This finding is in line with other researches for high-or middletemperature applications[START_REF] Kocak | Performance of laboratory scale packed-bed thermal energy storage using new demolition waste based sensible heat materials for industrial solar applications[END_REF][34][4]. Unfortunately, this optimum is not significant enough to be detected in experiments. One reason is may due to the stability of operations and measuring uncertainties. Another reason is may be caused by the regime in the change of flow behind obstacles or particles, which cannot be simulated in the 1D fluid model in Matlab. When the HTF flow distance in the packed bed increases and when the mass flow rate increases, the heat transfer efficiency of the regime behind the particle thereby decrease.

Figure 4 . 18 :

 418 Figure 4.18: Influences of flow velocity (Re) on energy efficiency and thermocline thickness: comparison between experiment and numerical results (TH: 50-70 °C, 𝑉𝑉 ̇𝑓𝑓=0.12-2.5 L min -1 ).

Figure 5 . 1 : 5 . 2 .

 5152 Figure 5.1: Photograph of multi-layered HHTPB system with latent and sensible heat fillers: (a) lateral view; (b) sectional view. The comparison of fluid temperature profiles with time variation in different height positions is illustrated in Figure 5.2. For both cases, dot line is the experimental results and solid line is the numerical results of the PCM model. In Figure 5.2 a, no obvious temperature difference is observed at the tank top because two flow distributors on the top of the tank to make uniform flow of HTF. While in Figure 5.2 b, the temperature curve at top (TC-7) shows an obvious jump because of the flow jet at the inlet. This point has been proved in Chapter 4 that the packed bed region can alleviated the flow jet influence near the middle tank. Overall, the model is in good agreement with two reference cases, showing a temperature standard deviation (SD) below 1 K as calculated. In all, this model can be used for further optimization studies.

Figure 5 . 2 :

 52 Figure 5.2: Validation of numerical model with [147] (Re=30) experimental works and multilayered experimental study in LTEN lab (𝑅𝑅𝑅𝑅=7).

Figure 5 . 3

 53 is the designed greenhouse integrating the thermocline TES system: the solar collector input, the greenhouse output, the TES tank, and the heat exchange system.

Figure 5 . 3 :

 53 Figure 5.3: Schematic of thermocline system in greenhouse.

  ∆𝑑𝑑 𝐷𝐷𝐸𝐸𝐷𝐷,𝑚𝑚𝑎𝑎𝑒𝑒 = 𝑑𝑑 𝐻𝐻 -𝑑𝑑 𝐶𝐶 = 50 K (5.14) Dynamic working temperature range (∆𝑑𝑑 𝐷𝐷𝐸𝐸𝐷𝐷 (𝑡𝑡)) is calculated based on the real time-solar radiation intensity.∆𝑑𝑑 𝐷𝐷𝐸𝐸𝐷𝐷 (𝑡𝑡) = 𝑑𝑑 𝑖𝑖𝑖𝑖 (𝑡𝑡) -𝑑𝑑 𝐶𝐶 = 𝐼𝐼(𝑖𝑖)•𝜂𝜂 𝑐𝑐𝑜𝑜𝑙𝑙𝑙𝑙𝑒𝑒𝑐𝑐𝑡𝑡𝑜𝑜𝑟𝑟 •𝐷𝐷 𝑐𝑐𝑜𝑜𝑙𝑙𝑙𝑙𝑒𝑒𝑐𝑐𝑡𝑡𝑜𝑜𝑟𝑟 𝑚𝑚̇𝑠𝑠 ,𝑐𝑐ℎ,𝐷𝐷𝐸𝐸𝐷𝐷 •𝐶𝐶 𝑝𝑝,𝑠𝑠(5.15)In order to set dynamic working temperature close to the steady working temperature range and without designing (proposing) a detailed surface area of solar collector. The ∆𝑑𝑑 𝐷𝐷𝐸𝐸𝐷𝐷 (𝑡𝑡) is evaluated according to the maximum steady temperature.∆𝑑𝑑 𝐷𝐷𝐸𝐸𝐷𝐷 (𝑡𝑡) = ∆𝑑𝑑 𝐷𝐷𝐸𝐸𝐷𝐷,𝑚𝑚𝑎𝑎𝑒𝑒 • 𝐼𝐼(𝑖𝑖) 𝐼𝐼 𝑚𝑚𝑡𝑡𝑒𝑒 (5.16) ► 𝐼𝐼 [W/m 2 ]is the solar radiation intensity or direct normal irradiation obtained from actual measurement data.

Figure 5 . 4

 54 Figure 5.4 is the meteorological data of four seasonal days for the first day in January, April, July, and October. It shows gas heating consumption happens mostly in the 24 h per day, but solar supply only in daytime.

Figure 5 . 4 :

 54 Figure 5.4: Meteorological data in the 1 st day of typical seasonal month (Jan., Apr., Jul., Oct.): (a) gas heating consumption; (b) daily radiation intensity.

Figure 5

 5

Figure 5 . 5 :

 55 Figure 5.5: Steady and dynamic inlet temperature of thermocline packed-bed tank for four seasonal days.

S2:

  defining the variables and objectives, initial and final condition for MOGA optimization. S3: initializing and run DC-3P model in cycling. S4: generation, selection, mutation, until to final condition to obtain the Pareto front.

Figure 5 . 6 :

 56 Figure 5.6: Flowchart of design methodology and multi-layered optimization process of the PCM thermocline packed-bed TES system.

)

  Control variables (x): All design variables were normalized. The layer thickness (𝐿𝐿 𝑖𝑖 * ) is selected because it is the basic layer variable of the multi-layered packing strategy. The phase change temperature (𝑑𝑑 𝑚𝑚,𝑖𝑖 * ) and thermal conductivity (𝜆𝜆 𝑃𝑃𝐶𝐶𝑃𝑃,𝑖𝑖 * ) are used since those are inherent properties of PCM and have relevant influence on thermal performance. Moreover, the maximum constraint of the mass flow rate in charging ( 𝑚𝑚̇𝑓𝑓 ,𝑒𝑒ℎ * ) and mass flow rate in discharging (𝑚𝑚̇𝑓𝑓 ,𝑚𝑚𝑖𝑖𝑠𝑠 * ) are determined to use the full tank volume based on the model validation ranges. The minimum constraint of the mass flow rate is equal to the initial design value because the tank cannot be full used.

Figure 5 . 7

 57 and listed in Table 5.5 were optimized. Design A and Design A+ are LHTPB tank, whereas Design B and design B+ are HHTPB tank that the lower layer is sensible filler. For Design A, where 5 variables is set the phase change temperature of upper/lower layer equal to the charging/discharging cutoff temperature, respectively. For Design A+ with 7 variables, the phase change temperature imposed. Other parameters for four cases are the same.

Figure 5 . 7 :

 57 Figure 5.7: Multi-layered packing configurations for optimization: two-layer optimization.

  Time step and grid independence are tested based on the designed PCM thermocline packedbed tank in Figure 5.8 in charging process for greenhouse. It obtained the standard deviation of charging efficiency and outlet temperature stay below below 1% when the nodes of height (𝑁𝑁 = 𝐻𝐻 ∆𝜕𝜕 ) × time (𝑀𝑀 = 𝑖𝑖 ∆𝑖𝑖 ) × particle radius (𝐹𝐹 = 𝐷𝐷 𝑝𝑝 ∆𝑟𝑟 𝑝𝑝

Figure 5 . 8 :

 58 Figure 5.8: Height node, time node, and particle radius node independence tests.

Figure 5 . 9 presents

 59 the steady and dynamic comparison results.As shown in Figure5.9 a, the PCM filler has the advantage of stabilizing the outlet temperature at around its phase change temperature than sensible fillers. But, the initial design tank of PCM60 has not shown a complete daytime storage loading after 8h, as well as the PCM30 filler tank. That is one of the reasons why the capacity ratio in charging of PCM fillers tank is lower than the rock fillers tank in Figure5.9 b. This results suggest that it's possible to improve thermal performance by designing phase change temperatures in different layers, based on one PCM with the similar volumetric heat capacity and enthalpy but different phase change temperature, like paraffin.

Figure 5 . 9 :

 59 Figure 5.9: Evaluation of steady and dynamic inlet temperature for one representative day in charging (1 st January, 1 st July): (a)(c) outlet temperature profile; (b)(d) capacity ratio. (N=300, M=300, F=10).

The result in Figure 5 .

 5 10 b shows the influence of phase change temperature on capacity and utilization ratio are converse, which suggests that filling different phase change temperature PCM in layers of tank maybe a good solution to contradiction.

Figure 5 . 10 :

 510 Figure 5.10: Variation of phase change temperature (𝑑𝑑 𝑚𝑚 ± 0.1 °C).

Figure 5 .

 5 11 is cycling test during 10 cycles based on the overall energy efficiency of the initial designed PCM tank. In cycling, each ending condition is the initial condition of next charging/discharging process. It was observed that the overall energy efficiency at the third cycles is relatively constant (0.4≲%) which indicates the system becomes stable. Thus, KPIs at the 3rd cycling can be set as performance indicator in cycling for optimization.

Figure 5 . 11 :

 511 Figure 5.11: Evaluation of cycling numbers.

Figure 5 . 12 .

