Search NASA⌕ Search

SEARCH · Search NASA

Results for “LIGHTHILL METHOD”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Computation of the sound generated by isotropic turbulence

The acoustic radiation from isotropic turbulence is computed numerically. A hybrid direct numerical simulation approach which combines direct numerical simulation (DNS) of the turbulent flow with the Lighthill acoustic analogy is utilized. It is demonstrated that the hybrid DNS method is a feasible approach to the computation of sound generated by turbulent flows. The acoustic efficiency in the simulation of isotropic turbulence appears to be substantially less than that in subsonic jet experiments. The dominant frequency of the computed acoustic pressure is found to be somewhat larger than the dominant frequency of the energy-containing scales of motion. The acoustic power in the simulations is proportional to epsilon (M(sub t))(exp 5) where epsilon is the turbulent dissipation rate and M(sub t) is the turbulent Mach number. This is in agreement with the analytical result of Proudman (1952), but the constant of proportionality is smaller than the analytical result. Two different methods of computing the acoustic power from the DNS data bases yielded consistent results.

Sarkar, S.↗
NASA NTRS1975

Remarks on the theory of aerodynamic noise

The accuracy of approximations employed in the Lighthill theory in current aerodynamic noise research is critically evaluated. Based on the method of matched asymptotic expansions, the full Navier-Stokes equations are expanded for small Mach numbers. To the first order, the near-field is generally nonisentropic. The pressure field (pseudo-sound) is generated by the incompressible Reynolds stresses in the turbulent flow and the velocity, pressure perturbation, and their derivatives on the boundaries. In the far-field, the first-order pressure (acoustic) field satisfying a linear wave equation is obtained by matching with the pseudo-sound field. A uniformly valid solution for the pressure field in a stationary or uniformly moving medium is obtained. The solution shows that the generation of the first-order aerodynamic noise does not depend on the viscous, thermal, or entropy effects in the adiabatic flow nor on the shear stress on a smooth rigid boundary.

Pan, Y. S.↗
NASA NTRS1990

Time-dependent jet flow and noise computations

Methods for computing jet turbulence noise based on the time-dependent solution of Lighthill's (1952) differential equation are demonstrated. A key element in this approach is a flow code for solving the time-dependent Navier-Stokes equations at relatively high Reynolds numbers. Jet flow results at Re = 10,000 are presented here. This code combines a computationally efficient spectral element technique and a new self-consistent turbulence subgrid model to supply values for Lighthill's turbulence noise source tensor.

Berman, C. H.↗
NASA NTRS1990

Using finite volume methods for aeroacoustics

This paper is concerned with the application of unsteady finite volume methods to the numerical calculation of aeroacoustic problems. Some discussion is made of how the acoustic analogy of Lighthill has led to a separation between the calculation of acoustic source, or flow, and the subsequent sound field. It is pointed out that for transonic flow this separation is not necessarily useful. The example problem of an impulsively started cylinder is given for speed of Mach .1 and .5. In the Mach .5 case a strong shock is followed as it develops. A further example of the cylinder stopping impulsively is given as well. MacCormack's explicit predictor-corrector method is used for all the examples.

Brentner, Kenneth S.↗
NASA NTRS1974

Investigation of the large scale coherent structure in a jet and its relevance to jet noise

A study was conducted to determine the causes of aircraft noise in large jet aircraft. It was determined that jet noise varies strongly with velocity and that significant pure tones are generated by rotor-stator interaction in the jet engines. An objective method for deducing the large eddy structure in a large jet is described. The provisions of lighthill's theory are analyzed and applied to investigating the nature of jet noise. There is considerable evidence that a large scale coherent structure exists in a jet and that this structure can play a major role in sound radiation. Mathematical models are developed to define the parameters of orthogonal decomposition, finite extent velocity field, homogeneous fields, and periodic velocity fields.

