The effect of small streamwise velocity distortion on the boundary layer flow over a thin flat plate with application to boundary layer stability theory

Researchers show how an initially linear spanwise disturbance in the free stream velocity field is amplified by leading edge bluntness effects and ultimately leads to a small amplitude but linear spanwise motion far downstream from the edge. This spanwise motion is imposed on the boundary layer flow and ultimately causes an order-one change in its profile shape. The modified profiles are highly unstable and can support Tollmein-Schlichting wave growth well upstream of the theoretical lower branch of the neutral stability curve for a Blasius boundary layer

The Role of Instability Waves in Predicting Jet Noise

There has been an ongoing debate about the role of linear instability waves in the prediction of jet noise. Parallel mean flow models, such as the one proposed by Lilley, usually neglect these waves because they cause the solution to become infinite. The resulting solution is then non-causal and can, therefore, be quite different from the true causal solution for the chaotic flows being considered here. The present paper solves the relevant acoustic equations for a non-parallel mean flow by using a vector Green s function approach and assuming the mean flow to be weakly non-parallel, i.e., assuming the spread rate to be small. It demonstrates that linear instability waves must be accounted for in order to construct a proper causal solution to the jet noise problem. . Recent experimental results (e.g., see Tam, Golebiowski, and Seiner,1996) show that the small angle spectra radiated by supersonic jets are quite different from those radiated at larger angles (say, at 90deg) and even exhibit dissimilar frequency scalings (i.e., they scale with Helmholtz number as opposed to Strouhal number). The present solution is (among other things )able to explain this rather puzzling experimental result

The Aeroacoustics of Slowly Diverging Supersonic Jets

This paper is concerned with utilizing the acoustic analogy approach to predict the sound from unheated supersonic jets. Previous attempts have been unsuccessful at making such predictions over the Mach number range of practical interest. The present paper, therefore, focuses on implementing the necessary refinements needed to accomplish this objective. The important effects influencing peak supersonic noise turn out to be source convection, mean flow refraction, mean flow amplification, and source non-compactness. It appears that the last two effects have not been adequately dealt with in the literature. The first of these because the usual parallel flow models produce most of the amplification in the so called critical layer where the solution becomes singular and, therefore, causes the predicted sound field to become infinite as well. We deal with this by introducing a new weakly non parallel flow analysis that eliminates the critical layer singularity. This has a strong effect on the shape of the peak noise spectrum. The last effect places severe demands on the source models at the higher Mach numbers because the retarded time variations significantly increase the sensitivity of the radiated sound to the source structure in this case. A highly refined (non-separable) source model is, therefore, introduced in this paper

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

Rapid distortion theory on transversely sheared mean flows of arbitrary cross section

This paper is concerned with Rapid Distortion Theory on transversely sheared mean flows that (among other things) can be used to analyze the unsteady motion resulting from the interaction of a turbulent shear flow with a solid surface. It expands on a previous analysis of Goldstein, Leib and Afsar (J. Fluid Mech. Vol. 824, pp. 477-51) that uses a pair of conservation laws to derive upstream boundary conditions for planar mean flows and extends these findings to transversely sheared flows of arbitrary cross section. The results, which turn out to be quite general, are applied to the specific case of a round jet interacting with the trailing edge of a flat plate and used to calculate the radiated sound field, which is then compared with experimental data taken at the NASA Glenn Research Center

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

JET Noise Prediction

Aerodynamic noise prediction has been an important and challenging research area since James Lighthill first introduced his Acoustic Analogy Approach over fifty years ago. This talk attempts to provide a unified framework for the subsequent theoretical developments in this field. It assumes that there is no single approach that is optimal in all situations and uses the framework as a basis for discussing the strengths weaknesses of the various approaches to this topic. But the emphasis here will be on the important problem of predicting the noise from high speed air jets. Specific results will presented for round jets in the 0.5 to 1.4 Mach number range and compared with experimental data taken on the Glenn SHAR rig. It is demonstrated that non-parallel mean flow effects play an important role in predicting the noise at the supersonic Mach numbers. The results explain the failure of previous attempts based on the parallel flow Lilley model (which has served as the foundation for most jet noise analyses during past two decades)

Generalized rapid-distortion theory on transversely sheared mean flows with physically realizable upstream boundary conditions : application to trailing edge problem

This paper is concerned with rapid distortion theory on transversely sheared mean flows which (among other things) can be used to analyze the unsteady motion resulting from the interaction of a turbulent shear flow with a solid surface. It extends previous analyses of Goldstein, Afsar & Leib (2013 a, b) which showed that the unsteady motion is completely determined by specifying two arbitrary convected quantities. The present paper uses a pair of previously derived conservation laws to derive upstream boundary conditions that relate these quantities to experimentally measurable flow variables. The result is dependent on the imposition of causality on an intermediate variable that appears in the conservation laws. Goldstein et al (2013a) related the convected quantities to the physical flow variables at the location of the interaction, but the results were not generic and hard to reconcile with experiment. That problem does not occur in the present formulation which leads to a much simpler and more natural result than the one given in Goldstein et al (2013a). We also show that the present formalism yields better predictions of the sound radiation produced by the interaction of a two-dimensional jet with the downstream edge of a flat plate than the Goldstein et al (2013a) result. The role of causality is also discussed