 512 is the Pareto front based on two objectives, the overall energy efficiency (𝜂𝜂 𝑜𝑜 ) and the combined capacity-utilization ratio (𝛶𝛶 𝑜𝑜 ), for MOGA optimization of two-layer arrangement. As exhibited, the Pareto front clearly shows the trade-off between maximizing 𝜂𝜂 𝑜𝑜 and 𝛶𝛶 𝑜𝑜 . Among design cases, the Design A+ (PCM-PCM) with two layer PCMs has the highest 𝜂𝜂 𝑜𝑜 and 𝛶𝛶 𝑜𝑜 , showing an optimal result, while the Design B (PCM80%-Sensible) with upper/lower layer of PCM/sensible rock filler shows the lowest 𝜂𝜂 𝑜𝑜 and 𝛶𝛶 𝑜𝑜 . The Design A (PCM80%-PCM20%) fixing the upper/bottom layer PCM temperature equal to the charging/discharging cutoff temperature is investigated. Contrast to Design A+, the Υ o of Design A+ is less changed and maintained at around 0.98, while Design A+ has a Υ o about 0.95. This difference demonstrates Design A+ is better than Design A, optimizing upper layer PCM is beneficial to enhancement of the storage and utilization ability by about 3% in LHTPB tank. The Design B that fixing the phase change temperature of the upper layer PCM that is equal to the cutoff temperature. Comparing to Design B+ (PCM-Sensible) that optimizing the upper layer PCM, it can improve the overall storage and utilization ratio of Υ o of tank in cycling by around 4% in HHTPB tank.

Figure 5 . 12 :

 512 Figure 5.12: Pareto front of Design A+ (PCMx%-PCM x%), A (PCM80%-PCM20%), B+ (PCM x%- Sensible), and B (PCM80%-Sensible).

Figure 5 .

 5 Figure 5.13 is the comparison results under the same initial condition for Design A+ and ROCK tank. As depicted, Design A+ shows higher value of 𝛶𝛶 𝑜𝑜 , 𝜂𝜂 𝑜𝑜 and, near 2 times (30-55%) stored/released energy than single ROCK tank in this study, which means the one advantage of PCM tank is the high energy storage capacity.

Figure 5 . 13 :

 513 Figure 5.13: Comparison of Design A+ and single ROCK tank based on a particular case of maximum energy efficiency in Pareto front.

Figure 5 .

 5 14 a of the LHTPB, three cases have the same maximum stored energy for different application requirements. It shows Design A+ has the highest stored/released energy ratio (𝐸𝐸 * = 𝐸𝐸 𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚,𝑚𝑚𝑡𝑡𝑒𝑒 𝐸𝐸 𝑟𝑟𝑒𝑒𝑙𝑙𝑒𝑒𝑡𝑡𝑠𝑠𝑒𝑒𝑚𝑚,𝑚𝑚𝑡𝑡𝑒𝑒 ) but constant low outlet temperature, a reference non-optimized case (half PCM80% and half PCM20%) has lowest E* but high outlet temperature. For HHTPB tank in Figure 5.14 b, Design B+ also shows larger E* but constant lower outlet temperature. An upper layer phase change temperature close to cutoff temperature is necessary for application like CSP, however, unsolidification PCM after discharging or utilized problem is serious in this types of cases. Therefore, if one wants to have a constant high outlet temperature (close to cutoff temperature) the Design A or Design B are good selections with fixed phase change temperature at the top. If only need constant outlet temperature, the Design A+ or B+ are the optimal case.

Figure 5 . 14 :

 514 Figure 5.14: Outlet temperature and stored/released energy at the third cycles.

Figure 5 .

 5 [START_REF] Alva | An overview of thermal energy storage systems[END_REF] is the fluid temperature profiles of the third cycle for Design A+ and Design B in charging. In cycling, the initial condition of third charging is the cutoff time of the second discharging, while the initial condition of discharging is the end of charging. As shown, the HTF (solid line) and PCM (dot line)

Figure 5 . 15 :

 515 Figure 5.15: HTF temperature profile in charging/discharging at steady inlet condition of the third cycles.

5. 5 . 3 .

 53 Effect of designed variablesTo clarify the influence trends of parameters, the MOGA results should be compared with designed variables, including the operational parameters (mass flow rate, 𝑚𝑚̇𝑓𝑓 ,𝑒𝑒ℎ * , 𝑚𝑚̇𝑓𝑓 ,𝑚𝑚𝑖𝑖𝑠𝑠 * ) and geometric configuration parameters (upper layer thickness L up * , phase change temperature 𝑑𝑑 𝑚𝑚,𝑜𝑜𝑝𝑝 * , 𝑑𝑑 𝑚𝑚,𝑙𝑙𝑜𝑜𝑤𝑤 * , thermal conductivity, 𝜆𝜆 𝑃𝑃𝐶𝐶𝑃𝑃,𝑜𝑜𝑝𝑝 * , 𝜆𝜆 𝑃𝑃𝐶𝐶𝑃𝑃,𝑙𝑙𝑜𝑜𝑤𝑤 * ). The obtained Pareto front results is also better to understand the relationship of different variables and designed objectives. All variables were normalized to obtain generic optimization strategy. Figure 5.16 presents objectives verse variables in the last genetic iteration.

•• Figure 5 .

 5 A higher phase change temperature enables to improve the 𝛶𝛶 𝑜𝑜 but decrease 𝜂𝜂 𝑜𝑜 , as shown in Figure 5.16 a b. In charging process, larger phase change temperature means smaller temperature gap with inlet temperature of TH, leading to smaller heat transfer rate between solid PCM and HTF and longer charging time (Figure 5.17). In discharging, the phenomenon is inverse, the improved the heat transfer rate and the decreased discharging time. According to the definition of overall energy efficiency, the overall efficiency 𝜂𝜂 𝑜𝑜 is thus decreased. Whereas the 𝛶𝛶 𝑜𝑜 means the combined effect of the total stored energy in charging and released energy in discharging, which is unclarified which one is dominant or both are positive in increasing 𝛶𝛶 𝑜𝑜 . 16 c d depicts MOGA results with thermal conductivity variation. It is found

Figure 5 . 16 :

 516 Figure 5.16: Multi-objective optimization results of objectives verse variables for Design A+.

Figure 5 . 17 :Figure 5 .

 5175 Figure 5.17: Charging and discharging time for MOGA results.5.5.4. Variables ranges

Figure 5 . 18 :

 518 Figure 5.18: Multi-objective optimization results of Pareto front plotted by dot color: the optimal variable ranges of Design A+.

Figure 5 .

 5 Figure 5.19 is the temperature profile under dynamic inlet of 1 st July of optimal Design A+ and reference Rock tank. As shown in rock tank, the thermocline thickness is almost 100% from the begin to the end, while in Design A+, it can alleviate the influence of fluctuated inlet temperature and compressed the thermocline thickness at t*=1 by around 20%.

Figure 5 . 19 :

 519 Figure 5.19: Temperature profiles at dynamic inlet condition in greenhouse in 1 st July: (a) Rock tank; (b) Design A+.

  2.2.1. Sensible heat fillers .................................................................................................................

2.2.2. Latent heat fillers ..................................................................................................................... 2.3. Influencing factors on thermal performance ................................................................ 2.3.1. Operational parameters ........................................................................................................ 2.3.2. Geometrical parameters ........................................................................................................

Table 2 . 1

 21 Thermophysical properties of common sensible heat fillers for thermocline packed-

	bed TES.

1 ) ρs•Cp,s (kJ m -3 K -1 ) Ref.

	Cast iron	7900	837	29.3	6612	[41]
	Steel	7870	565-571	49.8	4447-4494	[42][43]
	Magnesia fire brick	1150	3000	5.0	3450	[44]
	Coal fly ash brick	2600	735-1300	1.3-2.1	1911-3380	[45]
	Castable ceramic	3500	866	1.4	3031	[40]
	Blast furnace slag	2980	996	2-3.5	2968	[46]
	Alumina ceramic	3750	780	30	2925	[47]
	Steatite	2680	1068	2.5	2862	[43][48]
	Alumina	3670	750	21	2753	[45]
	Granite rock and sand	2643	1020	2.2	2696	[49]
	Concrete	2800	916	1.0	2565	[47][40]
						[50]
	Copper slag	3600	683 (300°C)	0.8	2450	[51]
	Aluminum	2700	896	204	2419	[43]
	Silicon carbide ceramic 3210	750	120	2408	[47]
	Quartzite rock and sand 2500	830	5.7	2075	[41]
	Silca fire brick	1820	1000	1.5	1820	[44]
	Soda-lime glass	2400	760	1.0	1824	[42]

Table 2 .

 2 2 lists several candidates of solid-liquid PCM fillers and the corresponding thermophysical properties. As explained in Figure 2.4, the material changes its phase from solid to liquid when temperature increases, and more amount of heat is exchanged during the latent storage in comparison to the sensible storage for the same temperature change.

Table 2 . 3

 23 Cost of materials for thermocline packed-bed TES.

	Materials

Obtained copyright permission of Elsevier [License No. 5207680260358, No. 5207680428546, Dec 14, 2021]

Table 2 . 4

 24 Single-layered PCM packed bed TES systems.

	Literatures	Years	H/D/W	TC/TH	Dp (mm)	ε	PCMs	Filler	Packings	HTFs	Flow		Exp./	Validation
			(m)	(°C)				shapes			rates		Num.	cases
	Chen and Yue [121]	1991	0.260/0.10 0/0.005	0/25	34	0.36-0.61	Water	Sphere	Horizontal	Air	2-5 min -1	L	Exp./ Num.	Designed setup
	Arkar et al. [74] 2007	1.52/0.34/ --	<36	50	0.388	Paraffin	Sphere	Rhombic	Air	--		Exp./ Num.	Designed setup
	Rady [122]	2009	0.200/0.04 5/0.0025	15/50	1.0-3.0 (~89.5%)	0.42	Rubitherm GR27 (21-29 °C); Rubitherm GR41 (31-45 °C)	Granule Random	Air	0-130 L h -1	Exp./ Num.	Designed setup
	Flueckiger and Garimella [36]	2014	18/21/--	300/60 0	--	--	--	--	--	Molte n salt	0.436 mm s -1		Num.	[104]

Table 2 .

