Obeida Farhat

Mahmoud Khaled

Jalal Faraj

Farouk Hachem

Rani Taher

Cathy Castelain

Peer-review under responsibility of the European Academy for Sustainable Development (EURACA

Keywords: Short Recent, Review, Waste Heat Recovery, Hybrid Energy Systems, Renewable Energy, Critical Analysis, Recommendations

Currently, the world is perceiving a change-over from its existing conventional energy sources to a future with optimized and inventive energy sources. Nowadays, the world is more and more oriented to the use of renewable energy sources to decrease the consumption form the conventional energy sources in particular the fuel energy. In addition, the use of renewable energy source decrease the impact of the conventional energy on the environment. For all these reasons, researchers are currently focusing on studies that implement and innovate methods for the purpose of optimizing and increasing the efficiency of existing renewable energy sources. Of the proposed methods are the hybrid systems. These systems are applicable in both residential and industrial sectors. However, hybrid systems can be applied to renewable energy, wind energy, fuel cell, Desalination, Heating, Ventilating, and Air Conditioning, Engines, Electric Vehicles, Heat Pump, Redrying, PV cells, Engines, Solar Cells, and many other systems. In this context, the aim of the present paper is to provide a short recent review focusing on the types and applications of hybrid renewable energy systems and hybrid recovery energy systems that are applied in industrial and residential sectors. Moreover, the environmental impact, cost and the efficiency will also be presented and discussed.

Introduction

In a global attempt to keep in pace with the needs of industrial evolution accompanied with global population growth, both leading to more human dependency on energy, the world's attitude is optimizing and resourcing all types of energy resources [START_REF]Energy systems in transition: Challenges and opportunities[END_REF]. Researchers estimation at 2010, assume that the energy demand will reach a 35% increase by 25 years [START_REF] Saghafifar | A review of unconventional bottoming cycles for waste heat recovery: Part I -Analysis, design, and optimization[END_REF]. The main reasons of the rise in demand of energy are the enormous industrial growth, and the depletion of fuel energy resources [START_REF] Ramadan | Recovering heat from hot drain water-Experimental evaluation, parametric analysis and new calculation procedure[END_REF]. Moreover, multiple reports showed the considerable rate of growth in world's energy demand due to an increase in the population [START_REF] Mahmoudi | A recent review of waste heat recovery by Organic Rankine Cycle[END_REF]. At least 50% of the applied energy is wasted in transportation, power generation, factories, housing sectors and many other activities [START_REF] Nithyanandam | Evaluation of metal foam based thermoelectric generators for automobile waste heat recovery[END_REF]. Efficiency and greenhouse gas emissions (GHG) enhancement are considered as great challenges concerning global warming in engineering industries [START_REF] Khordehgah | Waste heat recovery technologies and applications[END_REF]. Thus, novel technologies for improving energy efficiency are urgently required to save energy and reduce emissions [START_REF] Ouyang | Design and modeling of marine diesel engine multistage waste heat recovery system integrated with flue-gas desulfurization[END_REF]. Hence, to save energy and condense emissions, innovative mechanisms for enhancing energy efficiency are instantly required [START_REF] Ouyang | Design and modeling of marine diesel engine multistage waste heat recovery system integrated with flue-gas desulfurization[END_REF]. On the other hand, energy production and fuel consumption are developed perfectly by increasing efforts on renewable energy and energy management [START_REF] Khaled | Parametric Analysis of Heat Recovery from Exhaust Gases of Generators[END_REF]. For all these reasons, the present article is concerned with focusing on the types and applications of hybrid renewable energy systems and hybrid recovery energy systems that are applied in industrial and residential sectors. This review summarizes studies on Hybrid Energy Systems in four main sections including introduction. Section 2 deals with the types of hybrid systems. Section 3 deals with critical analysis and recommendations, and finally section 4 draws the main conclusions of the work.

The novelty of this short review paper resides in:

1. Classifying hybrid energy systems into hybrid renewable energy systems and hybrid heat recovery systems; 2. Reviewing studies concerning hybrid systems and their applications in real life; 3. Reviewing comparatively the different types of hybrid systems, advantages and disadvantages and corresponding effects on the efficiency of hybrid systems.

Nomenclature

GHG

Hybrid Energy Systems

Researchers are searching for novel ways reprocess the high amount of thermal energy being lost through exhaust gases [START_REF] Ramadan | Effect of Exhaust Gases Temperature on the Performance of a Hybrid Heat Recovery System[END_REF]. Unfortunately, these methods capability of increasing efficiency and recovering heat is limited. This limitation obligates urgently combining methods in hybrid form to reach better efficiency. However, with lowering cost of renewable energy systems, small sectors, especially housings, can now benefit from renewable energy technologies to produce electricity. Yet, many efforts should be done on the development of renewable energy and storage technologies in order to achieve promising results [START_REF] Cuesta | A critical analysis on hybrid renewable energy modeling tools: An emerging opportunity to include social indicators to optimise systems in small communities[END_REF]. By definition, a mechanism which combines multiple energy sources to give a corresponding energy output is called: Hybrid energy system (HES). Nevertheless, many factors are considered as challenges to HES. Environmental effect of exhausts in energy systems , high energy consumption, and amplified expenses are instances for these factors [START_REF] Maghami | Hybrid energy management with respect to a hydrogen energy system and demand response[END_REF]. HESs can be divided into two major types: Hybrid Renewable Energy Systems (HRES) and Hybrid Heat Recovery Systems (HHRS). These systems along with their main recent studies will be exposed in the following subsections.

