A micro gas turbine is designed to operate on the regenerativeBrayton cycle and is sized to produce 400kW of netelectric power. Air enters the compressor at
100kPa and 300K (dead state), and iscompressed in a centrifugal compressor with a
polytropic efficiency of 86%. The air leaving thecompressor enters a recuperator with
an 90% effectiveness and is heated before it enters thecombustor after suffering a
pressure loss of 2.5% of the compressor exit pressurein the high-pressure side of the
recuperator. The combustor is designed to burn methane(CH4) with excess air beyond
the stoichiometric ratio to maintain a 1250K turbineinlet temperature, based on the release of the reference enthalpyof combustion, ?HR, LV for CH4.The pressure drop in the combustor is 1.5%. The turbineexpands the combustion products with a polytropic efficiency of87%. The gas flowing through the turbine can betreated as air, albeit with a slightly higher mass flow toaccount for the fuel burned in the combustor and with atemperature-dependent cp. The exhaust gas (alsoassumed to be air with temperature-dependent cp)passes through the hot-side (lowpressure side) of the recuperatorand experiences a 3.5% pressure drop as it transfers heatto the high-pressure air exiting the compressor. The exhaust gas isthen discharged into the atmosphere (100kPa), experiencinga further 2.0% pressure drop in the exhaust system. Theair should be treated as a gas mixture with temperaturedependentspecific heat (use “AIR_ha†in ees). The electromechanicalefficiency of the turbine and its electric generator is92%. Fuel pump power can be ignored. Use EES software tosolve the problems.
a. Sketch the flow diagram of this system showing the key statepoints and show
these points on a T-s diagram.
b. Calculate the stoichiometric fuel/air mass ratio for methane(CH4). Include the
equation in your ees program.
c. Varying the compressor pressure ratio from 2.5 to12.5 in small increments of
0.5, conduct a parametric study to determine theoptimum compressor pressure
ratio, and plot the variation of the thermal efficiency with thecompressor
pressure ratio. Use ?HR to compute thefuel/air ratio, from which you can compute the equivalence ratio,?, relative to the stoichiometric fuel/air ratio given inthe lecture slides
d. What is the pressure ratio at the peak efficiency point(within 0.5)?
e. Compute the total air flow rate (kg/s) at the peakthermal efficiency point for
400kW of net electric power.
f. What is the equivalence ratio, ?, at the peakefficiency point, and the fuel injection
rate (kg/s) required to raise the temperature from therecuperator air exit
temperature, Tr, to the turbine inlettemperature, T3 = 1250K.
g. How much CO2 does this system produce at its peak efficiencypoint in kg/kW
of net output.
h. Assuming that the exergy of combustion is equal to–?G of the methane reaction
with air, calculate the exergy efficiency of this system as afunction of 4 pressure ratio and plot the results, assuming thatthe heat losses from the system boundary are negligible and that45% of the exhaust exergy will be beneficially utilized ina waste heat recovery system and the rest is wasted. Assume a deadstate temperature, To = 300K and deadstate pressure, Po = 100kPa (Obtain“–?G†for CH4 )
i. What is the pressure ratio corresponding to the peak exergyefficiency (within
0.5)?
j. Note 1: The isentropic efficiencies of thecompressor and the turbine can be
calculated from the corresponding polytropic efficiencies andpressure ratios
using the formulas given in the lecture with k =1.4.
k. Note 2: The specific heat of air in all thecalculations should be assumed to be
temperature-dependent. Use Air_ha in EES tocompute the enthalpy
and entropy of air in EES “Thermophysical properties/Realfluidsâ€.
