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Predicting viscous-range velocity gradient dynamics in large-eddy simulations of turbulence

Published online by Cambridge University Press:  20 December 2017

Perry L. Johnson Open the ORCID record for Perry L. Johnson [Opens in a new window]  and
Charles Meneveau Open the ORCID record for Charles Meneveau [Opens in a new window]
Perry L. Johnson
Affiliation:
Department of Mechanical Engineering and Center for Environmental and Applied Fluid Mechanics, Johns Hopkins University, Baltimore, MD 21218, USA
Charles Meneveau
Affiliation:
Department of Mechanical Engineering and Center for Environmental and Applied Fluid Mechanics, Johns Hopkins University, Baltimore, MD 21218, USA
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Abstract

The detailed dynamics of small-scale turbulence are not directly accessible in large-eddy simulations (LES), posing a modelling challenge, because many micro-physical processes such as deformation of aggregates, drops, bubbles and polymers dynamics depend strongly on the velocity gradient tensor, which is dominated by the turbulence structure in the viscous range. In this paper, we introduce a method for coupling existing stochastic models for the Lagrangian evolution of the velocity gradient tensor with coarse-grained fluid simulations to recover small-scale physics without resorting to direct numerical simulations (DNS). The proposed approach is implemented in LES of turbulent channel flow and detailed comparisons with DNS are carried out. An application to modelling the fate of deformable, small (sub-Kolmogorov) droplets at negligible Stokes number and low volume fraction with one-way coupling is carried out and results are again compared to DNS results. Results illustrate the ability of the proposed model to predict the influence of small-scale turbulence on droplet micro-physics in the context of LES.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 837 , 25 February 2018 , pp. 80 - 114
Copyright
© 2017 Cambridge University Press 

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Footnotes

‡

Present address: Department of Mechanical Engineering, Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA; Email address for correspondence: [email protected]

References

Ashurst, W. T., Kerstein, A. R., Kerr, R. M. & Gibson, C. H. 1987 Alignment of vorticity and scalar gradient with strain rate in simulated Navier–Stokes turbulence. Phys. Fluids 30 (8), 2343–2353.Google Scholar
Babler, M. U., Biferale, L., Brandt, L., Feudel, U., Guseva, K., Lanotte, A. S., Marchioli, C., Picano, F., Sardina, G., Soldati, A. et al. 2015 Numerical simulations of aggregate breakup in bounded and unbounded turbulent flows. J. Fluid Mech. 766, 104–128.Google Scholar
Balkovsky, E., Fouxon, A. & Lebedev, V. 2000 Turbulent dynamics of polymer solutions. Phys. Rev. Lett. 84 (20), 4765–4768.Google Scholar
Batchelor, G. K. 1980 Mass transfer from small particles suspended in turbulent fluid. J. Fluid Mech. 98, 609–623.Google Scholar
Behbahani, M., Behr, M., Hormes, M., Steinseifer, U., Arora, D., Coronado, O. & Pasquali, M. 2009 A review of computational fluid dynamics analysis of blood pumps. Eur. J. Appl. Maths 20, 363–397.Google Scholar
Betchov, R. 1956 An inequality concerning the production of vorticity in isotropic turbulence. J. Fluid Mech. 1 (05), 497–504.Google Scholar
Biferale, L., Meneveau, C. & Verzicco, R. 2014 Deformation statistics of sub-Kolmogorov-scale ellipsoidal neutrally buoyant drops in isotropic turbulence. J. Fluid Mech. 754, 184–207.Google Scholar
Bou-Zeid, E., Meneveau, C. & Parlange, M. 2005 A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys. Fluids 17 (2), 1–18.Google Scholar
