I’ve seen a lot of people asking questions about chiller capacity at different temperatures and I figured I would provide a pretty effective way to calculate it. This is how we size for multistage refrigeration systems, although usually I am working the opposite direction.
First, you need to establish an evaporator temperature (the temperature of the cold part of the chiller). This is basically the design temperature you want your cooled fluid (let’s say -69 C for an example), less your heat exchanger approach temperature (more on this later), and plus your suction superheat. Suction superheat is how much hotter than the “boiling point” the refrigerant is when it gets pulled back into the compressor at a given evaporator pressure. 3-5C is a pretty safe bet.
Approach temperature is probably the hardest thing to calculate accurately in refrigeration, and when dealing with someone else’s work (e.g. you bought a julabo off eBay) can be tricky. However, you can get decently close by measuring the temperature of the refrigerant entering the evaporator (ie the coil before it goes into a bath on a recirculating chiller) and the temperature on its way out (ie the temperature entering the compressor) under load. The way to think of this is “if I want the glycol to be -69C, how much colder does the refrigerant need to be to exchange that heat”. This is obviously a grossly incorrect way to actually calculate this because there are all sorts of mass transfers and such needed for the actual calculation. Let’s arbitrarily assign a value of 10C here, which is pretty lousy so it should give you a number lower than the actual chiller capacity. In our theoretical instance, this gives us an evap temp of -69 - 10 + 5 = -74C.
Next, we need to evaluate the evaporator pressure that we are operating at: to do this we will be looking up the “saturation pressure” at the refrigerant temperature (having already accounted for superheat, this is going to be your target temperature less your approach temp = -79C). There are a million saturation charts for each refrigerant, so pick any of them and look for the line that describes saturation at this temperature; it should also give a value for vapor density and enthalpy of vaporization at this pressure/temperature. This indicates how many watts per kg of refrigerant are removed from the system to boil the refrigerant and how much refrigerant is going to be moved by your compressor. Let’s choose r404a as our example here, and looking up a saturation chart gives us a density of .873 kg/m3 and a latent heat of 221 kj/kg at our -79C.
To complete this though, I’m sure you’ve realized you need an actual volumetric flow for the refrigerant. This is called the “swept volume”. Fantastically, this is easily found from most Copeland compressors using their OPI tool. For other compressors, I usually just use a cross reference to find an equivalent Copeland compressor and it comes out pretty close.
Now, knowing our swept volume, let’s say 42.6 m3/hr for a Copeland ZF41K5E and our density .873 kg/m3, and our latent heat, 221 kj/kg, we can calculate that the system uses 8220 Kj per hour to boil that refrigerant. Because one watt = one joule/second, and there are 3600 seconds per hour, we get 8220000/3600=2280W. This doesn’t take into account any sensible heat (ie subcooling), but in reality this is hardly ever a factor that comes close to the lack of precision of this method of calculation. You’ll also probably notice that for a single stage compressor system, the density is incredibly low at these low temperatures and accordingly so is the power output.
You may also think “wow, I didn’t realize my chiller could get that cold”. You are probably correct, what you are seeing is that although the chiller would have capacity to cool at that temperature, the power loss to environment (adiabatic loss) is greater than the output at some higher temperature. This is where the chiller will “stall” and usually where the manufacturer lists it’s low end temperature. Keep in mind that adiabatic loss increases massively with the delta t to the environment.
Now, you can also backtrack much of this information by evaluating performance at some higher temperature (ie how quickly can I cool 10kg of water 10C) and use the same formula to get any unknowns (approach and swept volume are usually the ones in question since you can look up the others).
The rule of thumb if you are building a refrigeration system is that the compression ratio (condenser pressure:evap pressure) should not be greater than 10:1. Any greater than this and you will end up roasting the compressor (caveat: liquid injected/vapor injected compressors). I haven’t taken the time to explain how to calculate condenser pressure, but I’m sure you can figure it out if you’re trying to build your own chiller. When you realize that you have a compressor with sufficient swept volume, but your evap pressure is 1/50 of your condenser pressure, you will need to either put compressors in series, dumping heat between them, or go to a cascade system where the condenser operates at a much lower temperature because it is connected to the evaporator of another refrigerant loop. The latter is more complicated but much more efficient as it allows use of refrigerants or cryogens that are much denser at lower temperatures than the conventional ones. If you are just trying to establish the capacity of your existing system (or one you are shopping for), calculating the capacity at the evaporator of the lowest stage should be sufficient because the manufacturer should have done their work and sized the upper stages appropriately.
I know this is very very crude and all the chiller pros are probably gonna hop on here and pick my lazy math apart, but if your goal is to figure out if X chiller will be able to cool some volume of something at the right temperature, it will probably get you at least within a model size. I hope this is helpful for y’all.
Long ass post but I was stuck at the airport and ran out of new posts to read.
