Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-05T13:57:15.817Z Has data issue: false hasContentIssue false
  • English
  • Français

A volume integral implementation of the Goldstein generalised acoustic analogy for unsteady flow simulations

Published online by Cambridge University Press:  23 August 2018

Vasily A. Semiletov  and
Sergey A. Karabasov Open the ORCID record for Sergey A. Karabasov [Opens in a new window]
Vasily A. Semiletov
Affiliation:
School of Engineering and Materials Science, Queen Mary University of London, London E1 4NS, UK GPU-Prime Ltd, Cambridge CB23 7DN, UK
Sergey A. Karabasov*
Affiliation:
School of Engineering and Materials Science, Queen Mary University of London, London E1 4NS, UK GPU-Prime Ltd, Cambridge CB23 7DN, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A new volume integral method based on the Goldstein generalised acoustic analogy is developed and directly applied with large-eddy simulation (LES). In comparison with the existing Goldstein generalised acoustic analogy implementations, the current method does not require the computation and recording of the expensive fluctuating stress autocovariance function in the seven-dimensional space–time. Until now, the multidimensional complexity of the generalised acoustic analogy source term has been the main barrier to using it in routine engineering calculations. The new method only requires local pointwise stresses as an input that can be routinely computed during the flow simulation. On the other hand, the new method is mathematically equivalent to the original Goldstein acoustic analogy formulation, and, thus, allows for a direct correspondence between different effective noise sources in the jet and the far-field noise spectra. The implementation is performed for conditions of a high-speed subsonic isothermal jet corresponding to the Rolls-Royce SILOET experiment and uses the LES solution based on the CABARET solver. The flow and noise solutions are validated by comparison with experiment. The accuracy and robustness of the integral volume implementation of the generalised acoustic analogy are compared with those based on the standard Ffowcs Williams–Hawkings surface integral method and the conventional Lighthill acoustic analogy. As a demonstration of its capabilities to investigate jet noise mechanisms, the new integral volume method is applied to analyse the relative importance of various noise generation and propagation components within the Goldstein generalised acoustic analogy model.