Arndt, R. E. A.↗
NASA NTRS2001

Noise Sources in a Low-Reynolds-Number Turbulent Jet at Mach 0.9

The mechanisms of sound generation in a Mach 0.9, Reynolds number 3600 turbulent jet are investigated by direct numerical simulation. Details of the numerical method are briefly outlined and results are validated against an experiment at the same flow conditions. Lighthill's theory is used to define a nominal acoustic source in the jet, and a numerical solution of Lighthill's equation is compared to the simulation to verify the computational procedures. The acoustic source is Fourier transformed in the axial coordinate and time and then filtered in order to identify and separate components capable of radiating to the far field. This procedure indicates that the peak radiating component of the source is coincident with neither the peak of the full unfiltered source nor that of the turbulent kinetic energy. The phase velocities of significant components range from approximately 5% to 50% of the ambient sound speed which calls into question the commonly made assumption that the noise sources convect at a single velocity. Space-time correlations demonstrate that the sources are not acoustically compact in the streamwise direction and that the portion of the source that radiates at angles greater than 45 deg. is stationary. Filtering non-radiating wavenumber components of the source at single frequencies reveals that a simple modulated wave forms for the source, as might be predicted by linear stability analysis. At small angles from the jet axis the noise from these modes is highly directional, better described by an exponential than a standard Doppler factor.

Freund, Jonathan B.↗
NASA NTRS1978

Computational flow development for unsteady viscous flows: Foundation of the numerical method

A procedure is presented for effective consideration of viscous effects in computational development of high Reynolds number flows. The procedure is based on the interpretation of the Navier-Stokes equations as vorticity transport equations. The physics of the flow was represented in a form suitable for numerical analysis. Lighthill's concept for flow development for computational purposes was adapted. The vorticity transport equations were cast in a form convenient for computation. A statement for these equations was written using the method of weighted residuals and applying the Galerkin criterion. An integral representation of the induced velocity was applied on the basis of the Biot-Savart law. Distribution of new vorticity, produced at wing surfaces over small computational time intervals, was assumed to be confined to a thin region around the wing surfaces.

Bratanow, T.↗
NASA NTRS2002

The Acoustic Analogy and Alternative Theories for Jet Noise Prediction

This paper describes several methods for the prediction of jet noise. All but one of the noise prediction schemes are based on Lighthill's or Lilley's acoustic analogy while the other is the jet noise generation model recently proposed by Tam and Auriault. In all the approaches some assumptions must be made concerning the statistical properties of the turbulent sources. In each case the characteristic scales of the turbulence are obtained from a solution of the Reynolds-averaged Navier Stokes equation using a k - epsilon turbulence model. It is shown that, for the same level of empiricism, Tam and Auriault's model yields better agreement with experimental noise measurements than the acoustic analogy. It is then shown that this result is not because of some fundamental flaw in the acoustic analogy approach: but, is associated with the assumptions made in the approximation of the turbulent source statistics. If consistent assumptions are made, both the acoustic analogy and Tam and Auriault's model yield identical noise predictions. The paper concludes with a proposal for an acoustic analogy that provides a clearer identification of the equivalent source mechanisms and a discussion of noise prediction issues that remain to be resolved.

Morris, Philip J.↗
NASA NTRS2002

The Acoustic Analogy and Alternative Theories for Jet Noise Prediction

This paper describes several methods for the prediction of jet noise. All but one of the noise prediction schemes are based on Lighthill's or Lilley's acoustic analogy while the other is the jet noise generation model recently proposed by Tam and Auriault. In all the approaches some assumptions must be made concerning the statistical properties of the turbulent sources. In each case the characteristic scales of the turbulence are obtained from a solution of the Reynolds-averaged Navier Stokes equation using a k-epsilon turbulence model. It is shown that, for the same level of empiricism, Tam and Auriault's model yields better agreement with experimental noise measurements than the acoustic analogy. It is then shown that this result is not because of some fundamental flaw in the acoustic analogy approach: but, is associated with the assumptions made in the approximation of the turbulent source statistics. If consistent assumptions are made, both the acoustic analogy and Tam and Auriault's model yield identical noise predictions. The paper concludes with a proposal for an acoustic analogy that provides a clearer identification of the equivalent source mechanisms and a discussion of noise prediction issues that remain to be resolved.

