A gas turbine power plant burns ethane gas in excess air,

producing $250MW$ of output power. It employs a single$-$

shaft gas turbine reheat cycle and is characterised by the

following data:

Compressor pressure ratio $=30$

Ambient conditions $=1$ bar &$300K$

Isentropic efficiency of compressor $=0\mathrm{.}9$

Isentropic efficiencies of turbines $=0\mathrm{.}9$ each

Inlet temperature of both turbines $=1800K$

Pressure loss in both combustors $=3\%$ of entry

pressure

Turbine exhaust pressure for second turbine $=1\mathrm{.}0$

bar

Combustion efficiency of both combustors $=0\mathrm{.}96$

Lower calorific value of fuel $=42M\frac{J}{k}g$

Take $C_p$ of air to be $1\mathrm{.}005kJk{g}^{-1}{K}^{-1}$&$C_p$ of the products to

be $1\mathrm{.}16k{J}^{-1}k{g}^{-1}{K}^{-1}.$ You can assume the combustion is

isobaric and optimal pressure ratio for turbines.

$($i$)$ Sketch the schematic diagram and show the process

on a T$-$s diagram

Calculate the following :

$($ii$)$ Equivalence ratio

$($iii$)$ The plant specific work in $k\frac{J}{k}g.$

$($iv$)$ The actual thermal efficiency.

$($v$)$ Quantify the benefits of reheating in terms of

a$)$ specific work and b$)$ efficiency.

$($vi$)$ Imagine you need to increase the thermal efficiency

of the turbine reheat cycle. Suggest a way this might

be achieved and then design a new cycle $($showing

schematic and T$-$S diagram$)$ and evaluate its

performance $($thermal efficiency$).$ Also state its new

equivalence ratio for a fixed turbine inlet temperature

of $1800K.$

$($vii$)$ Discuss how the performance of the cycle proposed

in part $($vi$)$ modifies with changes in turbine inlet

temperature. Please state all assumptions, and state

the limitation of this new cycle.

Note: If required, assume a heat exchanger effectiveness of $0\mathrm{.}8$

for parts $($vi$)$ and $($vii$).$