Hybrid Renewable Energy Systems

Currently, coupled with government and community support, renewable energy resources (RES) play a substantial role as a choice to meet industrial demands for power generation [START_REF] Nguyen | Multi-objective decision-making and optimal sizing of a hybrid renewable energy system to meet the dynamic energy demands of a wastewater treatment plant[END_REF]. Countries over the world depend on fossil fuels for energy generation. Yet, the perpetual reduction of fossil fuel and its environmental effects become a great alarm on economic growth in these countries. Renewable energy sources are now a necessity for the world as a substitute source of energy [START_REF] Salisu | Assessment of technical and economic feasibility for a hybrid PVwind-diesel-battery energy system in a remote community of north central Nigeria[END_REF]. Universally, there are many zones with both high geothermal heat flux and surface radiation, which makes incorporation of geothermal and solar energies conceivable. Usually, geothermal industries tend to target resources with high temperatures. Yet, most of geothermal resources can be used for moderate temperatures (less than 150 ℃). On the contrary, solar systems is incapable of feeding peak power demand during night hours, opposite to its performance during daylight hours. Thus, when combining both systems, geothermal fluids could be used as storage systems for excess of solar energy, while solar systems could be used to rise the temperature of geothermal fluids, therefore refining the efficiency of geothermal power generation. This combination is named as Hybrid Renewable Energy systems (HRES) [START_REF] Singh | Capacity optimization of grid connected solar/fuel cell energy system using hybrid ABC-PSO algorithm[END_REF]. Figure 1 shows main sources of HRE systems. On the other hand, certainly, global current work in energy market is on gradual change from conventional systems based on coal and natural gas to systems based on renewable energy sources, including existing solar energy and wind energy which lack continuity throughout the year. However, energy storage systems will be a requisite element of the energy systems of the future [START_REF] Bartela | A hybrid energy storage system using compressed air and hydrogen as the energy carrier[END_REF]. Else ways, energy storages present several superiorities such as power quality enhancement, lessening from the intermittency of renewable sources, enabling regulations in microgrid (MG) operation and balancing generation and demand. Hybrid energy storage systems (HESSs) specified by coupling two or more types of energy storage systems are developed as a solution to attain the desired performance [START_REF] Hajiaghasi | Hybrid energy storage system for microgrids applications: A review[END_REF]. Figure 2 shows different applications of HRESs. In electrical power system, HRESs based on power generation has arisen as a major revolution because of their ability of providing inexpensive and carbon free electricity to the customers [START_REF] Singh | Capacity optimization of grid connected solar/fuel cell energy system using hybrid ABC-PSO algorithm[END_REF]. For instance, a study using various types of biomass gasifiers in an off-grid renewable hybrid system composed of photovoltaic energy, hydrokinetic turbines and batteries, shows that the change of the cost in the apparatuses impacts the total cost of the system. However, the photovoltaic and fuel system have the highest sensitivity among other systems [START_REF] Cano | Energy analysis and techno-economic assessment of a hybrid PV/HKT/BAT system using biomass gasifier: Cuenca-Ecuador case study[END_REF]. In addition, a hybrid-energy system proposed on a steam-turbine power plant, allows applying variety of conventional sources (electricity, natural gas or coal) and RES (geothermal and solar heat, and/or waste biomass). This study shows that with waste biomass, gross power can be entirely derived from renewable sources, while with fossil fuel up to 35% can be derived from renewable sources [START_REF] Buscheck | Hybrid-energy approach enabled by heat storage and oxy-combustion to generate electricity with near-zero or negative CO2 emissions[END_REF]. Table 1 shows a summary for some recent HRES applications, technologies used and corresponding key results.

Table 1. Summary for some recent HRES applications.

Reference Main Objective Technology used Key Results

Improvement & Savings [START_REF] Khawaja | An integrated framework for sizing and energy management of hybrid energy systems using finite automata[END_REF] Sizing and energy management of hybrid energy systems using finite automata.

Solar system.

-80 kW reduction in size of PV -50% reduction in the size of Electrolyze and the hydrogen tank -35% decrease in the diesel generator working hours.

Energy & Economy [START_REF] Salisu | Assessment of technical and economic feasibility for a hybrid PVwind-diesel-battery energy system in a remote community of north central Nigeria[END_REF] Analysis of the effectiveness of a hybrid PV-wind-diesel-battery energy system applied in a remote community. Environment & Economy [START_REF] Singh | Capacity optimization of grid connected solar/fuel cell energy system using hybrid ABC-PSO algorithm[END_REF] Capacity optimization of grid connected solar/fuel cell energy system using hybrid ABC-PSO algorithm.

Solar-fuel cell.

-Total electricity demand could be met with a:

-106 kW solar photovoltaic; -8kW fuel cell; -45 kW electrolyze; -150 kg of hydrogen tank; -Levelized cost of energy of 0.104 $=kWh. Energy [START_REF] Manrique | Energy analysis of a proposed hybrid solar-biomass coffee bean drying system[END_REF] Studying of a hybrid solar-biomass coffee bean drying system. Solar-biomass system.

-80% reduction in operation cost. Economy [START_REF] Suresh | Modelling and optimization of an off-grid hybrid renewable energy system for electrification in a rural areas[END_REF] Proposing and enhancing a Hybrid PV-Wind Turbine-Pumped Hydro Storage Energy System in Coastline Communities.

Solar, wind turbine and Pumped Hydro Energy Storage systems.

-The minimum storage capacity of the system: 3930615 kWh;

-Levelized Cost of Energy 0.27 $/kWh; Energy [START_REF] Das | Optimal sizing of a stand-alone hybrid system for electric and thermal loads using excess energy and waste heat[END_REF] Optimum sizing of a hybrid system for electric and thermal loads using excess energy and waste heat.

Solar, wind turbine, Micro Gas Turbine and Li-ion battery.

-40% Drop in CO2 emissions -33% rise in renewable energy system fraction Environment [START_REF] Taghizadeh | Optimal thermal and electrical operation of the hybrid energy system using interval optimization approach[END_REF] Optimizing hybrid energy system to provide thermal and electrical operation.

Solar, fuel cell and battery system.

-5.52% lessening in total increase of operation cost with demand response program.

-13.28% lessening in Cost deviation with demand response program.

Economy [START_REF] Murugaperumal | Optimum design of hybrid renewable energy system through load forecasting and different operating strategies for rural electrification[END_REF] Proposing and estimating different working approaches for rural electrification using a hybrid renewable energy system Solar, wind turbine and bio generators system.

-Percentages of generated power:

-solar power: 86.8%

-wind power: 12.7% Not specified -bio generators power: 0.5%.

Losses: 6.8% battery bank losses. And 1.78% converter losses.

[25]

Economic and technical study of a heat and power combination system based on hybrid photovoltaic-fuel cell systems Solar system, fuel cell and thermal system.

-The net present cost of the optimized system is $1,006,293;

-The cost of energy $0.8399/kWh; -The system is not economically viable at present; it is technically possible.

Energy [START_REF] Kim | Techno-economic analysis of hybrid renewable energy system with solar district heating for net zero energy community[END_REF] Study of hybrid renewable energy system with solar heating for net zero energy community.

Solar system, Thermal energy and heat pump -Payback period: 6-year.

-Benefit-cost ratio: 1.7.

Economy [START_REF] Das | Techno-economic optimization of an off-grid hybrid renewable energy system using metaheuristic optimization approaches -Case of a radio transmitter station in India[END_REF] Economic and technical enhancement of an off-grid hybrid renewable energy system using metaheuristic optimization approaches -Case of a radio transmitter station in India. -cost is lower than conventional systems: 0.028 USD/kWh.

Energy & Economy [29]

A hybrid renewable energy system for water desalination using reverse osmosis: A review.

Replacement of fossil fuel with renewable

Economy (33)

A hybrid system of HHO generator-TEG waste heat recovery for CO reduction of a gasoline engine

Waste heat recovery on powering the HHO unit

For the case study: -Energy provided between 91 kJ and 169 kJ -Energy consumption of the HHO generator: 22.5 kJ.

Energy [30]

A hybrid system using direct contact membrane distillation for water production to harvest waste heat from the proton exchange membrane fuel cell. proton exchange membrane fuel cell and direct contact membrane distillation.

Compared with the single PEMFC system, as operating temperature varies from 328.15K to 348.15K, the energy utilization degree can be increased by 201%-266%. Energy [START_REF] Li | Sustainable and reliable design of reverse osmosis desalination with hybrid renewable energy systems through supply chain forecasting using recurrent neural networks[END_REF] Designing a desalination with Solar, wind and -HRES with optimized Energy hybrid renewable energy systems using persistent neural systems.

reverse osmosis systems.

installation contains: 111 photovoltaic panels and 5 wind turbines The designed system reduced potential loss of power supply probability by 18.3% compared with the base case.

