 The simple vapor compression refrigeration cycle is referred to as simple because it is the least complicated of the vapor compression refrigeration cycles we'll consider. We add devices and complexity in order to accomplish certain goals. In some cases, we might be trying to meet certain use cases, say, maybe you're using one cycle to maintain multiple refrigeration loads and therefore multiple evaporators. In other cases, we're trying to optimize our cycle for certain operating conditions. One such operating condition we can consider is a large temperature difference. Quotations are on the word large there because large is relative. For that, let's look at the simple cycles TS diagram. Remember that the horizontal displacement across the evaporator represents the heat transfer in. The horizontal displacement across the condenser represents the heat transfer out. The region enclosed by the cycle represents the network which is the network in which for the simple cases also the work in because there is no workout. Furthermore, remember that the saturation temperatures represent actual operating temperatures for the evaporator and condenser. For the evaporator to pull heat in from a space, it needs to operate at a lower temperature than its surroundings. For the condenser to push heat out to a space, it must operate at a higher temperature than its surroundings. Therefore, as the difference in temperature between your cold side and hot side increases, so too must the difference in saturation temperatures between your high pressure and low pressure. Therefore, a large temperature difference will require a large pressure difference. Now let's look at how pressure difference affects operating efficiency. If I were to move the low pressure line down and or move the high pressure line up in both cases, I'm going to be decreasing the difference in horizontal displacement between state four and state one. As a result of that smaller horizontal displacement, that means less heat removed from the refrigerated space. Even if I somehow didn't increase my network, a smaller Q in means a smaller coefficient of performance. Larger temperature difference implies larger pressure difference which implies smaller Q in which implies smaller C O P R. One solution to that problem is to split the refrigeration cycle across multiple refrigeration stages. You can think of that like literally putting refrigeration cycles end to end. The heat pushed out from one condenser is pulled in to the next evaporator. This is referred to as multi-stage refrigeration, which is sometimes called cascade refrigeration. In very low temperature refrigeration cycles, you might even need three or four stages of refrigeration. They may have different operating pressures, they may have different working fluids, but the principle is the same across each of them. We can improve the performance of a multi-stage refrigeration cycle a little bit by enclosing the condenser and evaporator together in a heat exchanger, like this. Note that as a result of this multi-stage refrigeration cycle, we can increase the refrigeration capacity corresponding to a certain temperature difference between high and low side saturation temperatures and we have also decreased the amount of work required to operate that refrigeration cycle. So we are decreasing the amount of work in and we are increasing the refrigeration capacity leading to a higher coefficient of performance. We analyze the multi-stage refrigeration cycle in the same way that we analyze the simple cycle just with more processes. We are still assuming that the inlet to our compressors are a saturated vapor because it would be a waste of energy for us to try to somehow super heat it in the evaporator and we assume the outlet of the condensers is a freshly condensed substance because it would be a waste of energy for us to try to compress it further or subcool it further. As a result, we have state points 1, 7, and 3 in this diagram as being on the saturated vapor or saturated liquid lines. We assume the expansion valves operate isenthalpically unless we're given enough information to deduce otherwise and we assume both compression processes occur isentropically unless we're given enough information to deduce otherwise. Our total power input is just going to be the mass flow rate through cycle B multiplied by the specific work in to cycle B which is just across the compressor from one to two plus the mass flow rate through cycle A multiplied by the specific work in to cycle A which is just going to be the specific work into the compressor between five and six. The total rate of heat rejection from the cycle is just going to be the condenser in cycle A, the total rate of heat absorbed by the cycle is just going to be the Q in to evaporator B and because we're treating it as being made up of simple refrigeration cycles we assume no workout terms. Now just like in the feedwater heaters in the Rankine cycle we can look at ways to try to improve the performance of our heat exchanger. The best form of heat exchange is going to be direct contact between the fluids but to do that we would be mixing together the low pressure side of cycle A and the high pressure side of cycle B. We would have to be splitting the stream at state