13.1 Rankine and Brayton cycles

Power plants use two main thermodynamic cycles: Rankine and Brayton. The Rankine cycle, used in steam power plants, involves water changing phases. The Brayton cycle, used in gas turbines, keeps air in gas form throughout.

Both cycles have similar processes but differ in working fluids and heat rejection. Rankine cycles are generally more efficient due to lower heat rejection temperatures. Understanding these cycles is key to analyzing power generation systems.

Rankine Cycle

Components of Rankine cycle

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• Boiler heats working fluid (water) to produce high-pressure steam
• Turbine expands steam converting thermal energy to mechanical work (electricity generation)
• Condenser condenses low-pressure steam back into liquid form (heat rejection to environment)
• Pump pressurizes liquid working fluid and returns it to boiler completing the cycle

Processes in Rankine cycle

1. Isentropic compression in pump pressurizes working fluid
2. Isobaric heat addition in boiler heats working fluid at constant pressure producing steam
3. Isentropic expansion in turbine expands steam generating mechanical work
4. Isobaric heat rejection in condenser condenses steam back into liquid at constant pressure

• Applications in power generation include steam power plants (coal, nuclear) using Rankine cycle as fundamental thermodynamic cycle

Brayton Cycle

Components of Brayton cycle

• Compressor compresses working fluid (air) to high pressure
• Combustion chamber heats compressed air by burning fuel (natural gas, kerosene)
• Turbine expands hot, high-pressure gases converting thermal energy to mechanical work
• Heat exchanger (optional) cools exhaust gases and preheats compressed air improving efficiency

Processes in Brayton cycle

1. Isentropic compression in compressor compresses working fluid
2. Isobaric heat addition in combustion chamber heats working fluid at constant pressure
3. Isentropic expansion in turbine expands hot gases generating mechanical work
4. Isobaric heat rejection to atmosphere or via heat exchanger at constant pressure

• Applications in gas turbines include jet engines for aircraft propulsion and gas turbine power plants for electricity generation

Rankine vs Brayton cycle efficiency

• Rankine cycle uses water undergoing phase changes, Brayton cycle uses gas (air) remaining gaseous
• Both have isobaric heat addition, but Rankine has isobaric heat rejection while Brayton has isobaric or heat exchanger rejection
• Both involve isentropic compression and expansion processes
• Rankine efficiency depends on max/min fluid temperatures, Brayton on compressor pressure ratio and max/min temperatures
• Brayton cycles generally have lower efficiencies than Rankine due to higher heat rejection temperature

Calculations for thermodynamic cycles

• Rankine cycle
  • Net work output $W_{net} = W_t - W_p$ (turbine work minus pump work)
  • Heat input $Q_b$ added in boiler
  • Thermal efficiency $\eta_{th} = \frac{W_{net}}{Q_b} = \frac{W_t - W_p}{Q_b}$
• Brayton cycle
  • Net work output $W_{net} = W_t - W_c$ (turbine work minus compressor work)
  • Heat input $Q_{in}$ added in combustion chamber
  • Thermal efficiency $\eta_{th} = \frac{W_{net}}{Q_{in}} = \frac{W_t - W_c}{Q_{in}}$
  • Pressure ratio $r_p$ (compressor outlet to inlet pressures) affects efficiency
    • $\eta_{th} = 1 - \frac{1}{r_p^{(\gamma-1)/\gamma}}$ where $\gamma$ is specific heat ratio