Morris, Philip J.↗
NASA NTRS2004

The Acoustic Analogy: A Powerful Tool in Aeroacoustics with Emphasis on Jet Noise Prediction

The acoustic analogy introduced by Lighthill to study jet noise is now over 50 years old. In the present paper, Lighthill s Acoustic Analogy is revisited together with a brief evaluation of the state-of-the-art of the subject and an exploration of the possibility of further improvements in jet noise prediction from analytical methods, computational fluid dynamics (CFD) predictions, and measurement techniques. Experimental Particle Image Velocimetry (PIV) data is used both to evaluate turbulent statistics from Reynolds-averaged Navier-Stokes (RANS) CFD and to propose correlation models for the Lighthill stress tensor. The NASA Langley Jet3D code is used to study the effect of these models on jet noise prediction. From the analytical investigation, a retarded time correction is shown that improves, by approximately 8 dB, the over-prediction of aft-arc jet noise by Jet3D. In experimental investigation, the PIV data agree well with the CFD mean flow predictions, with room for improvement in Reynolds stress predictions. Initial modifications, suggested by the PIV data, to the form of the Jet3D correlation model showed no noticeable improvements in jet noise prediction.

Farassat, F.↗
NASA NTRS2002

Acoustic Analogy and Alternative Theories for Jet Noise Prediction

Several methods for the prediction of jet noise are described. All but one of the noise prediction schemes are based on Lighthill's or Lilley's acoustic analogy, whereas the other is the jet noise generation model recently proposed by Tam and Auriault. In all of the approaches, some assumptions must be made concerning the statistical properties of the turbulent sources. In each case the characteristic scales of the turbulence are obtained from a solution of the Reynolds-averaged Navier-Stokes equation using a kappa-sigma turbulence model. It is shown that, for the same level of empiricism, Tam and Auriault's model yields better agreement with experimental noise measurements than the acoustic analogy. It is then shown that this result is not because of some fundamental flaw in the acoustic analogy approach, but instead is associated with the assumptions made in the approximation of the turbulent source statistics. If consistent assumptions are made, both the acoustic analogy and Tam and Auriault's model yield identical noise predictions. In conclusion, a proposal is presented for an acoustic analogy that provides a clearer identification of the equivalent source mechanisms, as is a discussion of noise prediction issues that remain to be resolved.

Morris, Philip J.↗
NASA NTRS2002

Measurement of Correlation Between Flow Density, Velocity, and Density*velocity(sup 2) with Far Field Noise in High Speed Jets

To locate noise sources in high-speed jets, the sound pressure fluctuations p', measured at far field locations, were correlated with each of radial velocity v, density rho, and phov(exp 2) fluctuations measured from various points in jet plumes. The experiments follow the cause-and-effect method of sound source identification, where correlation is related to the first, and correlation to the second source terms of Lighthill's equation. Three fully expanded, unheated plumes of Mach number 0.95, 1.4 and 1.8 were studied for this purpose. The velocity and density fluctuations were measured simultaneously using a recently developed, non-intrusive, point measurement technique based on molecular Rayleigh scattering. It was observed that along the jet centerline the density fluctuation spectra S(sub rho) have different shapes than the radial velocity spectra S(sub v), while data obtained from the peripheral shear layer show similarity between the two spectra. Density fluctuations in the jet showed significantly higher correlation, than either rhov(sub 2) or v fluctuations. It is found that a single point correlation from the peak sound emitting region at the end of the potential core can account for nearly 10% of all noise at 30 to the jet axis. The correlation, representing the effectiveness of a longitudinal quadrupole in generating noise 90 to the jet axis, is found to be zero within experimental uncertainty. In contrast rhov(exp 2) fluctuations were better correlated with sound pressure fluctuation at the 30 location. The strongest source of sound is found to lie at the centerline and beyond the end of potential core.

