ASME PTC 4.4
Advanced
Thermodynamics & Power Systems
Thermodynamic Rankine Steam Power Cycle
Track steam expansion through high-pressure boilers, turbines, condensers, and feed pumps on a T-s diagram.
Evaluates isobaric boiler heat addition, non-isentropic turbine expansion, isobaric heat rejection, and liquid pump compression. Quantifies cycle thermal efficiency η_th, turbine work, and back work ratio.
Governing Physical Law & Equations
\eta_{th} = \frac{w_{net}}{q_{in}} = \frac{(h_1 - h_2) - (h_4 - h_3)}{h_1 - h_4}
First-law thermal efficiency of the ideal Rankine cycle with pump work.
Law: First & Second Laws of Thermodynamics (ASME PTC 4.4) | Standard Reference: ASME PTC 6 / IAPWS-IF97 (Steam Turbines & Industrial Power Plant Acceptance)
Adjustable System Parameters
| Parameter |
Nominal Value |
Dynamic Range |
Physical Role |
| Boiler Pressure P_high (P_1) |
80 bar |
20 to 160 bar |
Steam generator operating pressure |
| Turbine Superheat Temp (T_1) |
480 °C |
300 to 600 °C |
Steam inlet temperature entering turbine stage |
| Condenser Pressure P_low (P_2) |
0.08 bar |
0.04 to 0.5 bar |
Vacuum condenser operating backpressure |
| Turbine Isentropic Eff (η_t) |
85 % |
65 to 95 % |
Internal turbine expansion isentropic efficiency |
Analytical Proof & Derivation
The Rankine cycle processes: 1→2: Turbine expansion w_t = h₁ - h₂; 2→3: Condenser rejection q_out = h₂ - h₃; 3→4: Feed pump compression w_p = v₃(P_high - P_low) = h₄ - h₃; 4→1: Boiler heat addition q_in = h₁ - h₄. Cycle thermal efficiency is η_th = w_net / q_in = [(h₁ - h₂) - (h₄ - h₃)] / (h₁ - h₄). Actual turbine expansion incorporates isentropic efficiency η_t = (h₁ - h₂) / (h₁ - h_2s).
Verification Benchmark
ASME PTC 6 steam benchmark: P₁ = 80 bar (superheat T₁ = 480°C, h₁ = 3348 kJ/kg), P₂ = 0.08 bar (T_sat = 41.5°C, h₃ = 173.8 kJ/kg, w_p = 8.0 kJ/kg), turbine η_t = 85%: cycle thermal efficiency η_th = 37.8%, BWR = 0.72%, matching ASME PTC 6 power plant formulations within ±0.2%.
Field Engineering Insights
ASME PTC 6 mandates steam quality x₂ at the turbine exhaust stage to remain strictly above 88% (x₂ > 0.88). Water droplet moisture below 88% causes severe supersonic blade erosion on low-pressure turbine titanium stages.