Scalar mixing in a Kelvin-Helmholtz shear layer and implications for Reynolds-averaged Navier-Stokes modeling of mixing layers

Morgan, Brandon E.

doi:10.1103/physreve.103.053108

Scalar mixing in a Kelvin-Helmholtz shear layer and implications for Reynolds-averaged Navier-Stokes modeling of mixing layers

Journal Article · Mon May 24 00:00:00 EDT 2021 · Physical Review E

DOI:https://doi.org/10.1103/physreve.103.053108· OSTI ID:1809165

^[1]

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

Large-eddy simulation of a temporally evolving Kelvin-Helmholtz (KH) mixing layer is performed with the tenth-order compact difference code miranda to examine the steady-state behavior of a passive scalar in a shear-driven mixing layer. It is shown that the integral behavior of scalar variance in a KH mixing layer behaves similarly to the integral behavior of scalar variance in a Rayleigh-Taylor (RT) mixing layer, and mixedness of the simulated KH shear layer tends towards a value of about 0.8. It is further shown that if the k-L-a-V Reynolds-averaged Navier-Stokes (RANS) model [B. E. Morgan et al., Phys. Rev. E 98, 033111 (2018)], calibrated to reproduce steady-state mixing in an RT layer, is applied to simulate a KH mixing layer, the RANS model will significantly overpredict the magnitude of scalar variance in the KH layer. A straightforward addition to the k-L-a-V model is then suggested, and self-similarity analysis is applied to determine constraints on model coefficients. Furthermore, it is shown that with the addition of a buoyancy production term in the model equation for scalar variance, it becomes possible to eliminate the model deficiency and match steady-state mixedness in simulations of both RT and KH mixing layers with a single model calibration.

View Accepted Manuscript (DOE)

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

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

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1809165

Alternate ID(s):: OSTI ID: 1809169

Report Number(s):: LLNL-JRNL--820388; 1031850

Journal Information:: Physical Review E, Journal Name: Physical Review E Journal Issue: 5 Vol. 103; ISSN 2470-0045

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (73)

