Compressor displacement vs mass flow

[SexyMF]

The data-sheet for my Danfoss compressor gives a 11.15 CM^3 displacement figure.

I know that MF = displacement(per unit of time) x refrigerant density.

How do I work out the mass-flow from this, given the data-sheet isn't displacement per unit time.

[[XC] gomeler]

Figure out the running speed of the compressor and then you have theoretical displacement per unit time. 60Hz compressors operate at 3600RPM while 50Hz compressors operate at 3000 RPM. I don't know if the spec-sheets compensate for the dead room when the piston is fully extended(ie combustion chamber on an internal combustion engine) or if there is an "efficiency" factor that must be utilized for accurate modeling.

[tiborrr]

In order to calculate mass flow you need to know the W[1-2'] not W[1-2]

W[1-2'] = m0 * (h2' - h1)

Where:
m0..... mass flow
h2'..... enthalpy @ constant entropy (s=const.) after compression
h2...... enthalpy after compression
W...... energy of compressor

You could also calculate m0 (mass flow) from this equation:

Q0 = m0 * (h1 - h5)

Where:
Q0 ..... energy flow of evaporator (cooling power)
m0 .... mass flow
h1 .... enthalpy prior compression / after evaporation
h4 ... enthalpy prior evaporation

Density of refrigerant changes with the state (liquid, gaseus) in which the freon is.



But yes, 50Hz compressor ~ 3000RPM which at. e.g. 11ccm means 0.033m^3 / min. You then take the density of your freon at certain temperature. For R290 - propane this would be:

V... Specifical volume

T(°C)...... Vliq (m3/kg).... Vgas (m3/kg)
__________________________________
-50°C ..... 0.001690 ........ 0.58
-40°C ..... 0.001725 ........ 0.38
...

Convert spec. volume to density (kg/m3), multiply it with your volume flow (m3/min) and there you have your mass flow (kg/min).

[DetroitAC]

I do that calculation by using the actual specsheet data, and correcting for the conditions I'm interested in.

The motors have a slip so they are not 3600 and 3000 RPM for 60 and 50Hz. I don't know what any compressor speed is actually since I haven't measured it, but I use 3450RPM and 2875 RPM.

Next what I do is calculate the actual volumetric efficiency of the specsheet test conditions. This number is very important and the VE is generally only about 60% or less, and it's a fairly reliable function of pressure ratio.

Then I use the VE at my pressure ratio of interest to calculate actual volumetric displacement at the condition I'm interested in. I use software to calculate the suction gas density. You then have mass flow rate.

You can't use Tiborr's first equation, this is more of a theoretical equation and the W is compressor shaft power. With a small hermetic there are large power losses in converting electricity to compressor input shaft power.

Tiborr's second equation is fine, that'll give you the required mass flow, which you can convert into your required suction gas volume flow. Really though, this problem is usually worked the other way around, with a compressor in hand and you want to know the performance.

That's generally the way these problems go for me. I have a compressor in mind and I want to cool a known load in Watts, and what I want to calculate is how cold the compressor is capable of holding that load.

[SexyMF]

Thanks heaps for the input people. I was hoping you would mention RPM and VE. I knew these are what I needed but I did not want to clutter the question.

I am interested in calculating a single stage design using coolpack. But the devil is in the detail. It appears that you can create a cycle which will have a required mass-flow but if the compressor can't provide this then your system just won't work?

I have some general questions also:

What are the additional lines are on the Mollier charts (quality lines?).

Is is better to condense at a temperature with the lowest vapour pressure (i.e. most liquid)?

How do you strike a good balance with mass flow and work done by the compressor (in terms of the affect on COP).