solve this problem step by step plz. thank u! A jet engine is modeled as a seria

Question

solve this problem step by step plz. thank u!

A jet engine is modeled as a serial combination of a compressor, an adiabatic constant pressure combustor, and a turbine (in that order). Air (considered to have a variable specific heat) is compressed through a compression pressure ratio of 8.25:1. Air enters the compressor at 14.7 psia and 60 degree F. Air leaves the combustor at 2.200 degree R. The compression isentropic efficiency is 83, and the turbine isentropic efficiency is 85%. An engineer claims that 5% of the air should be bypassed around the compressor and combustor, and used to cool the engine walls in a double-wall arrangement. If that is done, the air leaving the combustor can be increased in temperature 250 degree F, and the combustor pressure increased by 5 psi. It is claimed that the engine will produce more thrust. Assuming that the bypassed air produces no thrust, and ignoring fuel mass, is the engineering correct?

Explanation / Answer

Without bypass:

For compressor:

P2 / P1 = r^k

P2 / P1 = 8.25^1.4 = 19.19

T2s / T1 = (P2 / P1)^((k-1)/k)

T2s / (60+460) = 19.19^((1.4-1)/1.4)

T2s = 1209 R

Compressor Eff = (T2s - T1) / (T2 - T1)

0.83 = (1209 - 520) / (T2 - 520)

T2 = 1351 R

Compressor work = m*Cp*(T2 - T1) = m*Cp*(1351 - 520) = 831*m*Cp

For turbine: T3 / T4s = (P3 / P4)^((k-1)/k) = (P2/P1)^((k-1)/k)

2200 / T4s = 19.19^((1.4-1)/1.4)

T4s = 946 R

Turbine eff = (T3 - T4 ) / (T3 - T4s)

0.85 = (2200 - T4) / (2200 - 946)

T4 = 1134 R

Turbine work = m*Cp*(T3 - T4) = m*Cp*(2200 - 1134) = 1066*m*Cp

Thrust = Turbine work - compressor work

Thrust = 1066*m*Cp - 831*m*Cp

Thrust = 235*m*Cp

With Bypass:

P2 = 14.7*19.19+5 = 287.1 psi

T2s/T1 = (287.1/14.7)^((1.4-1)/1.4)

T2s = 1216 R

T2 = (1216-520)/0.83 + 520 = 1358 R

Wcomp = (0.95*m)*Cp*(1358-520) = 838 *(m*0.95)*Cp = 796.1*m*Cp

T3/T4s = (287.1/14.7)^((1.4-1)/1.4)

(2200+250) / T4s = (287.1/14.7)^((1.4-1)/1.4)

T4s = 1048 R

T4 = 2450 - (2450 - 1048)*0.85 = 1258 R

Wturb = (0.95*m)*Cp*(2450 - 1258) = 1132.4*m*Cp

Thrust = (1132.4-796.1)*m*Cp = 336.3*m*Cp

Hence, with Bypass, Thrust will be more.

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