Engineering topics

Leib, S. J.

Publications and source records attributed to Leib, S. J..

18 records

NASA NTRS2015

A Model for Jet-Surface Interaction Noise Using Physically Realizable Upstream Turbulence Conditions

This paper is a continuation of previous work in which a generalized Rapid Distortion Theory (RDT) formulation was used to model low-frequency trailing-edge noise. The research was motivated by proposed next-generation aircraft configurations where the exhaust system is tightly integrated with the airframe. Data from recent experiments at NASA on the interaction between high-Reynolds-number subsonic jet flows and an external flat plate showed that the power spectral density (PSD) of the far-field pressure underwent considerable amplification at low frequencies. For example, at the 900 observation angle, the low-frequency noise could be as much as 10dB greater than the jet noise itself. In this paper, we present predictions of the noise generated by the interaction of a rectangular jet with the trailing edge of a semi-infinite flat plate. The calculations are based on a formula for the acoustic spectrum of this noise source derived from an exact formal solution of the linearized Euler equations involving (in this case) one arbitrary convected scalar quantity and a Rayleigh equation Green's function. A low-frequency asymptotic approximation for the Green's function based on a two-dimensional mean flow is used in the calculations along with a physically realizable upstream turbulence spectrum, which includes a finite de-correlation region. Numerical predictions, based on three-dimensional RANS solutions for a range of subsonic acoustic Mach number jets and nozzle aspect ratios are compared with experimental data. Comparisons of the RANS results with flow data are also presented for selected cases. We find that a finite decorrelation region increases the low-frequency algebraic decay (the low frequency "rolloff") of the acoustic spectrum with angular frequency thereby producing much closer agreement with noise data for Strouhal numbers less than 0.1. Secondly, the large-aspectratio theory is able to predict the low-frequency amplification due to the jet-edge interaction reasonably well, even for moderate aspect ratio nozzles. We show also that the noise predictions for smaller aspect ratio jets can be fine-tuned using the appropriate RANS-based mean flow and turbulence properties.

Aircraft↗

NASA NTRS2008

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.

Goldstein, M. E.↗

NASA NTRS2007

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).

Goldstein, M. E.↗

NASA NTRS2004

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.

Goldstein, M. E.↗

NASA NTRS1997

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.

Goldstein, Marvin E.↗

NASA NTRS1993

A note on the distortion of a flat-plate boundary layer by free-stream vorticity normal to the plate

The purpose of this note is to construct a local solution that eliminates a residual velocity discontinuity in the inviscid portion of a solution obtained in a recent paper by Goldstein, Leib and Cowley (1992). This result is of importance because it shows that the solution obtained in that paper is entirely non-singular outside the viscous wall boundary layer and that any singularity in the problem will have to arise in the usual way through a breakdown in the viscous boundary layer.

Goldstein, M. E.↗

NASA NTRS1993

Three-dimensional boundary-layer instability and separation induced by small-amplitude streamwise vorticity in the upstream flow

We consider the effects of a small-amplitude, steady, streamwise vorticity field on the flow over an infinitely thin flat plate in an otherwise uniform stream. We show how the initially linear perturbation, ultimately leads to a small-amplitude but nonlinear cross flow far downstream from the leading edge. This motion is imposed on the boundary-layer flow and eventually causes the boundary layer to separate. The streamwise velocity profiles within the boundary layer become inflexional in localized spanwise regions just upstream of the separation point. The flow in these regions is therefore susceptible to rapidly growing inviscid instabilities.

Goldstein, M. E.↗

NASA NTRS1992

Distortion of a flat-plate boundary layer by free-stream vorticity normal to the plate

A nominally uniform flow over a semiinfinite flat plate is considered. The analysis shows how a small streamwise disturbance in the otherwise uniform flow ahead of the plate is amplified by leading-edge bluntness effects and eventually leads to a small-amplitude but nonlinear spanwise motion far downstream from the leading edge of the plate. This spanwise motion is then imposed on the viscous boundary-layer flow at the surface of the plate - causing an order-one change in its profile shape. This ultimately reduces the wall shear stress to zero, causing the boundary layer to undergo a localized separation, which may be characterized as a kind of bursting phenomenon that could be related to the turbulent bursts observed in some flat-plate boundary-layer experiments.

Goldstein, M. E.↗

NASA NTRS1991

Nonlinear evolution of subsonic and supersonic disturbances on a compressible free shear layer

The effects of a nonlinear-nonequilibrium-viscous critical layer on the spatial evolution of subsonic and supersonic instability modes on a compressible free shear layer is considered. It is shown that the instability wave amplitude is governed by an integrodifferential equation with cubic-type nonlinearity. Numerical and asymptotic solutions to this equation show that the amplitude either ends in a singularity at a finite downstream distance or reaches an equilibrium value, depending on the Prandtl number, viscosity law, viscous parameter and a real parameter which is determined by the linear inviscid stability theory. A necessary condition for the existence of the equilibrium solution is derived, and whether or not this condition is met is determined numerically for a wide range of physical parameters including both subsonic and supersonic disturbances. it is found that no equilibrium solution exists for the subsonic modes unless the temperature ratio of the low-to-high-speed streams exceeds a critical value, while equilibrium solutions for the most rapidly growing supersonic mode exist over most of the parameter range examined.

