Heat transfer modelling in a ventilated cavity loaded with food product: Application to a refrigerated vehicle

Journal of Food Engineering 113 (2012) 389–398

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Heat transfer modelling in a ventilated cavity loaded with food product: Application to a refrigerated vehicle M.H. Hoang a,⇑, O. Laguerre a, J. Moureh a, D. Flick b a b

Refrigeration Process Engineering, Irstea, 1, rue Pierre-Gilles De Gennes – CS 10030, 92761 Antony Cedex, France AgroParisTech, UMR 1445 Génie Industrie Alimentaire, 91300 Massy, France

a r t i c l e

i n f o

Article history: Received 3 April 2012 Received in revised form 22 June 2012 Accepted 30 June 2012 Available online 10 July 2012 Keywords: Refrigerated vehicle Heat transfer Load temperature

a b s t r a c t A simplified heat transfer model of a refrigerated vehicle was developed in which two loads (front and rear) are considered. The front load located near the supply air duct is subjected to higher air velocity and lower air temperatures compared with the rear load, leading to product temperature heterogeneity. The model takes into account heat transfer by convection between the internal air and the load, between the external air and the walls of vehicle and by conduction in these walls. Air infiltration during door openings is also considered. Model validation was carried out by comparing the calculated product temperatures with those obtained from transport of fruits and frozen foods in a semi-trailer. Good agreement between the experimental and calculated results was obtained. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction One hundred and twenty million tons of chilled food are transported each year in Europe (Guilpart and Guallar, 2003). With a European population of 500 million and its evolution in urban and rural zones and new dietary habits, transport is expanding in response to these trends. Product temperature control in refrigerated transport and in the cold chain in general is of major importance. In Europe, specifications for refrigerated vehicles are covered by the International Agreement for the Transport of Perishables (ATP), which has the status of a standard (Churi, 2004). The ability of a vehicle to transport chilled or frozen food can be defined according to the thermal characteristics of its insulating materials. The ATP classifies insulated vehicles and bodies as either ‘‘Normally Insulated Equipment’’ (K 6 0:7 Wm2 K 1 ) for chilled food transport or ‘‘Heavily Insulated Equipment’’ (K 6 0:4 Wm2 K 1 Þ for frozen food transport. The insulating capacity decreases over time and statistical data on the thermal characteristics of the vehicles in use from 1990 to 2001 illustrate this phenomenon reported by Panozzo et al. (1999) and Panozzo et al. (2001). The product temperature during transport is not only influenced by insulating capacity but also by door openings. Estrada-Flores and Eddy (2006) performed an experimental evaluation of insulation and mechanical refrigeration unit effectiveness on five refrigerated panel vans. It was shown that the temperature variability in the cargo correlated with the time required for the unit to recover temperature control after a door opening and the difference between the maximum and mini⇑ Corresponding author. Tel.: +33 1 40 96 61 21; fax: +33 1 40 96 60 75. E-mail address: [email protected] (M.H. Hoang). 0260-8774/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jfoodeng.2012.06.020

mum temperatures reached during a door opening cycle. Foster et al. (2003) measured infiltration through different entrances of a cold store and compared this infiltration with established analytical and computational fluid dynamics (CFD) models. They demonstrated that analytical and CFD models generally tended to overpredict infiltration. These authors showed that the analytical model developed by Gosney and Olama (1975) provided the closest comparison with the various experiments. Moureh and his team used experimental and CFD approaches to study flow and heat transfer in refrigerated enclosures loaded with plain or porous loads (Moureh et al., 2002, 2009a,c,d; Moureh and Flick, 2004; Moureh, 2007; Moureh, 2009b; Tapsoba et al., 2007). These authors used the Reynolds Stress Model of turbulence to simulate the airflow pattern and temperature distribution in a loaded refrigerated vehicle. The separation of the jet from the wall and the general behavior of airflow patterns related to the primary and secondary recirculations inside the vehicle were presented and compared with experimental results. Although CFD is a powerful simulation tool, its utilisation is limited because of the calculation time and computing capacities required. Several modelling approaches using electrical analogies to predict the airflow rate in spacing or channels between pallets or boxes were developed by Meffert and Van Beek (1983), Wang and Touber (1990), Zertal-Ménia et al. (2002). However, these simplified modelling approaches were not able to provide the load temperature. This paper presents heat transfer modelling in a refrigerated vehicle. A simplified model, based on the concept of ‘‘compartments’’ or ‘‘zones’’ was developed in order to drastically reduce the calculation time compared to the CFD approach. The model,