Cantwell, B. J. 1992 Exact solution of a restricted Euler equation for the velocity gradient tensor. Phys. Fluids 4 (4), 782–793.Google Scholar
Chen, J., Jin, G. & Zhang, J. 2016 Large eddy simulation of orientation and rotation of ellipsoidal particles in isotropic turbulent flows. J. Turbul. 17 (3), 308–326.Google Scholar
Chertkov, M. 2000 Polymer stretching by turbulence. Phys. Rev. Lett. 84 (20), 4761–4764.Google Scholar
Chertkov, M., Pumir, A. & Shraiman, B. I. 1999 Lagrangian tetrad dynamics and the phenomenology of turbulence. Phys. Fluids 11 (8), 2394–2410.Google Scholar
Chevillard, L. & Meneveau, C. 2006 Lagrangian dynamics and statistical geometric structure of turbulence. Phys. Rev. Lett. 97 (17), 174501.Google Scholar
Chevillard, L. & Meneveau, C. 2013 Orientation dynamics of small, triaxial-ellipsoidal particles in isotropic turbulence. J. Fluid Mech. 737, 571–596.Google Scholar
Chevillard, L., Meneveau, C., Biferale, L. & Toschi, F. 2008 Modeling the pressure Hessian and viscous Laplacian in turbulence: comparisons with direct numerical simulation and implications on velocity gradient dynamics. Phys. Fluids 20 (10), 101504.Google Scholar
Daling, P. S., Leirvik, F., Almås, I. K., Brandvik, P. J., Hansen, B. H., Lewis, A. & Reed, M. 2014 Surface weathering and dispersibility of MC252 crude oil. Mar. Pollut. Bull. 87 (1), 300–310.Google Scholar
De Tullio, M. D., Nam, J., Pascazio, G., Balaras, E. & Verzicco, R. 2012 Computational prediction of mechanical hemolysis in aortic valved prostheses. Eur. J. Mech. (B/Fluids) 35, 47–53.Google Scholar
De Vita, F., de Tullio, M. D. & Verzicco, R. 2016 Numerical simulation of the non-Newtonian blood flow through a mechanical aortic valve. Theor. Comput. Fluid Dyn. 30, 129–138.Google Scholar
Derakhti, M. & Kirby, J. T. 2014 Bubble entrainment and liquid–bubble interaction under unsteady breaking waves. J. Fluid Mech. 761, 464–506.Google Scholar
Donzis, D. A., Yeung, P. K. & Sreenivasan, K. R. 2008 Dissipation and enstrophy in isotropic turbulence: resolution effects and scaling in direct numerical simulations. Phys. Fluids 20 (4), 045108.Google Scholar
Dopazo, C., Cifuentes, L., Martin, J. & Jimenez, C. 2015 Strain rates normal to approaching iso-scalar surfaces in a turbulent premixed flame. Combust. Flame 162 (5), 1729–1736.Google Scholar
Dreeben, T. D. & Pope, S. B. 1998 Probability density function Monte Carlo simulation of near-wall turbulent flows. J. Fluid Mech. 357, 141–166.Google Scholar
Eaton, J. & Fessler, J. 1994 Preferential concentration of particles by turbulence. Intl J. Multiphase Flow 20, 169–209.Google Scholar
Eyink, G. L. & Aluie, H. 2009 Localness of energy cascade in hydrodynamic turbulence. I. Smooth coarse graining. Phys. Fluids 21 (2009), 1–9.Google Scholar
Fede, P., Simonin, O. & Villedieu, P.2006 Stochastic modeling of the turbulent subgrid fluid velocity along inertial particle trajectories. In Center for Turbulence Research Proceedings of the Summer Program 2006, pp. 247–258.Google Scholar
Germano, M. 1992 Turbulence: the filtering approach. J. Fluid Mech. 238, 325–336.Google Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids 3 (7), 1760–1765.Google Scholar
Gicquel, L. Y. M., Givi, P., Jaberi, F. A. & Pope, S. B. 2002 Velocity filtered density function for large eddy simulation of turbulent flows. Phys. Fluids 14 (3), 1196–1213.Google Scholar
Girimaji, S. S. & Pope, S. B. 1990 A diffusion model for velocity gradients in turbulence. Phys. Fluids A 2 (2), 242–256.Google Scholar
Graham, J., Kanov, K., Yang, X. I. A., Lee, M. K., Malaya, N., Burns, R., Eyink, G., Moser, R. D. & Meneveau, C. 2016 A Web Services-accessible database of turbulent channel flow and its use for testing a new integral wall model for LES DNS approach and simulation parameters. J. Turbul. 17 (2), 181–215.Google Scholar
