(h5=932.93 kj/kg. S0(T)=2.84856 kj/kg/K) at a tempreture of 900K and flow rate o
ID: 2994315 • Letter: #
Question
(h5=932.93 kj/kg. S0(T)=2.84856 kj/kg/K) at a tempreture of 900K and flow rate of 40 kg/s. Air at 500K (h2= 503.02 kj/kg, S0(T) = 2.21952 kj/kg/K) enters the compressor at flow rate of 40 kg/s. The states regenerator effectiveness is 0.85. the compressor discharge air and turbine exhaust are streams but with the same flow rate. Assume a negligible pressure drop for each stream.
(A) Determine the exit air temprature of the unknownregenerator outlet streams.
(B) Determine the heat transfer rate between the two streams.
(C) Determine the exergy destruction rate assuming T0 = 298K
Turbine exhaust gas (assume the properties of air) enters a gas turbine regenerator (h 5 = 932.93 kJ/kg, S 0 (T) = 2.84856 kJ/kg/K) at a temperature of 900 K and a flow rate of 40 kg/s. Air at 500 K (h 2 = 503.02 kJ/kg, S 0 (T) = 2.21952 kJ/kg/K) enters the regenerator at a flow rate of 40 kg/s. The stated regenerator effectiveness is 0.85. The compressor discharge air and turbine exhaust are separate streams but with the same flow rate. Assume a negligible pressure drop for each stream. (a) Determine the exit air temperature of the unknown regenerator outlet streams. (b) Determine the heat transfer rate between the two streams. (c) Determine the exergy destruction rate assuming T 0 = 298 K.Explanation / Answer
Assume constant cp=1.05 kJ/kgK for both streams
effectiveness= Q/Qmax
= m*cp(T3-T2) /(m*cp(T5-T2)
Since mass flow rates are same
0.85 = ( T3 - 500 ) / (900-500)
T3 = 840 K
Also, m*cp*(T3-T2) * m*cp(T5-T6)
840-500 = 900-T6
T6=560K
heat transer rate = 40*1.05*(840-500) = 14.28 MW
TdS=dh = cp*dT
dS=cp*dT/T
delta S = cp*ln(T2/T1)
Exergy destruction = T0 * S_gen
S_gen= m(S_out-S_in)
= m*cp*ln(To/Ti)
S_gen= 40*1.05*ln(560/900) + 40*1.05*ln(840/500) = 1.862 KJ/K
Exergy destruction = 298*1.862 = 554.91 KJ
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