### Abstract

Original language | English |
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Place of Publication | Eindhoven |

Publisher | Technische Universiteit Eindhoven |

Number of pages | 15 |

Publication status | Published - 2010 |

### Publication series

Name | CASA-report |
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Volume | 1069 |

ISSN (Print) | 0926-4507 |

### Fingerprint

### Cite this

*Boundary layer thickness effects of the hydrodynamic instability along an impedance wall*. (CASA-report; Vol. 1069). Eindhoven: Technische Universiteit Eindhoven.

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*Boundary layer thickness effects of the hydrodynamic instability along an impedance wall*. CASA-report, vol. 1069, Technische Universiteit Eindhoven, Eindhoven.

**Boundary layer thickness effects of the hydrodynamic instability along an impedance wall.** / Rienstra, S.W.; Darau, M.

Research output: Book/Report › Report › Academic

TY - BOOK

T1 - Boundary layer thickness effects of the hydrodynamic instability along an impedance wall

AU - Rienstra, S.W.

AU - Darau, M.

PY - 2010

Y1 - 2010

N2 - Abstract: The Ingard-Myers condition, modelling the effect of an impedance wall under a mean fl ow by assuming a vanishingly thin boundary layer, is known to lead to an ill-posed problem in time-domain. By analysing the stability of a linear-then-constant mean flow over a mass-spring-damper liner in a 2D incompressible limit, we show that the fl ow 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, which is complemented by a contourplot covering all parameter values. 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. Keywords: Aeroacoustics, Boundary layer stability, Impedance wall.

AB - Abstract: The Ingard-Myers condition, modelling the effect of an impedance wall under a mean fl ow by assuming a vanishingly thin boundary layer, is known to lead to an ill-posed problem in time-domain. By analysing the stability of a linear-then-constant mean flow over a mass-spring-damper liner in a 2D incompressible limit, we show that the fl ow 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, which is complemented by a contourplot covering all parameter values. 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. Keywords: Aeroacoustics, Boundary layer stability, Impedance wall.

M3 - Report

T3 - CASA-report

BT - Boundary layer thickness effects of the hydrodynamic instability along an impedance wall

PB - Technische Universiteit Eindhoven

CY - Eindhoven

ER -