Thermodynamic and Economic Analysis of a Refrigerator Display Cabinet Equipped with a DC Compressor and Electronic Expansion Valve

The use of an RDC unit for food preservation and display is an intensive energy-consuming process. The saving in energy consumption is an important issue in the development and design of all cooling processes. The compressor which is at the heart of the cooling process represents the most energy consuming part. Thus, a better-quality compressor will reduce energy consumption which is always required. RDCs play a vital role in food preservation around the world, where compliance with food display requirements is a prerequisite for taking advantage of market share competition and opportunities. Shopping malls, shops and retail markets increasingly need to use RDCs to offer a wide range of food product displays.

In recent years, much research has concentrated on energy savings in thermal systems to produce more energy saving systems without affecting performance. Refrigeration and air conditioning systems consume a lot of power in industrial applications. Furthermore, most air conditioning companies tend to use VRF technology in their systems to minimise power consumption and increase efficiency.

VRF refers to the ability of a system to control the rate of refrigerant flow to each evaporator. This will enable the supply of many evaporators of different capacities and configurations, individualised comfort control, simultaneous heating and cooling in different zones, and heat recovery from one zone to another.

A VRF air conditioning system is a technology improved by commercial companies. The updated technology in VRF systems offers a great scale of energy efficiency; these systems operate quietly and provide the user with full control of environmental temperatures. Traditional HVAC systems are often limited to one condensing unit, one compressor and one evaporator, while a VRF system is designed to specifically meet the needs of several independent consumers inside one commercial mall or building. One condensing unit can be connected to several evaporators, each of which is individually controlled.

Exergy analysis for a theoretical vapour compression refrigeration cycle utilizing R12, R22 and R134A was analysed by Khan et al. [1]. The investigations showed that various results were obtained for the effect of evaporating temperatures on COP and exergetic efficiency. Performance parameters such as entropy generation, COP and exergetic efficiency were investigated at different ambient conditions by Chopra et al. [2] for different refrigerants such as R152a, R600, R600a, R410a, R290, R1234yf, R404a and R134a. It was found that both the energy and exergy efficiencies of R134a are 8.97% and 5.38% lower than R152a and R600 respectively at -50℃ evaporating and 45℃ condensing temperatures. The exergetic analysis of an R134A-based actual vapour compression refrigeration cycle was presented by Yadav et al. [3]. The component’s exergetic destruction and the cycle’s exergetic efficiency were found. A detailed exergy analysis for a theoretical vapour compression refrigeration cycle using R404A, R407C and R410A was studied by Soni1 and Gupt [4]. A detailed experimental analysis of a 2TR (ton of refrigeration) vapour compression refrigeration cycle for different percentages of refrigerant charge using exergy analysis was presented by Anand and Tyagi [5]. Application of the two-phase ejector in a subcritical refrigeration system was discussed by Dudar et al. [6]. Results of exergy analysis of the system operating with various working fluids for various operating conditions were studied. Their study showed a possible exergy efficiency increase in the refrigeration compression cycle. Exergy analysis of a transcritical carbon dioxide refrigeration cycle with an expander was performed by Yang et al. [7] and an exergetic analysis on a vapour compression refrigerating system was described by Xu and Clodic [8]. Effect of pressure drop and longitudinal conduction on exergy destruction in a concentric-tube micro-fin tube heat exchanger is studied by Imteyaz and Zubair [9]. Different types of refrigerants such as R404A, R134A, R22, and R410A were investigated for different single as well as multi-stage systems of vapour compression refrigeration cycles by Morad et al. [10]. The differences in the thermal and mechanical exergies in each component of air-cooled air conditioning system were analyzed by Yoo et al. [11].

Based on above, and according to author’s best knowledge, no detailed thermodynamic analysis of an RDC unit was done using experimental data. In this study, the performance of a variable speed rotary compression controlled by a DC frequency inverter will be presented.

Compressor performance has been analysed by many researchers, but most assume that the compressor runs at a constant conventional speed. The main issue in this work is to study the effects of compressor performance under different speeds. Thus, the performance of the compressor may be improved, leading to achieve best energy saving and less exergy destruction.

Another issue will be discussed in this study, which is the electronic expansion valve performance. EEV controls the flow of refrigerant entering a direct expansion evaporator. It does this in response to signals sent by an electronic controller. Most companies try to change the old system to a new system using an electronic expansion valve instead of a mechanical one. Improving the performance of the EEV will in turn improve the efficiency of the refrigeration system as a result.

