In a stationary gas turbine engine, ambient air at 100 kPa and 300 degrees K enters the adiabatic compressor. After leaving it then enters an 80% effective regenerator (when one can be used) and, after leaving, then enters the high temperature heat exchanger from which it leaves at the 1200 degrees K turbine inlet temperature. This is accomplished by outside combustion gases which are counter-flowing in a second pipe. These combustion gases enter at a temperature of 1200 + delta T and leave at a temperature (delta T / 3) higher than the cycle air enters the heat exchanger.
Delta T = 300 (D/2.48)^1.2, delta T in degrees K and D is the diameter, in cm of the heat exchanger pipes. The combustion gases have a Cp = 1.15 kJ/kg degrees K, while the cycle air has a Cp = 1.0035 kJ/kg degrees K. The cycle air goes through the adiabatic turbine, goes through the regenerator, if one can be used, and passes through the low temperature heat exchanger where it is cooled to the compressor inlet temperature by a heat interaction with the ambient air.
The pressure drops in the low temperature heat exchanger and in both legs of the regenerator, if used, are 4% of the inlet pressures for the individual legs. The pressure drop of the cycle air in the high temperature heat exchanger is .02 P in (2.48 / D)^.75 where P in is the inlet pressure. There is negligible pressure drop of the combustion gases.
A) Find the net work per unit mass of cycle air, the thermal efficiency and the cyclic irreversibility per unit net work for all combustions of the following parameters.
Compressor pressure ratios 6, 9, 12, 15, and 18, adiabatic compressor efficiencies of .75 and .80, adiabatic turbine efficiencies of .85 and .90 and high temperature heat exchanger piping diameters, D, of 2.48, 1.24, .62, .31, and .155 cm.
B) What is the cycle pressure ratio, compressor efficiency, piping diameter D and turbine efficiency which gives the largest thermal efficiency? Put down also the thermal efficiency, the cyclic irreversibility per unit net work, and the network per unit mass.
C) For a compressor pressure ratio of 9, turbine efficiency of .85, compressor efficiency of .80 and piping diameter D = .62 cm, give the thermal efficiency, net work per unit mass and cyclic irreversibility per unit net work.
D) For all cases considered is there any one piping diameter D that is best for thermal efficiency, if so, what is it? Is there one best from the standpoint of irreversibility for all cases, if so, what is it?
E) For D = .62 cm, turbine efficiency .90 and compressor efficiency .75, what are the compressor ratios for which a regenerator should NOT be used?