 2

	Literatures	Years H/D/W	TC/TH	Dp	ε	Layers	PCMs & Tm	Packings	HTFs	Filler	Flow	Exp./	Validation
			(m)	(°C)	(mm)						shapes	rates	Num.	cases
	Yang et al.	2014	0.69/0.36	32/70	55	0.	1-3	Paraffin wax:	PCM1-PCM2-PCM3 Water	Sphere	2 L min -	Num.	[147]
	[60]		/--			84		(60-62 °C)				1
								(50-52 °C)
								(42-44 °C)
	Wu et al.	2016	14/4.9/--	290/39	40	0.	1-5	Molten salt:	PCM1-PCM2-	Molten salt	Sphere	--	Num.	[65]
	[134]			0		25		C1(375 °C)	PCM3-PCM4-	(60 wt%
								C2(360 °C)	PCM5-	NaNO3-40
								C3(340 °C)		wt % KNO3)
								C4(320 °C)
								C5(305 °C)
	Elfeky et al.	2018	7.3/10.6/	288/56	26.53	0.	1-3	Molten salt:	PCM1-PCM2-PCM3 Molten salt	Sphere	84.5175	Num.	[148]
	[59]		--	5		22		(382.1 °C)		(60 wt%		kg s -1
								(439.8 °C)		NaNO3-40 wt%
								(505 °C)		KNO3)
	Chirino et al.	2019	30/10/--	350/55	40	0.	1-3	PCM:	PCM1-PCM2-PCM3 Molten salt	Sphere	1058.2
	[133]			0		3		(380 °C)		(7.5 wt% NaCl-		kg s -1
								(435 °C)		24 wt% KCl-69
								(496 °C)		wt% ZnCl2)

5

Multi-layered PCM packed bed TES systems.

Table 2 .

 2 6Multi-layered sensible-PCM packed bed TES systems.

	Litera	Years H/D/W	TC/TH	PCM fillers				Sensible fillers		Pack	HTFs	Flow	Packing	Exp./N	Valida	Storage
	tures		(m)	(°C)	Materials	(mm) Dp	ε	Shape Filler	(mm) Materials Dp	ε	ing		rates		um.	tion cases	capacit y
								s
	Galion	2014	6.1/3.0/-	290/3	KOH	15	0.	Shpere Quarzite		0.	PCM	Molten salt	5.54	Random	Num.	[104]	--
	e et al.		-	90			22		rock-sand		22	-S-		kg s -1
	[143]											PCM
												*2
	Zanga	2015	0.168/0.	25/70	AISI 316	18	0.	Tubes	Rock	32	0.	PCM	Air	~0.015	PCM	Exp./N	Design	42
	neh et		400	0	stainless steel		55				4	-S		kg s -1	arranged	um.	ed	kWhth
	al.		/0.003		tubes & AlSi12										in 4 rows		setup
	[63]				for PCM
	Zhao	2016	14/32-	288/5	Top layer: 20	10	0.	Shpere Quarzite	19.05	0.	PCM	Molten salt	--	Uniform	Num.	[104]	250
	et al.		44/--	70	v% Li2CO3-60		34		rock-sand		22	1-S-	(60 wt%				[147]	MWt
	[28]				v% Na2CO3-							PCM	NaNO3-40
					20 v% K2CO3,							2	wt %KNO3
					Bottom layer:								)
					60 v%
					NaNO3-40 v%
					KNO3
	Abdul	2017	12/14.3	290/3	Top layer:	35	0.	Shpere Rock	33	0.	PCM	Molten salt	0.0005	--	Num.	[147]	100
	la and		8/--	90	PCM380* 1		35				22	1-S-	(60 wt%	774 m				MWh
	Reddy				Bottom layer:							PCM	NaNO3-40	s -1
	[146]				PCM300* 1							2	wt %KNO3
													)
	Liao	2018	10/6.5/--20/65	AlSi12	200	0.	Shpere Rock	0.2	0.	PCM	--	30 kg	--	Num.	[48]	>100
	et al.			0			40				4	-S-		s -1				MWh
	[84]											PCM						(only
																		rocks)

Table 3 . 1

 31 Studies of walls impacts on thermocline packed-bed system. With a wall Nusselt number (𝑁𝑁𝑁𝑁) of about 102, an optimum value of fluid flow rate can maximize the overall energy efficiency and minimize the steel shell stress.

	Studies	Year Dimensions	Exp.	Wall impacts			Main findings
		(Fluid/Solid/ Wall)	/Num .	Heat loss from wall	Wall energy	Near wall void fraction
				to ambient	storage	singularity
				(Yes/No)	(Yes/No)	(Yes/No)
	Beasley and	1984 2D/1D/1D	Exp./	Yes	Yes	Yes	• Effects of void fraction near the wall, wall heat capacity, and wall energy losses
	Clark [154]		Num.				on dynamic response are identified.
	Yang and	2010 2D/2D/--	Num.	Yes	No	No	• Heat loss for non-adiabatic boundary distorts the flow temperature
	Garimella [112]						distributions, but such influence becomes insignificant at large flow rate
							(𝑅𝑅𝑅𝑅>250).
	Xu et al. [41]	2012 2D/2D/2D	Num.	Yes	Yes	No	• Insulation tends to reduce temperature difference in the cross-section of tank.
	Bellan et al.	2014 2D/2D/--	Num.	Yes	No	No
	[108]
	Opitz and	2014 (1D,1D)/(1D,	Num.	Yes	No	Yes
	Treffinger	1D)/--
	[156]
	Mira-	2015 2D/2D/--	Num.	Yes	No	No
	Hernández et
	al. [153]
	Chang et al.	2016 2D/2D/--	Num.	Yes	No	No
	[114]
	Cascetta et al.	2016 2D/2D/--	Exp./	Yes	Yes	Yes	• Wall influences the radial temperature profile and the amount of the stored
	[157][148]		Num.				energy.
	Hoffmann et al.	2016 1D;	Num.	Yes	Yes	No
	[155]	1D/1D/1D
		(No wall heat
		radiation)
	Fernández-Torrijos et al. [158] • ELSihy et al. 2017 1D/1D/2D Num. Yes Yes No 2021 2D/2D/2D Num. Yes Yes No • Employing heat loss boundary condition causes a faster temperature drop of
	[159]						the HTF near the tank wall, forming a temperature gradient.
	This study	2022 1D/1D/--;	Num.	Yes	Yes	No	• Wall impact comparison on two different scale tanks.
		1D/1D/2D;
		1D/1D/1D;

• Heat loss through the wall increases with the decreasing insulation layer thickness, which is less than 1% of the inlet energy at a steady state. • A general heterogeneous model with two zones mean void fraction is from in the cross-section is developed and validated. • Heat loss under non-adiabatic conditions causes thermal-buoyancy-induced flow non-uniformities.

• Total heat loss during the cycle is negligible compared to the heat storage capacity. • Thermocline thickness is much more fluctuated in the near-wall region along the tank height than that in the center of the tank. • 1D-1P model is faster but another model integrated different phases of fluid, solid, and wall is more accurate.

• Over 5% of the energy storage capacity, the wall needs to be considered.

  𝑝𝑝,𝑠𝑠 •(𝑇𝑇 𝑜𝑜𝑜𝑜𝑡𝑡 -𝑇𝑇 0 )�𝑚𝑚𝑖𝑖 𝑑𝑑 𝑖𝑖𝑖𝑖𝑠𝑠 (𝑟𝑟) = 𝑑𝑑 𝑖𝑖𝑖𝑖𝑠𝑠,𝑒𝑒𝑖𝑖𝑚𝑚 ).

	• Discharging exergy efficiency considering walls
	For a given time, the discharging exergy efficiency considering walls (𝜂𝜂 𝑒𝑒,𝑚𝑚𝑖𝑖𝑠𝑠 ′	) (or second law
	efficiency) is the ratio of the exergy of outlet fluid released from the bed (∆𝐸𝐸 𝑒𝑒,𝑜𝑜𝑜𝑜𝑖𝑖 ) at a certain time
	to the exergy difference of all phases in packed bed before discharging (∆𝐸𝐸 𝑒𝑒,𝑠𝑠𝑖𝑖𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 ′	):
	𝜂𝜂 𝑒𝑒,𝑚𝑚𝑖𝑖𝑠𝑠 ′	=	∆𝐸𝐸 𝑒𝑒,𝑜𝑜𝑜𝑜𝑡𝑡 ∆𝐸𝐸 𝑒𝑒,𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 ′	=	∫ 𝑡𝑡 𝑚𝑚𝑖𝑖𝑠𝑠 0 ∆𝐸𝐸 𝑒𝑒,𝑠𝑠,𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 𝑚𝑚̇𝑠𝑠•𝐶𝐶 𝑝𝑝,𝑠𝑠 •�(𝑇𝑇 𝑜𝑜𝑜𝑜𝑡𝑡 -𝑇𝑇 𝐶𝐶 )-𝑇𝑇 0 •ln� 𝑇𝑇 𝑜𝑜𝑜𝑜𝑡𝑡 𝑇𝑇 𝐶𝐶 ′ +∆𝐸𝐸 𝑒𝑒,𝑠𝑠,𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 ′ +∆𝐸𝐸 𝑒𝑒,𝑤𝑤,𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 ′ +∆𝐸𝐸 𝑒𝑒,𝑖𝑖𝑡𝑡𝑠𝑠,𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 ��𝑚𝑚𝑖𝑖 ′	(3.31)
				∆𝐸𝐸 𝑠𝑠,𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 ′	𝑡𝑡 𝑚𝑚𝑖𝑖𝑠𝑠 0 +∆𝐸𝐸 𝑠𝑠,𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 ′	+∆𝐸𝐸 𝑤𝑤,𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 ′	+∆𝐸𝐸 𝑖𝑖𝑡𝑡𝑠𝑠,𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 ′	(3.30)

