Centrifugal Air Compressor Efficiency Calculation

When you want to say the efficiency of the compressor, there are two efficiencies. Polytropic efficiency which you can estimate and mechanical efficiency only compressor vendor knows. If you say only EFFICIENCY of compressor, it is the terminology of combination of polytropic and mechanical.

You may read the compressor efficiency from the tested performance curve. Do not read it from the estimated performance curve. Since mechanical efficiency is already vendor's own information, knowing politropic efficiency only is wothless.

So instead of calculation of the exsting compressor efficiency, it is better expression to measure the existing compressor efficiency.

Provided that you know inlet conditions (pressure, temperature, enthalpy) and discharge condition (pressure, temperature, enthalpy), mass flow rate, and driver's power consumption (is it a motor or steam turbine); (All these information are measured one!!!)

a = (discharge enthalpy[kJ/kg] - inlet enthaply[kJ/kg])*mass flow rate[kg/Sec]

a's unit is (KJ/Sec) in result.

b = driver power consumption (kJ/Sec)

efficiency = a / b * 100

Efficiency Improvement with the same process conditions for the same gas may not be possible without mechanical modification in most cases. Efficiency improvement means either increasing 'a' value or decreasing 'b' value or both.

Since for the same existing compressor with the same speed, inlet & discharge conditions, 'a' value can not be changed. In the same manner, 'b' value can not be changed for same existing driver. It means you need mechanical modification!!

If the driver is the steam turbine, you can increase the operating speed (but process condition such as discharge condition will differ) and it will slightly increase the efficiency, but more power consumption as a result of higher discharge condition.

Remember one thing. Improving efficiency does not always mean decreasing energy consumption. If your intention is to save energy in your system, you can recover some thermal energy from the discharged high pressure high temperature gas by adding some mechanical equipments and piping. This will need wide and deep thermal study.

Thanks for so much of inputs. further may i know some websites containing the graphs from which this enthalpy at different conditions may be calculated.

Hi,

the energy supplied to the compressed gas may be calculated by knowing only the temperature rise (using mCp(T2-T1) as long as you know Cp for your process gas (air?). This is equivalent to m(E2-E1).

The isentropic temperature rise is = press ratio^(ratio of specific heats -1)/ratio of specific heats X T1 (absolute). So isentropic power = m Cp x isentropic temp rise.

Thus the isentropic efficiency = isentropic temp rise / measured temp rise. For this you do not need to know anything about Cp for the gas, or its other properties except its ratio of specific heats. Measuring pressures and temperatures is (relatively) easy.

To find the total machine efficiency you will need to know the energy input. This could be electrical power input or mechanical work from some other source (diesel or petrol engine etc). For this you will need to know either the enthalpy from charts or Cp from a data book.

As yeonhoyu said you may be able to cool the compressed gas and use the waste heat for some other purpose to help reduce your overall plant power requirements.

If you are using multiple stages of compression it is thermodynamically more efficient to cool the gas between stages of compression.

More information might well enable us to help you more.

regards,

Could someone please provide an example calculation of mechanical efficiency with units for each of the terms used?

What exactly do I need to measure?

From what I have read here by yeonhoyu, one needs to measure the following in order to calculate the mechanical efficiency of compressing air:

i.e. Measure:
[1] Inlet air pressure
[2] Inlet air temperature
[3] Inlet enthalpy
[4] Discharge air pressure
[5] Discharge air temperature
[6] Discharge enthalpy
[7] Mass flow rate
[8] Driver's power consumption

but then the formula for efficiency does not use
[1] Inlet air pressure
[2] Inlet air temperature
[4] Discharge air pressure
[5] Discharge air temperature

From what I have read here by dieselphil, one only needs to measure pressure and temperature and the rest is obtained from a data book.

i.e. Measure
[1] Inlet air pressure
[2] Inlet air temperature
[4] Discharge air pressure
[5] Discharge air temperature
but then only a formula for isentropic efficiency is given.
Total machine efficiency is mentioned but no formula is given.

So.....
What is the formula to calculate the mechanical efficiency for compressing air?
Is there more than one formula?
Is this a multi-step calculation process?
What measurements do I need to make?
What data do I need to get from a table?
What are the symbols,names and units for each of these measurements or table data numbers?

As an example, I might make the following measurements:

[1] P1,Inlet air pressure measured with a pressure gauge.
This would typically be at atmospheric pressure, although in a multistage compressor, if I wanted to know the mechanical efficiency of a particular stage, then the inlet air pressure would be something other than atmospheric pressure; but for this example I will assume that I measured zero kPa gauge pressure or if absolute pressure is required I would use 101.325 kPa absolute pressure.

[2] T1,Inlet air temperature measured with a thermometer.
This might typically be room temperature, say 15 deg. C. but if absolute temperature is required then the units would be in kelvins (K) where T1 = 15 deg. C + 273.16 K = 288.16 K.

[3] Inlet enthalpy
I am not sure what sensor to use or how this is measured. From other reading, I see that this may be the same thing as specific enthalpy with units of joules per kilogram or kilojoules per kilogram or kJ/kg
Is the symbol for this H1 ??

[4] P2,Discharge air pressure measured with a pressure gauge.
In this example, assume that I measured 800 kPa with a pressure gauge. If absolute pressure were required then P2 = 101.325 + 800 kPa = 901.325 kPa.

[5] T2,Discharge air temperature measured with a thermometer.
In this example assume that I measured 60 deg.C. but if absolute temperature is required then the units would be in kelvins (K) where T2 = 288.16 K + 60 deg.C. = 348.16 K.

[6] Discharge enthalpy
Again, I am not sure what sensor to use or how this is measured. From other reading, I see that this may be the same thing as specific enthalpy with units of joules per kilogram or kilojoules per kilogram or kJ/kg
Is the symbol for this H2 ??

[7] Q,Mass flow rate
This will be difficult to measure because one will need a flowmeter and then one needs to adjust the reading to that which would have been obtained at standard temperature and pressure, which will depend on which standard one uses. Alternatively, if one is using a piston type compressor (instead of a centrifugal Air Compressor which is the topic of this Forum) then one could measure the piston diameter and stroke length, calculate the volume of each stroke and then multiple this by the rpm or strokes per unit time to get volume per unit time and then multiply by a mass of air per unit volume which then might need to be adjusted to or from some stand temperature and pressure. Hmm?? Units for mass flow rate would be kg/Sec.
In this example assume Q = .02 kg/Sec. (but how does one measure that? and is this a typical expected quantity for a 5 HP Air Compressor?)

[8] b,Driver's power consumption
Assume that one is using an electric motor. In this case one could use a watt meter or a multimeter and measure Voltage, Amperage and assume a power factor and then look for a formula to calculate power or if using a VFD one may get a display of power (output from VFD ???).
In this example assume that one is using a 5 HP electric motor and that one measures 3.73 kilojoule/second [kJ/s] or [kJ/Sec].

Well, except for not being able to measure enthalpy, we are almost able to measure mechanical efficiency.

Now, can someone complete this example and calculate what the mechanical efficiency would be for such a air compressor?