Laboratory observations of shear-layer instability in a stratified fluid Browand, F. K.; Winant, C. D. Boundary-Layer Meteorology, Vol. 5, Issue 1-2 https://doi.org/10.1007/BF02188312	journal	April 1973
Large-eddy and unsteady RANS simulations of a shock-accelerated heavy gas cylinder Morgan, B. E.; Greenough, J. A. Shock Waves, Vol. 26, Issue 4 https://doi.org/10.1007/s00193-015-0566-3	journal	April 2015
A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing Schwarzkopf, J. D.; Livescu, D.; Baltzer, J. R. Flow, Turbulence and Combustion, Vol. 96, Issue 1 https://doi.org/10.1007/s10494-015-9643-z	journal	September 2015
Evolution of Kelvin-Helmholtz billows in nature and laboratory De Silva, I. P. D.; Fernando, H. J. S.; Eaton, F. Earth and Planetary Science Letters, Vol. 143, Issue 1-4 https://doi.org/10.1016/0012-821X(96)00129-X	journal	September 1996
Passive scalar mixing in Mc <1 planar shear layer flows Wang, Bing; Wei, Wei; Zhang, Yunlong Computers & Fluids, Vol. 123 https://doi.org/10.1016/j.compfluid.2015.09.006	journal	December 2015
Measurements of turbulent mixing due to Kelvin–Helmholtz instability in high-energy-density plasmas Smalyuk, V. A.; Hurricane, O. A.; Hansen, J. F. High Energy Density Physics, Vol. 9, Issue 1 https://doi.org/10.1016/j.hedp.2012.10.001	journal	March 2013
Two-equation and multi-fluid turbulence models for Rayleigh–Taylor mixing Kokkinakis, I. W.; Drikakis, D.; Youngs, D. L. International Journal of Heat and Fluid Flow, Vol. 56 https://doi.org/10.1016/j.ijheatfluidflow.2015.07.017	journal	December 2015
Parametric investigation of the transition to turbulence in Rayleigh–Taylor mixing Morgan, Brandon E.; Black, Wolfgang J. Physica D: Nonlinear Phenomena, Vol. 402 https://doi.org/10.1016/j.physd.2019.132223	journal	January 2020
Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I Zhou, Ye Physics Reports, Vol. 720-722 https://doi.org/10.1016/j.physrep.2017.07.005	journal	December 2017
Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II Zhou, Ye Physics Reports, Vol. 723-725 https://doi.org/10.1016/j.physrep.2017.07.008	journal	December 2017
Mixing of a conserved scalar in a turbulent reacting shear layer Pantano, C.; Sarkar, S.; Williams, F. A. Journal of Fluid Mechanics, Vol. 481 https://doi.org/10.1017/S0022112003003872	journal	April 2003
On density effects and large structure in turbulent mixing layers Brown, Garry L.; Roshko, Anatol Journal of Fluid Mechanics, Vol. 64, Issue 4 https://doi.org/10.1017/S002211207400190X	journal	July 1974
The mixing layer at high Reynolds number: large-structure dynamics and entrainment Dimotakis, Paul E.; Brown, Garry L. Journal of Fluid Mechanics, Vol. 78, Issue 3 https://doi.org/10.1017/S0022112076002590	journal	December 1976
The three-dimensional evolution of a plane mixing layer: the Kelvin–Helmholtz rollup Rogers, Michael M.; Moser, Robert D. Journal of Fluid Mechanics, Vol. 243, Issue -1 https://doi.org/10.1017/S0022112092002696	journal	October 1992
The three-dimensional evolution of a plane mixing layer: pairing and transition to turbulence Moser, Robert D.; Rogers, Michael M. Journal of Fluid Mechanics, Vol. 247 https://doi.org/10.1017/S0022112093000473	journal	February 1993
Scalar mixing and reaction in plane liquid shear layers Karasso, P. S.; Mungal, M. G. Journal of Fluid Mechanics, Vol. 323 https://doi.org/10.1017/S0022112096000833	journal	September 1996
A new turbulent two-field concept for modeling Rayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz mixing layers Llor, Antoine; Bailly, Pascal Laser and Particle Beams, Vol. 21, Issue 3 https://doi.org/10.1017/S0263034603213033	journal	July 2003
Direct numerical simulation of a spatially developing compressible plane mixing layer: flow structures and mean flow properties Zhou, Qiang; He, Feng; Shen, M. Y. Journal of Fluid Mechanics, Vol. 711 https://doi.org/10.1017/jfm.2012.400	journal	September 2012
Methodology for determining coefficients of turbulent mixing model Zhang, You-sheng; He, Zhi-wei; Xie, Han-song Journal of Fluid Mechanics, Vol. 905 https://doi.org/10.1017/jfm.2020.726	journal	October 2020
Stratified shear turbulence: Evolution and statistics Werne, Joseph; Fritts, David C. Geophysical Research Letters, Vol. 26, Issue 4 https://doi.org/10.1029/1999GL900022	journal	February 1999
