H M Hoang
email: onrawee.laguerre@cemagref.fr

EVALUATION OF FOOD SAFETY ALONG THE COLD CHAIN BY DETERMINISTIC AND STOCHASTIC APPROACHES

Several surveys have shown temperature abuses in the last 3 steps of the cold chain: display cabinet, transport by consumer and domestic refrigerator. To evaluate the food safety, this work was carried out to predict the product temperature and microbial load evolutions in these steps. Deterministic models were used to take into account the heat transfer by convection, conduction and radiation inside the equipments. They were combined with stochastic models to take into account different sources of randomness: ambient temperature, thermostat setting, product position and residence time in the equipments etc. Distribution laws were developed to fit the survey data of these random parameters. The sampling values were used as input parameters of the heat transfer model to predict the temperature evolutions of a large number of products along the cold chain. Then, these temperature evolutions were applied to a growth model of Listeria monocytogenes to predict the bacterial contamination.

1.

INTRODUCTION

The evolution of food products along the cold chain in term of quality and safety is of major importance. The objective of this study is to develop a modelling methodology to predict the evolution of food products and its variability all along the cold chain. This methodology, taking into account various sources of randomness such as ambient temperature, product residence time etc., was applied to the 3 steps of the cold chain during which temperature abuses are often observed: refrigerated display cabinet, consumer shopping basket and domestic refrigerator. Indeed, according to a survey carried out by our team, the product temperature is often too high to ensure the food safety in these equipments (30% in the display cabinet and 40% in domestic refrigerators, [START_REF] Cemagref | La chaine du froid du fabricant au consommateur: résultats de l'audit ANIA/Cemagref[END_REF].

METHODOLOGY

The methodology will be illustrated for a part of the cold chain: from the display cabinet to the domestic refrigerator but the same approach could be used for the other steps of the cold chain (storage in cold room, transport…). The product of interest is pre-packaged meat. For this kind of product, survey data are available [START_REF] Cemagref | La chaine du froid du fabricant au consommateur: résultats de l'audit ANIA/Cemagref[END_REF]. The product evolution will be here characterized only by the temperature and the bacterial load. The same approach could also be used to follow other parameters such as moisture loss, vitamin degradation for other types of product.

The methodology is composed of: -a stochastic description of the logistic chain -a semi-deterministic description of the cold chain equipments -a deterministic description of the product evolution (temperature, bacterial load)

A large number of products are introduced at t=0 in the logistic chain (in the current study only the part of the logistic beginning in the display cabinet is considered). Each product is characterized at each time t by several state variables which are the mean product temperature and the bacterial load. The initial values of the product state variables can be considered either as constant for all product items or as random variables.

To avoid long calculation time to predict the evolution of all product items present in the equipments all over the time, this approach distinguishes the individual product of interest and the other products present in the equipment. These other products, called 'load', will not be followed individually but lumped together for each typical location.

The load temperature at each position of an equipment depends on some random parameters (ambient temperature, thermostat setting, thermal insulation of the shopping basket…). The load temperatures are estimated by a deterministic thermal model for each equipment taking into account conductive, radiative and convective heat exchanges.

In each equipment, the temperature evolution of the product of interest is predicted from its initial value (when the product is introduced in the equipment) and from the mean surrounding temperature which is the temperature of the load at the corresponding position. Finally, the bacterial load evolution is predicted from the temperature evolution.

STOCHASTIC DESCRIPTION OF THE LOGISTIC CHAIN

This study considers the logistic chain of three equipments:

-display cabinet (DC) -shopping basket (SB) -domestic refrigerator (Ref)

When the products are loaded in the display cabinet, they are placed preferentially in the rear part and the older products are moved to the front. In this way, the products with the closest best-before date have more chance to be taken by the consumers. To take into account this manipulation, two indexes k=1 and k=2 are used for the display cabinet, as shown in Figure 1. Only one type of display cabinet is considered here: open vertical type, which is the most common for pre-packaged meat.

Index k=3, is used for the shopping basket, even if this step is not really a refrigeration equipment.

Two kinds of domestic refrigerators are considered: static refrigerator (free convection) which is indexed by k=4 and ventilated refrigerator which is indexed by k=5.

The last step (k=K=6) corresponds to eating of the product. It is assumed that once a product is removed from the refrigerator, it is consumed (it does not return in refrigerator). From the literature [START_REF] Evans | Temperature and energy performance of refrigerated retail display and commercial catering cabinets under test conditions[END_REF] it appears that the products placed in the front part of the display cabinets are submitted to higher temperatures than the one placed in the rear and that product placed in the bottom part are often warmer than the ones placed in the top part. Therefore, 4 characteristic positions were considered in the display cabinet. In the same way (Laguerre and Flick, 2010), two characteristic positions were considered in the domestic refrigerator, the temperature being generally higher at the top than at the bottom especially for static refrigerators.

The logistic chain with probabilities of transition from one to another equipment and of position inside equipments is presented schematically in Figure 1. Equal probability was assumed for position. Probability for a product to be firstly placed at the rear of the display cabinet was estimated to be 80%. Probability for a product to be placed in a static or a ventilated refrigerator was estimated from the observed percentage in France [START_REF] Diouris | Réfrigérateurs et congélateurs domestiques: consommer moins et conserver mieux tout en préservant l'environnement[END_REF]. The distribution of residence time of pre-package meat in the display cabinet, shopping basket and domestic refrigerator was fitted by an exponential Probability Density Function (PDF) [START_REF] Cemagref | La chaine du froid du fabricant au consommateur: résultats de l'audit ANIA/Cemagref[END_REF].

SEMI-DETERMINISTIC DESCRIPTION OF THE COLD CHAIN EQUIPMENTS 4.1 Display cabinets (DC)

In this case study, only the open front vertical display cabinet is considered because it is mostly used for keeping chilled food in supermarket [START_REF] Gac | Le Froid dans les Magasins de Vente de Denrées Périssables[END_REF] especially pre-packaged meat. In order to take into account the non-uniformity of product temperature, 4 loads are considered: rear top, rear bottom, front top and front bottom (Figure 2a). (2)

Shopping basket

From the display cabinet to the domestic refrigerator, the product is transported in a shopping basket which is more or less thermally insulated (only one load position is considered). Two random parameters are considered: the mean temperature of the air surrounding the basket ( )

C T ext °
and the heat transfer conductance H (W.K -1 ) which depends on the basket insulation. The distribution of ext T is Gaussian PDF: mean value 17.2°C and standard deviation 5.8°C [START_REF] Cemagref | La chaine du froid du fabricant au consommateur: résultats de l'audit ANIA/Cemagref[END_REF]. Investigations in different countries showed that the majority of people did not use any food protection during transportation: 87.3% in the UK [START_REF] Evans | Consumer handling of chilled foods: Perception and practice[END_REF]; 84.5% in Slovenia [START_REF] Jevsnik | Consumers' awareness of food safety from shopping to eating[END_REF] and 81.4% in New Zealand [START_REF] Gac | Le Froid dans les Magasins de Vente de Denrées Périssables[END_REF]. So, it is assumed that there is 84% (mean of these 3 values) of the shopping basket having no insulation and 16% being thermally insulated. The heat transfer conductance was measured in our study for a non insulated basket:

Domestic refrigerators (Ref)

The domestic refrigerators are of two different types: static (without a fan, free convection) and ventilated (forced convection). Inside a static refrigerator, there is about 4°C temperature difference between top and bottom [START_REF] Laguerre | Heat transfer by natural convection in domestic refrigerators[END_REF]) while this difference is lower in a ventilated appliance.