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Nomenclature C Cp g hfl hrl H I K mfl mrl _ m _ eq m _ if m _ ir m _ ov erall m _r m p q Ra Rw Sf Sm Sr Sfl Srl T ext T th TS T fl T rl T a1 T a2 T a3 T a4 T a5 T a6 T out x

product heat capacity, J kg1 K1 air heat capacity, J kg1 K1 acceleration due to gravity, ms2 convective heat transfer coefficient between the front load and air, Wm2 K1 convective heat transfer coefficient between the rear load and air, Wm2 K1 height of vehicle door, m infiltration rate, m3s1 overall heat transfer coefficient (vehicle walls), Wm2 K1 mass of the front load, kg mass of the rear load,kg air mass flow rate, kg s1 equivalent supply air flow rate, kg s1 infiltration air mass flow rate for the front part, kg s1 infiltration air mass flow rate for the rear part, kg s1 overall air mass flow rate, kg s1 re-circulating air mass flow rate, kg s1 pressure, Pa heat of respiration of product, W kg1 the gas constant for air, Ra = 286.9 Jkg1K1 the gas constant for water vapour, Rw = 461.5 J kg1 K1 surface area of the front part of the vehicle, m2 mean surface area of the vehicle walls, m2 surface area of the rear part of the vehicle, m2 surface area of the front load, m2 surface area of the rear load, m2 external air temperature, °C air temperature near the thermostat sensor, °C supply air temperature, °C temperature of the front load, °C temperature of the rear load, °C air temperature before the heat exchange with the front load, °C air temperature after the heat exchange with the front load, °C temperature of air circulating around the front load, °C air temperature before the heat exchange with the rear load, °C air temperature after the heat exchange with rear load, °C temperature of air circulating around the rear load, °C air temperature flowing out of the pallet, °C specific humidity or humidity ratio

enabling the prediction of product temperature, takes into account the heat transfer by convection between the internal air and the load, between the external air and the cavity walls and by conduction in these walls. Different phenomena are considered: heterogeneity of air flow, the heat of respiration of the product, external air infiltration caused by door openings, etc. In the future, this model will be integrated into other models developed by our team (display cabinet - Laguerre et al. (2012); domestic refrigerator - Laguerre and Flick (2010). . .) in order to predict the time–temperature history of chilled and frozen foods throughout the cold chain. Analysis of the time–temperature history of a high number of product items will be used to identify the weak links in the cold chain. This will also help the operator to manage the logistics in order to avoid product losses. In fact, there are few studies taking into account several types of equipment used at the same time as proposed by our future work. The originality of our approach will be demonstrated in the future work since the models will take into account

Greek symbols coefficient of supply air distribution between front and rear parts, dimensionless bf ratio of mass flow rate between circulating and supply air in the front part br ratio of mass flow rate between circulating and supply air in the rear part c coefficient of distribution of non-bypass air, dimensionless d1 dimensionless convective heat transfer coefficient be-

a

h S

fl fl tween the front load and the air ¼ expððcaðb þ1Þmþ _ m _ if Þ C p Þ f

d2

dimensionless overall heat transfer coefficient between the internal and external air at the front part KS

f ¼ expðb ca mC _ pÞ f

d3

dimensionless convective heat transfer coefficient behrl Srl tween the rear load and the air ¼ expððcaðb þ1Þ _ m _ ir Þ C p Þ mþ r

d4

dimensionless overall heat transfer coefficient between the internal and external air in the rear part KSr ¼ expðb cð1 _ pÞ aÞ mC

k1

ratio of the mass flow rate between the infiltration air _ m and the supply air in the front part ¼ m_if ratio of mass flow rate between the infiltration air and _ the supply air in the rear part ¼ mm_ir 3 air density, kgm characteristic temperature increase related to the heat m qfl of respiration in the front load, °C ¼ ðcaðb þ1Þflmþ _ m _ Þ Cp

r

k2

q s1

if

f

s2

characteristic temperature increase related to the heat rl qrl of respiration of the rear load, °C ¼ ðcð1aÞðbmþ1Þ _ m _ ir Þ C p mþ r

Subscripts a air Ext exterior Int interior f front fl front load if infiltration air in the front part ir infiltration air in the rear part p constant pressure r rear rl rear load s supply th thermostat sensor

random parameters such as the ambient temperature, the product position and its residence time in the equipment, etc.

