Thermodynamics

Isentropic efficiencies are defined differently for different devices sinceeach device is set up to perform different tasks. Next we define the isentropicefficiencies of turbines, compressors, and nozzles by comparing theactual performance of these devices to their performance under isentropicconditions for the same inlet state and exit pressure.Isentropic Efficiency of TurbinesFor a turbine under steady operation, the inlet state of the working fluid andthe exhaust pressure are fixed. Therefore, the ideal process for an adiabaticturbine is an isentropic process between the inlet state and the exhaust pressure.The desired output of a turbine is the work produced, and the isentropicefficiency of a turbine is defined as the ratio of the actual workoutput of the turbine to the work output that would be achieved if theprocess between the inlet state and the exit pressure were isentropic:h T Actual turbine workIsentropic turbine work w aUsually the changes in kinetic and potential energies associated with a fluidstream flowing through a turbine are small relative to the change in enthalpyand can be neglected. Then the work output of an adiabatic turbine simplybecomes the change in enthalpy, and Eq. 7–60 becomesw s(7–60) w a wsP 2Chapter 7 | 371P 1h Inlet stateActual processh 11Isentropic processh 2ah 2s2s2aExitpressureh T h 1 h 2a(7–61)h 1 h 2swhere h 2a and h 2s are the enthalpy values at the exit state for actual andisentropic processes, respectively (Fig. 7–49).The value of h T greatly depends on the design of the individual componentsthat make up the turbine. Well-designed, large turbines have isentropicefficiencies above 90 percent. For small turbines, however, it may drop evenbelow 70 percent. The value of the isentropic efficiency of a turbine isdetermined by measuring the actual work output of the turbine and by calculatingthe isentropic work output for the measured inlet conditions and theexit pressure. This value can then be used conveniently in the design ofpower plants.s 2s = s 1FIGURE 7–49The h-s diagram for the actual andisentropic processes of an adiabaticturbine.sEXAMPLE 7–14Isentropic Efficiency of a Steam TurbineSteam enters an adiabatic turbine steadily at 3 MPa and 400°C and leaves at50 kPa and 100°C. If the power output of the turbine is 2 MW, determine (a)the isentropic efficiency of the turbine and (b) the mass flow rate of thesteam flowing through the turbine.Solution Steam flows steadily in a turbine between inlet and exit states. Fora specified power output, the isentropic efficiency and the mass flow rate areto be determined.Assumptions 1 Steady operating conditions exist. 2 The changes in kineticand potential energies are negligible.