(Solved): (20 points) A non-afterburning turbojet is being designed for operation at an altitude of 15km a ...

(20 points) A non-afterburning turbojet is being designed for operation at an altitude of $15\mathrm{km}$ and a Mach number of 1.8. The maximum stagnation temperature at the inlet of the turbine is $1500\mathrm{K}$. The fuel is a jet fuel having a LHV of $43124\mathrm{kJ}/\mathrm{kg}$ and ${\mathrm{f}}_{\mathrm{st}}$ is 0.06 . The following efficiencies apply at this Mach number: $\begin{array}{lll}{?}_{\mathrm{d}}=0.9& {?}_{\mathrm{b}}=0.98& {?}_{\mathrm{t}}=0.92\\ {?}_{\mathrm{c}}=0.9& {\mathrm{r}}_{\mathrm{b}}=0.97& {?}_{\mathrm{n}}=0.98\end{array}$ Use a gamma value of 1.4 up to the burner, and a value of 1.3 for the rest of the engine. Assume $\mathrm{R}$ is $0.287\mathrm{kJ}/\mathrm{kgK}$ throughout the engine. Plot the specific thrust, TSFC $,{?}_{th},{?}_p$, and ${?}_o$ as a function of $r_c$, the total pressure ratio across the compressor. Is there an optimum $r_c$ that minimizes TSFC? Is there an optimum $r_c$ that maximizes specific thrust? Consider a range of $r_c$ from 2 to 60 . Assume the exhaust is ideally expanded. Also plot the nozzle area ratio as a function of ${\mathrm{r}}_{\mathrm{c}}$