Brayton Cycle

The Brayton cycle (gas-turbine cycle) is an idealized thermodynamic cycle that models continuous-flow gas-turbine engines. It comprises four principal processes: (1) isentropic compression in a compressor, (2) constant-pressure heat addition in a combustor (or heat exchanger), (3) isentropic expansion in a turbine, and (4) constant-pressure heat rejection. The air-standard Brayton cycle assumes air as an ideal gas, constant specific heats, and reversible (ideal) compression/expansion for the ideal cycle. Key performance metrics are thermal efficiency, specific work (net work per unit mass), and power output for a given mass flow. For the ideal (internally reversible) Brayton cycle the pressure ratio across the compressor, rp = p2/p1, strongly controls cycle efficiency and work output. Regeneration, intercooling, and reheating are common modifications to improve performance.

Governing FormulaAssumptions: air as ideal gas with constant specific heats (cp, cv), k = cp/cv. Key relations and formulas (SI units): - Isentropic temperature relation: T2 = T1 * rp^{(k-1)/k}, T4 = T3 / rp^{(k-1)/k} (ideal isentropic compressor and turbine) - Pressure ratio: rp = p2 / p1 - Ideal Brayton thermal efficiency: eta_th = 1 - rp^{-(k-1)/k} - Specific compressor work (ideal): w_c = cp*(T2 - T1) - Specific turbine work (ideal): w_t = cp*(T3 - T4) - Net specific work: w_net = w_t - w_c = cp*[(T3 - T4) - (T2 - T1)] - Power (rate): W_dot = m_dot * w_net - Optimum pressure ratio for maximum net specific work (for fixed T1 and T3): rp_opt = (T3 / T1)^{k / [2 (k-1)]} Notes: use provided cp and k values when numerical values are needed. All temperatures in K, specific work in J/kg, power in W.

Knowledge Check

10 Questions

1.Which Brayton-cycle component performs the primary task of increasing the working fluid pressure prior to combustion?

2.For an ideal Brayton cycle with air (k = 1.4), inlet temperature T1 = 300 K and pressure ratio rp = 10, what is the ideal isentropic compressor outlet temperature T2? (Use T2 = T1 * rp^{(k-1)/k}. )

3.Using the same conditions (k = 1.4) and pressure ratio rp = 10, what is the ideal Brayton cycle thermal efficiency (η_th = 1 - rp^{-(k-1)/k})?

4.Consider an ideal Brayton cycle with rp = 10, k = 1.4, cp = 1005 J/kg·K, T1 = 300 K and turbine inlet temperature T3 = 1400 K. What is the net specific work w_net (J/kg) for the ideal cycle? (Use T2 = T1*rp^{(k-1)/k}, T4 = T3/rp^{(k-1)/k}, and w_net = cp[(T3 - T4) - (T2 - T1)].)

5.For a fixed turbine inlet temperature T3 and fixed ambient inlet temperature T1, how does increasing the compressor pressure ratio rp generally affect thermal efficiency and net specific work in the ideal Brayton cycle?

6.Calculate the optimal pressure ratio rp_opt for maximum net specific work for an ideal Brayton cycle with T1 = 300 K, T3 = 1200 K and k = 1.4. Use rp_opt = (T3/T1)^{k/[2(k-1)]}.

7.If the turbine isentropic efficiency falls below unity (less than ideal) while the compressor remains ideal, what is the expected effect on net specific work and cycle thermal efficiency (compared to the fully ideal cycle)?

8.For an ideal Brayton cycle with cp = 1005 J/kg·K, k = 1.4, mass flow m_dot = 2.0 kg/s, T1 = 300 K, pressure ratio rp = 8, and turbine inlet temperature T3 = 1300 K, what is the approximate shaft power output W_dot (in kW)? (Use ideal isentropic relations and W_dot = m_dot * w_net.)

9.A regenerative heat exchanger (regenerator) is sometimes added between turbine exhaust and compressor exit in a Brayton cycle. Under what condition does a regenerator provide a thermodynamic benefit (i.e., reduce required fuel/heat addition)?

10.For an ideal Brayton cycle with T1 = 288 K, rp = 5, T3 = 1400 K, k = 1.4 and cp = 1005 J/kg·K, compute the ideal specific compressor work w_c and specific turbine work w_t (both in kJ/kg). Use T2 = T1*rp^{(k-1)/k} and T4 = T3/rp^{(k-1)/k}.