HRES systems applications summary shows high dependency on PV cells. Solar systems play a significant role in most of the HRESs. However, these systems are more applicable on large industrial sectors. This combination can happen by adding wind power, biomass, bio generators, hydrogen systems and many other systems. Optimization attempts on reducing GHG, reducing the size of PV, reducing CO2 emissions, increasing RES fraction and lessening generators working hours. These attempts aim for reducing size and cost, increasing efficiency, and reducing GHG. Thus, savings are revolved around economic, environmental and energy. However, challenges for HRES systems are summarized in Figure 3.

Hybrid Heat Recovery Systems

Due to population and industrial growth globally, pollutants of transportation division present a main source of pollution. Yet, 80% of Carbon and 90% of Nitric oxide are contributed by this division. Currently, Battery electric vehicles are used as an option to decrease environmental pollution. Yet, the driving range and battery lifespan are still a great challenge due to its large-scale commercialization [START_REF] Yang | Investigation of integrated uninterrupted dual input transmission and hybrid energy storage system for electric vehicles[END_REF]. However, conventional ICE has only 30-40% efficiency. Most of the lost energy is in the form of exhaust heat, where some can be recovered by Thermoelectric generators, thus reducing CO2 emissions and fuel consumption [START_REF] Muralidhar | Modeling of a hybrid electric heavy duty vehicle to assess energy recovery using a thermoelectric generator[END_REF]. Hybrid power gas engine heat pump (HPGHP) is an innovative air conditioning system that uses a power battery as an secondary power source to attain efficient engine functioning [START_REF] Chen | Experimental research and energy consumption analysis on the economic performance of a hybrid-power gas engine heat pump with LiFePO4 battery[END_REF]. On the other hand, environmental calamity necessitates using cleaner energy sources for many sectors. Hydrogen is used for transportation as a main or secondary source of energy (fuel) in vehicles. It is the conversion of the automotive industry from petrol and diesel into a sustainable fuel [START_REF] Salek | Novel hybrid system of pulsed HHO generator/TEG waste heat recovery for CO reduction of a gasoline engine[END_REF]. Figure 4 shows different applications of HHRSs. However, Figure 5 shows the main challenges which face HHRS systems globally. Due to the depletion of fossil fuels and serious pollution emissions, hybrid electric vehicles (HEVs) are gradually replacing internal combustion engines (ICE) vehicles as people's walking tools [START_REF] Lü | Energy management of hybrid electric vehicles: A review of energy optimization of fuel cell hybrid power system based on genetic algorithm[END_REF]- [START_REF] Nader | Brayton cycles as waste heat recovery systems on series hybrid electric vehicles[END_REF]. A super capacitor-based HESS is wild becoming the automotive industry trend. However, many attempts of integrating multi-speed transmission in HEVs are applied to enhance electric machine efficiency [START_REF] Muralidhar | Modeling of a hybrid electric heavy duty vehicle to assess energy recovery using a thermoelectric generator[END_REF], [START_REF] Ruan | The application of hybrid energy storage system with electrified continuously variable transmission in battery electric vehicle[END_REF]. Figure 6 shows some advantages of HEV. Though researches on HEVs present many advantages, more researches should be done on these systems in order to achieve higher efficiency of the engine, longer life span, cheaper maintenance and better green systems. On the other hand, absorption-compression heat pump is an efficient system for recovering low-temperature waste heat leading to the enhancement of efficiency in industrial sector [START_REF] Liu | A high-temperature hybrid absorption-compression heat pump for waste heat recovery[END_REF], [START_REF] Wu | A novel internally hybrid absorption-compression heat pump for performance improvement[END_REF]. Table 2 shows applications on HHRSs further remarkable outcomes. Proton exchange membrane fuel cell integrated with a hybrid-energy heat pump.

-Supply temperatures of 10 •C for cooling.

-Supply temperatures of 40-60 •C for heating.

-Maximum power density of 4.341 kW/m2 in cooling mode; -Maximum power density of 5.357 kW/m2 in heating mode; [START_REF] Farshi | Thermoeconomic analysis of a new ejector boosted hybrid heat pump (EBHP) and comparison with three conventional types of heat pumps[END_REF] Novel ejector boosted hybrid heat pump. Not specified.

-Unit product cost of heat pumps increase is linked with two factors: Increasing the pinch point temperature difference Reducing the weak solution concentration.

[47] Hybrid heat recovery system based on vapor compression refrigeration and liquid desiccant dehumidification -60 °C return water temperature liquid-gas mass flow rate ratio of 3.2-3.4 -boiler heating capacity: 7 MW -Thermal efficiency of a boiler can be increased from 90% to 104% -R134a as a refrigerant.

-White smoke can be avoided.

[48] hybrid absorptioncompression heat pump.

-High-temperature saturated steam production (> 130 °C) -160 °C supplied heat temperature -Better choice for the hybrid system in actual application: Ammonia-rich solution mass fraction <0.6 circulation >0.7 is a

Analysis show that sensible heat of flue gas and supply temperatures are the main boundary conditions to be specified in most of the research studies in heat pump. Nevertheless, remarkable outcomes can be summarized by: increasing payback period, increasing coefficient of performance (COP), and decreasing exhaust flue gas temperatures [START_REF] Liu | A high-temperature hybrid absorption-compression heat pump for waste heat recovery[END_REF], [START_REF] Farshi | Thermoeconomic analysis of a new ejector boosted hybrid heat pump (EBHP) and comparison with three conventional types of heat pumps[END_REF], [START_REF] Liu | Working domains of a hybrid absorption-compression heat pump for industrial applications[END_REF]. However, some studies on HHRS based on vapor compression refrigeration and liquid desiccant dehumidification (HVAC)f are reviewed [START_REF] Yang | Theoretical performance analysis of a new hybrid air conditioning system with two-stage energy recovery in cold winter[END_REF], [START_REF] Cui | Experimental study and energy saving potential analysis of a hybrid air treatment cooling system in tropical climates[END_REF], [START_REF] Zhang | A hybrid flue gas heat recovery system based on vapor compression refrigeration and liquid desiccant dehumidification[END_REF], main outcomes are presented in Figure 7.

Critical analysis and recommendations

In line with the worldwide fears for increased GHG emissions, the industrial market tends to shift towards more environmentally methods to meet strict emission standards. However, future energy generation will be depending strictly on renewable energy sources due to the rapid reduction of conventional sources of energy. Moreover, HRESs drawbacks are being marginalized by many researchers, and it is not capable of eliminating the need for conventional sources of energy. Then, after analyzing studies on HRSs with its types and applications, it is recommended to:

• Focus on decreasing the cost of HRESs to meet the commercial market capacity.

• Enhance the efficiency of HRESs by optimizing these systems.

• Increase efforts HRESs to become more mature and applicable in daily life residential and industrial needs, which in return will decrease the demand on fossil fuels, and thus the HHRSs.

• Emphasize on HHRSs applications in industrial sectors.

• Approach studies to focus on enhancing HHRSs, thus decreasing the cost of these systems which will meet the market needs, and therefore reducing the usage of fossil fuels. • Apply multiple HHRSs on the same application, to recover the exhaust after previous recovery.

• Study coupling HHRSs with HRESs to meet highest efficiencies, with best environmental and economic results. • Facilitate legal transactions in countries that set restrictions on HRESs • Work on combining HRES and HHRS which will profit promising results.

