Numerical Simulation of Heat Transfer and Fluid Flow at Different Stacking Modes in a Refrigerated Room: Application of Pyramidal Stacking Modes

Abstract

By means of the porous media theory, computational fluid dynamic models of heat transfer and fluid flow at different pack stacking modes in a refrigerated room are elaborated. A practical case is simulated, where brick-shaped packs with aquatic products, partially frozen to 261.15 K, are loaded in the room to complete the freezing process down to 255.15 K, followed by long-term frozen food storage at the latter standard temperature. The best freezing completion effect (defined as the maximum reduction of the highest product temperature during a certain residence time) is achieved by using the pyramidal stacking mode whose upper package is in the center of four lower packages (UPF-PSM) with two piles. The highest temperature of aquatic products at a two-pile-UPF-PSM can be reduced from 261.15 to 255.60 K for a residence time of 24 h. Within the same time, the product temperature becomes most uniform at a UPF-PSM. Simultaneously, the best uniformity of flow distribution and highest efficiency of air circulation in a refrigerated room are obtained by using the neat stacking mode (NSM) during the long-term frozen storage. Furthermore, a comprehensive stacking mode is proposed (using UPF-PSM for freezing completion and NSM for long-term frozen storage), which enhances both the freezing completion effect and the efficiency of air circulation in the studied refrigerated room.

1. Introduction

With the improvement of living standards, many aquatic products, such as squids, tunas, sea basses, puffer fishes and turbots are increasingly demanded by the consumers due to the advantages of low-fat content and high-quality proteins [1,2,3,4,5]. In order to maintain the high quality of aquatic products during the long term, it is necessary to store fresh aquatic products in a suitably low-temperature environment, e.g., at 272.25, 268.15, 263.15 or 255.15 K [6,7,8]. The best solution is a cold chain defined by IIR and ASHRAE as the series of actions and equipment applied to maintain a product within a specified low-temperature range from harvest/production to consumption. Thus, uninterrupted temperature-controlled transport and storage systems for refrigerated products form part of the cold chain [9,10]. Refrigerated warehouses are key facilities used along the cold chain to maintain the quality and safety of aquatic products during frozen storage [11].

Optimization of stacking modes is one of the research focuses to improve the food quality in refrigerated warehouses. In recent years, computational fluid dynamic (CFD) is widely used in the field of the cold chain, due to the high resolution of flow distribution in time and space, accurate determination of temperature distribution and powerful visualization capabilities [12,13,14]. Defraeye et al. [15] investigated the cooling rate of the citrus fruit in refrigerated containers and found that reducing the airflow bypass between pallets could increase the cooling rate of agricultural products. Fu et al. [16] studied the temperature distribution in refrigerated trucks with aquatic products placed under the refrigeration unit. The heights of aquatic products under the refrigeration unit were 0, 0.533, 1.066 and 1.6 m. It was found out that the most uniform temperature distribution occurred when lacking any products under the refrigeration unit. Jiang et al. [17] put forward a baffle structure of refrigerated containers, which could reduce the cooling time at least 22.9%. Based on the numerical simulation, Guo et al. [18] discovered that the “gaps on both sides and middle” stacking mode could achieve the most uniform temperature distribution. The freezing completion effect in aquatic products has been assessed by the decrease of the highest temperature of aquatic products for the residence time. Thus, Ho et al. [19] simulated a refrigerated warehouse with stacked packages and found that larger air velocity and refrigerating units with lower locations could promote the freezing completion effect and the temperature uniformity in the warehouse. Kolodziejczyk et al. [20] examined a refrigerated warehouse for vegetables and developed a heat transfer model by user-defined functions. Tian et al. [21] simulated a refrigerated warehouse and found that the uniformity of flow distribution can be improved by increasing gaps between goods.

Research of diverse stacking modes usually focuses on the freezing completion effect in food, the uniformity of flow and temperature distributions, etc. The pyramidal stacking mode (PSM) has been proposed [22], but not analyzed. Therefore, the present study investigated and reports numerical simulation results for four PSMs and their corresponding neat stacking modes (NSMs) possessing the same top views. The freezing completion effect in aquatic products, the temperature uniformity of products and of flow distribution, and the efficiency of air circulation in a refrigerated room, are analyzed. The objective is to assess the application of PSMs, and to identify the best performing stacking modes under the concerned experimental conditions.

