
#1
Feb1211, 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 nonafterburning 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]). Ondesign conditions are as follows: [tex] \pi_{cR}=15, M_{oR}=2.0, \tau_{\lambda{R}}=7.0 [/tex] Find the required ratio of nozzle throat area (offdesign) to nozzle throat area (ondesign) for the engine operating at the same flight Mach number (2.0) but at the offdesign condition such that [tex]\tau_\lambda=6.0[/tex]. My work: Using Mach number 2 Ondesign [tex] \tau_{rR}=0.8, \pi_{rR}=.458, \tau_{cR}=2.168, \tau_{tR}=.867, \pi_{tR}=.607 [/tex] [tex] \tau_{tR}=1\frac{\tau_{rR}}{\tau_{\lambda{R}}}(\tau_{cR}1)=1\frac{.8}{7}(2.1681)=.867 [/tex] Offdesign Same values as ondesign because Mach number does not change. [tex] \tau_{r}=0.8, \pi_{r}=.458, \tau_{c}=2.168, \tau_{t}=.867, \pi_{t}=.607 [/tex] Using given [tex]\lambda=6[/tex] for offdesign: [tex] \tau_t=1\frac{\tau_r}{\tau_\lambda}(\tau_c1)=1\frac{.8}{6}(2.1681)=.844 [/tex] Hence, the area ratio: [tex] \frac{A_8}{A_{8R}}=\frac{\tau_t^\frac{1}{2}}{\pi_T}\frac{\pi_{tR}}{\tau _{tR}^\frac{1}{2}}=.9866. [/tex] Is this correct? This seems a little too easy. 


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