$333\_$HW$\_9.$pdf $(173$ KB$)$

Problem $5$: $(30$ Marks$)$ A gas turbine power plant operates on the simple Brayton eycle with air as the working fluid and delivers $32$ MW of power. The minimum and maximum temperatures in the cycle are $310$ and $900$ K $,$ and the pressure of air at the compressor exit is $8$ times the value at the compressor inlet. Assuming an isentropic efficiency of $80$ percent for the compressor and $86$ percent for the turbine, determine the mass flow rate of air through the cycle. Account for the variation of specific heat with temperature.

a$.$ Draw the Brayton cycle on a Ts diagram such that the start of the compression process is called state $1$ and so on$.$ Include both the adiabatic and isentropic compression and expansion processes. $(5$ Marks$)$

b$.$ The enthalpy at the beginning of the compression. $(2$ Marks$)$

c$.$ The isentropic enthalpy after the compression process. $(3$ Marks$)$ Note: Feel free to use an online interpolation calculator.

d$.$ The enthalpy at the end of the heat addition process. $(2$ Marks$)$

e$.$ The isentropic enthalpy after the expansion process. $(3$ Marks$)$

f$.$ Amount of the heat input. $(2$ Marks$)$

g$.$ The actual turbine work output. $(4$ Mark$)$ Ans. $355\mathrm{.}7k\frac{J}{k}g$

h$.$ The actual compressor work input, $(4$ Mark$)$ Ans. $315\mathrm{.}025k\frac{J}{k}g$

i$.$ Thermal efficiency of the cycle? $(2$ Marks$)$

j$.$ The mass flow rate of the air? $(3$ Marks$)$ Ans: $786\mathrm{.}6k\frac{g}{s}$