Question

For an ideal gas-turbine cycle with two stages of compression and two stages of expansion, the pressure ratio across each stage of the compressor and turbine is 3. The air enters each stage of the compressor at 300 K and each stage of the turbine at 1200K. Using variable specific heats, determine the back work ratio and the thermal efficiency of the cycle, assuming

(a)no regenerator is used,

(b)a regenerator with 75% effectiveness is used.

Answer 1

A)

Work done in the first compressor =

where

• T1 = inlet temp of compressor 1 = 300 K
• T2 = outlet temp of compressor 2 =
  • PR = pressure ratio across compressor 1 = 3
  • = 1.4 (for air)
• Cp1 = specific heat at constant pressure at compressor inlet = 1.007 kJ/kgK
• Cp2 = specific heat at constant pressure at compressor outlet = 1.013 kJ/kgK

Work done by the second compressor = Work done by the first compressor = 113.86 kJ/kg

Total compressor work = 2 x 113.86 = 227.72 kJ/kg

Work done by the first turbine =

where

• T5 = inlet temp of turbine 1 = 1200 K
• T6 = outlet temp of turbine 2 =
  • PR = pressure ratio across compressor 1 = 3
  • = 1.4 (for air)
• Cp5 = specific heat at constant pressure at turbine inlet = 1.173 kJ/kgK
• Cp6 = specific heat at constant pressure at turbine outlet = 1.116 kJ/kgK

Work done by the second turbine = Work done by the first turbine = 429.18 kJ/kg

Total turbine work = 2 x 429.18 = 858.36 kJ/kg

Total heat input =

where

• Cp5 = specific heat at constant pressure at turbine 1 inlet = 1.173 kJ/kgK
• Cp4 = specific heat at constant pressure at compressor outlet = 1.013 kJ/kgK
• Cp7 = specific heat at constant pressure at turbine 2 inlet = 1.173 kJ/kgK
• Cp6 = specific heat at constant pressure at turbine 1 outlet = 1.116 kJ/kgK
• T5 = 1200 K
• T4 = 410.62 K
• T7 = 1200 K
• T6 = 876.72 K

Q = 1420.82 kJ/kg

W(net) = W(turb-total) - W(comp-total) = 858.36 - 227.72 = 630.64 kJ/kg

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Back Work Ratio =

Thermal efficiency =

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B)

Everything remains the same regarding compressor and turbine:

• W(turbine-total) = 858.36 kJ/kg
• W(comp-total) = 227.72 kJ/kg
• W(net) = 630.64 kJ/kg

Total heat input =

where

• Cp5 = specific heat at constant pressure at turbine 1 inlet = 1.173 kJ/kgK
• Cp9 = specific heat at constant pressure at regenerator outlet = 1.089 kJ/kgK
• Cp7 = specific heat at constant pressure at turbine 2 inlet = 1.173 kJ/kgK
• Cp6 = specific heat at constant pressure at turbine 1 outlet = 1.116 kJ/kgK
• T5 = 1200 K
• T9 =
  • T8 = 876.72 K
  • T4 = 410.62 K
  • = effectiveness of regenerator used
• T7 = 1200 K
• T6 = 876.72 K

Q = 1008.93 kJ/kg

W(net) = W(turb-total) - W(comp-total) = 858.36 - 227.72 = 630.64 kJ/kg

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Back Work Ratio = [remains same]

Thermal efficiency =

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