Greene, J. M. & Kim, J.-S. 1987 The calculation of Lyapunov spectra. Phys. D 24 (1–3), 213–225.Google Scholar
Guasto, J. S., Rusconi, R. & Stocker, R. 2012 Fluid mechanics of planktonic microorganisms. Annu. Rev. Fluid Mech. 44, 373–400.Google Scholar
Honeycutt, R. L. 1992 Stochastic Runge–Kutta algorithms. I. White noise. Phys. Rev. A 45 (2), 600–603.Google Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161–179.Google Scholar
Jeong, E. & Girimaji, S. S. 2003 Velocity-gradient dynamics in turbulence: effect of viscosity and forcing. Theor. Comput. Fluid Dyn. 16 (6), 421–432.Google Scholar
Johansen, O., Brandvik, P. J. & Farooq, U. 2013 Droplet breakup in subsea oil releases – Part 2: predictions of droplet size distributions with and without injection of chemical dispersants. Mar. Pollut. Bull. 73 (1), 327–335.Google Scholar
Johnson, P. L., Hamilton, S. S., Burns, R. & Meneveau, C. 2017 Lagrangian stretching of fluid elements and vorticity in a turbulent channel flow using a database task-parallel particle tracking algorithm. Phys. Rev. Fluids 2, 014605.Google Scholar
Johnson, P. L. & Meneveau, C. 2015 Large-deviation joint statistics of the finite-time Lyapunov spectrum in isotropic turbulence. Phys. Fluids 27 (8), 085110.Google Scholar
Johnson, P. L. & Meneveau, C. 2016 A closure for Lagrangian velocity gradient evolution in turbulence using recent deformation mapping of initially Gaussian fields. J. Fluid Mech. 804, 387–419.Google Scholar
Johnson, P. L. & Meneveau, C. 2017a Restricted Euler dynamics along trajectories of small inertial particles in turbulence. J. Fluid Mech. 816, R2.Google Scholar
Johnson, P. L. & Meneveau, C. 2017b Turbulence intermittency in a multiple-time-scale Navier–Stokes-based reduced model. Phys. Rev. Fluids 2, 072601(R).Google Scholar
Junk, M. & Illner, R. 2007 A new derivation of Jeffery’s equation. J. Math. Fluid Mech. 9, 455–488.Google Scholar
Kanov, K. & Burns, R. 2015 Particle tracking in open simulation laboratories. In ACM/IEEE Conference on Supercomputing. ACM.Google Scholar
Karp-Boss, L., Boss, E. & Jumars, P. A. 1996 Nutrient fluxes to planktonic osmotrophs in the presence of fluid motion. Oceanogr. Mar. Biol. 34, 71–107.Google Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 299–303.Google Scholar
Kuerten, J. G. & Vreman, A. W. 2005 Can turbophoresis be predicted by large-eddy simulation? Phys. Fluids 17 (1), 011701.Google Scholar
Lamorgese, A. G., Pope, S. B., Yeung, P. K. & Sawford, B. L. 2007 A conditionally cubic-Gaussian stochastic Lagrangian model for acceleration in isotropic turbulence. J. Fluid Mech. 582, 423–448.Google Scholar
Lee, M., Malaya, N. & Moser, R. D. 2013 Petascale direct numerical simulation of turbulent channel flow on up to 786K cores. In International Conference for High Performance Computing. ACM Press.Google Scholar
Li, Y. & Meneveau, C. 2005 Origin of non-Gaussian statistics in hydrodynamic turbulence. Phys. Rev. Lett. 95 (16), 164502.Google Scholar
Li, Y., Perlman, E., Wan, M., Yang, Y., Meneveau, C., Burns, R., Chen, S., Szalay, A. & Eyink, G. 2008 A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence. J. Turbul. 9 (31), 1–29.Google Scholar
Lilly, D. K. 1967 The representation of small-scale turbulence in numerical simulation experiments. In Proceedings of IBM Scientific Computing Symp. on Environmental Sciences (ed. Gladstone, H. H.), pp. 195–210. IBM.Google Scholar
Lund, T. S. & Rogers, M. M. 1994 An improved measure of strain state probability in turbulent flows. Phys. Fluids 6 (5), 1838–1847.Google Scholar
Maffettone, P. & Minale, M. 1998 Equation of change for ellipsoidal drops in viscous flow. J. Non-Newtonian Fluid Mech. 78 (2–3), 227–241.Google Scholar
