rankine-cycle-advanced

name	rankine-cycle-advanced
description	Advanced Rankine cycle — reheat, regeneration, feedwater heaters (open/closed), supercritical steam, cycle efficiency analysis, T-s diagram, turbine stage design.
metadata	{"priority":7,"promptSignals":{"phrases":["Rankine cycle","steam cycle","reheat Rankine","regenerative cycle","feedwater heater","supercritical steam","steam turbine efficiency"],"minScore":3}}

Advanced Rankine Cycle — Complete Skill

Basic Rankine Cycle

States: 1-pump inlet (saturated liquid), 2-pump exit, 3-boiler exit (superheated), 4-turbine exit (wet or superheated)

Efficiency: η_th = w_net / q_in = (w_turbine - w_pump) / q_boiler

w_turbine = h₃ - h₄ (ideal) w_pump = v₁(P₂-P₁) ≈ h₂ - h₁ (incompressible, v₁ ≈ specific volume at inlet) q_in = h₃ - h₂

For actual turbine: η_turbine = (h₃-h₄)/(h₃-h₄s) [isentropic efficiency, typically 0.80–0.90] For actual pump: η_pump = (h₂s-h₁)/(h₂-h₁) [typically 0.75–0.85]

Reheat Cycle

After high-pressure turbine → reheated in boiler → low-pressure turbine

Benefits:

• Increases moisture content at LP turbine exit (prevents blade erosion)
• Slightly increases cycle efficiency (typically +2–4%)
• Enables higher boiler pressure

Analysis: w_net = (h₃-h₄) + (h₅-h₆) - w_pump q_in = (h₃-h₂) + (h₅-h₄) [boiler + reheater] η = w_net / q_in

Reheat pressure: typically 20–25% of initial pressure Reheat temperature: typically = initial steam temperature

Regenerative Cycle (Feedwater Heaters)

Bleed steam from turbine stages → heat feedwater → reduce heat rejection

Open (Direct Contact) Feedwater Heater

Extracted steam mixes directly with feedwater Mass balance at heater: y × h_bleed + (1-y) × h_condensate = h_fwh,exit Solve for bleed fraction y: y = (h_fwh - h_condensate) / (h_bleed - h_condensate)

Efficiency gain: reduces fuel input for same output (condensate enters boiler at higher T)

Closed Feedwater Heater

Shell-and-tube; no direct mixing; requires drain cascade or pump More complex but allows pressurized condensate return

Multi-Stage Regeneration

Modern power plants: 6–10 feedwater heaters Optimum bleed pressure for n heaters: extractions equally spaced in T-s space Each heater raises feedwater temperature incrementally from condenser to boiler

Cycle efficiency with regeneration: η_regenerative > η_basic Rankine by 5–15% depending on stages

Steam Conditions and Turbine Stages

Subcritical

P₀ < 22.1 MPa (critical point of water) Typical utility: 16–18 MPa, 560–580°C → η ≈ 40–43%

Supercritical

P₀ > 22.1 MPa; single phase throughout heating Typical: 24–28 MPa, 600°C → η ≈ 44–46% Ultra-supercritical (USC): 30+ MPa, 620–640°C → η ≈ 46–48% Advanced USC: 35 MPa, 700°C → η ≈ 50%+ (Ni-alloy headers/turbines needed)

Combined Cycle (CCGT)

Gas turbine Brayton cycle topping + Rankine steam cycle bottoming GT exhaust → HRSG → steam turbine Overall η ≈ 58–62% (LHV basis)

Turbine Stage Design (Impulse/Reaction)

Velocity triangles: Stage work: W_stage = U(C_θ1 + C_θ2) [per unit mass] C_θ = tangential velocity; U = blade speed

Degree of reaction: R = h_drop_rotor / h_drop_stage R = 0: impulse stage (all drop in nozzle) R = 0.5: 50% reaction (equal drop in nozzle and rotor) — most common for HP/LP turbines

Stage loading coefficient: ψ = W_stage / U² = ΔC_θ / U [typically 1.0–2.0]

Flow coefficient: φ = C_a / U [axial velocity / blade speed; typically 0.5–1.0]

Condenser Design

Surface condenser: shell-and-tube; steam on shell side; cooling water in tubes Condensing pressure: 5–15 kPa (0.05–0.15 bar absolute) → T_sat = 33–55°C Lower pressure → higher efficiency; requires larger condenser

Cooling water: typically 20–30°C supply; 8–12°C rise Heat load: Q_condenser = ṁ_steam × h_fg (at condenser pressure)

Steam Properties Reference Points

At 560°C, 16 MPa: h₃ ≈ 3450 kJ/kg; s₃ ≈ 6.6 kJ/kg·K At condenser (0.1 bar): h₁ ≈ 191 kJ/kg (liquid); h_fg ≈ 2392 kJ/kg; T_sat = 45°C Steam tables from IAPWS-IF97 standard

Output

Provide: cycle configuration (basic/reheat/regenerative), η_thermal [%], w_net [kJ/kg], q_in [kJ/kg], steam states (h, T, P, x at each point), bleed fraction y for each heater, turbine/pump actual efficiencies, heat rate [kJ/kWh], back work ratio.