Lighthill's Analogy Research Articles

Numerical analysis of the error in the sound power predicted through the Lighthill acoustic analogy

AbstractThis article gives rigorous numerical analysis of the error in prediction of aeroacoustic noise via Lighthill analogy. The first fundamental and intractable problem considered herein is to predict the sound power generated by aerodynamic noise on surfaces. We give a full analysis of three methods of prediction. The second fundamental difficulty in the numerical analysis of aeroacoustics is the limited regularity of the underlying turbulent flow. This is treated herein by giving a negative norm error analysis which reduces the required regularity. We also give a comprehensive analysis of a fully discrete scheme including effects of the error coming into acoustic equation from the turbulent flow simulation. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 204–234,2012

Simulation and analysis of infrasound generated by severe storms.

Recent observations and longstanding theoretical considerations suggest that a tornado can have a detectable signature in the infrasound of a severe storm. To reliably distinguish the vortex signal from extraneous noise, it is important to advance current understanding of the different mechanisms that produce infrasound in atmospheric convection. Without detailed observations of the acoustic sources within a storm, numerical modeling may be the best method of investigation. This avenue of research is being explored with the Regional Atmospheric Modeling System customized to simulate aeroacoustics. By comparison to analytical results, it has been shown that the model adequately generates the infrasound of vortices and basic diabatic cloud processes. Given these encouraging results, the model is now being used to simulate the infrasound of various convective systems and individual storm features including a towering cumulonimbus (with multiple hydrometeor categories) and artificially forced tornadoes with realistic structure and fluctuations. This presentation will expound a convenient technique for analyzing the sources of infrasound in a complex storm simulation based on an acoustic wave equation (Lighthill analogy) for the perturbation Exner function. It will also provide some computational evidence that moderate‐to‐strong tornadoes can emit stronger 0.1–1 Hz infrasound than generic storms. [Work supported by NSF‐ATM‐0832320].

Low-dimensional characteristics of a transonic jet. Part 2. Estimate and far-field prediction

Complementary low-dimensional techniques are modified to estimate the most energetic turbulent features of a Mach 0.85 axisymmetric jet in the flow's near-field regions via spectral linear stochastic estimation. This model estimate is three-dimensional, comprises all three components of the velocity field and is time resolved. The technique employs the pressure field as the unconditional input, measured within the hydrodynamic periphery of the jet flow where signatures (pressure) are known to comprise a reasonable footprint of the turbulent large-scale structure. Spectral estimation coefficients are derived from the joint second-order statistics between coefficients that are representative of the low-order pressure field (Fourier-azimuthal decomposition) and of the low-order velocity field (proper orthogonal decomposition). A bursting-like event is observed in the low-dimensional estimate and is similar to what was found in the low-speed jet studies of others. A number of low-dimensional estimates are created using different velocity–pressure mode combinations from which predictions of the far-field acoustics are invoked using Lighthill's analogy. The overall sound pressure level (OASPL) directivity is determined from the far-field prediction, which comprises qualitatively similar trends when compared to direct measurements at r/D=75. Retarded time topologies of the predicted field at 90° and 30° are also shown to manifest, respectively, high- and low-frequency wave-like motions when using a combination of only the low-order velocity modes (m=0, 1, 2). This work thus constitutes a first step in developing low-dimensional and dynamical system models from hydrodynamic pressure signatures for estimating and predicting the behaviour of the energy-containing events that govern many of the physical constituents of turbulent flows.

Noise generation in an unstable boundary-layer flow over a flexible wall

The boundary-layer flow, for instance along a sonar dome, gives rise to hydrodynamic noise due to the pressure fluctuations. The prediction of the resulting self-noise received by the sonar antenna is based on models, which in general take only partially into account the flexibility of the dome wall. The present work readdresses the problem of hydrodynamic noise, considering the geometrically simplified model of a two-dimensional unstable boundary-layer flow along an elastic plate with clamped ends. The incompressible Navier-Stokes equations are fully coupled to the elastic plate model and the system is numerically solved for various plate materials. The unstable flow dynamics is analyzed with respect to the wall properties. The Fourier-transformed stress tensor is then used in the framework of Lighthill's analogy to determine the generated radiative sound, emphasizing the effect of wall-flexibility. This work is supported by Thales Underwater System and DCNS.

Shock-induced noise in 2D sub- and supersonic mixing layers

A numerical code solving acoustic analogies to predict shock-induced noise is developed. Both Lighthill's analogy and the one of Ffowcs-Williams and Hawkings (FWH) are implemented and compared to the acoustic far field of the direct numerical simulation (DNS) in detail. In addition to this the linearized Euler Equations (LEE) are used to propagate into the acoustic far field and the results are also compared to the DNS-data. With a two dimensional mixing layer in a subsonic test case and a Reynolds number based on the initial shear layer thickness of , a first application of the code is performed. To investigate the shock-induced noise, a two dimensional supersonic mixing layer with an impinging oblique shock is simulated. The results of the analogies for the shock-induced noise are in good agreement with the acoustic far field of the DNS. The accuracy of the FWH-method is better than the one of Lighthill's analogy.

