The adiabatic efficiency of a centrifugal compressor can be calculated using the following formula:
Adiabatic Efficiency = (Actual Compressor Work Output – Polytropic Work Input) / (Actual Compressor Work Output – Adiabatic Work Input)
where:
- Actual Compressor Work Output: This is the work output of the compressor, which can be calculated as the product of the mass flow rate of the gas and the difference in specific enthalpy between the inlet and outlet of the compressor. Mathematically, Actual Compressor Work Output = Mass Flow Rate x (Specific Enthalpy at Outlet – Specific Enthalpy at Inlet).
- Polytropic Work Input: This is the work input required to compress the gas assuming a polytropic compression process. It can be calculated using the polytropic compression equation:
(Pressure Ratio)^[(k – 1)/k] = (T2/T1)^[(k – 1)/k]
where:
- Pressure Ratio: This is the ratio of the outlet pressure to the inlet pressure of the compressor.
- T1 and T2: These are the inlet and outlet temperatures of the gas, respectively.
- k: This is the ratio of specific heats of the gas.
Once the polytropic work input is obtained, it can be calculated as follows:
Polytropic Work Input = Mass Flow Rate x (Specific Enthalpy at Inlet x [(Pressure Ratio)^[(k – 1)/k] – 1]/(k – 1))
- Adiabatic Work Input: This is the work input required to compress the gas assuming an adiabatic compression process. It can be calculated using the adiabatic compression equation:
(Pressure Ratio)^[(k – 1)/k] = T2/T1
where:
- Pressure Ratio: This is the ratio of the outlet pressure to the inlet pressure of the compressor.
- T1 and T2: These are the inlet and outlet temperatures of the gas, respectively.
- k: This is the ratio of specific heats of the gas.
Once the adiabatic work input is obtained, it can be calculated as follows:
Adiabatic Work Input = Mass Flow Rate x (Specific Enthalpy at Inlet x [(Pressure Ratio)^[(k – 1)/k] – 1])
Once these values are obtained, the adiabatic efficiency of the centrifugal compressor can be calculated as the ratio of the difference between the actual compressor work output and the polytropic work input to the difference between the actual compressor work output and the adiabatic work input. The result will be a decimal value, which can be converted to a percentage by multiplying by 100.
It is important to note that the adiabatic efficiency of a centrifugal compressor is affected by various factors, including the design of the compressor, the gas properties, and the operating conditions of the compressor. Therefore, the calculated efficiency may differ from the actual efficiency of the centrifugal compressor in practice.