The load temperatures depend on the position and on two random parameters: the air temperature in the kitchen ext T and the thermostat setting th T which depends on consumer habits. In order to take into account the non uniformity of product temperature, 2 load positions are considered: top and bottom (Figure 2b). ext T and th T can be fitted by normal distributions (Laguerre and Flick, 2010b):

-for ext T : mean value 16.7°C and standard deviation value 3.1°C

-for th T : mean value 6.0°C and standard deviation value 2.3°C

The load temperatures can be calculated from the equipment parameters by following relations (Laguerre and Flick, 2010b):

-

DETERMINISTIC DESCRIPTION OF THE PRODUCT EVOLUTION

Two product state variables are considered: the mean product temperature and the microbial load.

Evolution of the mean product temperature T

Inside display cabinet or refrigerator (k=1, 2, 4, 5), using a lumped thermal model, the mean temperature of the product of interest tends to the load temperature at its position -The mass m and the thermal capacity of the product C are considered to be constant. For this case study of pre-packaged meat, m=0.250kg and C=3500 J.kg -1 K -1 .

In the shopping basket, a similar model is applied:

( ) T T H dt dT mC ext k - = =3 (6)
The heat transfer conductance H l.k was measured for each position l of each equipment: display cabinet (k=1 and 2) and refrigerator (k=4 and 5). For this purpose, the product (initial temperature T 0 ) was placed at position l of equipment k at time t 0 =0. A thermocouple was placed at the product's centre to measure the evolution of product temperature T. The expected temperature evolution can be presented by the equations 7 and 8:

( )

      - - + = mc t H T T T T k l k l load

Evolution of microbial load N

As a primary model, a simple first order growth was assumed:

( ) ( ) t N dt t dN µ = (9)
where N(t) is microbial load at time instant t, 0 N is initial load (CFU/g) and.µ is specific growth rate (s -1 ).

The dependence of the specific growth rate µ on the temperature is described by the square root model of [START_REF] Ratkowsky | Relationship between temperature and growth rate of bacterial cultures[END_REF]:

( ) min T T b - = µ (10)
where T min is the minimum temperature under which there is no bacterial growth and b is a coefficient. For Listeria monocytogenes, [START_REF] Duh | Modeling the effect of temperature on the growth rate and lag time of Listeria innocua and Listeria monocytogenes[END_REF] reported that T min =0°C and b=0.00035 s -1/2 K -1 More sophisticated model proposed by [START_REF] Baranyi | A non-autonomous differential equation to model bacterial growth[END_REF] and [START_REF] Zwietering | Application of predictive microbiology to estimate the number of Bacillus cereus in pasteurised milk at the point of consumption[END_REF] could also be used with the same approach. The aim of the present study is to illustrate the potentiality of the methodology, but not to predict accurately the microbial growth of specific species in a specific food product.

RESULTS AND DISCUSSION

For a simulation of 100000 product items, Figure 5 shows a cumulative distribution of final/initial ratio of bacterial load for the part of the cold chain (from the display cabinet to domestic refrigerator). It can be observed that for 50% of the product items, the bacteria multiplication is less than 3.31 which is very acceptable. However, the bacterial multiplication is higher than 200 for 5% of the product items, which can be dangerous for consumer. The estimated multiplication of more than 10 4 for 1% of the products could certainly lead to food poisoning. This fraction of the products is still statistically representative because it represents 1000 items. But it is to be reminded that a simple bacterial growth model was used. For this kind of extreme analysis, the microbial growth model should be improved to take into account influence of the initial load, the initial physiological state and the variability of the growth parameters. for 95% of product log (N F /N I )≤ 4.00 or N F /N I ≤ 9.98x10 3 for 99% of product

CONCLUSIONS

A methodology combining deterministic heat transfer models for the refrigeration equipments and stochastic models to take account of various sources of randomness in the cold chain was proposed. It enables the prediction of the temperature evolution of a large number of products. Theses temperature evolutions can then be used to estimate bacterial growth. Thus, this approach can contribute to evaluate food safety along the cold chain.

8.

Figure 1 :

 1 Figure 1: Logistic chain: probability of product transfer from an equipment to another (italic), probability of product position (bold in circle)

Figure 2 .

 2 Figure 2. Heat transfer model considering (a) 4 load positions in an open vertical display cabinet (b) 2 loads positions in domestic refrigerator.

Figure 3 .

 3 Figure 3. Equipment and product state variables and parameters.

  by linear relations (equations 1, 2, 3 & 4).

  the temporal evolution of the product temperature T and ( ) * ln T is presented in Figure4.

FigureFigure 4 .

 4 Figure 4b illustrates how the characteristic time k l ,τ can be calculated.

Figure 5 .

 5 Figure 5. Cumulative distribution of final/initial ratio of bacterial load at the end of the cold chain (display cabinet, shopping basket and domestic refrigerator) for total product items of 100 000.

ACKNOWLEDGEMENT

The research leading to this result has received funding from European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement n° 245288.


N D Tran

P Dabert

Patricia Arlabosse

Influence of drying conditions on the survival of pathogens in dried digestates

Influence of drying conditions on the survival of pathogens in dried digestates

MATERIALS AND METHODS

 The digestate was sampled in a plant processing pig liquid manure with residues from the agro food industry. After 60 days of digestion and 15 days of post-digestion, the digestate is dewatered in a decanter centrifuge before sampling.  The samples were extruded through a disk with circular dies of 12 mm, forming a bed of extrudates on the dryer perforated grid. The initial mass of the bed was fixed at 500g.  Drying experiments were conducted in a discontinuous pilot-scale dryer reproducing most of the operating conditions prevailing in a full scale continuous belt dryer. The drying experiment in the a priori most favourable conditions for pathogens inactivation (T air =140 o C, Y=0.0223 kg/kg and V=2 m/s) was selected for C. Perfringens enumeration. The different exposure times ranged from 10 to 50 minutes. After a period of adaptation, the curves exhibit a narrow plateau, which is quickly followed by a long falling rate zone. Pure internal transfer limitations appear for a moisture content close to 0.7 (d.b.).

Surface temperature ( o C)

The drying rate curves are similar to those classically observed for municipal sewage sludge.

Log 10 reduction of C. perfringens shows a linear decline over time, whatever the drying conditions. At 140 o C, the digestate reaches a dry solid content of 82% after 50 minutes. Even if the product temperature is quite high after 30 minutes of drying, C. perfringens is still detected in the dried digestate. Convective drying has proven to be inefficient to inactivate C. perfringens, whatever the timetemperature conditions investigated (70 o C for 3.5 hours or 140 o C for 50 minutes).

