5.29 A gas turbine cycle utilizes a counterflow regenerative heat exchanger as shown in Figure P5.29. Air enters the compressor at atmospheric conditions, 1 atm and 70°F, with a mass flow rate of 15,000 lbm/h. The exhaust pressure of the compressor is 7 atm. The compressor is operating with an isentropic efficiency of 75%. The regenerator preheats the air entering the combustion chamber, thus reducing the fuel requirement and increasing the thermal efficiency of the cycle. The regenerator in the cycle has a UA product of 20,000 Btu/h·°F.

Combustion gases (which can be modeled as air) leave the combustion chamber at 2300°F. The combustion gases then pass through the turbine that has an isentropic efficiency of 72%. Assume that the pressure drops in all heat exchangers and connecting piping is negligible. Even though the temperature varies significantly in this cycle, the average heat capacity evaluated between the highest and lowest temperatures in the cycle can be used for analysis of the regenerator. Use the ideal gas law to model the properties of air and determine the following:

a. Net power delivered by the cycle (hp).

b. Heat transfer rate required at the combustion chamber (Btu/hr).

c. Thermal efficiency of the cycle.

d. Investigate the effect of the size of the regenerator by plotting the thermal efficiency of the cycle as a function of the regenerator UA value for the range 0 ≤ UA ≤ 50,000 Btu/h·°F. What is the significance of UA = 0 Btu/h·°F?