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f18_sp - F18 – Lecture Notes 1 Prandtl-Meyer Waves 2...

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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 flow 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 flow angle to be a flowfield variable, like M or V . Across each Mach wave of the fan, the flow 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 µ V V dV du µ M a c h w a v e d dV µ tan From the u- V and du- dV velocity triangles, it is evident that d and dV are related by dV 1 d = tan µ V assuming d is a small angle. With sin µ = 1 /M , we have 1 cos µ 1 − sin 2 µ 1 − 1 /M 2 M 2 − 1 = = = = tan µ...
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f18_sp - F18 – Lecture Notes 1 Prandtl-Meyer Waves 2...

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