Progress in Exergy, Energy, and the Environment || Flow and Heat Transfer Characteristics of an...

Flow and Heat Transfer Characteristics of an EmptyRefrigerated Container 60Ersin Alptekin, Mehmet Akif Ezan, and Nuri Kayansayan

Abstract

To preserve the quality and the shelf life of perishable foods, it is essential to analyze the airflow distribution inside a

refrigerated truck for maintaining homogeneous temperature throughout. This study is an initiation of such analysis, and

air distribution patterns of ceiling-slot ventilated enclosure are numerically investigated for three different geometries.

Numerical analysis is carried out by using ANSYS-FLUENT software which is based on control volume approach. In the

analysis, the container’s cross-sectional area is kept constant. However, by changing the container length as 6 m, 8 m, and

13.3 m, the aspect ratio of the container is varied accordingly. The air velocity at the slot exit is varied in such a way that

Reynolds number of the discharge flow covers the range between 20 and 1.23 � 105.

A three-dimensional solution domain is considered in the analysis and is identified by a total number of 2.5 � 106

meshes. The Reynolds Stress Model (RSM) is applied in solving turbulent Navier–Stokes equations at each computa-

tional node. The validity of the present computational method is checked by generating and comparing the results with

available work in literature. The flow distribution patterns of empty container indicate that there exist circulation zones

close to the surface at the opposite of air discharged slot. In fact, two different vortices at two perpendicular planes

coexist. The location of these circulation zones does not change with the discharge flow rate, but the circulation intensity

increases as the flow rate increases. It is determined that variation of the container aspect ratio affects the flow behavior.

For the case of container length at 13.3 m, the flow at the upper surface separates at a distance of 11.5 m from the air

injection plane.

Keywords

Refrigerated vehicle � Airflow distribution � Food transportation � Cold chain

Introduction

Cold chain is generally used to define a combination of temperature-controlled supply systems in food industry.

As illustrated in Fig. 60.1, from the cold storage (or warehouse) to the client, the food must be kept in a predefined

temperature range to preserve its quality and increase the shelf life. According to Flick et al. [1] about 60 % of food products

require refrigeration process in the cold chain. They also stated that inadequate storage or transport conditions cause

corruption of 25–30 % of global food production. This huge amount of loss can be regained by designing each component of

the cold chain properly.

As indicated by Hoang et al. [2], 120 million tons of chilled foods are transported each year in Europe. With the expansion

of the urban areas, the temperature control of frozen foods in refrigerated vehicles becomes crucial. Hoang et al. also

mentioned that the ATP (International Agreement for the Transport of Perishables) separates the refrigerated vehicles into

E. Alptekin (*) � M.A. Ezan � N. KayansayanDepartment of Mechanical Engineering, Dokuz Eylul University, 35397, Tinaztepe, Buca, Izmir, Turkey

e-mail: [email protected]; [email protected]; [email protected]

I. Dincer et al. (eds.), Progress in Exergy, Energy, and the Environment,DOI 10.1007/978-3-319-04681-5_60, # Springer International Publishing Switzerland 2014

641

mailto:[email protected]



two categories, which are “Normally Insulated” and “Heavily Insulated” vehicles. Heavily insulated trucks are adequate for

frozen food transportation with an overall heat transfer coefficients less than 0.4 W/m2K, and normally insulated trucks are

considered to be proper for chilled foods (U � 0.7 W/m2K). In these trucks, the main issue is to control the temperature

distribution within a narrow range. To accomplish this in large volume (V > 50 m3) transportation, the cooling system is

usually driven by an engine separated from the vehicle’s main engine. The positioning of the evaporator is a critical issue in

acquiring homogeneous temperature distribution inside the container. Neglecting the small influences of radiation and

natural convection, the cooling process is mainly controlled by forced convection, and the homogenous temperature

distribution may be achieved by optimization of the flow distribution inside the container.