Conclusions

present manuscript concerned a short recent review on hybrid renewable and heat recovery systems in residential and industrial applications. Based on the literature presented, studies show that renewable energy systems became a necessity due to the decay of non-renewable sources. However, Hybrid energy systems are classified into Hybrid Renewable Energy Systems HRESs and Hybrid Heat Recovery Systems HHRSs. For HRESs, the main sources of energy are: solar, biomass, wind and geothermal energy, while the main challenges are: sustainability, social criteria, environmental and economic factor. On the other hand, for HHRSs, studies show that HVAC systems optimization focuses on increasing payback period, increasing COP, and decreasing exhaust flue gas temperatures. Nevertheless, the enhancement of HEV should work on attaining higher efficiency of the engine, longer life span, cheaper maintenance and better green systems. Moreover, the sensible heat of flue gas and supply temperatures are the main boundary conditions to be specified in most of the research studies in heat pump. Finally, HHRS and HRES combination presents the largest promising challenge for future work.

Fig. 1

 1 Fig. 1 Main Sources of HRE Systems

Fig. 2 .

 2 Fig. 2. Applications of HRESs.

-

  Cost of energy: 0.110$/kWh; -Present cost: 1.01$; -Operating cost: 4723$; -Renewable fraction: 98.3%; -Greenhouse gas emission: 2889.36 kg/year;

- 2 - 28 ]

 228 Panel area of solar photovoltaic system: 548.67 m Biogas generator size of 16 kW, battery bank of 21 units, -Converter size of 30 kW -Upper reservoir volume of 2081.5m3 -Total net present cost: $0.813 million. Economy [Waste heat recovery system based on steam ejector and WTA predrying in solar/lignite hybrid power plants. Solar aided+ predrying systems. For 1000 MW lignite-fired power plant: -21.6 from 46.6 MW of steam waste heat recovered; -1.62% of thermal efficiency increase;

  d to 60,000 m 3 /d Wind energy plants: 1 m 3 /d to 250,000 m 3 /d Wind-PV hybrid energy plants: 3 m 3 /d to 83,000 m 3 /d -Cost: Photovoltaic Energy plants: 34.21 $/m 3 to 0.825 $/m 3 . Wind energy plants: 15.75 $/m 3 to 0.66 $/m 3 . Wind-PV hybrid energy plants: 6.12 $/m 3 to 1.4 $/m 3 .

Fig. 3 .

 3 Fig. 3. Challenges for HRESs.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Applications of HRESs

Fig. 6 .

 6 Fig. 6. Advantages of HEV.

Fig. 7 .

 7 Fig. 7. Main outcomes of HHR for HVAC systems.

Table 2 .

 2 Applications on HHRSs.

	Reference	Applied Technology	Boundary Condition(s)	Remarkable Outcomes
	[40]	Absorption-compression heat pump.	-Sensible heat of flue gas below 150 °C. -Generate saturated steam at 0.5 MPa (151.8 °C).	-Exergy output of the system is 55.82 kW -COP reach 5.49; -Exhaust flue gas Temperature 94.7 °C -Payback period: 6.26 years.
	[42]	Parallel hybrid powertrain -Organic Rankine cycle on a Diesel Engine	-900 kW fast passenger ferry Diesel engine	-No extra load on the engine -Increased fuel consumption -Local emissions could be reduced
	[43]	A new hybrid air conditioning system (HAC)	Heat exchangers, including a packed bed and three 3/39 air-water finned coils	-Average energy saving rate of 44.0%. -Average power saving per hour is 13.41 Wm 2 .
	[44]	A hybrid air treatment cooling system	-Intake rate of outdoor air: 15 to 2.5 L/s per person	-Chilled water supply temperature can be raised from 7 C to 12 C -COP of chiller reaches 19% increase


Zahra Wehbi
email: zahra.w.wehbi@gmail.com

Rani Taher

Jalal Faraj

Mohamad Ramadan

Cathy Castelain

Mahmoud Khaled

A Short Review of Recent Studies on Wastewater Heat Recovery Systems: Types and Applications

Keywords: Heat Recovery, Wastewater, Heat Exchanger

Reducing energy consumption has its direct impact on the worldwide environmental status. Smart energy processes must be adopted in order to enhance the reduction capacity of energy usage. In this view, both renewable energy as well as heat recovery strategy has been used in a wide range of engineering applications. With this in mind, hot wastewater is considered as a valuable source of energy that could be recovered. The present paper illustrates an overall review on the waste water heat recovery systems (WWHR). All systems can be classified based on their structural configuration and application. It has been shown that under some conditions a 50% energy could be stored or recovered using a heat recovery system. In addition, all systems are considered as an economic as well as environmental effective methods.

Introduction

Currently, worldwide attention is centralized on climate and environmental changes. Urban residential areas and buildings occupy large proportions of energy which are considered as the main sources of greenhouse and CO2 emissions [START_REF] Zhou | Modelling future trends of annual embodied energy of urban residential building stock in China[END_REF] [START_REF] Rivera | Implications of passive energy efficiency measures on life cycle greenhouse gas emissions of high-rise residential building envelopes[END_REF]. Based on some studies, building sector contributes up to 30% of energy used worldwide; this energy is mainly used for either heating/cooling applications or for the production of hot water, which is quite prominent inside buildings [START_REF] Lyu | A general method to evaluate the applicability of natural energy for building cooling and heating: Revised degree hours[END_REF] [START_REF] Tyagi | Phase change material based advance solar thermal energy storage systems for building heating and cooling applications: A prospective research approach[END_REF]. Particularly as shown in Fig. 1, China accounts for 9.78% of the total world energy consumption, where 30% of this energy is consumed by buildings [START_REF] Yang | Testing for Energy Recovery Ventilators and Energy Saving Analysis with Air-Conditioning Systems[END_REF]. Another study shows that 40% of the total energy consumption is shared by building sectors in the European Union, which is also responsible for 36% of the total EU CO2 emissions [START_REF] Ilie | Study on technical and economical solutions for improving air conditioning efficiency in building sector[END_REF].

