Christopher K. W. Tam

Computational aeroacoustics - Issues and methods

Computational fluid dynamics (CFD) has made tremendous progress especially in aerodynamics and aircraft design over the past 20 years. An obvious question to ask is why not use CFD methods to solve aeroacoustics problems ? Most aerodynamics problems are time independent, whereas aeroacoustics problems are, by definition, time dependent. The nature, characteristics, and objectives of aeroacoustics problems are also quite different from the commonly encountered CFD problems. There are computational issues that are unique to aeroacoustics. For these reasons computational aeroacoustics requires somewhat independent thinking and development. The objectives of this paper are twofold. First, issues pertinent to aeroacoustics that may or may not be relevant to computational aerodynamics are discussed. The second objective is to review computational methods developed recently that are designed especially for computational aeroacoustics applications. Some of the computational methods to be reviewed are quite different from traditional CFD methods. They should be of interest to the CFD and fluid dynamics communities.

On the tones and pressure oscillations induced by flow over rectangular cavities

Experimental measurements of the frequencies of discrete tones induced by flow over rectangular cavities were carried out over a range of low subsonic Mach numbers to provide a reliable data base for (aircraft wheel well) cavity noise consideration. A mathematical model of the cavity tones and pressure oscillation phenomenon based on the coupling between shear layer instabilities and acoustic feedback is developed to help in understanding the tone generation mechanism. Good agreement is found between discrete tone frequencies predicted by the model and experimental measurements over a wide range of Mach numbers. Evidence of tones generated by the cavity normal mode resonance mechanism at very low subsonic Mach numbers is also presented.

The sources of jet noise: experimental evidence

The primary objective of this investigation is to determine experimentally the sources of jet mixing noise. In the present study, four different approaches are used. It is reasonable to assume that the characteristics of the noise sources are imprinted on their radiation fields. Under this assumption, it becomes possible to analyse the characteristics of the far-field sound and then infer back to the characteristics of the sources. The first approach is to make use of the spectral and directional information measured by a single microphone in the far field. A detailed analysis of a large collection of far-field noise data has been carried out. The purpose is to identify special characteristics that can be linked directly to those of the sources. The second approach is to measure the coherence of the sound field using two microphones. The autocorrelations and cross-correlations of these measurements offer not only valuable information on the spatial structure of the noise field in the radial and polar angle directions, but also on the sources inside the jet. The third approach involves measuring the correlation between turbulence fluctuations inside a jet and the radiated noise in the far field. This is the most direct and unambiguous way of identifying the sources of jet noise. In the fourth approach, a mirror microphone is used to measure the noise source distribution along the lengths of high-speed jets. Features and trends observed in noise source strength distributions are expected to shed light on the source mechanisms. It will be shown that all four types of data indicate clearly the existence of two distinct noise sources in jets. One source of noise is the fine-scale turbulence and the other source is the large turbulence structures of the jet flow. Some of the salient features of the sound field associated with the two noise sources are reported in this paper.

On the Two Components of Turbulent Mixing Noise from Supersonic Jets

It is argued that because of the lack of intrinsic length and time scales in the core part of the jet flow, the radiated noise spectrum of a high-speed jet should exhibit similarity. A careful analysis of all the axisymmetric supersonic jet noise spectra in the data-bank of the Jet Noise Laboratory of the NASA Langley Research Center has been carried out. Two similarity spectra, one for the noise from the large turbulence structures/instability waves of the jet flow, the other for the noise from the fine-scale turbulence, are identified. The two similarity spectra appear to be universal spectra for axisymmetric jets. They fit all the measured data including those from subsonic jets. Experimental evidence are presented showing that regardless of whether a jet is supersonic or subsonic the noise characteristics and generation mechanisms are the same. There is large turbulence structures/instability waves noise from subsonic jets. This noise component can be seen prominently inside the cone of silence of the fine-scale turbulence noise near the jet axis. For imperfectly expanded supersonic jets, a shock cell structure is formed inside the jet plume. Measured spectra are provided to demonstrate that the presence of a shock cell structure has little effect on the radiated turbulent mixing noise. The shape of the noise spectrum as well as the noise intensity remain practically the same as those of a fully expanded jet. However, for jets undergoing strong screeching, there is broadband noise amplification for both turbulent mixing noise components. It is discovered through a pilot study of the noise spectrum of rectangular and elliptic supersonic jets that the turbulent mixing noise of these jets is also made up of the same two noise components found in axisymmetric jets. The spectrum of each individual noise component also fits the corresponding similarity spectrum of axisymmetric jets.

Jet mixing noise from fine-scale turbulence

It is known that turhulent mixing noise from high-speed jets consists of two components. They are the noise from large turbulent structures in the form of Mach wave radiation and the less directional fine-scale turbulence noise. The Mach wave radiation dominates in the downstream direction. The fine-scale turbulence noise dominates in the sideline and upstream directions. A semiempirical theory is developed for the prediction of the spectrum, intensity, and directivity of the fine-scale turhulence noise. The prediction method is self-contained. The turbulence information is supplied by the k-e turhulence model. The theory contains three empirical constants beyond those of the k-e model. These constants are determined by best fit of the calculated noise spectra to experimental measurements. Extensive comparisons between calculated and measured noise spectra over a wide range of directions of radiation,jet velocities, and temperatures have heen carried out. Excellent agreements are found. It is believed that the present theory offers significant improvements over current empirical or semiempirical jet noise prediction methods in use. There is no first principle jet noise theory at the present time.