3.1 External cooling load

One chiller cabinet will be used in this study. The dimensions of the open-front refrigerated display cabinet are 1.83m long, 0.586m wide and 1.435m high. The ambient air is 25℃ at 50% RH, the internal air is 2℃ at 50% RH. The roof and floor walls are all insulated with 45mm polyurethane which has a thermal conductivity value 0.023 W/m.K. The overall heat transfer coefficient is calculated using Fourier's law. The following equations are used to calculate the overall heat transfer coefficient of walls. [12]:

$U=\frac{1}{R_{t h}}$         (1)

$R_{t h}=R_{0}+\sum_{1}^{n} \frac{x_{n}}{k_{n}}+R_{i}$         (2)

$R_{t h}=0.10+\frac{0.045}{0.023}+0.12=2.17 \mathrm{m}^{2} . \mathrm{K} / \mathrm{W}$

$U=\frac{1}{R_{t h}}=\frac{1}{2.17}=0.46 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$

The ground temperature of the refrigerator is assumed 2℃. Typical value of the convection heat transfer coefficient (h) is (2-25) W/m².K and its value will be assumed 10 W/m².K. To calculate the transmission load, the conduction and convection heat transfer formula is used by Incropera [12]:

For conduction

$Q=U \times A\left(T_{0}-T_{i}\right)$            (3)

For convection

$Q=h \times A\left(T_{a}-T_{i}\right)$          (4)

The dimension of the RDC unit used in this work is shown in the following Table 1.

Table 1. RDC dimension

On the front side, the convection formula is used because heat losses here will be between the inside cold air and outside hot air, and Table 3 shows the convection heat loss from the front freezer side.

Table 2. The evaporator conduction load from walls

The cooling load from the product exchange is calculated as being the heat brought into the refrigerator from new products which are at a higher temperature.

The freezer is used to store cheese; approximately 250 kg of cheese arrive each day divided by 14 hours at a temperature of 10℃ and a specific heat capacity of cheese is 2.15 kJ/ kg.℃.

The heat exchange formula is used for heating capacity losses from cheese to freezer

$\begin{aligned} Q &=(250 \mathrm{kg} / 14 \mathrm{h}) \times 2.15 \mathrm{kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C} \times\left(10^{\circ} \mathrm{C}-2^{\circ} \mathrm{C}\right) \\ &=5.11 \mathrm{kW} \end{aligned}$

3.2 Internal heat load

The heat generated by the lighting is calculated using the lighting heating load formula:

Q= n x t, W         (5)

If two LED lamps of 18W-power each are used, the heat will be:

Q= 2 x 18W = 36 W

In this refrigerator, the evaporator, with two fans rated at 10W each, the heat generated by the fan motors in the evaporator will be:

Q = 2 x 10W = 20 W

3.3 Total cooling load

To calculate the total cooling load, we add all the calculated values to get:

Transmission load: 0.064 kW

Convection load: 0.520 Kw

Product load: 5.110 kW

Internal load: 0.036 kW

Equipment load: 0.020 kW

Total = 5.75 kW

A safety factor of (5%) should be applied to account for errors and possible variations from design point. Thus,

The total load will be 5.75 x1.05 = 6.0 kW = 1.7 TR.

3.4 Refrigeration cycle

1.png

Figure 1. Schematic drawing of vapor compression refrigeration cycle

The vapor-compression refrigeration cycle is the common cycle used for refrigerators and air conditioning systems. Figure 1 shows the main components of a refrigeration cycle, which are compressor, condenser, evaporator and expansion valve, which are classified into two types: traditional and electronic expansion valves are shown in Figure 3. Figure 2 shows the main processes of the ideal vapour-compression refrigeration cycle on T-s diagram, and it consists of four processes:

1-2 Isentropic compression in a compressor.

2-3 Constant-pressure heat rejection in a condenser.

3-4 Throttling in an expansion device.

4-1 Constant-pressure heat absorption in an evaporator.

2.png

Figure 2. T-s diagram for the ideal vapor-compression refrigeration cycle

3.png

Figure 3. Electronic expansion valve

3.5 Mollier (h-s) chart of the ref. R404a

The following values and parameters, specified below, are selected from the Mollier chart of the refrigerant R404a for the operating pressure range of 4.3913 bars to 18.2 bars for the design of a display cabinet refrigerator structure for 250kg of cheese.

h₁= 362.6 kJ/kg   s₁= 1.6202     kJ/kg.K

h_2s = 386.15 kJ/kg   s₂=  1.6202     kJ/kg.K

h₃= 242.6 kJ/kg   s₃= 1.1465     kJ/kg.K

h₄= 242.6 kJ/kg    s₄= 1.1636      kJ/kg.K

The vapor-compression refrigeration cycle is operating between a low-temperature reservoir at T_L and a high-temperature reservoir at T_H. The maximum COP of a refrigeration cycle operating between temperature limits is given by Çengel [13].

