On analysis and stochastic modeling of the particle kinetic energy equation in particle-laden isotropic turbulent flows

Pietrzyk, Kyle; Horwitz, Jeremy K.; Najjar, Fady M.; Minich, Roger W.

doi:10.1063/5.0075650

Title: On analysis and stochastic modeling of the particle kinetic energy equation in particle-laden isotropic turbulent flows

Journal Article · 20 January 2022 · Physics of Fluids

DOI: https://doi.org/10.1063/5.0075650 · OSTI ID:1860899

^[1];

^[2];

^[2]; Minich, Roger W. ^[2]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Stanford Univ., CA (United States)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

In this study, we analyze three-dimensional particle-laden, isotropic turbulence to develop an understanding of inertial particle dynamics from a kinetic energy perspective. Data trends implying inhomogeneous sampling of the flow by particles are identified and used to support a proposed particle behavior: particles appear to accumulate in regions of low flow kinetic energy over time because they lose kinetic energy and slow down in such regions, ultimately causing them to spend more time there. To elucidate this behavior, we derive a particle kinetic energy equation from the particle momentum equation, which incorporates inertial effects through the Schiller–Naumann drag correlation. Upon extracting fundamental physics from this equation, hypotheses regarding the role of the Stokes number in the temporal change of particle kinetic energy and the previously proposed particle behavior are evaluated using simulation data considering three Stokes numbers. Finally, a Fokker–Planck equation is used to derive the steady-state probability density function of the particle kinetic energy. The model fits the simulation data well and provides a tool for further investigation into understanding preferential concentration, as well as a reduced order model for predicting particle kinetic energy in turbulent flows.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1860899

Report Number(s):: LLNL-JRNL-827712; 1042313

Journal Information:: Physics of Fluids, Journal Name: Physics of Fluids Journal Issue: 1 Vol. 34; ISSN 1070-6631

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (55)

