A multispecies turbulence model for the mixing and de-mixing of miscible fluids

References

• Spalding DB. Two-fluid models of turbulence. In: Dwoyer DL, Hussaini MY, Voigt RG, editors. Theoretical approaches to turbulence. New York, NY: Springer; 1985. p. 279–302.
   Google Scholar
• Knapp P, Martin M, Yager-Elorriaga D, et al. A novel, magnetically driven convergent Richtmyer-Meshkov platform. Phys Plasmas. 2020;27(9):092707.
   Web of Science ®Google Scholar
• Youngs DL. Modelling turbulent mixing by Rayleigh-Taylor instability. Phys D: Nonlin Phenom. 1989;37(1):270–287.
   Google Scholar
• Read KI. Experimental investigation of turbulent mixing by Rayleigh-Taylor instability. Phys D: Nonlin Phenom. 1984;12(1–3):45–58.
   Google Scholar
• Livescu D, Wei T, Petersen MR. Direct numerical simulations of Rayleigh-Taylor instability. J PhysConf Ser. 2011;318(8):082007.
   Google Scholar
• Livescu D, Wei T, Brady P. Rayleigh-Taylor instability with gravity reversal. Phys D: Nonlin Phenom. 2021;417:132832.
   Web of Science ®Google Scholar
• Dimonte G, Schneider M. Turbulent Rayleigh-Taylor instability experiments with variable acceleration. Phys Rev E. 1996;54(4):3740.
   Web of Science ®Google Scholar
• Dimonte G, Schneider M. Density ratio dependence of Rayleigh-Taylor mixing for sustained and impulsive acceleration histories. Phys Fluid. 2000;12(2):304–321.
   Web of Science ®Google Scholar
• Dimonte G, Ramaprabhu P, Andrews M. Rayleigh-Taylor instability with complex acceleration history. Phys Rev E. 2007;76(4):046313.
   Web of Science ®Google Scholar
• Zhou Y. Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I. Phys Rep. 2017;720:1–136.
   Google Scholar
• Zhou Y. Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II. Phys Rep. 2017;723:1–160.
   Google Scholar
• Speziale CG. Analytical methods for the development of Reynolds-stress closures in turbulence. Annu Rev Fluid Mech. 1991;23(1):107–157.
   Google Scholar
• Dimonte G, Tipton R. K-L turbulence model for the self-similar growth of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities. Phys Fluid. 2006;18(8):085101.
   Web of Science ®Google Scholar
• Banerjee A, Gore RA, Andrews MJ. Development and validation of a turbulent-mix model for variable-density and compressible flows. Phys Rev E. 2010;82(4):046309.
   Web of Science ®Google Scholar
• Morgan BE, Wickett ME. Three-equation model for the self-similar growth of Rayleigh-Taylor and Richtmyer-Meskov instabilities. Phys Rev E. 2015;91(4):043002.
   Web of Science ®Google Scholar
• Morgan BE, Schilling O, Hartland TA. Two-length-scale turbulence model for self-similar buoyancy-, shock-, and shear-driven mixing. Phys Rev E. 2018;97(1):013104.
   PubMed Web of Science ®Google Scholar
• Grégoire O, Souffland D, Gauthier S. A second-order turbulence model for gaseous mixtures induced by Richtmyer-Meshkov instability. J Turbul. 2005;6:N29.
   Web of Science ®Google Scholar
• Gauthier S, Bonnet M. A k-ϵ model for turbulent mixing in shock-tube flows induced by Rayleigh–Taylor instability. Phys Fluid A: Fluid Dyn. 1990;2(9):1685–1694.
   Web of Science ®Google Scholar
• Besnard D, Harlow F, Rauenzahn R, et al. Turbulence transport equations for variable-density turbulence and their relationship to two-field models. Los Alamos National Laboratory, NM (United States); 1992 (Technical Report LA-12303-MS).
   Google Scholar
• Stalsberg-Zarling K, Gore R. The BHR2 turbulence model: incompressible isotropic decay, Rayleigh-Taylor, Kelvin-Helmholtz and homogeneous variable-density turbulence (U). Los Alamos National Laboratory; 2011 (Technical Report (LA-UR-11-04773)).