Leib, S. J.↗

NASA NTRS1990

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.

Goldstein, M. E.↗

NASA NTRS1989

Nonlinear evolution of oblique waves on compressible shear layers

The effects of critical-layer nonlinearity on spatially growing oblique instability waves on compressible shear layers between two parallel streams are considered. The analysis shows that mean temperature nonuniformities cause nonlinearity to occur at much smaller amplitudes than it does when the flow is isothermal. The nonlinear instability wave growth rate effects are described by an integrodifferential equation which bears some resemblance to the Landau equation, in that it involves a cubic-type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. Inviscid solutions always end in a singularity at a finite downstream distance, but viscosity can eliminate this singularity for certain parameter ranges.

Goldstein, M. E.↗

NASA NTRS1989

Nonlinear interaction between the sinuous and varicose instability modes in a plane wake

The nonlinear interaction between sinuous and varicose instability modes in a plane wake is examined in the nonlinear-nonequilibrium critical layer regime. Equations governing the evolution of the instability wave amplitudes and critical layer vorticity distributions are derived. Numerical solutions for these equations are obtained for a number of wake defects and initial amplitude ratios. The results show that the primary effects of the nonlinear interaction are the suppression of the varicose mode and the downstream shift of the peak of the sinuous mode.

Leib, S. J.↗

NASA NTRS1988

Nonlinear roll-up of externally excited free shear layers

The effects of strong critical-layer nonlinearity on the spatially growing instabilities of a shear layer between two parallel streams are considered. A composite expansion technique is used to obtain a single formula that accounts for both shear-layer spreading and nonlinear critical-layer effects. Nonlinearity causes the instability to saturate well upstream of the linear neutral stability point. It also produces vorticity roll-up that cannot be predicted by linear theory.

Goldstein, M. E.↗

NASA NTRS1987

Roll-up of vorticity in adverse-pressure-gradient boundary layers

It is shown how the unsteady, nonlinear critical-layer equation determines the evolution of instability waves in a weak adverse-pressure-gradient boundary layer. Numerical solutions show that the nonlinearity halts the growth of these inviscidly unstable waves. The stabilizing effect of nonlinearity, in the present case, can be described as a consequence of either the increase (toward zero) of the phase jump across the critical layer or the roll-up of the critical-layer disturbance vorticity.

Goldstein, M. E.↗

NASA NTRS1987

Generation of Tollmien-Schlichting waves on interactive marginally separated flows

This paper is concerned with the interaction of very-long-wavelength free-stream disturbances with the small but abrupt changes in the mean flow that occur near the minimum-skin-friction point in an interactive marginally separated boundary layer. The source frequency is chosen so that the eigensolutions with that frequency have an 'interactive' structure in the region of marginal separation. The eigensolution wavelength scale must then differ from the lengthscale of the marginal separation, and a composite expansion technique has to be used to obtain the solution. The initial instability wave amplitude turns out to be exponentially small, but eventually dominates the original disturbance owing to its exponential growth. It then begins to decay but ultimately turns into a standard spatially growing Tollmien-Schlichting wave much further downstream.

Goldstein, M. E.↗

NASA NTRS1986

The generation of capillary instabilities on a liquid jet

The coupling between imposed disturbances and capillary instabilities on a liquid jet is examined. It is shown that in most physical situations the forcing produces neutral waves, which can then turn into growing waves as the profile relaxes or may be amplified nonlinearly by a mechanism of the type considered by Akylas and Benney (1980). The effectiveness of the coupling is expressed quantitatively by numerically computed values of the 'coupling coefficient'.

Leib, S. J.↗

NASA NTRS1986

Convective and absolute instability of a viscous liquid jet

The effect of viscosity on the capillary instability of a liquid jet is examined. The critical Weber number for convective instability is determined as a function of Reynolds number and comparison is made with the inviscid limit. It is shown that certain waves that are neutral in the inviscid case exhibit growth for finite Reynolds numbers.

Leib, S. J.↗

NASA NTRS1985

Generation of capillary instabilities by external disturbances in a liquid jet

The receptivity problem in a circular liquid jet is considered. A time harmonic axial pressure gradient is imposed on the steady, parallel flow of a jet of liquid emerging from a circular duct. Using a technique developed in plasma physics a casual solution to the forced problem is obtained over certain ranges of Weber number for a number of mean velocity profiles. This solution contains a term which grows exponentially in the downstream direction and can be identified with a capillary instability wave. Hence, it is found that the externally imposed disturbances can indeed trigger instability waves in a liquid jet. The amplitude of the instability wave generated relative to the amplitude of the forcing is computed numerically for a number of cases.

Leib, S. J.↗