# Reheat and Regeneration in Brayton cycle.

## Homework Statement

1. In a set-up of Brayton cycle , I know that the turbine has to give a greater magnitude of work output than the magnitude of the work done by the compressor (because the turbine has to run the compressor)....but the turbine and compressor are at the ends of the same shaft, then how how we make the turbine do more work?

2. The whole idea of reheat in Brayton cycle is to increase the efficiency of the cycle-- but efficiency = Wout/ Qin (Heat going in)....so the reheater, which provides extra heat energy increases drastically the value of the denominator, Qin...then how does the efficiency increase?

3. Lastly, In Brayton cycle, I know that reheat has the effect of reducing the efficiency of the cycle if not combined with regeneration...whereas in the Rankine, reheat doesn't need to be accompanied by regernartion...what is the basic reason for this difference?

## The Attempt at a Solution

2. I asked my prof about this...he said that the reheater forms a different system, so we don't consider the heat from the reheater while calculating efficiency of the cycle....but this doesn't make sense.

3. Both the Brayton and Rankine cycle are vapour cycles, so I don't understand why the difference exists.

## Answers and Replies

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"1. In a set-up of Brayton cycle , I know that the turbine has to give a greater magnitude of work output than the magnitude of the work done by the compressor (because the turbine has to run the compressor)....but the turbine and compressor are at the ends of the same shaft, then how how we make the turbine do more work?"

- Imagine a 50cc piston compressor feeding a 100cc piston air-engine. In between the two, air is heated to twice the displacement, under constant pressure. The two pistons have the same piston-head-area. Average force to the piston-heads during compression and expansion are therefore the same. The stroke of the motor is 2d, the compressor has stroke d. Work-total will be according to the work-law: W=F*d: W=(F*2d)-(F*d)= F*d (This is my choice of equation, presumably not the choice of scholars, but it illustrates well for understanding, I think.)

Similar in a turbine setup. The turbine has larger capacity, and is fed larger volume gas due to heating, than the compressor, therefore the package delivers positive work.

"2. The whole idea of reheat in Brayton cycle is to increase the efficiency of the cycle-- but efficiency = Wout/ Qin (Heat going in)....so the reheater, which provides extra heat energy increases drastically the value of the denominator, Qin...then how does the efficiency increase?"

-I don't know too much about Brayton- reheaters, but if you mean afterburners on jetfighters, I don't think they will help your milage, but they will add to kinetic energy (speed and mass) of exhaust, thus thrust/power, in a simple manner, after the turbine. One might say they increase the efficiency of the engine in terms of power to weight.

"3. Lastly, In Brayton cycle, I know that reheat has the effect of reducing the efficiency of the cycle if not combined with regeneration...whereas in the Rankine, reheat doesn't need to be accompanied by regernartion...what is the basic reason for this difference?"

- Again, not good at Brayton, but Rankine-reheating is simply an attempt to make Rankine more Carnot. In Carnot-ideal-cycle the expanding gas produces work while it is heated at constant pressure and temperature. In Rankine, by taking the gas out of the turbine at intermediate pressure and temperature to heat it, then put it back in another turbine to continue expanding it, the gas is "sort of" heated while expanding, "sort of" at constant temperature and pressure. This results in a "mended", slightly more ideal cycle, rather than expanding the gas through the turbine entirely without heating it, which was the previous approach.

Last expantion-stage is adiabatic, without heating, in both Carnot- and Rankine-cycles, to reach T-cold before condensation/cooling.