Skip to main content Accessibility help
Hostname: page-component-5d6d958fb5-27v8q Total loading time: 0.474 Render date: 2022-11-27T13:42:31.283Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "displayNetworkTab": true, "displayNetworkMapGraph": false, "useSa": true } hasContentIssue true

Sound and turbulence modulation by particles in high-speed shear flows

Published online by Cambridge University Press:  18 July 2019

David A. Buchta*
Coordinated Science Laboratory, University of Illinois at Urbana–Champaign, Urbana, IL 61801, USA
Gregory Shallcross
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
Jesse Capecelatro
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
Email address for correspondence:


High-speed free-shear-flow turbulence, laden with droplets or particles, can radiate weaker pressure fluctuations than its unladen counterpart. In this study, Eulerian–Lagrangian simulations of high-speed temporally evolving shear layers laden with monodisperse, adiabatic, inertial particles are used to examine particle–turbulence interactions and their effect on radiated pressure fluctuations. An evolution equation for gas-phase pressure intensity is formulated for particle-laden flows, and local mechanisms of pressure changes are quantified over a range of Mach numbers and particle mass loadings. Particle–turbulence interactions alter the local pressure intensity directly via volume displacement (due to the flow of finite-size particles) and drag coupling (due to local slip velocity between phases), and indirectly through significant turbulence changes. The sound radiation intensity near subsonic mixing layers increases with mass loading, consistent with existing low Mach number theory. For supersonic flows, sound levels decrease with mass loading, consistent with trends observed in previous experiments. Particle-laden cases exhibit reduced turbulent kinetic energy compared to single-phase flow, providing one source of their sound changes; however, the subsonic flow does not support such an obvious source-to-sound decomposition to explain its sound intensity increase. Despite its decrease in turbulence intensity, the louder particle-laden subsonic flows show an increase in the magnitude and time-rate-of-change of fluid dilatation, providing a mechanism for its increased sound radiation. Contrasting this, the quieter supersonic particle-laden flows exhibit decreased gas-phase dilatation yet its time-rate-of-change is relatively insensitive to mass loading, supporting such a connection.

JFM Papers
© 2019 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.)