Sound generated by instability waves of supersonic flows. Part 2. Axisymmetric jets

A solution describing the spatial evolution of small-amplitude instability waves and their associated sound field of axisymmetric supersonic jets is found using the method of matched asymptotic expansions (see Part 1, Tam & Burton 1984). The inherent axisymmetry of the problem allows the instability waves to be decomposed into azimuthal wave modes. In addition, it is found that because of the cylindrical geometry of the problem the gauge functions of the inner expansion, unlike the case of two-dimensional mixing layers, are no longer just powers of e. Instead they contain logarithmic terms. To test the validity of the theory, numerical results of the solution are compared with the experimental measurements of Troutt (1978) and Troutt & McLaughlin (1982). Two series of comparisons at Strouhal numbers 0.2 and 0.4 for a Mach-number 2.1 cold supersonic jet are made. The data compared include hot-wire measurements of the axial distribution of root-mean-squared jet centreline mass-velocity fluctuations and radial and axial distributions of near-field pressure-level contours measured by microphones. The former is used to test the accuracy of the inner (or instability-wave) solution. The latter is used to verify the correctness of the outer solution. Very favourable overall agreements between the calculated results and the experimental measurements are found. These very favourable agreements strongly suggest that the method of solution developed in Part 1 paper is indeed valid. Furthermore, they also offer concrete support to the proposition made previously by a number of investigators that instability waves are important noise sources in supersonic jets.

The drag on a cloud of spherical particles in low Reynolds number flow

A formula for the drag exerted on a cloud of spherical particles of a given particle size distribution in low Reynolds number flow is derived. It is found that the drag experienced by a particle depends only on the first three moments of the distribution function. A treatment of viscous interaction between N particles to the lowest order is carried out systematically. By appealing to the concept of ‘randomness’ of the particle cloud, equations describing the averaged properties of the fluid motion are derived. The averages are formed over a statistical ensemble of particle configurations. These mean flow equations so obtained are in a form resembling a generalized version of Darcys empirical equation for the motion of fluid in a porous medium. The physical meaning of these equations is discussed.

Shock associated noise of supersonic jets from convergent-divergent nozzles

Abstract Results of experimental and theoretical studies of the characteristics of shock associated noise from imperfectly expanded supersonic jets over an extensive range of underexpanded and overexpanded operating conditions are described. This kind of broadband noise is believed to be generated by the weak but coherent interaction between the downstream propagating large scale turbulent flow structures in the mixing layer of the jet and the nearly periodic shock cell system. Theoretical reasoning based on this mechanism leads to the scaling formula that the intensity of shock associated noise varies as (Mj2 − Md2)2 where Mj and Md are the fully expanded jet operating Mach number and nozzle design Mach number, respectively. This formula holds for underexpanded as well as overexpanded jet Mach numbers. In addition, a peak frequency formula is also derived from the same model. The noise intensity, directivity and spectra of supersonic jets from a convergent-divergent nozzle of design Mach number 1·67 were measured in an anechoic facility over the Mach number range of 1·1 to 2·0. The effect of jet temperature was investigated by operating the jet at three temperature conditions. These sets of data provide sufficient information for fully assessing the relative importance and characteristics of shock associated noise of supersonic jets from convergent-divergent nozzles. Comparisons between theoretical results and measurements show very favorable agreement.

RADIATION AND OUTFLOW BOUNDARY CONDITIONS FOR DIRECT COMPUTATION OF ACOUSTIC AND FLOW DISTURBANCES IN A NONUNIFORM MEAN FLOW

It is well known that Euler equations support small amplitude acoustic, vorticity and entropy waves. To perform high quality direct numerical simulations of flow generated noise problems, acoustic radiation boundary conditions are required along inflow boundaries. Along boundaries where the mean flow leaves the computation domain, outflow boundary conditions are needed to allow the acoustic, vorticity and entropy disturbances to exit the computation domain without significant reflection. A set of radiation and outflow boundary conditions for problems with nonuniform mean flows are developed in this work. Flow generated acoustic disturbances are usually many orders of magnitude smaller than that of the mean flow. To capture weak acoustic waves by direct computation (without first separating out the mean flow), the intensity of numerical noise generated by the numerical algorithm and the radiation and outflow boundary conditions (and the computer) must be extremely low. It is demonstrated by a test problem ...

The radiation of sound by the instability waves of a compressible plane turbulent shear layer

The problem of acoustic radiation generated by instability waves of a compressible plane turbulent shear layer is solved. The solution provided is valid up to the acoustic far-field region. It represents a significant improvement over the solution obtained by classical hydrodynamic-stability theory which is essentially a local solution with the acoustic radiation suppressed. The basic instability-wave solution which is valid in the shear layer and the near-field region is constructed in terms of an asymptotic expansion using the method of multiple scales. This solution accounts for the effects of the slightly divergent mean flow. It is shown that the multiple-scales asymptotic expansion is not uniformly valid far from the shear layer. Continuation of this solution into the entire upper half-plane is described. The extended solution enables the near- and far-field pressure fluctuations associated with the instability wave to be determined. Numerical results show that the directivity pattern of acoustic radiation into the stationary medium peaks at 20 degrees to the axis of the shear layer in the downstream direction for supersonic flows. This agrees qualitatively with the observed noise-directivity patterns of supersonic jets.