Formula Sheet: Power Cycles (Rankine, Brayton)

Table of Contents
1. Thermodynamic Fundamentals for Power Cycles
2. Rankine Cycle (Vapor Power Cycle)
3. Brayton Cycle (Gas Turbine Cycle)
4. Comparative Performance Parameters
5. Component Analysis
6. Second Law Analysis
7. Practical Considerations and Limitations
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Thermodynamic Fundamentals for Power Cycles

Basic Property Relationships

• Specific enthalpy: \[h = u + Pv\] where h = specific enthalpy (Btu/lbm or kJ/kg), u = specific internal energy (Btu/lbm or kJ/kg), P = pressure (lbf/ft² or Pa), v = specific volume (ft³/lbm or m³/kg)
• Quality (dryness fraction): \[x = \frac{m_g}{m_g + m_f} = \frac{m_g}{m_{total}}\] where x = quality (dimensionless, 0 ≤ x ≤ 1), m_g = mass of vapor, m_f = mass of liquid
• Two-phase mixture properties: \[h = h_f + x \cdot h_{fg}\] \[s = s_f + x \cdot s_{fg}\] \[v = v_f + x \cdot v_{fg}\] where h_f = saturated liquid enthalpy, h_fg = enthalpy of vaporization, s_f = saturated liquid entropy, s_fg = entropy of vaporization, v_f = saturated liquid specific volume, v_fg = specific volume change during vaporization
• Isentropic process for ideal gas: \[\frac{T_2}{T_1} = \left(\frac{P_2}{P_1}\right)^{\frac{k-1}{k}}\] where T = absolute temperature (°R or K), P = absolute pressure (psia or kPa), k = specific heat ratio = c_p/c_v
• Pressure-volume relationship for isentropic process: \[P_1 v_1^k = P_2 v_2^k\]

First Law of Thermodynamics - Steady Flow

• General steady flow energy equation (SFEE): \[\dot{Q} - \dot{W} = \dot{m}\left[(h_2 - h_1) + \frac{V_2^2 - V_1^2}{2g_c} + g(z_2 - z_1)\right]\] where Q̇ = heat transfer rate (Btu/hr or kW), Ẇ = work rate/power (Btu/hr or kW), ṁ = mass flow rate (lbm/hr or kg/s), V = velocity (ft/s or m/s), g_c = gravitational conversion constant (32.174 lbm·ft/lbf·s² or 1 kg·m/N·s²), g = gravitational acceleration (32.174 ft/s² or 9.81 m/s²), z = elevation (ft or m)
• Simplified SFEE (neglecting KE and PE): \[\dot{Q} - \dot{W} = \dot{m}(h_2 - h_1)\] This form is typically used for power cycle components

Efficiency Definitions

• Isentropic (adiabatic) efficiency of turbine: \[\eta_t = \frac{h_1 - h_2}{h_1 - h_{2s}} = \frac{W_{actual}}{W_{isentropic}}\] where h_2s = enthalpy at exit if process were isentropic, h₂ = actual exit enthalpy
• Isentropic efficiency of compressor/pump: \[\eta_c = \frac{h_{2s} - h_1}{h_2 - h_1} = \frac{W_{isentropic}}{W_{actual}}\] where h_2s = enthalpy at exit if process were isentropic, h₂ = actual exit enthalpy
• Thermal efficiency: \[\eta_{th} = \frac{W_{net}}{Q_{in}} = \frac{Q_{in} - Q_{out}}{Q_{in}} = 1 - \frac{Q_{out}}{Q_{in}}\] where W_net = net work output, Q_in = heat added, Q_out = heat rejected
• Heat rate (for power plants): \[HR = \frac{Q_{in}}{W_{net}} = \frac{3412}{\eta_{th}}\] where HR = heat rate (Btu/kW·hr), 3412 is the conversion factor from kW to Btu/hr
• Back work ratio: \[BWR = \frac{W_{compressor}}{W_{turbine}}\] Measure of the fraction of turbine work used to drive the compressor

Rankine Cycle (Vapor Power Cycle)

