# Compressor Water Cooled Chiller Thermal Calculations

#### David Gin

Hi All,

Is there a list of thermodynamics equations regarding the chiller process from condenser, evaporator, compressor to the regulator.

Say I have chiller load at 90%, what set of equations could I use to determine the supply temperature of chill water and condenser supply temperature to set to reduce that load to say 85% while keeping the same flow rate?

There's the usual estimate of Q = 500 * GPM * dT, but it is insufficient for my needs.

Thank you.

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#### Mech_Engineer

Gold Member
If I understand correctly this is an analysis of a water chiller used to cool a heat exchanger from a refrigeration cycle. If you know the heat output from that cycle's heat exchanger, can you just directly calculate how much water flow is needed using water's specific heat capacity?

#### David Gin

If I understand correctly this is an analysis of a water chiller used to cool a heat exchanger from a refrigeration cycle. If you know the heat output from that cycle's heat exchanger, can you just directly calculate how much water flow is needed using water's specific heat capacity?
What I am looking for is a set of equation showing the relationship between the chilled water supply setpoint and the compressor load(centrifugal compressor % running). I understands that Q(Load) = Efficiency * Q(Chiller) and Q = cp * Flow * density * dT. But how would this relates to compressor load? Thank you for your time.

#### russ_watters

Mentor
Three issues here:
1. There is no simple equation for this. It depends on the combined dynamics of the chiller and load.
2. You have too many unknowns: Load is not just a function of supply temperature. It either is what it is or is determined by its own potentially complicated system dynamics.
3. I suspect there is more to this problem than you are telling us. If you elaborate on the problem you are trying to solve, we will undoubtedly be able to provide better help.

#### David Gin

Three issues here:
1. There is no simple equation for this. It depends on the combined dynamics of the chiller and load.
2. You have too many unknowns: Load is not just a function of supply temperature. It either is what it is or is determined by its own potentially complicated system dynamics.
3. I suspect there is more to this problem than you are telling us. If you elaborate on the problem you are trying to solve, we will undoubtedly be able to provide better help.
Hi Russ,
There are more to this problem but I would first like to be educated on this:
Say for a given chiller system, I would like the evaporator water leaving temperature set at say 6C with a 4000gpm flow rate and the evaporator returning temperature at 14C. Now I know that the total cooling RT is Q = 500 * GPM * dF, but how would this translate to the RLA of the chiller compressor?

#### russ_watters

Mentor
The only way for a real chiller to calculate that would be to get a performance map from the manufacturer. I say "map" because in addition to evaporator flow and temperature, you need condenser flow and temperature. The manufacturer should be able to provide the efficiency at those conditions, from which you can calculate the RLA.

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