Panda, Jayanta↗
NASA NTRS1983

Comparison of forward flight effects theory of A. Michalke and U. Michel with measured data

The scaling laws of a Michalke and Michel predict flyover noise of a single stream shock free circular jet from static data or static predictions. The theory is based on a farfield solution to Lighthill's equation and includes density terms which are important for heated jets. This theory is compared with measured data using two static jet noise prediction methods. The comparisons indicate the theory yields good results when the static noise levels are accurately predicted.

Rawls, J. W., Jr.↗
NASA NTRS1992

Report on the final panel discussion on computational aeroacoustics

Some important conclusions about future prospects for aeroacoustics in general, and for computational aeroacoustics in particular, that were reached in the course of the Final Panel Discussion of the Workshop on Computational Aeroacoustics held from 6 to 9 April 1992 by ICASE and NASA Langley Research Center are summarized by the panel chairman. Aeroacoustics must now be involved in interactions with computational fluid dynamics (as applied not only to deterministic flows but also to the statistical characteristics of turbulence), while additionally incorporating rigorous comparisons with experiment. The new Computational Aeroacoustics will press forward in two parallel ways. In one of them, CFD will be used to determine aeroacoustic source strengths, the associated radiation being derived by the Acoustic Analogy approach in one of its forms. In the other, a direct Computational Aeroacoustics will apply CFD techniques over a region extending beyond the flow field so as to include at least the beginnings of the acoustic far field. There are some particularly important areas of study, including rotor noise, boundary-layer noise, and the noise of supersonic jets, where it is strongly recommended that use of both methods is continued. On the other hand, important problems of the diffraction of radiation from aeroacoustic sources around complicated aircraft shapes will require the use of comprehensively Computational Aeroacoustics, while Acoustic Analogy methods seem better suited to estimating subsonic jet noise. The study of model problems to allow comparisons with experiment will be valuable in both lines of attack.

Lighthill, James↗
NASA NTRS1979

Laminar boundary-layer flow of non-Newtonian fluid

A solution for the two-dimensional and axisymmetric laminar boundary-layer momentum equation of power-law non-Newtonian fluid is presented. The analysis makes use of the Merk-Chao series solution method originally devised for the flow of Newtonian fluid. The universal functions for the leading term in the series are tabulated for n from 0.2 to 2. Equations governing the universal functions associated with the second and the third terms are provided. The solution together with either Lighthill's formula or Chao's formula constitutes a simple yet general procedure for the calculation of wall shear and surface heat transfer rate. The theory was applied to flows over a circular cylinder and a sphere and the results compared with published data.

Lin, F. N.↗
NASA NTRS1997

An Analytical Comparison of the Acoustic Analogy and Kirchhoff Formulation for Moving Surfaces

The Lighthill acoustic analogy, as embodied in the Ffowcs Williams-Hawkings (FW-H) equation, is compared with the Kirchhoff formulation for moving surfaces. A comparison of the two governing equations reveals that the main Kirchhoff advantage (namely nonlinear flow effects are included in the surface integration) is also available to the FW-H method if the integration surface used in the FW-H equation is not assumed impenetrable. The FW-H equation is analytically superior for aeroacoustics because it is based upon the conservation laws of fluid mechanics rather than the wave equation. This means that the FW-H equation is valid even if the integration surface is in the nonlinear region. This is demonstrated numerically in the paper. The Kirchhoff approach can lead to substantial errors if the integration surface is not positioned in the linear region. These errors may be hard to identify. Finally, new metrics based on the Sobolev norm are introduced which may be used to compare input data for both quadrupole noise calculations and Kirchhoff noise predictions.

