Question

A micro gas turbine is designed to operate on the regenerative Brayton cycle and is sized to produce 400kW of net electric power. Air enters the compressor at

100kPa and 300K (dead state), and is compressed in a centrifugal compressor with a

polytropic efficiency of 86%. The air leaving the compressor enters a recuperator with

an 90% effectiveness and is heated before it enters the combustor after suffering a

pressure loss of 2.5% of the compressor exit pressure in 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 turbine inlet temperature, based on the release of the reference enthalpy of combustion, ?HR, LV for CH4. The pressure drop in the combustor is 1.5%. The turbine expands the combustion products with a polytropic efficiency of 87%. The gas flowing through the turbine can be treated as air, albeit with a slightly higher mass flow to account for the fuel burned in the combustor and with a temperature-dependent cp. The exhaust gas (also assumed to be air with temperature-dependent cp) passes through the hot-side (lowpressure side) of the recuperator and experiences a 3.5% pressure drop as it transfers heat to the high-pressure air exiting the compressor. The exhaust gas is then discharged into the atmosphere (100kPa), experiencing a further 2.0% pressure drop in the exhaust system. The air should be treated as a gas mixture with temperaturedependent specific heat (use “AIR_ha” in ees). The electromechanical efficiency of the turbine and its electric generator is 92%. Fuel pump power can be ignored. Use EES software to solve the problems.

a. Sketch the flow diagram of this system showing the key state points 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 to 12.5 in small increments of

0.5, conduct a parametric study to determine the optimum compressor pressure

ratio, and plot the variation of the thermal efficiency with the compressor

pressure ratio. Use ?HR to compute the fuel/air ratio, from which you can compute the equivalence ratio, ?, relative to the stoichiometric fuel/air ratio given in the 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 peak thermal efficiency point for

400kW of net electric power.

f. What is the equivalence ratio, ?, at the peak efficiency point, and the fuel injection

rate (kg/s) required to raise the temperature from the recuperator air exit

temperature, Tr, to the turbine inlet temperature, T3 = 1250K.

g. How much CO2 does this system produce at its peak efficiency point 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 a function of 4 pressure ratio and plot the results, assuming that the heat losses from the system boundary are negligible and that 45% of the exhaust exergy will be beneficially utilized in a waste heat recovery system and the rest is wasted. Assume a dead state temperature, To = 300K and dead state pressure, Po = 100kPa (Obtain “–?G” for CH4 )

i. What is the pressure ratio corresponding to the peak exergy efficiency (within

0.5)?

j. Note 1: The isentropic efficiencies of the compressor and the turbine can be

calculated from the corresponding polytropic efficiencies and pressure ratios

using the formulas given in the lecture with k = 1.4.

k. Note 2: The specific heat of air in all the calculations should be assumed to be

temperature-dependent. Use Air_ha in EES to compute the enthalpy

and entropy of air in EES “Thermophysical properties/Real fluids”.

Answer 1

a)

b)

• CH4 + 2(O2) ? CO2 + 2(H20)

  If we look up the atomic weights of the atoms that make up octane and oxygen, we get the following numbers:

  Carbon (C) = 12.01

  Oxygen (O) = 16

  Hydrogen (H) = 1.008

  • So 1 molecule of methane has a molecular weight of: 1 * 12.01 + 4 * 1.008 = 16.042
  • One oxygen molecule weighs: 2 * 16 = 32
  • The oxygen-fuel mass ratio is then: 2 * 32 / 1 * 16.042 = 64 / 16.042
  • So we need 3.99 kg of oxygen for every 1 kg of fuel
  • Since 23.2 mass-percent of air is actually oxygen, we need : 3.99 * 100/23.2 = 17.2 kg air for every 1 kg of methane.

  So the stoichiometric air-fuel ratio of methane is 17.2.

• When the composition of a fuel is known, this method can be used to derive the stoichiometric air-fuel ratio. For the most common fuels, this, however, is not necessary because the ratios are known:

  • Natural gas: 17.2
  • Gasoline: 14.7
  • Propane: 15.5
  • Ethanol: 9
  • Methanol: 6.4
  • Hydrogen: 34
  • Diesel: 14.6

  You may find it interesting that methanol and ethanol both have a very low air-fuel ratio, while the carbon chain length is comparable to methane and ethane. The reason for this is that alcohols like methanol and ethanol already carry oxygen themselves, which reduces the need for oxygen from the air.