Agrawal, K., Holloway, W., Milioli, C. C., Milioli, F. E. & Sundaresan, S. 2013 Filtered models for scalar transport in gas–particle flows. Chem. Engng Sci. 95, 291300.CrossRefGoogle Scholar
Agrawal, K., Loezos, P. N., Syamlal, M. & Sundaresan, S. 2001 The role of meso-scale structures in rapid gas-solid flows. J. Fluid Mech. 445, 151185.CrossRefGoogle Scholar
Alkislar, M. B. & Butler, G. W.2007 Significant improvements on jet noise reduction by chevron–microjet combination. AIAA Paper 2007-3598, pp. 21–23.Google Scholar
Anderson, T. B. & Jackson, R. 1967 Fluid mechanical description of fluidized beds. Equations of motion. Ind. Engng Chem. Fundam. 6 (4), 527539.CrossRefGoogle Scholar
Balachandar, S. & Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111133.CrossRefGoogle Scholar
Battista, F., Gualtieri, P., Mollicone, J. P. & Casciola, C. M. 2018 Application of the exact regularized point particle method (ERPP) to particle laden turbulent shear flows in the two-way coupling regime. Intl J. Multiphase Flow 101, 113124.CrossRefGoogle Scholar
Bowes, W., Rumpf, D., Bowler, D., Carnes, R., Fratarangelo, P., Heiser, W. H., Hu, D. L., Moin, P. & Voorhees, W. J.2009 Report on jet engine noise reduction. Tech. Rep. Naval Research Advisory Committee.Google Scholar
Briley, W. R. & McDonald, H. 1977 Solution of the multidimensional compressible Navier–Stokes equations by a generalized implicit method. J. Comput. Phys. 24 (4), 372397.CrossRefGoogle Scholar
Buchta, D. A.2016 Crackle noise from high-speed free-shear-flow turbulence. PhD thesis, University of Illinois at Urbana–Champaign.Google Scholar
Buchta, D. A. & Freund, J. B. 2017 The near-field pressure radiated by planar high-speed free-shear-flow turbulence. J. Fluid Mech. 832, 383408.CrossRefGoogle Scholar
Buchta, D. A. & Freund, J. B. 2019 Intense sound radiation by high-speed flow: turbulence structure, gas properties, and near-field gas dynamics. Phys. Rev. Fluids 4, 044605.CrossRefGoogle Scholar
Capecelatro, J. & Buchta, D. 2017 Direct numerical simulation of noise suppression by water injection in high-speed flows. In 55th AIAA Aerospace Sciences Meeting. AIAA.Google Scholar
Capecelatro, J. & Desjardins, O. 2013 An Euler–Lagrange strategy for simulating particle-laden flows. J. Comput. Phys. 238, 131.CrossRefGoogle Scholar
Capecelatro, J., Desjardins, O. & Fox, R. O. 2015 On fluid-particle dynamics in fully developed cluster-induced turbulence. J. Fluid Mech. 780, 578635.CrossRefGoogle Scholar
Capecelatro, J., Desjardins, O. & Fox, R. O. 2018 On the transition between turbulence regimes in particle-laden channel flows. J. Fluid Mech. 845, 499519.CrossRefGoogle Scholar
Cleckler, J., Elghobashi, S. & Liu, F. 2012 On the motion of inertial particles by sound waves. Phys. Fluids 24 (3), 033301.CrossRefGoogle Scholar
Clift, R., Grace, J. R. & Weber, M. E. 2005 Bubbles, Drops, and Particles. Courier Corporation.Google Scholar
Crighton, D. G. 1975 Basic principles of aerodynamic noise generation. Prog. Aerosp. Sci. 16 (1), 3196.CrossRefGoogle Scholar
Crighton, D. G. & Ffowcs Williams, J. E. 1969 Sound generation by turbulent two-phase flow. J. Fluid Mech. 36 (3), 585603.CrossRefGoogle Scholar
Dai, Q., Jin, T., Luo, K. & Fan, J. 2018 Direct numerical simulation of particle dispersion in a three-dimensional spatially developing compressible mixing layer. Phys. Fluids 30 (11), 113302.Google Scholar
Debisschop, J. R., Chambres, O. & Bonnet, J. P. 1994 Velocity field characteristics in supersonic mixing layers. Exp. Therm. Fluid Sci. 9 (2), 147155.Google Scholar
Eaton, J. K. & Fessler, J. R. 1994 Preferential concentration of particles by turbulence. Intl J. Multiphase Flow 20, 169209.CrossRefGoogle Scholar
Elghobashi, S. & Truesdell, G. C. 1993 On the two-way interaction between homogeneous turbulence and dispersed solid particles. I. Turbulence modification. Phys. Fluids A 5 (7), 17901801.CrossRefGoogle Scholar
Elliott, G. S. & Samimy, M. 1990 Compressibility effects in free shear layers. Phys. Fluids A 2 (7), 12311240.CrossRefGoogle Scholar
Ffowcs Williams, J. E. 1963 The noise from turbulence convected at high speed. Phil. Trans. R. Soc. Lond. A 255 (1061), 469503.Google Scholar
Ffowcs Williams, J. E. & Maidanik, G. 1965 The Mach wave field radiated by supersonic turbulent shear flows. J. Fluid Mech. 21, 641657.CrossRefGoogle Scholar
Fox, R. O. 2014 On multiphase turbulence models for collisional fluid–particle flows. J. Fluid Mech. 742, 368424.CrossRefGoogle Scholar