   Google Scholar
• Schwarzkopf JD, Livescu D, Gore RA, et al. Application of a second-moment closure model to mixing processes involving multicomponent miscible fluids. J Turbul. 2011;12:N49.
   Web of Science ®Google Scholar
• Schwarzkopf JD, Livescu D, Baltzer JR, et al. A two-length scale turbulence model for single-phase multi-fluid mixing. Flow Turbul Combus. 2016;96(1):1–43.
   Web of Science ®Google Scholar
• Youngs DL. Numerical simulation of turbulent mixing by Rayleigh-Taylor instability. Phys D: Nonlin Phenom. 1989;37(1–3):270–287.
   Google Scholar
• Youngs D. Numerical simulation of mixing by Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Laser Partic Beams 1994;12(4):725–750.
   Web of Science ®Google Scholar
• Kokkinakis IW, Drikakis D, Youngs DL, et al. Two-equation and multi-fluid turbulence models for Rayleigh–Taylor mixing. Inte J Heat Fluid Flow. 2015;56:233–250.
   Web of Science ®Google Scholar
• Cihonski AJ, Clark TT, Gore RA. A framework for a multispecies mix model with independent species transport and applications to de-mixing processes. Los Alamos National Lab.; 2015. (Tech. rep. NM (LA-UR-15-20485)).
   Google Scholar
• Cook AW. Enthalpy diffusion in multicomponent flows. Phys Fluid. 2009;21(5):055109.
   Web of Science ®Google Scholar
• Livescu D, Ristorcelli JR, Gore RA, et al. High-Reynolds number Rayleigh-Taylor turbulence. J Turbul. 2009;10:N13.
   Web of Science ®Google Scholar
• Livescu D, Ristorcelli J. Variable-density mixing in buoyancy-driven turbulence. J Fluid Mech. 2008;605:145–180.
   Web of Science ®Google Scholar
• Aslangil D, Livescu D, Banerjee A. Variable-density buoyancy-driven turbulence with asymmetric initial density distribution. Phys D: Nonlin Phenom. 2020;406:132444.
   Web of Science ®Google Scholar
• Aslangil D, Livescu D, Banerjee A. Effects of Atwood and Reynolds numbers on the evolution of buoyancy-driven homogeneous variable-density turbulence. J Fluid Mech. 2020;895:A12.
   Web of Science ®Google Scholar
• Ristorcelli JR, Hjelm N. Initial moments and parameterizing transition for Rayleigh–Taylor unstable stochastic interfaces. J Turbul. 2010;11:N46.
   Web of Science ®Google Scholar
• Sinha K, Balasridhar S. Conservative formulation of the k-ε turbulence model for shock-turbulence interaction. AIAA Journal. 2013;51(8):1872–1882.
   Web of Science ®Google Scholar
• Gittings M, Weaver R, Clover M, et al. The RAGE radiation-hydrodynamic code. Comput Sci Disc. 2008;1(1):015005.
   Google Scholar
• Goncharov VN. Analytical model of nonlinear, single-mode, classical Rayleigh-Taylor instability at arbitrary Atwood numbers. Phys Rev Lett. 2002;88(13):134502.
   PubMed Web of Science ®Google Scholar
• Rollin B, Andrews MJ. On generating initial conditions for turbulence models: the case of Rayleigh–Taylor instability turbulent mixing. J Turbul. 2013;14(3):77–106.
   Web of Science ®Google Scholar
• Canfield J, Denissen N, Francois M, et al. A comparison of interface growth models applied to Rayleigh–Taylor and Richtmyer–Meshkov instabilities. J Fluids Eng. 2020;142(12):121108.
   Web of Science ®Google Scholar
• Braun NO, Gore RA. A passive model for the evolution of subgrid-scale instabilities in turbulent flow regimes. Phys D: Nonlin Phenom. 2020;404:132373.
   Web of Science ®Google Scholar
• Andrews MJ, Youngs DL, Livescu D, et al. Computational studies of two-dimensional Rayleigh-Taylor driven mixing for a tilted-rig. J Fluids Eng. 2014;136(9):091212.
   Web of Science ®Google Scholar
• Youngs DL. Rayleigh–taylor mixing: direct numerical simulation and implicit large eddy simulation. Phys Scrip. 2017;92(7):074006.
