4.1. CFD simulation and experimental tests

A refrigeration vertical cabinet with four shelves (Figure 19) was the basis of the simulation; the dimensions of the cabinet (L W H) are 1900 796 1911 mm.

The axial fans (2) induce the airflow over the evaporator coil (3), placed at the bottom front part of the cabinet. A limited amount of air is fed into the unit, passing through the perforated plate behind the shelves (4), while the most significant amount of air flows through the horizontal

Figure 18. Cooling load components.

Food Chilling Methods and CFD Analysis of a Refrigeration Cabinet as a Case Study http://dx.doi.org/10.5772/intechopen.69136 59

increases when the number of "holes" increases, leading to the increase of the temperature inside the display case and of its power consumption; as a result, the products inside the cabinet are stored at temperatures higher that the recommended ones. Moreover, the infiltration of exterior humid air inside the case results in additional ice formation over the evaporator coils, thus reducing the heat transfer and the efficiency of the refrigeration system; therefore, the defrosting cycles become more frequent, further increasing the power consumption.

Some estimations show that 72–75% of the cooling load is used in order to counteract the effect of warm air infiltrations through the air curtain (Figure 18) and can reach even 90% if the operating conditions are not suitable [11]; 50% of the power consumption of a supermarket is

CFD simulation was applied to a vertical display cabinet with four shelves, and in order to evaluate the temperature gradient, the following stages were taken into account: preprocessing —geometry set-up and design of the discretization scheme; processing—introduction of the boundary conditions and calculation; post-processing—visualization of the velocity and tem-

A refrigeration vertical cabinet with four shelves (Figure 19) was the basis of the simulation;

The axial fans (2) induce the airflow over the evaporator coil (3), placed at the bottom front part of the cabinet. A limited amount of air is fed into the unit, passing through the perforated plate behind the shelves (4), while the most significant amount of air flows through the horizontal

the dimensions of the cabinet (L W H) are 1900 796 1911 mm.

due to the refrigeration and freezing cabinets.

4.1. CFD simulation and experimental tests

Figure 18. Cooling load components.

perature fields.

58 Refrigeration

Figure 19. Vertical display cabinet with four shelves. 1, base grill (GRA); 2, fans; 3, evaporator coil; 4, perforated plate; 5, air plenum; 6, thermal insulation; 7, horizontal grill (GPA); 8, shelves.

grill (7), thus creating the air curtain. The air curtain covers the front part of the shelves over their entire length; the air flows downward and is extracted through the base grill (1). The air curtain dimensions are as follows: thickness B = 60 mm; width of the shelves Ws = 350 mm.

The geometry of the air channels was used as a basis for producing the 3D model of the cabinet. The finite volumes discretization of the domain consisted of 1,585,690 nodes, being denser in the lower region of the cabinet (Figure 20).

In order to obtain the real boundary conditions, during the experimental tests, the refrigeration cabinet was placed inside a class 3 climatic chamber (according to EN-ISO 23953 and EN 441/4— Figure 21), which allowed the adjustment of different parameters of the ambient air (velocity, temperature, and humidity). During the tests, the air flow inside the chamber was parallel with the longitudinal axis of the cabinet, with a velocity of 0.2 m/s.

Figure 20. Structured discretization. a, view of the discretization domain; b, cross-section of the discretization domain.

Figure 21. Placement of the vertical refrigeration cabinet inside the climatic chamber.

Table 2 summarizes the transducers used in the experiments; the placement of the temperature, humidity, and velocity sensors in front of each shelf is shown in Figure 22a; temperature, humidity, and velocity sensors were also placed at the exit of the horizontal grill (GPA, Figure 22b); all the transducers were connected to a central data acquisition unit (Figure 22c). The sensors were placed in three vertical planes along the cabinet length: left, middle, and right (1, 2, 3, Figure 23).


Table 2. Summary of the transducers and their characteristics.

