Unit 6: Air Standard Cycles

Air Standard Cycles

• Air standard cycles are used to model the operation of internal combustion engines.
• Assumptions:
  • The engine operates on a closed cycle with a fixed mass of air.
  • The combustion process is replaced by an equivalent energy addition process.
  • The exhaust process is replaced by an equivalent energy rejection process.
  • The air behaves like an ideal gas with constant specific heat.

Otto Cycle

• Named after Nikolaus A. Otto.
• Consists of four processes: suction, compression, expression, and exhaust.
• Assumptions:
  • Ideal gas behavior.
  • Constant specific heat capacities.
  • No heat transfer during compression and expansion strokes.
  • No friction or other losses.
• Efficiency calculation:
  • Work done: W = pdV = (p3V3 - p4V4) + (p2V2 - p1V1).
  • Heat input: Q_in = m * cp * (T3 - T2).
  • Heat output: Q_out = m * cp * (T4 - T1).
  • Efficiency: η = W / Q_in = (1 - (Q_out / Q_in)).
• Theoretical efficiency: η = 1 - (1/r)^(-1), where r is the compression ratio.

Diesel Cycle

• Models the operation of a diesel engine.
• Consists of four processes: compression, fuel injection and combustion, expansion, and exhaust.
• Assumptions:
  • Ideal gas behavior.
  • Constant specific heat capacities.
  • No heat transfer during compression and expansion strokes.
  • No friction or other losses.
• Efficiency calculation:
  • Work done: W = pdV = (p3V3 - p4V4) + (p2V2 - p1V1).
  • Heat input: Q_in = m * cv * (T3 - T2).
  • Heat output: Q_out = m * cv * (T4 - T1).
  • Efficiency: η = W / Q_in = (1 - (Q_out / Q_in)).
• Theoretical efficiency: η = 1 - (1/r)^(-1) * (1 - (1/)^(-1)), where r is the compression ratio and is the cutoff ratio.

Dual Cycle

• Combines elements of the Otto and Diesel cycles.
• Consists of four processes: compression, fuel injection and combustion, expansion, and exhaust.
• Assumptions:
  • Ideal gas behavior.
  • Constant specific heat capacities.
  • No heat transfer during compression and expansion strokes.
  • No friction or other losses.
• Efficiency calculation:
  • Work done: W = pdV = (p3V3 - p4V4) + (p2V2 - p1V1).
  • Heat input: Q_in = m * cv * (T3 - T2).
  • Heat output: Q_out = m * cv * (T4 - T1).
  • Efficiency: η = W / Q_in = (1 - (Q_out / Q_in)).
• Theoretical efficiency: η = 1 - (1/r)^(-1) * (1 - (1/)^(-1)) * (T2/T3).

Brayton Cycle

• Models the operation of a gas turbine engine.
• Consists of four processes: compression, isobaric heat addition, expansion, and isobaric heat rejection.
• Assumptions:
  • Ideal gas behavior.
  • Constant specific heat capacities.
  • No heat transfer during compression and expansion strokes.
  • No friction or other losses.
• Efficiency calculation:
  • Work done: W = pdV = (p3V3 - p4V4) + (p2V2 - p1V1).
  • Heat input: Q_in = m * cp * (T3 - T2).
  • Heat output: Q_out = m * cp * (T4 - T1).
  • Efficiency: η = W / Q_in = (1 - (Q_out / Q_in)).
• Theoretical efficiency: η = 1 - (1/PR)^(-1) * (TR - 1) / ( (TR - 1)), where PR is the pressure ratio and TR is the temperature ratio.

Comparison of Cycles

• Auto (Otto) Cycle: lower efficiency (~25-30%), lower mean effective pressure (MEP), and lower work output.
• Diesel Cycle: higher efficiency (~40-45%), higher mean effective pressure (MEP), and higher work output.
• Dual Cycle: efficiency between Otto and Diesel cycles (~35-40%), mean effective pressure (MEP) between Otto and Diesel cycles, and work output between Otto and Diesel cycles.

Rankine Cycle

• Models the operation of a steam turbine power plant.
• Consists of four processes: isentropic compression, isobaric heat addition, isentropic expansion, and isobaric heat rejection.
• Modified Rankine Cycle:
  • Reheat: increases the average temperature of heat addition.
  • Regeneration: reduces the temperature difference between heat addition and rejection.
  • Superheating: increases the steam temperature and reduces condensation losses.

Comparison of Rankine and Carnot Cycles

• Rankine Cycle: used in steam power plants, involves water as the working fluid, and has a typical efficiency of 33-40%.
• Carnot Cycle: ideal cycle, not practical for implementation, involves an ideal gas as the working fluid, and has a maximum possible efficiency of η = 1 - (Tc/Th).
• Comparison: Rankine cycle is more practical and widely used, while Carnot cycle is ideal and theoretical.

Learn about the approximations made in thermodynamic analysis of internal combustion engines, including closed cycle operation and energy addition/rejection processes.