Gas Turbines

Gas turbines operate on the Brayton (or Joule) cycle: air is compressed, fuel is added and combusted at (approximately) constant pressure, and the hot gases expand through a turbine producing work. Practical gas-turbine systems include real-component irreversibilities (compressor and turbine efficiencies), pressure losses, and often heat-recovery (regenerators) or intercooling/reheating stages. Key performance metrics are thermal efficiency (ratio of net work output to heat input), specific work (work per unit mass of working fluid), and specific fuel consumption (fuel mass flow per unit power). Turbomachinery limits (surge, stall, blade stresses, and material temperature limits) and component matching (compressor-turbine work balance) are central to design and operation.

Governing FormulaUseful relations (assume ideal gas behavior for air/gases unless stated): - Isentropic temperature relation: T2s = T1 * (P2/P1)^{(γ-1)/γ} - Isentropic compression/expansion work (per unit mass) for constant cp: w_isentropic = cp*(Tout_s - Tin) - Compressor actual outlet temperature with isentropic efficiency η_c: Tout = Tin + (T_out_s - Tin)/η_c - Turbine actual outlet temperature with isentropic efficiency η_t: Tout = Tin - η_t*(Tin - T_out_s) - Ideal Brayton thermal efficiency (constant cp): η_th = 1 - (1 / r_p^{(γ-1)/γ}), where r_p = P2/P1 - Net specific work: w_net = w_turbine - w_compressor - Heat added per unit mass (fuel energy per unit mass of working fluid): q_in = cp_hot*(T3 - T2_actual) - Fuel mass per unit mass of working fluid: m_fuel = q_in / LHV (LHV = lower heating value of fuel) - Specific fuel consumption (SFC, kg fuel per kWh): SFC = m_fuel / (w_net / 3600) = (m_fuel * 3600) / w_net (with w_net in J/kg) Assumptions should be stated with each problem (γ, cp, efficiencies, and LHV if needed).

Knowledge Check

10 Questions

1.For an ideal Brayton cycle operating with air (γ = 1.4), what is the thermal efficiency if the compressor pressure ratio r_p = 10? (Assume constant specific heats.)

2.Air enters a compressor at T1 = 300 K and P1 = 100 kPa. The compressor pressure ratio is 8. Assume γ = 1.4, cp = 1005 J·kg⁻¹·K⁻¹, and compressor isentropic efficiency η_c = 0.85. What is the actual compressor specific work (approx.) in kJ/kg?

3.A turbine expands hot gas from T3 = 1400 K across the same pressure ratio of 8 back to the compressor inlet pressure. Assume γ = 1.33 for hot gas, cp = 1150 J·kg⁻¹·K⁻¹, and turbine isentropic efficiency η_t = 0.88. What is the turbine specific work output (approx.) in kJ/kg?

4.Using the compressor and turbine results from the previous two questions (compressor work ≈ 287 kJ/kg, turbine work ≈ 572 kJ/kg) and cp_hot = 1150 J·kg⁻¹·K⁻¹, what is the thermal efficiency of the actual cycle if T2_actual = 585.5 K and T3 = 1400 K? (Compute η = w_net / q_in.)

5.Using the values q_in = 936.7 kJ per kg working fluid and net work w_net = 285 kJ/kg (from previous questions), and fuel LHV = 43 MJ/kg, what is the specific fuel consumption (SFC) in g/kWh? (Assume 1 kWh = 3600 kJ.)

6.For a Brayton cycle with a fixed compressor inlet temperature and a fixed turbine inlet temperature (T1 and T3 fixed), how does increasing the compressor pressure ratio r_p generally affect cycle performance?

7.What is the primary effect of a regenerator (heat exchanger) in a gas-turbine cycle, and what limitation does it have?

8.Distinguish between compressor stall and surge in axial compressors. Which statement is correct?

9.For a single compressor stage (or a single-stage equivalent) with pressure ratio 1.5 and air with γ = 1.4, what is the isentropic temperature ratio T2s/T1 (approx.)?

10.A simple combined cycle uses a gas turbine with thermal efficiency 35%. The heat-recovery steam generator (HRSG) can recover 60% of the gas-turbine exhaust heat (i.e., 60% of the remaining input energy after the gas turbine), and the steam (bottoming) cycle converts the recovered heat to work with 30% efficiency. What is the approximate combined-cycle efficiency?