Basic Ideal Rankine Cycle

• Cycle components and processes:
  • Process 1→2: Isentropic compression in pump (s₁ = s₂)
  • Process 2→3: Constant pressure heat addition in boiler
  • Process 3→4: Isentropic expansion in turbine (s₃ = s₄)
  • Process 4→1: Constant pressure heat rejection in condenser
• Pump work (ideal, incompressible fluid): \[w_{pump} = v_1(P_2 - P_1) = \frac{h_2 - h_1}{\text{(ideal)}}\] where w_pump = specific pump work (Btu/lbm or kJ/kg), v₁ = specific volume at pump inlet (ft³/lbm or m³/kg), typically v_f at condenser pressure
• Pump work with efficiency: \[w_{pump,actual} = \frac{v_1(P_2 - P_1)}{\eta_p} = \frac{h_{2s} - h_1}{\eta_p}\] \[h_2 = h_1 + \frac{h_{2s} - h_1}{\eta_p}\] where η_p = pump isentropic efficiency
• Turbine work (ideal): \[w_{turbine} = h_3 - h_4\] where h₃ = turbine inlet enthalpy, h₄ = turbine exit enthalpy (isentropic)
• Turbine work with efficiency: \[w_{turbine,actual} = \eta_t(h_3 - h_{4s})\] \[h_4 = h_3 - \eta_t(h_3 - h_{4s})\] where h_4s = isentropic exit enthalpy
• Heat added in boiler: \[q_{in} = h_3 - h_2\]
• Heat rejected in condenser: \[q_{out} = h_4 - h_1\]
• Net work output: \[w_{net} = w_{turbine} - w_{pump} = (h_3 - h_4) - (h_2 - h_1)\] or equivalently: \[w_{net} = q_{in} - q_{out}\]
• Cycle thermal efficiency: \[\eta_{Rankine} = \frac{w_{net}}{q_{in}} = \frac{(h_3 - h_4) - (h_2 - h_1)}{h_3 - h_2} = 1 - \frac{h_4 - h_1}{h_3 - h_2}\]
• Mass flow rate from power output: \[\dot{m} = \frac{\dot{W}_{net}}{w_{net}}\] where Ẇ_net = net power output (kW or hp)

Rankine Cycle with Reheat

• Process sequence:
  • Steam expands in high-pressure (HP) turbine from state 3 to state 4
  • Steam is reheated in boiler from state 4 to state 5
  • Steam expands in low-pressure (LP) turbine from state 5 to state 6
• Total turbine work: \[w_{turbine} = (h_3 - h_4) + (h_5 - h_6)\] where subscripts: 3 = HP turbine inlet, 4 = HP turbine exit/reheat inlet, 5 = reheat exit/LP turbine inlet, 6 = LP turbine exit
• Total heat added: \[q_{in} = (h_3 - h_2) + (h_5 - h_4)\] Heat is added in both the primary boiler and reheater
• Net work: \[w_{net} = w_{turbine} - w_{pump} = (h_3 - h_4) + (h_5 - h_6) - (h_2 - h_1)\]
• Thermal efficiency with reheat: \[\eta_{reheat} = \frac{w_{net}}{q_{in}} = \frac{(h_3 - h_4) + (h_5 - h_6) - (h_2 - h_1)}{(h_3 - h_2) + (h_5 - h_4)}\]
• Note: Reheat increases turbine work and reduces moisture content at turbine exit, improving efficiency and reducing blade erosion. Optimal reheat pressure is typically 20-25% of maximum pressure.

Rankine Cycle with Regeneration (Open Feedwater Heater)

• Extraction fraction: \[y = \frac{\dot{m}_{extracted}}{\dot{m}_{total}}\] where y = fraction of steam extracted from turbine for feedwater heating
• Energy balance on open feedwater heater (mixing chamber): \[y \cdot h_{extracted} + (1-y) \cdot h_{condensate} = 1 \cdot h_{feedwater,out}\] \[y = \frac{h_{feedwater,out} - h_{condensate}}{h_{extracted} - h_{condensate}}\] where h_extracted = enthalpy of extraction steam, h_condensate = enthalpy of condensate entering heater, h_{feedwater,out} = enthalpy of feedwater leaving heater (typically saturated liquid at extraction pressure)
• Turbine work per unit mass entering turbine: \[w_{turbine} = (h_{in} - h_{extraction}) + (1-y)(h_{extraction} - h_{exit})\] Only fraction (1-y) continues through the LP section
• Pump work (two pumps for open FWH): \[w_{pump,total} = w_{pump1} + w_{pump2}\] where pump 1 operates on the full condensate flow and pump 2 operates on the feedwater
• Heat added: \[q_{in} = h_{boiler,out} - h_{boiler,in}\] The feedwater entering boiler is at higher enthalpy due to regeneration
• Thermal efficiency with regeneration: \[\eta_{regen} = \frac{w_{turbine} - w_{pump,total}}{q_{in}}\] Regeneration increases cycle efficiency by reducing average temperature at which heat is rejected