2. Models and Methods

2.1. Physical Model

This study used a refrigerated room built at the Harbin University of Commerce [23]. The coordinate system origin is in the center of the inner surface of the floor of the refrigerated room in Figure 1a. The interior dimensions of this refrigerated room were 8.7 m length × 5.0 m width × 2.7 m height. The refrigerated room walls were 0.15 m thick and made of polyurethane foam. The room was equipped with a couple of refrigerating units whose dimensions were 1.0 m length × 0.4 m width × 0.5 m height. The latter were placed in the middle of the top front of the refrigerated room. The distances between the refrigerating units and the adjacent walls were 0.5 m, while the distance between the two refrigerating units was 2.23 m. The room is depicted in Figure 1a, while the air delivery is illustrated in Figure 1b. The air velocity was 13 m/s. The temperature of airflow outgoing from the two refrigerating units was 255.15 K, thereby providing a standard temperature of frozen food storage. The temperature outside the refrigerated room was 293.15 K [23].

The dimensions of product packages were 1.3 m length × 1.1 m width × 0.7 m height. Eight stacking modes are demonstrated in Figure 2: (i) two pyramidal stacking modes whose upper package was on the center of four lower packages (UPF-PSMs), (ii) two pyramidal stacking modes whose upper package was in the center of two lower packages (UPT-PSMs), and (iii) their four corresponding NSMs. The lengths L1-16 in Figure 2 were: L1 = L6 = 0.45 m, L2 = L5 = L11 = 0.4 m, L3 = 0.325 m, L4 = L7 = L8 = L9 = 0.25 m, L10 = 0.2 m, L12 = L13 = L14 = L15 = L16 = 0.1 m. The initial product temperature was 261.15 K. The geometric description of refrigerated room, refrigerating units and product packages (stacked as shown in Figure 2) was performed by means of the SolidWorks 2014 software [24].

Three stacking approaches were used in this study. The first was to ensure that the heights of package piles for PSMs and corresponding NSMs were the same; the second approach was to provide the same bottom areas of package piles for PSMs and corresponding NSMs; the third approach aimed that as many as possible packages with different stacking modes are placed in the refrigerated room.

Unstructured tetrahedral meshes of the models were created by Workbench 18.0 [25]. The skewness for all models was below 0.9.

2.2. Mathematical Model

2.2.1. Model Assumptions

The following simplifying assumptions were made [26,27,28,29,30]:

(1)

The flow medium is incompressible air.

(2)

According to the Boussinesq assumption, the air is considered to be both a Boussinesq fluid and a Newtonian fluid.

(3)

The effects of air leakage and solar radiation are ignored.

(4)

Packages and aquatic products are considered as aquatic product package units, which are idealised as porous media.

(5)

The effect of temperature on the thermal physical parameters of air and packages is neglected, given the incoming products are already partially frozen.

2.2.2. Governing Equations

In the models developed, forced convection heat transfer was assumed. As the Reynolds number exceeds 10⁶, the fluid is turbulent and, therefore, the k-ε turbulence model was used. Equations for three-dimensional unsteady-state flow distribution and porous medium were employed, including three-dimensional continuity equation, momentum equation and energy equation, which are as follows [28,31,32,33,34].

(1)

Three-dimensional continuity equation:

$$\frac{\partial \rho }{\partial t}+\overrightarrow{\nabla }\left(\rho \overrightarrow{v} \right)=0$$

(1)

(2)

Momentum equations:

$$\frac{\partial }{\partial t}\left(\rho v_i\right)+\frac{\partial }{\partial x_i}\left(\rho v_i{v}_j\right)=\frac{\partial }{\partial x_i}\left[-p·{\delta }_{ij}+\mu \left(\frac{\partial v_i}{\partial x_i}+\left(\frac{\partial v_j}{\partial x_i}\right)\right)\right]+\rho ·g_i$$

(2)

$$\frac{\partial }{\partial t}\left(\rho v_i\right)+\frac{\partial }{\partial y_i}\left(\rho v_i{v}_j\right)=\frac{\partial }{\partial y_i}\left[-p·{\delta }_{ij}+\mu \left(\frac{\partial v_i}{\partial y_i}+\left(\frac{\partial v_j}{\partial y_i}\right)\right)\right]+\rho ·g_i$$

(3)

$$\frac{\partial }{\partial t}\left(\rho v_i\right)+\frac{\partial }{\partial z_i}\left(\rho v_i{v}_j\right)=\frac{\partial }{\partial z_i}\left[-p·{\delta }_{ij}+\mu \left(\frac{\partial v_i}{\partial z_i}+\left(\frac{\partial v_j}{\partial z_i}\right)\right)\right]+\rho ·g_i$$

