A simple turbojet engine $($zero bypass, no afterburner$)$ is designed for flight at $10$ km above sea level and Mach $0\mathrm{.}72.$ The compressor pressure ratio is $12$ and the maximum allowable engine temperature is $1650$ K $.$ You may assume standard air properties throughout, typical values of component efficiencies$1,$ and a fuel heating value of $\backslash (42,000\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kg$\}\backslash ).$ The target thrust is $\backslash (25,000\backslash$mathrm$\{$~N$\}\backslash )$ at the stated conditions.

a$)$ Calculate $($and state$)$ the required mass flow rate $($i$.$e$.,$ "size" the engine$).$

b$)$ Find the Thrust Specific Fuel Consumption under these conditions and state the value as $\backslash (\backslash$mathrm$\{$X$\}\backslash$mathrm$\{$hr$\}^\{-1\}\backslash ).$

c$)$ Examine the nozzle exit conditions. Is the nozzle properly matched, over$-$expanded or under$-$expanded?

d$)$ Run a parametric analysis showing the effect of changing the compressor pressure ratio and the peak temperature by $\backslash (\backslash$pm $20\backslash \%\backslash )$ from the design values. Show a contour plot of the effect of these changes with Thrust along the $\backslash ($ x $\backslash )$ axis and TSFC on the $\backslash ($ y $\backslash )-$axis. Add turbine exit temperature as an overlaid contour parameter $($Hint: this is one of those colorful plots discussed in class$).$

e$)$ Comment briefly on the results from step d$.$ What design changes seem to result in performance improvement? The same core engine specifications $2$ will now be used to develop a two$-$shaft turbofan that 'will also provide $\backslash (25,000\backslash$mathrm$\{$~N$\}\backslash )$ thrust at $10$ km and Mach $0\mathrm{.}72.$ Use typical values for component efficiencies, but force the fan, which will have a pressure ratio of $1\mathrm{.}4,$ to have an isentropic efficiency of $\backslash (0\mathrm{.}86^\{3\}\backslash ).$

f$)$ Seek the optimum bypass ratio that will give best fuel consumption.

g$)$ State your final results for mass flow rates, bypass ratio, and TSFC$,$ all at the stated flight conditions.

h$)$ Run both engines $($baseline turbojet and turbofan$)$ at sea level, static conditions, and state the thrusts generated $(2$ answers$).$ Comment on any anomalous results.

Please show no more than two GasTurb printouts in support.