The Influence of Turbulence on Plankton Predation Strategies Lewis, D. M.; Pedley, T. J. Journal of Theoretical Biology, Vol. 210, Issue 3 https://doi.org/10.1006/jtbi.2001.2310	journal	June 2001
The Fokker-Planck Equation Risken, Hannes Springer Series in Synergetics https://doi.org/10.1007/978-3-642-61544-3	book	January 1996
Effects of vortex pairing on particle dispersion in turbulent shear flows Chein, R.; Chung, J. N. International Journal of Multiphase Flow, Vol. 13, Issue 6 https://doi.org/10.1016/0301-9322(87)90066-8	journal	November 1987
Preferential concentration of particles by turbulence Eaton, J. K.; Fessler, J. R. International Journal of Multiphase Flow, Vol. 20 https://doi.org/10.1016/0301-9322(94)90072-8	journal	August 1994
Turbulence effects on droplet growth and size distribution in clouds—A review Pinsky, M. B.; Khain, A. P. Journal of Aerosol Science, Vol. 28, Issue 7 https://doi.org/10.1016/S0021-8502(97)00005-0	journal	October 1997
Filtered particle tracking in isotropic turbulence and stochastic modeling of subgrid-scale dispersion Pozorski, Jacek; Apte, Sourabh V. International Journal of Multiphase Flow, Vol. 35, Issue 2 https://doi.org/10.1016/j.ijmultiphaseflow.2008.10.005	journal	February 2009
Analyzing preferential concentration and clustering of inertial particles in turbulence Monchaux, Romain; Bourgoin, Mickael; Cartellier, Alain International Journal of Multiphase Flow, Vol. 40 https://doi.org/10.1016/j.ijmultiphaseflow.2011.12.001	journal	April 2012
Correction scheme for point-particle models applied to a nonlinear drag law in simulations of particle-fluid interaction Horwitz, J. A. K.; Mani, A. International Journal of Multiphase Flow, Vol. 101 https://doi.org/10.1016/j.ijmultiphaseflow.2018.01.003	journal	April 2018
Particle-resolved simulation of freely evolving particle suspensions: Flow physics and modeling Tavanashad, Vahid; Passalacqua, Alberto; Subramaniam, Shankar International Journal of Multiphase Flow, Vol. 135 https://doi.org/10.1016/j.ijmultiphaseflow.2020.103533	journal	February 2021
Stochastic modeling of direct radiation transmission in particle-laden turbulent flow Banko, Andrew J.; Villafañe, Laura; Kim, Ji Hoon Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 226 https://doi.org/10.1016/j.jqsrt.2019.01.005	journal	March 2019
Clustering of aerosol particles in isotropic turbulence Chun, Jaehun; Koch, Donald L.; Rani, Sarma L. Journal of Fluid Mechanics, Vol. 536 https://doi.org/10.1017/S0022112005004568	journal	July 2005
Acceleration statistics of heavy particles in turbulence Bec, J.; Biferale, L.; Boffetta, G. Journal of Fluid Mechanics, Vol. 550, Issue -1 https://doi.org/10.1017/S002211200500844X	journal	February 2006
Turbulent clustering of stagnation points and inertial particles Chen, L.; Goto, S.; Vassilicos, J. C. Journal of Fluid Mechanics, Vol. 553, Issue -1 https://doi.org/10.1017/S0022112006009177	journal	April 2006
Self-similar clustering of inertial particles in homogeneous turbulence Yoshimoto, Hiroshi; Goto, Susumu Journal of Fluid Mechanics, Vol. 577 https://doi.org/10.1017/S0022112007004946	journal	April 2007
Effects of the preferential segregation of droplets on evaporation and turbulent mixing Reveillon, Julien; Demoulin, Francois-Xavier Journal of Fluid Mechanics, Vol. 583 https://doi.org/10.1017/S0022112007006180	journal	July 2007
The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields Maxey, M. R. Journal of Fluid Mechanics, Vol. 174 https://doi.org/10.1017/S0022112087000193	journal	January 1987
Collision statistics in an isotropic particle-laden turbulent suspension. Part 1. Direct numerical simulations Sundaram, Shivshankar; Collins, Lance R. Journal of Fluid Mechanics, Vol. 335 https://doi.org/10.1017/S0022112096004454	journal	March 1997
Enskog kinetic theory for monodisperse gas–solid flows Garzó, V.; Tenneti, S.; Subramaniam, S. Journal of Fluid Mechanics, Vol. 712 https://doi.org/10.1017/jfm.2012.404	journal	September 2012
Interphasial energy transfer and particle dissipation in particle-laden wall turbulence Zhao, Lihao; Andersson, Helge I.; Gillissen, Jurriaan J. J. Journal of Fluid Mechanics, Vol. 715 https://doi.org/10.1017/jfm.2012.492	journal	January 2013
Two-way coupled stochastic model for dispersion of inertial particles in turbulence Pai, Madhusudan G.; Subramaniam, Shankar Journal of Fluid Mechanics, Vol. 700 https://doi.org/10.1017/jfm.2012.89	journal	April 2012