point eight some of it would be going across to what is currently state point five some of it would be going down into state point three and we would have to be recombining a stream from whatever the outlet of the heat exchanger was with the outlet at state point two. For that we model a cycle like this. We are splitting the stream at the outlet of the expansion valve on the high pressure refrigeration cycle some of it is brought directly into a mixing chamber the rest of it is taken through a low pressure refrigeration cycle. We assume the stream is split by phase in a device referred to as a flash chamber. The flash chamber takes a mixed stream at state point six some of it leaves at seven as a liquid some of it leaves at three as a vapor that's due to the mechanical operation of the flash chamber itself this box is not a very good diagram of how a flash chamber works for that let's take a closer look at the flash chamber in an actual flash chamber you are bringing in a mixed stream some amount of liquid some amount of vapor you are separating it with gravity pulling the liquid down and pushing the vapor up you accumulate liquid on one side and vapor on the other then to make sure that there's no liquid entrained in the vapor you typically push it through a mesh to collect as much liquid as you can to condense and rejoin the rest of the liquid the vapor that makes it through the mesh leaves at the vapor outlet the flash chamber flashes off the vapor splitting a mixed stream into liquid and vapor in this cycle we have a high pressure at which our condenser operates then we expand to an intermediate pressure where the stream is split some of it the vapor goes into the mixing chamber the rest of it the liquid goes down into a low pressure refrigeration cycle in the low pressure side we have a low pressure at which our evaporator operates and then we have two compressors one taking it from low pressure to intermediate pressure one taking it from intermediate pressure to high pressure note that these nine state points have different mass flow rates there is one mass flow rate at nine four five and six from this state point numbering scheme there is some mass flow rate at seven eight one and two and then we know the mass flow rate at two and three must sum together to equal nine it might be useful to characterize what proportion of mass flow rate leaves at seven and three that would allow us to reduce the number of variables that we are trying to keep track of as we build equations for this cycle for that we could come up with a variable say y and use y to represent the proportion of mass flow rate that leaves at one side or the other in this case let's just consider the amount of mass flow rate that leaves at three divided by the mass flow rate that enters at state six so y here represents the proportion of mass flow rate at six that leaves at three then we could write one minus y the remaining proportion of the fluid the amount that leaves as liquid as m dot seven over m dot six so if twenty percent of the stream left as a vapor the remaining eighty percent leaves as liquid but we don't even need to call this a new variable we don't need to identify why because we will already have how much of that mixture is a vapor and how much of it is a liquid the mass flow rate that leaves at three is just whatever mass flow rate at six is vapor the mass flow rate at six itself is the sum of the mass flow rate at six that is vapor and the mass flow rate at six that is liquid therefore the proportion of mass flow rate at six that is vapor divided by mass flow rate at six that is mixture is the quality at state six the quality is abbreviated here with an x and it represents the amount of mass of mixture that is vapor. Then we can write the proportion m.7 over m.6 as being 1 minus x6. We could call it something else, but we don't need to, because we already have a way of referring to how much of the mixed stream is vapor and liquid. If we determine the quality at state 6, we know the relative proportions of massful rate directly going to the mixing chamber and going down to the low-pressure refrigeration cycle. If we look at the TS diagram, we can get a better idea of what's happening. We have a stream at 4 and 5 that represents how much heat is being pushed out of our condenser. It's expanded across an expansion valve at state 6. Some of it leaves as liquid, some of it leaves as vapor, 7 and 3 respectively. The stream at 7 is expanded again down to the low-pressure at state 0.8. It is pushed across an evaporator, which evaporates it and does not superheat it to state 0.1. The process from 1 to 2 is an isentropic compression process unless we're given enough information to deduce otherwise, so we draw it as a vertical line up to the intermediate pressure. And then state points 2 and 3 are mixed together to produce 9, which is going to be between the 2. Its relative position between 3 and 2 is going to be represented by the proportion of massful rates at 3 and 2. We could relate that again to its quality. Then state 0.9 goes into an isentropic compression process to the high-pressure at state 0.4. And that's our multi-stage vapor compression refrigeration cycle with flash intercooling. For more context, let's try an example problem.