Even though numerous experimental and numerical results have been published for thermal behavior of warehouses,

there are few studies conducted related with the refrigerated vehicles. As a pioneer, Moureh and his colleagues numerically

and experimentally examined the flow and thermal behavior of a refrigerated container under several conditions. Moureh

et al. [3] used FLUENT CFD software to obtain velocity distribution in empty and loaded containers. They compared the

predicted velocity field with experimental LDA (Laser Doppler Anemometer) measurements. Two different turbulence

models are implemented, k-ε and RSM. As a result, RSM turbulence model showed good agreement with the experimental

data. After this pioneer study, Moureh and his colleagues conducted many other researches related with the refrigerated

containers. Moureh and Flick [4] represented dimensionless temperature distribution inside container for one selected case at

a single Reynolds number and a container length. In addition, Moureh and Flick [5] experimentally and numerically studied

the temperature and velocity distributions inside a loaded container for two different spacings between loads, and the spacing

is taken to be at 1 cm and 2 cm. Later, Moureh and Flick [6] tried to improve the performance of the container ventilation by

locating the inlet section near lateral surface. They compared the ventilation efficiency for lateral and central inlet

orientations. Besides, Moureh et al. [7] tried to improve the cooling effect by changing the air duct configuration. Unlike

the previous numerical models, in this study, Moureh and his colleagues considered loads as porous medium to achieve more

realistic velocity field.

In this study, air is discharged from the evaporator located at midsection of front surface having half width of the

container. Suction, on the other hand, takes places at all surfaces except the discharge plane of the evaporator. First, the flow

field is studied and the circulation zones are identified. To do this, flow Reynolds number and container aspect ratio have

varied, and the local and the average heat transfer characteristics of such a flow are computed. The refrigerated truck is

assumed to be moving for external flow simulations. Thus, the container’s overall heat transfer coefficients and heat gains

through the container surfaces are realistically evaluated.

Material and Method

Definition of the Problem

The geometry and the size of the refrigerated container are provided in Fig. 60.2. The evaporator is located at the center of

the front surface, and the spacing between the ceiling and the evaporator is 4 cm. Air is supplied to the computational domain

from the inlet section as represented in Fig. 60.2 and collected by the openings at the bottom, lateral, and top surfaces of the

evaporator. The container cross-sectional area is kept constant, but the length is varied, so that the aspect ratio (L/H) is in

the range between 2.4 and 5.32.

Fig. 60.1 Cold chain

642 E. Alptekin et al.

Governing Equations and Solution Method

To simplify the problem, instead of solving time-dependent governing equations, time averaged Reynolds-Averaged-

Navier–Stokes (RANS) equations are solved. Considering steady and incompressible flow conditions, the principle of

conservation of mass, momentum, and energy can be satisfied by the following equations:

Mass:

∂∂xi

uið Þ ¼ 0 ð60:1Þ

Momentum:

∂∂xj

ρuiuj� � ¼ � ∂p

∂xiþ ∂∂xj

μ∂ui∂xj

þ ∂uj∂xi

� �� ρu

0iu

0j

� �ð60:2Þ

Energy:

∂∂xi

ρCρuiT� � ¼ ∂

∂xjk∂T∂xj

� ρCρu0jT

0� �

ð60:3Þ

where u and u0 indicate the average and fluctuating velocities, respectively. Similarly, T and T0 represent the mean and

instantaneous temperatures. Turbulence modeling by using RSM (Reynolds Stress Model) has been in use by many authors.

Norton et al. [8] discussed the pros and cons of eddy viscosity and Reynolds stress closure models in turbulence modeling for

confined rooms with adverse pressure gradients and flow separations. It is determined that RSM provided reasonable

predictions for flow separations and Coanda effects. Similarly, Schalin and Nielsen [9] and Moureh and Flick [6] indicated

that for three-dimensional flow in confined spaces, RSM method of calculations predicts the experimental results with a

maximum of 10 % deviation. As a result, Reynolds Stress Model (RSM) is considered in this study for modeling the 3D

turbulent flow.

