can anyone solve this problem??? A jet engine is modeled as a serial combination

Question

can anyone solve this problem???

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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