Maniero, R., Masbernat, O., Climent, E. & Risso, F. 2012 Modeling and simulation of inertial drop break-up in a turbulent pipe flow downstream of a restriction. Intl J. Multiphase Flow 42, 1–8.Google Scholar
Marchioli, C. 2017 Large-eddy simulation of turbulent dispersed flows: a review of modelling approaches. Acta Mech. 228 (3), 741–771.Google Scholar
Marchioli, C. & Soldati, A. 2015 Turbulent breakage of ductile aggregates. Phys. Rev. E 91 (5), 1–8.Google Scholar
Martin, J., Dopazo, C. & Valiño, L. 1998 Dynamics of velocity gradient invariants in turbulence: restricted Euler and linear diffusion models. Phys. Fluids 10 (8), 2012–2025.Google Scholar
Maxey, M. R. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441–465.Google Scholar
Mazzitelli, I. M., Toschi, F. & Lanotte, A. S. 2014 An accurate and efficient Lagrangian sub-grid model. Phys. Fluids 26 (9), 095101.Google Scholar
Meneveau, C. 2011 Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows. Annu. Rev. Fluid Mech. 43, 219–245.Google Scholar
Meneveau, C. & Katz, J. 2000 Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32, 1–32.Google Scholar
Meneveau, C. & Lund, T. S. 1994 On the Lagrangian nature of the turbulence energy cascade. Phys. Fluids 6 (8), 2820.Google Scholar
Meneveau, C. & Poinsot, T. 1991 Stretching and quenching of flamelets in premixed turbulent combustion. Combust. Flame 86 (4), 311–332.Google Scholar
Minier, J. 2015 On Lagrangian stochastic methods for turbulent polydisperse two-phase reactive flows. Prog. Energy Combust. Sci. 50, 1–62.Google Scholar
Minier, J. 2016 Statistical descriptions of polydisperse turbulent two-phase flows. Phys. Rep. 665, 1–122.Google Scholar
Minier, J., Cao, R. & Pope, S. B. 2003 Comment on the article an effective particle tracing scheme on structured/unstructured grids in hybrid finite volume/PDF Monte Carlo methods by Li and Modest. J. Comput. Phys. 186, 356–358.Google Scholar
Minier, J. P., Chibbaro, S. & Pope, S. B. 2014 Guidelines for the formulation of Lagrangian stochastic models for particle simulations of single-phase and dispersed two-phase turbulent flows. Phys. Fluids 26, 113303.Google Scholar
Moeng, C.-H. 1984 A large-eddy-simulation model for the study of planetary boundary-layer turbulence. J. Atmos. Sci. 41 (13), 2052–2062.Google Scholar
Moin, P., Squires, K., Cabot, W. & Lee, S. 1991 A dynamic subgrid scale model for compressible turbulence and scalar transport. Phys. Fluids 3 (11), 2746–2757.Google Scholar
Nelkin, M. 1990 Multifractal scaling of velocity derivatives in turbulence. Phys. Rev. A 42 (12), 7226–7229.Google Scholar
Orszag, S. A. 1971 On the elimination of aliasing in finite difference schemes by filtering high-wavenumber components. J. Atmos. Sci. 28, 1074.Google Scholar
Ott, E. 1993 Chaos in Dynamical Systems. Cambridge University Press.Google Scholar
Ottino, J. M. 1989 The Kinematics of Mixing, Stretching, Chaos, and Transport. Cambridge University Press.Google Scholar
Park, G. I., Bassenne, M., Urzay, J. & Moin, P. 2017 A simple dynamic subgrid-scale model for LES of particle-laden turbulence. Phys. Rev. Fluids 2 (4), 044301.Google Scholar
Pope, S. B. 1985 PDF methods for turbulent reactive flows. Prog. Energy Combust. Sci. 11, 119–192.Google Scholar
Pope, S. B. 1994 Lagrangian PDF methods for turbulent flows. Annu. Rev. Fluid Mech. 26, 23–63.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Pope, S. B. 2002 A stochastic Lagrangian model for acceleration in turbulent flows. Phys. Fluids 14 (7), 2360–2375.Google Scholar
Porté-Agel, F., Meneveau, C. & Parlange, M. B. 2000 A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer. J. Fluid Mech. 415 (2000), 261–284.Google Scholar
Procaccia, I., L’Vov, V. S. & Benzi, R. 2008 Colloquium: Theory of drag reduction by polymers in wall-bounded turbulence. Rev. Mod. Phys. 80, 225–247.Google Scholar