Equations (60.1), (60.2), and (60.3) are solved with the aid of ANSYS-FLUENT software [10]. Software is based on the

control volume approach of Patankar [11]. QUICK scheme [12] is applied for discretization of convective terms, and

SIMPLE [13] algorithm is adapted for solution of momentum and continuity equations. For evaluating the turbulence

boundary layer near the wall, “log-law” function is used [14]. Computational domain is divided into nonuniform quadrilat-

eral grids. To capture the temperature, velocity, and pressure gradients close to the solid surface, fine grids are generated.

Convergence criteria for all conservation equations are taken to be 10�5.

Outlet Section

Inlet Section

H = 2.5 m

L = 6 m, 8 m and 13.3 m

W = 2.5 m

Fig. 60.2 Geometry of the container and evaporator

60 Flow and Heat Transfer Characteristics of an Empty Refrigerated Container 643

Boundary Conditions and Mesh Independency

Because of container symmetry, half of the computational domain is taken into account, and at the symmetry plane, the

boundary condition is set to be ∂ϕ/∂x|x ¼ W/2 ¼ 0. Uniform velocity (win) and temperature (Tin) profiles are assumed at

the inlet section of the evaporator. On the container walls, no slip condition is sufficed by u ¼ v ¼ w ¼ 0. Due to large

insulation thickness at the bottom and front (i.e., surface with evaporator) surfaces, these surfaces are assumed to be

adiabatic (∂T/∂n|surface ¼ 0). The insulation material is selected to be polyurethane, with k ¼ 0.02 W/mK, and the thickness

of the insulation layers are 100 cm, 85 cm, and 80 cm for the ceiling, lateral, and rear surfaces, respectively. On the top,

lateral, and rear surfaces, the combine effect of solar radiation, convection, and surface emission is considered, and the

following energy balance equation is defined at those surfaces:

�k∂T∂n

��surface

¼ αIsolar � σε T4 � T4sky

� h1 T � T1ð Þ ð60:4Þ

where α and Isolar are the surface absorptivity and the incident solar radiation, respectively. Meteorological data of Izmir,

Turkey, for June 21st at 1 PM noon are considered for solar radiation intensity (Isolar), the sky (Tsky), and atmospheric (Tatm)temperatures.

Average heat transfer coefficient (h) for each surface is evaluated by considering the results of a preliminary analysis. To

solve 3D flow over the truck and container combination, at a velocity of 90 km/h, a total of 16 million hybrid grids are

generated. The flow patterns around the truck are represented in Fig. 60.3. At the top and back sides of the container,

separation of flow can easily be located. As a result of this preliminary analysis, average heat transfer coefficients for three

surfaces are calculated as given in Table 60.1. The predicted heat transfer coefficients are compared with the well-known

correlation over a flat plate [15]. Comparative results show that the numerical heat transfer coefficients are approximately

30 % higher than that calculated by theoretical methods.

To get numerical results free of mesh size, the same geometry at the same flow conditions is studied for three different

mesh sizing which are respectively 2.5 million, 4.5 million, and 10 million. As indicated in Fig. 60.4, no remarkable change

of results is detected due to change in mesh size. Therefore, 2.5 million mesh is selected for the current study.

Fig. 60.3 Flow patterns around the refrigerated truck

Table 60.1 Mean heat transfer coefficients for external surfaces of container

Surface

Mean heat transfer coefficient, h (W/m2K)

Predicted

Theoretical

Correlation Result

Top 64.48 NuL ¼ 0:037Re4=5L Pr1=3 50.73

Lateral 66.18 56.4

Rear 42.05 � �


Results and Discussion

In this section, first the validity of the numerical method is discussed with regenerating the numerical data for the same

geometry and flow conditions as studied experimentally by Moureh and Flick [6]. After that, the influence of selected

parameters on the heat transfer inside the container is evaluated.