Investigation of sub-Kolmogorov inertial particle pair dynamics in turbulence using novel satellite particle simulations Ray, Baidurja; Collins, Lance R. Journal of Fluid Mechanics, Vol. 720 https://doi.org/10.1017/jfm.2013.24	journal	February 2013
A stochastic model for the relative motion of high Stokes number particles in isotropic turbulence Rani, Sarma L.; Dhariwal, Rohit; Koch, Donald L. Journal of Fluid Mechanics, Vol. 756 https://doi.org/10.1017/jfm.2014.461	journal	September 2014
Stochastic Lagrangian model for hydrodynamic acceleration of inertial particles in gas–solid suspensions Tenneti, Sudheer; Mehrabadi, Mohammad; Subramaniam, Shankar Journal of Fluid Mechanics, Vol. 788 https://doi.org/10.1017/jfm.2015.693	journal	January 2016
The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 1. Simulations without gravitational effects Ireland, Peter J.; Bragg, Andrew D.; Collins, Lance R. Journal of Fluid Mechanics, Vol. 796 https://doi.org/10.1017/jfm.2016.238	journal	May 2016
Stochastic theory and direct numerical simulations of the relative motion of high-inertia particle pairs in isotropic turbulence Dhariwal, Rohit; Rani, Sarma L.; Koch, Donald L. Journal of Fluid Mechanics, Vol. 813 https://doi.org/10.1017/jfm.2016.859	journal	January 2017
Clustering of rapidly settling, low-inertia particle pairs in isotropic turbulence. Part 1. Drift and diffusion flux closures Rani, Sarma L.; Gupta, Vijay K.; Koch, Donald L. Journal of Fluid Mechanics, Vol. 871 https://doi.org/10.1017/jfm.2019.204	journal	May 2019
Stochastic models for capturing dispersion in particle-laden flows Lattanzi, Aaron M.; Tavanashad, Vahid; Subramaniam, Shankar Journal of Fluid Mechanics, Vol. 903 https://doi.org/10.1017/jfm.2020.625	journal	September 2020
Effect of preferential concentration on turbulent collision rates Reade, Walter C.; Collins, Lance R. Physics of Fluids, Vol. 12, Issue 10 https://doi.org/10.1063/1.1288515	journal	January 2000
A model for preferential concentration Sigurgeirsson, H.; Stuart, A. M. Physics of Fluids, Vol. 14, Issue 12 https://doi.org/10.1063/1.1517603	journal	December 2002
Pair dispersion and preferential concentration of particles in isotropic turbulence Zaichik, Leonid I.; Alipchenkov, Vladimir M. Physics of Fluids, Vol. 15, Issue 6 https://doi.org/10.1063/1.1569485	journal	January 2003
Self-similar clustering of inertial particles and zero-acceleration points in fully developed two-dimensional turbulence Goto, Susumu; Vassilicos, J. C. Physics of Fluids, Vol. 18, Issue 11 https://doi.org/10.1063/1.2364263	journal	November 2006
Unmixing in random flows Wilkinson, M.; Mehlig, B.; Östlund, S. Physics of Fluids, Vol. 19, Issue 11 https://doi.org/10.1063/1.2766740	journal	November 2007
Refinement of the probability density function model for preferential concentration of aerosol particles in isotropic turbulence Zaichik, Leonid I.; Alipchenkov, Vladimir M. Physics of Fluids, Vol. 19, Issue 11 https://doi.org/10.1063/1.2813044	journal	November 2007
A unified sweep-stick mechanism to explain particle clustering in two- and three-dimensional homogeneous, isotropic turbulence Coleman, S. W.; Vassilicos, J. C. Physics of Fluids, Vol. 21, Issue 11 https://doi.org/10.1063/1.3257638	journal	November 2009
Particle response and turbulence modification in isotropic turbulence Squires, Kyle D.; Eaton, John K. Physics of Fluids A: Fluid Dynamics, Vol. 2, Issue 7 https://doi.org/10.1063/1.857620	journal	July 1990
Preferential concentration of particles by turbulence Squires, Kyle D.; Eaton, John K. Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 5 https://doi.org/10.1063/1.858045	journal	May 1991
Kinetic energy balance in turbulent particle-laden channel flow Pan, Qingqing; Xiang, Hong; Wang, Ze Physics of Fluids, Vol. 32, Issue 7 https://doi.org/10.1063/5.0012570	journal	July 2020
Flight-crash events in turbulence Xu, H.; Pumir, A.; Falkovich, G. Proceedings of the National Academy of Sciences, Vol. 111, Issue 21 https://doi.org/10.1073/pnas.1321682111	journal	May 2014
Statistical models for spatial patterns of heavy particles in turbulence Gustavsson, K.; Mehlig, B. Advances in Physics, Vol. 65, Issue 1 https://doi.org/10.1080/00018732.2016.1164490	journal	January 2016
Preferential concentration of heavy particles in turbulence Obligado, Martín; Teitelbaum, Tomás; Cartellier, Alain Journal of Turbulence, Vol. 15, Issue 5 https://doi.org/10.1080/14685248.2014.897710	journal	April 2014
