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Turbine Inlet & Exhaust Thermodynamic Operating Parameters

ASME PTC 6 & IEC 60045-1 Multi-Stage Rankine Expansion Architecture

Thermodynamic Expansion & Power Diagnostics

Gross Generator Power
--
-- kW gross
Exhaust Moisture Fraction
--
-- quality
Actual Steam Rate (ASR)
--
-- TSR theoretical
Blade Erosion Risk Status
--
-- limit 12%
Actual Enthalpy Drop (Delta h)
--
Btu / lb steam
Part-Load Generation (W_oper)
--
-- part-load ASR
Willans Line No-Load Flow (W_0)
--
lb / hr spinning idle

Interactive Mollier h-s Expansion & Willans Line Profile

Rankine Expansion State Points & Performance Summary

State Point Pressure Temperature / Quality Specific Enthalpy (h) Specific Entropy (s) Physical Condition

Mathematical Formulations & Thermodynamic Derivations

Steam turbine cycle performance is formulated via high-pressure Rankine expansion across impulse and reaction stages per ASME PTC 6 and IEC 60045-1. Steam expansion is evaluated on the Mollier enthalpy-entropy ($h-s$) diagram.

1. Inlet Steam Properties (Superheated Region): h1 = 1050 + 0.48 * ( T1 - T_sat ) + 0.35 * P1_psia^0.6 (Btu / lb, approx) s1 = Entropy evaluated at (P1, T1) 2. Isentropic Exhaust Enthalpy (h_2s): If condensing into 2-phase mixture at P2: x_2s = ( s1 - s_f2 ) / s_fg2 h_2s = h_f2 + x_2s * h_fg2 Isentropic Head: Delta h_isen = h1 - h_2s 3. Actual Enthalpy Drop & Exhaust State: Delta h_act = Delta h_isen * ( Eff_isen / 100 ) h2_actual = h1 - Delta h_act x_2_actual = ( h2_actual - h_f2 ) / h_fg2 Moisture_fraction (y) = 1.0 - x_2_actual 4. Gross Power Output: P_gross_kW = [ W_lb_hr * Delta h_act * (Eff_mech / 100) * (Eff_gen / 100) ] / 3412.14 P_gross_MW = P_gross_kW / 1000.0 5. Theoretical & Actual Steam Rates (TSR / ASR): TSR = 3412.14 / Delta h_isen (lb / kWh) ASR = 3412.14 / [ Delta h_act * (Eff_mech/100) * (Eff_gen/100) ] (lb / kWh) 6. Willans Line Formulation: W_0 = W_rated * ( W0_pct / 100 ) Slope m = ( W_rated - W_0 ) / P_gross_kW W(P) = W_0 + m * P

If exhaust moisture exceeds 12%, last-stage titanium or stellite-shielded blades suffer rapid droplet erosion, leading to unbalance, severe bearing vibration, and forced plant outages.

1. Excessive Exhaust Moisture (>12%) Eroding Last-Stage Blades

When steam expands too far into the wet dome without reheat, fine mist coalesces on stationary diaphragm vanes into large water droplets. These droplets detach and impact the supersonic spinning tips of last-stage blades at relative velocities exceeding 1,200 ft/s. Moisture exceeding 12% creates severe leading-edge scalloping and erosion notches, triggering fatigue blade throwing that destroys the entire LP turbine rotor.

2. Over-Throttling at Part Load Destroying Rankine Efficiency

In throttle-governed turbines operating at 40% to 60% load, the main governor valve constricts steam flow, dropping inlet pressure from 900 psig down to 400 psig via isenthalpic throttling. Because throttling is purely isenthalpic, no shaft work is produced during the pressure drop. Available isentropic enthalpy drops by over 30%, causing part-load heat rates to spike and burning massive excess boiler fuel.

3. Wet Steam Water Induction Shock Warping Turbine Rotors

Inadequate attemperator spray control or failed boiler drum level trips can send liquid water slugs into the main steam piping. When water droplets enter the 900°F HP turbine casing, differential thermal shock contracts the bottom of the casing faster than the top. The casing bows upward into a banana shape, causing irreversible high-speed rubs against rotor labyrinth seals and catastrophic rotor seizure.

4. Condenser Vacuum Degradation Causing Exhaust Hood Overheating

If condenser cooling water temperature rises or air removal ejectors fail, condenser backpressure rises from 1.5 inHgA to 6.0 inHgA. Because the pressure ratio across the LP stages collapses, the last-stage blades do zero work and begin churning dense steam like a fan. Windage friction generates intense localized heating, pushing exhaust hood temperatures past 200°F and distorting low-pressure bearing pedestals.

5. Loss of Gland Steam Sealing Pressure Inducing Air In-Leakage

Turbine rotor shaft ends penetrating sub-atmospheric casing zones must be sealed by positive-pressure gland steam (typically 2.5 to 5 psig). If the gland steam regulator fails, cold atmospheric air is sucked across shaft seals directly into the condenser. Oxygen dissolves into the condensate, triggering catastrophic pitting in deaerator tanks and feed-water preheaters while blanketing condenser tubes with non-condensable gas.

Frequently Asked Questions

What is the maximum allowable exhaust moisture fraction in a condensing steam turbine? +
What is the Baumann rule for steam turbine wet expansion? +
What is Willans Line and how does it describe part-load steam turbine efficiency? +
What is the difference between an extraction-backpressure and a condensing steam turbine? +
How does throttle governing cause thermodynamic irreversibility compared to nozzle governing? +
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