Turbulent transport and mixing in transitional RayleighTaylor unstable flow: A priori assessment of gradientdiffusion and similarity modeling
Abstract
Data from a 1152×760×1280 direct numerical simulation of a RayleighTaylor mixing layer modeled after a smallAtwoodnumber waterchannel experiment is used to investigate the validity of gradient diffusion and similarity closures a priori. The budgets of the mean flow, turbulent kinetic energy, turbulent kinetic energy dissipation rate, heavyfluid mass fraction variance, and heavyfluid mass fraction variance dissipation rate transport equations across the mixing layer were previously analyzed at different evolution times to identify the most important transport and mixing mechanisms. Here a methodology is introduced to systematically estimate model coefficients as a function of time in the closures of the dynamically significant terms in the transport equations by minimizing the L2 norm of the difference between the model and correlations constructed using the simulation data. It is shown that gradientdiffusion and similarity closures used for the turbulent kinetic energy K, turbulent kinetic energy dissipation rate ε, heavyfluid mass fraction variance S, and heavyfluid mass fraction variance dissipation rate χ equations capture the shape of the exact, unclosed profiles well over the nonlinear and turbulent evolution regimes. Using orderofmagnitude estimates for the terms in the exact transport equations and their closure models, it is shown that several of the standard closures formore »
 Authors:

 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Texas A & M Univ., College Station, TX (United States); Southwest Research Institute, San Antonio, TX (United States)
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1466921
 Alternate Identifier(s):
 OSTI ID: 1413370
 Report Number(s):
 LLNLJRNL740553
Journal ID: ISSN 24700045; PLEEE8; 894615
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review E
 Additional Journal Information:
 Journal Volume: 96; Journal Issue: 6; Journal ID: ISSN 24700045
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 42 ENGINEERING
Citation Formats
Schilling, Oleg, and Mueschke, Nicholas J. Turbulent transport and mixing in transitional RayleighTaylor unstable flow: A priori assessment of gradientdiffusion and similarity modeling. United States: N. p., 2017.
Web. doi:10.1103/PhysRevE.96.063111.
Schilling, Oleg, & Mueschke, Nicholas J. Turbulent transport and mixing in transitional RayleighTaylor unstable flow: A priori assessment of gradientdiffusion and similarity modeling. United States. doi:10.1103/PhysRevE.96.063111.
Schilling, Oleg, and Mueschke, Nicholas J. Thu .
"Turbulent transport and mixing in transitional RayleighTaylor unstable flow: A priori assessment of gradientdiffusion and similarity modeling". United States. doi:10.1103/PhysRevE.96.063111. https://www.osti.gov/servlets/purl/1466921.
@article{osti_1466921,
title = {Turbulent transport and mixing in transitional RayleighTaylor unstable flow: A priori assessment of gradientdiffusion and similarity modeling},
author = {Schilling, Oleg and Mueschke, Nicholas J.},
abstractNote = {Data from a 1152×760×1280 direct numerical simulation of a RayleighTaylor mixing layer modeled after a smallAtwoodnumber waterchannel experiment is used to investigate the validity of gradient diffusion and similarity closures a priori. The budgets of the mean flow, turbulent kinetic energy, turbulent kinetic energy dissipation rate, heavyfluid mass fraction variance, and heavyfluid mass fraction variance dissipation rate transport equations across the mixing layer were previously analyzed at different evolution times to identify the most important transport and mixing mechanisms. Here a methodology is introduced to systematically estimate model coefficients as a function of time in the closures of the dynamically significant terms in the transport equations by minimizing the L2 norm of the difference between the model and correlations constructed using the simulation data. It is shown that gradientdiffusion and similarity closures used for the turbulent kinetic energy K, turbulent kinetic energy dissipation rate ε, heavyfluid mass fraction variance S, and heavyfluid mass fraction variance dissipation rate χ equations capture the shape of the exact, unclosed profiles well over the nonlinear and turbulent evolution regimes. Using orderofmagnitude