1

  N.D. Tran 1 , P. Dabert 2 and P. Arlabosse 1 Université de Toulouse; Mines Albi; CNRS; Centre RAPSODEE, France 2 Irstea, UR GERE, Rennes, France contact.Patricia.Arlabosse@mines-albi.fr www.rapsodee.mines-albi.

  Constant air temperature (70 -140 o C), humidity (0.01 -0.023 kg/kg d.a) and superficial velocity (1 -2 m/s) were set at the inlet of the through-flow drying chamber.  C. Perfringens were quantified following NF EN ISO 7937 standard in the raw and partially dried digestates. Thermo-tolerance is represented by the decimation time, D T , in the first-order decline in microorganism population, N. Digestates, the nutrient-rich by-products remaining after the anaerobic digestion, are commonly used as soil improvers or organic fertilizers. cost of transport while stabilising and even sanitizing the digestates. Within the framework of the DIVA project, funded by the French National Research Agency, our objective was to assess the energy and environmental issues regarding digestate convective drying.  The present work focuses on the thermotolerance of Clostridium perfringens, a grampositive, sporeforming, rod-shaped, non-motile bacterium, often used as an indicator to measure the efficiency of inactivation treatments.


Figures of French anaerobic digestion

The potential amount of organic waste collectable in France is about 214 million tons (Figure 1). About 70% is made of solid wastes from agriculture and municipalities. Although, so far, most common applications of anaerobic digestion were for industrial effluent and urban sludge treatment (Table 1), actual development concerns mainly agricultural and territorial units. About a hundred new plants are under construction or study in these sectors.

Field studies and agronomic value of digestates

• Literature is poor and contradictory • Global trend is interest for bioavailable nitrogen that may increase crop yields compared to undigested substrates (6 to 20% increases for digestate from agriculture residues) • Crop yields generally lower with digestate fertilization than those obtained with mineral fertilizers but long-term effect can be expected • Results vary greatly with weather conditions suggesting that key points are improving the application materials to limit ammonia volatilization and get more data about ammonia and volatile fatty acid plant poisoning as well as back effect of organic matter.

State of the art of digestates production in France and of their agronomic value

Agricultural AD system Dabert P.

Management of organic residues from anaerobic digestion is becoming a critical topic for the entire biogas production in France since digestate is still considered as a waste by French regulation. A review of digestates composition and agronomic value was done to help changing its status from waste to product.

  Figure 1: Million tons of organic waste and residues in France

Figure 2 :

 2 Figure 2: Nutrient composition (mini, mean, maxi g/kg DM) of about 160 digestates of various origins compiled from ADEME / RITTMO 2011 and data from the agricultural sector. BIOW: biowaste; GW: greenwaste; AM: mixture of animal manures; ABP: animal by-products; AI: agrifood industry waste; BM: bovine manure and PM: pig manure, F: French agricultural data. *, only 2 data(mini 189, mean 204, maxi 219)

1,2 , Berger S. 3 , Couturier C. 3 , Beline F. 1,2 ,Tremier Anne 1,2

	(1) Irstea, UR GERE, 17 avenue de Cucillé, CS 64427, F-35044 Rennes, FR.
	(2) Université européenne de Bretagne, FR
	(3) Solagro, 75 voie du T.O.E.C, 31 076 Toulouse cedex 3, FR
	Mechanically separated
	municipal waste AD system
	$ is dry matter for Industry and Agriculture, people equivalent for wastewater and raw matter for household waste

Characteristics of about 160 raw digestates

		0	50	100	150	• Basic pH around 8		0	50	100	150
	Other substrates BIOW -GW AM AM -ABP -BIOW AM -ABP AI BM PM FBM FPM	N tot	N-NH4		// 160 // 173 // 240 // 166	• Variable depending on the substrate digested nutrients composition • High levels of NPK for digestates from pig manure and animal by-products • Higher NH 4 /Ntot and lower C/N ratio for digestate compared to their substrates • Excess of copper and zinc for agricultural digestates • Biological parameters are usually not a problem except for Clostridium perfringens.	Other substrates BIOW -GW AM AM -ABP -BIOW AM -ABP AI BM PM FBM FPM	P2O5 K2O	// 261 // 154 // *

Table 1 .

 1 Plants and biogas production (excluding landfill gas in France in 2011 (data from ATEE, Club Biogaz 2011)


Quentin Danel
email: quentin.danel@voila.fr

Christelle Perilhon
email: christelle.perilhon@cnam.fr

Pierre Podevin
email: pierre.podevin@cnam.fr

Plamen Punov
email: plamen_punov@tu-sofia.bg

Stéphanie Lacour
email: stephanie.lacour@irstea.fr

Georges Descombes
email: georges.descombes@cnam.fr

WORKING FLUID SELECTION OF RANKINE-HIRN CYCLE ACCORDING TO THE HEAT SOURCE

Keywords: Rankine -Hirn cycle, waste heat recovery, simulation

This paper presents our simulation model of Rankine-Hirn cycle. This model is developed for sizing and for the working fluid choice of a test bench of Rankine-Hirn cycle for engine waste heat recovery. The heat source characteristics were measured on a diesel tractor engine during work in field. The simulation tool allows to study some of static operating points. An iterative calculation is used to find the best parameters as pressure or working fluid flow rate according to some constraints such as heat exchanger surface or maximum pressure. We identify that each fluid is adapted for a limited range of temperature heat source. For our application, ethanol and water are the adapted working fluids. These results define the future control laws of the waste heat recovery system.

Introduction

This paper presents a preliminary study for a conception of Rankine-Hirn waste heat recovery (WHR) system. The aim of this system is the reduction of vehicles fuel consumption. Analysis of the heat source shows us the best operating range for heat recovery. The Rankin-Hirn cycle model allows to find the best operating parameters and working fluid according to our heat source and pressure and temperature constraints. It appears that each fluid has a preferred heat source temperature range of use. However this difference between fluids is not significant when the heat exchanger achieves a critical size which which depends on the heat source power. Finally this model provides the best control parameters of the Rankin-Hirn system to maximize the recovery efficiency.

The heat source

The heat source studied is a tractor engine exhaust system. It is a 6.6 liter six cylinder diesel engine with maximum power of 110 kW. The data used were measured on a diesel tractor engine during work in field. This application promises a better performance than for cars because tractors work long time at high load. Our data coupled with simulation shows that a third part of fuel enthalpy is rejected with exhaust gases. The exhaust gases temperature is essentially between 350°C and 450°C. Punov et. al. [START_REF] Punov | Possibilities of waste heat recovery on tractor engines[END_REF] showed that this enthalpy contains 40% to 55% of exergy. The most frequent heat power of exhaust gases is about 70kW, so we can hope an exergy of 30kW for this point. In practice any thermal engine can recover all of this exergy but this study shows the interest and the potential of waste heat recovery.

Model of thermodynamic cycle

The model simulates a theoretic endo-reversible Rankine -Hirn cycle, with or without super-heating. Only sub-critical cycles are simulated. A calculation code was developed in Python [START_REF] Van Rossum | Python tutorial[END_REF] and CoolProp [START_REF] Bell | Pure and Pseudo-pure Fluid Thermophysical Property Evaluation and the Open-Source Thermophysical Property Library CoolProp[END_REF] database was used for fluids properties.