JFM classification

Acoustics: Aeroacoustics Mathematical Foundations: Computational methods Acoustics: Jet noise
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 853 , 25 October 2018 , pp. 461 - 487
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Afsar, M. Z., Goldstein, M. E. & Fagan, A. 2011 Enthalpy-flux/momentum-flux coupling in the acoustic spectrum of heated jets. AIAA J. 49 (11), 2522–2531.Google Scholar
Afsar, M. Z., Sescu, A. & Leib, S. J.2016 Predictive capability of low frequency jet noise using an asymptotic theory for the adjoint vector Green’s function in non-parallel flow. AIAA Paper 2016–2804.Google Scholar
Afsar, M. Z., Sescu, A., Sassanis, V. & Lele, S. K. 2017 Supersonic jet noise predictions using a unified asymptotic approximation for the adjoint vector Green’s function and LES data. In 23rd AIAA/CEAS Aeroacoustics Conference, AIAA AVIATION Forum. AIAA Paper 2017–3030.Google Scholar
Bogey, C. & Bailly, C. 2010 Influence of nozzle-exit boundary-layer conditions on the flow and acoustic fields of initially laminar jets. J. Fluid Mech. 663, 507–540.Google Scholar
Bogey, C., Bailly, C. & Juve, D.2001 Noise computation using Lighthill’s equation with inclusion of mean flow–acoustic interactions. AIAA Paper 2001-2255.Google Scholar
Bogey, C., Marsden, O. & Bailly, C. 2012 Influence of initial turbulence level on the flow and sound fields of a subsonic jet at a diameter-based Reynolds number of 105 . J. Fluid Mech. 701, 352–385.Google Scholar
Brentner, K. S. & Farassat, F. 1998 Analytical comparison of the acoustic analogy and Kirchhoff formulation for moving surfaces. AIAA J. 36 (8), 1379–1386.Google Scholar
Bres, G. A., Jaunet, V., Le Rallic, M., Jordan, P., Colonius, T. & Lele, S. K.2015 LES for jet noise: the importance of getting the boundary layer right. AIAA Paper 2015-2535.Google Scholar
Bres, G. A., Nichols, J. A., Lele, S. K., Ham, F. E., Schlinker, R. H., Reba, R. A. & Simonich, J. C. 2012 Unstructured large eddy simulation of a hot supersonic over-expanded jet with chevrons. In 18th AIAA/CEAS Aeroacoustics Conference, 33rd AIAA Aeroacoustics Conference. AIAA Paper 2012-2213.Google Scholar
Bridges, J.2010 Establishing consensus turbulence statistics for hot subsonic jets. AIAA Paper 2010-3751.Google Scholar
Bridges, J. & Wernet, M.2003 Measurements of aeroacoustic sound sources in turbulent jets. AIAA Paper 2003-3130.Google Scholar
Cavalieri, A. V. G., Rodriguez, D., Jordan, P., Colonius, T. & Gervais, Y. 2013 Wavepackets in the velocity field of turbulent jets. J. Fluid Mech. 730, 559–592.Google Scholar
Chintagunta, A., Naghibi, S. E. & Karabasov, S. A. 2018 Flux-corrected dispersion-improved CABARET schemes for linear and nonlinear wave propagation problems. Comput. Fluids 169, 111–128.Google Scholar
Curle, N. 1955 The influence of solid boundaries upon aerodynamic sound. Proc. R. Soc. Lond. A 231 (1187), 505–514.Google Scholar
Depuru Mohan, N. K., Dowling, A. P., Karabasov, S. A., Xia, H., Graham, O., Hynes, T. P. & Tucker, P. G. 2015 Acoustic sources and far-field noise of chevron and round jets. AIAA J. 53 (9), 2421–2436.Google Scholar
Faranosov, G. A., Goloviznin, V. M., Karabasov, S. A., Kondakov, V. G., Kopiev, V. F. & Zaitsev, M. A. 2013 CABARET method on unstructured hexahedral grids for jet noise computation. Comput. Fluids 88, 165–179.Google Scholar
Ffowcs Williams, J. E. 1963 The noise from turbulence convected at high speed. Phil. Trans. R. Soc. Lond. 255, 469–503.Google Scholar
Ffowcs Williams, J. E. & Hawkings, D. L. 1969 Sound generation by turbulence and surfaces in arbitrary motion. Phil. Trans. R. Soc. Lond. A 264, 32142.Google Scholar
di Francescantonio, P. 1997 A new boundary integral formulation for the prediction of sound radiation. J. Sound Vib. 202 (4), 491–509.Google Scholar
Freund, J. B. 2003 Noise-source turbulence statistics and the noise from a Mach 0.9 jet. Phys. Fluids 15 (6), 1788–1799.Google Scholar
Fureby, C. & Grinstein, F. F. 2002 Large eddy simulation of high-Reynolds-number free and wall-bounded flows. J. Comput. Phys. 181, 68–97.Google Scholar
Goldstein, M. E. 1975 The low frequency sound from multipole sources in axisymmetric shear flows, with application to jet noise. J. Fluid Mech. 70 (3), 595–604.Google Scholar
Goldstein, M. E. 2002 A unified approach to some recent developments in jet noise theory. Intl J. Aeroacoust. 1 (1), 1–16.Google Scholar
Goldstein, M. E. 2003 A generalized acoustic analogy. J. Fluid Mech. 488, 315–333.Google Scholar
Goldstein, M. E. 2010 Relation between the generalized acoustic analogy and Lilley’s contributions to aeroacoustics. Intl J. Aeroacoust. 9 (4–5), 401–418.Google Scholar
Goldstein, M. E. 2011 Recent developments in the application of the generalized acoustic analogy to jet noise prediction. Intl J. Aeroacoust. 10 (2–3), 89–116.Google Scholar
Goldstein, M. E. & Leib, S. J. 2008 The aero-acoustics of slowly diverging supersonic jets. J. Fluid Mech. 600, 291–337.Google Scholar
Goldstein, M. E. & Leib, S. J.2016 Azimuthal source non-compactness and mode coupling in sound radiation from high-speed axisymmetric jets. AIAA Paper 2016-2803.Google Scholar
Goldstein, M. E., Sescu, A. & Afsar, M. Z. 2012 Effect of non-parallel mean flow on the Green’s function for predicting the low-frequency sound from turbulent air jets. J. Fluid Mech. 695, 199–234.Google Scholar