where the ∆𝐸𝐸 𝑠𝑠𝑖𝑖𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 ′ is calculated by the energy at the initial state (that is 𝑑𝑑 𝑓𝑓 = 𝑑𝑑 𝑠𝑠 = 𝑑𝑑 𝐻𝐻 , 𝑑𝑑 𝑤𝑤 (𝑟𝑟) = 𝑑𝑑 𝑤𝑤,𝑖𝑖𝑖𝑖𝑖𝑖 , 𝑑𝑑 𝑖𝑖𝑖𝑖𝑠𝑠 (𝑟𝑟) = 𝑑𝑑 𝑖𝑖𝑖𝑖𝑠𝑠,𝑖𝑖𝑖𝑖𝑖𝑖 ) to the fully discharged state (that is 𝑑𝑑 𝑜𝑜𝑜𝑜𝑖𝑖 = 𝑑𝑑 𝐶𝐶 , 𝑑𝑑 𝑓𝑓 = 𝑑𝑑 𝑠𝑠 = 𝑑𝑑 𝐶𝐶 , 𝑑𝑑 𝑤𝑤 (𝑟𝑟) = 𝑑𝑑 𝑤𝑤,𝑒𝑒𝑖𝑖𝑚𝑚 ,

35 )

 35 𝑑𝑑 𝑒𝑒𝑜𝑜𝑖𝑖𝑜𝑜𝑓𝑓𝑓𝑓,𝑚𝑚𝑖𝑖𝑠𝑠 = 𝑑𝑑 0.8 = 𝑑𝑑 𝐶𝐶 + 20% • (𝑑𝑑 𝐻𝐻 -𝑑𝑑 𝐶𝐶 ) (3.36)

		𝑇𝑇-𝑇𝑇 𝐶𝐶 𝑇𝑇 𝐻𝐻 -𝑇𝑇 𝐶𝐶	(3.37)
	𝑡𝑡 * = 𝑡𝑡 •	𝑜𝑜 𝑠𝑠 𝐻𝐻	(3.38)
	𝑡𝑡 𝐸𝐸 * = 𝑡𝑡 •	𝑚𝑚̇𝑠𝑠•𝐶𝐶 𝑝𝑝 •(𝑇𝑇 𝐻𝐻 -𝑇𝑇 𝐶𝐶 ) ∆𝐸𝐸 𝑒𝑒,𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚,𝑚𝑚𝑡𝑡𝑒𝑒 ′	(3.39)
	𝑧𝑧 * =	𝜕𝜕 𝐻𝐻		(3.40)
	𝑟𝑟 * =	𝑟𝑟 𝑅𝑅 𝑖𝑖𝑡𝑡	(3.41)
	𝐿𝐿 𝑤𝑤 * =	𝐿𝐿 𝑤𝑤 𝑅𝑅 𝑖𝑖𝑡𝑡𝑡𝑡	(3.42)
	𝜆𝜆 𝑤𝑤 * =	𝜆𝜆 𝑤𝑤 𝜆𝜆 𝑠𝑠	(3.43)

• Dimensionless parameters Normalized parameters are defined for better comparison under different operational conditions. The dimensionless temperature (𝑑𝑑 * ), time based on flow velocity (𝑡𝑡 * ), time based on energy (𝑡𝑡 𝐸𝐸 * ), height (𝑧𝑧 * ), radius (𝑟𝑟 * ), wall thickness (𝐿𝐿 𝑤𝑤 * ), and wall thermal conductivity (𝜆𝜆 𝑤𝑤 * ) are introduced: 𝑑𝑑 * =

Table 3 .

 3 3 summarizes the thermo-physical properties for HTF, solid fillers, and tank body materials. The first case widely used for model validation[START_REF] Bayón | Simulation of thermocline storage for solar thermal power plants: From dimensionless results to prototypes and real-size tanks[END_REF][START_REF] Hoffmann | A thermocline thermal energy storage system with filler materials for concentrated solar power plants: Experimental data and numerical model sensitivity to different experimental tank scales[END_REF][START_REF] Flueckiger | Thermomechanical simulation of the solar one thermocline storage tank[END_REF]] is a 10 MWe packed-

bed TES tank for a solar thermal power plant in which Caloria HT 43 is used as HTF under the operating temperature range of 179.2-295.5 °C

[START_REF] Fass | MWe solar thermal central receiver pilot plant: thermal storage subsystem evaluationfinal report[END_REF][START_REF] Douglas | MWe solar thermal central receiver pilot plant mode 5 (test 1150) and mode 6 (test 1160) test report[END_REF]

. The second case is a 2.3 MWht packedbed pilot-scale molten salt TES tank from Sandia lab provided by Pacheco et al.

[START_REF] Pacheco | Development of a molten-salt thermocline thermal storage system for parabolic trough plants[END_REF]

, with an operating temperature range of 290-390 °C. The molten salt used is a mixture of 60 wt% NaNO3 and 40 wt% KNO3. At last, a hypothetical lab-scale TES water tank with a smaller size and lower temperature range of 20-75 °C is introduced to simulate the thermal performance under different operations. The ambient temperature of 20 °C was set as a reference for all cases.

Table 3 . 2

 32 Operational and geometric parameters of packed-bed TES tanks.

	Parameters	Units Solar thermal pilot	Sandia	laboratory	Hypothetical
			plant	tank	pilot-scale	tank	lab-scale tank
			[155,176,177]		[104]
	HTF	--	Caloria Ht-43		Molten salt	Water
	Solid filler	--	Granite rock and sand Quartzite rock and	Quartzite rock
					sand	and sand
	Tank height (H)	m	12.0		6.0	0.4
	Tank middle radius (Rmid) m	9.10		1.50	0.11
	Wall thickness (Lw)	m	0.10		0.04	0.01
	Insulation thickness (Lins) m	0.20		0.20	0.04
	Porosity (ε)	--	0.22		0.22	0.22
	Packed bed volume (Vb)	m 3	3053.60		40.20	12.56×10 -3
	Particle diameter (Dp)	m	4.61×10 -3		19.05×10 -3	5.00×10 -3
	HTF mass flow rate (ṁf)	kg s -1 23.00		5.46	8.30×10 -3
	TH/TC	°C	295.2/179.2		390/290	75/20
	Wall materials	--	Steel wall (ASTM 537 class 2) Steel wall	Polycarbonate
						wall
	Insulation	--	Mineral wool		Mineral wool	Mineral wool
	Discharging time	h	8.0		3.0	0.5
	Spatial node in height	--	200		200	200

Table 3 . 3

 33 Thermophysical properties of HTF, solid fillers and tank body materials.

	Solid fillers	ρs (kg m -3 )	Cp,s ( J kg -1 K -1 ) λs (W m -1 K -1 )	ρs•Cp,s (kJ	Ref.
					m -3 K -1 )
	Granite rock and sand	2643	1020	2.20	2696	[49]
	Quartzite rock and sand	2500	830	5.69	2075	[41]
	Soda-lime glass	2400	760	1.00	1824	[42]
	Tank body materials	ρw (kg m -3 ) Cp,w ( J kg -1 K -1 ) λw (W m -1 K -1 )	ρw•Cp,w (kJ
					m -3 K -1 )
	Steel wall (ASTM 537 class 2)	7850	475	47.00	3728	[175]
	Steel wall	7800	470	35.00	3666	[41]
	Polycarbonate wall	1200	1170	0.20	1404	--
	Insulation of mineral wool	70*	960	0.036	67.2	[137]
	Fluids	ρf (kg m -3 )	Cp,f ( J kg -1 K -1 )	λf (W m -1 K -1 )	μ (Pa s)
	Caloria HT-43 (237.2 °C)	701	2700	0.16	7.6×10 -4	[155]
	60 wt% NaNO3 and 40 wt%	1874	1502	0.51	2.5×10 -3	[41,83]
	KNO3 (340 °C)
	Water (47.5 °C)	990	4187	0.634	5.8×10 -4	[30,178]

Table 3 .4Difference between

 3

	Models	Average	Maximum difference	Standard	Root Mean Square
		difference (∆𝑻𝑻 ���� ,	(∆𝑻𝑻 𝒎𝒎𝒎𝒎𝒎𝒎 , K)	Deviation	difference (RMS, K)
		K)		(SD, K)
	1D-2P	2.91	12.7	2.80	4.06
	1D-3P	3.63	12.5	3.44	5.02
	1.5D-4P	3.56	12.3	3.40	4.93

experimental and numerical results of the Sandia pilot-scale tank

[START_REF] Pacheco | Development of a molten-salt thermocline thermal storage system for parabolic trough plants[END_REF]

for different models: mean difference for different times 0, 0.5, 1, 1.5, and 2h.

  thermal diffusivity time 𝑡𝑡 𝑚𝑚𝑖𝑖𝑓𝑓𝑓𝑓 * pilot-scale tank, respectively, and is 0.65 and 2.8 in the lab-scale tank. Lower 𝑡𝑡 𝑚𝑚𝑖𝑖𝑓𝑓𝑓𝑓 * shows fast heat transfer speed from wall to fluid. For this reason, 𝑑𝑑 𝑤𝑤 * is almost horizontal at different discharging times in pilot-scale tank.

