Comparison of veracity and application of different CFD turbulence models for refrigerated transport

Journal Pre-proof Comparison of veracity and application of different CFD turbulence models for refrigerated transport

Jia-Wei Han, Wen-Ying Zhu, Zeng-Tao Ji PII:

S2589-7217(19)30028-5

DOI:

https://doi.org/10.1016/j.aiia.2019.10.001

Reference:

AIIA 14

To appear in: Received date:

20 August 2019

Revised date:

18 September 2019

Accepted date:

1 October 2019

Please cite this article as: J.-W. Han, W.-Y. Zhu and Z.-T. Ji, Comparison of veracity and application of different CFD turbulence models for refrigerated transport, (2019), https://doi.org/10.1016/j.aiia.2019.10.001

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© 2019 Published by Elsevier.

Journal Pre-proof

Comparison of veracity and application of different CFD turbulence models for refrigerated transport Jia-Wei Han1,2*, Wen-Ying Zhu1,2 and Zeng-Tao Ji1,2 1

National Engineering Research Center for Information Technology in Agriculture, Beijing 100097, China;

2

National Engineering Laboratory for Agri-product Quality Traceability, Beijing Academy of Agricultural and Forestry

Sciences, Beijing 100097, China

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*Author for correspondence. Tel.: +86 10 51503168; Fax: +86 10 51503750.

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Email: [email protected](J.-W. Han)

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Abstract: The objective of this study was to establish a comprehensively verified 3D CFD model of this

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experimental platform to simulate the airflow and heat transfer at different unsteady turbulence model

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(standard κ-，RNG κ-，Realizable κ-, standard κ-ω, SST κ-ω and RSM), and to predict the temporal-spatial temperature and velocity variations during cooling. Good agreement between model prediction and measured

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data was obtained. The root-mean-square error (RMSE) were 1.049 °C,1.033 °C,1.039 °C,1.037 °C,1.014 °C

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and 1.064 °C for standard κ-，RNG κ-，Realizable κ-，standard κ-ω，SST κ-ω and RSM, respectively. There were no significant differences in different turbulence models on simulating the temperature distribution, and it was similar to solve the energy equation on different turbulence models with two-equation eddy viscosity. This study also revealed that the simulation values of high Reynolds numbers turbulence model (e.g. standard κ-，RNG κ-，Realizable κ- and RSM) were slightly lower than measured values near the plane wall. After comparing the accuracy of six two-equation turbulence models, the SST κ-ω model shows more accurate predictions by a comparison of the experimental and simulated results. This research provided reliable method for better understanding and selecting CFD turbulence models to refrigerated transport of fresh fruit. Keywords: Cold chain, computational fluid dynamics (CFD), numerical analysis, cooling, turbulence model. 1

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1. Introduction Refrigerated transport is an important link in fresh apples cold-chain logistics, and temperature control is vital to the entire cold chain transport system for apple. In addition, it is the key to ensuring the quality and safety of food and to reducing losses of perishable products (Moureh and Flick, 2004). Fresh apples that require refrigerated transport are very sensitive to temperature variations; overtemperatures accelerate the respiration of agricultural products and increase food loss; under temperatures cause cold damage. Both are

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bad for the products and cause severe economic losing to suppliers (Han et al., 2016).

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In recent years, to achieve accurately mastering temperature control, optimize cargo stacking, select the

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best air speed and minimize energy consumption for refrigerated transport of apple, many researchers

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(Estrada-Flores and Eddy, 2006; Moureh et al., 2009; Tassou et al., 2009; Hoang et al., 2012) used

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computational fluid dynamics (CFD) to studies and analyses of the characteristics of airflow and temperature distribution inside transport compartments and to improve the traditional analytical approach for object

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simplification and for calculating the solution. This approach has allowed us to overcome many restrictions

