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# Gas turbine efficiency.

## Gas turbine efficiency.

(OP)
Hello,

I am an student, and doing a project involving a gas turbine, and for that we need to calculate the different efficiencies of the gas turbine (compressor, thermal etc.)

I am currently stucked at the turbine efficiency.

Whenever i try to calculate the effieciencies I either get a number greater than one, or a number smaller than zero.

I am currently using this formule:

eff=(T[3]-T[4])/T[3]*(1-(1/(P[3]/P[4])^(gamma-1)/gamma

This one is equal -0.626 = -62.6%

I have also tried to use the formula using the polytropic efficiency. Doing so:

T3/T4 = (P3/P4)^p.eff*(gamma-1)/gamma solving for p.eff

eff = (1-(1/(P3/P4))^p.eff*(gamma-1)/gamma)/1-(1/(P3/P4))^(gamma-1)/gamma

which results in a negative number.

The formaly is from 50 years of gas turbines, a book I picked up at our library.
So far the system has been calculated as a brayton cycle. I have temperatures and pressures.
Anyone who can help? :)
Hope this post wont clasify me as a lazy student.
Replies continue below

### RE: Gas turbine efficiency.

I think you need to add a few parentheses, and make sure you are using absolute temperatures and pressures

"Nobody expects the Spanish Inquisition!"

### RE: Gas turbine efficiency.

for isentropic efficiency, I find:
eff,i = (T3-T4)/(T3-T4,ideal)
T4, ideal = T3*(P3/P4)^[(g-1)/g]
where g= Cp/Cv

for polytropic efficiency , I find
T4/T3=(P4/P3)^[(g-1)*eff,p/g]
so eff,p=g/(g-1)*Ln(T4/T3)/Ln(P4/P3)

absolute P and T should be used.
In real turbines that use staged combustion and cooling air inflow there sometimes is controversy on the value of T3 to use.

"Nobody expects the Spanish Inquisition!"

### RE: Gas turbine efficiency.

(OP)
Great, thanks!

The results seems much better now.

Mathias Kjeldahl

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