	(𝑡𝑡 𝑚𝑚𝑖𝑖𝑓𝑓𝑓𝑓 *	=	𝐿𝐿 2 𝛼𝛼 •	* 𝑖𝑖 𝐸𝐸 𝑖𝑖 ) is around 0.01 and 2.2 for wall and
	insulation in the

Table 3 . 5

 35 Values of different HTC* for two tanks at average temperature (Tave).

TableA 3.2

  Value range of parameters for sensitivity analysis.

	Parameters	Symbols Units	Ranges

Pilot-scale tank Lab-scale tank

	Particle diameter	𝐷𝐷 𝑝𝑝	cm	0.2-1.0	0.2-1.0
	Porosity	𝜀𝜀	--	0.2-0.4	0.2-0.4
	Mass flow rate* 1	𝑚𝑚 𝑓𝑓 ̇	kg s -1	3-10	8.3×10 -3 -24.8×10 -3
	Wall thickness* 2	𝐿𝐿 𝑤𝑤	cm	4-15	0.3-1.0
	Wall thermal conductivity	𝜆𝜆 𝑤𝑤	W m -1 K -1	0.2-60	0.2-60
	Wall volumetric heat capacity* 3	𝜌𝜌 𝑤𝑤 • 𝐶𝐶 𝑝𝑝, 𝑤𝑤 J m -3 K -1 (×10 5 ) 15-66	15-66
	Solid thermal conductivity	𝜆𝜆 𝑠𝑠	W m -1 K -1	0.1-35	0.1-35
	Solid volumetric heat capacity* 3	𝜌𝜌 𝑠𝑠 • 𝐶𝐶 𝑝𝑝 ,𝑠𝑠	J m -3 K -1 (×10 5 ) 15-66	15-66
	*2 Wall thickness for both tanks is determined according to the similar ratio range (wall
	thickness/tank height).

*1 Mass flow rate for both tanks is determined according to the similar interfacial velocity range. *3 Volumetric heat capacity for solid and wall are in range between the low (like glass or plastic)

Table 4 . 1

 41 Summary of experimental investigations on SHTPB TES systems.

	Studies	Years	Solid	HTFs	𝑻𝑻 𝑪𝑪 /𝑻𝑻 𝑯𝑯	𝜺𝜺	𝑯𝑯/	Number of	Diffuser	Insula	Num./	Tested	Main findings
			fillers		(°C)		𝑫𝑫 𝒕𝒕𝒎𝒎𝒕𝒕𝒕𝒕	thermocouples		tion	Exp.	parameters in
							(m)	& arrangement				Exp.
	Faas et al.	1986	Granite	Caloria	179.2/	0.22	12/1	--	--	Yes	Exp.	--	• Low Rankine-cycle efficiency of 21% due to limited upper
	[176][177]		Rock and	® HT	295.5		8.2						temperature of TES tank.
			sand	43
	Meier et al.	1991	Rock	Air	150/55	0.36	1.2/0	--(axial)	--	Yes	Exp.	--	• Considerable heat losses through the wall.
	[48]				0		.15						• Smaller measured pressure drop than predicted due to
													low flow resistance near wall.
	Pacheco et	2002	Quartzite	Molten	290/39	0.22	6/3	--(axial and	Yes	Yes	Num./	--	• Thermocline thickness well predicted by the model.
	al. [104]		rock &	salt	0			radial)			Exp.		• higher heat loss than predicted due to the lack of
			sand										insulation on the top cover of the tank.
	Yang et al.	2012	Rock	Molten	300/50	0.2	2/1	12 (axial)	No	Yes	Num./	--	• Higher thermal storage capacity and efficiency by using
	[197]			salt	0						Exp.		fillers with higher density and specific heat, but also higher
													entropy generation (Num.).
	Yin et al.	2014/	Zirconiu	Molten	290/39	--	0.6/0	6 (axial)	Yes	Yes	Exp.	• Inlet HTF	• Heat storage efficiency is smaller than 80% due to the
	[117][189]	2017	m &	salt	0		.12			(heati		temperature	thermocline expansion.
			silicon carbide							ng strap)		• Flow rate • Mixed fillers	• Thermocline evolution influenced by HTF velocity. • Piston flow pattern achieved by buffering effect of porous
													fillers.
	Anderson	2014	Alumina	Air	20/120 0.4	10/9.	--(5 for axial	No	Yes	Num./	--	• Vessel heat loss is acceptable due to only loss 12% of
	et al. [198]						56	outer tank			Exp.		supplied energy.
								surface)
	Bruch et al.	2014	Silica	Oil	≤ 300	0.27	3/1	250 (for fillers	Yes	Yes	Num./	• Cycling	• No significant inhomogeneity of radial temperature
	[90]		gravel &					and HTF, axial			Exp.	number	distribution.
			silica sand					and radial circle)					• Differed thermocline behavior between multiple cycle and single cycle operation.
													• Impact of metal tank wall on the thermocline moving in
													charging.
	Cascetta et	2015/	Alumina	Air	25/300 0.385	1.8/0	19 (axial equally	Yes	Yes	Num./	• Cycling	• 40% radial temperature profile affected by metal wall heat,
	al.	2016				-	.58	spaced),			Exp.	number	which cannot be predicted by 1D model.
	[148][193]					0.395		5 (radial,					• 60% reduction of stored energy after 4 cycles.
								decreasing
								distance),
								10 (axial outer
								surface)
								5 (circumferential
								outer surface)
	Hoffmann	2016/	Quartzite	Rapese	160/21	0.4	1.8/0	32 (axial and	No	Yes	Num./	• Flow rate	• Higher heat losses and heat diffusion due to low HTF flow
	et al.	2017	rock	ed oil	0		.4	radial equally			Exp.	• Particle size	rate.
	[155][34]							spaced)					• Stronger forced convection due to high HTF flow rate.
													• Maximum discharging efficiency of 75% at an optimal flow
													rate of 0.3 kg s -1 .

Table 4 . 2

 42 Tested SHTPB configurations.

	Configurations	Diameter of	Diffuser	Insulation	𝜺𝜺	Flow	𝑻𝑻 𝑪𝑪 /𝑻𝑻 𝑯𝑯
		the glass sphere 𝑫𝑫 𝒑𝒑	position z1 (mm)	thickness (mm)		rate (L min -1 )	(°C)
		(mm)
	Case 1	7	--	25	0.38	0.3-1.5	20/(50,
							60, 70)
	Case 2	7	--	--	0.38	0.3	20/70
	Case 3	10	--	25	0.39	0.3-1.5	20/(50,
							60, 70)
	Case 4	10	--	--	0.39	0.3	20/70
	Case 5	10	10	25	0.39	1.5	20/(50,
							60, 70)
	Case 6	10	35	25	0.39 (bed	1.5	20/(50,
					region)		60, 70)

Table 4 . 3

 43 Thermophysical properties of different materials used in this study.

		Material	Density ρ	Heat	Thermal	Kinematic
			(kg m -3 )	capacity Cp	conductivity λ	viscosity μ
				(J kg -1 K -1 )	(W m -1 K -1 )	(Pa s)
	Fluid (47.5 °C)	Water	990	4187	0.634	5.8×10 -4
	[178][30]
	Ambient (20 °C, 100	Air	1.17	1004	2.63×10 -2	1.8×10 -5
	kPa)
	Solid media (20 °C)	Soda lime glass	2463	840	1.129	--
	Wall (20 °C)	Transparent	1200	1170	0.200	--
		polycarbonate
	Insulation (20 °C)	Black nitrile	160	1350	0.0412	--
		rubber

  Capacity ratio (𝐶𝐶 𝑟𝑟𝑎𝑎𝑖𝑖𝑖𝑖𝑜𝑜 )[START_REF] Hänchen | High-temperature thermal storage using a packed bed of rocks -Heat transfer analysis and experimental validation[END_REF] [7][START_REF] Roux | Thermocline thermal energy storage optimisation combining exergy and life cycle assessment[END_REF] in charging is the comparison of the actual stored energy and the theoretical maximum stored energy. Theoretically, 𝐶𝐶 𝑟𝑟𝑎𝑎𝑖𝑖𝑖𝑖𝑜𝑜 = 1 refers to fully and 𝐶𝐶 𝑟𝑟𝑎𝑎𝑖𝑖𝑖𝑖𝑜𝑜 < 1 represents partially utilized tank region in charging/discharging, so that better energy utilization ratio means smaller tank volume.Utilization ratio (𝑈𝑈 𝑟𝑟𝑎𝑎𝑖𝑖𝑖𝑖𝑜𝑜 )[START_REF] Li | Optimization of the packed-bed thermal energy storage with cascaded PCM capsules under the constraint of outlet threshold temperature[END_REF] [START_REF] Elfeky | Influence of inlet temperature on the performance of cascade and hybrid storage tank for CSP plants[END_REF] in discharging process.