Validation of the Methodology

Recent experimental work of Moureh and Flick [6] that provides flow patterns inside a refrigerated vehicle is selected

for comparison of present methodology. The container studied by Moureh has the same cross-sectional dimensions as

H ¼ W ¼ 2.5 m with the present study, and the container length is taken to be 13.3 m. Unlike the present study geometry,

the air inlet section is at the top, and the outlet is at the bottom of the front plane. Moureh and Flick studied the airflow

characteristics of such a container both experimentally and numerically. In their analysis, LDA is used to capture the

velocity distributions on the symmetry surface. In addition, the inlet velocity is taken to be 11 m/s, and the turbulence

intensity of entering flow is defined to be 10 %. Moureh’s results and the present study are compared for the same flow

geometry and flow conditions.

In Fig. 60.5, airflow patterns on the symmetry plane of the container are compared with the experimental and numerical

results of the reference work. On the symmetry plane of the container, two separated circulation zones are formed. Owing to

the viscous effects, flow separates from the upper surface and generates a secondary circulation at the rear region of the

container. As illustrated in Fig. 60.5, this study results predict the experimental results of the reference work fairly

accurately. In Fig. 60.6, decay of the jet axis velocity in longitudinal direction is given and represents Moureh’s experimental

results within acceptable engineering accuracy.

Fig. 60.4 Influence of number

of grids on the jet velocity decay


Fig. 60.5 Comparison of airflow patterns with the reference work. (a) Experimental results [6]. (b) Numerical results [6]. (c) Current predictions

12

10 Moureh and Flick (2005)

Current Study

Length of the Container (m)

W (m/s)

ExperimentalNumerical

8

6

4

2

0

-20 2 4 6 8 10 12 14

Fig. 60.6 Comparison of

velocity variation on jet axis

with the reference work


Parametric Results

In order to evaluate the effect of inlet velocity on heat transfer through container surfaces, the flow Reynolds number is

varied in the range of 20–1.23 � 105. In Reynolds number definition, characteristic length is taken to be hydraulic diameter

of the evaporator exit section. In addition, the container length is varied so that the container aspect ratio (H/L) assumes the

following values 2.4, 3.2, and 5.32. Hence, as shown in Table 60.2, a total of eight parameters are varied in the analysis.

Effect of Reynolds NumberFlow patterns and isotherms are illustrated in Fig. 60.7 for various Reynolds numbers. Temperature contours are represented

in nondimensional form as T* ¼ (T � Tin)/(Tout � Tin). As the Re number increases from 20 to 1.23 � 105, intensity of

circulation increases and dominates the rear side region of the container. From Fig. 60.7, one can clearly see the Coanda

effect for Re > 20. Coanda effect is defined as the tendency of the fluid jet which is attracted to a nearby surface. After

leaving the inlet section, because of Coanda effect, flow becomes attached to the ceiling surface; however, depending on the

Reynolds number, flow separates from the surface after travelling a certain distance. At low Re numbers (Re � 2,000), flow

separates from the ceiling and creates secondary circulation zone at the rear side of the enclosure.

The existence of reverse flow for various Reynolds numbers are revealed with representing the velocity distribution along

the container length calculated at the jet axis (see Fig. 60.8). For Re ¼ 20, almost 75 % of the enclosure is stagnant.

However, for Re ¼ 200 and 2,000, flow separation from the ceiling is observed at container lengths approximately

z/L ¼ 0.9 and 0.95, respectively. At higher Reynolds numbers, Re � 12,300, there is no separation of flow and a single

circulation zone forms. Increasing Reynolds number slightly changes the velocity variation especially at Reynolds numbers

above 61,500.

Referring to Table 60.3, increasing the Reynolds number decreases the mean air temperature of the container. In fact,

average temperature decreases from 25.47 �C to �9.68 �C by increasing the Reynolds number as indicated in the table. As

shown in Fig. 60.7, container temperature distributions become more uniform at high Reynolds numbers. As seen by

Fig. 60.9, average values of inner surface heat transfer coefficients assume high values as the Reynolds number increases.

Due to decrease in surface thermal resistance, the surface heat gains assume asymptotic values accordingly.