(4)

(3)

Energy equation:

$$\begin{gathered} \frac{\partial }{\partial t}\left(\epsilon ·{\rho }_f·E_f+\left(1-\epsilon \right){\rho }_f·E_p\right)+\nabla ·\left(\overrightarrow{v}\left({\rho }_f·E_f+p\right)\right) \\ =\nabla \left[k_{ef}·\nabla ·T-\left(\sum h_i\overrightarrow{J_j}\right)\right]+S_e \end{gathered}$$

(5)

$$S_e=-\left({\displaystyle \sum }_{j=1}^3{D}_{ij}\mu v_j+\frac{1}{2}{\displaystyle \sum }_{j=1}^3{C}_{ij}\rho \left|\overrightarrow{v_j}\right|v_i\right)$$

(6)

$$D=\frac{150{\left(1-\xi \right)}^2}{d^2{\xi }^3}$$

(7)

$$C=\frac{3.5{\left(1-\xi \right)}^2}{d{\xi }^3}$$

(8)

2.2.3. Boundary Conditions

(1)

Inlet boundary

The cold air outlets of two refrigerating units were set as velocity-inlet boundaries. A standard temperature of frozen food storage of 255.15 K was used in this study, so the temperature of cold air outlets was set at the same temperature. The air velocity was set as 13 m/s [23].

(2)

Outlet boundary

The return air outlets of two refrigerating units were set as outflow boundaries.

(3)

Wall boundary

For the Robin boundary condition, walls of the refrigerated room were characterized by their thermal conductivity, which was 0.022 W/(m$·$K) for polyurethane [35]. The temperature from the outer side of the wall, outside the refrigerated room, was 293.15 K [23].

(4)

Packages of aquatic products

Aquatic products and their packages form product package units whose physical and thermophysical parameters are shown in

Table 1. Physical and thermophysical parameters of product package units [36,37,38].

	Density	Specific Heat Capacity	Thermal Conductivity
Unit	kg/m3	J/(kg$·$K)	W/(m$·$K)
Value	1020	1400	0.4

[36,37,38]. The packages of aquatic products were considered as porous media, with a porosity of 0.3 [16]. The effective diameter of porous medium was determined by the lengths of fresh fish, which was 0.18 m on average [39]. The initial temperature of aquatic products was 261.15 K.

2.2.4. Solution Methods

The temperature distribution inside the stacked product packages was simulated by means of the Fluent module of the commercial software package ANSYS Workbench, which uses the finite-volume method for numerical solving the governing equations of fluid dynamics, similarly to previous research [16]. The objective was to investigate the freezing completion effect within a product residence time of 24 h. The time step was 1800 s with 20 iterations per step. The k-ε turbulence model was adopted. The type of the solver was Pressure-Based [16]. Discrete formats for momentum, energy, turbulent kinetic energy and turbulent dissipation rate were First Order Upwind [16]. The scheme of pressure-velocity coupling was SIMPLE [16].

3. Results and Discussion

3.1. Verification

The models developed to simulate the behavior of diverse stacking modes were initially tested and calibrated via a simplified scenario where the unsteady-state temperature distribution in the empty refrigerated room at the Harbin University of Commerce was determined theoretically and then compared with previously published experimental data [23]. These data represent the temperature at multiple measurement points in the studied room. Two X-Z planes with y = 1 and 2.2 m heights are chosen for measurements. Temperature cloud diagrams of these two planes are demonstrated in Figure 3a,b, respectively. The locations of measurement points 1–32 are shown in Figure 3c,d. The lengths L17-32 are: L17 = 0.1 m, L18 = L19 = L20 = L21 = L22 = 0.9 m, L23 = L24 = L25 = L26 = 1.74 m, L27 = 0. 5 m, L28 = 0.4 m, L29 = 2.48 m, L31 = 2.74 m, L30 = L32 = 0.5 m.

The initial temperature of the simulated room was 293.15 K. The experimental and simulated data at 24 h after the beginning of room refrigeration are displayed and compared in

Table 2. Comparison of temperatures at 24 h after the start of room refrigeration.