2. Development of a simplified heat transfer model in a refrigerated vehicle 2.1. Model description 2.1.1. Airflow pattern The airflow pattern inside a loaded refrigerated vehicle proposed by Moureh (2007) was considered. As shown in Fig. 1a, in a real situation, airflow through a pallet load is the mix of: _ 1 ; temperature T S ; - Cold air from supply duct: mass flow rate m - Warm air from the neighbouring pallet loads: mass flow rates _2&m _ 3 ; temperatures T 2 & T 3 ; respectively. m

M.H. Hoang et al. / Journal of Food Engineering 113 (2012) 389–398

391

Fig. 1. Diagram showing the air flow pattern around one pallet.

The mixed air then exchanges with the product and flows out at temperature T out . Because of the difficulty inherent in estimating the mass flow _2 & m _ 3 ) and its temperature (T 2 & T 3 ), rate of the warm air (m the airflow pattern is simplified by using the concept of equivalent supply air flow rate (Fig. 1b). It is considered that the supply air (temperature T S ) enters the pallet load with an equivalent _ eq . A part of the outflow (mass flow rate supply air flow rate m _ r , temperature T out ) re-circulates around the pallet load. For the m

Overall airflow rate: real pattern Equivalent supply airflow rate: simplified pattern

Pallet number 1

2

3

…

pallets inside the vehicle

16

Fig. 2. Overall and equivalent airflow rate in slotted filled pallets (Moureh, 2009b).

heat balance, one can consider simply that the equivalent supply _ eq enters the pallet load at TS and flows out at Tout, the air flow m _ r ) is not involved. The equivre-circulating flow (mass flow rate m _ eq is determined so that the heat exalent supply air flow rate m change between air and the product is the same as that under real conditions. Fig. 2 shows the overall mass flow rate _ 1þm _ 2þm _3¼m _ eq þ m _ r ) and the equivalent supply air flow rate (m _ eq through various pallet loads. This result was obtained from a m simulation of a vehicle loaded with 16 slotted filled boxes Moureh, 2009b. It is noted that the ratio of the overall and the equivalent supply air flow rate is rather high for the first pallet loads ( 5 times), but decreases along the vehicle. For the last pallet loads (number 11 to 16), the overall and equivalent supply air flow rates are almost the same. Because the studied vehicle is not equipped with an air distribution duct, only a little quantity of cold air can reach the last pallet loads. 2.1.2. Model structure The concept of equivalent supply air flow rate and of re-circulating air described in 2.1.1. is used to build our model of heat transfer between the air and the product inside a refrigerated vehicle (Fig. 3). Two loads, front and rear, are considered in order to represent the product temperature heterogeneity in the vehicle. Each load is characterized by its temperature (Tfl for the front load and Trl for the rear load), mass (mfl and mrl), and heat of respiration _ (qfl and qrl). The supply air (temperature TS and mass flow rate m) enters at the top left section of the cavity. Part of this air flows directly to the return air duct without interacting with the load (bypass air). The ratios of the mass flow rates of bypass and nonbypass air are represented by the coefficients 1  c and c; respec-

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M.H. Hoang et al. / Journal of Food Engineering 113 (2012) 389–398

Fig. 3. Simplified heat transfer model in a refrigerated vehicle (side view).

tively. The non-bypass supply air is divided into two parts: one goes to the front load (coefficient of distribution a) and the other to the rear load (1  a). Re-circulating air around the loads is also considered. The ratio of mass flow rate between re-circulating and supply air is represented by the coefficients bf (for front load) and br (for rear load). The temperature of this air is higher than that of supply air because of heat transfer with the load and with the air outside the vehicle. The infiltration of outside air through the door _ if and m _ ir ). is also taken into account (mass flow ratesm In our model, it is considered that the thermostat sensor is located near the return duct in such a manner that the return air temperature is equal to T th ; which implies a hypothesis of perfect regulation of the cold production system. The external air temperature T ext and the return air temperature T th are the input parameters of the model which enables the supply air temperature TS, the air temperature above and below the load (Ta1, Ta2, Ta4 and Ta5.) and the load temperatures (Tfl - front and Trl - rear) to be calculated. 2.2. Heat balance equations In order to simplify the model development, the thermal inertia of the air is neglected compared to that of the load. Heat balance equations are developed for the two loads and different zones inside the vehicle. Four white rectangles (I, II, III and IV, Fig. 3) represent the heat exchange between air and loads (I&III) and the heat losses through walls (II&IV). The mixing zones of different air flows above the loads and at the return air are also considered. 2.2.1. Heat balance for the air above the front load The air above the front load (temperature T a1 ) is the mixing of: – Air from the supply air duct (temperature T S , mass flow rate _ ca m) – Infiltration air from outside (temperature T ext , mass flow rate

