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does anyone know, how I can find a transonic airfoil (high subsonic, Ma=0.88) with a high critical mach number?

I know that if I know c,0,min = minimal pressure coefficient of the airfoil, then I can calculate the critical mach number.

But when I use Xfoil for plotting the pressure distribution, I only get a nice picture, but I can not write out the data for the pressure distribution. otherwise I could determine the critical mach number.

Maybe someone has some hints for me?

Thank you

Lucas

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    $\begingroup$ If you enter the flow conditions correctly, XFOIL will plot a dashed line at the critical c$_p$. $\endgroup$
    – Peter Kämpf
    Feb 29, 2020 at 12:00

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First I have to say that XFOIL is not the right tool for such a high Mach number. Professor Drela has written ISES to address the shortcomings of XFOIL at transsonic speed.

Next, the critical Mach number is well defined as $$c_{p_{crit}} = \frac{2}{\gamma\cdot Ma_{\infty}^2}\cdot\left(\left(\frac{2}{\gamma+1} + \frac{\gamma-1}{\gamma+1}\cdot Ma_{\infty}^2\right)^{\frac{\gamma}{\gamma-1}}-1\right)$$ which can be simplified for air as $$c_{p_{crit}} \approx \frac{1}{0.7\cdot Ma_{\infty}^2}\cdot\left(\left(\frac{5+Ma_{\infty}^2}{6}\right)^{3.5}-1\right)$$

$\gamma$ is the ratio of specific heats and is 1.405 for air.

For $Ma_{\infty}$ = 0.88 this is -0.23 which is too little to even accommodate a moderately thick airfoil without supersonic flow. Therefore, your wing needs sweep to function well. Even then, I recommend a supercritical airfoil which will have supersonic areas at this speed but without a big drag penalty. Take your pick.

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It sounds like you're looking for a Supercritical section, so this NASA report on Supercritical Airfoils may be of use.

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