Validation of a Time Domain Formulation for Propeller Noise Prediction

The present paper is oriented at the definition of a series of validation test cases for the far-field subsonic formulation of Farassat in the time domain, solving the Lighthill analogy for aeroacoustics in the Ffowcs William-Hawkings formulation for far-field noise predictions. The focus will be on the definition, validation and verification of four test cases for far-field acoustic propagation. The test cases are: (i) a rotating rotor with a pre-defined body force, (ii) a translating and rotating small disk case with a moving observer, (iii) a conventional helicopter rotor case, (iv) and the consistency test known as the Isom thickness noise. The acoustic pressure signature, sound pressure level and directivity have been calculated for each test case. Graphical outputs and comparisons of results with those of analytical solutions are presented.

Noise radiated by a non-isothermal, temporal mixing layer

The ability of Lighthill's analogy to predict the sound radiated by a transitional mixing layer is evaluated by means of direct numerical simulation (DNS). The specific case of low Mach number flows with density variations is investigated. In order to limit the global computational cost, the acoustic source information is based on numerical results where the sound waves have been removed. It is shown that the low Mach number approximation coupled with the acoustic analogy can lead to very accurate predictions for the radiated sound if the acoustic sources in Lighthill's equation are taken into account carefully. Results for the acoustic intensity deduced from a repeated use of the Lighthill's analogy over a wide range of Mach numbers allow us to discuss the adequacy of scaling laws proposed by previous authors (J. Sound Vib. 28(3), 563–585, 1973; 31(4), 391–397, 1973; 48(1), 95–111, 1976) for the prediction of noise from hot jets.

Effects of compliant coatings on radiated sound from a rigid-wall turbulent boundary layer

A theoretical model is developed to investigate the effect of compliant coatings on radiated sound from low Mach-number turbulent boundary layers over otherwise rigid surfaces. Lighthill's analogy is employed and the primary noise source is assumed to be from wall-pressure fluctuations. Parametric studies are performed on the behavior of the material properties such as the speed of sound and density of compliant coatings. Comparisons are made between the results from coated and uncoated rigid walls. At low frequencies, compliant coatings are not effective for noise reduction. At high frequencies, coating materials with low speed of sound and low density provide significant noise reduction.

Effects of flexible walls on radiated sound from a turbulent boundary layer

In this paper, radiated sound from low Mach number turbulent boundary layers is studied using Lighthill's analogy. The focus is on investigating the behavior of wall pressure fluctuations on a flexible wall boundary. Comparisons are made between the results from rigid and flexible walls. At low frequencies, the flexible wall results have shown much higher levels of power spectra. At high frequencies, the spectra of the flexible wall sound radiation merge with those of the rigid wall sound radiation. These trends are in agreement with other experimental and theoretical results in literature. This theoretical study of the two-dimensional turbulent boundary layer clarifies the effects of a flexible wall on radiated sound in low Mach number flows.

Sound Generation in Compressible Mixing Layers

Direct numerical simulations have been performed to clarify the sound generation mechanism in two-dimensional temporally evolving compressible mixing layers. The sound generation in mixing layer is governed by the variations of vorticity which are induced by the Kelvin-Helmholtz instability. The pressure fluctuations with high frequency are observed in the period of vortex roll-up, and the amplitude of pressure fluctuations increase on the occasion of vortex pairing. The acoustic source term is governed by the Reynolds stress component and the viscous component is negligible. The effects of convective Mach number Mc on sound generation are also investigated. Both the pressure fluctuations and acoustic source term increase with the increase of convective Mach number. For Mc=0.6, shock wave called 'eddy shocklet' is produced by the vortex pairing, which dominates the sound generation from the mixing layer at high Mc. The far field sound computed by DNS is compared with the predictions based on the acoustic analogies derived by Powell and Lighthill. The prediction by Powell's analogy shows a good agreement with DNS, while the pressure fluctuations predicted by Lighthill's analogy are low compared with the DNS results after the vortex pairing.

Sound Generation in Chemically Reacting Mixing Layers.

Direct numerical simulations have been performed to clarify the sound generation mechanism in a two-dimensional chemically reacting compressible mixing layers. The effects of heat release on the mechanism of sound generation are investigated. The dominant acoustic source term in Lighthill's equation is entropy component, while the Reynolds stress component and viscous component are considerably small. The maximum pressure fluctuation in the far-field increases with the increase of heat release parameter and Damkohler number, which suggests that the characteristics of sound are mainly determined by the heat release in reacting mixing layers. The far-field sound computed by DNS is compared with the predictions based on the acoustic analogies derived by Powell and Lighthill. Both analogies fail to predict the far-field sound in the reacting mixing layer. Lighthill's analogy gives quite large pressure fluctuation and Powell's analogy gives lower pressure compared with DNS. In this study, an analogy including Powell's source term entropy term is prmoposed. The pressure fluction predicted by the proposed analogy shows a good agreement with the DNS results.

Sound Generation in Compressible Mixing Layers.