This system consists of an evaporator, an expander, a condenser and a pump. The waste heat is absorbed through the evaporator to vaporize the pressurized working fluid. Vapor energy is mechanized in the expander and the expanded vapor is condensed. The low pressure liquid working fluid is pumped and the cycle starts again. The model considers the heat exchanger like counter flow.

The pump work and the pressure drop in the circuit are neglected. Thermal capacity of exhaust gases is considered constant, cp gaz =1,157 kJ /kg . K . The pinch point method is used to calculate the results. Input parameters of the model are the followings: -Hot source temperature and gas mass flow -Cold source temperature -Surface A and heat exchange coefficients U of the hot heat exchanger -Maximum and minimum pressure of the cycle -Super-heating temperature An iterative calculation links the pinch point and the surface of the heat exchanger. The ΔTln of each area of the exchanger (fig. 3) is used for total surface A calculation.

ΔTln= ( ΔT x -ΔT 0 ) ln ( ΔT x ΔT 0 ) (1)
Qexchange =U . A. ΔTln The power on the expander shaft is: Ẇ = ṁworkingfluid . Δh workingfluid [START_REF] Barrieu | Power from Wasted Heat : Challenges and Opportunities of Rankine Based Systems for Passenger Vehicles[END_REF] Most interesting results to find the best operating point parameters are maximum power and global exergetic efficiency. The thermal power available is calculate with ambient temperature as reference.

Q= ṁgas . cp gas . ( T gas -T 0) [START_REF] Daccord | Exhaust Heat Recovery with Rankine piston expander[END_REF] The second law of thermodynamics allow to obtain the maximum useful energy of exhaust gases.

Ėx= Δ Ḣ -T 0 . Δ Ṡ (7) Ė x gas = ṁgas . cp gas . ( T gaz -T 0 ) . ( 1-T 0 . ln T gas T 0 T gas -T 0 ) (8)
The global efficiencies are :

η II = Ẇ Ė x gas (9)
Heat transfer efficiencies :

η= Qworkingfluid Qgas (10)
The best exergetic efficiency is searched for each hot source temperature by an iterative method. Control parameters are working fluid mass flow, pressure and the super heating temperature.

Results

Three fluids are analyzed, water, ethanol and R245fa. These fluids are the most commonly studied and used for Rankine -Hirn and organic Rankine cycle (ORC) [START_REF] Quoilin | Dynamic modeling and optimal control strategy of waste heat recovery Organic Rankine Cycles[END_REF][START_REF] Barrieu | Power from Wasted Heat : Challenges and Opportunities of Rankine Based Systems for Passenger Vehicles[END_REF][START_REF] Daccord | Exhaust Heat Recovery with Rankine piston expander[END_REF][START_REF] Espinosa | Rankine cycle for waste heat recovery on commercial trucks: approach, constraints and modelling[END_REF]. The first objective is to find the best working fluid for the hot source temperature range. This study is conducted with no limit in pressure and super heating. The heat exchanger surface is considered infinite. The cold source is fixed at 100°C. This temperature was chosen because it is a value compatible with the engine coolant temperature and it is not necessary to depressurize condenser for water. Others fluids are studied with the same cold source temperature.

A first simulation is released for Hirn cycle, i.e. super-heating. Each fluid provides a better performance than others for a limited range of hot source temperature (fig. 4). R245fa is better for a temperature lower than 200°C, ethanol is better between 200°C and 400°C and water is prefereable for temperatures higher than 400°C. R245fa seems to be not enough efficient for the studied temperature range, which is from 300°C to 500°C. Ethanol efficiency increases rapidly until a maximum and decreases after that. On the other hand, water efficiency increases slowly after an important increase.

Significant increasing of efficiency occurs when the hot source temperature exceeds the critical temperature of the working fluid. Critical temperatures are 241.56°C for ethanol and 373.946°C for water.

A second simulation (fig. 5) studies the Rankine cycle without constraints, but unlike the previous simulation the fluid is not super-heated. The maximum efficiency is slightly lower than with super-heating but the main difference concerns the water for which the efficiency decreases after the maximum. This decreasing is more important for ethanol than with super-heating. R245fa is a dry fluid The super heating does not allows a benefit [START_REF] Quoilin | Dynamic modeling and optimal control strategy of waste heat recovery Organic Rankine Cycles[END_REF] for dry and isentropic fluids, so the results are the same. Water and ethanol are wet fluids, then the super-heating gets a profit.

The optimal evaporating temperature of the Rankine cycle (fig. 6) reaches a maximum which is the critical temperature before a weak decrease for highest hot source temperatures. This comportment was described by Chambadal [START_REF] Chambadal | Les centrales nucléaires[END_REF].

Just after the fast efficiency increase (fig. 7) the optimal super-heating temperature is reduced to a minimum. The temperature at this point corresponds to the critical temperature of the fluid. The super heating temperature increases anew when the gas temperature exceeds the critical temperature of the fluid. So when the gas temperature is slightly higher than the critical temperature of the fluid, Rankine cycle is better but for higher or lower temperature Hirn cycle is preferable. The temperature evolution according to the heat exchange shows (fig. 8) that an optimal choice of fluid and working fluid temperature can limit the difference between the hot and cold fluids and reduce the exergetic destruction.

For a gas temperature higher than the critical temperature of the fluid, the evolution of the fluid liquid phase temperature follows the gas temperature evolution shape. For this case, the exergetic efficiency is very high because all amount of the heat is transferred to the working fluid with the minimal exergetic destruction. These examples need an infinite heat exchanger but it shows that even if the heat exchanger is infinite an efficiency of 100% is impossible due to the non-constant heat capacity of the fluid. The fig. 9 shows the evolution of the heat transfer efficiency to the working fluid. In case of an infinite heat exchanger, the global efficiency mainly depends on the heat exchange efficiency which depends on the fluid characteristics. Ethanol and water are studied here but each fluid offered a preferred range of use of hot source temperatures. In the second study a constraint of heat exchanger surface is introduced. Only ethanol and water are studied: R245fa provides lower performances so it is not studied in this case. The pressure is limited to 30bar and the super-heating is fixed at 30°C higher than the evaporation temperature. The role of super heating is not only for the efficiency improve but also for the protection of the expander which can be damaged by droplets appearance during the expansion. Fig. 10 shows the results obtained for the two fluids with a heat exchanger surface in range of 1 to 12 m².

The hot source power is 40kW. For another power these surfaces give different results. The result for a heat exchanger of 12m² is very close to the infinite exchanger and the best range of efficiency is clearly different for ethanol and water. In the case of a reduced heat exchanger surface, the exergetic efficiency for both fluids cannot be distinguished for low temperatures but the efficiency with water as working fluid remains higher for higher temperatures.