In order to overcome this high energy demands and costs, several alternatives have been promoted, such as renewable energy sources (solar energy [START_REF] Kuskaya | Residential solar energy consumption and greenhouse gas nexus: Evidence from Morlet wavelet transforms[END_REF][10], wind energy [START_REF] Zhou | Harvesting wind energy in low-rise residential buildings: Design and optimization of building forms[END_REF] [START_REF] Ge | Energy production features of rooftop hybrid photovoltaic-wind system and matching analysis with building energy use[END_REF] and geothermal energy [START_REF] Neves | State of the nation: Customizing energy and finances for geothermal technology in the United States residential sector[END_REF] [START_REF] Liu | Suitability and feasibility study on the application of groundwater source heat pump (GWSHP) system in residential buildings for different climate zones in China[END_REF]), energy management and control systems [START_REF] Brandi | A predictive and adaptive control strategy to optimize the management of integrated energy systems in buildings[END_REF] and energy recovery systems [START_REF] Barreto | An innovative window heat recovery (WHR) system with heat pipe technology: Analytical, CFD, experimental analysis and building retrofit performance[END_REF][START_REF] Alhajri | A conceptual efficient design of energy recovery systems using a new energy-area key parameter[END_REF]. Energy recovery systems are considered one of the most important solutions, where they permits reducing energy consumption by transferring lost energy from one system to another, considering heat loss as a key-element in this process [START_REF] Xu | Simulation study on exhaust turbine power generation for waste heat recovery from exhaust of a diesel engine[END_REF] [START_REF] Zhang | Waste energy recovery and energy efficiency improvement in China's iron and steel industry[END_REF]. In buildings, water heating represents the largest contribution of energy consumption, and from an energy recovery point of view, hot waste water that is disposed into the sewage system from sinks, dishwashers, showers …etc., is considered as a valuable source of heat loss. It is noticed that the interest in wastewater heat recovery units has been increased recently using different processes. In this view and to the authors' best knowledge, there are few studies that aim to provide intensive reviews about heat recovery from various sources such as engines [START_REF] Burnete | Review of thermoelectric generation for internal combustion engine waste heat recovery[END_REF][21], industrial systems [START_REF] Shahzad | Performance analysis of a novel double stage multifunctional open absorption heat pump system: An industrial moist flue gas heat recovery application[END_REF] [START_REF] Ge | Alloy selections in high-temperature metal hydride heat pump systems for industrial waste heat recovery[END_REF] and from building sectors mainly from chimneys [START_REF] Khalil | Enhancement of waste heat recovery from vertical chimney via thermoelectric generators by heat spreader[END_REF] [START_REF] Khalil | 3D study of the impact of aspect ratio and tilt angle on the thermoelectric generator power for waste heat recovery from a chimney[END_REF] and HVAC systems [START_REF] Sukarno | Non-dimensional analysis for heat pipe characteristics in the heat pipe heat exchanger as energy recovery device in the HVAC systems[END_REF][START_REF] Ramadan | Parametric analysis of air-water heat recovery concept applied to HVAC systems: Effect of mass flow rates[END_REF][START_REF] Garayo | Optimal combination of an air-to-air thermoelectric heat pump with a heat recovery system to HVAC a passive house dwelling[END_REF]. However, none of the previous studies provide a comprehensive review that would present the classifications of the waste water heat recovery systems used and their applications in buildings.

The present paper is dedicated to focus on the existing recent studies. This review will consider the recent available technologies that deal with wastewater heat recovery systems mainly coming from hot drain water. After reviewing the literature, the work can be done by classifying the available technologies based on their configurations and installations taking into consideration the effect of several parameters on their effectiveness and performance. The paper is organized as follows: Section 2 will present the potential and principle behind waste water heat recovery systems. The existing structural types of waste water heat recovery systems will be clarified in section 3. Section 4 will be devoted to showing different studies using various configurations for wastewater heat recovery systems. Finally, Sections 5 and 6 will be dedicated to the discussion and conclusions respectively. SDW shower drain water

Nomenclature

Wastewater heat recovery

Potential of energy in wastewater

Heat recovery from wastewater is a highly activated technology in countries like the UK, Norway, USA and Netherlands where a large amount of hot wastewater is produced every year and especially from residential buildings. For example, in a Dutch house, the average temperature of drain water is about 27 ºC, giving a heat potential of 21.3 MJ/home/day [START_REF] Frijns | The potential of (waste) water as energy carrier[END_REF][START_REF] Schmid | Sewage Water: interesting heat source for[END_REF][START_REF] Hofman | Water and energy as inseparable twins for sustainable solutions[END_REF]. Generally, the hot water generated from buildings has a high thermal capacity and its average temperature can range between 40-50 ºC. In Netherlands and Switzerland, the heat loss from buildings that can be found in the sewer systems and originated from waste hot water, contributes about 40% and 30% of the total energy loss from buildings respectively, keeping the rest for other applications and building envelopes. With this in mind, studies have shown that implementing an energy recovery system in the sewar network or inside buildings through a heat exchanger can help exploit the heat loss from domestic hot water better than studying treatment optimization [START_REF] Pomianowski | Sustainable and energy-efficient domestic hot water systems: A review[END_REF].

Concept of wastewater heat recovery system

As this paper takes into consideration the heat recovery from drain water mainly at the building level, Fig. 2 presents a schematic of different drain water sources. Heating a supply water before entering the water heater by the heat carried from the drain water is the main idea behind this concept, in other terms raising the water supply temperature after passing through the drainage system as a preheating step [START_REF] Kretschmer | Analysing wastewater temperature development in a sewer system as a basis for the evaluation of wastewater heat recovery potentials[END_REF] [START_REF] Prado | Water heating through electric shower and energy demand[END_REF]. Fig. 3 shows the working principle of a heat exchanger which represents the main component in a WWHR system. Various types of heat exchangers may be installed within systems in order to perfectly adopt the best heat transfer state. The temperature difference between the supply water and drain water will result in a heat transfer rate that will be affected by the heat transfer area and the thickness of water. Their installations in any residential building depend on several parameters, such as the building architecture and the availability in space where different types of WWHR units can be used. Copper pipes are commonly used in the WWHR system's application due to their high conductivity ensuring the best heat transfer, in addition to their ability to reduce fouling inside the pipes, hence reducing the need for periodic cleaning. [START_REF] Peereboo | Recovering heat from shower water in dwellings[END_REF][START_REF] Ip | Waste heat recovery from showers: case study of a university sport facility in the UK[END_REF][START_REF] Wong | Shower water heat recovery in high-rise residential buildings of Hong Kong[END_REF][START_REF] Zaloum | Drain water heat recovery characterization and modeling[END_REF].

Classifications of WWHR systems

Based on the literature, the heat exchanger type and structure used can be categorized according to three groups based on their structure: vertical systems (including storage tanks), horizontal systems and oriented systems. In general, the setup of the WWHR system reviewed doesn't have any mechanical part, having a lifetime of over 30 years. Usually, studies conducted on this process take into account the structure, capacity, performance and the financial sides of waste water heat recovery treatment. Most of the publications were implemented experimentally, while some rely on numerical simulations where the analysis of these systems is concentrated on the energetical and economic sides of waste water heat recovery systems and some on their environmental benefits. In the previous decades, the work on wastewater heat recovery systems focused on giving a preliminary study on this domain. However recently, studies can be categorized according to the type of configurations used, as shown in Fig. 4. [39][40].

WWHR systems' applications

Non-coupled systems

Non-coupled systems use different structures of a heat exchanger to heat upcoming cold water without an additional system where they are usually connected directly with the sewage pipe lines.

Vertical systems

This type is commonly used and is characterized by a gravity film heat exchanger as shown in Fig. 5. The system consists of a main inner pipe with a spiral coil wrapped around it, that has a higher heat transfer area compared to a straight pipe. The heat transfer in this type of heat exchanger is affected by the geometry of the design, including the number of coil loops. The hot water flows (inside buildings temperature can be above 60 ℃) at the top of the main pipe and adheres to the inlet walls. Cold water is supplied to the spiral coil where extracting heat from hot water starts until leaving the system at the top of the unit with warm water [START_REF] Manouchehri | An experimental analysis of the impact of temperature on falling film drain water heat recovery system effectiveness[END_REF][START_REF] Słys | Financial analysis of the implementation of a Drain Water Heat Recovery unit in residential housing[END_REF][START_REF] Ramadan | Recovering heat from hot drain water-Experimental evaluation, parametric analysis and new calculation procedure[END_REF]. Some recent studies on single systems using vertical heat exchangers are presented in Table 1 giving the most important results from those studies.