Brentner, Kenneth S.↗
NASA NTRS1998

On Wave Processes in the Solar Atmosphere

This grant was awarded by NASA/MSFC to The University of Alabama in Huntsville (UAH) to investigate the physical processes responsible for heating and wind acceleration in the solar atmosphere, and to construct theoretical, self-consistent and time-dependent solar wind models based on the momentum deposition by finite amplitude and nonlinear Alfven waves. In summary, there are three main goals of the proposed research: (1) Calculate the wave energy spectra and wave energy fluxes carried by magnetic non- magnetic waves. (2) Find out which mechanism dominates in supplying the wave energy to different parts of the solar atmosphere. (3) Use the results obtained in (1) and (2) to construct theoretical, self-consistent and time- dependent models of the solar wind. We have completed the first goal by calculating the amount of non-radiative energy generated in the solar convection zone as acoustic waves and as magnetic tube waves. To calculate the amount of wave energy carried by acoustic waves, we have used the Lighthill-Stein theory for sound generation modified by Musielak, Rosner, Stein & Ulmschneider (1994). The acoustic wave energy fluxes for stars located in different regions of the Hertzsprung-Russell (H-R) diagram have also been computed. The wave energy fluxes carried by longitudinal and transverse waves along magnetic flux tubes have been calculated by using both analytical and numerical methods. Our analytical approach is based a theory developed by Musielak, Rosner & Ulmschnelder and Musielak, Rosner, Gall & Ulmschneider, which allows computing the wave energy fluxes for linear tube waves. A numerical approach has been developed by Huang, Musielak & Ulmschneider and Ulmschneider & Musielak to compute the energy fluxes for nonlinear tube waves. Both methods have been used to calculate the wave energy fluxes for stars located in different regions of the HR diagram (Musielak, Rosner & Ulmschneider 1998; Ulmschneider, Musielak & Fawzy 1998). Having obtained the wave energy fluxes for acoustic and magnetic tube waves, we have investigated the behavior of these waves in the solar and stellar atmospheres. The results of our extensive studies have been published in many papers and presented at numerous scientific meetings. In these studies we have investigated different aspects of propagation of acoustic and magnetic waves, the efficiency of energy transfer along magnetic structures in the solar atmosphere, and behavior of Alfven waves in stgeady and expanding solar and stellar atmospheres. Recently, we have used some of these results to construct first purely theoretical, two component and time-dependent models of solar and stellar chromospheres. Finally, to address the third goal, we have constructed first fully theoretical, self-consistent and time dependent wind models based on the momentum deposition by non-linear Alfven waves. The full set of single-fluid MHD equations with the background flow has been solved by using a modified version of the ZEUS MHD code. The constructed wind models are radially symmetric with the magnetic field decreasing radially and the initial outflow is described by the standard Parker wind solution. In contrast to previous studies, no assumptions regarding wave linearity, wave damping, and wave-flow interaction are made; the models thus naturally account for the backreaction of the wind on the waves as well as for the nonlinear interaction between different types of MHD waves. The models have been used to explain the origin of fast speed streams in solar coronal holes. The obtained results clearly demonstrate that the momentum deposition by Alfven waves in the solar wind can be sufficient to explain the origin of fast stream components of the solar wind. The range of wave amplitudes required to obtain the desired results seems to be in good agreement with recent observations.

Musielak, Z. E.↗
NASA NTRS1974

Conical flow near singular rays

The steady flow of an ideal gas past a conical body is investigated by the method of matched asymptotic expansions, with particular emphasis on the flow near the singular ray occurring in linearized theory. The first-order problem governing the flow in this region is formulated, leading to the equation of Kuo, and an approximate solution is obtained in the case of compressive flow behind the main front. This solution is compared with the results of previous investigations with a view to assessing the applicability of the Lighthill-Whitham theories.

Zahalak, G. I.↗