Persistence of a Kelvin-Helmholtz instability complex in the upper troposphere: KELVIN-HELMHOLTZ INSTABILITY IN THE TROPOSPHERE Kelley, M. C.; Chen, C. Y.; Beland, R. R. Journal of Geophysical Research: Atmospheres, Vol. 110, Issue D14 https://doi.org/10.1029/2004JD005345	journal	July 2005
Reynolds number effects on Rayleigh–Taylor instability with possible implications for type Ia supernovae Cabot, William H.; Cook, Andrew W. Nature Physics, Vol. 2, Issue 8 https://doi.org/10.1038/nphys361	journal	July 2006
Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified cylindrical shells Mikaelian, Karnig O. Physics of Fluids, Vol. 17, Issue 9 https://doi.org/10.1063/1.2046712	journal	September 2005
K-L turbulence model for the self-similar growth of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities Dimonte, Guy; Tipton, Robert Physics of Fluids, Vol. 18, Issue 8 https://doi.org/10.1063/1.2219768	journal	August 2006
Artificial fluid properties for large-eddy simulation of compressible turbulent mixing Cook, Andrew W. Physics of Fluids, Vol. 19, Issue 5 https://doi.org/10.1063/1.2728937	journal	May 2007
Enthalpy diffusion in multicomponent flows Cook, Andrew W. Physics of Fluids, Vol. 21, Issue 5 https://doi.org/10.1063/1.3139305	journal	May 2009
Direct numerical simulation of a mixing layer downstream a thick splitter plate Laizet, Sylvain; Lardeau, Sylvain; Lamballais, Eric Physics of Fluids, Vol. 22, Issue 1 https://doi.org/10.1063/1.3275845	journal	January 2010
Statistics and scaling of turbulence in a spatially developing mixing layer at Reλ = 250 Attili, Antonio; Bisetti, Fabrizio Physics of Fluids, Vol. 24, Issue 3 https://doi.org/10.1063/1.3696302	journal	March 2012
Role of shocks and mix caused by capsule defects Bradley, P. A.; Cobble, J. A.; Tregillis, I. L. Physics of Plasmas, Vol. 19, Issue 9 https://doi.org/10.1063/1.4752014	journal	September 2012
Experimental observations of turbulent mixing due to Kelvin–Helmholtz instability on the OMEGA Laser Facility Smalyuk, V. A.; Hansen, J. F.; Hurricane, O. A. Physics of Plasmas, Vol. 19, Issue 9 https://doi.org/10.1063/1.4752015	journal	September 2012
The high-energy-density counterpropagating shear experiment and turbulent self-heating Doss, F. W.; Fincke, J. R.; Loomis, E. N. Physics of Plasmas, Vol. 20, Issue 12 https://doi.org/10.1063/1.4839115	journal	December 2013
Large eddy simulation requirements for the Richtmyer-Meshkov instability Olson, Britton J.; Greenough, Jeff Physics of Fluids, Vol. 26, Issue 4 https://doi.org/10.1063/1.4871396	journal	April 2014
Hydrodynamic instability growth and mix experiments at the National Ignition Facility Smalyuk, V. A.; Barrios, M.; Caggiano, J. A. Physics of Plasmas, Vol. 21, Issue 5 https://doi.org/10.1063/1.4872026	journal	May 2014
Development of the CD Symcap platform to study gas-shell mix in implosions at the National Ignition Facility Casey, D. T.; Smalyuk, V. A.; Tipton, R. E. Physics of Plasmas, Vol. 21, Issue 9 https://doi.org/10.1063/1.4894215	journal	September 2014
The Shock/Shear platform for planar radiation-hydrodynamics experiments on the National Ignition Facilitya) Doss, F. W.; Kline, J. L.; Flippo, K. A. Physics of Plasmas, Vol. 22, Issue 5 https://doi.org/10.1063/1.4918354	journal	May 2015
Exact statistical results for binary mixing and reaction in variable density turbulence Ristorcelli, J. R. Physics of Fluids, Vol. 29, Issue 2 https://doi.org/10.1063/1.4974517	journal	February 2017
Improving ICF implosion performance with alternative capsule supports Weber, C. R.; Casey, D. T.; Clark, D. S. Physics of Plasmas, Vol. 24, Issue 5 https://doi.org/10.1063/1.4977536	journal	May 2017
Mitigation of X-ray shadow seeding of hydrodynamic instabilities on inertial confinement fusion capsules using a reduced diameter fuel fill-tube MacPhee, A. G.; Smalyuk, V. A.; Landen, O. L. Physics of Plasmas, Vol. 25, Issue 5 https://doi.org/10.1063/1.5025183	journal	May 2018
Hydrodynamic instabilities seeded by the X-ray shadow of ICF capsule fill-tubes MacPhee, A. G.; Smalyuk, V. A.; Landen, O. L. Physics of Plasmas, Vol. 25, Issue 8 https://doi.org/10.1063/1.5037816	journal	August 2018
