TY - GEN

T1 - Reprint of: Mean flow boundary layer effects of hydrodynamic instability of impedance wall

AU - Rienstra, S.W.

AU - Darau, M.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

U2 - 10.1016/j.piutam.2010.10.014

DO - 10.1016/j.piutam.2010.10.014

M3 - Conference contribution

T3 - Procedia IUTAM

SP - 124

EP - 132

BT - IUTAM Symposium on Computational Aero-Acoustics for Aircraft Noise Prediction (Southampton, UK, March 29-31, 2010)

A2 - Astley, R.J.

A2 - Gabard, G.

ER -