Question

In: Mechanical Engineering

a simple ideal Brayton cycle with air as the working fluid has a pressure ratio of...

a simple ideal Brayton cycle with air as the working fluid has a pressure ratio of 10. The air enters the compressor at 520 R and the turbine at 2000 R. Accounting for the variation of specific heats with temperature, determine (a) the ait temperature at the compressor exit, (b) the back work ratio, and (c) the thermal efficiency.

Expert Solution

Pressure ratio r_p = 10

Compressor inlet temperature T₁= 520R

Turbine inlet temperature to T₃ = 2000 R

Since we are considering variable specific heats the specific heat at constant pressure and specific heat at constant volume will be different at different temperatures.

At T₁= 520R from ideal gas properties of air tables

At T₃ = 2000 R from ideal gas properties of air tables

Process 1-2 is isentropic compression

At P_r2 = 12.47 from ideal gas properties of air

(b)

Process 3-4 is isentropic expansion

We know that

At P_r4 = 17.4 from ideal gas properties of air

The work required by compressor is expressed as

The work done by turbine is expressed as

The back work ratio

(c) The thermal efficiency

Heat supplied

Net work is expressed as

Therefore the thermal efficiency

samet mamat answered 3 years ago

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