Question

Regenerator in, 1 in, 2 Combust or 1Combustor 2 lb 4 ail Turbine Compressor Turbine cycle Figure 3. Regenerative two-stage gas turbine with reheat.

4. A regenerative two-stage gas turbine with reheat operating on the standard-air Brayton cycle is illustrated in Figure 3. In an ideal Brayton cycle, the processes in the turbines and compressor are adiabatic and isentropic, and the air flows through the combustor and heat exchangers at constant pressure.
   a) Show that the maximum total work output is developed when the pressure ratio is the same across each stage, if the temperature at the inlet to each turbine stage is the same. (You may assume steady state, ignore potential and kinetic energies and use a cold air-standard analysis);

b)    Derive the thermal efficiency of the regenerative two-stage Brayton cycle, in terms of the enthalpies h1, h2, h3, h4, ha, hb and the regenerator effectiveness ηreg=(hx-h2)/(h4-h2), assuming steady state and ignoring potential and kinetic energies;

c)  Based on the results of part (b), define the isentropic efficiencies of the Turbine 1, Turbine 2 and compressor, ηt,1 , ηt,2 and ηc, respectively.

Answer 1

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