Goloviznin, V. M. & Samarskii, A. A. 1998 Finite difference approximation of convective transport equation with space splitting time derivative. J. Matem. Mod. 10 (1), 86–100.Google Scholar
Hussein, H. J., Capp, S. P. & George, W. K. 1994 Velocity measurements in a high-Reynolds-number, momentum conserving, axisymmetric, turbulent jet. J. Fluid Mech. 258, 31–75.Google Scholar
Ingraham, D. & Bridges, J. E.2017 Validating a monotonically-integrated large eddy simulation code for subsonic jet acoustics. AIAA Paper 2017-0456.Google Scholar
Karabasov, S. A. 2010 Understanding jet noise. Phil. Trans. R. Soc. Lond. A 368, 3593–3608.Google Scholar
Karabasov, S. A., Afsar, M. Z., Hynes, T. P., Dowling, A. P., McMullan, W. A., Prokora, C. D., Page, G. J. & McGuirk, J. J. 2010 Jet noise: acoustic analogy informed by large eddy simulation. AIAA J. 48 (7), 1312–1325.Google Scholar
Karabasov, S. A., Bogey, C. & Hynes, T. P. 2013 An investigation of the mechanisms of sound generation in initially laminar, subsonic jets using the Goldstein acoustic analogy. J. Fluid Mech. 714, 24–57.Google Scholar
Karabasov, S. A. & Goloviznin, V. M. 2009 Compact accurately boundary adjusting high-resolution technique for fluid dynamics. J. Comput. Phys. 228, 7426–7451.Google Scholar
Karabasov, S. A. & Hynes, T. P.2006 Adjoint linearized Euler solver in the frequency domain for jet noise modelling. AIAA Paper 2006-2673.Google Scholar
Karabasov, S. A. & Sandberg, R. D. 2015 Influence of free stream effects on jet noise generation and propagation within the Goldstein acoustic analogy approach for fully turbulent jet inflow boundary conditions. Intl J. Aeroacoust. 14 (3–4), 413–430.Google Scholar
Lau, J. C, Morris, P. J. & Fisher, M. J. 1979 Measurements in subsonic and supersonic free jets using a laser velocimeter. J. Fluid Mech. 93 (1), 1–27.Google Scholar
Leib, S. J. & Goldstein, M. E. 2011 Hybrid source model for predicting high-speed jet noise. AIAA J. 49 (7), 1324–1335.Google Scholar
Leib, S. J., Ingraham, D. & Bridges, J. E.2017 Evaluating source terms of the generalized acoustic analogy using the jet engine noise reduction (JENRE) code. AIAA Paper 2017-0459.Google Scholar
Lighthill, M. J. 1952 On sound generated aerodynamically. Part I. General theory. Proc. R. Soc. Lond. 211 (1107), 564–587.Google Scholar
Lilley, G. M. 1958 On the noise from air jets. Aero. Res. Counc. R&M 20, 376.Google Scholar
Markesteijn, A. P. & Karabasov, S. A. 2018 CABARET solutions on graphics processing units for NASA jets: grid sensitivity and unsteady inflow condition effect. C. R. Méc. doi:10.1016/j.crme.2018.07.004.Google Scholar
Morris, P. J. & Zaman, K. B. M. Q. 2010 Velocity measurements in jets with application to noise source modeling. J. Sound Vib. 329, 394–414.Google Scholar
Najafi-Yazdi, A., Bres, G. A. & Mongeau, L. 2011 An acoustic analogy formulation for moving sources in uniformly moving media. Proc. R. Soc. Lond. A 467 (2125), 144–165.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Samanta, A., Freund, J. B., Wei, M. & Lele, S. K. 2006 Robustness of acoustic analogies for predicting mixing-layer noise. AIAA J. 44, 2780–2786.Google Scholar
Semiletov, V. A. & Karabasov, S. A. 2013 CABARET scheme with conservation-flux asynchronous time-stepping for nonlinear aeroacoustics problems. J. Comput. Phys. 253 (15), 157165.Google Scholar
Semiletov, V. A. & Karabasov, S. A.2014a Adjoint linearised Euler solver for Goldstein acoustic analogy equations for 3D non-uniform flow sound scattering problems: verification and capability study. AIAA Paper 2014-2318.Google Scholar
Semiletov, V. A. & Karabasov, S. A. 2014b CABARET scheme for computational aero acoustics: extension to asynchronous time stepping and 3D flow modelling. Intl J. Aeroacoust. 13 (3–4), 321–336.Google Scholar
Semiletov, V. A. & Karabasov, S. A. 2017 On the similarity scaling of jet noise sources for low-order jet noise modelling based on the Goldstein generalised acoustic analogy. Intl J. Aeroacoust. 16 (6), 476–490.Google Scholar
Semiletov, V. A., Karabasov, S. A., Chintagunta, A. & Markesteijn, A. P.2015 Empiricism-free noise calculation from LES solution based on Goldstein generalized acoustic analogy: volume noise sources and meanflow effects. AIAA Paper 2015-2536.Google Scholar
Shur, M. L., Spalart, P. R. & Strelets, M. Kh. 2005 Noise prediction for increasingly complex jets. Part I: methods and tests. Part II: applications. Intl J. Aeroacoust. 4 (3–4), 21366.Google Scholar
Shur, M. L., Spalart, P. R., Strelets, M. Kh. & Travin, K. T. 2015 An enhanced version of DES with rapid transition from RANS to LES in separated flows. Turbulence Flow Combust. 95 (4), 709737.Google Scholar
SILOETProgramme. Rolls-Royce private data.Google Scholar
Tam, C. K. W. & Auriault, L. 1998 Mean flow refraction effects on sound from localized sources in a jet. J. Fluid Mech. 370, 149–174.Google Scholar
Tam, C. K. W., Viswanathan, K., Ahuja, K. K. & Panda, J. 2008 The sources of jet noise: experimental evidence. J. Fluid Mech. 615, 253–992.Google Scholar
Viswanathan, K. 2004 Aeroacoustics of hot jets. J. Fluid Mech. 516, 39–82.Google Scholar
Viswanathan, K. 2009 Mechanisms of jet noise generation: classical theories and recent developments. Intl J. Aeroacoust. 615, 253–992.Google Scholar
Welch, P. D. 1967 The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust. 15, 70–73.Google Scholar
Witze, P. O. 1974 Centerline velocity decay of compressible free jets. AIAA J. 12 (4), 417–418.Google Scholar