Inertial-particle dynamics in turbulent flows: caustics, concentration fluctuations and random uncorrelated motion Gustavsson, K.; Meneguz, E.; Reeks, M. New Journal of Physics, Vol. 14, Issue 11 https://doi.org/10.1088/1367-2630/14/11/115017	journal	November 2012
New insights from comparing statistical theories for inertial particles in turbulence: I. Spatial distribution of particles Bragg, Andrew D.; Collins, Lance R. New Journal of Physics, Vol. 16, Issue 5 https://doi.org/10.1088/1367-2630/16/5/055013	journal	May 2014
Path coalescence transition and its applications Wilkinson, M.; Mehlig, B. Physical Review E, Vol. 68, Issue 4 https://doi.org/10.1103/PhysRevE.68.040101	journal	October 2003
Time irreversibility of the statistics of a single particle in compressible turbulence Grafke, Tobias; Frishman, Anna; Falkovich, Gregory Physical Review E, Vol. 91, Issue 4 https://doi.org/10.1103/PhysRevE.91.043022	journal	April 2015
Heavy inertial particles in turbulent flows gain energy slowly but lose it rapidly Bhatnagar, Akshay; Gupta, Anupam; Mitra, Dhrubaditya Physical Review E, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRevE.97.033102	journal	March 2018
Analysis of the clustering of inertial particles in turbulent flows Esmaily-Moghadam, Mahdi; Mani, Ali Physical Review Fluids, Vol. 1, Issue 8 https://doi.org/10.1103/PhysRevFluids.1.084202	journal	December 2016
Sweep-Stick Mechanism of Heavy Particle Clustering in Fluid Turbulence Goto, Susumu; Vassilicos, J. C. Physical Review Letters, Vol. 100, Issue 5 https://doi.org/10.1103/PhysRevLett.100.054503	journal	February 2008
Clustering by Mixing Flows Duncan, Kevin; Mehlig, Bernhard; Östlund, Stellan Physical Review Letters, Vol. 95, Issue 24 https://doi.org/10.1103/PhysRevLett.95.240602	journal	December 2005
Heavy Particle Concentration in Turbulence at Dissipative and Inertial Scales Bec, J.; Biferale, L.; Cencini, M. Physical Review Letters, Vol. 98, Issue 8 https://doi.org/10.1103/PhysRevLett.98.084502	journal	February 2007
The Langevin Equation: With Applications to Stochastic Problems in Physics, Chemistry and Electrical Engineering Coffey, William T.; Kalmykov, Yuri P. World Scientific Series in Contemporary Chemical Physics, Vol. 28 https://doi.org/10.1142/10490	book	May 2017
Turbulent Dispersed Multiphase Flow Balachandar, S.; Eaton, John K. Annual Review of Fluid Mechanics, Vol. 42, Issue 1 https://doi.org/10.1146/annurev.fluid.010908.165243	journal	January 2010
P ARTICLE -T URBULENCE I NTERACTIONS IN A TMOSPHERIC C LOUDS Shaw, Raymond A. Annual Review of Fluid Mechanics, Vol. 35, Issue 1 https://doi.org/10.1146/annurev.fluid.35.101101.161125	journal	January 2003
Preferential Concentration of Cloud Droplets by Turbulence: Effects on the Early Evolution of Cumulus Cloud Droplet Spectra Shaw, Raymond A.; Reade, Walter C.; Collins, Lance R. Journal of the Atmospheric Sciences, Vol. 55, Issue 11 https://doi.org/10.1175/1520-0469(1998)055%3C1965:PCOCDB%3E2.0.CO;2	journal	June 1998
Ergodic and non-ergodic clustering of inertial particles Gustavsson, K.; Mehlig, B. EPL (Europhysics Letters), Vol. 96, Issue 6 https://doi.org/10.1209/0295-5075/96/60012	journal	December 2011
Caustics in turbulent aerosols Wilkinson, M.; Mehlig, B. Europhysics Letters (EPL), Vol. 71, Issue 2 https://doi.org/10.1209/epl/i2004-10532-7	journal	July 2005

Similar Records

Prediction of the particle-laden jet with a two-equation turbulence model

Journal Article · 1984 · Int. J. Multiphase Flow; (United States) · OSTI ID:5084951

Elghobashi, S; Abou -Arab, T; Moustafa, A; +1 more

Particle-to-fluid heat transfer in particle-laden turbulence

Journal Article · 2018 · Physical Review Fluids · OSTI ID:1461646

Pouransari, Hadi; Mani, Ali

A hybrid stochastic-deconvolution model for large-eddy simulation of particle-laden flow

Journal Article · 2013 · Physics of Fluids (1994) · OSTI ID:22257161

Kuerten, J. G. M.; Zeegers, J. C. H.; Liew, R.; +2 more

Related Subjects

42 ENGINEERING
Newtonian mechanics
energy equations
fundamental physics
statistical mechanics models
stochastic processes
turbulent flows

Title: On analysis and stochastic modeling of the particle kinetic energy equation in particle-laden isotropic turbulent flows

Citation Formats

References (55)

Similar Records

Related Subjects