1.2. Thermodynamic performance of refrigeration system

for the high temperature cycle and a condenser for the low temperature cycle. The partition temperature, which is the temperature of the evaporator of the upper cycle, is an important design parameter. It influences the total shaft work requirement of the cycle as will be seen in

A multi-stage cycle is normally implemented when the pressure ratio between the heat rejection and heat absorption pressures is high and when cooling is required at different temperature levels. For example, in a two-level cycle, illustrated in Figure 2(a), the cooling duty is satisfied at two different evaporation temperatures using a single refrigerant expanded to two different pressure levels. Introducing two cooling levels reduces the refrigerant flow in the low temperature cycle that in its turn reduces the overall power requirement of the cycle [2].

Decomposing a complex cycle into an assembly of simple vapor compression cycles is an alternative approach for predicting the power demand of a complex cycle. For example, a

Figure 2. (a) Multi-level refrigeration cycle—two heat sources and a single heat sink; (b) decomposition into simple

Section 1.2.1.

4 Refrigeration

cycles.

1.1.3. Multi-stage refrigeration cycle

1.1.4. Decomposing of complex refrigeration cycle

The performance of a refrigeration system can be characterized by an actual coefficient of performance COPact that is defined as the ratio of the heat absorbed Qevap to the shaft work consumed W:

$$\text{COP}\_{\text{act}} = \frac{Q\_{\text{evap}}}{W} \tag{1}$$

An ideal refrigeration cycle could be based on a Carnot cycle, for which the ideal coefficient of performance COPid can be defined by:

$$\text{COP}\_{\text{id}} = \frac{T\_{\text{evap}}}{T\_{\text{cond}} - T\_{\text{evap}}} \tag{2}$$

Where Tevap is the evaporating temperature (K) and Tcond is the condensing temperature (K).

As a rule of thumb, the shaft work can be approximately estimated with a coefficient of performance ratio, η, typically equal to 0.6 [1, 2].

$$\mathcal{W} = \eta \frac{\mathcal{Q}\_{\text{evap}}}{\text{COP}\_{\text{id}}} \tag{3}$$

The next section examines the possibility of using the typical value for η (0.6) to calculate the shaft work requirement of a cascade refrigeration cycle.

## 1.2.1. Example 1: performance and shaft work evaluation of a cascade refrigeration cycle

This example evaluates the coefficient of performance ratio and the shaft work requirement of a cascade refrigeration cycle for a range of condensing temperatures (40, 30 or 20�C), cooling duty of 523 kW, and evaporation temperature of �82�C. In the cascaded refrigeration cycle, as shown in Figure 1(b), ethylene and propylene are used in the lower and upper cycles, respectively.

In this example, the total shaft work requirement will be calculated using rigorous simulation and compared with the shaft work predicted using Carnot model (η = 0.6). Aspen HYSYS is applied for simulation of the cycles with physical properties calculated by choosing Soave-Redlich-Kwong as the fluid package. In the simulation, the partition temperature Tpart between the two cycles is optimized to minimize the total shaft work of the cascaded cycle. Tpart is allowed to change between the lowest temperature that the upper cycle can operate at, which is the normal boiling point for the refrigerant of the upper cycle, and the maximum temperature at which the lower cycle can reject the heat. At each partition temperature, the total shaft work of the cascaded cycles is calculated by adding the shaft work consumption of the upper cycle and the lower cycle. Then, the optimal partition temperature is identified by optimizing the shaft work as shown in Figure 3.

Figure 3. Calculation the optimal partition temperature of ethylene-propylene cascade cycle (Tevap = �82�C, Tcond = 40�C and Qevap = 523 kW).


Table 1. Comparison of total shaft work calculated by rigorous simulation and Carnot model using fixed value of coefficient of performance ratio, η.

Results in Figure 3 show that the optimum partition temperature is closest to the first evaporation level of the upper cycle rather than the last evaporation level of the lower cycle; a similar conclusion was reported by Lee [8].

In Table 1, it may be seen that the coefficient of performance ratio (η) is below 0.6, which is the typical value for η [2]. In terms of shaft work requirement, the results in Table 1 show that the error is significantly larger if the 'typical' ratio of 0.6 is used to predict shaft work requirement of the refrigeration cycle. Therefore, using a single value for the efficiency factor η is not the correct way to evaluate the refrigeration system performance. Section 2 proposes a new shortcut approximation of COPact [3].