If the heat transfer is relatively low compared to hot source power, the advantage of each fluid for a limited range of hot source temperatures disappears. The fluid which presents the higher critical temperature becomes then the most interesting fluid for the entire range of hot source temperature. For our application the temperature range extends from 300°C to 500°C so with a large heat exchanger ethanol and water are interesting. Ethanol provides a better efficiency between 300°C and 400°C and water is better for a higher range. But in practice we are limited by the size and the price of the heat exchanger. The size will be between 2 and 3m². For this size, ethanol offers same performances as water below 350°C and lower performances above this temperature.

The pressure (fig. 11) evolution of limited 30 bar and 30°C super-heating cycle case shows that the pressure should not be always at 30 bar. So, to optimize the system in varying conditions, it is necessary to control these parameters.

Conclusions

The effect of the fluid properties and the heat exchanger size on the WHR efficiency has been studied in this paper. We observed that each fluid presents a preffered temperature range of use. The optimal temperature of Rankine-Hirn cycle depends on the critical temperature of the working fluid.

With these considerations ethanol and water present advantages respectively in the range from 300°C to 400°C and from 400°C to 500°C. These two fluids are interesting for hot source studied. But these first results have been obtained with an infinite heat exchanger. When we consider a limited heat exchanger surface, performance decreases with the surface. This decreasing is not constant: the maximum efficiency of each fluid tends to the same limit when the temperature is inferior to the lowest critical temperature of all fluids. But the efficiency of the fluid which presents the lowest critical temperature decreases below its critical temperature. With the constraint of heat exchanger surface, water seems to be a better working fluid for the studied application.

( 2 ) 3 ) 4 )Fig. 1 :FigFig. 3 :

 23413 Fig. 1 : Waste heat recovery system

Fig. 4 :

 4 Fig. 4 : Exergetic efficiency (η II ) of Hirn cycle without constraints. Cycle with super-heating.

Fig. 5 :Fig. 6 :

 56 Fig. 5 : Exergetic efficiency (η II ) for Rankine cycle without constraints. Cycle without super-heating.

Fig. 8 :Fig. 9 :

 89 Fig.8: Temperatures profiles of water and gas in the infinite heat exchanger for gas inlet temperature of 300, 400 and 500°C

Fig. 10 :

 10 Fig. 10 : WHR system global efficiency (η II ) for different size of heat exchanger.

Fig. 11 :

 11 Fig. 11 : Optimal pressure in function of heat source temperature


Francesco Baldi
email: francesco.baldi@chalmers.se

Stephanie Lacour
email: stephanie.lacour@irstea.fr

Quintan Danel
email: quentin.danel@outlook.fr

Ulrik Larsen
email: ulrik.larsen@chalmers.se

Dynamic modelling and analysis of the potential for waste heat recovery on Diesel engine driven applications with a cyclical operational profile

Keywords: Waste heat recovery, Diesel engines, dynamic modelling, agricultural machines

As the world faces the challenge of the need for decreasing the anthropogenic carbon footprint, the continuous economic growth puts additional stress on the need for increased energy systems efficiency. In this context, waste heat recovery is identified as one of the most viable solutions for reducing the fuel consumption of existing systems in transportation.

In this paper, we present an analysis of the potential of a waste heat recovery system applied to Diesel engine-driven systems where the operational cycle is dynamic but reducible to a limited number of operational modes. The analysis is applied to a case study for which this operational pattern is of particular relevance: a machine for sugar beet harvesting. The existence of periodical low-load periods forces to bypass the waste heat recovery turbine to avoid water condensation during the expansion. Hence, we propose the use of a thermal inertia to keep the required level of steam superheating during low-load periods.

The results of the study showed an improvement of 27% in the recoverable exergy of the flow at the heat exchanger cold outlet when the heat exchanger wall thickness was increased from 0.5 mm to 2.5 mm. The results also show that a limited amount of the overall heat exchange inertia contributes to such improvement

Introduction

Internal combustion engines (ICE) are by large the most employed prime mover technology for transportation, in particular on land and sea. Their wide diffusion, together with the expected increasing trend in fuel prices and the challenge of global warming, has led to widespread efforts aiming at reducing ICEs fuel consumption. More than half of the energy input to an ICE is wasted to the environment in the form of hot exhaust gas or cooling water [START_REF] Bourhis | Energy and Exergy Balances for Modern Diesel and Gasoline Engines[END_REF] and for this reason waste heat recovery systems (WHRS) are among the most studied solutions for improving ICEs energy efficiency [START_REF] Armstead | Review of waste heat recovery mechanisms for internal combustion engines[END_REF]. Among the different technologies available for WHR applications to ICEs, the Rankine cycle is traditionally regarded as one of the most efficient and reliable solutions [START_REF] Armstead | Review of waste heat recovery mechanisms for internal combustion engines[END_REF]; extensive work has been proposed in relation to the application of Rankine cycles in road transport (see, among others, [START_REF] Charles | Review of organic Rankine cycles for internal combustion engine exhaust waste heat recovery[END_REF][START_REF] Espinosa Tilman | Rankine cycle for waste heat recovery on commercial trucks: approach, constraints and modelling[END_REF][START_REF]Analyzing the optimization of an organic Rankine cycle system for recovering waste heat from a large marine engine containing a cooling water system[END_REF][START_REF] Macián | Methodology to design a bottoming Rankine cycle, as a waste energy recovering system in vehicles. Study in a HDD engine[END_REF][START_REF] Tianyou | A review of researches on thermal exhaust heat recovery with Rankine cycle[END_REF][START_REF] Shokati | Thermodynamic and heat transfer analysis of heat recovery from engine test cell by Organic Rankine Cycle[END_REF]), as well as in the maritime sector [START_REF] Larsen | Design and optimisation of organic Rankine cycles for waste heat recovery in marine applications using the principles of natural selection[END_REF][START_REF] Livanos | Techno-economic investigation of alternative propulsion plants for Ferries and RoRo ships[END_REF][START_REF] Kalikatzarakis | Multi-criteria selection and thermo-economic optimization of Organic Rankine Cycle system for a marine application[END_REF][START_REF] Dimopoulos | Modelling and optimization of an integrated marine combined cycle system[END_REF][START_REF] Shu | A review of waste heat recovery on twostroke IC engine aboard ships[END_REF][START_REF] Burel | Improving sustainability of maritime transport through utilization of Liquefied Natural Gas (LNG) for propulsion[END_REF][START_REF] Choi | Thermodynamic analysis of a dual loop heat recovery system with trilateral cycle applied to exhaust gases of internal combustion engine for propulsion of the 6800 TEU container ship[END_REF]. Road and maritime applications normally differ markedly in terms of their operative conditions. WHRS design for application in international shipping focuses on steady-state conditions (and, often, on one individual operating point) due to typically stationary operations of such systems. On the other hand, road applications require focus on transient operations, which leads to the existence of extensive literature on WHR control systems [START_REF] Feru | Experimental Validation of a Dynamic Waste Heat Recovery System Model for Control Purposes[END_REF][START_REF] Quoilin | Dynamic modeling and optimal control strategy of waste heat recovery Organic Rankine Cycles[END_REF]. Even in the latter case, however, although observations from real operations are sometimes used to weight the selected operating points (see, for instance, [START_REF] Espinosa Tilman | Rankine cycle for waste heat recovery on commercial trucks: approach, constraints and modelling[END_REF]), the WHRS design still relies on steady state methods. Heating and cooling periods are sometimes considered [START_REF] Lee | Dynamic Response of a 50 kW Organic Rankine Cycle System in Association with Evaporators[END_REF] but this is mainly done in order to estimate the time of response rather than for optimising the heat recovery potential. Non-road machinery, particularly agricultural machines, and inland shipping vessels constitute a significant share of respectively land-and sea-based transportation. These vehicles generally follow clearly identifiable operating cycles which are significantly dynamic but follow a determinate, repeatable pattern. In addition, compared to cars and trucks, these applications show higher engine load coefficient and exhaust temperatures [START_REF] Espinosa Tilman | Rankine cycle for waste heat recovery on commercial trucks: approach, constraints and modelling[END_REF][START_REF]Analyzing the optimization of an organic Rankine cycle system for recovering waste heat from a large marine engine containing a cooling water system[END_REF][START_REF] Lacour | Waste heat recovery on tractor engine: exergy analysis of exhaust in transient conditions[END_REF][START_REF] Nielsen | Design and modeling of an advanced marine machinery system including waste heat recovery and removal of sulphur oxides[END_REF]. Hence, being in between steady-state generator and heavy-transient road engines for both size and transient behaviour, heavy non-road engines (marine or agriculture) should have specifically designed heat recovery systems. Several studies are dedicated to the dynamic performance of single-phase heat exchangers [START_REF] Hadidi | Loi de reponse d'un echangeur thermique soumis a des echelons de temperature aux entrees[END_REF][START_REF] Henrion | Comportement en regime transitoire de divers types d'echangeurs de chaleur ; Modelisation et consequences[END_REF] as well as to two-phase ones [START_REF] Quoilin | Dynamic modeling and optimal control strategy of waste heat recovery Organic Rankine Cycles[END_REF][START_REF] Morales-Ruiz | Numerical resolution of the liquid-vapour two-phase flow by means of the two-fluid model and a pressure based method[END_REF][START_REF] Feru | Two-phase plate-fin heat exchanger modeling for waste heat recovery systems in diesel engines[END_REF]; however, the subject of the optimisation of the design of the WHRS evaporator based on dynamic cycle performance still remains unclear. The aim of this paper is to study the dynamic behaviour the boiler heat exchanger of a WHRS, which is the dynamically most critical part of the system [START_REF] Feru | Experimental Validation of a Dynamic Waste Heat Recovery System Model for Control Purposes[END_REF][START_REF] Feru | Modeling and Control of a Parallel Waste Heat Recovery System for Euro-VI Heavy-Duty Diesel Engines[END_REF]. Focus is on analysing how different design parameters, of a tubular exchanger, influence the recovery potential, with particular focus on the role of the inertia of the heat exchanger wall.

