Figure 1: Vapor-Compression Refrigeration Cycle
T-s diagram
We want to design a vapor-compression refrigeration cycle to absorb heat from a cool environment and reject it to a warm environment. The design is to be based upon the ideal vapor-compression refrigeration cycle, with four components: a cooler (where we reject the heat), a throttle, a heater (where we absorb the heat), and a compressor.
The challenge in refrigeration (and air conditioning, etc.) is to remove heat from a low temperature source and dump it at a higher temperature sink. Compression refrigeration cycles in general take advantage of the idea that highly compressed fluids at one temperature will tend to get colder when they are allowed to expand. If the pressure change is high enough, then the compressed gas will be hotter than our source of cooling (outside air, for instance) and the expanded gas will be cooler than our desired cold temperature. In this case, we can use it to cool at a low temperature and reject the heat to a high temperature.
Vapor-compression refrigeration cycles specifically have two additional advantages. First, they exploit the large thermal energy required to change a liquid to a vapor so we can remove lots of heat out of our air-conditioned space. Second, the isothermal nature of the vaporization allows extraction of heat without raising the temperature of the working fluid to the temperature of whatever is being cooled. This is a benefit because the closer the working fluid temperature approaches that of the surroundings, the lower the rate of heat transfer. The isothermal process allows the fastest rate of heat transfer.
An ideal refrigeration cycle looks much like a reversed Carnot heat engine or a reversed Rankine cycle heat engine. The primary distinction being that refrigeration cycles lack a turbine, using a throttle instead to expand the working fluid. (Of course, a turbine could be incorporated into a refrigeration cycle if one could be designed to deal with liquids, but the useful work output is usually too small to justify the cost of the device.)
The cycle operates at two pressures, Phigh and Plow, and the statepoints are determined by the cooling requirements and the properties of the working fluid. Most coolants are designed so that they have relatively high vapor pressures at typical application temperatures to avoid the need to maintain a significant vacuum in the refrigeration cycle.
The T-s diagram for a vapor-compression refrigeration cycle is shown below.
Figure 1: Vapor-Compression Refrigeration Cycle
T-s diagram
Figure 2: Basic refrigeration cycle layout |
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For purposes of illustration, we will assume that a refrigeration system used to cool air for an office environment. It must be able cool the air to 15.5°C (about 60°F) and reject heat to outside air at 32°C (90°F).
We have several working fluids available for use in refrigeration cycles. Four of the most common working fluids are available in CyclePad: R-12, R-22, R-134, and ammonia. (Nitrogen is also available for very low temperature refrigeration cycles.) We will choose R-22 for this example.
We will examine each statepoint and component in the refrigeration cycle where design assumptions must be made, detailing each assumption. As we can see from the example design constraints, very few numbers need be specified to describe a vapor-compression refrigeration cycle. The rest of the assumptions are determined by applying reasoning and background knowledge about the cycle. The two principle numerical design decisions are determining Phigh and Tlow, at the cooler outlet and the compressor inlet.
The cooler (also known as the condenser) rejects heat to the surroundings. Initially, the compressed gas (at S1) enters the condenser where it loses heat to the surroundings. During this constant-pressure process, the coolant goes from a gas to a saturated liquid-vapor mix, then continues condensing until it is a saturated liquid at state 2. Potentially, we could cool it even further as a subcooled liquid, but there is little gain in doing so because we have already removed so much energy during the phase transition from vapor to liquid.
We choose Phigh so that we can reject heat to the environment. Phigh is the same as P2, and P2 determines the temperature at state S2, T2. (T2 is just the saturation temperature at Phigh). This temperature must at least be higher than that of the cooling source, otherwise no cooling can occur.
However, if T2 is too high (that is, higher than the critical temperature TC for the working fluid), then we will be beyond the top of the saturation dome and we will loose the benefits of the large energy the fluid can reject while it is being cooled. Furthermore, it is often impractical and unsafe to have very high pressure fluids in our system and the higher P2 we choose, the higher T1 must be, leading to additional safety concerns. To find an applicable pressure, use the saturation tables to find a pressure which is somewhere between the saturation pressure of the warm air yet still in the saturation region.