	𝐶𝐶 𝑟𝑟𝑎𝑎𝑖𝑖𝑖𝑖𝑜𝑜 =	∆𝐸𝐸 𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚 ∆𝐸𝐸 𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚,𝑚𝑚𝑡𝑡𝑒𝑒	=	∆𝐸𝐸 𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚,𝑠𝑠 +∆𝐸𝐸 𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚,𝑠𝑠 ∆𝐸𝐸 𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚,𝑚𝑚𝑡𝑡𝑒𝑒,𝑠𝑠 +∆𝐸𝐸 𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚,𝑚𝑚𝑡𝑡𝑒𝑒,𝑠𝑠	(4.8)
	𝑈𝑈 𝑟𝑟𝑎𝑎𝑖𝑖𝑖𝑖𝑜𝑜 =	∆𝐸𝐸 𝑜𝑜𝑜𝑜𝑡𝑡 -∆𝐸𝐸 𝑖𝑖𝑡𝑡 ∆𝐸𝐸 𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚,𝑚𝑚𝑡𝑡𝑒𝑒	=	∫ 𝑡𝑡 𝑚𝑚𝑖𝑖𝑠𝑠 0 ∆𝐸𝐸 𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚,𝑚𝑚𝑡𝑡𝑒𝑒,𝑠𝑠 +∆𝐸𝐸 𝑠𝑠𝑡𝑡𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚,𝑚𝑚𝑡𝑡𝑒𝑒,𝑠𝑠 �𝑚𝑚̇𝑠𝑠•𝐶𝐶 𝑝𝑝,𝑠𝑠 •(𝑇𝑇 𝑜𝑜𝑜𝑜𝑡𝑡 -𝑇𝑇 𝑖𝑖𝑡𝑡 )�𝑚𝑚𝑖𝑖	(4.9)

Table 4 . 5

 45 The uncertainties of measured and calculated parameters. The standard uncertainty is defined by standard deviation:

	Measured parameters		Uncertainties
	Temperature	𝑑𝑑	± 0.37 K
	Volumetric flow rate	𝑉𝑉 ̇𝑓𝑓	± 1%
	Particle diameter* 1	𝐷𝐷 𝑃𝑃	± 0.1 mm
	Solid density* 1	𝜌𝜌	± 1.6% (40 kg m -3 )
	Thermal conductivity* 1	𝜆𝜆	± 0.001 W m -1 K -1
	Specific heat capacity* 1	𝐶𝐶 𝑝𝑝	± 8 J kg -1 K -1
	Calculated parameters* 2
	Porosity	𝜀𝜀	± 0.004
	Energy efficiency	𝜂𝜂 𝑒𝑒ℎ	± 5%
	Capacity ratio Thermocline thickness	𝐶𝐶 𝑟𝑟𝑎𝑎𝑖𝑖𝑖𝑖𝑜𝑜 𝐿𝐿 𝑖𝑖ℎ𝑒𝑒𝑟𝑟𝑚𝑚𝑜𝑜𝑒𝑒𝑙𝑙𝑖𝑖𝑖𝑖𝑒𝑒 *	± 2% ± 5% (20 mm)
	Assess measurement error:

*1

  [START_REF] Galione | Numerical simulations of thermal energy storage systems with phase change materials. 30th ISES Bienn Sol World Congr[END_REF][65][95][59][180]:

		𝐶𝐶 𝑝𝑝,𝑃𝑃𝐶𝐶𝑃𝑃,𝑠𝑠		,			(𝑑𝑑 < 𝑑𝑑 𝑚𝑚1 )
	𝐶𝐶 𝑝𝑝,𝑃𝑃𝐶𝐶𝑃𝑃 (𝑑𝑑) = � 𝐶𝐶 𝑝𝑝,𝑃𝑃𝐶𝐶𝑃𝑃.𝑠𝑠𝑙𝑙 =	𝐶𝐶 𝑝𝑝,𝑃𝑃𝐶𝐶𝑃𝑃.𝑠𝑠 +𝐶𝐶 𝑝𝑝,𝑃𝑃𝐶𝐶𝑃𝑃.𝑙𝑙 2	+	𝐻𝐻 𝑚𝑚 𝑇𝑇 𝑚𝑚2 -𝑇𝑇 𝑚𝑚1	, (𝑑𝑑 𝑚𝑚1 < 𝑑𝑑 < 𝑑𝑑 𝑚𝑚2 )	(5.1)
		𝐶𝐶 𝑝𝑝,𝑃𝑃𝐶𝐶𝑃𝑃,𝑙𝑙		,			(𝑑𝑑 𝑚𝑚2 < 𝑑𝑑)
		𝜌𝜌 𝑃𝑃𝐶𝐶𝑃𝑃,𝑠𝑠	,				(𝑑𝑑 < 𝑑𝑑 𝑚𝑚1 )
	𝜌𝜌 𝑃𝑃𝐶𝐶𝑃𝑃 (𝑑𝑑) = �	𝜌𝜌 𝑃𝑃𝐶𝐶𝑃𝑃,𝑠𝑠𝑙𝑙 =	𝜌𝜌 𝑃𝑃𝐶𝐶𝑃𝑃,𝑠𝑠 +𝜌𝜌 𝑃𝑃𝐶𝐶𝑃𝑃,𝑙𝑙 2	,	(𝑑𝑑 𝑚𝑚1 < 𝑑𝑑 < 𝑑𝑑 𝑚𝑚2 )	(5.2)
	𝜌𝜌 𝑃𝑃𝐶𝐶𝑃𝑃,𝑙𝑙	,				(𝑑𝑑 𝑚𝑚2 < 𝑑𝑑)
		𝜆𝜆 𝑃𝑃𝐶𝐶𝑃𝑃,𝑠𝑠		,			(𝑑𝑑 < 𝑑𝑑 𝑚𝑚1 )
	𝜆𝜆 𝑃𝑃𝐶𝐶𝑃𝑃 (𝑑𝑑) = � 𝜆𝜆 𝑃𝑃𝐶𝐶𝑃𝑃,𝑠𝑠𝑙𝑙 =	𝜆𝜆 𝑃𝑃𝐶𝐶𝑃𝑃,𝑠𝑠 +𝜆𝜆 𝑃𝑃𝐶𝐶𝑃𝑃,𝑙𝑙 2	,		(𝑑𝑑 𝑚𝑚1 < 𝑑𝑑 < 𝑑𝑑 𝑚𝑚2 )	(5.3)
		𝜆𝜆 𝑃𝑃𝐶𝐶𝑃𝑃,𝑙𝑙		,			(𝑑𝑑 𝑚𝑚2 < 𝑑𝑑)
	𝐻𝐻 𝑚𝑚,𝑃𝑃𝐶𝐶𝑃𝑃 (𝑑𝑑) = 𝐶𝐶 𝑝𝑝,𝑃𝑃𝐶𝐶𝑃𝑃 (𝑑𝑑) • 𝑑𝑑			(5.4)

  ∆𝐸𝐸 𝑠𝑠𝑖𝑖𝑜𝑜𝑟𝑟𝑒𝑒𝑚𝑚,𝑃𝑃𝐶𝐶𝑃𝑃(𝑑𝑑) = 𝑉𝑉 𝑃𝑃𝐶𝐶𝑃𝑃 • � 𝜌𝜌 𝑃𝑃𝐶𝐶𝑃𝑃,.𝑠𝑠 • 𝐶𝐶 𝑝𝑝,𝑃𝑃𝐶𝐶𝑃𝑃,𝑠𝑠 • (𝑑𝑑 -𝑑𝑑 𝐶𝐶 ) , (𝑑𝑑 < 𝑑𝑑 𝑚𝑚1 ) 𝜌𝜌 𝑃𝑃𝐶𝐶𝑃𝑃,𝑠𝑠 • 𝐶𝐶 𝑝𝑝,𝑃𝑃𝐶𝐶𝑃𝑃,𝑠𝑠 • (𝑑𝑑 𝑚𝑚1 -𝑑𝑑 𝐶𝐶 ) + 𝜌𝜌 𝑃𝑃𝐶𝐶𝑃𝑃,𝑠𝑠𝑙𝑙 • 𝐶𝐶 𝑝𝑝,𝑃𝑃𝐶𝐶𝑃𝑃,𝑠𝑠𝑙𝑙 • (𝑑𝑑 -𝑑𝑑 𝑚𝑚1 ), (𝑑𝑑 𝑚𝑚1 < 𝑑𝑑 < 𝑑𝑑 𝑚𝑚2 ) 𝜌𝜌 𝑃𝑃𝐶𝐶𝑃𝑃,𝑠𝑠 • 𝐶𝐶 𝑝𝑝,𝑃𝑃𝐶𝐶𝑃𝑃,𝑠𝑠 • (𝑑𝑑 𝑚𝑚1 -𝑑𝑑 𝐶𝐶 ) + 𝜌𝜌 𝑃𝑃𝐶𝐶𝑃𝑃,𝑠𝑠𝑙𝑙 • 𝐶𝐶 𝑝𝑝,𝑃𝑃𝐶𝐶𝑃𝑃,𝑠𝑠𝑙𝑙 • (𝑑𝑑 𝑚𝑚2 -𝑑𝑑 𝑚𝑚1 ) + 𝜌𝜌 𝑃𝑃𝐶𝐶𝑃𝑃,𝑠𝑠 • 𝐶𝐶 𝑝𝑝,𝑃𝑃𝐶𝐶𝑃𝑃,𝑙𝑙 • (𝑑𝑑 -𝑑𝑑 𝑚𝑚2 ), (𝑑𝑑 𝑚𝑚2 < 𝑑𝑑)

Table 5 . 1

 51 Main parameters for validation of PCM packed-bed TES system. The capsule has a volume of 2.5 ml and surface area of 1.25 mm 2[START_REF] Soto | Thermal cycling aging of encapsulated phase change material -Compressed expanded natural graphite composite[END_REF].

