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

  • Perry L. Johnson (a1) and Charles Meneveau (a1)
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.

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Present address: Department of Mechanical Engineering, Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA; Email address for correspondence: perryj@stanford.edu

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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), 23432353.
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, 104128.
Balkovsky, E., Fouxon, A. & Lebedev, V. 2000 Turbulent dynamics of polymer solutions. Phys. Rev. Lett. 84 (20), 47654768.
Batchelor, G. K. 1980 Mass transfer from small particles suspended in turbulent fluid. J. Fluid Mech. 98, 609623.
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, 363397.
Betchov, R. 1956 An inequality concerning the production of vorticity in isotropic turbulence. J. Fluid Mech. 1 (05), 497504.
Biferale, L., Meneveau, C. & Verzicco, R. 2014 Deformation statistics of sub-Kolmogorov-scale ellipsoidal neutrally buoyant drops in isotropic turbulence. J. Fluid Mech. 754, 184207.
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), 118.
Cantwell, B. J. 1992 Exact solution of a restricted Euler equation for the velocity gradient tensor. Phys. Fluids 4 (4), 782793.
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), 308326.
Chertkov, M. 2000 Polymer stretching by turbulence. Phys. Rev. Lett. 84 (20), 47614764.
Chertkov, M., Pumir, A. & Shraiman, B. I. 1999 Lagrangian tetrad dynamics and the phenomenology of turbulence. Phys. Fluids 11 (8), 23942410.
Chevillard, L. & Meneveau, C. 2006 Lagrangian dynamics and statistical geometric structure of turbulence. Phys. Rev. Lett. 97 (17), 174501.
Chevillard, L. & Meneveau, C. 2013 Orientation dynamics of small, triaxial-ellipsoidal particles in isotropic turbulence. J. Fluid Mech. 737, 571596.
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.
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), 300310.
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, 4753.
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, 129138.
Derakhti, M. & Kirby, J. T. 2014 Bubble entrainment and liquid–bubble interaction under unsteady breaking waves. J. Fluid Mech. 761, 464506.
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.
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), 17291736.
Dreeben, T. D. & Pope, S. B. 1998 Probability density function Monte Carlo simulation of near-wall turbulent flows. J. Fluid Mech. 357, 141166.
Eaton, J. & Fessler, J. 1994 Preferential concentration of particles by turbulence. Intl J. Multiphase Flow 20, 169209.
Eyink, G. L. & Aluie, H. 2009 Localness of energy cascade in hydrodynamic turbulence. I. Smooth coarse graining. Phys. Fluids 21 (2009), 19.
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.
Germano, M. 1992 Turbulence: the filtering approach. J. Fluid Mech. 238, 325336.
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids 3 (7), 17601765.
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), 11961213.
Girimaji, S. S. & Pope, S. B. 1990 A diffusion model for velocity gradients in turbulence. Phys. Fluids A 2 (2), 242256.
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), 181215.
Greene, J. M. & Kim, J.-S. 1987 The calculation of Lyapunov spectra. Phys. D 24 (1–3), 213225.
Guasto, J. S., Rusconi, R. & Stocker, R. 2012 Fluid mechanics of planktonic microorganisms. Annu. Rev. Fluid Mech. 44, 373400.
Honeycutt, R. L. 1992 Stochastic Runge–Kutta algorithms. I. White noise. Phys. Rev. A 45 (2), 600603.
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161179.
Jeong, E. & Girimaji, S. S. 2003 Velocity-gradient dynamics in turbulence: effect of viscosity and forcing. Theor. Comput. Fluid Dyn. 16 (6), 421432.
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), 327335.
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.
Johnson, P. L. & Meneveau, C. 2015 Large-deviation joint statistics of the finite-time Lyapunov spectrum in isotropic turbulence. Phys. Fluids 27 (8), 085110.
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, 387419.
Johnson, P. L. & Meneveau, C. 2017a Restricted Euler dynamics along trajectories of small inertial particles in turbulence. J. Fluid Mech. 816, R2.
Johnson, P. L. & Meneveau, C. 2017b Turbulence intermittency in a multiple-time-scale Navier–Stokes-based reduced model. Phys. Rev. Fluids 2, 072601(R).
Junk, M. & Illner, R. 2007 A new derivation of Jeffery’s equation. J. Math. Fluid Mech. 9, 455488.
Kanov, K. & Burns, R. 2015 Particle tracking in open simulation laboratories. In ACM/IEEE Conference on Supercomputing. ACM.
Karp-Boss, L., Boss, E. & Jumars, P. A. 1996 Nutrient fluxes to planktonic osmotrophs in the presence of fluid motion. Oceanogr. Mar. Biol. 34, 71107.
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 299303.
Kuerten, J. G. & Vreman, A. W. 2005 Can turbophoresis be predicted by large-eddy simulation? Phys. Fluids 17 (1), 011701.
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, 423448.
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.
Li, Y. & Meneveau, C. 2005 Origin of non-Gaussian statistics in hydrodynamic turbulence. Phys. Rev. Lett. 95 (16), 164502.
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), 129.
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. 195210. IBM.