Method

Activity monitoring

Three sugar beet harvesters are selected to participate in a campaign designed to cover the whole season of harvest. A tractor with a smaller engine was also equipped and monitored more than a year to get a whole cultural cycle. The choice of the vehicles was made so to be representative of the most commonly employed agricultural machines on the European market. The experiment campaign was conducted in between September 2011 and December 2012 for the harvesters and from November 2010 up to February 2012 for the tractor. Details about these agricultural machineries are given in the Table 1, while more information concerning the operations of gathering and processing the measured data is available in [START_REF] Lacour | A model to assess tractor operational efficiency from bench test data[END_REF]. More information on the gathering and processing of measured data is available in [START_REF] Lacour | A model to assess tractor operational efficiency from bench test data[END_REF].

Determination of the reference cycle

Four main operational conditions for the selected machines were identified:  Transport (high speed)  Harvesting (high speed and torque)  Idling (zero torque)  Transition (intermediate torque)

All measured points were categorised as above, and the distributions of engine operations in terms of speed and torque are represented in Figure 1: The analysis of the measured data suggests that the amount of time spent for transport is just 3% of the total and it corresponds to a very broad spectrum of engine speed and power. Such behaviour is also observed in the "transition" phase, up to 12% of the time, which corresponds to manoeuvers and to short distance transfers between fields. The average duration of the harvesting phase was calculated to 7.5 hours, with little variation between different machines. This phase takes the largest share of machines operations and is carried out in a regular manner, in proximity of a fixed operational point which varies between different fields only to a limited degree. Operational breaks of the duration of 20-50 minutes are relatively common but unpredictable; finally, 4-12% of the time is spent idling, which generally happen for a duration of 208 seconds. Finally, transitions between one working line and the following one generally last 53 seconds. The temperature and mass flow rate of the exhaust gas are measured on a dynamometer for different engine speeds and torques, see Fig. 2. The measurements show that, while the exhaust gas temperature is relatively high during the harvesting phase, it drops to lower levels during idling and manoeuvring. A similar behaviour can also be observed for the exhaust gas flow. The cyclic operations of the studied machines during harvesting can be observed in Figure 3a. Since the harvesting part of the operations occupies the largest share of the time and occurs at high loads, this condition presents the largest potential for improvements in fuel consumption. Starting from the conditions observed during measurement campaigns and represented in Figure 3a, a reference cycle was selected for the simulation of the dynamic behaviour of the evaporator. The simulated conditions in terms of inlet temperature and mass flow at the hot inlet are represented in Figure 3b, and include an initial warming-up period of 600 seconds, followed by three working cycles of 360 seconds each, composed of 300 seconds harvesting (with exhaust temperature and flow respectively of 623 K and 0.25 kg/s) and 60 seconds manoeuvring (523 K and 0.15 kg/s).

Heat exchanger 3.1 Dynamic heat exchanger modelling

In order to model the dynamic performance of the heat exchanger, as previously described, a onedimensional model, based on the principle of finite volumes, was set up. Although computationally more expensive, finite volume models are more numerically reliable in dynamic simulation [START_REF] Quoilin | Sustainable energy conversion through the use of organic Rankine cycles for waste heat recovery and solar applications[END_REF]. A number of 40 equally sized volumes was selected as a good compromise between computational time and intensity of numerical instabilities. For each volume the following set of equations was solved at the metal of the inner pipe:

  , m i j dQ x t                  , 1 , 1 t , , hm cm m m m j m i j m m m j m i j ii Q Q A T x T x t A T x t T x t dt            , (1)
      , , , hm i j hm hm h i j m i j Q x t h A T x t T x t     , (2)
      , , , cm i j cm cm c i j m i j Q x t h A T x t T x t     , (3)
Where λm represents the thickness of the heat exchanger wall, Ahm and Acm the outer and inner surface of the wall respectively, Am the heat exchange surface between the elements of the wall, and the subscripts h,c and m respectively represent the hot, cold fluid and the wall metal. The heat transfer coefficients hcm and hhm are calculated as follows:

w,e 1 w,i 1 ln(r / r )

2 hm h m h h        , ( 4
)
where the convective heat transfer coefficients hh and hc are estimated using correlations available from scientific literature. For the hot fluid and for the cold fluid in sub-cooled liquid and superheated vapour forms the Colburn correlation was used, which has the following form:

