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Unformatted text preview: on of Thermodynamics by Y. A. Çengel & M. A. Boles 759 Turbine, Compressor (Pump), and Nozzle Efficiencies Most steadyflow devices operate under adiabatic conditions, and the ideal process for these devices is the isentropic process. The parameter that describes how a device approximates a corresponding isentropic device is called the isentropic or adiabatic efficiency. It is defined for turbines, compressors, and nozzles as follows: Turbine: The isentropic work is the maximum possible work output that the adiabatic turbine can produce; therefore, the actual work is less than the isentropic work. Since efficiencies are defined to be less than 1, the turbine isentropic efficiency is defined as ηT = Actual turbine work w = a Isentropic turbine work ws ηT ≅ h1 − h2 a h1 − h2 s Welldesigned large turbines may have isentropic efficiencies above 90 percent. Small turbines may have isentropic efficiencies below 70 percent.
Chapter 7  59 Student Study Guide for 5th edition of Thermodynamics by Y. A. Çengel & M. A. Boles 760 Compressor and Pump: The isentropic work is the minimum possible work that the adiabatic compressor requires; therefore, the actual work is greater than the isentropic work. Since efficiencies are defined to be less than 1, the compressor isentropic efficiency is defined as T1 P1 WC Compressor or pump T2 P2 Isentropic compressor work ws = Actual compressor work wa h −h ηC ≅ 2s 1 h2 a − h1 ηC = Welldesigned compressors have isentropic efficiencies in the range from 75 to 85 percent. Review the efficiency of a pump and an isothermal compressor on your own. Chapter 7  60 Student Study Guide for 5th edition of Thermodynamics by Y. A. Çengel & M. A. Boles 761 Nozzle: The isentropic kinetic energy at the nozzle exit is the maximum possible kinetic energy at the nozzle exit; therefore, the actual kinetic energy at the nozzle exit is less than the isentropic value. Since efficiencies are defined to be less than 1, the nozzle isentropic efficiency is defined as T1 P1 V1 Nozzle T2 P2 V2 V22a 2 V22s 2 Actual KE at nozzle exit V22a / 2 ηN = = Isentropic KE at nozzle exit V22s / 2
For steadyflow, no work, neglecting potential energies, and neglecting the inlet kinetic energy, the conservation of energy for the nozzle is V22a h1 = h2 a + 2 Chapter 7  61 Student Study Guide for 5th edition of Thermodynamics by Y. A. Çengel & M. A. Boles 762 The nozzle efficiency is written as ηN ≅ h1 − h2 a h1 − h2 s Nozzle efficiencies are typically above 90 percent, and nozzle efficiencies above 95 percent are not uncommon. Example 714 The isentropic work of the turbine in Example 76 is 1152.2 kJ/kg. If the isentropic efficiency of the turbine is 90 percent, calculate the actual work. Find the actual turbine exit temperature or quality of the steam. ηT = w Actual turbine work = a Isentropic turbine work ws kJ kJ ) = 1037.7 kg kg wa = ηT ws = (0.9)(1153.0 h1 − h2 a ηT ≅ h1 − h2 s
Now to find the actual exit state for the steam. From Example 76, steam enters the turbine at 1 MPa, 600oC, and expands to 0.01 M...
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 Fall '08
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