Question

This is problem 8-7 from El-Wakil’s Powerplant Technology book -- air at 14.696 psia, 40 degF, and with 65 percent relative humidity enters the compressor of a gas turbine cycle. The compressor and turbine have the same pressure ratio of 6 and polytropic efficiencies of 0.8 and 0.9, respectively. Water at 60 degF is injected into the compressor exit air, saturating it. Calculate (a) the air temperature after water injection (b) the percent increase in mass flow rate due to water injection, (c) the compressor work in Btus per pound mass of original air, and (d) the compressor work if water is injected during the compression process to the same temperature as (a), in Btus per pound mass of original air. Use a constant c_p = 0.24 Btu/lb_mdegRankine.

Answer 1

Given that,

Air at pressure , P₁ = 14.696 Psi

                        T₁ = 40⁰ F

               relative humididty , = 0.65

Pressure ratio , r = 6

   _n = 0.8 & 0.9

    T₂ = 60⁰ F

a) Air temp after injection, T₃ = ?

b) % increase in mass flow rate= ?

c) Compressor work during original air =?

d) Compressor work after injection =?

And also use , C_p = 0.24 Btu / lb ⁰ Rankine

a) we know that,

    _n = 0.8

    T₃ - T₁ / ₂ - T₁ = 0.8

    T₃ - 40 / 60 - 40 = 0.8

    T₃ - 40 = 20 X 0.8 = 16

     T₃ = 56⁰F

b) % increase in mass flow rate =?

we know that , for case 1 Q = mC_p ( T₃ - T₁ )

                      Q = m X 0.24 ( 56 - 40)

                      m = 0.26 Q

   For case 2 , Q = mC_p (T₂ - T₁)

                       Q = m X 0.24( 60 - 40)

                     m = 0.2Q

        The % change in m = 71.4%

c)    Compresssor work , W = C_p ( T₂ - T₁ )

                                         = 0.24 ( 60 - 40 )

                                         = 4.8 Btu/lb

d) Compressor work after water injected , W = C_p (T₃ - T₁ )

                                                                 = 0.24 ( 56 - 40)

                                                                  = 3.84 Btu / lb