  1/3 0.8 N 0.023 u Re Pr 
The two-phase heat exchange coefficient was calculated using the correlation based on fluid quality reported by [START_REF] Böckh | Heat transfer: basics and practice[END_REF] for convection boiling and hereafter reported:

  2 ph hx          0.5 2 2.2 0.01 1.5 0.7 0.4 0.37 0.01 0.67 0 0 0 1 1 1.2 1 8 1 l l g h h x x x R x x R h                    , (5)
Where hl0 and hg0 represent the convective heat flow of the liquid and the gas phases, calculated using the Colburn correlation, x is the quality and R is the ratio of the density of the liquid over the gas phase. This correlation has the advantage of being continuous with quality. In order to reduce computational time, the coefficients of ( 6) are calculated once when the first boiling occurs, and then updated as a function of the mass flow on the hot side as proposed by Quoilin [START_REF] Quoilin | Sustainable energy conversion through the use of organic Rankine cycles for waste heat recovery and solar applications[END_REF] and shown in [START_REF] Tianyou | A review of researches on thermal exhaust heat recovery with Rankine cycle[END_REF]:

  0.5 2 2, , h ph ph nom h nom m hh m      , (6)
The evolution of the temperatures in the heat exchanger over time is calculated according to a Eulerian approach; the properties at the instant j+1 are therefore calculated based on the heat exchange properties evaluated at the instant j. For the heat exchanger wall this reduces to [START_REF] Tianyou | A review of researches on thermal exhaust heat recovery with Rankine cycle[END_REF]:

      1 , , , m i m i j m i j j T x t T x t dQ x t   , (7)
For the hot and cold fluid, the equation of mass and energy conservation (Equations 8 and 9) were solved simultaneously:

1, , ,

i i t i t it d m m dt    , (8) 1, 1, , , , ,
i t i t i t i t i t ît dU m h m h dQ dt     , (9)
By combining ( 8) and ( 9) the explicit form can be obtained:

11 1, , , , 1, ,, ,, i
t i t i t i t i t î t î t i t i t h h Q mm hh                    . ( 10
)
Equation ( 10) is only valid under the assumption of constant pressure. This assumption was used in order to save computational time and because in this study it was decided to have constant inlet pressure on both sides of the heat exchanger. Pressure losses and their influence of the thermal behaviour of the two fluids were hence neglected.

The presence of fast transients can lead of numerical instabilities and to the insurgence of back flows, particularly in relation to the sharp variation in the density of water in proximity of the liquid saturation line. In this case this was solved as suggested by Quoilin et al. [START_REF] Quoilin | Methods to Increase the Robustness of Finite-Volume Flow Models in Thermodynamic Systems[END_REF] by smoothing the density function between saturated liquid and vapour with 0.1 quality. This solution, although physically incorrect, allows minimizing inaccuracies in energy and mass balance, while keeping low computational time and ensuring high numerical robustness [START_REF] Quoilin | Methods to Increase the Robustness of Finite-Volume Flow Models in Thermodynamic Systems[END_REF]. Further assumptions were employed for the sake of reducing computational time:  Uniform specific heat in the exhaust gas, calculated at the mean temperature in the exhaust of the previous time step.  Ideal gas behaviour for water vapour. This assumption is justified given the low water/steam pressure employed in this study [START_REF] Cengel | Fundamentals of thermal-fluid sciences. 2nd editio[END_REF].  Equal vapour heat exchange properties during evaporation and condensation. The heat exchange coefficient of the two-phase mix on the cold side of the exchanger was assumed to only depend on the vapour quality as expressed in Equation ( 5), with no distinction between evaporation and condensation.

Heat exchanger design

For the case under study it was decided to use a simple concentric pipe design in order to reduce the complexity of the simulation. The heat exchanger is designed to have the hot fluid flowing in the outer pipe, while the cold fluid flows in four smaller inner pipes. This configuration is chosen in order to enhance the heat exchange surface while keeping a limited flow area on the cold side. The temperature of the hot fluid is considered to be uniform radially. A sketch of the heat exchanger cross section is provided in Figure 4. Table 2 summarises the geometric parameters of the heat exchanger in the reference case. These are chosen as a compromise between obtaining a reasonable degree of superheating at the steam outlet of the exchanger and reducing the physical size of the exchanger. Copper is chosen as material for the heat exchanger, and it is assumed that thermal properties (conductivity, specific heat capacity and density) are constant with temperature. The influence of the thickness of the inner pipe in the tubular heat exchanger as a mean for increasing heat exchanger inertia was tested in this study. The integral of the exergy flow at the outlet of the exchanger on the cold side over a full manoeuvring and working cycle was used as a performance indicator. It was also assumed that if the quality of the cold fluid at the heat exchanger outlet dropped below one, the exergy flow available for recovery is equal to zero.

   

, 0 0 0 , 0 c out vsat rec c c out vsat if h h EX m h h T s s if h h              (11)
This corresponds to a hypothetical control system bypassing the recovery turbine in specified conditions of the cold fluid to prevent turbine damaging as a result of the formation of droplets in the final turbine stages.

Simulations

The model described in Sections 3.1 and 3.2 was used to simulate the behaviour of a tubular heat exchanger where the hot fluid is subject to variations in inlet flow and enthalpy.

The hot fluid is exhaust gas of a Diesel engine, with a molar composition of 67% nitrogen, 10% oxygen, 12% carbon dioxide and 11% water, and a pressure of 0.11 MPa. The cold fluid used in this study is water, at a pressure of 0.4 MPa and a mass flow of 0.015 kg/s; these values were chosen based on the requirement of having superheated steam at the heat exchanger cold outlet with a sufficient degree of superheating. Water inlet conditions are assumed to be constant. The thickness of the heat exchanger was varied between different simulations in order to test its influence on the performance of the heat exchanger. Three different cases were investigated: 1. Fixed heat exchanger length. This corresponds to the "unconstrained" case, since in this case both the outer surface of the inner pipe and the total mass of the heat exchanger increase with the thickness of the pipe. 2. Fixed outer surface of the inner pipe. Since the hot side of the exchange is the limiting factor, increasing the outer surface of the inner pipe significantly benefits the overall heat exchange process. In order to isolate this effect, in this case the length of the exchanger was modified in accordance with the metal thickness to keep a constant value for the total heat exchange area on the outer side of the inner pipes. 3. Fixed heat exchanger mass. In several applications, weight is a constraint that should be accounted for. In this case, similarly to the previous one, the length of the heat exchanger is adapted to keep a constant heat exchanger mass. Figures 5a and5b show the influence of varying the wall thickness of the heat exchanger in the three different cases on the total heat exchange surface on the hot side and on the total mass of the heat exchanger, respectively. Figure 4 shows that, when no constraints are set, both surface and mass of the heat exchanger increase with increased wall thickness; on the other hand

Results and discussion

Heat exchange properties in the reference case

Figure 6 shows the performance of the heat exchanger in the reference case, both in steady-state and dynamic perspective. Figure 6a suggests, as expected, that the gas side of the heat exchanger represents the limiting factor for the exchange, which is confirmed by the temperature of the heat exchanger wall which closely follows that of the cold fluid. The heat exchange coefficients calculated in the model for the different parts of the heat exchanger are presented in Table 4. The convective heat exchange coefficient in the superheated part of the exchanger is particularly high as a consequence of the high speed of the fluid in this part.