Another installation scenario that can be used based on vertical systems relies on using a storage tank where the use of the WWHR system is to heat or preheat the water before being stored before being heated up to match the building requirements using means like heat pumps (see Fig. 6.) [44][45]. These studies have shown their economic and environmental benefits in some cases, in addition to their promising performance. The challenge behind WWHR systems is sometimes the low temperature and the fact that part of the drain water heat is wasted inside or outside the system's envelope. With this in mind, the boiler/electric heater has to be installed just after the recovery system for better performance. Regardless of the geometry, any increase in main and drain sides' temperatures will increase the effectiveness.

[42]

Experimental, Numerical

Analysis based on preheating water step.

Preheating water is considered to be beneficial financially.

Its effectiveness increases with shower length and water consumption.

[43] Experimental Parametric analysis based on experimental setup.

Effectiveness increases with boiler output temperature.

[44] Experimental Hot water is discharged into a cylindrical tank with a spiral tube that carrying the cold water.

High temperature is available due to limited mixing between cold and hot flows, leading to better heat recovery.

[45]

Experimental, Numerical

The tank is charged with hot water coming from hot water tank.

The maximum heat transfer occurred at the lower flow rates. The capacity to recover about 34% to 60% from the available energy in the drain water.

[46] Experimental, Numerical

A drain water heat recovery storage unit based on PCM plates.

A maximum of 800 kJ of heat can be removed from the drain source where 50% of the thermal energy can be provided for the next stage of a washing machine.

[47] Experimental Comparison between solar water heat and drain heat recovery system.

The drain water heat recovery system is much costlier effective than SWH in saving energy.

[48] Experimental Performance study based on flow rates and wetting sides.

The effectiveness of the heat exchanger drops with the increase of flow rates. [49]

Experimental, Numerical

Parametric analysis of a multi-drain heat recovery system for heating/preheating cold water.

A case study in Lebanon for a drain temperature of 25℃ showed,the energy used is reduced from from 102.2 kWh to 410.9 kWh monthly. The increase in money saving is from 13.3 $ to 53.4 $. The monthly emissions reduction is increased from 72.5 kg to 291.7 kg.

[50] Experimental Performance of falling film DWHR system based on heat exchanger effectiveness and side wetting.

In partial wetting conditions, a reduction of about 28% in effectiveness would occur.

[51] Experimental

The impact of having unequal flow rates on main and drain sides inside falling film heat exchanger.

Flow rates can highly affect the performance of the DWHR system and any change in inlet flow rates can also affect the performance regardless of other design parameters. national saving of 808 GWh for one shower per home. Which accounts for a reduction of over 400,000 tons of CO2.

The effectiveness reaching 45% increased with increasing the loops of the system, thinner cold-water pipe, and low flow rates of drain water.

[54] Experimental Study of effectiveness for two horizontal DWHR systems: brand new baffled heat exchanger and a normal heat exchanger Based on lab conditions, the baffled heat exchanger is of higher effectiveness value than the normal one.

Horizontal systems

Residential buildings in some cases may not have enough space to install a vertical unit below shower trays. Horizontal WWHR systems may be sufficient where it can be installed also in different public sectors. These systems use a simple single pass counter flow heat exchanger connected directly to a water heater, as shown in Fig. 7. It is clear that in the vertical unit the water will flow around the whole boundary of the pipe, ensuring a high conductive efficiency. In the horizontal system, the water flows at the bottom of the pipe, reducing the heat transfer rates. This system is rarely used since in some cases its efficiency is considered limited compared to a vertical system. Some studies on horizontal systems are shown in Table 2. [START_REF] Peereboo | Peereboom Recovering heat from shower water in dwellings[END_REF] [START_REF] Ip | Waste heat recovery from showers: case study of a university sport facility in the UK[END_REF]. When comparing between the aforementioned setups, it can be shown that the effectiveness of the heat exchanger used can reach up to 50% and 60% for horizontal and vertical installations in some cases respectively. This difference is due to the fact that vertically installed heat exchangers can ensure heat transfer across the whole boundary of the pipe system, while the horizontal setup uses only a specific part of the pipe for heat transfer. In addition, the overall efficiency of the system is mainly affected by factors like: showering time, cold water temperature, flowrates, fouling effect, flow regime inside pipes and the temperature between the shower head and the drain point, where these factors differ between studies.

Inclined systems

In designing some buildings, a tilt angle between the drain system heat exchanger and the vertical line should be considered. The function of this inclined type of heat exchanger is similar to the vertical system. However, while measuring the change of effectiveness compared to a vertical system, it is shown that it started with a reduction of 4% with a tilt angle 2° caused by a non-uniform flow [START_REF] Manouchehri | Impact of small tilt angles on the performance of falling film drain water heat recovery systems[END_REF].

Coupled systems with heat pumps

Hybridization between WWHR systems and other energy applications is a promising approach. Very few studies combined the WWHR system with solar domestic water heaters for better efficiencies [START_REF] Tanha | Performance of two domestic solar water heaters with drain water heat recovery units: Simulation and experimental investigation[END_REF] [START_REF] Liu | Application of an exhaust heat recovery system for domestic hot water[END_REF]. However, the main focus is coupling the WWHR system with a heat pump [START_REF] Baek | A study on the design and analysis of a heat pump heating system using wastewater as a heat source[END_REF] [START_REF] Zhao | Study of the performance of an urban original source heat pump system[END_REF]. It is well known that a heat pump is a device that performs a fully reversible cycle which transfers energy from one medium to another under the basis of a circulating fluid called refrigerant [START_REF] Vering | Towards an integral decision-making process applied to the refrigerant selection in heat pumps[END_REF][START_REF] Guzzardi | Refrigerant mass distribution in an invertible air-towater heat pump: effect of the airflow velocity[END_REF][START_REF] Xu | Experimental investigation on control strategy of electric vehicle heat pump with refrigerant injection at low temperature[END_REF]. It has three thermal energy sources: air, ground and water [START_REF] Han | A new method for field test of the heating capacity of air source heat pumps[END_REF][START_REF] Fan | A proofof-concept study of a novel ventilation heat recovery vapour injection air source heat pump[END_REF][START_REF] Ceglia | Exergetic and exergoeconomic analysis of an experimental Ground Source Heat Pump system coupled with a thermal storage based on Hardware in Loop[END_REF][START_REF] Jung | A comprehensive review of thermal potential and heat utilization for water source heat pump systems[END_REF]. The use of wastewater source heat pumps has been increased due to their energy-savings properties and performance [START_REF] Chen | Techno-economic control strategy optimization for water-source heat pump coupled with ice storage district cooling system[END_REF][START_REF] Wang | Experiments on the characteristics of a sewage water source heat pump system for heat recovery from bath waste[END_REF][START_REF] Jung | Comprehensive multi-criteria evaluation of water source heat pump systems in terms of building type, water source, and water intake distance[END_REF][START_REF] Wang | Performance improvement of air-source heat pump heating system with variable water temperature difference[END_REF]. Installation of urban sewage source heat pumps has been considerably increased [START_REF] Zhang | Field test analysis of an urban sewage source heat pump system performance[END_REF][START_REF] Liu | Application of a heat pump system using untreated urban sewage as a heat source[END_REF][START_REF] Qunli | Technology and economic analysis of sewage source heat pump combined type district heating method[END_REF]. Table 3 provides some recent studies on the available applications using heat pumps.