Direct numerical simulation of spatially developing highly compressible mixing layer: Structural evolution and turbulent statistics Zhang, Dongdong; Tan, Jianguo; Yao, Xiao Physics of Fluids, Vol. 31, Issue 3 https://doi.org/10.1063/1.5087540	journal	March 2019
Mixing in ICF implosions on the National Ignition Facility caused by the fill-tube Weber, C. R.; Clark, D. S.; Pak, A. Physics of Plasmas, Vol. 27, Issue 3 https://doi.org/10.1063/1.5125599	journal	March 2020
A k ‐ε model for turbulent mixing in shock‐tube flows induced by Rayleigh–Taylor instability Gauthier, Serge; Bonnet, Michel Physics of Fluids A: Fluid Dynamics, Vol. 2, Issue 9 https://doi.org/10.1063/1.857576	journal	September 1990
Mixing transition and the cascade to small scales in a plane mixing layer Moser, R. D.; Rogers, M. M. Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 5 https://doi.org/10.1063/1.858094	journal	May 1991
The evolution of a plane mixing layer with spanwise nonuniform forcing Collis, S. Scott; Lele, Sanjiva K.; Moser, Robert D. Physics of Fluids, Vol. 6, Issue 1 https://doi.org/10.1063/1.868035	journal	January 1994
Direct simulation of a self‐similar turbulent mixing layer Rogers, Michael M.; Moser, Robert D. Physics of Fluids, Vol. 6, Issue 2 https://doi.org/10.1063/1.868325	journal	February 1994
Development of the indirect‐drive approach to inertial confinement fusion and the target physics basis for ignition and gain Lindl, John Physics of Plasmas, Vol. 2, Issue 11 https://doi.org/10.1063/1.871025	journal	November 1995
Rayleigh–Taylor instability evolution in ablatively driven cylindrical implosions Hsing, W. W.; Barnes, Cris W.; Beck, J. B. Physics of Plasmas, Vol. 4, Issue 5 https://doi.org/10.1063/1.872326	journal	May 1997
Progress toward Ignition and Burn Propagation in Inertial Confinement Fusion Lindl, John D.; McCrory, Robert L.; Campbell, E. Michael Physics Today, Vol. 45, Issue 9 https://doi.org/10.1063/1.881318	journal	September 1992
Unified prediction of reshocked Richtmyer–Meshkov mixing with K-L model Xiao, Mengjuan; Zhang, Yousheng; Tian, Baolin Physics of Fluids, Vol. 32, Issue 3 https://doi.org/10.1063/5.0002312	journal	March 2020
Two-equation and multi-fluid turbulence models for Richtmyer–Meshkov mixing Kokkinakis, Ioannis W.; Drikakis, Dimitris; Youngs, David L. Physics of Fluids, Vol. 32, Issue 7 https://doi.org/10.1063/5.0010559	journal	July 2020
Modeling of turbulent mixing with an improved K–L model Xiao, Mengjuan; Zhang, Yousheng; Tian, Baolin Physics of Fluids, Vol. 32, Issue 9 https://doi.org/10.1063/5.0019363	journal	September 2020
Prediction of turbulent separation over a backward-facing smooth ramp Wasistho, B.; Squires, K. D. Journal of Turbulence, Vol. 6 https://doi.org/10.1080/14685240500055012	journal	January 2005
Application of a second-moment closure model to mixing processes involving multicomponent miscible fluids Schwarzkopf, John D.; Livescu, Daniel; Gore, Robert A. Journal of Turbulence, Vol. 12 https://doi.org/10.1080/14685248.2011.633084	journal	January 2011
Reynolds-averaged Navier–Stokes initialization and benchmarking in shock-driven turbulent mixing Haines, Brian M.; Grinstein, Fernando F.; Schwarzkopf, John D. Journal of Turbulence, Vol. 14, Issue 2 https://doi.org/10.1080/14685248.2013.779380	journal	February 2013
Evaluation of augmented RSM for interaction of homogeneous turbulent mixture with shock and rarefaction waves Griffond, Jérôme; Soulard, Olivier Journal of Turbulence, Vol. 15, Issue 9 https://doi.org/10.1080/14685248.2014.919395	journal	June 2014
Self-similarity of a Rayleigh–Taylor mixing layer at low Atwood number with a multimode initial perturbation Morgan, B. E.; Olson, B. J.; White, J. E. Journal of Turbulence, Vol. 18, Issue 10 https://doi.org/10.1080/14685248.2017.1343477	journal	June 2017
XLIII. On discontinuous movements of fluids No authors listed The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 36, Issue 244 https://doi.org/10.1080/14786446808640073	journal	November 1868
XLVI. Hydrokinetic solutions and observations Thomson, William The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 42, Issue 281 https://doi.org/10.1080/14786447108640585	journal	November 1871
