3 replies to this topic

[Art Montemayor]

AFDMello:

The relation between the suction and discharge temperatures of a gas during any single compression step is:

T₂ = T₁ (R_C) ^(k-1)/k

where,
T₂ = the compressor’s discharge absolute temperature, ^oK
T₁ = the compressor’s suction absolute temperature, ^oK
R_C = the compression ratio (P2/P1)
P₂ = the compressor’s discharge absolute pressure, barA
P₁ = the compressor’s suction absolute pressure, barA
k = the ratio of the gaseous fluid’s specific heats (Cp/Cv)

In a reciprocating compressor the compression takes place at close to isentropic conditions (entropy change = 0), and the above equation holds true. In a centrifugal machine, however, the compression process is more nearly a polytropic one and the value of k is substituted by a value of “n” – n being the characteristic of the gas that determines its compression performance. The usual centrifugal compressor is uncooled internally, and hence operates with polytropic characteristics having an “n” greater than “k”.

Please take a look at the attached simplified flow diagram. Note that there are two possible values for the suction pressure of the centrifugal compressor: before your suction damper vanes or after the damper vanes. It makes a big difference to the machine and I’ll assume you mean that P1 (the pressure after the suction damper vanes is the 4.7 barG (5.713 barA) that you cite. Also note that you don’t indicate clearly what the loads on the water-cooled condenser or the evaporator are. For example, do the cited tons/hour mean refrigerant flow or water flow and process fluid flow? Without the density of the process fluid one can’t determine the heat load because of a lack of identifying the heat capacity of the process fluid. You also need the terminal temperature conditions on the exchangers.

Note if you go to:
http://webbook.nist....hemistry/fluid/
which is the NIST free database website for refrigerant thermodynamic values, you will see that at the conditions of 15.5 ^oC and 5.713 barA you have LIQUID R-134A and not VAPOR R-134A. I suspect that the pressure at P2 is really 4.7 barA – which would make P1 even less, maybe 4.5 barA (approx. 5.51 barG). This would put your suction vapor in the correct thermo zone and make it safe for the compressor.

Note that you can calculate the absolute discharge temperature out of your centrifugal compressor if you know the value of “n”. You obviously have the means to identify the values of the actual suction temperature and pressure going into the compressor (not before the damper vanes!) and the compression ratio. If you have a spreadsheet or a Hewlett-Packard calculator, the exercise should be easy.

You should be able to get the “n” value from your Compressor curves or from the compressor manufacturer. While you’re at it, you could check with them about what the design discharge temperature is and under what conditions. The information should be very interesting and helpful.

One more note: All the text books and articles I’ve read in over 40 years have failed to specify just what are the temperature conditions for calculating the “k” or “n”. Two reciprocating compressor manufacturers confided in me that they used 150 oF as the average stage temperature at which to calculate the Cp and Cv. I have been looking for an academic answer or response to this but have never succeeded in getting one. That’s just another example of the need for practical engineers in the field. The academics are so above the actual compression application that they forget that the damn gas is increasing in temperature and Cp and Cv are both dependent on temperature – so what is the temperature that you base your “k” or “n” at?

I hope this helps out.

Attached Files

•  AFD_Mello_Refrig_Cycle.doc   28.5KB   101 downloads

[Martin Sneesby]

Lots of useful advice here but it should probably be noted that the difference between k (adiabatic exponent) and n (polytropic exponent) is the efficiency:

n / (n-1) = eff * k / (k-1)

The equation supplied by Art gives you the adiabatic discharge temperature, but your compressor will be adding heat to the process so the actual discharge temperature will be higher than this value.

T2 / T1 = (Rc) ^ (k-1)/k

Using the same equation with n instead of k will give you the manufacturer's expected discharge temperature. If your actual measured value is higher than this, your compressor is operating sub-optimally.

Martin Sneesby
Advanced Process Engineering & Simulation Services