Few are the papers that clearly studied the hybridization between heat pumps and WWHR system. Coupling between the heat pump and the heat recovery system works as an enhancement of the heat pump's performance, a heat source for the evaporator or as a booster for the heat recovery system. Such objectives can lead to better satisfying the heating and hot water demands inside residential buildings. In other words, the heat recovered here can be assessed Fig. 8. Coupling between heat pump system and drain water heat recovery system easily relying on an enhanced heat recovery ratio which is convenient for a better supply demand formula. Fig. 8 shows an example of a coupling between wastewater heat recovery system and w heat pump system. This drain system can be attached also to the evaporator.

Discussion

The diversity in construction and utilization of heat recovery systems from wastewater showed the capability of these units to reduce energy consumption as well as reduce environmental pollution. Large amounts of wastewater with a high temperature and flow rate goes through sewage every year, which is a motivating element for governments to install this technology and especially from shower where it consumes the highest amount of energy. Different concluding remarks were noticed throughout this review:

1-China has dominated a large number of researches in this domain and then Canada comes in second place where several studies were published in it.

2-

The setup designs in different publications can be classified into different configurations that lie in two criteria's: single and hybrid systems. Hybrid systems may use heat pumps coupled with a heat recovery system or a solar heater. Other types of hybrid applications could be used, like a typical coupling between exhaust gas heat recovery with wastewater.

3-Almost all the studies implemented an experimental setup, where few studies assess their research with a numerical simulation, where a low discrepancy between numerical simulations and experimental analysis was noted among all. However, the numerical approach should be broadened since it allows deeper understanding of the heat transfer phenomena that will occur in such systems.

4-Various types of heat exchangers were used throughout studies where the heat transfer performance through it is dominated by the temperature difference between hot and cold flows. In most cases, a helical type of heat exchanger is used. However, a more advanced form of heat exchanger could be utilized to enhance the heat transfer is a heat exchanger coupled to phase change material which may offer a higher efficiency. An optimal COP of 4.97 with condenser and evaporator optimized temperatures.

[77] Experimental Gravity film

The performance of a vertical DWHR system with a heat pump under different drain water flows.

Sizing the recovery system is important to match the drain water profiles. For 5 apartments, the available energy recovered from drain is 23.3 kWh.

[78]

Experimental, Numerical Gravity film Performance of vertical DWHR with heat pump

The heat recovery is affected by the contact heat resistance between the inner and outer pipe of the heat exchanger reaching 25%. Flow rate and inlet temperature affect the effectiveness and the heat recovery ratio respectively. Under the given condition, the heat recovery ratio ranges between 32 and 50%.

[79] Experimental NA A novel heat pump water heater for shower assisted with shower drain water. A waste heat extraction device with water pre-heater was installed.

Water pre-heated loops showed a better performance where more waste heat in the SDW could be recovered with a COP increased from 2.19 to 3.21.

The energy consumption of the system increased by increasing the water flow rates and shower temperature.

The design can save 70% energy compared to an electrical water heater. Where, the total energy saving was is 659 kW h/year, and with a saving of ¥336 per year.

[80]

Numerical, Experimental Gravity film

The performance of drain heat recovery system for enhancing the performance of a heat pump under several scenarios

The COP can be increased by increasing the air supply temperature and the flow rate of the drain. The scenario using a condenser and evaporator with the heat recovery system isthe most likely to improve the heat pump's performance. The saved money is up to 47$/month. The amount of reduced energy is 365 kWh. And the amount of CO2 reduction is increased from 82 to 259kg as the drain water inlet temperature increases from 20℃ to 50℃.

5-

In most cases, the wastewater source is a shower, which is due to the fact that this source is available in all residential zones. Nevertheless, other typical residential applications that provide hot waste water could be used as a heat source where they are yet investigated.

6-

The performance of different trends on experimental setups and numerical studies lies in the fact that the flow rates and temperature difference between cold and hot flows has a significant effect on the heat recovery efficiency. While, losses like conduction and convection through the walls of WWHR system have a slight effect on its potential.

7-Barriers a-Technical Barriers • Fouling Almost all types of wastewater may contain bio-substances which will lead to de-fouling within the surface of a heat exchanger in a biological growth form. These precipitations will affect in reducing heat transfer efficiency. Nonetheless, in order to minimize bio-fouling growth, different cleaning systems should be installed inside WWHR system tubes.

• Contamination

The majority of works were compiled that wastewater in some cases may be contaminated, so untreated sewage water may cause a serious problem like fouling in the unit, which will reduce the potential of recovering heat for long term usage.

•

Pressure Drop Increasing the cold flow temperature will decrease system efficiency where special attention should be given to the pressure drop inside the cold pipe in a way increasing the effectiveness of the unit. b-Social Barriers Management systems and high-tech buildings can be built by a limited number of countries which have sufficient economic and social capacities, thus helping to develop and support this technology worldwide. Meanwhile, different social or scientific organizations should be taking this technology into consideration in their awareness campaigns in coordination with the governments and ministries in order to ensure financial support and a full knowledge of these systems and help to facilitate and improve the lives of citizens. c-Economic Barriers The WWHR system's expenses and maintenance costs are considered high especially when dealing with complicated systems that are coupled with heat pumps or solar systems. This economic problem is contracting the use of this technology since it would not be available for all society levels.

Conclusions and future perspectives

Waste water heat recovery can be considered as an indirect renewable energy source. It is not only a bounteous source of heat, but it is also available in each house. What's more, due to its thermal characteristics, it can be easily extracted and reutilized in other applications. The present paper conducted an inclusive review on the available (WWHRS)s, highlighting their potential in the field of energy efficiency and energy saving. The studies are presented according to their timeline of publication and categorized based on their type of installation.

From a practical point of view, the heat exchanger is the core of (WWHRS)s, where it can greatly influence its performance. A counter flow heat exchanger is usually used since it allows better heat transfer. (WWHRS)s can be classified within three main configurations: vertical including storage tank based systems, horizontal and oriented. Moreover, the recovery systems are categorized within two categories: Single systems and Hybrid systems. Single systems mainly rely on the heat transfer process. While the hybrid type uses a heat pump or a solar system coupled with a WWHRS.

Nevertheless, the main parameters that affect the heat performance of (WWHRS)s are: viscosity of water, hot and cold temperatures, ambient temperature and flow rates. It has been remarked that the effectiveness of (WWHRS)s is higher when coupled to a heat pump where the COP may exceed 6 in some configurations. It was also noticed that increasing the hot flow rate and temperature would increase both effectiveness and efficiency of the system. Economically, the average payback period for single systems is seven years whereas for hybrid systems it is five years. Furthermore, several obstacles should be taken into consideration in order to preserve the performance of (WWHRS)s, such as fouling, contamination and pressure drop.