Pumir, A. & Wilkinson, M. 2011 Orientation statistics of small particles in turbulence. New J. Phys. 13, 093030.Google Scholar
Pumir, A., Xu, H. & Siggia, E. D. 2016 Small-scale anisotropy in turbulent boundary layers. J. Fluid Mech. 804, 5–23.Google Scholar
Ray, B. & Collins, L. R. 2014 A subgrid model for clustering of high-inertia particles in large-eddy simulations of turbulence. J. Turbul. 15 (6), 366–385.Google Scholar
Saddoughi, S. G. & Veeravalli, S. V. 1994 Local isotropy in turbulent boundary layers at high Reynolds number. J. Fluid Mech. 268, 333–372.Google Scholar
Sagaut, P. 2006 Large Eddy Simulation for Incompressible Flows, 3rd edn. Springer.Google Scholar
Sawford, B. 2001 Turbulent relative dispersion. Annu. Rev. Fluid Mech. 33, 289–317.Google Scholar
Schumacher, J., Scheel, J. D., Krasnov, D., Donzis, D. A., Yakhot, V. & Sreenivasan, K. R. 2014 Small-scale universality in fluid turbulence. Proc. Natl Acad. Sci. USA 111 (30), 10961–10965.Google Scholar
Sheikhi, M. R. H., Givi, P. & Pope, S. B. 2009 Frequency-velocity-scalar filtered mass density function for large eddy simulation of turbulent flows Frequency-velocity-scalar filtered mass density function for large eddy simulation of turbulent flows. Phys. Fluids 21, 075102.Google Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations. Mon. Weath. Rev. 91 (3), 99–164.Google Scholar
Spandan, V., Verzicco, R. & Lohse, D. 2016 Deformation and orientation statistics of neutrally buoyant sub-Kolmogorov ellipsoidal droplets in turbulent Taylor–Couette flow. J. Fluid Mech. 809, 480–501.Google Scholar
Sreenivasan, K. R. & Antonia, R. A. 1997 The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29 (1), 435–472.Google Scholar
Vieillefosse, P. 1982 Local interaction between vorticity and shear in a perfect incompressible fluid. J. Phys. 43, 837–842.Google Scholar
Vieillefosse, P. 1984 Internal motion of a small element of fluid in an inviscid flow. Phys. A 125, 150–162.Google Scholar
Vitale, F., Nam, J., Turchetti, L., Behr, M., Raphael, R., Annesini, M. C. & Pasquali, M. 2014 A multiscale, biophysical model of flow-induced red blood cell damage. AIChE J. 60 (4), 1509–1516.Google Scholar
Voth, G. A. & Soldati, A. 2017 Anisotropic particles in turbulence. Annu. Rev. Fluid Mech. 49, 249–276.Google Scholar
Waclawczyk, M., Pozorski, J. & Minier, J.-P. 2004 Probability density function computation of turbulent flows with a new near-wall model. Phys. Fluids 16 (5), 1410–1422.Google Scholar
Wan, M., Xiao, Z., Meneveau, C., Eyink, G. L. & Chen, S. 2010 Dissipation-energy flux correlations as evidence for the Lagrangian energy cascade in turbulence. Phys. Fluids 22 (6), 061702.Google Scholar
White, C. M. & Mungal, M. G. 2008 Mechanics and prediction of turbulent drag reduction with polymer additives. Annu. Rev. Fluid Mech. 40 (1), 235–256.Google Scholar
Wilcox, D. C. 2006 Turbulence Modeling for CFD, 3rd edn. DCW Industries.Google Scholar
Wilczek, M. & Friedrich, R. 2009 Dynamical origins for non-Gaussian vorticity distributions in turbulent flows. Phys. Rev. E 80, 016316.Google Scholar
Wilczek, M. & Meneveau, C. 2014 Pressure Hessian and viscous contributions to velocity gradient statistics based on Gaussian random fields. J. Fluid Mech. 756, 191–225.Google Scholar
Yoshizawa, A. 1982 A statistically-derived subgrid model for the large-eddy simulation of turbulence. Phys. Fluids 25 (9), 1532–1538.Google Scholar
Yu, H., Kanov, K., Perlman, E., Graham, J., Frederix, E., Burns, R., Szalay, A., Eyink, G. & Meneveau, C. 2012 Studying Lagrangian dynamics of turbulence using on-demand fluid particle tracking in a public turbulence database. J. Turbul. 13 (August 2015), N12.Google Scholar