Freund, J. B. 1997 Proposed inflow/outflow boundary condition for direct computation of aerodynamic sound. AIAA J. 35 (4), 740742.CrossRefGoogle Scholar
Gilinsky, M., Bhat, T. & Seiner, J. 1994 Supersonic gasdispersional jets – models and applications. In 32nd Aerospace Sciences Meeting and Exhibit. AIAA.Google Scholar
Glasser, B. J., Sundaresan, S. & Kevrekidis, I. G. 1998 From bubbles to clusters in fluidized beds. Phys. Rev. Lett. 81, 18491852.CrossRefGoogle Scholar
Goebel, S. G. & Dutton, J. C. 1991 Experimental study of compressible turbulent mixing layers. AIAA J. 29 (4), 538546.CrossRefGoogle Scholar
Greska, B. J.2005 Supersonic jet noise and its reduction using microjet injection. PhD thesis, Florida State University.CrossRefGoogle Scholar
Gualtieri, P., Battista, F. & Casciola, C. M. 2017 Turbulence modulation in heavy-loaded suspensions of tiny particles. Phys. Rev. Fluids 2 (3), 034304.CrossRefGoogle Scholar
Gualtieri, P., Picano, F. & Casciola, C. M. 2009 Anisotropic clustering of inertial particles in homogeneous shear flow. J. Fluid Mech. 629, 2539.CrossRefGoogle Scholar
Gunn, D. J. 1978 Transfer of heat and mass to particles in fixed and fluidised beds. Intl J. Heat Mass Transfer 21, 467476.CrossRefGoogle Scholar
Henderson, B. 2010 Fifty years of fluidic injection for jet noise reduction. Intl J. Aeroacoust. 9 (1-2), 91122.CrossRefGoogle Scholar
Himelblau, H., Kern, D. L., Manning, J. E., Piersol, A. G. & Rubin, S.2001 Dynamic environmental criteria. NASA Tech. Handbook NASA-HDBK-7005.Google Scholar
Houim, R. W. & Oran, E. S. 2016 A multiphase model for compressible granular–gaseous flows: formulation and initial tests. J. Fluid Mech. 789, 166220.CrossRefGoogle Scholar
Ignatius, J. K., Sathiyavageeswaran, S. & Chakravarthy, S. R. 2014 Hot-flow simulation of aeroacoustics and suppression by water injection during rocket liftoff. AIAA J. 53 (1), 235245.CrossRefGoogle Scholar
Jordan, P. & Colonius, T. 2013 Wave packets and turbulent jet noise. Annu. Rev. Fluid Mech. 45 (1), 173195.CrossRefGoogle Scholar
Kaltenbach, M., Maschke, C. & Klinke, R. 2008 Health consequences of aircraft noise. Dtsch. Arztebl Int. 105 (31–32), 548556.Google ScholarPubMed
Kleinman, R. & Freund, J. B. 2008 The sound from mixing layers simulated with different ranges of turbulence scales. Phys. Fluids 20 (10), 101503.CrossRefGoogle Scholar
Krothapalli, A., Venkatakrishnan, L., Lourenco, L., Greska, B. & Elavarasan, R. 2003 Turbulence and noise suppression of a high-speed jet by water injection. J. Fluid Mech. 491, 131159.CrossRefGoogle Scholar
Laufer, J. 1961 Aerodynamic noise in supersonic wind tunnels. J. Aero. Sci. 28 (9), 685692.Google Scholar
Laufer, J., Schlinker, R. & Kaplan, R. E. 1976 Experiments on supersonic jet noise. AIAA J. 14 (4), 489497.CrossRefGoogle Scholar
Leboissetier, A., Okong’o, N. & Bellan, J. 2005 Consistent large-eddy simulation of a temporal mixing layer laden with evaporating drops. Part 2. A posteriori modelling. J. Fluid Mech. 523, 3778.CrossRefGoogle Scholar
Lhuillier, D., Theofanous, T. G. & Liou, M. 2010 Multiphase flows: compressible multi-hydrodynamics. In Handbook of Nuclear Engineering, pp. 18131912. Springer.CrossRefGoogle Scholar
Lighthill, M. J. 1952 On sound generated aerodynamically I. General theory. Proc. R. Soc. Lond. A 211 (1107), 564587.Google Scholar
Lighthill, M. J. 1956 Viscosity effects in sound waves of finite amplitude. In Surveys in Mechanics (ed. Batchelor, G. K. & Davies, R. M.), pp. 250351. Cambridge University Press.Google Scholar
Ling, Y., Balachandar, S. & Parmar, M. 2016 Inter-phase heat transfer and energy coupling in turbulent dispersed multiphase flows. Phys. Fluids 28 (3), 033304.CrossRefGoogle Scholar
Marchioli, C. & Soldati, A. 2002 Mechanisms for particle transfer and segregation in a turbulent boundary layer. J. Fluid Mech. 468, 283315.CrossRefGoogle Scholar
Mattsson, K., Svärd, M. & Nordström, J. 2004 Stable and accurate artificial dissipation. J. Sci. Comput. 21 (1), 5779.CrossRefGoogle Scholar
Mehrabadi, M., Tenneti, S., Garg, R. & Subramaniam, S. 2015 Pseudo-turbulent gas-phase velocity fluctuations in homogeneous gas–solid flow: fixed particle assemblies and freely evolving suspensions. J. Fluid Mech. 770, 210246.CrossRefGoogle Scholar
Miller, R. S. & Bellan, J. 1999 Direct numerical simulation of a confined three-dimensional gas mixing layer with one evaporating hydrocarbon-droplet-laden stream. J. Fluid Mech. 384, 293338.CrossRefGoogle Scholar
Murray, N. E. & Lyons, G. W. 2016 On the convection velocity of source events related to supersonic jet crackle. J. Fluid Mech. 793, 477503.CrossRefGoogle Scholar