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in experiments, such as manpower requirements, material resources and long test periods (Nahor et al., 2005). However, in the process of applying CFD models to predict airflow, heat and mass transfer, some authors chose a CFD turbulence model referring to previous literatures or personal experiences, they did not evaluate the accuracy of the different turbulent models under the present operating conditions, which might increase blindness to the simulation process and decrease the accuracy of the simulation results. Therefore, reasonable selection of CFD turbulence model is a critical step to improve the accuracy of CFD solutions, which is also a highlight of research for refrigerated transport of apple. The objective of this study was to establish a comprehensively verified 3D CFD model of this experimental platform to simulate the airflow and heat transfer at different two-equation eddy viscosity turbulence models (e.g., standard κ-, RNG κ-, Realizable κ-, standard κ-ω, SST κ-ω and RSM), and to 2

Journal Pre-proof predict the temporal-spatial temperature and velocity variations during cooling. Furthermore, the optimal turbulence model for refrigerated transport of apple was determined by combining the accuracy of the simulation results between different CFD turbulence models. The validation of the model was performed by a comparison of the calculated time-averaged temperature magnitudes with the mean temperature measured by RFID sensors.

2. Literature review

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Computational Fluid Dynamics (CFD) is a simulation tool for modelling fluid-flow problems and is based on

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solving the governing flow equations (Zhao et al., 2016). With the rapid development of computing power

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and commercial CFD packages, the accuracy of such simulations and their reliability are being constantly

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improved. This technology has been widely used in various fields because they reduce the need for complex

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field experiments (e.g., food processing, agro-environment industry and ocean engineering, etc.). Some researchers (Alvarez et al., 2003; Tutar et al., 2009; Delete et al., 2009; Ferrua et al., 2011; Delete et al., 2012)

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have used CFD simulations to analyze how packaging design impacts airflow as well as the heat and mass

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transfer processes of agricultural products that are packaged in vented cases. These works demonstrate that such simulations are not only feasible but also reliable. To better understand airflow in refrigeration trucks and the related temperature distribution and to minimize spatial temperature variations, some groups have used CFD simulations to study the characteristics of airflow inside such compartments and the related heat and mass transfer (Moureh and Flick 2004; Tapsoba et al. 2007). These studies demonstrate that numerical CFD simulations can provide a new insight and understanding to the likely performance of food equipment at the design stage and confidence in the quality or safety of food products (Xia and Sun, 2002). However, the accuracy of the CFD simulation depend strongly on the selection of turbulence model for different application scenarios, which leads to the choice of turbulence model is the key to improving the accuracy of the results of the simulation. The following provides some studies to determine the optimal turbulence model 3

Journal Pre-proof by comparing the simulated and experimental velocity and temperature distribution in a specific field of application. Moureh and Flick (2005) developed a reduced-scale CFD model to evaluate the performance of various turbulence closure models including the high and low Reynolds number form of the two-equation k–ɛ model, and the more advanced RSM. The results show that only RSM is able to predict correctly the separation of the wall jet and the general behaviour of air motion related to the primary and to the secondary recirculations.

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Tapsoba et al. (2007) established a reduced-scale CFD model to investigate the influence of different

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turbulence models (i.e., standard k–ɛ and RSM) on the accuracy of airflow patterns prediction through a

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ceiling-slot ventilated enclosure loaded by slotted boxes. The simulation results show that no great

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differences were found between standard k–ɛ and RSM in terms of velocity prediction in high velocity zones.

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However, this difference increased in lower velocity areas located in the rear, which was attributed to the low level of velocities and the uncertainty of these two turbulence models in the stagnant zones where no main

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flow is identified. Furthermore, the results show that the major difference between the two models concerns

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the jet behaviour rather than local velocity values, i.e., the standard k–ɛ model underestimated the jet deflection in the inlet area, but the RSM model show a relatively better prediction accuracy in a stronger jet deflection and the adherence point. Defraeye et al. (2011) established sphere model to evaluate the performance of several steady Reynolds-averaged Navier–Stokes turbulence models and boundary layer modelling approaches. The results show that the SST κ-ω turbulence model showed a very good performance for all evaluated flow parameters (drag coefficient, Nusselt number, separation angle and recirculation length) when combined with low-Reynolds number modelling (LRNM) of the boundary layer. Table 1 presents the recent studies on optimization of velocity and temperature distributions inside a refrigerated vehicle for food transport. Table 1 Summary of recent studies (2009–2019) that focus on optimizing the cooling performance of 4

Journal Pre-proof refrigerated vehicle. Reference

Material

Turbulence model

Remark

Moureh et al.