	Terms	Symbols Units	Nallusamy's	Validation cases in LTeN
				experiment [147]	lab [76]
				[60][221][81] [146]
	Tank type	--	--	Stainless-steel	Polycarbonate cylinder
				cylinder tank	tank
	Height of tank	H	m	0.46	0.398
	Internal bed radius	Rint	m	0.18	0.097
	Outer wall radius	Rmid	m	0.185	0.1
	External insulation radius	Rext	m	0.235	0.125
	Volume of tank (*Rint)	--	L	47	11.8
					Upper layer Lower layer
	Fillers	--	--	Paraffin capsule	(1/3, v%):	(2/3, v%):
					Paraffin	Glass sphere
					expanded
					graphite
					capsule
	Porosity	𝜺𝜺	--	0.49	0.59	0.38
	Shape	--	--	Sphere	Cylinder	Sphere
	Capsule characteristic	Lc, or Dp	mm	55	20*	7
	length, or capsule
	diameter
	Capsule shell thickness	--	mm	0.8	0.5	--
	PCM melting temperature	Tm	°C	60±0.1	69±0.5	--
	PCM phase change	ΔHm	J g -1	213	230	--
	enthalpy
	Capsule shell material	--	--	High-density	Aluminium	--
				polyethylene (HDPE)
	Insulation layer	--	--	Glass wool	Bitrile rubber
	HTF	--	--	Water	Water
	Operational temperatures	TC/TH	°C	32/70	20/75
	Flow rate	𝑉𝑉 ̇𝑓𝑓	L min -1 2	0.5

*

Table 5 . 2

 52 Greenhouse application data: the semi-fermée CTIFL-Carquefou system* 1[START_REF] Serres | Bilan énergétique global des besoins et des ressources, prédimensionnement des moyens de production et de stockage[END_REF]. Data collected from 3 rd December 0:00 in 2014 to 1 st November 23:00 in 2015 (334 days). *2 The energy consumption contains the gas heating to keep constant temperature and the extra electrical energy for ventilation which is not discussed here. The selection of maximum data eliminating the abnormal data.

		Output (energy consumption) * 2	Input (energy supply) * 3
		Required gas heating energy, EGH * 2	Solar radiation I
		(22:00-10:00) *6	(10:00-18:00) *6
	Total *5	136 KWh/m²/an (334 days)	967 kWh/m²/an (334 days)
	Maximum* 4 1 KWh/m²/day (12 h)	6 kWh/m²/day (10 h)

*1 *3 The data is collected from outside of greenhouse. *4 *5 Three unit greenhouse units have total surface area around 𝑆𝑆 𝐺𝐺𝐻𝐻 =900 m 2 .

Table 5 . 3

 53 Initial tank parameters and design results for greenhouse application.

	Tank parameters	Symbols	Value
	PCM:paraffin [147]	Tm	60±0.5 °C
		∆𝐻𝐻 𝑚𝑚 𝜌𝜌 𝑃𝑃𝐶𝐶𝑃𝑃,𝑠𝑠 • 𝐶𝐶 𝑝𝑝,𝑃𝑃𝐶𝐶𝑃𝑃,𝑠𝑠	213 J g -1 1.6 × 10 6 J m -3 K -1
		𝜌𝜌 𝑃𝑃𝐶𝐶𝑃𝑃,𝑙𝑙 • 𝐶𝐶 𝑝𝑝,𝑃𝑃𝐶𝐶𝑃𝑃,𝑙𝑙	1.8 × 10 6 J m -3 K -1 ]
	HTF: water	𝜌𝜌 𝑓𝑓 • 𝐶𝐶 𝑝𝑝,𝑓𝑓	4.13 × 10 6 J m -3 K -1
	Porosity	𝜀𝜀	0.5
	Tank aspect ratio	H/Dtank	2
	Particle diameter	𝐷𝐷 𝑝𝑝	50 mm
	Steady working temperature	𝑑𝑑 𝐶𝐶 /𝑑𝑑 𝐻𝐻	20/70 °C
	Cutoff	--	20%
	Assumed discharging energy efficiency 𝜂𝜂 𝑚𝑚𝑖𝑖𝑠𝑠,𝐷𝐷𝐸𝐸𝐷𝐷	0.85
	Assumed overall efficiency	𝜂𝜂 𝑜𝑜,𝐷𝐷𝐸𝐸𝐷𝐷	0.8
	Solar system efficiency	𝜂𝜂 𝑒𝑒𝑜𝑜𝑙𝑙𝑙𝑙𝑒𝑒𝑒𝑒𝑖𝑖𝑜𝑜𝑟𝑟	0.5
	Designed parameter	Symbols	Value
	Tank volume	𝑉𝑉 𝐷𝐷𝐸𝐸𝐷𝐷	16.45 m 3
	Diameter	𝐷𝐷 𝑖𝑖𝑎𝑎𝑖𝑖𝑡𝑡	2.19 m
	Charging time	𝑡𝑡 𝑒𝑒ℎ	8 h
	Discharging time	𝑡𝑡 𝑚𝑚𝑖𝑖𝑠𝑠	12 h
	Charging mass flow rate	𝑚𝑚̇𝑓𝑓 ,𝑒𝑒ℎ	0.673 kg s -1 (40.78 L min -1 , Re=15)
	Discharging mass flow rate	𝑚𝑚̇𝑓𝑓 ,𝑚𝑚𝑖𝑖𝑠𝑠	0.422 kg s -1 (25.59 L min -1 , Re=10)

Table 5 . 4

 54 Variables and objective functions definition of the multi-objective genetic algorithm (MOGA) optimization. Liquid and solid phase thermal conductivity are assumed as the same for PCM.

	Design variables	Symbols	Contraints Actual value
	PCM layer thickness *1 PCM phase change temperature	𝐿𝐿 𝑖𝑖 * = 𝑑𝑑 𝑚𝑚,𝑖𝑖 𝐿𝐿 𝑖𝑖 𝐻𝐻 * = , ∑ 𝐿𝐿 𝑖𝑖 * = 1 𝑇𝑇 𝑚𝑚,𝑖𝑖 -T 𝑐𝑐 𝑇𝑇 𝐻𝐻 -𝑇𝑇 𝑐𝑐	[0.1 0.9] [0.2 0.8]	--𝑑𝑑 𝑚𝑚,𝑖𝑖 ∈ [𝑑𝑑 20% 𝑑𝑑 80% ] *5
	PCM thermal conductivity *2	𝜆𝜆 𝑃𝑃𝐶𝐶𝑃𝑃,𝑖𝑖 *	=	𝜆𝜆 𝑃𝑃𝐶𝐶𝑃𝑃,𝑖𝑖 -𝜆𝜆 𝑃𝑃𝐶𝐶𝑃𝑃 (𝑚𝑚𝑖𝑖𝑖𝑖) 𝜆𝜆 𝑃𝑃𝐶𝐶𝑃𝑃 (𝑚𝑚𝑎𝑎𝑒𝑒)-𝜆𝜆 𝑃𝑃𝐶𝐶𝑃𝑃 (𝑚𝑚𝑖𝑖𝑖𝑖)	[0 1]	𝜆𝜆 𝑃𝑃𝐶𝐶𝑃𝑃 ∈ [0.2 20]
	Mass flow rate in charging *3	𝑚𝑚̇𝑓𝑓 ,𝑒𝑒ℎ *	=	𝑚𝑚̇𝑠𝑠 ,𝑐𝑐ℎ (𝑚𝑚𝑎𝑎𝑒𝑒)-𝑚𝑚̇𝑠𝑠 ,𝑐𝑐ℎ (𝑚𝑚𝑖𝑖𝑖𝑖) 𝑚𝑚̇𝑠𝑠-𝑚𝑚̇𝑠𝑠 ,𝑐𝑐ℎ (𝑚𝑚𝑖𝑖𝑖𝑖)	[0 1]	𝑚𝑚̇𝑓𝑓 ,𝑒𝑒ℎ ∈ [0.673 1.65]
	Mass flow rate in discharging *3	𝑚𝑚̇𝑓𝑓 ,𝑚𝑚𝑖𝑖𝑠𝑠 *	=	𝑚𝑚̇𝑠𝑠-𝑚𝑚̇𝑠𝑠 ,𝑚𝑚𝑖𝑖𝑠𝑠 (𝑚𝑚𝑖𝑖𝑖𝑖) 𝑚𝑚̇𝑠𝑠 ,𝑚𝑚𝑖𝑖𝑠𝑠 (𝑚𝑚𝑎𝑎𝑒𝑒)-𝑚𝑚̇𝑠𝑠 ,𝑚𝑚𝑖𝑖𝑠𝑠 (𝑚𝑚𝑖𝑖𝑖𝑖)	[0 1]	𝑚𝑚̇𝑓𝑓 ,𝑚𝑚𝑖𝑖𝑠𝑠 *	∈[0.422 1.65]
	Indicators	Objective functions *4	--	--
	Overall energy efficiency	𝐹𝐹 1 =max [𝜂𝜂 𝑜𝑜 = 𝜂𝜂 𝑒𝑒ℎ • 𝜂𝜂 𝑚𝑚𝑖𝑖𝑠𝑠 ]	--	--
	Overall storage/utilization	𝐹𝐹 2 = max [γo=(Uratio+Cratio)/2]	--	--
	ratio
	*1 i is the packing layer number.

*2 *3 The Re of mass flow rate in charging/discharging are all within validation ranges of [15 40].

