Mean flow boundary layer effects of hydrodynamic instability of impedance wall

S.W. Rienstra, M. Darau

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The Ingard-Myers condition, modelling the effect of an impedance wall under a mean flow by assuming a vanishing boundary layer, is known to lead to an ill-posed problem in time-domain. By analysing the stability of a mean flow, uniform except for a linear boundary layer of thickness h, in the incompressible limit, we show that the flow is absolutely unstable for h smaller than a critical hc and convectively unstable or stable otherwise. This critical hc is by nature independent of wave length or frequency and is a property of liner and mean flow only. An analytical approximation of hc is given for a mass-spring-damper liner. For an aeronautically relevant example, hc is shown to be extremely small, which explains why this instability has never been observed in industrial practice. A systematically regularised boundary condition, to replace the Ingard-Myers condition, is proposed that retains the effects of a finite h, such that the stability of the approximate problem correctly follows the stability of the real problem.
Originele taal-2Engels
Plaats van productieEindhoven
UitgeverijTechnische Universiteit Eindhoven
Aantal pagina's10
StatusGepubliceerd - 2010

Publicatie series

NaamCASA-report
Volume1012
ISSN van geprinte versie0926-4507

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  • Citeer dit

    Rienstra, S. W., & Darau, M. (2010). Mean flow boundary layer effects of hydrodynamic instability of impedance wall. (CASA-report; Vol. 1012). Technische Universiteit Eindhoven.