PRACTICAL CONSIDERATIONS AND COP
For a simple circuit, using the working fluid Refrigerant R134a, evaporating at -5°C and condensing at 35°C, the pressures and enthalpies will be as shown in Figure 2.3:
Enthalpy of fluid entering evaporator = 249.7kJ/kg
Enthalpy of saturated vapour leaving evaporator = 395.6kJ/kg
Cooling effect = 395.6 — 249.7 = 145.9kJ/kg
Enthalpy of superheated vapour leaving compressor (isentropic compression) = 422.5
Since the vapour compression cycle uses energy to move energy, the ratio of these two quantities can be used directly as a measure of the performance of the system. As noted in Chapter 1 this ratio is termed the coefficient of performance (COP). The ideal or theoretical vapour compression cycle COP is less than the Carnot COP because of the deviations from ideal processes mentioned in Section 2.2. The ideal vapour compression cycle COP is dependent on the properties of the refrigerant, and in this respect some refrigerants are better than others as will be shown in Chapter 3.
Transfer of heat through the walls of the evaporator and condenser requires a temperature difference as illustrated in Figure 2.6. The larger the heat exchangers are, the lower will be the temperature differences, and so the closer
Heat flows from the refrigerant which condenses back to liquid
Figure 2.6 The temperature rise or ‘lift’ of the refrigeration cycle is increased by temperature differences in the evaporator and condenser
The fluid temperatures will be to those of the load and condensing medium. The COP of the cycle is dependent on the condenser and evaporator temperature differences (see Table 2.1).
Table 2.1 COP values for cooling a load at -5°C, with an outside air temperature of 35°C (refrigerant R404A)
1 The ideal vapour compression cycle with constant enthalpy expansion and isentropic adiabatic compression with refrigerant R404A.
2 The vapour compression cycle as above and with 70% efficient compression with R404A and no other losses.
3 SEI is the ratio between the actual COP and the Carnot COP with reference to the cooling load and outside air temperatures, i. e. when the heat exchanger temperature differences, A T are zero. SEI decreases as AT increases due to less effective heat exchangers. Values are shown for the cycle with 70% efficient compression. Actual values will tend to be lower due to pressure drops and other losses.
Table 2.1 shows how the Carnot COP decreases as the cycle temperature lift increases due to larger heat exchanger temperature differences, AT.
The practical effects of heat exchanger size can be summarized as follows:
Larger evaporator: (1) Higher suction pressure to give denser gas entering the compressor and therefore a greater mass of gas for a given swept volume, and so a higher refrigerating duty; (2) Higher suction pressure, so a lower compression ratio and less power for a given duty.
Larger condenser: (1) Lower condensing temperature and colder liquid entering the expansion valve, giving more cooling effect; (2) Lower discharge pressure, so a lower compression ratio and less power.
A refrigeration circuit is to cool a room at 0°C using outside air at 30°C to reject the heat. The refrigerant is R134a. The temperature difference at the evaporator and the condenser is 5 K. Find the Carnot COP for the process, the Carnot COP for the refrigeration cycle and the ideal vapour compression cycle COP when using R134a.
Carnot COP for 0°C (273 K) to 30°C (303 K)
(303 — 273)
Refrigeration cycle evaporating -5°C, condensing 35°C, Carnot COP
(308 — 268)
Cooling effect = 395.6 — 249.7 = 145.9kJ/kg Compressor energy input = 422.5 — 395.6 = 26.9kJ/kg Ideal R134a vapour compression cycle COP
Since there are additionally mechanical and thermal losses in a real circuit the actual COP will be even lower. For practical purposes in working systems, the COP is the ratio of the cooling effect to the compressor input power.
System COP normally includes all the power inputs associated with the system, i. e. fans and pumps in addition to compressor power. A ratio of System COP to Carnot COP (for the process) is termed system efficiency index, SEI.
This example indicates that care must be taken with definitions when using the terms efficiency and COP.
A pressure-enthalpy chart in which the liquid and the vapour states of the fluid are to scale, sometimes called a Mollier chart, is drawn in Figure 2.7 for R404A.
A refrigeration cycle is represented by A, Ah B, C, Cb D. With a compression efficiency of 70% the final temperature at the end of compression, as shown on the chart, is approximately 65°C. The value is dependent on the refrigerant and the compressor efficiency. This is a more practical cycle because the vapour leaving the evaporator is superheated (A to A1) and the liquid leaving the condenser subcooled (C to C1). Superheat and subcooling occupy quite small sections of the diagram, but they are very important for the effective working of the system. Superheat ensures that no liquid arrives at the compressor with the vapour where it could cause damage. Subcooling ensures that liquid only flows through the line from the condenser to the control or expansion valve. If some vapour is present here, it can cause excessive pressure drop and reduction in performance of the system. Therefore in Figure 2.7 the gas leaving the evaporator is superheated to point A1 and the liquid subcooled to C1. Taking these factors
Figure 2.7 Pressure—enthalpy or Mollier diagram for R404A showing vapour compression cycle
Into account, the refrigerating effect per unit mass flow rate A — D) and the compressor energy (B — Aj) may be read off directly in terms of enthalpy of the fluid. In practice pressure losses will occur across the compressor inlet and outlet, and there will be pressure drops through the heat exchangers and piping and these can also be plotted on the chart. There will also be some heat loss to atmosphere from the compressor and discharge piping.
The position of D inside the curve indicates the proportion of flash gas at that point. The condenser receives the high-pressure superheated gas, B, cools it down to saturation temperature, condenses it to liquid, C, and finally subcools it slightly, Ci. The energy removed in the condenser, or heat rejection (B — C1) is seen to be the refrigerating effect plus the heat of compression.
Computer software is available to make all these calculations and the usual reference for refrigerant property data is NIST Refprop. Nevertheless an understanding of the P-h or Mollier diagram is essential when designing or diagnosing a vapour compression cycle.
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