Effect of the Container LengthFigure 60.10 shows the flow patterns and isotherms for three different lengths of the container. For the suction design

considered in this study, a stagnant region takes place just below the evaporator suction line. As indicated in Fig. 60.10,

increasing the container length increases the size of the stagnant region; this in turn deteriorates the uniformity of air

temperature distribution of the container. Specifically for container length at 13.3 m, due to separation of flow from the

ceiling surface at a length ratio z/L ¼ 0.88 (see Fig. 60.11), the temperature distribution even becomes worse. Table 60.4

presents the average air temperatures at three different container lengths. One may conclude that the length effect on average

temperature is insignificant. Besides, as in Fig. 60.12, the heat gain per unit surface area varies insignificantly at all surfaces.

Table 60.2 Parameters that are used in the current study

Case Reynolds number Inlet temperature Length of the container

#1 20

�10 �C

8 m

#2 200

#3 2,000

#4 1.23 � 104

#5 6.23 � 104

#6 1.23 � 105

#7 1.23 � 105 13.3 m

#8 6 m


0.000.100.190.290.380.480.580.670.770.870.961.061.151.25

0.00

0.0000.0080.0150.0230.0310.0380.0460.0540.0620.0690.0770.0850.0920.100

0.100.190.290.380.480.580.670.770.870.961.061.151.25

a

b

c

d

e

f

Fig. 60.7 Airflow patterns and isotherms on the symmetry surface. (a) Re ¼ 20. (b) Re ¼ 200. (c) Re ¼ 2,000. (d) Re ¼ 1.23 � 104. (e)Re ¼ 6.15 � 104. (f) Re ¼ 1.23 � 105


Table 60.3 Average air temperatures at various inlet conditions

Reynolds number 20 200 2,000 1.23 � 104 6.15 � 104 1.23 � 105

Tmean 25.47 �C 16.74 �C 1.07 �C �7.26 �C �9.38 �C �9.68 �C

Fig. 60.9 Influence of flow Reynolds number on heat transfer. (a) Heat transfer coefficients. (b) Heat gains

Fig. 60.8 Decay of velocity

on jet axis


Fig. 60.10 Airflow patterns and isotherms on the symmetry surface. (a) L ¼ 6 m. (b) L ¼ 8 m. (c) L ¼ 13.3 m

Fig. 60.11 Decay of velocity

on jet axis

Table 60.4 Average air temperatures at various container lengths

Container length 6 m 8 m 13.3 m

Tmean �9.72 �C �9.68 �C �9.47 �C


Conclusions

Flow and heat transfer characteristics of an empty container used for frigorific transportation is numerically studied.

The container has constant cross-sectional dimensions of 2.5 m � 2.5 m, and the length is varied in such a way that the

container aspect ratio takes the values of 2.4, 3.2, and 5.32. Identifying the turbulent stresses, Reynolds Stress Model is

adopted. Similar studies of literature are also recalculated and compared by this method of solution. Satisfactory results

indicate that RSM method of analysis is appropriate for studying the flow inside of refrigerated containers.

In the analysis, the flow Reynolds number is changed by varying the flow injection rate at the evaporator outlet. For

aspect ratios between 2.4 and 3.2, no separation of flow from the upper surface is noted. However, in a region close to the

rear surface of the container, two separate vorticities perpendicular to each other occur at flow Reynolds numbers greater

than 200. Occurrence of these vorticities indicates that a stagnant region develops at the rear side of the container.

For aspect ratio 5.32, the flow separates from the upper surface of the container at a length ratio z/L ¼ 0.88. Similar

to smaller aspect ratios, two distinct circulation zones occurs but their plane of occurrence is different from the cases with

H/L ¼ 2.4 and 3.2.

Nondimensional temperature, T*, should vary in the range between 0 and 1. If it is greater than the unity, at a particular

location, then that location would not be affected heat transfer wise by the airflow in the container. In the analysis, as

the Reynolds number increases, T* assumes less than 0.1 for the entire container region. This also indicates that at high

Reynolds numbers, temperature uniformity throughout the container is satisfactorily obtained. In addition, as the Reynolds

number increases, the volumetric mean temperature of air in the container drastically drops and approaches to the exit

temperature at the evaporator.

