Isentropic Processes
Isentropic processes are those in which entropy remains constant, the substance will have the same entropy
value before as after the process. In thermodynamics an isentropic process is one which is a internally reversible, adiabatic process.
The second law of thermodynamics states that
. For an isentropic process which by definition is reversible (meaning the equation is equal) there is no transfer of energy by heat as its adiabatic. This means that change in Q = 0 and as temperature cannot be 0, change in entropy must be 0 meaning the process is isentropic.
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Isentropic Efficiency
Turbines
For a turbine the desired output is the work produced, and the isentropic efficiency is defined as "the ratio of the actual work output of the turbine to the work output that would be achieved if the process between the inlet and the exit pressure were isentropic".
The changes in kinetic and potential energies of a fluid through a turbine are small and can therefore be neglected.
As Work is th
e sum of the change in flow energy, internal energy, kinetic energy and potential energy.
And as flow energy + internal energy = enthalpy the equation for efficiency can be reduced to:
Where h2a is the actual exit enthalpy and h2s is the isentropic exit enthalpy.
Compressors
For a compressor the efficiency is defined as "the ratio of the work input required to raise the pressure of a gas to a specified value in an isentropic manner to the actual work input"
Note how the isentropic work is now the numerator rather than denominator. This is because Ws is smaller than Wa and otherwise the efficiency would always be over 100%. When it comes to compressors the isentropic value is the minimum where as in turbines it is the maximum.
Nozzles
Nozzles are essentially devices that speed up the flow of a fluid through it. Therefore the isentropic efficiency is the ratio of the actual kinetic energy at the exit and the isentropic kinetic energy.