Rankine Cycle with Regeneration (Closed Feedwater Heater)

• Energy balance on closed feedwater heater: \[y(h_{extracted} - h_{drains,out}) = (1)(h_{feedwater,out} - h_{feedwater,in})\] \[y = \frac{h_{feedwater,out} - h_{feedwater,in}}{h_{extracted} - h_{drains,out}}\] where extracted steam does not mix with feedwater; heat exchange occurs through tube walls
• Drains handling options:
  • Cascaded backward: Drains flow to next lower pressure heater
  • Pumped forward: Drains pumped into main feedwater line
• For multiple feedwater heaters: Sequential energy balances must be written for each heater, starting from the highest pressure heater and working backward

Moisture Content and Steam Quality

• Moisture content at turbine exit: \[\text{Moisture} = 1 - x_4\] where x₄ = quality at turbine exit
• Maximum allowable moisture: Typically 10-12% (x ≥ 0.88-0.90) to prevent turbine blade erosion
• Entropy at turbine exit (for finding quality): \[s_4 = s_3 = s_f + x_4 \cdot s_{fg}\] \[x_4 = \frac{s_4 - s_f}{s_{fg}}\] where properties are evaluated at condenser pressure

Brayton Cycle (Gas Turbine Cycle)

Basic Ideal Brayton Cycle

• Cycle components and processes:
  • Process 1→2: Isentropic compression in compressor (s₁ = s₂)
  • Process 2→3: Constant pressure heat addition in combustor
  • Process 3→4: Isentropic expansion in turbine (s₃ = s₄)
  • Process 4→1: Constant pressure heat rejection (to atmosphere or in heat exchanger)
• Pressure ratio: \[r_p = \frac{P_2}{P_1} = \frac{P_{max}}{P_{min}}\] where r_p = compressor pressure ratio
• Temperature ratios for ideal gas (isentropic processes): \[\frac{T_2}{T_1} = \left(\frac{P_2}{P_1}\right)^{\frac{k-1}{k}} = r_p^{\frac{k-1}{k}}\] \[\frac{T_3}{T_4} = \left(\frac{P_3}{P_2}\right)^{\frac{k-1}{k}} = r_p^{\frac{k-1}{k}}\] where k = specific heat ratio (typically 1.4 for air)
• Compressor work (ideal, constant c_p): \[w_{comp} = c_p(T_2 - T_1) = c_p T_1\left[r_p^{\frac{k-1}{k}} - 1\right]\] where c_p = specific heat at constant pressure (Btu/lbm·°R or kJ/kg·K)
• Compressor work with efficiency: \[w_{comp,actual} = \frac{c_p(T_{2s} - T_1)}{\eta_c}\] \[T_2 = T_1 + \frac{T_{2s} - T_1}{\eta_c} = T_1 + \frac{T_1\left(r_p^{\frac{k-1}{k}} - 1\right)}{\eta_c}\]
• Turbine work (ideal, constant c_p): \[w_{turb} = c_p(T_3 - T_4) = c_p T_3\left[1 - r_p^{-\frac{k-1}{k}}\right]\]
• Turbine work with efficiency: \[w_{turb,actual} = \eta_t \cdot c_p(T_3 - T_{4s})\] \[T_4 = T_3 - \eta_t(T_3 - T_{4s}) = T_3 - \eta_t T_3\left[1 - r_p^{-\frac{k-1}{k}}\right]\]
• Heat added: \[q_{in} = c_p(T_3 - T_2)\]
• Heat rejected: \[q_{out} = c_p(T_4 - T_1)\]
• Net work output: \[w_{net} = w_{turb} - w_{comp} = c_p[(T_3 - T_4) - (T_2 - T_1)]\]
• Thermal efficiency (ideal, cold air standard): \[\eta_{Brayton} = \frac{w_{net}}{q_{in}} = 1 - \frac{T_4 - T_1}{T_3 - T_2} = 1 - \frac{T_1}{T_2} = 1 - r_p^{-\frac{k-1}{k}}\] Efficiency depends only on pressure ratio for ideal cycle with constant properties
• Back work ratio: \[BWR = \frac{w_{comp}}{w_{turb}} = \frac{T_2 - T_1}{T_3 - T_4}\] For gas turbines, BWR is typically 40-80% (much higher than steam cycles)

Optimum Pressure Ratio

• For maximum specific work output (fixed T₁ and T₃): \[r_{p,opt} = \left(\frac{T_3}{T_1}\right)^{\frac{k}{2(k-1)}}\] This maximizes net work per unit mass flow
• Note: Maximum efficiency occurs at higher pressure ratios than maximum work. Practical designs balance efficiency and work output considerations.