Current study investigates the essential features of the flow and describes the heat transfer characteristics of an empty

refrigerated container. Further studies should be conducted to evaluate the effect of loading conditions on the flow and on the

heat transfer characteristics in a frigorific container.

Acknowledgment This research is supported by Republic of Turkey Ministry of Science, Industry and Technology under the grant number:

01114.STZ.2011-2 and Dokuz Eylul University Scientific Research Foundation Grant BAP-Project number: 2013.KB.FEN.9.

Fig. 60.12 Influence of container length on heat transfer


Nomenclature

cp Specific heat, J/kgK

DH Hydraulic diameter of the inlet section, m

h Convective heat transfer coefficient, W/m2K

H, L, W Height, length, and width of the container, m

Isolar Incident solar radiation, W/m2

k Thermal conductivity, W/mK

Nu Nusselt number, hL/kp Pressure, Pa

Pr Prandtl number

Re Reynolds number, ρDHwin/μT Temperature, �CT* Dimensionless temperature, T* ¼ (T � Tin)/

(Tout � Tin)u, v, w Velocity components on Cartesian geometry, m/s

U Overall heat transfer coefficient, W/m2K

V Volume of the container, m3

x, y, z Cartesian coordinates, m

Greek Letters

α Surface absorptivity

ε Surface emissivity

μ Viscosity, Ns/m2

ρ Density, kg/m3

References

1. Flick D, Hoang HM, Alvarez G, Laguerre O (2012) Combined deterministic and stochastic approaches for modeling the evolution of food products along the cold

chain. Part I: Methodology. Int J Refrigeration 35:907–914

2. Hoang MH, Laguerre O, Moureh J, Flick D (2012) Heat transfer modelling in a ventilated cavity loaded with food product: application to a refrigerated vehicle. J

Food Eng 113:389–398

3. Moureh J, Menia N, Flick D (2002) Numerical and experimental study of airflow in a typical refrigerated truck configuration loaded with pallets. Comput Electron

Agric 34:25–42

4. Moureh J, Flick D (2003) Wall air–jet characteristics and airflow patterns within a slot ventilated enclosure. Int J Therm Sci 42:703–711

5. Moureh J, Flick D (2004) Airflow pattern and temperature distribution in a typical refrigerated truck configuration loaded with pallets. Int J Refrigeration

27:464–474

6. Moureh J, Flick D (2005) Airflow characteristics within a slot-ventilated enclosure. Int J Heat Fluid Flow 26:12–24

7. Moureh J, Tapsoba S, Derens E, Flick D (2009) Air velocity characteristics within vented pallets loaded in a refrigerated vehicle with and without air ducts. Int J

Refrigeration 32:220–234

8. Norton T, Sun DW, Grant J, Fallon R, Dodd V (2007) Applications of computational fluid dynamics (CFD) in the modelling and design of ventilation systems in

the agricultural industry: a review. Bioresour Technol 98:2386–2414

9. Schalin A, Nielsen PV (2004) Impact of turbulence anisotropy near walls in room airflow. Indoor Air 14:159–168

10. ANSYS Inc (2009) ANSYS-FLUENT 14.0 theory guide. ANSYS Inc

11. Patankar SV (1982) Numerical heat transfer and fluid flow. Taylor & Francis, New York, NY

12. Leonard BP (1979) A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput Meth Appl Mech Eng 19:59–98

13. Patankar SV, Spalding DV (1972) A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Int J Heat Mass Transfer

15:1787–1806

14. Launder BE, Spalding DB (1974) Numerical computation of turbulent flows. Comput Meth Appl Mech Eng 3:269–289

15. Incropera FP, DeWitt DP, Bergman TL, Lavine AS (2007) Fundamentals of heat and mass transfer. Wiley, New York, NY


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