The vapor compression cycle is a common foundation for many PE problems. It’s also the main mechanism behind many air conditioning units so you can expect to encounter some problems relating to the vapor compression cycle especially if taking the HVAC examination. The vapor compression cycle is essentially a Rankine cycle run in reverse. The basic components of this type of cycle are a compressor, a condenser, a throttling valve, and an evaporator:
These types of cycles typically run between a "high" and "low" temperature. The low temperature is the temperature of the fluid at points 4 and 1 across the evaporator and the high temperature is the temperature at points 2 and 3 across the condenser.
Unless otherwise stated in the problem statement, you can make some common assumptions that will simplify the solution.
Assume the working fluid (i.e. the refrigeration fluid) is a saturated vapor. This is usually the case as compressing a vapor/liquid mix is unduly difficult and can create too much wear on the compressor. Also, this aids the calculations since the enthalpy and entropy terms for that point are taken right from the associated tables without any need to calculate a quality ratio first.
Depending on whether a compressor is given an efficiency in the problem statement or not the process from point 1 to 2 across the compressor will either be considered isentropic (S1=S2) or irreversible and non-adiabatic (S2> S1). If the compressor efficiency is known, Equation 1 can be used to calculate the actual enthalpy at point 2 when the enthalpy of point one is known.
The process from point 2 to 3 is considered isothermal therefore while the enthalpy will change across the condenser T3=T2. Given this assumption, h3 can be determined from tables or T-s or T-h charts for the given working fluid.
Once h3 is determined h4 is easily given since the throttling process in the vapor compression cycle is considered isenthalpic. When the refrigeration fluid gets throttled, the enthalpy remains the same, the temperature decreases, the entropy increases, and the quality increases.
The process diagrams for this cycle with the above assumptions are shown in Figures 1 and 2.
Typically, the performance of a vapor compression cycle is given as the coefficient of performance. Unlike efficiency, this number is always greater than one. COP is unit less and typical ranges are from 3 to 10. The coefficient of performance is defined as the capacity of the cycle (the usable refrigeration the cycle can achieve typically in tons or BTU/HR) over the energy used and expelled by the rest of the cycle:
Example 1
An ideal vapor compression cycle using R134a has a refrigeration load of 5 tons. The cycle operates between -15F and 100F. Determine the coefficient of performance.
A)
B)
C)
D)