Figures 24 and 25 present the experimental results referring to the air velocity and temperature at the exit from the horizontal grill (GPA). The experimental data were then filtered using a C+ + program; Figures 26 and 27 show the filtered results.

Based on the charts presented in Figures 26 and 27, polynomial functions for the velocity and temperature variations were defined as:

a. velocity functions:

• left plane:

$$f(\upsilon\_{\nu}, \tau) = (-1.4 \cdot 10^{16} \cdot \upsilon^{10} + 4.4 \cdot 10^{15} \cdot \upsilon^{9} - 5.6 \cdot 10^{14} \cdot \upsilon^{8} + 3.9 \cdot 10^{13} \cdot \upsilon^{7} - 1.6 \cdot 10^{12} \cdot \upsilon^{6} + \dots)(5)$$

$$4.1 \cdot 10^{10} \cdot \upsilon^{5} - 6.1 \cdot 10^{8} \upsilon^{4} + 4.8 \cdot 10^{6} \cdot \upsilon^{3} - 22484 \cdot \upsilon^{2} + 162.5 \cdot \upsilon \right) + A\_{1} \cdot \sin \left( 6.283 \cdot \tau/T\_{1} \right);$$

• middle plane:

Food Chilling Methods and CFD Analysis of a Refrigeration Cabinet as a Case Study http://dx.doi.org/10.5772/intechopen.69136 61

$$f(v\_2, \tau) = (1.1 \cdot 10^{16} \cdot v^{10} - 4 \cdot 10^{15} \cdot v^9 + 5.6 \cdot 10^{14} \cdot v^8 - 4.3 \cdot 10^{13} \cdot v^7 + 1.9 \cdot 10^{12} \cdot v^6 - \tag{6}$$

$$5.2 \cdot 10^{10} \cdot v^5 + 7.7 \cdot 10^8 v^4 - 5.8 \cdot 10^6 \cdot v^3 + 18574 \cdot v^2 + 4.2 \cdot v) + A\_2 \cdot \sin\left(6.283 \cdot \tau/T\_2\right);$$

• right plane:

<sup>f</sup>ðv3, <sup>τ</sup>Þ ¼ ð�2:<sup>1</sup> � 1015 � <sup>v</sup><sup>10</sup> <sup>þ</sup> <sup>6</sup>:<sup>9</sup> � 1014 � <sup>v</sup><sup>9</sup> � <sup>9</sup>:<sup>5</sup> � 1013 � <sup>v</sup><sup>8</sup> <sup>þ</sup> <sup>7</sup> � 1012 � <sup>v</sup><sup>7</sup> � <sup>3</sup> � 1011 � <sup>v</sup><sup>6</sup> <sup>þ</sup> <sup>7</sup>:<sup>5</sup> � <sup>10</sup><sup>9</sup> � <sup>v</sup><sup>5</sup> � <sup>1</sup> � 108 <sup>v</sup><sup>4</sup> <sup>þ</sup> <sup>8</sup>:<sup>7</sup> � 105 � <sup>v</sup><sup>3</sup> � <sup>11436</sup> � <sup>v</sup><sup>2</sup> <sup>þ</sup> <sup>167</sup>:<sup>91</sup> � <sup>v</sup>Þ þ <sup>A</sup><sup>3</sup> � sin <sup>ð</sup>6:<sup>283</sup> � <sup>t</sup>=T3Þ: (7)

	- left plane:

Table 2 summarizes the transducers used in the experiments; the placement of the temperature, humidity, and velocity sensors in front of each shelf is shown in Figure 22a; temperature, humidity, and velocity sensors were also placed at the exit of the horizontal grill (GPA, Figure 22b); all the transducers were connected to a central data acquisition unit (Figure 22c). The sensors were placed in three vertical planes along the cabinet length: left, middle, and

Model Purpose Precision

Measurement of air velocity at the exit of GPA grill �0.015

Figure 21. Placement of the vertical refrigeration cabinet inside the climatic chamber.