Figure 6b shows how the manoeuvring phase generates a drop in outlet steam quality that continues for several minutes even after higher flow and temperature in the exhaust are restored. This results in the potential for heat recovery being limited by the potential damages arising in the expander of the system due to the formation of water droplets. Such configuration, as Figure 6b suggest, would allow the effective functioning of the WHR system only for a limited fraction of the total time spent on the field. 6b therefore suggests that despite the limited duration of the manoeuvring phase, the performance of the system would still be heavily affected by its presence for up to four minutes after the machine started its operations again at full power. In real applications this situation would be partially mitigated by the presence of a control system able to reduce the water mass flow sufficiently to ensure continuity in the operations of the expander. However, these observations suggest that a more efficient system could be designed if such variability was taken into account from a design rather than from a control perspective.

Working cycle

Figure 6a shows the cumulated recoverable exergy over one manoeuvring cycle according to [START_REF] Kalikatzarakis | Multi-criteria selection and thermo-economic optimization of Organic Rankine Cycle system for a marine application[END_REF] as a function of inner wall thickness for the three investigated cases. The observation of Figure 7a suggests that in the case where no constraints are put, the simultaneous increase in exchange surface and exchanger mass allows, for increased pipe wall thickness, a higher rate of total recovered exergy; this trend tends to reach a saturation point over 2 mm thickness, which relates to approaching the pinch limit in the heat exchanger at the beginning of the evaporation phase. From this type of analysis it does not appear clearly, however, what is the contribution of respectively increased exchange surface and increased inertia.

In the case where the mass of the exchanger is kept constant, it appears that the exchange surface is the dominant aspect to account for, and that in applications where the total mass of the exchanger constitutes a limiting boundary condition, the designer should seek to maximise the exchange surface. In the case of a tubular heat exchanger, this translates into minimizing the wall thickness by reducing it to the minimum limit required for structural resistance. The case at constant outer exchange surface shows the existence of a growing trend with thickness, which represents the effect of increased inertia. This effect can improve the recovered exergy over an entire cycle by 27% when pipe thickness is increased from 1 mm to 2.5 mm, shown in Figure 7a. The evolution of cold side outlet temperature in this case (Figure 8) shows that the drop in outlet steam enthalpy during manoeuvring happens with similar speed in all cases, regardless the thickness of the heat exchanger wall. In the cases where the wall is thicker, however, the steam at the heat exchanger outlet becomes superheated faster after the end of the manoeuvring phase.

The reason for such behaviour can be explained from the observation of Figure 9. In the case with 0.5 mm wall thickness (Figure 9a), the recovery is initially faster but later slowed down by the arrival of the colder flow from the heat exchanger inlet, which has not been heated as much because of the low inertia. In the case with wall thickness 2.5 mm (Figure 9b), instead, there is no initial recovery, but the overall process is made faster by the fact that the drop in enthalpy in the exchanger stages close to the cold inlet is lower. This behaviour suggests that, although the increase in heat exchanger inertia seems to bring an improvement in the transient performance of the heat exchanger in terms of recoverable exergy, in practice the largest part of the gain comes from the initial part of the heat exchanger. In particular, the part of the heat exchanger included between 0.2 and 0.3 fraction of the overall length contributes the most. The cold fluid in this part of the heat exchanger becomes sub-cooled liquid during low-load periods while evaporation takes place when the load is higher (see Figure 10); this leads to significant changes in the temperature of the heat exchanger wall during transients and consequently to higher contribution from heat storage. The part of the exchanger located between 0.3 and 0.9 of the overall heat exchanger length, where the cold fluid is in the vapour state during the whole simulation, does not change temperature and therefore does not contribute to increasing the inertia of the heat exchanger.

Conclusions

In this paper we investigated the potential for improving the available recoverable exergy from agricultural machines operations by modifying the evaporator's inertia. The cyclical behaviour of these machines, which was described in Section 2.2, justifies the effort of trying to avoid turbine cut-out during the short manoeuvring breaks which regularly occur between two high-load harvesting phases.

The results presented in this paper suggested that increasing the inertia of the heat exchanger, which in this study was modelled by an increase in the inner heat exchanger wall, can be a solution for improving the dynamic performance of the whole system. When the pipe thickness is increased from 1 mm to 2.5 mm the exergy flow at the cold outlet of the heat exchanger integrated over one harvesting-manoeuver cycle increased by 27%, at constant heat exchange surface, as a consequence of the higher amount of time during which the outlet cold flow is in the superheated steam region. These results therefore suggest that heat exchanger inertia, in addition to exchange coefficient and surface, should be taken into account in the design process of waste heat recovery systems working with a cyclic, dynamic operational profile.

Fig. 1 :

 1 Statistic distribution of the harvesting operations. (a) Engine speed; (b) engine torque; (c) speed versus torque

Fig. 2 -Fig. 3 .

 23 Fig. 2 -Exhaust temperature (a) and exhaust flow rate (b) according to fuel consumption measurements made on a bench test for steady-state conditions for the Perkins engine.

Fig. 4 .

 4 Fig. 4. Cross-section of the heat exchanger modelled in this study.

Fig. 5 .

 5 Fig. 5. Heat exchanger properties as a function of inner pipe thickness for the three investigated cases. a) inner pipe outer surface and b) total mass

Fig. 6 .

 6 Fig. 6. Temperature profiles for the reference heat exchanger. a) Steady-state temperatures along the exchanger and b) temperature evolution over time at exchanger inlet and outlet.

Fig. 7 .Fig. 8 .

 78 Fig. 7. Integrated values over one working-manoeuvring cycle for different wall thickness and for different cases. a) Recoverable exergy and b) Average temperature

Fig. 9 .Fig. 10 .

 910 Fig. 9. Cold-side enthalpy evolution for two working-manoeuvring cycles. Different lines correspond to different locations along the heat exchanger. Case at fixed hot-side surface. a) 0.5 mm wall thickness and b) 2.5 mm wall thickness.

Table 1 .

 1 Summary of the machines involved in the experimental campaign

	Name	Moreau Lexis	Vervaet Beet Holmer	MF 6475
	Year of experiment	2011	2012	2011	2012	2011
	Number of operations	53	74	68	126	132
	Record duration (hours)	104	214	257	788	330
	Hours per operations	3.14	3.96	5.35	7.43	2.5
	Engine type	PENTA		DAF	MAN	PERKINS
		TWD1240VE	MX13.375	D2876 LE	1106D-E66TA
	Engine power (kW)	275	275	375	383	105

Table 2 :

 2 Summary of the reference geometrical parameters of the heat exchanger

	Property

Table 4 .

 4 Steady-state heat transfer coefficients of the reference heat exchanger.

	Convective heat exchange coefficient [W/mK]	Min	Mean	Max
	Gas side		96.1
	Water side (liquid)	490	849	1170
	Water side (phase change)	1240	2250	2950
	Water side (superheated steam)	1220	1230	1240
	The observation of Figure


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