*4 Performance indictors has been defined in Chapter 4 of Section 4.2. *5 x% =20% or 80% means the phase change temperature 𝑑𝑑 𝑚𝑚 is equal to x%•(𝑑𝑑 𝐻𝐻 -𝑑𝑑 𝐶𝐶 ).

Table 5 . 5

 55 Evaluation index of thermal performance.

	Configura	Layers		Tank	Varia	Variables
	tions			type	ble
				s	num
					bers
		Upper *2 lower *2			𝐿𝐿 𝑜𝑜𝑝𝑝 *	𝑑𝑑 𝑚𝑚,𝑜𝑜𝑝𝑝 *	𝑑𝑑 𝑚𝑚,𝑙𝑙𝑜𝑜𝑤𝑤 *	𝜆𝜆 𝑃𝑃𝐶𝐶𝑃𝑃,𝑜𝑜𝑝𝑝 *	𝜆𝜆 𝑃𝑃𝐶𝐶𝑃𝑃,𝑙𝑙𝑜𝑜𝑤𝑤 *	𝑚𝑚̇𝑓𝑓 ,𝑒𝑒ℎ *	𝑚𝑚̇𝑓𝑓 ,𝑚𝑚𝑖𝑖𝑠𝑠 *
	Design	PCMx%	PCMx%	LLTP	7	√ √	√	√	√	√	√
	A+			B
	Design A	PCM80%	PCM20%	LHTP	5	√ --	--	√	√	√	√
				B
	Design	PCMx%	Sensible HLTP	5	√ √	--	√	--	√	√
	B+			B
	Design B	PCM80%	Sensible HHT	4	√ --	--	√	--	√	√
				PB
	*1 i is the layer number, 'up'=upper layer, 'low'=lower layer.

*2 x% means the PCM phase change temperature 𝑑𝑑 𝑚𝑚 is equal to x%•(𝑑𝑑 𝐻𝐻 -𝑑𝑑 𝐶𝐶 ).

Table 5 . 6

 56 Selected special optimal results and designed variables from Pareto front of Design A+.

	Optimizatio	Overall	Charging	Dischargin	Operationa	Geometrical parameters
	n						g		l
									parameter
									s
		Unit (-)	𝜼𝜼 𝒓𝒓	𝜰𝜰 𝒓𝒓	𝜂𝜂 𝑒𝑒ℎ	Cratio	𝜂𝜂 𝑚𝑚𝑖𝑖𝑠𝑠	Uratio	𝑚𝑚̇𝑓𝑓 ,𝑒𝑒ℎ *	𝑚𝑚̇𝑓𝑓 ,𝑚𝑚𝑖𝑖𝑠𝑠 *	𝐿𝐿 𝑚𝑚,𝑜𝑜𝑝𝑝 *	𝑑𝑑 𝑚𝑚,𝑜𝑜𝑝𝑝 *	𝑑𝑑 𝑚𝑚,𝑙𝑙𝑜𝑜𝑤𝑤 *	𝜆𝜆 𝑃𝑃𝐶𝐶𝑃𝑃,𝑜𝑜𝑝𝑝 *	𝜆𝜆 𝑃𝑃𝐶𝐶𝑃𝑃,𝑙𝑙𝑜𝑜𝑤𝑤 *
	De	Max 𝜂𝜂 𝑜𝑜	0.88	0.98	0.91	0.99	0.97 0.96	0.19	0.34	0.50	0.35	0.20	0.73	0.64
	sig	Max 𝛶𝛶 𝑜𝑜	0.74	0.98	0.76	0.99	0.97 0.97	0.19	0.26	0.53	0.39	0.49	0.69	0.83
	n A+	Tradeoff	0.82	0.98	0.84	0.99	0.97 0.97	0.18	0.27	0.56	0.38	0.32	0.73	0.79

Table 5 . 7

 57 Selected special optimal results and designed variables from Pareto front of Design B+.

		Optimizati	Overall		Charging	Discharging	Operational	Geometrical
		on							parameters	parameters
		Unit (-)	𝜂𝜂 𝑜𝑜	𝛶𝛶 𝑜𝑜	𝜂𝜂 𝑒𝑒ℎ	Cratio	𝜂𝜂 𝑚𝑚𝑖𝑖𝑠𝑠	Uratio	𝑚𝑚̇𝑓𝑓 ,𝑒𝑒ℎ *	𝑚𝑚̇𝑓𝑓 ,𝑚𝑚𝑖𝑖𝑠𝑠 *	𝐿𝐿 𝑚𝑚,𝑜𝑜𝑝𝑝 *	𝑑𝑑 𝑚𝑚,𝑜𝑜𝑝𝑝 *	𝜆𝜆 𝑃𝑃𝐶𝐶𝑃𝑃,𝑜𝑜𝑝𝑝 *
	Desig	Max 𝜂𝜂 𝑜𝑜	0.86 0.96 0.88	0.97 0.97	0.95	0.25	0.13	0.15	0.26 0.47
	n B+	Maxi 𝛶𝛶 𝑜𝑜	0.79 0.98 0.81	0.99 0.98	0.97	0.15	0.29	0.90	0.38 0.73
		Tradeoff	0.84 0.98 0.87	0.99 0.97	0.97	0.16	0.30	0.90	0.28 0.72

Table 5 .

 5

	Configuration	𝑳𝑳 𝒖𝒖𝒑𝒑 *	𝑳𝑳 𝒍𝒍𝒓𝒓𝒍𝒍 *	𝑻𝑻 𝒎𝒎,𝒖𝒖𝒑𝒑 *	𝑻𝑻 𝒎𝒎,𝒍𝒍𝒓𝒓𝒍𝒍 *	𝝀𝝀 𝒇𝒇𝑪𝑪𝒇𝒇,𝒖𝒖𝒑𝒑 *	𝝀𝝀 𝒇𝒇𝑪𝑪𝒇𝒇,𝒍𝒍𝒓𝒓𝒍𝒍 *
	Ref. PCM80%-	0.50	0.5	0.80	0.20	<0.1	<0.1
	PCM20%
	Design A	0.15	0.75	0.80	0.20	0.45	0.72
	Design A+	0.50	0.5	0.35	0.20	0.73	0.63
	Design B	0.1	0.9	0.8	--	0.24	--
	Design B+	0.15	0.75	0.26	--	0.47	--

[START_REF] Lou | Optimized flow distributor for stabilized thermal stratification in a single-medium thermocline storage tank: A numerical and experimental study[END_REF]

Maximizing overall energy efficiency optimal variables of four design cases and a reference case.

Table 5 . 9

 59 KPIs results for dynamic input of inlet temperature based on MOGA results.

	Configuration	KPIs	Steady condition	Dynamic condition
				Jan.	Apr.	Jul.	Dec.
	ROCK tank	𝜂𝜂ch	0.89	0.38	0.48	0.80	0.49
		Cratio	0.97	0.13	0.46	1.00*	0.63
	Design A+	𝜂𝜂ch	0.91	0.48	0.76	0.90	0.87
		Cratio	0.99	0.11	0.47	1.00*	0.71

Acknowledgements 1 THESE DE DOCTORAT DE NANTES UNIVERSITE Acknowledgements I Acknowledgments Thesis work is certainly an individual work, but it cannot be fruition without the corporation and assistance of groups. I would like to thank to people in this group that support me to construct this 'building'. First of all, I have greatly appreciated my supervisor -Prof. Lingai LUO, for her everlasting guidance during my three-year study. Her knowledge, motivation and numerous advices are of importance to my thesis work and to my future work. I am also deepest grateful to my co-supervisor -Dr. Nicolas BAUDIN, having accompanied me from the beginning of this thesis. His constant encourage inspires when I depressed and his instruction give me direction on solving troubles in thesis. I would like to give thanks to my co-supervisor -Dr. Jeŕôme SOTO, for guiding me and enriching me with his individual expertise. His profound knowledge and patience facilitated the realization of this thesis.

At last, greatly thankful to the Chinese Scholarship Council for funding me (No.

The measurement uncertainty of average temperature is around 0.15 K and integration uncertainty is below than that. From the uncertainties of center (C), middle (B), and outer (A) position, the middle and outer position thermocouples has higher error than the center position due to the less thermocouples numbers. In the beginning, the relative uncertainty of stored energy is larger because less hot water enters the tank. When it becomes stable, the relative uncertainty is around 1%. Chapter 5

Optimization of thermocline packed-bed system with PCM fillers for greenhouse application

Abstract

This chapter aims the optimization of a thermocline packed-bed storage tank for a given greenhouse application through a multi-layer and multi-material configuration. This system is able to solve the problems of the low utilization and lower efficiency of conventional uniform layer packing tank. Phase change material (PCM) is used to improve efficiency of storage.

The objective of this chapter are as below:

• Validate the model for PCM through a lab-scale multi-layered latent-sensible heat storage tank experimental data.

• Design an initial TES tank on the meteorology and heating consumption data of a greenhouse in Carquefou, France.

• Propose a methodology for designing a given tank through multi-objective genetic algorithm (MOGA) optimization in multiple cycles.

• Propose a solution to stabilize inlet temperature and low utilization of system in multiple cycles.

• Compare steady and seasonal operation in the application for the greenhouse in different utilization scenario to find shortcomings for improving future work. Then, various influences, including the inlet configuration, the insulation, the filler size, and the operating parameters, on the thermocline in radial and axial direction based on a basic sensible heat filler tank are investigated. After that, the multi-layered configuration optimization of phase change material storage tank using a multi-objective genetic algorithm in multiple cycling is carried out by integrating the tank into an agriculture greenhouse application. The thermal performance of optimal tanks in seasonal operations is studied to find the potential for improvement of future work.

Keywords