Brayton Cycle with Regeneration

• Regenerator: Heat exchanger that transfers heat from hot turbine exhaust (state 4) to compressed air before combustor (state 2)
• Regenerator effectiveness: \[\varepsilon = \frac{T_x - T_2}{T_4 - T_2} = \frac{\text{Actual heat transfer}}{\text{Maximum possible heat transfer}}\] where ε = regenerator effectiveness (0 ≤ ε ≤ 1), T_x = temperature of air leaving regenerator (entering combustor), T₂ = compressor exit temperature, T₄ = turbine exit temperature
• Temperature after regeneration: \[T_x = T_2 + \varepsilon(T_4 - T_2)\]
• Heat added with regeneration: \[q_{in} = c_p(T_3 - T_x) = c_p(T_3 - T_2) - \varepsilon \cdot c_p(T_4 - T_2)\] Less fuel required due to preheating
• Thermal efficiency with regeneration: \[\eta_{regen} = 1 - \frac{c_p(T_y - T_1)}{c_p(T_3 - T_x)} = 1 - \frac{T_1(T_4/T_1 - 1)}{T_3(1 - T_2/T_3) - \varepsilon T_2(T_4/T_2 - 1)}\] where T_y = temperature of exhaust leaving regenerator (if analyzed)
• Simplified for ideal regenerator (ε = 1, T_x = T₄): \[\eta_{ideal,regen} = 1 - \frac{T_1}{T_3} \cdot r_p^{\frac{k-1}{k}}\]
• Condition for regeneration benefit: Regeneration is beneficial when T₄ > T₂, which occurs at lower pressure ratios. At high pressure ratios, T₂ > T₄ and regeneration is not possible.
• Maximum pressure ratio for regeneration: \[r_{p,max} = \left(\frac{T_3}{T_1}\right)^{\frac{k}{2(k-1)}}\] Above this pressure ratio, T₂ ≥ T₄ and no heat can be recovered

Brayton Cycle with Intercooling

• Purpose: Reduce compressor work by cooling air between compression stages
• Two-stage compression with intercooling: \[w_{comp,total} = c_p[(T_{2a} - T_1) + (T_{2b} - T_3)]\] where states: 1 = inlet to first compressor, 2a = exit from first compressor, 3 = exit from intercooler (inlet to second compressor), 2b = exit from second compressor
• Optimum intermediate pressure (minimum work): \[P_{int,opt} = \sqrt{P_1 \cdot P_2}\] \[\left(\frac{P_{int}}{P_1}\right)_{opt} = \sqrt{\frac{P_2}{P_1}} = \sqrt{r_p}\] Occurs when pressure ratio is equal across both stages
• Minimum compressor work (ideal intercooling to T₁, equal pressure ratios): \[w_{comp,min} = 2c_p T_1\left[r_p^{\frac{k-1}{2k}} - 1\right]\] Compare to single-stage: \(w_{comp,single} = c_p T_1\left[r_p^{\frac{k-1}{k}} - 1\right]\)
• For n stages of compression with intercooling: \[\left(\frac{P_i}{P_{i-1}}\right)_{opt} = r_p^{1/n}\] Each stage has pressure ratio equal to \(r_p^{1/n}\)

Brayton Cycle with Reheat

• Purpose: Increase turbine work by reheating gas between expansion stages
• Two-stage expansion with reheat: \[w_{turb,total} = c_p[(T_3 - T_{4a}) + (T_{3r} - T_4)]\] where states: 3 = inlet to first turbine, 4a = exit from first turbine, 3r = exit from reheater (inlet to second turbine), 4 = exit from second turbine
• Optimum intermediate pressure (maximum work): \[P_{int,opt} = \sqrt{P_3 \cdot P_4}\] Equal pressure ratio across both turbine stages
• Heat added with reheat: \[q_{in,total} = c_p[(T_3 - T_2) + (T_{3r} - T_{4a})]\] Includes both primary combustor and reheater

