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.
|Titel||IUTAM Symposium on Computational Aero-Acoustics for Aircraft Noise Prediction (Southampton, UK, March 29-31, 2010)|
|Redacteuren||R.J. Astley, G. Gabard|
|Status||Gepubliceerd - 2010|
|ISSN van geprinte versie||1877-7058|
Rienstra, S. W., & Darau, M. (2010). Mean flow boundary layer effects of hydrodynamic instability of impedance wall. In R. J. Astley, & G. Gabard (editors), IUTAM Symposium on Computational Aero-Acoustics for Aircraft Noise Prediction (Southampton, UK, March 29-31, 2010) (blz. 124-132). (Procedia Engineering; Vol. 6). https://doi.org/10.1016/j.proeng.2010.09.014