Measurement Point	Measured Temperature (K)	Simulated Temperature (K)	Absolute Error (K)	Relative Error (%)	Measurement Point	Measured Temperature (K)	Simulated Temperature (K)	Absolute Error (K)	Relative Error (%)
1	256.1	255.155	0.945	0.37	17	255.7	255.159	0.541	0.21
2	256.3	255.154	1.146	0.45	18	255.4	255.154	0.246	0.10
3	256.2	255.153	1.047	0.41	19	255.3	255.155	0.145	0.06
4	256.5	255.155	1.345	0.52	20	255.6	255.159	0.441	0.17
5	255.1	255.161	0.061	0.02	21	255.7	255.158	0.542	0.21
6	254.9	255.157	0.257	0.10	22	255.5	255.155	0.345	0.14
7	254.6	255.156	0.556	0.22	23	255.4	255.155	0.245	0.10
8	255.2	255.161	0.039	0.02	24	255.8	255.158	0.642	0.25
9	255.3	255.160	0.140	0.05	25	254.2	255.150	0.950	0.37
10	255.1	255.155	0.055	0.02	26	254.0	255.150	1.150	0.45
11	255.0	255.155	0.155	0.06	27	254.3	255.150	0.850	0.33
12	255.3	255.160	0.140	0.05	28	254.4	255.150	0.750	0.29
13	255.5	255.159	0.341	0.13	29	255.9	255.154	0.746	0.29
14	255.3	255.154	0.146	0.06	30	256.2	255.153	1.047	0.41
15	255.1	255.154	0.054	0.02	31	256.8	255.153	1.647	0.64
16	255.4	255.159	0.241	0.09	32	256.4	255.154	1.246	0.49

. The maximum absolute and relative errors are 1.647 K and 0.64%, respectively. Therefore, the simulation results are acceptable.

3.2. Freezing Completion Effect in Aquatic Products at Different Stacking Modes

The freezing completion effect is assessed by the decrease of the highest product temperature within a residence time of 24 h. The larger is the decrease of the highest product temperature, the greater is the freezing completion effect.

The refrigerated room temperature is maintained at 255.15 K. The temperature distributions in eight stacking modes were analyzed. In a vertical direction, the XY plane with z = 2.4 m was considered. In the horizontal direction, the XZ planes with y = 0.35, 1.05 and 1.75 m were studied.

Four temperature distributions for NSMs (vertical direction) are shown in Figure 4. These are for one-pile, two-pile, three-pile and six-pile arrangements. The temperature distributions (vertical direction) for the corresponding PSMs are demonstrated in Figure 5.

As shown in Figure 4, the highest product temperatures for the four NSMs are 259.42, 259.26, 258.57 and 258.47 K, while the temperature reductions are 1.73, 1.89, 2.58 and 2.68 K, respectively. In addition, as indicated in Figure 5, the highest product temperatures for the four PSMs are 255.79, 255.60, 258.37 and 258.33 K, with temperature reductions of 5.36, 5.55, 2.78 and 2.82 K, respectively. The temperature differences between NSMs and their corresponding PSMs are 3.63, 3.65, 0.2 and 0.14 K, respectively. The freezing completion effect at PSMs is better than the effect at NSMs for a residence time of 24 h. More gaps among package piles can enhance the freezing completion effect because of the increased heat exchange areas [18,40]. Moreover, the freezing completion effects at UPF-PSMs are much better than that at UPT-PSMs. As compared with UPT-PSMs, the use of UPF-PSMs enlarges the areas of return air and wider the gaps between package piles. Larger space for the return air and wider gaps between package piles facilitate the forced convection in the refrigerated room [16].

Four temperature distributions in NSMs (horizontal direction) are shown in Figure 6. These NSMs are for one-pile, two-pile, three-pile and six-pile arrangements. The temperature distributions (horizontal direction) in the corresponding PSMs are illustrated in Figure 7.

As shown in Figure 6 and Figure 7, the isothermal surfaces have the form of concentric ellipses. Cold air is blown from the outlets of two refrigerating units, and circulated through the top and the bottom of the refrigerated room. Afterwards, the exhausted air is collected back via the return outlets of the refrigerating units. The cold air moves around each package, so the freezing completion process is performed by gradually increasing the food ice fraction from the surface to the centre of each package. In temperature cloud diagrams, red areas (some10% of the highest temperatures) are defined as relatively high temperature zones (RHTZs). For NSMs and UPT-PSMs, the RHTZs are in the center of each package pile. However, as shown in Figure 7a,b, in case of UPF-PSMs with two-piles, RHTZs are offset in two opposite directions, which is due to wider gaps between two package piles. For NSMs and UPT-PSMs, the widths of gaps are almost equal, but when using UPF-PSMs, the middle gap can be much wider than the gaps on both two sides. Wider gaps can ease the forced convection in the refrigerated room, thereby improving the heat transfer rate [16].

