Skip to main content Accessibility help
×
Home
Hostname: page-component-55597f9d44-54jdg Total loading time: 0.422 Render date: 2022-08-15T09:12:52.635Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

Large-eddy simulation of particle-laden turbulent flows

Published online by Cambridge University Press:  16 October 2008

M. BINI
Affiliation:
Mechanical Engineering Department, Imperial College London, Exhibition Road, London SW7 2AZ, UK
W. P. JONES
Affiliation:
Mechanical Engineering Department, Imperial College London, Exhibition Road, London SW7 2AZ, UK

Abstract

A large-eddy-based methodology for the simulation of turbulent sprays is discussed. The transport equations for the spatially filtered gas phase variables, in which source terms accounting for the droplet effects are added, are solved together with a probabilistic description of the liquid phase. The probabilistic approach for the liquid phase is based on the transport equation for the spatially filtered joint probability density function of the variables required in order to describe the state of the liquid phase. In this equation, unclosed terms representing the filtered Lagrangian rates of change of the variables describing the spray are present. General modelling ideas for subgrid-scale (SGS) effects are proposed. The capabilities of the approach and the validity of the closure models, with particular with respect to the SGS dispersion, are investigated through application to a dilute particle-laden turbulent mixing layer. It is demonstrated that the formulation is able to reproduce very closely the measured properties of both the continuous and dispersed phases. The large-eddy simulation (LES) results are also found to be entirely consistent with the experimentally observed characteristics of droplet–gas turbulence interactions. Consistent with direct numerical simulation (DNS) studies of isotropic turbulence laden with particles where the entire turbulence spectrum is found to be modulated by the presence of particles, the present investigation, which comprises the effects of particle transport upon the large-scale vortical structures of a turbulent shear flow, highlights what appears to be a selective behaviour; few large-scale frequencies gain energy whereas the remaining modes are damped.