Orange

RSM

To investigate experimentally and numerically the airflow pattern throughout a

(2009)

vehicle enclosure loaded with vented pallets filled with spherical objects under isothermal conditions.

Moureh et al.

Hollow

(2009)

spheres

celluloid

RSM

To assess the ability of CFD numerical modelling with the RSM to predict the principal characteristics of the flows developed by a confined wall jet in both clear and porous medium regions.

Ahmed et al.

—

—

To investigate the inclusion of paraffin-based PCMs in the standard trailer walls as a

(2010)

heat transfer reduction technology.

Zwierzycki et

Frozen poultry

—

An original computer software for heat exchange simulation was created and

al. (2011)

verified. Apricots,

peaches

(2012)

and nectarines

Laguerre et al.

—

—

A simplified heat transfer model of a refrigerated vehicle was developed to drastically reduce the calculation time compared to the CFD approach.

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Hoang et al.

—

To present the influence of input variables (ambient and thermostat setting temperatures) and equipment parameters (dimension, airflow rate, insulation) on the

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(2014)

load temperatures. Realizable κ-ɛ

—

To investigate the heat and mass infiltration rates across the doorway of a

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Lafaye et al. (2015)

medium-size truck body. Citrus

—

Apple

SST κ-ω

To show the added value of a more holistic cold-chain evaluation, as illustrated for

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Defraeye et al. (2016)

the case of the ambient loading protocol for a partial cold disinfestation treatment.

Getahun et al.

cooling inside a fully loaded refrigerated shipping container (reefer) based on porous

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(2017)

A numerical model was developed and validated to predict airflow and produce

medium approach.

—

Smagorinsky

(2018) Jara

To simulate velocity and temperature distributions inside a refrigerated vehicle a

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Gaedtke et al.

lattice Boltzmann method combined with a Smagorinsky turbulence model

et

al.

SST κ-ω

—

transport.

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(2019)

To predict the temperature distribution inside a refrigerated vehicle for food

3. Materials and methods 3.1. Physical model

This study is based on an experimental platform which was similar to a refrigerated vehicle or a small-scale cold storage. Its interior dimensions are 4.0 m deep × 2.0 m wide ×2.5 m high. Figure 1 shows a diagram of the refrigerated compartment. The wall of the refrigerated compartment was 15-cm thick and is made of polyurethane foam. The refrigerated compartment was equipped with a cooling unit with exterior dimensions of 0.35 × 0.53 × 0.354 m3.

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1. Cooling unit 2. Grating plate 3. Virtual slice 4. Return air inlet 5. Air-conditioning outlet

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Note：● denotes the temperature test points, “+” denotes vertical lines, “a、b、c、d” denotes the location of the vertical lines where the velocities were measured (Section 1.3.1)

3.2.1. Setup

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3.2. Experiment design

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Fig.1 The structure diagram of experimental platform and equipment deployment

To ensure that the experiment was accurate and reliable, the refrigerated compartment was completely sealed during cooling and its cooling temperature was maintained at 4 °C. The internal temperature within refrigerated compartment was ~20 °C. The space of refrigerated compartment was divided into seven imaginary slices (S1-S7) along X-coordinate axis, as shown in Fig. 1. Each slice had six RFID (Radio Frequency Identification Devices) temperature sensor tags distributed (see Fig. 1), and a total of 42 RFID tags were used inside the refrigerated compartment. The temperatures were recorded within 1 min of sampling over temperatures ranging from −20 to 60 °C. a, b, c and d denotes the location of the vertical lines. Six anemometers were arranged on each vertical line, with 50cm of distance between each other. To verify 6

Journal Pre-proof the accuracy of the simulation results, we used the experimental temperature and airflow velocity values to compare with the results of the simulation.

3.3. Equipment parameters The RFID tags used to measure the temperature at the monitoring points. Their operating temperature ranged from −20 to 60 °C and their accuracy was ±0.5 °C. The air velocity was measured with an anemometer (TES-1341, TES Electrical Electronic Corp., Taipei), which had a range of 0 to 30 m/s and an

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accuracy of ±0.03 m/s. The air temperature and relative humidity (%RH) was measured with a temperature

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and humidity digital recorder (179-TH, Apresys Inc., USA), which had operating ranges of −40 to 100 °C

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and 0% to 100% and an accuracy of ±0.3 °C and ±3%, respectively.