_ if m

– Air circulating around the front load (temperature T a3 , mass _ flow rate bf ca m)

_ if T ext þ bf camT _ þm _ if ÞT a1 ðcaðbf þ 1Þ _ Sþm _ a3 ¼ ðcaðbf þ 1Þm camT þ k1 ÞT a1  bf ca T a3  caT S ¼ k1 T ext ð1Þ where k1 ¼

_ if m _ m

2.2.2. Heat exchange between the air and the front load (rectangle I) Convective exchange (heat transfer coefficient hfl ) takes place between the air (temperature T a1 ) and the front load (temperature T fl ). After this exchange, the air temperature is T a2

_ þm _ if ÞC p dT a ¼ hfl ðT 1  T a ÞdSfl ) ðcaðbf þ 1Þm ðT a2  T f Þ ¼ d1 ðT a1  T f Þ ) d1 T a1  T a2 þ ð1  d1 ÞT fl ¼ 0 where d1 ¼ exp



hfl Sfl _ m _ if Þ C p ðcaðbf þ1Þmþ

ð2Þ 

2.2.3. Heat losses through the walls (rectangle II) In order to respect the mass conservation of air, it is considered _ if ) flows out that a part of the air (temperature T a2 ; mass flow rate m _ flows towards of the vehicle. The second part (mass flow rate ca m) _ flows around the return air. The third part (mass flow rate bf ca m) the front load. It is assumed that there is heat exchange between the third part and the external air through the vehicle walls. After this exchange, the air temperature is T a3 :

_ p dT a ¼ KðT ext  T a ÞdS1 ) ðT a3  T ext Þ ¼ d2 ðT a2  T ext Þ ) bf ca mC d2 T a2  T a3 ¼ ðd2  1ÞT ext where d2 ¼ exp



KSf _ p bf ca mC



ð3Þ

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2.2.4. Heat balance in the front load The variation in the internal energy of the front load is the sum of the heat generated by product respiration and by the heat exchange by convection with air. At steady state, this energy is constant.

dT fl _ þm _ if ÞC p ðT a1  T a2 Þ mfl C ¼ mfl qfl þ ðcaðbf þ 1Þ m dt At steady state,

dT fl dt

¼ 0, so:

ð4Þ

mfl qfl s1 ¼ ðcaðbf þ1Þ _ m _ if Þ C p mþ

2.2.5. Heat balance in the return air As cited previously, it’s assumed that the thermostat position is near the return air duct and its regulation is perfect. Thus, the temperature of the return air is constant (T th ). This air is the product of mixing of the bypass air (temperatureT S ) and the air under the front and the rear loads (temperatureT a2 and T a5 respectively).

_ a5 þ ð1  cÞmT _ S ¼ mT _ th _ a2 þ cð1  aÞmT ca mT ) ca T a2 þ cð1  aÞT a5 þ ð1  cÞT S ¼ T th

ð5Þ

2.3. Matrix formulation of the equations in steady state The same procedure is applied to the rear load. For the steady state, the equations developed previously can be summarized in matrix form.

AX ¼ BT ext þ CT th þ D

ð6Þ

where

0

0 B1d B 1 B B 0 B B B 0 B A¼B B 0 B B 0 B B 0 B B @ 0 0

1

This coefficient describes the distribution of the supply air between the front and rear parts. The value of this coefficient depends on the presence or absence of distribution ducts in the vehicle: - When air is evenly distributed (in presence of distribution ducts): a ¼ 0:5. - In the absence of distribution ducts: the coefficient a in this case is estimated from data on the equivalent supply airflow _ eq . In fact, m _ eq represents the amount of supply air that rate m participates in the heat exchange with the product (see para_ eq in a vehicle loaded with graph 2.1.1). The distribution of m _ eq 16 slotted filled pallet loads is shown in Fig. 2. The sum of m for pallets No.1 to 8 could represent the mass flow rate of the _ In the same way, the sum of supply air in the front part ca m:. _ eq for pallets No. 9 to 16 can represent the mass flow rate of m _ Then, a value the supply air in the rear partcð1  aÞ m: a = 0.78 is obtained. 3.2. Ratio of mass flow rate between recirculating air and supply air, b This ratio is also estimated in the case of a refrigerated truck loaded with slotted filled boxes Moureh, 2009b. The circulating

