Computational Aerodynamics Questions & Answers | |
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Try again now.
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The problem with your logic is that $\partial \xi_x / \partial \xi$ is not zero because $\xi_x$ can vary along the the $\xi$ coordinate. Similarly, $\partial \eta_x / \partial \eta$ is also not zero because $\eta_x$ can vary along $\eta$. Good question, 2 points bonus.
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The problem in your math is here: $$ \overset{\sim}{W_0}+\overset{\sim}{W_1}=\frac{1}{(\epsilon + \beta_0)^2+(\epsilon + \beta_1)^2} $$ This is not correct. Rather: \begin{align} \overset{\sim}{W_0}+\overset{\sim}{W_1}&=\frac{\gamma_0}{(\epsilon + \beta_0)^2}+\frac{\gamma_1}{(\epsilon + \beta_1)^2}\\ &=\frac{\gamma_0 (\epsilon + \beta_1)^2+ \gamma_1 (\epsilon + \beta_0)^2}{(\epsilon + \beta_0)^2(\epsilon + \beta_1)^2}\\ \end{align}
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The cowl starts where the domain ends. So, there is no need to grid the cowl and there's hence no need to know the cowl length. The important thing is that your waves (either the Mach waves for the Prandtl-Meyer compression fan case or the shock waves for the 3-oblique-shock case) all meet at the same point and such a point is located exactly at the domain exit.
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Yes, for problem 3, there should be 3 oblique shocks and the pressure ratio across each shock should be the same. You need to design your inlet so that these 3 shocks appear, have all the same pressure ratio, and meet at one point. I am not sure what you don't understand. Can you explain better the problem?
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$\pi$ |