Fig. 1 .

 1 Fig. 1. Percentage of energy consumed by buildings in several countries [5-8].

Fig. 2 .

 2 Fig. 2. Schematic of wastewater sources inside a house.

Fig. 3 .

 3 Fig. 3. Working principle of waste water heat recovery systems.

Fig. 4 .

 4 Fig. 4. Flow diagram of the classification of the WWHR system reviewed.

Fig. 5 .

 5 Fig. 5. Schematic of a vertical WWHR system assisted in a shower drain.

Fig. 7 .Fig. 6 .

 76 Fig. 7. Schematic of a simple single-pass horizontal installation of WWHR unit.

Table 1 .

 1 Recent studies on single systems with a vertical heat exchanger

	Ref. Methodology	Approach	Main findings
	[41] Experimental	Effect of inlet temperature on system's effectiveness.

Table 2 .

 2 Studies on single systems using horizontal heat exchanger.

	Ref. Methodology	Approach	Main findings
				Saved energy reached is up to 15% which is
	[52] Experimental	Study based on shower time, water flow and inlet temperature on energy savings.	an increase from 104 MWh to 406 MWh, with a drainage pipe of 50mm diameter and 1.5m counter flow heat exchanger long
	[53]	Experimental, Numerical	A study on a copper pipe inserted inside a drainage plastic pipe.

The full implementation of the DWHR in every household in Ireland could amount to a

Table 3 .

 3 Studies on coupled systems with heat pump

	Ref.	Methodology	Heat exchanger	Approach	Main findings
	[76]	Experimental, Numerical	Counter flow heat exchanger	A heat pump water heater assisted by shower wastewater with thermodynamic models.


Mioara Joldes
email: joldes@laas.fr

Validated Numerics: Algorithms and Practical Applications in Aerospace

My lecture will survey some classical and recent validated computing algorithms based on the theory of set-valued analysis, in suitable functional spaces, as well as by combining symbolic and numerical computations. These techniques are illustrated with some applications which appear in practical space mission analysis and design. This is only a short summary of the talk.

Introduction to rigorous computing

The field of rigorous computing [START_REF] Tucker | Validated Numerics: A Short Introduction to Rigorous Computations[END_REF], sometimes called validated computing as well, uses numerical computations, yet is able to provide rigorous mathematical statements about the obtained results, such as sure and reasonably tight error bounds. Examples where the accuracy of numeric results has to be guaranteed range from computer-assisted proofs in dynamical systems to more practical engineering problems like the control of critical systems (spacecraft engines, surgical robots and so on).

Traditional validated computing methods are based on arbitrary precision libraries and interval arithmetic computations [START_REF] Moore | Interval Analysis[END_REF], a simple set arithmetic, which always returns an interval guaranteed to contain the correct result. To further bridge the gap between experimental mathematics and computer proofs, the symbolic-numeric aspect is considered: modern computer algebra algorithms (rooted in commutative and differential algebra) are employed via approximation theory (in suitable functional spaces) to obtain efficient approximations and analytic error bounds [START_REF] Bréhard | Validated and numerically efficient Chebyshev spectral methods for linear ordinary differential equations[END_REF].

In this context, we provide an introduction to the theory of set-valued analysis and to some related symbolic-numeric algorithms. Firstly, we focus on effectively computing and manipulating various kinds of ball arithmetic (e.g., made by a polynomial approximation together with a validated error bound). We consider Taylor series expansions as well as series expansions based on orthogonal polynomials and associated approximation algorithms (Taylor and Chebyshev models) [START_REF] Benoit | Rigorous uniform approximation of D-finite functions using Chebyshev expansions[END_REF][START_REF] Brisebarre | Chebyshev interpolation polynomial-based tools for rigorous computing[END_REF]. Broadly speaking, the idea of working with polynomial approximations instead of functions is analogous to using floating-point arithmetic instead of real numbers [START_REF] Epstein | Ultra-arithmetic I: function data types[END_REF][START_REF] Trefethen | Computing numerically with functions instead of numbers[END_REF]: various generalized Fourier series, including Chebyshev series, play the role of floating-point numbers. However, one comprises a function space counterpart of interval arithmetic by providing rigorous truncation error bounds. The main appeal of this approach is the ability to solve functional equations rigorously using enclosure methods [START_REF] Kaucher | Self-validating numerics for function space problems[END_REF][START_REF] Neumaier | Taylor forms -use and limits[END_REF].

Secondly, we exploit approximation algorithms mainly related to D-finite functions i.e., solutions of linear differential equations with polynomial coefficients. This property allows for developing a uniform theoretic and algorithmic treatment of these functions, an idea that has led to many symbolic computation applications in recent years [START_REF] Salvy | Linear differential equations as a data-structure[END_REF].

Finally, we present the basic principles of a posteriori Newton-like validation methods, which allow for proving particular existence statements and explicit a posteriori bounds, for actual solutions to certain differential equations, using a combination of analytical arguments and numerical computations [START_REF] Bréhard | Validated and numerically efficient Chebyshev spectral methods for linear ordinary differential equations[END_REF].

An example: the computation of orbital collision probability

An illustration of these techniques is related to the efficient finite precision evaluation of certain numerical functions. For instance, in [START_REF] Serra | Fast and accurate computation of orbital collision probability for short-term encounters[END_REF], we deal with the computation of the orbital collision probability between two space objects involved in a so-called short-term encounter. In brief, a dramatically increasing number of space debris, located mainly in Low Earth Orbits, constitute a serious hazard for operational satellites. It is thus critical to provide adequate mitigation and avoidance strategies, when a conjunction includes at least one active satellite. Usually, the relative debris-satellite positions and velocities are only approximately known, hence the risk of an on-orbit collision is modeled as a collision probability. Under some additional hypotheses, the probability of collision is reduced to the integral of a 2D Gaussian probability density function over a disk. If it is evaluated to be sufficiently high, a collision avoidance maneuver is decided, but each such maneuver reduces the remaining satellite fuel and thus its active in-orbit life. Yet, a wrong computation which underestimates the risk, could result in the satellite loss. This implies that both efficient and accurate algorithms are needed for this evaluation. The computational method presented in [START_REF] Serra | Fast and accurate computation of orbital collision probability for short-term encounters[END_REF] is based on a power series expression for the integral, derived by use of Laplace transform and D-finite functions properties. Furthermore, a finite precision evaluation method with reduced cancellation [START_REF] Gawronski | Reduced cancellation in the evaluation of entire functions and applications to the error function[END_REF] is employed. Analytic bounds on the truncation error are also derived and are used to obtain a very accurate algorithm.

First implemented and tested on a very large number of practical cases from a database by the French Space Agency (CNES), an implementation of this algorithm has been embedded and tested on board on the ESOC OPS-SAT 3-Units CubeSat satellite via the CNES ASTERIA software [START_REF] Thomassin | Asteria : Autonomous collision risks management[END_REF].

Conclusion

The previous example shows that computer algebra can provide the theoretical and algorithmic tools needed to design highly efficient symbolic-numeric algorithms and implementations, with practical reach for critical systems, where the accuracy of numeric results has to be guaranteed, like those arising in attitude and orbit control systems of spacecraft.