Figures 24 and 25 present the experimental results referring to the air velocity and temperature at the exit from the horizontal grill (GPA). The experimental data were then filtered using a C+

Temperature RTD, SEM 105 P Ambient air temperature measurement �0.1�C Temperature TC with PTFE insulation Temperature measurement inside the cabinet �0.2�C

Humidity SEM 105H-3 Air humidity inside the cabinet and in the climatic test chamber

Based on the charts presented in Figures 26 and 27, polynomial functions for the velocity and

<sup>f</sup>ðv1, <sup>τ</sup>Þ ¼ ð�1:<sup>4</sup> � <sup>10</sup><sup>16</sup> � <sup>v</sup><sup>10</sup> <sup>þ</sup> <sup>4</sup>:<sup>4</sup> � 1015 � <sup>v</sup><sup>9</sup> � <sup>5</sup>:<sup>6</sup> � <sup>10</sup><sup>14</sup> � <sup>v</sup><sup>8</sup> <sup>þ</sup> <sup>3</sup>:<sup>9</sup> � 1013 � <sup>v</sup><sup>7</sup> � <sup>1</sup>:<sup>6</sup> � 1012 � <sup>v</sup><sup>6</sup><sup>þ</sup>

<sup>v</sup><sup>4</sup> <sup>þ</sup> <sup>4</sup>:<sup>8</sup> � 106 � <sup>v</sup><sup>3</sup> � <sup>22484</sup> � <sup>v</sup><sup>2</sup> <sup>þ</sup> <sup>162</sup>:<sup>5</sup> � <sup>v</sup>Þ þ <sup>A</sup><sup>1</sup> � sin <sup>ð</sup>6:<sup>283</sup> � <sup>τ</sup>=T1Þ;

(5)

�0.3%

m/s

+ program; Figures 26 and 27 show the filtered results.

Table 2. Summary of the transducers and their characteristics.

temperature variations were defined as:

a. velocity functions: • left plane:

<sup>4</sup>:<sup>1</sup> � 1010 � <sup>v</sup><sup>5</sup> � <sup>6</sup>:<sup>1</sup> � 108

• middle plane:

right (1, 2, 3, Figure 23).

Velocity Hot wire sensor,

VelociCalc

Transducer type

60 Refrigeration

$$\mathbf{g}(t,\tau) = t\_{1\text{mol}} + A\_{11} \cdot \sin\left(\frac{6.283 \cdot \tau}{T\_{11}}\right);\tag{8}$$

• middle plane:

$$\log(t,\tau) = t\_{2mol} + A\_{22} \cdot \sin\left(\frac{6.283 \cdot \tau}{T\_{22}}\right);\tag{9}$$

• right plane:

$$\mathbf{g}(t,\tau) = t\_{3md} + A\_{22} \cdot \sin\left(\frac{6.283 \cdot \tau}{T\_{33}}\right). \tag{10}$$

The above functions were introduced as user defined functions (UDF) into the numeric model.

### 4.2. The numeric model

The general equation for the incompressible flow of a fluid for a dependent variable Φ (Φ = 1 for the continuity equation; Φ = v for the momentum equation; Φ = t for the energy equation) is [12]:

$$\frac{\partial}{\partial \mathbf{x}\_i} \left( \rho \nu \phi - \Gamma\_\phi \frac{\partial \phi}{\partial \mathbf{x}\_i} \right) = \mathbf{S}\_\phi. \tag{11}$$

The model is based on the following assumptions:


The model is based on two equations (one for the turbulent kinetic energy and the other one for the dissipation rate of the turbulent kinetic energy), using the SIMPLE algorithm. The

Figure 22. Placement of the sensors and the central data acquisition unit. a, placement of the temperature, humidity, and velocity sensors inside the cabinet; b, placement of the temperature, humidity, and velocity sensors at GPA grill; c, view of the central data acquisition unit.

calculation is an iterative process, using the pressure-velocity coupling algorithm, in which the momentum and continuity equations, based on pressure, is solved simultaneously, and the terms referring to the pressure gradient and mass flow rate are discretized implicitly.