0

ca

caðbf þ 1Þ þ k1

0

bf ca

0

0

0

d1

1

0

0

0

0

0

d2

1

0

0

0

1

1

0

0

0 0

1c cð1  aÞ

0 0

ca 0

0 0

cð1  aÞðbr þ 1Þ þ k2

1  d3

0

0

0

0

d3

0

0

0

0

0

0

0

0

0

0

0

1

0 1 0 1 0 0 k1 T1 B0C B 0 C BT C B0C B C C B B 2C B C B C C C B B B C B0C B d2  1 C B TS C B0C B C C C B B B C B C C C B B B C B0C B 0 C B T a1 C B s1 C B C C C B B B C C B C C B B0C ; D ¼ 1 ; C ¼ ; B ¼ 0 X¼B T B C C B B a2 C B C B C C C B B B C B0C B k2 C B T a3 C B0C B C C C B B B C B0C B 0 C B T a4 C B0C B C C C B B B C B C C C B B B C @0A @ d4  1 A @ T a5 A @0A 0 0 T a6 s2 0

3. Estimation of coefficients 3.1. Coefficient of supply air distribution a

T a1 þ T a2 ¼ s1 where

n _i¼m _ if þ m _ ir ¼ 60 average infiltration mass flow rate: m qI is considered. This approximation makes it possible to take into account the infiltration of external air using the steady state approach.

0

1

The system of Eq. (6) is programmed using Matlab and allows rapid calculation of the load and air temperatures inside the vehicle: the CPU time is less than 1 min for one simulation. The effect of the door openings can be averaged over the transport period. For example, if the door is opened during n minutes every hour with an instantaneous infiltration rate I (m3s1), the

0

0

0

1

C C C C 0 0 C C 0 0 C C C cð1  aÞ 0 C C 0 br cð1  aÞ C C C 1 0 C C d4 1 A 1 0 0

0

airflow rate can be calculated by subtracting the equivalent airflow rate from the overall one (data from Fig. 2):

_r¼m _ ov erall  m _ eq m

ð7Þ

By its definition:

b¼

_r m _ meq

ð8Þ

So, it was estimated from the data (Fig. 2) that bf ¼ 2:3 for the front part (average value for the boxes numbered 1 to 8) and br ¼ 0:3 for the rear part (average value for the boxes numbered 9–16). However, the low values of air mass flow rate in the rear part can produce a high uncertainty for br : These data were obtained, however, in the case of no distribution duct. In the other case, there is more air in the rear part and a higher br value is expected.

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M.H. Hoang et al. / Journal of Food Engineering 113 (2012) 389–398

3.3. Coefficient of non bypass air distribution c

q¼

To the best of our knowledge, there is no reported value for this coefficient in the literature. The value of c is to be expected between 0.7 and 0.9.

I ¼ 0:221Sdoor ðgHÞ0:5



qint  qext qint

0: 5

2 1 þ ðqint =qext Þ0: 333

!1: 5 ð9Þ

- This model was validated by experimental verifications during cold store door openings (Foster et al. (2003)). The authors also noted that in spite of a maximum overestimation of 38.6%, this model predicts results in a better manner than all other tested models. - The air density is a function of the temperature and humidity as shown below:

ð10Þ

- It is supposed that during the transport timeDt trans ; the door is opened N open times with an opening duration of Dtopen :. Using the steady state approximation (cf. paragraph 2.3), the average infiltration can be expressed as:

3.4. Infiltration mass flow rate As a first approach, the model of Gosney and Olama (1975), was used to estimate the infiltration flow rate during door openings. These authors proposed a mathematical expression of the infiltration rate - Eq. (9):

p ð1 þ xÞ Ra T 1 þ x RRw a

_ ir ¼ m _r _ if þ m m

N open Dt open Dt trans

ð11Þ

Although it can be expected that there is more infiltration on the rear load than on the front load, according to our knowledge, no information on the infiltration distribution is available in the literature. As a first approach, it is assumed that:

