Turbulent transport and mixing in transitional RayleighTaylor unstable flow: A priori assessment of gradientdiffusion and similarity modeling
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:

^{[1]};
^{[2]}
 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:
 Report Number(s):
 LLNLJRNL740553
Journal ID: ISSN 24700045; PLEEE8; 894615
 Grant/Contract Number:
 AC5207NA27344
 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)
 Research Org:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org:
 USDOE National Nuclear Security Administration (NNSA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 42 ENGINEERING
 OSTI Identifier:
 1466921
 Alternate Identifier(s):
 OSTI ID: 1413370
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.,
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. 2017.
"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}
}