$\operatorname{COP}_{R-C}=\frac{T_{L}}{T_{H}-T_{L}}$               (6)

Exergy destruction for major components of a refrigeration system is written as follows:-

Compressor:

$\dot{X}_{\text {dest}, 1-2}=T_{\mathrm{o}} \dot{S}_{g e n, 1-2}=\dot{m} T_{\mathrm{o}}\left(s_{2}-s_{1}\right)$        (7)

Condenser:  

$\dot{X}_{\text {dest}, 2-3}=T_{\mathrm{o}} \dot{S}_{g e n, 2-3}=T_{\mathrm{o}}\left[\dot{m}\left(s_{3}-s_{2}\right)+\frac{\dot{Q}_{H}}{T_{H}}\right]$                (8)

Expansion Valve:

$\dot{X}_{\text {dest}, 3-4}=T_{\mathrm{o}} \dot{S}_{\text {qen}, 3-4}=\dot{m} T_{\mathrm{o}}\left(s_{4}-s_{3}\right)$                (9)

Evaporator:

$\dot{X}_{\text {dest}, 4-1}=T_{\mathrm{o}} \dot{S}_{g e n, 4-1}=T_{0}\left[\dot{m}\left(s_{1}-s_{4}\right)+\frac{\dot{Q}_{L}}{T_{L}}\right]$             (10)

The total energy destruction associated with the refrigeration cycle is the summation of the energy destruction for each component of the cycle:

$\dot{X}_{\text {dest}, \text {total}}=\dot{X}_{\text {dest}, 1-2}+\dot{X}_{\text {dest}, 2-3}+\dot{X}_{\text {dest}, 3-4}+\dot{X}_{\text {dest}, 4-1}$           (11)

The second law of efficiency (Exergy Efficiency) of the refrigeration cycle is equal to the ratio of actual COP to maximum COP for the cycle:

$\eta_{I I}=\frac{C O P_{R}}{C O P_{R-C}}$             (12)

The error or uncertainty analysis in an experimental work quantifies the difference between measured and true value of a thermo physical quantity of a material. The uncertainty in the estimate of the true value provides a rational way of evaluating the significance of the scatter on repeated trials [14].

$C O P_{R-C}=f\left(T_{L}, T_{H}\right)$             (13)

$\Delta C O P_{R-C}=\sqrt{\left(\frac{\partial C O P_{R-C}}{\partial T_{L}} \cdot \Delta T_{L}\right)^{2}+\left(\frac{\partial C O P_{R-C}}{\partial T_{H}} \cdot \Delta T_{H}\right)^{2}}$             (14)

where,

$\frac{\partial C O P_{R-C}}{\partial T_{L}}=\frac{T_{H}}{\left(T_{H}-T_{L}\right)^{2}}$             (15)

$\frac{\partial C O P_{R-C}}{\partial T_{H}}=\frac{-T_{L}}{\left(T_{H}-T_{L}\right)^{2}}$             (16)

• For traditional cycle:

From Table 5, the actual evaporative and condenser temperature are -6.2℃ and 29.9℃, respectively. $\Delta T_{L}=\Delta T_{H}=0.1^{\circ} \mathrm{C}$. Substituting in Eqns. (14), (15) and (16):

$\begin{aligned} \operatorname{COP}_{R-c}=7.4 \text { and } & \Delta C O P_{R-\text {Carnot}} =& 0.030973 \end{aligned}$

The percentage of uncertainty in evaluating $C O P_{R-C}$ of traditional cycle is:

$\begin{aligned} \frac{\Delta C O P_{R}-C}{C O P_{R-C}} \times 100 \% &=\frac{0.030973}{7.4} \times 100 \% =\pm 0.42 \% \end{aligned}$

• For VRF system:

From Table 5, the actual evaporative and condenser temperature are -7℃ and 18.9℃, respectively. $\Delta T_{L}=\Delta T_{H}=0.1^{\circ} \mathrm{C}$. Substituting in Eqns. (14), (15) and (16).

$\begin{aligned} \operatorname{COP}_{R-c}=10.3 & \text { and } \Delta C O P_{R} \text { -Carnot } =0.058872 \end{aligned}$

The percentage of uncertainty in evaluating $C O P_{R-C}$ of VRF system is:

$\begin{aligned} \frac{\Delta C O P_{R}-C}{C O P_{R-C}} \times 100 \% &=\frac{0.058872}{10.3} \times 100 \% =\pm 0.57 \% \end{aligned}$

Table 5. The required parameters which are collected from Danfoss data logger