_ ir _ if ¼ m m

ð12Þ

3.5. Overall heat transfer coefficient, K The measured values of K for 24 normally insulated vehicles and 70 heavily insulated vehicles were reported by Panozzo et al., 2001.

a

N: Nectarine; A: Apricot; P: Peach

b

c High level: 1.8 m

Thermal sensor

Bottom level: Thermal sensor 0.4 m inserted within a fruit

d

Type Semi – refrigerated trailler

Container

Fruit

Refrigerating unit

Length

13.3m

Height

2.6m

Width

2.5m

Maxima (Carrier)

Air ducts providing 2 inlet sections: 0 and 10 m Fig. 4. Refrigerated trailer characteristics, load composition and thermal sensor details related to full-scale experiment: (a) load composition, (b) sensor location, (c) thermal sensor details, (d) refrigerated trailer characteristics.

M.H. Hoang et al. / Journal of Food Engineering 113 (2012) 389–398

From these data, the mean value of K is calculated: K mean; normally ¼ 0:51 Wm2 K 1 and K mean; heav ily insulated ¼ 0:37 Wm2 K 1 .

insulated

4. Comparison between experimental and numerical results 4.1. Transportation of fruits An experiment was carried out by our team for real transport of fruits (800 km, 11 h) in a refrigerated semi-trailer performed in France between a horticultural hub located in the ‘‘Bouches du Rhône’’ region and a distribution hub in the Paris area. The fruits were: apricots, peaches and nectarines loaded in 25 pallets (Fig. 4a). In order to characterize the temperature distribution inside the vehicle, the air and product temperatures were recorded using sensors placed at the bottom and top of the 9 investigated pallet loads (Fig. 4b). There were two types of sensors: thermometer TESTO (resolution + 0.1 °C, accuracy + 0.5 °C) and wireless sensor SPY (resolution + 0.5 °C, accuracy + 1.0 °C) (Fig. 4c). The sensors were inserted in fruits and placed in selected positions (bottom/top) at a depth of 5 cm in the pallet loads, near the lateral walls of the truck. These sensors were recovered at the end of the transport operation. The characteristics of the vehicle are described in Fig. 4d. To represent the steady state, the air and product temperatures at the end of the transport operation are presented in Fig. 5. This figure also shows the average air temperature at the inlet, the outlet, above the products and outside the vehicle. It should be noted that the use of the air duct brought cold air to the rear part. Therefore, the pallet loads (1 and 13) located at the extremities (in the front and at the rear parts of the container) were maintained at appropriate temperatures of 9.7 and 7.8 °C, respectively (at the bottom levels of the pallet loads), this being close to the set point temperature (6 °C). However, in this case, higher temperatures are encountered in the middle part of the container due to the presence of local stagnant areas which tend to predominate half-way between the air injections (at 0 and 10 m from the front of the container).

395

In order to be able to compare the measured air and product temperatures and the results of the simulation under the same conditions, the door openings (twice, each time for 15 min) and the heat of respiration of the fruits were taken into account. The main parameters used for the simulation are presented in Table 1. The values of these parameters were estimated from the data reported in Tapsoba (2006) and the K value was obtained from the data of Panozzo et al. (2001). The heat of respiration of the fruits was estimated using IIR data (1971). The two load temperatures of the model correspond to the minimal and maximal product temperatures. So, in order to compare the measured results with those obtained using simulation, the measured temperatures are divided into two groups: one with the 9 lowest temperatures and one with the 9 highest temperatures. The mean temperature of each group is then calculated and compared with the two load temperatures obtained using simulation. This indicates that in the presence of air distribution ducts, the two loads of the model should not be considered as ‘‘front’’/ ’’rear’’ but rather as ‘‘well-ventilated’’/’’poorly ventilated’’ parts. Fig. 6 shows a comparison between experimental and calculated air and load temperatures for a ¼ 0:7; b ¼ 2:3 and c ¼ 0:8. It can be observed that for these parameter values, the model slightly over-predicts the air and load temperatures in the front part and slightly under-predicts the air and load temperatures in the rear part. The maximum difference, however, is only 1 K. One of the challenges inherent in simulation is to estimate the coefficient of air distribution a, b and c. A sensitivity study was carried out and the results are presented in Fig. 7. The variation in a Fig. 7a can greatly change the load temperature. As a increases, there is more cold air coming to the front load, as a consequence, its temperature Tfl decreases while the temperature of the rear load Trl increases. It should be noted that the load temperatures obtained with a = 0.8 are closer to the experimental values than those obtained with a = 0.7. The two load temperatures obtained using simulation, Tfl & Trl, are greater than the thermostat temperature Tth while for the experiment: Tfl_experimental < Tth < Trl_experimental. Therefore, the