For a residence time of 24 h, the freezing completion effects at PSMs are better than those at their corresponding NSMs, especially at UPF-PSMs. The application of UPF-PSMs can ensure the fastest freezing completion process.

The highest temperatures in all horizontal planes are summarized in Figure 8. The temperature gradually drops from the bottom to the top of the refrigerated room, because closer positions to the refrigerating units afford more intense forced convection, which enhances the freezing completion effect. All curves are fitted as linear functions by means of Equation (9). The absolute values of $a_1$ can be seen in

Table 3. Absolute values of slope a₁ in Equation (9).

Stacking Modes	a1	Stacking Modes	a1
NSMs with one-pile	0.200	NSMs with three-piles	0.310
UPF-PSMs with one-pile	0.025	UPT-PSMs with three-piles	0.315
NSMs with two-piles	0.190	NSMs with six-piles	0.200
UPF-PSMs with two-piles	0.040	UPT-PSMs with six-piles	0.355

. The $a_1$ values for NSMs and UPT-PSMs are of the same order, while those for UPF-PSMs are much smaller. For a residence time of 24 h, aquatic products at UPF-PSMs almost reach a steady state, while the other modes are still in the course of intense heat exchange. Along with the temperature uniformity in products, the uniformity of flow distribution and the efficiency of air circulation in a refrigerated room need to be analysed as well. The objects of further studies were UPF-PSMs with two-piles, UPT-PSMs with six-piles, NSMs with two-piles and NSMs with six-piles.

$$T_m=a_{1}H+b_1$$

(9)

Numerical experiments with longer time steps were conducted as well. It was found that NSMs require over twice-longer residence time, as compared with UPF-PSMs, to achieve the same freezing completion effect. Simultaneously, the number of packages at NSMs was no more than twice as large as that of packages at UPF-PSMs. For two-piles, the number of studied packages at UPF-PSM was 54; while 28 packages were accommodated in an NSM arrangement. If the number of packages is the same at both stacking modes, UPF-PSMs completes freezing quicker. The more packages there are, the more expressed this advantage is.

3.3. Temperature Uniformity of Aquatic Products

To assess the temperature uniformity in products at different stacking modes, the temperature coefficient of variation ($TCOV$) was selected as a studied parameter [36]. The $TCOV$ is the ratio of the standard temperature deviation to the average temperature. At lower ratios, the temperature gradients are smaller, so the temperature uniformity is better. The calculation formula for $TCOV$ is as follows:

$$TCOV=\frac{1}{T_{ave-t}}\sqrt{\frac{1}{n-1}{\displaystyle \sum }_{i=1}^n{\left(T_{i-t}-T_{ave-t}\right)}^2}$$

(10)

The centers of each package were chosen as the measurement points. As depicted in Figure 9, the trends of $TCOV$ at UPT-PSMs and the corresponding NSMs are similar. For a residence time of 10 h, two peaks of $TCOV$ occur, amounting to $1.10\times {10}^{-3}$ and $1.07\times {10}^{-3}$. The latter is due the fact that the gaps between adjacent package piles at these two stacking modes are narrower (0.1 m), which makes it difficult for the cold air to pass through the space at the beginning. The values of $TCOV$ at UPF-PSMs and the corresponding NSMs are also increasing first, and then decreasing with the time variation, but the peak times are 2 and 16 h, respectively. In addition, the peaks of $TCOV$ are smaller, i.e., $2.76\times {10}^{-4}$ and $9.15\times {10}^{-4}$, respectively. In all cases, the temperature uniformity gradually improves after the peak times. Wider gaps facilitate the forced convection in the refrigerated room, so the product temperature uniformity can thus be improved. The peak of $TCOV$ at UPF-PSMs is the smallest one. Moreover, the $TCOV$ at UPF-PSMs reaches its lowest value for a residence time of 24 h. Therefore, the best temperature uniformity of aquatic products is obtained by using UPF-PSMs.

