Aeroacoustics of subsonic turbulent shear flows

Sound generation in turbulent shear flows is examined. The emphasis is on simultaneous calculation of the turbulent flow along with the resulting sound generation rather than the alternative acoustic analogy approach. The first part of the paper is concerned with solid surface interaction. The second part concentrates on the sound generated by turbulence interacting with itself

The 90 deg Acoustic Spectrum of a High Speed Air Jet

Tam and Auriault successfully predicted the acoustic spectrum at 90deg to the axis of a high speed air jet by using an acoustic equation derived from ad hoc kinetic theory-type arguments. The present paper shows that similar predictions can be obtained by using a rigorous acoustic analogy approach together with actual measurements of the relevant acoustic source correlations. This puts the result on a firmer basis and enables its extension to new situations and to the prediction of sound at other observation angles

A Hybrid RANS/LES Approach for Predicting Jet Noise

Hybrid acoustic prediction methods have an important advantage over the current Reynolds averaged Navier-Stokes (RANS) based methods in that they only involve modeling of the relatively universal subscale motion and not the configuration dependent larger scale turbulence. Unfortunately, they are unable to account for the high frequency sound generated by the turbulence in the initial mixing layers. This paper introduces an alternative approach that directly calculates the sound from a hybrid RANS/LES flow model (which can resolve the steep gradients in the initial mixing layers near the nozzle lip) and adopts modeling techniques similar to those used in current RANS based noise prediction methods to determine the unknown sources in the equations for the remaining unresolved components of the sound field. The resulting prediction method would then be intermediate between the current noise prediction codes and previously proposed hybrid noise prediction methods

The Effect of Nonlinear Critical Layers on Boundary Layer Transition

Asymptotic methods are used to describe the nonlinear self-interaction between pairs of oblique instability modes that eventually develops when initially linear and spatially growing instability waves evolve downstream in nominally two-dimensional and spanwise periodic laminar boundary layers. The first nonlinear reaction takes place locally within a so-called 'critical layer' with the flow outside this layer consisting of a locally parallel mean flow plus an appropriate superposition of linear instability waves. The amplitudes of these waves are determined by either a single integro-differential equation or by a pair of integro-differential equations with quadratic to quartic-type nonlinearities

Leading Edge Receptivity at Subsonic and Moderately Supersonic Mach Numbers

This chapter is a review of the receptivity and resulting global instability of boundary layers due to free-stream vortical and acoustic disturbances at subsonic and moderately supersonic Mach numbers. The vortical disturbances produce an unsteady boundary layer flow that develops into oblique instability waves with a viscous triple-deck structure in the downstream region. The acoustic disturbances (which have phase speeds that are small compared to the free stream velocity) produce boundary layer fluctuations that evolve into oblique normal modes downstream of the viscous triple-deck region. Asymptotic methods are used to show that both the vortically and acoustically-generated disturbances ultimately develop into modified Rayleigh modes that can exhibit spatial growth or decay depending on the nature of the receptivity process

The development of a mixing layer under the action of weak streamwise vortices

The action of weak, streamwise vortices on a plane, incompressible, steady mixing layer is examined in the large Reynolds-number limit. The outer, inviscid region is bounded by a vortex sheet to which the viscous region is confined. It is shown that the local linear analysis becomes invalid at streamwise distances O(epsilon(sup -1)), where epsilon is much less than 1 is the cross flow amplitude, and a new nonlinear analysis is constructed for this region. Numerical solutions of the nonlinear problem show that the vortex sheet undergoes an O(1) change in position and that the solution is ultimately terminated by the appearance of a singularity. The corresponding viscous layer shows downstream thickening, but appears to remain well behaved up to the singular location

Nonlinear Instability of a Uni-directional Transversely Sheared Mean Flow

It is well known that the presence of a weak cross flow in an otherwise two-dimensional shear flow results in a spanwise variation in the mean streamwise velocity profile that can lead to an amplification of certain three-dimensional disturbances through a kind of resonant-interaction mechanism (Goldstein and Wundrow 1994). The spatial evolution of an initially linear, finite-growth-rate, instability wave in such a spanwise-varying shear flow is considered, The base flow, which is governed by the three-dimensional parabolized Navier-Stokes equations, is initiated by imposing a spanwise- periodic cross-flow velocity on an otherwise two-dimensional shear flow at some fixed streamwise location. The resulting mean-flow distortion initially grows with increasing streamwise distance, reaches a maximum and eventually decays through the action of viscosity. This decay, which coincides with the viscous spread of of the shear layer, means that the local growth rate of the instability wave will eventually decrease as the wave propagates downstream. Nonlinear effects can then become important within a thin spanwise-modulated critical layer once the local instability-wave amplitude and growth rate become sufficiently large and small, respectively. The amplitude equation that describes this stage of evolution is shown to be a generalization of the one obtained by Goldstein and Choi (1989) who considered the related problem of the interaction of two oblique modes in a two-dimensional shear layer

Emission of Sound From Turbulence Convected by a Parallel Mean Flow in the Presence of a Confining Duct

An approximate method for calculating the noise generated by a turbulent flow within a semi-infinite duct of arbitrary cross section is developed. It is based on a previously derived high-frequency solution to Lilley's equation, which describes the sound propagation in transversely-sheared mean flow. The source term is simplified by assuming the turbulence to be axisymmetric about the mean flow direction. Numerical results are presented for the special case of a ring source in a circular duct with an axisymmetric mean flow. They show that the internally generated noise is suppressed at sufficiently large upstream angles in a hard walled duct, and that acoustic liners can significantly reduce the sound radiated in both the upstream and downstream regions, depending upon the source location and Mach number of the flow

Structure of the Small Amplitude Motion on Transversely Sheared Mean Flows

This paper considers the small amplitude unsteady motion of an inviscid non-heat conducting compressible fluid on a transversely sheared mean flow. It extends a previous result given in Goldstein (1978(b) and 1979(a)) which shows that the hydrodynamic component of the motion is determined by two arbitrary convected quantities in the absence of solid surfaces or other external sources. The result is important because it can be used to specify appropriate boundary conditions for unsteady surface interaction problems on transversely sheared mean flows in the same way that the vortical component of the Kovasznay (1953) decomposition is used to specify these conditions for surface interaction problems on uniform mean flows. But unlike the Kovasznay (1953) case the arbitrary convected quantities no longer bear a simple relation to the physical variables. One purpose of this paper is to derive a formula that relates these quantities to the (physically measurable) vorticity and pressure fluctuations in the flow

Effect of Free Stream Turbulence and Other Vortical Disturbances on a Laminar Boundary Layer

This paper is concerned with the effect of free-stream turbulence on the pretransitional flat-plate boundary layer. It is assumed that either the turbulence Reynolds number or the downstream distance (or both) is small enough so that the flow can be linearized. The dominant disturbances in the boundary layer, which are of the Klebanoff type, are governed by the linearized unsteady boundary-region equations, i.e., the Navier Stokes equations with the streamwise derivatives neglected in the viscous and pressure-gradient terms. The turbulence is represented as a superposition of vortical free-stream Fourier modes, and the corresponding individual Fourier component solutions to the boundary-region equations are obtained numerically. The results are then superposed to compute the root mean square of the fluctuating streamwise velocity in the boundary layer produced by the actual free-stream turbulence. The calculated boundary-layer disturbances are in good quantitative agreement with the experimentally observed Klebanoff modes when strong low-frequency anisotropic effects are included in the free-stream turbulence spectrum. We discuss some additional effects that may need to be accounted for in order to obtain a complete description of the Klebanoff modes