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3.4. Mathematical model

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3.4.1. Model assumptions

To simplify calculations and still properly describe the experimental system, we made the following

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assumptions:

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–Air is considered to be an incompressible fluid with constant properties. –Air is regarded as a Newtonian fluid and a Boussinesq fluid, and the gas medium is considered to be transparent in the visible range.

– We neglect radiation between the air, and the walls. – Any effect of experimental instruments on airflow is negligible.

3.4.2. Governing equations The flow in the free-airflow zone is solved by using the Reynolds-average Navier–Stokes(RANS) equations. Conservation of mass gives

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Journal Pre-proof   a   a ui   0. t xi

（1）

Conservation of momentum gives   a u  p  div a uU   div a gradu   t x    u' 2   u' v'   u' w'  a a a       Su  x  y z  



 

 



（2a）

  a v  p  div a vU   div a gradv   t y

 



 



  a w  p  div a wU   diva gradw   t z    u' w'   v' w'   w' 2  a a a       Sw x y z  



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 

 

（2c）

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

（2b）

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   u' v'   v' 2   v' w'  a a a       Sv  x  y z  

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Conservation of energy gives

    aT   div aUT   div gradT    t  c p ,a     a u' T'   a v' T'   a w' T'      S x y z  

 

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 



（3）

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

where a is the air density (kg/m3), t is time (s), U is the velocity vector (m/s),u, v, and w are the

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air-velocity components (m/s) in the x, y, and z directions, respectively, p is the fluid pressure (N/m2), μa is the dynamic viscosity (Pa·s), cp,a is the air specific heat capacity [J/(kg·K)], and Su, Sv, and Sw represent a source term in the x, y, and z directions, respectively. This work only considers the effect of gravity in the free-airflow zone, so Su = Sw = 0, Sv = −ag, where g is the acceleration due to gravity (m/s2), ui ' u j ' is the specific Reynolds stress term(RST), and i and j are Cartesian coordinates. In the RANS equations,  u'i u' j is a new unknown quantity, which represents the effects of turbulence fluctuations. In order to close the RANS equations, the relationship between time-averaged values and fluctuating values must be established by introducing new turbulent model equation. A common turbulent model is eddy viscosity model, which employs the Boussinesq hypothesis to relate the Reynolds 8

Journal Pre-proof stresses to the mean velocity gradients (Eq. 4), and another turbulent model embodied in the Reynolds Stresos Model (RSM), is to solve transport equations for each of the terms in the Reynolds stress tensor (Eq. 6). In many cases, models based on the Boussinesq hypothesis perform very well, and the additional computational expense of the RSM is not justified. However, the RSM is clearly superior in situations where the anisotropy of turbulence has a dominant effect on the mean flow. Such cases include highly swirling flows and stress-driven secondary flows (Ansys, 2010). According to the number of differential equation

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to determine t , the eddy viscosity model was classified as one-equation and two-equations model (e.g.,

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standard κ-，RNG κ-，Realizable κ-，standard κ-ω and SST κ-ω). Due to the two equations model is widely

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used in engineering projects and thereby only the different two equation model were compared and analyzed

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in this study.

t

  ρu u' u'     ρu' u' x x

（4）



（5）







    u' k  p δ kj u'i δik u' j  u'i u' j  μ x k  x k k  k     k

i

j

i

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

 ρu'i u' j



u' i u' i 1 2  u'  v' 2  w' 2 2 2

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

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 u u j  2  u        t i  ij  u' i u' j   t  i    x  x i   j x i  3 

Cij



j

DT, ij

DL, ij

 u' u' j  u j u' j  u   2μ u'i  ρ u'i u' k  u' j u' k i  ρβ g i u' j θ  g j u'i θ  p i   Fij   x j x i  x k x k  x k x k            Gij 