Direct numerical simulations have been performed to clarify the sound generation mechanism in a two-dimensional temporally evolving compressible mixing layers. The sound generation in mixing layer is governed by the variations of vorticity which are induced by the Kelvin-Helmholtz instability. The pressure fluctuations with high frequency are observed in the period of vortex roll-up, and the amplitude of pressure fluctuations increase on the occasion of vortex pairing. The acoustic source term is governed by the Reynolds stress component and the viscous component is negligible. The effects of convective Mach number Mc on sound generation are also investigated. Both the pressure fluctuations and acoustic source term increase with the increase of convective Mach number. For Mc=0.6, shock wave called'eddy shocklet, is produced by the vortex pairing, which dominates the sound generation from the mixing layer at high Mc. The far-field sound computed by DNS is compared with the predictions based on the acoustic analogies derived by Powell and Lighthill. The prediction by Powell's analogy shows a good agreement with DNS, while the pressure fluctuations predicted by Lighthill's analogy are low compared with the DNS results after the vortex pairing.

CAA activities at ONERA using LES

Most CAA applications rely on hybrid methods providing the radiated sound (using the Lighthill analogy, Kirchhoff integral or linearized Euler equations) from unsteady CFD. In that context, LES is widely considered as a compromise between full DNS and unsteady RANS. For two years, ONERA has undertaken studies aiming at understanding and applying LES in CAA. Former works focused on coupling LES to the Lighthill analogy. One typical application was the prediction of the noise generated by vortex shedding at the trailing edge of a thick flat plate. The incompressible LES was performed on a Cartesian mesh using the ONERA ‘‘pegase’’ code. The far-field noise was computed using the Curle formulation and favorably compared to airfoil noise experiments. More recently, a theoretical study analyzed the contribution of the LES subgrid scale model, or cutoff wave number, to the noise production computed from the Lighthill tensor, concluding that modeling this contribution may be important to correctly estimating the acoustic field. Other CAA applications of LES are now under progress: flap side-edge noise from high-lift devices of landing aircraft, and jet noise, with comparison of the Kirchhoff integral and Lighthill analogy. Coupling LES with linearized Euler equations is also a topic of interest.

Computation of jet mixing noise due to coherent structures: the plane jet case

A computational approach to the prediction of jet mixing noise is described. It is based on Lighthill's analogy, used together with a semi-deterministic modelling of turbulence (SDM), where only the large-scale coherent motion is evaluated. The features of SDM are briefly illustrated in the case of shear layers, showing that suitable descriptions of the mean flow and of the large-scale fluctuations are obtained. Aerodynamic calculations of two cold fully expanded plane jets at Mach numbers 0.50 and 1.33 are then carried out. The numerical implementation of Lighthill's analogy is described and different integral formulations are compared for the two jets. It is shown that the one expressed in a space–time conjugate (κ, ω)-plane is particularly convenient and allows a simple geometrical interpretation of the computations. Acoustic results obtained with this formulation are compared to relevant experimental data. It is concluded that the radiation of subsonic jets cannot be explained only by the contribution of the turbulent coherent motion. In this case, directivity effects are well recovered but the acoustic spectra are too narrow and limited to the low-frequency range. In contrast at Mach number 1.33, especially in the forward quadrant, results are satisfactory, showing that coherent structures indeed provide the main source of supersonic jet mixing noise.

Computation of quadrupole noise using acoustic analogy

Acoustic analogy computations of vortex shedding noise were carried out in the context of a two-dimensional, low-Mach-number laminar flow past a NACA 0012 airfoil at chord Reynolds number of 10 4 . The incompressible Navier-Stokes equations were solved numerically to give an approximate description of the near-field flow dynamics and the acoustic source functions. The radiated far-field noise was computed based on Curle's extension to the Lighthill analogy. This study emphasizes an accurate evaluation of the Reynolds stress quadrupoles in the presence of an extensive wake. An effective method for separating the physical noise source from spurious boundary contributions caused by eddies crossing a permeable computational boundary is presented. The effect of retarded-time variations across the source region is also examined. Computational solutions confirm that the quadrupole noise is weak compared with the noise due to lift and drag dipoles when the freestream Mach number is small. The techniques developed in this study are equally applicable to flows in which the volume quadrupoles act as a prominent noise source.

Jet noise generation mechanism

The breakdown process of the initial large-scale structures into substructures near the end of the potential core is examined and the production of aerosound as a result is discussed. The quadrupole-like directivity pattern of jet noise is numerically obtained by applying the large-eddy simulation (LES) technique for the fluid flow. The Lighthill analogy is used to obtain the acoustic far field. Most of the sound comes from a region near the end of the potential core. A discussion to explain this quasiaxisymmetric directivity pattern is given. The directivity maximum is obtained at about 45° from the axis of the jet exhaust. This will be explained in terms of turbulent velocities. The convective effect on sources is introduced by ray tracing to calculate retarded times. The result is to obtain more radiation downstream, as is observed. The relation of this correction to the Lighthill theory will be discussed.