Question

A gas turbine engine is considered in a race car design. The engine operates on two stages of compression with intercooling and two stages of expansion. The pressure ratio across each stage of the compressor and the turbine is 7. The air enters each stage of the compressor at 300K and each stage of the turbine at 1300K. Using air standard assumptions determine:

Thermal efficiency and back work ratio if no regenerator is used;
Thermal efficiency and back work ratio if a regenerator with effectiveness of 90 % is used

Answer 1

Given

· The engine operates on two stages of compression with intercooling and two stages of expansion.

· The pressure ratio across each stage of the compressor and the turbine, P₂/P₁ = 7

· Temperature at the compressor, T₁ = 300K

· Temperature at each stage of the turbine, T₅ = T₇ = 1300 K

1. No generator is used

From the thermodynamics steam table, for T₁ = 300 K

At the value of Pr₂ = 9.702, we can determine that

For T₅ = T₇ = 1300 K,

At the value of Pr₆ = 47.2714, we can determine that

The work into the compressor is given as

The work into the turbine is given as

Therefore, the back-work ratio is

The energy into the cycle is given as

The efficiency is given as

2. A regenerator with 90% effectiveness is used

With a generator in place, the work of the turbine stages and the compressor stages remains the same, therefore the back-work ratio is also the same.

But the energy input in the form of heat will change.

The efficiency with 90% effectiveness is

Note:

· P_r = Relative Pressure

· h = Specific Enthalpy