Φij

Pij

（6）

 ij

where t is the turbulent viscosity(Pa·s), δij is the Kronecker delta, (δij=1 when i = j, otherwise δij=0), k is the turbulent kinetic energy(m2/s2), Cij is the convective term, DT，ij is the turbulent diffusion term, DL,ij is the molecular viscous diffusion term, Pij is the production term on shear stress, Gij is the buoyancy produced item, Φij is the pressure strain correlation term, ij is the viscous dissipation term, Fij is the production term on system rotates,

δik, δkj, and δij is the Kronecker delta,  is the thermal expansion

coefficient of fluid(K-1),  is the scalar variable (e.g., composition concentration and temperature), 9

u'm is

Journal Pre-proof the time-averaged values fluctuating velocity and expressed in a tensor form.

3.4.3. Initial conditions and boundary conditions We used the relevant initial conditions and boundary conditions in solving the set of governing equations. – Inflow boundary. The velocity-inlet boundary conditions were used to define the airflow velocity at the air-conditioning outlet (Fig. 1). The airflow velocity and temperature were set at the experimentally

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measured values (4 m/s and 4 °C).

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– Outlet boundary. Outflow boundary conditions were set at return air inlet. The outlet boundary

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conditions were imposed at a fully developed flow section. The outlet velocity was computed based on mass

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balance, and the gradients normal to the flow direction of the other variables were also set to zero at the exit

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section (Kuznik F, 2007).

– Wall boundaries. We used no-slip-velocity boundary conditions at the internal wall surfaces of

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refrigerated compartment. At the wall, the flow velocity, which is vertical or parallel to the wall, is assumed

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to be zero. A constant temperature of 20 °C was set at the wall surfaces, which served to initialize the values in the energy equations.

– Porous jump boundary. The grating plate was set as the porous jump boundary and its porosity φ is equal to ~0.95.

3.4.4. Discretization and analysis of mesh sensitivity The first step of a CFD analysis is to design the system geometry and discretize it into a three-dimensional computational grid (Denys, 2005). The geometry was discretized by using a Hex mesh. The geometry was discretized into an structured mesh of 236623 cells. At all wall surfaces, a boundary-layer mesh was used whose thickness was determined by requiring final y+ values to be less than five. The resulting spatial discretisation error was estimated by means of Richardson extrapolation (Roache, 1994; 10

Journal Pre-proof Franke, 2007), and about 0.20 % for the wall shear stress at the wall surfaces. In addition, the maximum skewness and wall y+ were less than 0.95 and 3.5, respectively. To simulate the dynamics, we used a time step of 60 s and 20 iterations per time step. We used the pressure implicit with splitting of operators (PISO) algorithm to couple pressure to velocity. We used the second-order upwind scheme for the convection terms that describe flow and turbulence, and we imposed a convergence criterion of 10−4 for continuity, momentum, and turbulence and 10−6 for the energy equations. The simulation was done on a 32-bit Windows-7 computer

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with a 3.10 GHz Intel® Core™2 i5 CPU and 4 GB RAM.

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4. Results and discussions

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4.1. Comparison of accuracy of temperature simulation

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Fig. 2 compares the simulated and experimental temperatures in the refrigerated compartment as

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functions of time for different CFD turbulence models. As can see from Fig. 2, the simulated temperatures did not differ significantly between turbulence models. The values of RMSE ((Root mean square error) for

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standard κ-，RNG κ-，Realizable κ-，standard κ-ω，SST κ-ω and RSM was 1.049 °C, 1.033 °C, 1.039 °C,

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1.037 °C, 1.014 °C、1.064 °C, respectively. Therefore, the different turbulence models do not significantly influence the simulating value of heat transfer inside a refrigerated compartment or cold storage, meanwhile indicated that different CFD turbulence models have a same accuracy in solving the energy equation (i.e., Eq. 3). This result is attributed to the fact that different assumptions or treatment of RST is the major difference between eddy viscosity model (i.e., standard κ-，RNG κ-，Realizable κ-，standard κ-ω，SST κ-ω) and RSM, meanwhile Reynolds stress term mainly represents the effects of turbulence fluctuations on the momentum equation (Eq. 2a-c). However, there are minor deviations between the temperature simulation values of different turbulence models and this can be attributed to numerical oscillations. In addition, we consider the deviations to be satisfactory in view of the various parameters controlling the simulation and experiment; for example, variations exist in experimental air-inflow velocity, air temperature, thermophysical properties of 11

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the air, numerical oscillations, and so forth.

