### Samenvatting

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-2 | Engels |
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Plaats van productie | Eindhoven |

Uitgeverij | Technische Universiteit Eindhoven |

Aantal pagina's | 10 |

Status | Gepubliceerd - 2010 |

### Publicatie series

Naam | CASA-report |
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Volume | 1012 |

ISSN van geprinte versie | 0926-4507 |

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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.