Spatial Instability of Boundary Layer Along Impedance Wall

Abstract

A numerical analysis is made of the hydro-acoustical spatial instability, apparently occurring in a mean flow with thin boundary layer along a locally reacting lined duct wall. This problem is of particular interest because unstable behaviour of liner and mean flow has been observed only very rarely.It is found that this instability quickly disappears for increasing boundary layer thickness. Specifically, for boundary-layer-thickness based Helmholtz numbers ωδ/c 0 of the order of 0.1 the growth rate vanishes and the instability disappears. This corresponds to very thin boundary layers for practical values of frequencies that occur in aero-engine applications, which is in turn in good agreement with the fact that in industrial practice no instabilities are observed.For low duct-radius based Helmholtz numbers (∼ 1), the instability exists for rather large values of δ as an almost neutrally stable wave. This is qualitatively in good agreement with the experimental observations of Ronneberger and Auregan.It is shown by a Rayleigh-type stability criterion that impedance related hydrodynamic instabilities of temporal type do not occur for mean flows with strictly negative 2nd derivative (the usual situation).

Compressible turbulent channel flow with impedance boundary conditions

“…Such hydrodynamic instability is, however, driven by the wall-normal wave propagation resulting from resonant excitation of the tuned IBCs (as discussed in section V A), therefore leading to the designation of hydro-acoustic instability. This type of instability was theoretically predicted by Rienstra and co-workers [8][9][10] and experimentally identified in few previous works 11 in very similar flow configurations.…”

“…Numerous theoretical investigations by Rienstra and co-workers 2,[8][9][10] , together with some companion experimental efforts 11 , have looked at the stability properties of boundary layers over homogeneous IBCs. In particular, the presence of hydro-acoustic instabilities was predicted under specific conditions, which were deemed to be rarely found in aeronautical practice.…”

A wave expansion method for acoustic propagation in lined flow ducts

“…However, there have been a number of studies in recent years, which have identified problems with Myers condition resulting from the modelling assumptions. There are doubts as to whether the Myers model deals correctly with hydrodynamic modes in the boundary layer [19,20,21]. Since the boundary condition is the limit of an infinitely thin boundary layer, or the boundary layer being collapsed into a vortex sheet, when applied with slipping mean flow it may exhibit an instability comparable to the Kelvin-Helmholtz free-shear-layer instability.…”

Linear Stability with Respect to the Initial Value Perturbations in the Presence of Solutions of the Linearized Equation Having Strictly Positive Exponential Growth Rate

“…For describing the instantaneous acoustic perturbation propagation in a gas flowing through a lined duct, the authors of [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] consider the nonlinear Euler equations governing the gas flow and the solution of these equations describing the gas flow. After that, the…”