estimates for the terms in the exact transport equations and their closure models, it is shown that several of the standard closures for the turbulent production and dissipation (destruction) must be modified to include Reynoldsnumber scalings appropriate for RayleighTaylor flow at small to intermediate Reynolds numbers. The latetime, large Reynolds number coefficients are determined to be different from those used in shear flow applications and largely adopted in twoequation Reynoldsaveraged NavierStokes (RANS) models of RayleighTaylor turbulent mixing. In addition, it is shown that the predictions of the Boussinesq model for the Reynolds stress agree better with the data when additional buoyancyrelated terms are included. It is shown that an unsteady RANS paradigm is needed to predict the transitional flow dynamics from early evolution times, analogous to the small Reynolds number modifications in RANS models of wallbounded flows in which the productiontodissipation ratio is far from equilibrium. Although the present study is specific to one particular flow and one set of initial conditions, the methodology could be applied to calibrations of other RayleighTaylor flows with different initial conditions (which may give different results during the earlytime, transitional flow stages, and perhaps asymptotic stage). Finally, the implications of these findings for developing highfidelity eddy viscositybased turbulent transport and mixing models of RayleighTaylor turbulence are discussed.},
doi = {10.1103/PhysRevE.96.063111},
journal = {Physical Review E},
number = 6,
volume = 96,
place = {United States},
year = {2017},
month = {12}
}
Web of Science
Works referenced in this record:
O NE P OINT C LOSURE M ODELS FOR B UOYANCY D RIVEN T URBULENT F LOWS
journal, January 2002
 Hanjalić, K.
 Annual Review of Fluid Mechanics, Vol. 34, Issue 1
The Structure of Shear Driven Mixing With an Unstable Thermal Stratification
journal, March 1996
 Snider, D. M.; Andrews, M. J.
 Journal of Fluids Engineering, Vol. 118, Issue 1
A priori analyses of three subgridscale models for oneparameter families of filters
journal, May 2000
 Pruett, C. David; Adams, Nikolaus A.
 Physics of Fluids, Vol. 12, Issue 5
Development and validation of a turbulentmix model for variabledensity and compressible flows
journal, October 2010
 Banerjee, Arindam; Gore, Robert A.; Andrews, Malcolm J.
 Physical Review E, Vol. 82, Issue 4
Analysis of turbulent transport and mixing in transitional Rayleigh–Taylor unstable flow using direct numerical simulation data
journal, October 2010
 Schilling, Oleg; Mueschke, Nicholas J.
 Physics of Fluids, Vol. 22, Issue 10
A Procedure for Using DNS Databases
journal, March 1998
 Parneix, S.; Laurence, D.; Durbin, P. A.
 Journal of Fluids Engineering, Vol. 120, Issue 1
Measurements of molecular mixing in a highSchmidtnumber Rayleigh–Taylor mixing layer
journal, July 2009
 Mueschke, Nicholas J.; Schilling, Oleg; Youngs, David L.
 Journal of Fluid Mechanics, Vol. 632
The effect of turbulence modelling on the CFD simulation of buoyant diffusion flames
journal, March 2002
 Liu, F.; Wen, J. X.
 Fire Safety Journal, Vol. 37, Issue 2
Natural convection in partitioned twodimensional enclosures at higher Rayleigh numbers
journal, May 1996
 Hanjalić, K.; Kenjereš, S.; Durst, F.
 International Journal of Heat and Mass Transfer, Vol. 39, Issue 7
Investigation of Rayleigh–Taylor turbulence and mixing using direct numerical simulation with experimentally measured initial conditions. I. Comparison to experimental data
journal, January 2009
 Mueschke, Nicholas J.; Schilling, Oleg
 Physics of Fluids, Vol. 21, Issue 1
RANSBased Very Large Eddy Simulation of Thermal and Magnetic Convection at Extreme Conditions
journal, October 2005
 Hanjalić, K.; Kenjereš, S.
 Journal of Applied Mechanics, Vol. 73, Issue 3
A possible explanation of countergradient fluxes in homogeneous turbulence
journal, May 1996
 Gerz, Thomas; Schumann, Ulrich
 Theoretical and Computational Fluid Dynamics, Vol. 8, Issue 3
Investigation of Rayleigh–Taylor turbulence and mixing using direct numerical simulation with experimentally measured initial conditions. II. Dynamics of transitional flow and mixing statistics
journal, January 2009
 Mueschke, Nicholas J.; Schilling, Oleg
 Physics of Fluids, Vol. 21, Issue 1
Passive scalar mixing: Analytic study of time scale ratio, variance, and mix rate
journal, July 2006
 Ristorcelli, J. R.