Nicolai, C., Jacob, B. & Piva, R. 2013 On the spatial distribution of small heavy particles in homogeneous shear turbulence. Phys. Fluids 25 (8), 083301.CrossRefGoogle Scholar
Norum, T. D.2004 Reductions in multi-component jet noise by water injection. In 10th AIAA/CEAS Aeroacoustics Conference, AIAA Paper 2004-2976.Google Scholar
Noymer, P. D. & Glicksman, L. R. 2000 Descent velocities of particle clusters at the wall of a circulating fluidized bed. Chem. Engng Sci. 55 (22), 52835289.CrossRefGoogle Scholar
Okong’o, N. A. & Bellan, J. 2004 Consistent large-eddy simulation of a temporal mixing layer laden with evaporating drops. Part 1. Direct numerical simulation, formulation and a priori analysis. J. Fluid Mech. 499, 147.CrossRefGoogle Scholar
Pantano, C. & Sarkar, S. 2002 A study of compressibility effects in the high-speed turbulent shear layer using direct simulation. J. Fluid Mech. 451, 329371.CrossRefGoogle Scholar
Papamoschou, D.2000 Linear model of Mach wave suppression in a dual-stream jet. In 6th Aeroacoustics Conference and Exhibit. AIAA.CrossRefGoogle Scholar
Parmar, M., Haselbacher, A. & Balachandar, S. 2012 Equation of motion for a sphere in non-uniform compressible flows. J. Fluid Mech. 699, 352375.CrossRefGoogle Scholar
Phillips, O. M. 1960 On the generation of sound by supersonic turbulent shear layers. J. Fluid Mech. 9, 128.CrossRefGoogle Scholar
Reeks, M. W. 1983 The transport of discrete particles in inhomogeneous turbulence. J. Aero. Sci. 14 (6), 729739.CrossRefGoogle Scholar
Ribner, H. S.1962 Aerodynamic sound from fluid dilatations. Tech. Rep. 86. University of Toronto Inst. Aerophysics.Google Scholar
Ristorcelli, J. R.1997 Fluctuating dilatation rate as an acoustic source. Tech. Rep. Institute for Computer Applications in Science and Engineering.Google Scholar
Rouson, D. W. I. & Eaton, J. K. 2001 On the preferential concentration of solid particles in turbulent channel flow. J. Fluid Mech. 428, 149169.CrossRefGoogle Scholar
Sarkar, S. 1992 The pressure–dilatation correlation in compressible flows. Phys. Fluids 4 (12), 26742682.CrossRefGoogle Scholar
Schiller, L. & Naumann, A. 1933 Fundamental calculations in gravitational processing. Z. Verein. Deutsch. Ing. 77, 318320.Google Scholar
Shaffer, F., Gopalan, B., Breault, R. W., Cocco, R., Karri, S. B., Hays, R. & Knowlton, T. 2013 High speed imaging of particle flow fields in CFB risers. Powder Technol. 242, 8699.CrossRefGoogle Scholar
Strand, B. 1994 Summation by parts for finite difference approximations for d/dx. J. Comput. Phys. 110 (1), 4767.CrossRefGoogle Scholar
Svärd, M., Carpenter, M. H. & Nordström, J. 2007 A stable high-order finite difference scheme for the compressible Navier–Stokes equations, far-field boundary conditions. J. Comput. Phys. 225 (1), 10201038.CrossRefGoogle Scholar
Tenneti, S., Garg, R. & Subramaniam, S. 2011 Drag law for monodisperse gas-solid systems using particle-resolved direct numerical simulation of flow past fixed assemblies of spheres. Intl J. Multiphase Flow 37 (9), 10721092.CrossRefGoogle Scholar
Tenneti, S., Sun, B., Garg, R. & Subramaniam, S. 2013 Role of fluid heating in dense gas–solid flow as revealed by particle-resolved direct numerical simulation. Intl J. Heat Mass Transfer 58 (1), 471479.CrossRefGoogle Scholar
Vishnampet, R.2015 An exact and consistent adjoint method for high-fidelity discretization of the compressible flow equations. PhD thesis, University of Illinois at Urbana-Champaign.Google Scholar
Vishnampet, R., Bodony, D. J. & Freund, J. B. 2015 A practical discrete-adjoint method for high-fidelity compressible turbulence simulations. J. Comput. Phys. 285, 173192.CrossRefGoogle Scholar
Vreman, A. W., Sandham, N. D. & Luo, K. H. 1996 Compressible mixing layer growth rate and turbulence characteristics. J. Fluid Mech. 320, 235258.CrossRefGoogle Scholar
Zoppellari, E. & Juve, D.1997 Reduction of jet noise by water injection. In 3rd AIAA/CEAS Aeroacoustics Conference, AIAA Paper 97-1622, pp. 267–274.Google Scholar
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the or variations. ‘’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Sound and turbulence modulation by particles in high-speed shear flows
Available formats

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Sound and turbulence modulation by particles in high-speed shear flows
Available formats

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Sound and turbulence modulation by particles in high-speed shear flows
Available formats

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *