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Unformatted text preview: F18 Lecture Notes 1. Prandtl-Meyer Waves 2. Shock-Expansion Theory (Supersonic Airfoils) Reading: Anderson 9.6, 9.7 Prandtl-Meyer Waves Wave ow relations An expansion fan, sometimes also called a Prandtl-Meyer expansion wave , can be considered as a continuous sequence of infinitesimal Mach expansion waves. To analyze this continuous change, we will now consider the ow angle to be a owfield variable, like M or V . Across each Mach wave of the fan, the ow direction changes by d , while the speed changes by dV . Oblique-shock analysis dictates that only the normal velocity component u can change across any wave, so that dV must be entirely due to the normal-velocity change du . 1 1 2 2 1 2 M M V V dV du u V u V V dV du M a c h w a v e d dV tan From the u- V and du- dV velocity triangles, it is evident that d and dV are related by dV 1 d = tan V assuming d is a small angle. With sin = 1 /M , we have 1 cos 1 sin 2 1 1 /M 2 M 2 1 = = = = tan...
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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.
- Fall '05