 Physics of Fluids, Vol. 18, Issue 7
Modeling of scalar dissipation in partially premixed turbulent flames
journal, April 2007
 Mura, Arnaud; Robin, Vincent; Champion, Michel
 Combustion and Flame, Vol. 149, Issue 12
Multicomponent Reynoldsaveraged Navier–Stokes simulations of Richtmyer–Meshkov instability and mixing induced by reshock at different times
journal, November 2013
 MoránLópez, J. T.; Schilling, O.
 Shock Waves, Vol. 24, Issue 3
Theoretical expression for the countergradient vertical heat flux
journal, October 1972
 Deardorff, J. W.
 Journal of Geophysical Research, Vol. 77, Issue 30
Optimal estimation for largeeddy simulation of turbulence and application to the analysis of subgrid models
journal, October 2006
 Moreau, A.; Teytaud, O.; Bertoglio, J. P.
 Physics of Fluids, Vol. 18, Issue 10
Convective rolls and heat transfer in finitelength RayleighBénard convection: A twodimensional numerical study
journal, December 2000
 Kenjereš, S.; Hanjalić, K.
 Physical Review E, Vol. 62, Issue 6
Direct investigation of the Ktransport equation for a complex turbulent flow
journal, June 2003
 Schmitt, Francois; Merci, Bart; Dick, Erik
 Journal of Turbulence, Vol. 4
KL turbulence model for the selfsimilar growth of the RayleighTaylor and RichtmyerMeshkov instabilities
journal, August 2006
 Dimonte, Guy; Tipton, Robert
 Physics of Fluids, Vol. 18, Issue 8
Scalar Variance Transport in the Turbulence Modeling of Propulsive Jets
journal, January 2001
 Chidambaram, N.; Dash, S. M.; Kenzakowski, D. C.
 Journal of Propulsion and Power, Vol. 17, Issue 1
Variable Turbulent SchmidtNumber Formulation for Scramjet Applications
journal, March 2006
 Xiao, X.; Edwards, J. R.; Hassan, H. A.
 AIAA Journal, Vol. 44, Issue 3
Towards an extended scalar dissipation equation for turbulent premixed combustion
journal, April 2003
 Mura, Arnaud; Borghi, Roland
 Combustion and Flame, Vol. 133, Issue 12
Modeling Scramjet Flows with Variable Turbulent Prandtl and Schmidt Numbers
journal, June 2007
 Xiao, X.; Hassan, H. A.; Baurle, R. A.
 AIAA Journal, Vol. 45, Issue 6
The CounterGradient Heat Flux in the Lower Atmosphere and in the Laboratory
journal, September 1966
 Deardorff, J. W.
 Journal of the Atmospheric Sciences, Vol. 23, Issue 5
Robust Locally Weighted Regression and Smoothing Scatterplots
journal, December 1979
 Cleveland, William S.
 Journal of the American Statistical Association, Vol. 74, Issue 368
Transport Equations in Turbulence
journal, January 1970
 Daly, Bart J.
 Physics of Fluids, Vol. 13, Issue 11
CFD predictions for chemical processing in a confined impingingjets reactor
journal, January 2006
 Liu, Ying; Fox, R. O.
 AIChE Journal, Vol. 52, Issue 2
The density ratio dependence of selfsimilar Rayleigh–Taylor mixing
journal, November 2013
 Youngs, David L.
 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 371, Issue 2003
A k ‐ε model for turbulent mixing in shock‐tube flows induced by Rayleigh–Taylor instability
journal, September 1990
 Gauthier, Serge; Bonnet, Michel
 Physics of Fluids A: Fluid Dynamics, Vol. 2, Issue 9
On the Spectrum of Isotropic Temperature Fluctuations in an Isotropic Turbulence
journal, April 1951
 Corrsin, Stanley
 Journal of Applied Physics, Vol. 22, Issue 4
Concentration fluctuations in a round turbulent free jet
journal, January 1971
 Spalding, D. B.