Fig. 5. Air and product temperature distribution in a full-scale experiment Moureh et al. (2009a). (a) Air temperature, (b) Product temperature.

Table 1 Parameter values used in the heat transfer model of a refrigerated vehicle in the case of transportation of fruit. Parameters

Dimensions Reference

hfl = hrl = 10 K = 0.51 _ fl = m _ rl = 9500 m _ = 1.4 m _ ir = 0.01 _ if = m m q = 0.055 Sf = Sr = 74 Sfl = Srl = 116.6

2

1

Wm K Wm2 K1 kg kg s1 kg s1 W kg1 m2 m2

Tapsoba (2006) Panozzo et al. (2001)normally insulated vehicle Tapsoba (2006) Tapsoba (2006) Tapsoba (2006) IIR (1971) Tapsoba (2006) Tapsoba (2006)

15

Text

Load temperature

13

Air temperature

13

Trl

12

Tfl

11

11

Trl_experimental

9

Tth Tfl_experimental

8 7

Trl

12

Tfl

11

Trl_experimental

9

Tth Tfl_experimental

8 7

7

Ta4

Tth

TS 5 5

7

1 2 3 4 5 (b) Sensitivity study of βf = βr (α = 0.7 & γ = 0.8)

Ta6

Ta3

Ta1

βf_reference

10

0 Tfl

0.5 0.6 0.7 0.8 0.9 1 (a) Sensitivity study of α (βf = βr=2.3 & γ = 0.8)

13

Trl 9

αreference

10

0.4

9

11

13

15

Experimental temperature (°C) Fig. 6. Comparison between the experimental and calculated temperatures with parameters from Table 1, a ¼ 0:7; b ¼ 2:3, c ¼ 0:8 (transportation of fruit).

thermostat temperature Tth alone is controlled, the risk of over freezing (Tfl_experimental < Tth) (frozen of vegetables for example) or overheating (Trl_experimental > Tth) of the refrigerated product is not detected. The variations in b Fig. 7b) and c (Fig. 7c) do not have much influence on the load temperature. The two load temperatures (front and rear) increase slightly when b increases because of a greater influence of the recirculating air whose temperature is higher than that of the supply air. The opposite trend is observed when c increases: the two load temperatures decrease because greater quantities of cold supply air can reach them. 4.2. Transport of frozen food The transport of frozen food (spinach, whiting, fish finger and ice cream) in a semi-trailer equipped with air distribution ducts was performed by Cemagref (Bennahmias (1984)). The products were loaded in 30 pallet loads and thermocouples were inserted inside 22 products in order to measure their temperature. A round trip between Monsoult (France) and Asti (Italy) was carried out (84 h for the trip from France to Italy and 144 h for the return trip). To represent the product temperature in steady state, the mean value during the last 12 h was calculated and reported in Fig. 8. This figure also shows the mean temperature of the supply air, the return air and the external air during the two journeys. These mean temperatures of 22 products were divided into two groups: ‘‘wellventilated one’’ with the 11 lowest temperatures and ‘‘poorly ventilated’’ one with the 11 highest temperatures. The mean temperature of each group was then calculated. These values were used afterwards for comparison with the numerical results. Because there is no heat of respiration in the case of frozen food, it can be considered that T a1 ¼ T a2 ¼ T fl and T a4 ¼ T a5 ¼ T rl . This was a long-distance transport operation, there were no door

Load temperature (°C) (°C )

Calculated temperature (°C)

Input temperature for the model

Load temperature (°C)

M.H. Hoang et al. / Journal of Food Engineering 113 (2012) 389–398

Load temperature (°C) (°C )

396

13

Trl

12

Tfl

11

γreference Trl_experimental

10 9

Tth Tfl_experimental

8

7 0.65

0.7 0.75 0.8 0.85 0.9 0.95 (c) Sensitivity study of γ (βf = βr=2.3 & α= 0.7)