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Fig.2 Average temperature of refrigerated compartment as a function of time

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4.2. Comparison of accuracy of airflow velocity simulation Figure 3 shows the distribution of air velocity along the Y axis at the location of the vertical lines a, b, c

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and d, and compares the experimental and simulated air velocity in the refrigerated compartment as functions

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of height for different turbulence models. It is clear from Fig. 3 that the standard κ-, Realizable κ-，RSM produced a lower simulated air velocity at the location of the vertical lines a, c and d (i.e., near-wall flow or the region of low Reynolds number) compared to the other turbulence models. For the location of the vertical lines a, the standard κ-ω model has the highest simulated air velocity. Meanwhile the standard κ-ω model has a large deviation between the simulation and experimental results of air velocity, especially at y-coordinate of 0.5 and 2. For the location of the vertical lines c, RNG κ- and SST κ-ω have the highest simulated air velocity, and the simulated results were terribly close between them. However, the simulated results of SST κ-ω model had a better agreement with the experimental results (see Fig. 4). For the location of the vertical lines b (the region of fully developed turbulent), there was no statistically significant difference in the simulated air velocity between different turbulence models. However, standard κ-，RNG κ-，Realizable κ-， 12

Journal Pre-proof RSM and standard κ-ω produced a higher simulated air velocity compared to SST κ-ω, and the simulated results of SST κ-ω model had the best agreement with the experimental results (see Fig. 4). The results can again be attributed to different assumptions or treatment of RST between eddy viscosity model and RSM. The RST was indirect solved by determining turbulence viscosity t for eddy viscosity model and t is regarded as anisotropic during the solution process. However, the RST was direct solved by establishing the differential equations for RSM. Overall, for the region of low Reynolds number or fully developed turbulent,

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the predicted air velocity of SST κ-ω model was compared with experimental result and showed the best

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consistency with the later.

Note: The letters (a),(b),(c) and (d) corresponding to the location of the vertical lines a, b, c and d, respectively.

Fig.3 Changing process of air velocity along the height in the Y axis direction

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Fig.4 The average relative deviation of the predicted velocity relative to the measured values

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5. Conclusion

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This work establishes a 3D physical model of a refrigerated compartment and uses CFD unsteady model

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to compare the temperature and velocity distribution inside the refrigerated compartment between different

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turbulence models. The results show that no significant difference is observed in the simulated temperatures between different turbulence models. The values of RMSE for standard κ-, RNG κ-, Realizable κ-,

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standard κ-ω, SST κ-ω and RSM are 1.049 °C, 1.033 °C, 1.039 °C, 1.037 °C, 1.014 °C、1.064 °C, respectively. This indicates that the predicted results are consistent with the measured results. Furthermore, for near-wall flow or the region of low Reynolds number, standard κ-，RNG κ-，Realizable κ-，RSM produced a relatively low simulated velocity and standard κ-ω produced a relatively high simulated velocity compares to the measured results. For the region of fully developed turbulent, standard κ-，RNG κ-，Realizable κ-， RSM and standard κ-ω produced a relatively high simulated velocity compares to the measured results. Finally, the SST κ-ω model was the best option for refrigerated vehicle or a small-scale cold storage of fresh fruit.

Acknowledgements 14

Journal Pre-proof This work was supported by National Key Technology R&D Program of China (No. 2018YFD0701000 and 2018YFD0701003), Research and Development Projects in Key Areas of Guangdong Province, China (No.2019B020225001),National Engineering Laboratory for Agri-product Quality Traceability, Beijing Academy of Agricultural and Forestry Sciences (No. PT2019-26), and Opening Foundation of National Engineering Laboratory for Agri-product Quality Traceability, Beijing Technology & Business University (No. AQT-2019-YB3).

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Research highlights

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(1) A 3D physical model of a refrigerated compartment was established. (2) Local and average airflow inside refrigerated compartment were analyzed. (3) Comparing the accuracy of six two-equation turbulence models for refrigerated transport.

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