# Efficiency of the Regenerative Brayton Cycle

Therefore:
Ideal Regenerator:

#### Thermal Efficiency

:
Assume: IG, constant CP<. and CV
1st Law, Combustor:
1st Law, Turbine:
1st Law, Compressor:
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### Ch 9, Lesson F, Page 3 - Efficiency of the Regenerative Brayton Cycle

• Thermal efficiency is desired over required, right ?
• Be careful with the signs on the work terms because Wcomp is a negative number because work is done ON the system.
• Next, let’s apply the 1st Law to the combustor, the turbine and the compressor, individually.
• These equations can be simplified based on the cold air-standard assumptions.
• That is, the air behaves as an ideal gas and the heat capacities are constant at their values at 25oC.
• Now, let’s think about the regenerator.
• In an infinitely large regenerator, stream 2 would be heated all the way up to the temperature of stream 5 before it leaves the heat exchanger.
• Let’s assume we such an infinitely large or ideal regenerator.  That means that T3 = T5.
• What does this mean in terms of the 1st Law for the turbine and the combustor ?
• It means that QH must be equal to Wturb.  So, what does that tell us about the thermal efficiency of the cycle ?
• Well, when we replace QH with Wturb in the thermal efficiency equation and substitute the 1st Law  for the work of the turbine and the compressor, good things start to happen.
• The mass flow rate and heat capacity cancel out and we are left with only temperatures.
• Now, we need a little algebraic slight of hand to put this equation into a form that is easier to understand.
• Let’s factor a T1 out of the numerator and a T4 out of the denominator.
• But why did we do this.  Flip the page and see.