Fig. 7. Sensitivity study: load temperature according to a (a), bf and br (b) and c (c) (transportation of fruit).

openings and the external air infiltration can be considered as neg_ if ¼ m _ ir ¼ 0: ligible: m The main parameters used for the simulation are presented Table 2. Two simulations were carried out: France to Italy journey and the Italy to France journey. The simulation results (a ¼ 0:7; b ¼ 2:3 and c ¼ 0:7) are compared with the experimental ones (Fig. 9). Good prediction of the supply air temperature TS (0.4 K and 0.2 K difference for the two simulations) was obtained. The model slightly under-predicts the load temperature in the case of the first journey (France to Italy, Text = 24.4 °C; Tth = 26.8 °C) and over-predicts the load temperature in the second journey (Text = 26.5 °C; Tth = 25.0 °C). This difference can be explained by the change in input temperature Text and Tth. A maximum 0.7 K difference is observed between the experimental and calculated load temperatures. 5. Conclusion A simplified heat transfer model was developed for a refrigerated vehicle. In order to represent the heterogeneity of product temperature in the vehicle, two loads are considered in the model: a well-ventilated one (generally near the front) and a weakly ventilated one (generally near the rear). The calculation of locally higher or lower product temperatures within front and rear loads requires the use of CFD models. However, the main advantage of the model developed in this study is its low CPU computing time. For example, the calculation of load and air temperatures presented in section 4.1 takes less than 1 min, whereas the corresponding CPU time related to the CFD model is estimated to be

M.H. Hoang et al. / Journal of Food Engineering 113 (2012) 389–398

397

Fig. 8. Mean temperature of product, supply air (TS), return air (Tth) and external air temperature (Text) during the transportation of a frozen product Bennahmias (1984). (a) France to Italy journey (Text = 24.4 °C; Tth = -26.8 °C), (b) Italy to France journey (Text = 26.5 °C; Tth = 25.0 °C).

Table 2 Parameter values used in the heat transfer model of a refrigerated vehicle in the case of transportation of frozen food. Parameters

Dimensions

Reference

K = 0.37 _ = 1.7 m _ if = m _ ir = 0 m q=0 Sf = Sr = 67

Wm2 K1 kg s1 kg s1 W kg1 m2

Panozzo et al. (2001)heavily insulated vehicle Bennahmias (1984) Bennahmias (1984) Bennahmias (1984) Bennahmias (1984)

60 h for the same configuration (Moureh et al. 2009c). This aspect enables the rapid evaluation of the influence of the input parameters such as external temperature, door openings, wall insulation, thermostat setting, heat of respiration, etc. on the load temperatures. The model can also take into account the presence of air distribution ducts and the by-pass between the supply and return air ducts. It was validated by comparison with the experimental data obtained during real transport of chilled and frozen food products.

M.H. Hoang et al. / Journal of Food Engineering 113 (2012) 389–398

a

-24

Calculated temperature (°C) Calculated temperature (°C)

398

-25

Acknowledgements The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7/ 2007-2013) under Grant agreement No. 245288.

Trl -26

References -27

Tfl

TS

-28

-29

-30

-30

-29

TS

b

-28

-27

-26

-25

-24

Experimental temperature (°C) (°C) Experimental temperature

-22

Calculated temperature (°C) Calculated temperature (°C)

Trl -23

-24

Tfl -25

-26

TS -27

-28 -28

-27

-26

-25

-24

-23

-22

Experimental Experimental temperature temperature (°C) (°C) Fig. 9. Comparison between the experimental and calculated temperatures with parameters from Table 2 (transportation of a frozen product), a ¼ 0:7; b ¼ 2:3 and c ¼ 0:7. (a) France to Italy journey (Text = 24.4 °C; Tth = -26.8 °C), (b) Italy to France journey (Text = 26.5 °C; Tth = 25.0 °C).

This model allows the prediction of the maximal and minimal load temperature. It will be integrated into those developed for refrigerated display cabinets (Laguerre et al. (2012)), domestic refrigerators (Laguerre and Flick (2010)) and enable the prediction of product temperature evolution throughout the cold chain. In fact, there are few studies which take into account several links in a cold chain at a time such as that proposed for our future work. Quality and microbiological evolution can also be coupled with this approach and the developed model can then be used as a risk evaluation tool.

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