 Chemical Engineering Science, Vol. 26, Issue 1
Application of the energydissipation model of turbulence to the calculation of flow near a spinning disc
journal, November 1974
 Launder, B. E.; Sharma, B. I.
 Letters in Heat and Mass Transfer, Vol. 1, Issue 2
Multicomponent Reynoldsaveraged Navier–Stokes simulations of reshocked Richtmyer–Meshkov instabilityinduced mixing
journal, March 2013
 MoránLópez, J. Tiberius; Schilling, Oleg
 High Energy Density Physics, Vol. 9, Issue 1
A study of Favre averaging in turbulent flows with chemical reaction
journal, December 1991
 Chen, Changsi; Riley, James J.; McMurtry, Patrick A.
 Combustion and Flame, Vol. 87, Issue 34
About Boussinesq's turbulent viscosity hypothesis: historical remarks and a direct evaluation of its validity
journal, September 2007
 Schmitt, François G.
 Comptes Rendus Mécanique, Vol. 335, Issue 910
Turbulent combustion modeling
journal, March 2002
 Veynante, Denis; Vervisch, Luc
 Progress in Energy and Combustion Science, Vol. 28, Issue 3
The kL turbulence model for describing buoyancydriven fluid instabilities
journal, September 2006
 Chiravalle, Vincent P.
 Laser and Particle Beams, Vol. 24, Issue 3
Rayleigh–Taylor turbulence: selfsimilar analysis and direct numerical simulations
journal, May 2004
 Ristorcelli, J. R.; Clark, T. T.
 Journal of Fluid Mechanics, Vol. 507
Modelling of the correlation between velocity and reactive scalar gradients in turbulent premixed flames based on DNS data
journal, July 2008
 Mura, Arnaud; Tsuboi, Kazuya; Hasegawa, Tatsuya
 Combustion Theory and Modelling, Vol. 12, Issue 4
Application of a Reynolds stress turbulence model to the compressible shear layer
journal, May 1991
 Sarkar, S.; Lakshmanan, B.
 AIAA Journal, Vol. 29, Issue 5
Closure of the Reynolds stress and scalar flux equations
journal, January 1988
 Jones, W. P.; Musonge, P.
 Physics of Fluids, Vol. 31, Issue 12
A new approach to modelling nearwall turbulence energy and stress dissipation
journal, May 2002
 JakirliĆ, S.; HanjaliĆ, K.
 Journal of Fluid Mechanics, Vol. 459
Progress in Favré–Reynolds stress closures for compressible flows
journal, September 1999
 Adumitroaie, V.; Ristorcelli, J. R.; Taulbee, D. B.
 Physics of Fluids, Vol. 11, Issue 9
Locally Weighted Regression: An Approach to Regression Analysis by Local Fitting
journal, September 1988
 Cleveland, William S.; Devlin, Susan J.
 Journal of the American Statistical Association, Vol. 83, Issue 403
The prediction of laminarization with a twoequation model of turbulence
journal, February 1972
 Jones, W. P.; Launder, B. E.
 International Journal of Heat and Mass Transfer, Vol. 15, Issue 2
Experimental characterization of initial conditions and spatiotemporal evolution of a smallAtwoodnumber Rayleigh–Taylor mixing layer
journal, October 2006
 Mueschke, Nicholas J.; Andrews, Malcolm J.; Schilling, Oleg
 Journal of Fluid Mechanics, Vol. 567
Scalar Fluctuation Modeling for HighSpeed Aeropropulsive Flows
journal, May 2007
 Brinckman, Kevin W.; Calhoon, William H.; Dash, Sanford M.
 AIAA Journal, Vol. 45, Issue 5
A termbyterm direct numerical simulation validation study of the multienvironment conditional probabilitydensityfunction model for turbulent reacting flows
journal, August 2007
 Smith, S. T.; Fox, R. O.
 Physics of Fluids, Vol. 19, Issue 8
Modelling of turbulent scalar flux in turbulent premixed flames based on DNS databases
journal, February 2006
 Nishiki, S.; Hasegawa, T.; Borghi, R.
 Combustion Theory and Modelling, Vol. 10, Issue 1
On density effects and large structure in turbulent mixing layers
journal, July 1974
 Brown, Garry L.; Roshko, Anatol
 Journal of Fluid Mechanics, Vol. 64, Issue 4