The Role of Mixing in Astrophysics Arnett, D. The Astrophysical Journal Supplement Series, Vol. 127, Issue 2 https://doi.org/10.1086/313364	journal	April 2000
Development and validation of a turbulent-mix model for variable-density and compressible flows Banerjee, Arindam; Gore, Robert A.; Andrews, Malcolm J. Physical Review E, Vol. 82, Issue 4 https://doi.org/10.1103/PhysRevE.82.046309	journal	October 2010
Three-equation model for the self-similar growth of Rayleigh-Taylor and Richtmyer-Meskov instabilities Morgan, Brandon E.; Wickett, Michael E. Physical Review E, Vol. 91, Issue 4 https://doi.org/10.1103/PhysRevE.91.043002	journal	April 2015
Turbulent transport and mixing in transitional Rayleigh-Taylor unstable flow: A priori assessment of gradient-diffusion and similarity modeling Schilling, Oleg; Mueschke, Nicholas J. Physical Review E, Vol. 96, Issue 6 https://doi.org/10.1103/PhysRevE.96.063111	journal	December 2017
Two-length-scale turbulence model for self-similar buoyancy-, shock-, and shear-driven mixing Morgan, Brandon E.; Schilling, Oleg; Hartland, Tucker A. Physical Review E, Vol. 97, Issue 1 https://doi.org/10.1103/PhysRevE.97.013104	journal	January 2018
Large-eddy simulation and Reynolds-averaged Navier-Stokes modeling of a reacting Rayleigh-Taylor mixing layer in a spherical geometry Morgan, Brandon E.; Olson, Britton J.; Black, Wolfgang J. Physical Review E, Vol. 98, Issue 3 https://doi.org/10.1103/PhysRevE.98.033111	journal	September 2018
Modeling of Rayleigh-Taylor mixing using single-fluid models Kokkinakis, Ioannis W.; Drikakis, Dimitris; Youngs, David L. Physical Review E, Vol. 99, Issue 1 https://doi.org/10.1103/PhysRevE.99.013104	journal	January 2019
Direct numerical simulation and Reynolds-averaged Navier-Stokes modeling of the sudden viscous dissipation for multicomponent turbulence Campos, Alejandro; Morgan, Brandon E. Physical Review E, Vol. 99, Issue 6 https://doi.org/10.1103/PhysRevE.99.063103	journal	June 2019
Validation of a Turbulent Kelvin-Helmholtz Shear Layer Model Using a High-Energy-Density OMEGA Laser Experiment Hurricane, O. A.; Smalyuk, V. A.; Raman, K. Physical Review Letters, Vol. 109, Issue 15 https://doi.org/10.1103/PhysRevLett.109.155004	journal	October 2012
Measurements of an Ablator-Gas Atomic Mix in Indirectly Driven Implosions at the National Ignition Facility Smalyuk, V. A.; Tipton, R. E.; Pino, J. E. Physical Review Letters, Vol. 112, Issue 2 https://doi.org/10.1103/PhysRevLett.112.025002	journal	January 2014
Late-Time Mixing Sensitivity to Initial Broadband Surface Roughness in High-Energy-Density Shear Layers Flippo, K. A.; Doss, F. W.; Kline, J. L. Physical Review Letters, Vol. 117, Issue 22 https://doi.org/10.1103/PhysRevLett.117.225001	journal	November 2016
Rayleigh-Taylor Instability and Laser-Pellet Fusion Bodner, Stephen E. Physical Review Letters, Vol. 33, Issue 13 https://doi.org/10.1103/PhysRevLett.33.761	journal	September 1974
Two-Dimensional Simulation of Fluid Instability in Laser-Fusion Pellets Lindl, J. D.; Mead, W. C. Physical Review Letters, Vol. 34, Issue 20 https://doi.org/10.1103/PhysRevLett.34.1273	journal	May 1975
Development of a two-stream mixing layer from tripped and untripped boundary layers Bell, James H.; Mehta, Rabindra D. AIAA Journal, Vol. 28, Issue 12 https://doi.org/10.2514/3.10519	journal	December 1990
Applications of shock-induced mixing to supersonic combustion Yang, Joseph; Kubota, Toshi; Zukoski, Edward E. AIAA Journal, Vol. 31, Issue 5 https://doi.org/10.2514/3.11696	journal	May 1993

Similar Records

Large-eddy simulation and Reynolds-averaged Navier-Stokes modeling of a reacting Rayleigh-Taylor mixing layer in a spherical geometry

Journal Article · Mon Sep 17 00:00:00 EDT 2018 · Physical Review E · OSTI ID:1548329

Two self-similar Reynolds-stress transport models with anisotropic eddy viscosity

Journal Article · Tue Nov 14 23:00:00 EST 2023 · Physical Review. E · OSTI ID:2274884

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Kelvin-Helmholtz instability
flow instability
shear layer turbulence
turbulence
turbulent mixing

Scalar mixing in a Kelvin-Helmholtz shear layer and implications for Reynolds-averaged Navier-Stokes modeling of mixing layers

Citation Formats

References (73)

Similar Records

Related Subjects