For reference, TC for our four working fluids are given below.
| Critical Temperatures
of some refrigerants |
|
|---|---|
| substance | TC (°C) |
| R-12 (CCL2F2) | 111.85 |
| R-22 (CHCLF2) | 96.15 |
| R-134a (CF3CH2F) | 101.05 |
| ammonia (NH3) | 132.35 |
For our example using R-22, we must be able to reject heat to air that is 32°C. We can choose if T2 to be anywhere between that number and the 96°C TC. We'll choose it to be 40°C for now.
Figure 3: Vapor-Compression Refrigeration Cycle
COP versus Thigh in the cooler
The usual design assumption for an ideal heater in a refrigeration cycle is that it is isobaric (no pressure loss is incurred from forcing the coolant through the coils where heat transfer takes place). Since the heating process typically takes place entirely within the saturation region, the isobaric assumption also ensures that the process is isothermal.
Of course, we would get the same isothermal behavior if we were to start the compression before the fluid was completely saturated. Further, there would seem to be a benefit in that statepoint S1 (see Figure 1) would be closer to the saturation dome on the Phigh isobar, allowing the heat rejection to be closer to isothermal and, therefor, more like the Carnot cycle.
It turns out that, for increased efficiency, we can choose S4 such that S1 is on the saturation dome, instead of outside of it in the superheat region. Figure 4 shows the T-s diagrams for two refrigeration cycles, one where S4 is a saturated vapor and the other (in light green) where S4 has been moved further into the saturation dome to allow S1 to be a saturated vapor.
Figure 4: T-s diagram for different compressor conditions
Figure 5: COP versus compressor inlet quality
Tlow occurs within the saturation dome, so it determines Plow as well. We know that Tlow must at least be cooler than the desired temperature of the stuff we wish to cool, otherwise no cooling will occur. An examination of the saturation tables for our refrigerants shows that setting Tlow at, for instance 15° C, still allows for fairly high pressures (4 to 7 atmospheres, typically). So, while this tells us how low Plow must be, it does not tell us how low it can be.
There are several major practical considerations limiting Plow. Fundamentally, we must concern ourselves with the properties of our working fluids. Examination of the saturation table for R-22 shows that at atmospheric pressure, the saturation temperature is already very cold (about -40°C). For small-scale air-conditioning applications, we have no desire to create a stream of extremely cold air, both due to safety concerns and because cold air holds very little moisture and can be uncomfortably dry. For larger-scale applications, this is less of a concern because we can always mix the cold, dry air with warmer, wetter air to make it comfortable.
Another hardware consideration is that it is fairly difficult to maintain a very low-pressure vacuum using the same compressor that will achieve high pressure at its outlet. Choosing a Tlow that results in a Plow of 0.1 atmospheres is probably not practical if we intend to have Phigh up near 10 atmospheres.
This brings us to the other reason we cannot make Tlow too small. Examining Figure 1 again, we see that the lower Plow is, the further out to the right (higher entropy) the saturated vapor will be at statepoint S4. Statepoint S4 has the same entropy as S1, and the further to the right S1 is along the Phigh pressure isobar, the hotter S1 must be. This high temperature is undesirable from both efficiency and safety standpoints.
The figure below shows the relationship between Tlow and the cycle's coefficient of performance (COP). We note that the higher Tlow, the better the COP. The practical limit on Tlow is heat transfer rate in the evaporator; having Tlow too close to the temperature of the stuff we wish to cool results in low heat transfer rates.
Figure 6: Vapor-Compression Refrigeration Cycle
COP versus Tlow
Download the CyclePad design of the refrigeration cycle.
Whalley, P.B. 1992. Basic Engineering Thermodynamics. Oxford University Press. ISBN: 0-19-856255-1
Haywood, R.W. 1980. Analysis of Engineering Cycles. Pergamon Press. ISBN: 0-08-025440-3
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Contributed by: M. E. Brokowski
Initial Entry: 12/14/97
Last Edited: 12/16/97
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