Homework check (too easy) with on/off design analysis for variable area turbojet

by roldy
Tags: analysis, check, design, homework, on or off, turbojet, variable
roldy is offline
Feb12-11, 02:25 PM
P: 194
I'm studying on variable area turbojet problems in the book and I can't seem to get past this problem.

Consider the performance of an ideal non-afterburning turbojet with flow at station 4(turbine entrance) and station 8 (nozzle throat) choked. A4 is fixed and A8 is varied in order to maintain constant compressor total pressure ratio ([tex]\pi_c[/tex]).

On-design conditions are as follows:
\pi_{cR}=15, M_{oR}=2.0, \tau_{\lambda{R}}=7.0

Find the required ratio of nozzle throat area (off-design) to nozzle throat area (on-design) for the engine operating at the same flight Mach number (2.0) but at the off-design condition such that [tex]\tau_\lambda=6.0[/tex].

My work:

Using Mach number 2


\tau_{rR}=0.8, \pi_{rR}=.458, \tau_{cR}=2.168, \tau_{tR}=.867, \pi_{tR}=.607



Same values as on-design because Mach number does not change.
\tau_{r}=0.8, \pi_{r}=.458, \tau_{c}=2.168, \tau_{t}=.867, \pi_{t}=.607

Using given [tex]\lambda=6[/tex] for off-design:


Hence, the area ratio:
\frac{A_8}{A_{8R}}=\frac{\tau_t^\frac{1}{2}}{\pi_T}\frac{\pi_{tR}}{\tau _{tR}^\frac{1}{2}}=.9866.

Is this correct? This seems a little too easy.
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