Combined Cycle (Intercooling, Reheat, and Regeneration)

• Net work: \[w_{net} = w_{turb,total} - w_{comp,total}\] Sum of all turbine stages minus sum of all compressor stages
• Heat added: \[q_{in} = \text{Heat in combustor} + \text{Heat in reheater} - \text{Heat recovered in regenerator}\]
• Thermal efficiency: \[\eta_{combined} = \frac{w_{net}}{q_{in}}\]
• Note: Intercooling decreases cycle efficiency but increases net work and specific power. Reheat and regeneration both increase efficiency.

Actual Gas Turbine Considerations

• Variable specific heats: When temperature range is large, use: \[w = h_2 - h_1\] where enthalpy is obtained from gas tables (air tables) rather than assuming constant c_p
• Relative pressure for isentropic processes (air tables): \[\frac{P_2}{P_1} = \frac{P_{r2}}{P_{r1}}\] where P_r = relative pressure (dimensionless) from air tables at given temperature
• Compressor work (variable specific heats): \[w_{comp,s} = h_{2s} - h_1\] \[w_{comp,actual} = \frac{h_{2s} - h_1}{\eta_c}\]
• Turbine work (variable specific heats): \[w_{turb,s} = h_3 - h_{4s}\] \[w_{turb,actual} = \eta_t(h_3 - h_{4s})\]

Comparative Performance Parameters

Power Plant Performance Metrics

• Specific fuel consumption (SFC): \[SFC = \frac{\dot{m}_{fuel}}{\dot{W}_{net}}\] where SFC = specific fuel consumption (lbm/hp·hr or kg/kW·hr), ṁ_fuel = fuel mass flow rate
• Specific work output: \[w_{specific} = \frac{\dot{W}_{net}}{\dot{m}_{working fluid}}\] where units are (Btu/lbm or kJ/kg)
• Capacity factor: \[CF = \frac{\text{Actual energy produced}}{\text{Maximum possible energy}}\] Ratio of actual plant output to rated capacity over a time period

Cycle Comparison

• Rankine cycle characteristics:
  • Lower back work ratio (1-2%)
  • Requires external water source and cooling
  • Higher thermal efficiency for same peak temperatures
  • Larger and heavier equipment
  • Lower maximum cycle temperature limited by materials
• Brayton cycle characteristics:
  • Higher back work ratio (40-80%)
  • Can use atmospheric air (open cycle)
  • Lower efficiency without regeneration
  • More compact and lighter
  • Can achieve higher turbine inlet temperatures
  • Faster startup and response
• Combined cycle (Brayton + Rankine): \[\eta_{combined} = \eta_{gas} + \eta_{steam}(1 - \eta_{gas})\] Uses gas turbine exhaust to generate steam for Rankine cycle; achieves efficiencies above 60%

Component Analysis

Turbine Analysis

• Power output: \[\dot{W}_{turbine} = \dot{m}(h_{in} - h_{out})\] where Ẇ_turbine = turbine power output (kW or hp)
• For steam turbine with extraction: \[\dot{W}_{turbine} = \dot{m}_1(h_1 - h_2) + \dot{m}_3(h_2 - h_3)\] where ṁ₁ = inlet flow, ṁ₃ = flow continuing after extraction = ṁ₁ - ṁ_extracted
• Velocity at turbine exit (if significant): \[V_{exit} = \sqrt{2g_c(h_{in} - h_{out} - w_{shaft})}\] Used when kinetic energy is not negligible

Compressor/Pump Analysis

• Power requirement: \[\dot{W}_{comp} = \dot{m}(h_{out} - h_{in})\]
• For multistage compressor: \[\dot{W}_{total} = \sum_{i=1}^{n} \dot{W}_i = \dot{m}\sum_{i=1}^{n}(h_{out,i} - h_{in,i})\]
• Pump power (SI units): \[\dot{W}_{pump} = \frac{\dot{m} \cdot v \cdot \Delta P}{\eta_p}\] where v = specific volume (m³/kg), ΔP = pressure rise (Pa), result in watts
• Pump power (US units): \[\dot{W}_{pump,hp} = \frac{\dot{V} \cdot \Delta P}{1714 \cdot \eta_p}\] where V̇ = volumetric flow rate (gpm), ΔP = pressure rise (psi), 1714 is conversion constant