3.4. Uniformity of Flow Distribution

The uniformity of flow distribution is closely related to the freezing completion effect in aquatic products. To investigate the uniformity of flow distribution, a coefficient of velocity non-uniformity ($k_v$) was considered [41]. Lower $k_v$ means that the uniformity of flow distribution is better. The calculation formula for $k_v$ is:

$$k_v=\frac{1}{v_{ave-t}}\sqrt{\frac{1}{n}{\displaystyle \sum }_{i=1}^n{\left(v_{i-t}-v_{ave-t}\right)}^2}$$

(11)

The locations of measurement points can be seen in Figure 10a. Three measurement X-Z planes (y = 0.35, 1.05 and 1.75 m) were selected with six measurement points on each plane. The lengths L33-38 are: L33 = 1.1 m, L34 = L35 = 2.175 m, L36 = 0.2 m, L37 = 2.95 m, L38 = 0.15 m. The measurement points are symmetrical with respect to X-Z plane (y = 0).

As shown in Figure 10b, the four $k_v$ curves are increasing first, and then decreasing with time. All maximums of $k_v$ occur at a residence time of 2 h. The maximums are larger at UPF-PSMs and UPT-PSMs and amount to 1.67 and 1.23, respectively. The maximums of the corresponding NSMs are smaller and equal to 0.84 and 0.77, respectively. First, the low-temperature space in the refrigerated room is larger when using PSMs at constant air supply temperature and speed; more time is necessary for the flow distribution in a larger low-temperature space to become uniform. Second, the geometry of low temperature environment is more regular at NSMs, which decreases the differences in the air velocity at various locations. Furthermore, after the peak time of 2 h, $k_v$ is gradually improved and equalised, but a little difference still exists. For UPF-PSMs, UPT-PSMs and their corresponding NSMs $k_v$ reaches stable values with time at 0.66, 0.64, 0.60 and 0.53, respectively. Such a stabilisation is important, given the frozen storage takes about or over 6 months [1,7,8]. It was found out that the uniformity of flow distribution during frozen storage is best at NSMs.

3.5. Efficiency of Air Circulation in a Refrigerated Room

The efficient air circulation in a refrigerated room saves the unnecessary waste of energy, thereby reducing carbon emissions and environmental damages [42]. To assess the efficiency of air circulation, the energy utilization coefficient ($\eta$) was selected as a studied parameter [43], where a higher $\eta$ means a better efficiency. The calculation formula is:

$$\eta =\frac{T_h-T_0}{T_n-T_0}$$

(12)

As depicted in Figure 11, the four $\eta$ curves are increasing first, and then decreasing time. The peak residence times of these $\eta$ curves are 2 h, when all $\eta$ go down and become gradually constant in time. The maximums of $\eta$at UPF-PSMs, UPT-PSMs and their corresponding NSMs are 1.60, 2.33, 1.87 and 2.00, respectively. During the long frozen storage (6 or more months) [1,7,8], it is important to achieve an $\eta$, which is constant in time. After freezing completion, these four stacking modes are stabilised around different constant values of $\eta$ (namely 0.86, 0.79, 0.91 and 0.89). For NSMs, these constant $\eta$ balues are larger than those for PSMs. Therefore, the application of NSMs provides a higher efficiency of the air circulation in the studied refrigerated room during frozen storage.

The above-mentioned studies demonstrate that the freezing completion effect and the product temperature uniformity are superior when applying UPF-PSMs. Simultaneously, for long-term frozen storage, superior uniformity of flow distribution and efficiency of air circulation in the room can be achieved by means of NSMs. Thus, a comprehensive stacking mode can be proposed, which is applies UPF-PSMs in the freezing completion process, followed by NSMs during long-term frozen storage.

4. Conclusions

The freezing completion effect and the temperature uniformity in aquatic products, along with the uniformity of flow distribution and the efficiency of air circulation in a refrigerated room, are analyzed for different stacking modes. The results of this work can be outlined as follows:

(1)

The freezing completion effect is the best when using UPF-PSMs with two-piles, which can reduce the highest temperature in the product pack from 261.15 to 255.60 K within a residence time of 24 h.

(2)

When the UPF-PSMs are used, the product temperature uniformity in the freezing completion process is the best. TCOV at UPF-PSMs becomes smallest for a residence time of 24 h; however, when using NSMs in a long-term frozen storage, k_v is smaller, while η is larger, as compared with the other modes. Thus, the uniformity of flow distribution and the efficiency of air circulation in the studied refrigerated room appear to be superior.

(3)

Based on the capabilities of PSMs and NSMs, a comprehensive stacking mode can be proposed. The latter applies UPF-PSMs in the freezing completion process and NSMs during long-term frozen storage. The comprehensive stacking mode can thus improve both processes of freezing completion and long-term frozen storage. Moreover, the higher efficiency of air circulation in the refrigerated room can reduce the energy expenditure and carbon footprint, thereby mitigating the global warming.