Mechanical engineering

Do not copy chegg solution and also not ai solution that one's are wrong do it by yourself

A schematic layout of a combined cycle gas$-$steam power plant is shown in Fig. $1.$ The toping

cycle is a simple gas turbine that operates on a Brayton cycle with a capacity of $131$ MW and

$35\%$ electrical efficiency. The mass flow rate of air $($at $27C)$ and the exhaust gases are $24000$

$k\frac{g}{m}in$ and $28500k\frac{g}{m}in,$ respectively. The temperature of the exhaust gases at the inlet of

the heat recovery boiler is $560C.$ The minimum thresholds of the gas turbine exhaust gas

outlet temperature of $120C$ must be maintained to avoid condensation in ducts and piping.

Assuming that the heat recovery boiler can recover $58\%$ of the available heat in the exhaust

gas and the specific heat for the exhaust gas is $1\mathrm{.}0163k\frac{J}{k}g.K.$

The steam produced by the exhaust gas boiler at a rate of $226,800k\frac{g}{h}$ is introduced into a

steam turbine at a temperature of $520C$ and a pressure of $6$ MPa $.$ Steam exits the turbine at

a pressure of $15$ kPa and enters the pump as a saturated liquid. Assuming an isentropic

efficiency for the pump of the Rankine cycle is $90\%$ and that of the turbine is $95\%.$ The inlet

water temperature from the cooling tower to the condenser is $30C,$ and the exit temperature

of the water is $70C.$ The specific heat of water is $4\mathrm{.}18k\frac{J}{k}g.K.$ Kinetic and potential energy

and exergy are negligible. The dead state properties are taken as $25C$ and $101$ kPa $.$

$($a$)$ Determine:

$($i$)$ the net power output of the steam turbine $($units: MW$).$

$($ii$)$ the combined cycle power output $($units: MW$),$

$($iii$)$ the combined cycle efficiency $($units: $\%),$

$($iv$)$ the exergy input to the steam turbine $($units: MW$)$

$($v$)$ the exergy output from the steam turbine $($units: MW$)$

$($vi$)$ the exergy destruction in the exhaust gas boiler $($units: MW$)$

$($vii$)$ the exergy destruction in the steam turbine $($units: MW$)$

$($viii$)$ the exergy destruction in the condenser $($units: MW$)$

$($b$)$ Assuming the exhaust gas boiler has an overall heat transfer coefficient of $1750\frac{W}{m^2}*K,$

determine the heat transfer area for the exhaust gas boiler by choosing the suitable heat

exchanger type. Justify your selection of the heat exchange device.

$($c$)$ Discuss the strategies to improve the performance of a simple gas turbine and a simple

Rankine cycle of the steam turbine in a combined cycle gas$-$steam turbine power plant.

Fig. $1$: Gas turbine$-$steam turbine combined cycle power plant.