Heat Exchanger Analysis

• Heat transfer rate: \[\dot{Q} = \dot{m}_{hot}(h_{in,hot} - h_{out,hot}) = \dot{m}_{cold}(h_{out,cold} - h_{in,cold})\]
• Log mean temperature difference (LMTD) method: \[\dot{Q} = UA \cdot LMTD\] \[LMTD = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1/\Delta T_2)}\] where U = overall heat transfer coefficient (Btu/hr·ft²·°F or W/m²·K), A = heat transfer area (ft² or m²), ΔT₁ and ΔT₂ = temperature differences at each end
• Effectiveness-NTU method: \[\varepsilon = \frac{Q_{actual}}{Q_{max}} = \frac{C_h(T_{h,in} - T_{h,out})}{C_{min}(T_{h,in} - T_{c,in})}\] where C = ṁc_p = heat capacity rate, C_min = minimum of C_hot and C_cold

Second Law Analysis

Entropy and Irreversibility

• Entropy generation: \[S_{gen} = \Delta S_{system} + \Delta S_{surroundings} = \sum \frac{\dot{Q}}{T} + \dot{S}_{gen}\] where S_gen ≥ 0 for all real processes
• Isentropic efficiency from entropy: For turbine with entropy generation: \[s_2 = s_1 + s_{gen}\] \[\eta_t = \frac{h_1 - h_2}{h_1 - h_{2s}}\] where h_2s corresponds to s_2s = s₁
• Exergy (availability): \[\psi = (h - h_0) - T_0(s - s_0)\] where ψ = specific exergy (Btu/lbm or kJ/kg), subscript 0 denotes dead state (environment)
• Exergy destruction: \[X_{destroyed} = T_0 \cdot S_{gen}\] Measure of work potential lost due to irreversibilities
• Second law efficiency: \[\eta_{II} = \frac{\text{Exergy recovered}}{\text{Exergy supplied}} = \frac{X_{useful}}{X_{in}}\]

Carnot Efficiency (Theoretical Maximum)

• Carnot cycle efficiency: \[\eta_{Carnot} = 1 - \frac{T_L}{T_H}\] where T_L = absolute temperature of cold reservoir (°R or K), T_H = absolute temperature of hot reservoir (°R or K)
• Note: All real cycles operate at lower efficiency than Carnot cycle operating between same temperature limits. Used as benchmark for comparison.
• Carnot COP for refrigeration: \[COP_{Carnot,R} = \frac{T_L}{T_H - T_L}\]
• Carnot COP for heat pump: \[COP_{Carnot,HP} = \frac{T_H}{T_H - T_L}\]

Practical Considerations and Limitations

Material and Operating Constraints

• Maximum steam temperature (Rankine): Typically limited to 540-565°C (1000-1050°F) by superheater material constraints in conventional plants; advanced materials allow up to 620°C (1150°F)
• Condenser pressure (Rankine): Limited by cooling water temperature; typical range 0.5-10 kPa (0.07-1.5 psia)
• Turbine inlet temperature (Brayton): Limited by turbine blade materials and cooling technology; modern gas turbines: 1200-1600°C (2200-2900°F)
• Pressure ratio practical limits (Brayton): Typically 10-40 for aircraft engines, 15-20 for industrial gas turbines
• Minimum steam quality: Maintain x ≥ 0.88-0.90 to prevent excessive erosion of turbine blades

Performance Degradation Factors

• Pressure drops: Real cycles experience pressure drops in heat exchangers, piping, and combustors: \[\Delta P_{loss} = P_{ideal} - P_{actual}\] Reduces cycle efficiency and work output
• Heat losses: Heat loss from components to surroundings reduces efficiency: \[Q_{loss} = UA(T_{component} - T_{ambient})\]
• Mechanical losses: Bearing friction, windage losses reduce net power: \[\eta_{mechanical} = \frac{W_{shaft}}{W_{indicated}}\] Typically 0.95-0.99 for large turbines
• Generator efficiency: \[\eta_{generator} = \frac{P_{electrical}}{P_{shaft}}\] Typically 0.96-0.99 for large generators
• Overall plant efficiency: \[\eta_{overall} = \eta_{thermal} \times \eta_{mechanical} \times \eta_{generator}\]