   Web of Science ®Google Scholar
• Youngs DL. Application of monotone integrated large eddy simulation to Rayleigh-Taylor mixing. Philos Trans Roy Soc A: Math Phys Eng Sci. 2009;367(1899):2971–2983.
   PubMed Web of Science ®Google Scholar
• Pope S. Turbulent flows. Cambridge University Press; 2000. p. 141.
   Google Scholar
• Baltzer JR, Livescu D. Variable-density effects in incompressible non-buoyant shear-driven turbulent mixing layers. J Fluid Mech. 2020;900:A16.
   Web of Science ®Google Scholar
• Bell JH, Mehta RD. Development of a two-stream mixing layer from tripped and untripped boundary layers. AIAA Journal. 1990;28(12):2034–2042.
   Web of Science ®Google Scholar
• Barre S, Alem D, Bonnet JP. Experimental study of a normal shock/homogeneous turbulence interaction. AIAA Journal. 1996;34:968–974.
   Web of Science ®Google Scholar
• Kitamura T, Nagata K, Sakai Y, et al. Changes in divergence-free grid turbulence interacting with a weak spherical shock wave. Phys Fluid. 2017;29(6):065114.
   Web of Science ®Google Scholar
• Agui JH, Briassulis G, Andreopoulos Y. Studies of interactions of a propagating shock wave with decaying grid turbulence: velocity and vorticity fields. J Fluid Mech. 2005;524:143.
   Web of Science ®Google Scholar
• McManamen BDD, North S, Bowersox R. Velocity and temperature fluctuations in a high-speed shock-turbulence interaction. J Fluid Mech. 2021;913:A10.
   Web of Science ®Google Scholar
• Larsson J, Lele SK. Direct numerical simulation of canonical shock/turbulence interaction. Phys Fluids. 2009;21(12):126101.
   Web of Science ®Google Scholar
• Ryu J, Livescu D. Turbulence structure behind the shock in canonical shock-vortical turbulence interaction. J Fluid Mech. 2014;756:R1.
   Web of Science ®Google Scholar
• Ribner HS. Convection of a pattern of vorticity through a shock wave; 1954 (NACA-TN-2864).
   Google Scholar
• Moore FK. Unsteady oblique interaction of a shock wave with a plane disturbance; 1953 (NACA-TR-1165).
   Google Scholar
• Mahesh K, Lele SK, Moin P. The influence of entropy fluctuations on the interaction of turbulence with a shock wave. J Fluid Mech. 1997;334:353–379.
   Web of Science ®Google Scholar
• Lele SK. Shock-jump relations in a turbulent flow. Phys Fluid A: Fluid Dyn. 1992;4(12):2900–2905.
   Web of Science ®Google Scholar
• Sinha K, Mahesh K, Candler GV. Modeling shock unsteadiness in shock/turbulence interaction. Phys Fluids. 2003;15(8):2290–2297.
   Web of Science ®Google Scholar
• Braun N, Gore R. On primitive variable behaviour near shocks in ensemble-averaged methods. J Turbul. 2018;19(10):868–888.
   Web of Science ®Google Scholar
• Andronov VA, Bakhrakh SM, Meshkov EE, et al. An experimental investigation and numerical modeling of turbulent mixing in one-dimensional flows. Soviet Physic Doklady. 1982;27:393.
   Google Scholar
• Gauthier OG, Souffland D, Gauthier S. A second-order turbulence model for gaseous mixtures induced by Richtmyer—Meshkov instability. J Turbul. 2005;6:N29.
   Web of Science ®Google Scholar
• El Rafei M, Flaig M, Youngs D, et al. Three-dimensional simulations of turbulent mixing in spherical implosions. Phys Fluid. 2019;31(11):114101.
   Web of Science ®Google Scholar
• Joggerst C, Nelson A, Woodward P, et al. Cross-code comparisons of mixing during the implosion of dense cylindrical and spherical shells. J Comput Phys. 2014;275:154–173.
   Web of Science ®Google Scholar
• Flaig M, Clark D, Weber C, et al. Single-mode perturbation growth in an idealized spherical implosion. J Comput Phys. 2018;371:801–819.
   Web of Science ®Google Scholar
• Ristorcelli R, Bakosi J. Coupled multi-species mixing in variable-density turbulence: a Fokker Planck approach; 2021 (Los Alamos Technical Report LA-UR-21-21229).
   Google Scholar