Question

The rate of heat addition to an air-standard Brayton cycle is 3.4 times 109 Btu/h. The pressure ratio for the cycle is 15 and the minimum and maximum temperatures are 520°R and 3000°R, respectively. Determine (a) the thermal efficiency of the cycle. (b) the mass flow rate of air, in lb/h. (c) the net power developed by the cycle, in Btu/h.

Answer 1

The cycle will have two isobaric and two reversible processes

T1=520R. T3= 3000R

rp= compression ratio = 15, Y= ratio of specific heats for air = 1.4

Thermal efficiency = 1- 1/(r_p)^(Y-1)/Y    =1 -1/(15)^0.4/1.4= 0.5387 or 53.87%

T2/T1= (rP) (Y-1)/Y= 15 (0.4/1.4) =2.17, T2= 520*2.17= 1128.4 R

T3/T4= 1.67, T3= 3200/1.67= 1916 R

Cp =0.244 Btu/lb.R

WC= 0.244*(1128.4-520)= 148 Btu/lb

WT= 0.244*(3000-1916)=264.49 Btu/lb

Work ratio = (WT-WC)/WT= (264.49-148)/264.49=0.44

Power output= 3.4*109*0.44 btu/hr=163.06 Btu/hr

m*Cp*(1916-1128.4)= 3.4*109

Cp =0.244

m = 5.74 lb/hr