Type
Papers
Copyright
Copyright © Cambridge University Press 2008

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

Ahmed, A. M. & Elghobashi, S. 2000 On the mechanism of modifying the structure of turbulent homogeneous shear flows by dispersed particles. Phys. Fluids 12, 29062930.CrossRefGoogle Scholar
Aliseda, A., Cartellier, A., Hainaux, F. & Lasheras, J. C. 2002 Effect of preferential concentration on the settling velocity of heavy particles in homogeneous isotropic particles. J. Fluid Mech. 468, 77105.CrossRefGoogle Scholar
Bellan, J. 2000 Perspectives on large eddy simulation for sprays: issues and solutions. Atomiz. Sprays 10, 409425.CrossRefGoogle Scholar
Bini, M. 2006 Large eddy simulation of particle and droplet laden flows with stochastic modelling of sub-filter scales. PhD thesis, Imperial College, University of London, London, (UK).Google Scholar
Bini, M. & Jones, W. P. 2007 Particle acceleration in turbulent flows: a class of non-linear stochastic models for intermittency and heavy tailed pdfs. Phys. Fluids 19 (3), 035104.CrossRefGoogle Scholar
Boivin, M., Simonin, O. & Squires, K. D. 1998 Direct numerical simulation of turbulence modulation by particles in isotropic turbulence. J. Fluid Mech. 375, 235263.CrossRefGoogle Scholar
Bosse, T., Kleiser, L. & Meiburg, E. 2006 Small particles in homogeneous turbulence: settling velocity enhancement by two-way coupling. Phys. Fluids 18, 027102.CrossRefGoogle Scholar
Branley, N. 1999 Large eddy simulation of non-premixed turbulent flames. PhD thesis, Imperial College, University of London, London, UK.Google Scholar
Branley, N. & Jones, W. P. 1999 Large eddy simulation of a turbulent non-premixed swirling flame. In Engineering Turbulence Modelling and Measurements 4 (ed. Lawrence, D. & Rodi, W.), pp. 861870. Elsevier.Google Scholar
Branley, N. & Jones, W. P. 2001 Large eddy simulation of a turbulent non-premixed. Combust. Flame 127, 19141934.CrossRefGoogle Scholar
Buyevich, Y. A. 1971 Statistical hydromechanics of disperse systems. Part 1. Physical background and general equations. J. Fluid Mech. 49, 489507.CrossRefGoogle Scholar
Buyevich, Y. A. 1972 a Statistical hydromechanics of disperse systems. Part 2. Solution of the kinetic equation for suspended particles. J. Fluid Mech. 52, 345355.CrossRefGoogle Scholar
Buyevich, Y. A. 1972 b Statistical hydromechanics of disperse systems. Part 3. Pseudo-turbulent structure of homogeneous suspensions. J. Fluid Mech. 56, 313336.CrossRefGoogle Scholar
Crowe, C. T. 1982 Numerical models for dilute gas–particle flows. Trans. ASME I: J. Fluids Engng 104, 297305.Google Scholar
Dopazo, C. 1994 Turbulent Reactive Flows: Recent Developments in PDF Methods, chap. 7, pp. 375474. Academic.Google Scholar
Druzhinin, A. 2001 The influence of particle inertia on the two-way coupling and modification of isotropic turbulence by micro-particles. Phys. Fluids 13, 37383755.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, 17901801.CrossRefGoogle Scholar
Feller, W. 1968 Probability Theory and Applications. Wiley.Google Scholar
Ferrante, A. & Elghobashi, S. 2003 On the physical mechanism of two way coupling in particle-laden isotropic turbulence. Phys. Fluids 15, 315330.CrossRefGoogle Scholar
Fessler, J. R., Kulick, J. D. & Eaton, J. K. 1994 Preferential concentration of heavy particles in a turbulent channel flow. Phys. Fluids 6, 37423749.CrossRefGoogle Scholar
Gardiner, C. W. 2002 Handbook of Stochastic Methods. Springer.Google Scholar
Germano, M. 1986 Differential filters for the large eddy simulation of turbulent flows. Phys. Fluids 29, 17551757.CrossRefGoogle Scholar
Germano, M. 1992 Turbulence: the filtering approach. J. Fluid Mech. 238, 325336.CrossRefGoogle Scholar
Gore, R. A. & Crowe, C. T. 1989 Effect of particle size on modulating turbulent intensity. Intl J. Multiphase Flow 15, 279285.CrossRefGoogle Scholar
Ijzermans, R. H. A., Hagmeijer, R. & van Langen, P. J. 2007 Accumulation of heavy particles around a helical vortex filament. Phys. Fluids 19, 107102.CrossRefGoogle Scholar
Jones, W. P. & Wille, M. 1996 a Large eddy simulation of a plane jet in a cross flow. Intl J. Heat Fluid Flow 17, 296306.CrossRefGoogle Scholar
Jones, W. P. & Wille, M. 1996 b Large eddy simulation of a round jet in a cross-flow. In Engineering Turbulence Modelling and Experiments 3 (ed. Rodi, W. & Bergeles, G.), pp. 199208. Heraklion, Crete.CrossRefGoogle Scholar
Kaiser, G. 1994 A Friendly Guide to Wavelets. Birkhäuser.Google Scholar
Kida, S. & Ohkitani, K. 1992 Spatiotemporal intermittency and instability of a forced turbulence. Phys. Fluids 4, 10181027.CrossRefGoogle Scholar
Klein, M., Sadiki, A. & Janicka, J. 2003 A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulations. J. Comput. Phys. 186, 652665.CrossRefGoogle Scholar