Lund, T. S. & Rogers, M. M. 1994 An improved measure of strain state probability in turbulent flows. Phys. Fluids 6 (5), 18381847.
Maffettone, P. & Minale, M. 1998 Equation of change for ellipsoidal drops in viscous flow. J. Non-Newtonian Fluid Mech. 78 (2–3), 227241.
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, 18.
Marchioli, C. 2017 Large-eddy simulation of turbulent dispersed flows: a review of modelling approaches. Acta Mech. 228 (3), 741771.
Marchioli, C. & Soldati, A. 2015 Turbulent breakage of ductile aggregates. Phys. Rev. E 91 (5), 18.
Martin, J., Dopazo, C. & Valiño, L. 1998 Dynamics of velocity gradient invariants in turbulence: restricted Euler and linear diffusion models. Phys. Fluids 10 (8), 20122025.
Maxey, M. R. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441465.
Mazzitelli, I. M., Toschi, F. & Lanotte, A. S. 2014 An accurate and efficient Lagrangian sub-grid model. Phys. Fluids 26 (9), 095101.
Meneveau, C. 2011 Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows. Annu. Rev. Fluid Mech. 43, 219245.
Meneveau, C. & Katz, J. 2000 Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32, 132.
Meneveau, C. & Lund, T. S. 1994 On the Lagrangian nature of the turbulence energy cascade. Phys. Fluids 6 (8), 2820.
Meneveau, C. & Poinsot, T. 1991 Stretching and quenching of flamelets in premixed turbulent combustion. Combust. Flame 86 (4), 311332.
Minier, J. 2015 On Lagrangian stochastic methods for turbulent polydisperse two-phase reactive flows. Prog. Energy Combust. Sci. 50, 162.
Minier, J. 2016 Statistical descriptions of polydisperse turbulent two-phase flows. Phys. Rep. 665, 1122.
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, 356358.
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.
Moeng, C.-H. 1984 A large-eddy-simulation model for the study of planetary boundary-layer turbulence. J. Atmos. Sci. 41 (13), 20522062.
Moin, P., Squires, K., Cabot, W. & Lee, S. 1991 A dynamic subgrid scale model for compressible turbulence and scalar transport. Phys. Fluids 3 (11), 27462757.
Nelkin, M. 1990 Multifractal scaling of velocity derivatives in turbulence. Phys. Rev. A 42 (12), 72267229.
Orszag, S. A. 1971 On the elimination of aliasing in finite difference schemes by filtering high-wavenumber components. J. Atmos. Sci. 28, 1074.
Ott, E. 1993 Chaos in Dynamical Systems. Cambridge University Press.
Ottino, J. M. 1989 The Kinematics of Mixing, Stretching, Chaos, and Transport. Cambridge University Press.
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.
Pope, S. B. 1985 PDF methods for turbulent reactive flows. Prog. Energy Combust. Sci. 11, 119192.
Pope, S. B. 1994 Lagrangian PDF methods for turbulent flows. Annu. Rev. Fluid Mech. 26, 2363.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
Pope, S. B. 2002 A stochastic Lagrangian model for acceleration in turbulent flows. Phys. Fluids 14 (7), 23602375.
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), 261284.
Procaccia, I., L’Vov, V. S. & Benzi, R. 2008 Colloquium: Theory of drag reduction by polymers in wall-bounded turbulence. Rev. Mod. Phys. 80, 225247.
Pumir, A. & Wilkinson, M. 2011 Orientation statistics of small particles in turbulence. New J. Phys. 13, 093030.
Pumir, A., Xu, H. & Siggia, E. D. 2016 Small-scale anisotropy in turbulent boundary layers. J. Fluid Mech. 804, 523.
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), 366385.
Saddoughi, S. G. & Veeravalli, S. V. 1994 Local isotropy in turbulent boundary layers at high Reynolds number. J. Fluid Mech. 268, 333372.
Sagaut, P. 2006 Large Eddy Simulation for Incompressible Flows, 3rd edn. Springer.
Sawford, B. 2001 Turbulent relative dispersion. Annu. Rev. Fluid Mech. 33, 289317.
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), 1096110965.
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.
Smagorinsky, J. 1963 General circulation experiments with the primitive equations. Mon. Weath. Rev. 91 (3), 99164.
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, 480501.
Sreenivasan, K. R. & Antonia, R. A. 1997 The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29 (1), 435472.
Vieillefosse, P. 1982 Local interaction between vorticity and shear in a perfect incompressible fluid. J. Phys. 43, 837842.
Vieillefosse, P. 1984 Internal motion of a small element of fluid in an inviscid flow. Phys. A 125, 150162.
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), 15091516.
Voth, G. A. & Soldati, A. 2017 Anisotropic particles in turbulence. Annu. Rev. Fluid Mech. 49, 249276.
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), 14101422.
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.
White, C. M. & Mungal, M. G. 2008 Mechanics and prediction of turbulent drag reduction with polymer additives. Annu. Rev. Fluid Mech. 40 (1), 235256.
Wilcox, D. C. 2006 Turbulence Modeling for CFD, 3rd edn. DCW Industries.
Wilczek, M. & Friedrich, R. 2009 Dynamical origins for non-Gaussian vorticity distributions in turbulent flows. Phys. Rev. E 80, 016316.
Wilczek, M. & Meneveau, C. 2014 Pressure Hessian and viscous contributions to velocity gradient statistics based on Gaussian random fields. J. Fluid Mech. 756, 191225.
Yoshizawa, A. 1982 A statistically-derived subgrid model for the large-eddy simulation of turbulence. Phys. Fluids 25 (9), 15321538.
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.
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