Klimontovich, I. L. 1969 The Statistical Theory of Non-equilibrium Processes in a Plasma. Pergamon.Google Scholar
Kloeden, P. E. & Platen, E. 1992 Numerical Solution of Stochastic Differential Equations. Springer.CrossRefGoogle Scholar
Kobayashi, H., Masutani, S. M., Azuhata, S., Arashi, N. & Hishinuma, Y. 1988 Transport Phenomena in Turbulent Flows – Theory, Experiment and Simulations (ed. Hirata, M. & Kasagi, N.) pp. 433446. Hemisphere.Google Scholar
Kulick, J. D., Fessler, J. R. & Eaton, J. K. 1994 Particle response and turbulence modification in fully developed channel flow. J. Fluid Mech. 277, 109134.CrossRefGoogle Scholar
La Porta, A., Voth, G. A., Crawford, A. M., Alexander, J. & Bodenschatz, E. 2002 Fluid particle accelerations in fully developed turbulence. Nature 409, 10171019.CrossRefGoogle Scholar
Lazaro, B. J. & Lasheras, J. C. 1989 Particle dispersion in a turbulent, plane, free shear layer. Phys. Fluids A 1, 10351044.CrossRefGoogle Scholar
Lazaro, B. J. & Lasheras, J. C. 1992 a Particle dispersion in the developing free shear layer. Part 1. Unforced flow. J. Fluid Mech. 235, 135178.Google Scholar
Lazaro, B. J. & Lasheras, J. C. 1992 b Particle dispersion in the developing free shear layer. Part 2. Forced flow. J. Fluid Mech. 235, 179221.CrossRefGoogle Scholar
Lefebvre, A. H. 1989 Atomization and Sprays. Hemisphere.Google Scholar
Liboff, R. L. 1998 Kinetic Theory: Classical, Quantum and Relativistic Descriptions. Prentice-Hall.Google Scholar
Longmire, E. K. & Eaton, J. K. 1992 Structure of a particle-laden round jet. J. Fluid Mech. 236, 217257.CrossRefGoogle Scholar
Lund, T. S., Wu, X. & Squires, D. 1998 Generation of turbulent inflow data for spatially-developing boundary layer simulations. J. Comput. Phys. 140, 233258.CrossRefGoogle Scholar
Lundgren, T. 1967 Distribution functions in the statistical theory of turbulence. Phys. Fluids 10 (5), 969975.CrossRefGoogle Scholar
Marcu, B. & Meiburg, E. 1996 a The effect of streamwise braid vortices on the particle dispersion in a plane mixing layer. I. Equilibrium points and their stability. Phys. Fluids 8, 715733.CrossRefGoogle Scholar
Marcu, B. & Meiburg, E. 1996 b Three-dimensional features of particle dispersion in a nominally plane mixing layer. Phys. Fluids 8, 22662268.CrossRefGoogle Scholar
Marcu, B., Meiburg, E. & Raju, N. 1996 The effect of streamwise braid vortices on the particle dispersion in a plane mixing layer. II. Nonlinear particle dynamics. Phys. Fluids 8, 734753.CrossRefGoogle Scholar
di Mare, F. 2002 Large eddy simulation of reacting and non-reacting flows in complex geometries. PhD thesis, Imperial College, University of London, London, UK.Google Scholar
di Mare, L. & Jones, W. P. 2003 LES of turbulent flow past a swept fence. Intl J. Heat Fluid Flow 24, 606615.CrossRefGoogle Scholar
di Mare, L., Klein, M., Jones, W. P. & Janicka, J. 2006 Synthetic turbulence inflow conditions for large eddy simulation. Phys. Fluids 18, 025107.CrossRefGoogle Scholar
Martin, E. & Meiburg, E. 1994 The accumulation and dispersion of heavy particles in forced two-dimensional mixing layers. i. The fundamental and sub harmonic cases. Phys. Fluids 6, 11161132.CrossRefGoogle Scholar
Mashayek, F. & Pandya, R. V. R. 2003 Analytical description of particle/droplet laden turbulent flows. Prog. Energy Combust. Sci. 29, 329378.CrossRefGoogle Scholar
Maxey, M. & Riley, J. J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 883889.CrossRefGoogle Scholar
Maxey, M. R. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441465.CrossRefGoogle Scholar
Miller, R. S. & Bellan, J. 2000 Direct numerical simulation and sub-grid of transitional droplet laden temporal mixing layer. Phys. Fluids 12, 650671.CrossRefGoogle Scholar
Minier, J. & Peirano, E. 2001 The pdf approach to turbulent polydispersed two phase flows. Phys. Rep. 352, 1214.CrossRefGoogle Scholar
Mordant, N., Metz, P., Michel, O. & Pinton, J. 2001 Measurement of Lagrangian velocity in fully developed turbulence. Phys. Rev. Lett. 87, 214501.CrossRefGoogle ScholarPubMed
Okong'o, N. & Bellan, J. 2000 A priori sub-grid analysis of temporal mixing layers with evaporating droplets. Phys. Fluids 12, 15731591.CrossRefGoogle Scholar
Okong'o, N. & Bellan, J. 2004 Consistent large-eddy simulation of a temporal mixing layer with evaporating drops. Part 1: Direct numerical simulation, formulation and a priori analysis. J. Fluid Mech. 499, 147.CrossRefGoogle Scholar
Piomelli, U. 1999 Large eddy simulation: achievements and challenges. Prog. Aerospace Sci. 35, 335362.CrossRefGoogle Scholar
Piomelli, U. & Liu, J. 1995 Large eddy simulation of rotating channel flows using a localised dynamic model. Phys. Fluids 7 (4), 893–848.CrossRefGoogle Scholar
Raju, N. & Meiburg, E. 1995 The accumulation and dispersion of heavy particles in forced two-dimensional mixing layers. Part 2: The effect of gravity. Phys. Fluids 7, 12411264.CrossRefGoogle Scholar
Reeks, M. W. 1980 Eulerian direct interaction applied to the statistical motion of particles in a turbulent fluid. J. Fluid Mech. 97, 569590.CrossRefGoogle Scholar
Reeks, M. R. 1991 On a kinetic equation for the transport of particles in turbulent flows. Phys. Fluids A 3, 446456.CrossRefGoogle Scholar
Reeks, M. R. 1992 On the continuum equations for dispersed particles in nonuniform flows. Phys. Fluids A 4, 12911303.CrossRefGoogle Scholar
Reeks, M. R. 1993 On the constitutive relations for dispersed particles in nonuniform flows. I: Dispersion in a simple shear flow. Phys. Fluids A 5, 750761.CrossRefGoogle Scholar
Righetti, M. & Romano, G. P. 2004 Particle–fluid interactions in a plane near-wall turbulent flow. J. Fluid Mech. 505, 93121.CrossRefGoogle Scholar
Risken, H. 1984 The Fokker Planck Equation. Springer.CrossRefGoogle Scholar
Scheffer, R. W., Hartmann, V. & Dibble, R. W. 1987 Conditional sampling of velocity in a turbulent non premixed propane jet. AIAA J. 25, 13181330.CrossRefGoogle Scholar
Schmidt, H. & Schumann, U. 1989 Coherent structure of the convective boundary layer derived from large-eddy simulation. J. Fluid Mech. 200, 511562.CrossRefGoogle Scholar
Sirignano, W. A. 1999 Fluid Dynamics and Transport of Droplet and Sprays. Cambridge University Press.CrossRefGoogle Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations. I- the basic experiment. Mon. Weather Rev. 91, 99165.2.3.CO;2>CrossRefGoogle Scholar
Squires, K. D. & Eaton, J. K. 1990 Particle response and turbulence modification in isotropic turbulence. Phys. Fluids A 2, 11911203.CrossRefGoogle Scholar
Squires, K. D. & Eaton, J. K. 1991 Preferential concentration of particles by turbulence. Phys. Fluids A 3, 11691178.CrossRefGoogle Scholar
Steinstrasser, D. 1994 Large eddy simulation of fully developed pipe flow. Master's thesis, Diplomarbeit, Imperial College, London.Google Scholar
Subramaniam, S. 2000 Statistical representation of a spray as a point process. Phys. Fluids 12, 24132431.CrossRefGoogle Scholar
Subramaniam, S. 2001 a Statistical modeling of sprays using the droplet distribution function. Phys. Fluids 13, 624642.CrossRefGoogle Scholar
Subramaniam, S. 2001 b Erratum: Statistical modeling of sprays using the droplet distribution function. Phys. Fluids 13, 2743.CrossRefGoogle Scholar
Thomson, D. J. 1987 Criteria for the selection of stochastic models of particles trajectories in turbulent flows. J. Fluid Mech. 180, 529556.CrossRefGoogle Scholar
Torrence, C. & Compo, G. P. 1998 A practical guide to wavelet analysis. Bull. Am. Met. Soc. 79, 6178.2.0.CO;2>CrossRefGoogle Scholar
Voth, G. A., La Porta, A., Crawford, A. M., Alexander, J. & Bodenschatz, E. 2002 Measurement of particle accelerations in fully developed turbulence. J. Fluid Mech. 469, 121160.CrossRefGoogle Scholar
Wang, P. & Maxey, M. R. 1993 Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 256, 2768.CrossRefGoogle Scholar
Wen, F., Kamalu, N., Chung, J. N., Crowe, C. T. & Troutt, T. R. 1992 Particle dispersion by vortex structures in plane mixing layers. Trans. ASME I: J. Fluids Engng 4, 657.Google Scholar
Wille, M. 1997 Large eddy simulation of jets in cross flows. PhD thesis, Department of Chemical Engineering, Imperial College of Science, Technology and Medicine, London SW7 2BY.Google Scholar
Williams, F. A. 1958 Spray combustion and atomization. Phys. Fluids 1, 541545.CrossRefGoogle Scholar
Williams, F. A. 1985 Combustion Theory: The Theory of Chemically Reacting Flow Systems. Benjamin Cummings.Google Scholar
Yaglom, A. M. 1957 Some classes of random fields in n-dimensional space. Theory Prob. Applics. 3, 273320.CrossRefGoogle Scholar
Yanenko, N. N. 1971 The Method of Fractional Steps. Springer.CrossRefGoogle Scholar
Yuu, S., Ueno, T. & Umekage, T. 2001 Numerical simulation of the high Re number slit nozzle gas–particle jet using sub-grid scale coupling LES. Chem. Engng Sci 56, 42934307.CrossRefGoogle Scholar
Zeff, B., Lanterman, D., McAllister, R., Roy, R., Kostelich, E. & Lathrop, D. 2003 Measuring intense rotation and dissipation in turbulent flows. Nature 421, 146149.CrossRefGoogle ScholarPubMed
113
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org 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 @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ 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.

Large-eddy simulation of particle-laden turbulent 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.

Large-eddy simulation of particle-laden turbulent 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.

Large-eddy simulation of particle-laden turbulent 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? *