Large-eddy simulation of mixing in a recirculating shear flow

The flow field and mixing in an expansion-ramp geometry is studied using large-eddy simulation (LES) with subgrid scale (SGS) modelling. The expansion-ramp geometry was developed to investigate enhanced mixing and flameholding characteristics while maintaining low total-pressure losses. Passive mixing was considered without taking into account the effects of chemical reactions and heat release, an approximation that is adequate for experiments conducted in parallel. The primary objective of the current work is to validate the LES–SGS closure in the case of passive turbulent mixing in a complex configuration and, if successful, to rely on numerical simulation results for flow details unavailable via experiment. Total (resolved-scale plus subgrid contribution) probability density functions (p.d.f.s) of the mixture fraction are estimated using a presumed beta-distribution model for the subgrid field. Flow and mixing statistics are in good agreement with the experimental measurements, indicating that the mixing on a molecular scale is correctly predicted by the LES–SGS model. Finally, statistics are shown to be resolution-independent by computing the flow for three resolutions, at twice and four times the resolution of the coarsest simulation.

[1]  J. Shan,et al.  Reynolds-number effects and anisotropy in transverse-jet mixing , 2006, Journal of Fluid Mechanics.

[2]  Paul E. Dimotakis,et al.  Mixing and combustion with low heat release in a turbulent shear layer , 1984, Journal of Fluid Mechanics.

[3]  P. Dimotakis,et al.  Similarity of the concentration field of gas-phase turbulent jets , 1990, Journal of Fluid Mechanics.

[4]  M. Rogers,et al.  A priori testing of subgrid models for chemically reacting non-premixed turbulent shear flows , 1997, Journal of Fluid Mechanics.

[5]  D. Pullin,et al.  A vortex-based subgrid stress model for large-eddy simulation , 1997 .

[6]  F. Harris.  On the use of windows for harmonic analysis with the discrete Fourier transform , 1978, Proceedings of the IEEE.

[7]  C. L. Ribault.  Large Eddy simulation of passive scalar in compressible mixing layers , 2008 .

[8]  R. Hanson,et al.  Mixing efficiency measurements using a modified cold chemistry technique , 2004 .

[9]  M. Lesieur,et al.  Spectral large-eddy simulation of isotropic and stably stratified turbulence , 1992, Journal of Fluid Mechanics.

[10]  J. Andreopoulos.  On the structure of jets in a crossflow , 1985, Journal of Fluid Mechanics.

[11]  Ugo Piomelli,et al.  Large-eddy simulation of a three-dimensional shear-driven turbulent boundary layer , 2000, Journal of Fluid Mechanics.

[12]  P. Dimotakis,et al.  The mixing layer at high Reynolds number: large-structure dynamics and entrainment , 1976, Journal of Fluid Mechanics.

[13]  John K. Eaton,et al.  A Review of Research on Subsonic Turbulent Flow Reattachment , 1981 .

[14]  I. M. O T A K I S.  The mixing transition in turbulent flows , 2022 .

[15]  E. E. Zukoski,et al.  A Study of the Interaction of Gaseous Jets from Transverse Slots with Supersonic External Flows , 1968 .

[16]  E. T. Curran,et al.  Scramjet Engines: The First Forty Years , 2001 .

[17]  Carlos Pantano,et al.  LES approach for high Reynolds number wall-bounded flows with application to turbulent channel flow , 2008, J. Comput. Phys..

[18]  P. Moin,et al.  A further study of numerical errors in large-eddy simulations , 2003 .

[19]  M. Arienti,et al.  A level set approach to Eulerian-Lagrangian coupling , 2003 .

[20]  Gareth P. Williams,et al.  Conservation properties of convection difference schemes , 1970 .

[21]  Ralf Deiterding,et al.  A low numerical dissipation patch-based adaptive mesh refinement method for large-eddy simulation of compressible flows , 2007, J. Comput. Phys..

[22]  D. Pullin,et al.  Hybrid tuned center-difference-WENO method for large eddy simulations in the presence of strong shocks , 2004 .

[23]  Alan R. Kerstein,et al.  A linear-eddy model of turbulent scalar transport and mixing , 1988 .

[24]  S. Menon,et al.  LES of scalar mixing in supersonic mixing layers , 2005 .

[25]  Ronald K. Hanson,et al.  Time evolution and mixing characteristics of hydrogen and ethylene transverse jets in supersonic crossflows , 2006 .

[26]  Gregory C. Burton,et al.  The nonlinear large-eddy simulation method applied to Sc≈1 and Sc⪢1 passive-scalar mixing , 2008 .

[27]  Dale Pullin,et al.  Large-eddy simulation and multiscale modelling of a Richtmyer–Meshkov instability with reshock , 2006, Journal of Fluid Mechanics.

[28]  P. Dimotakis,et al.  Turbulent shear-layer mixing at high Reynolds numbers: effects of inflow conditions , 1998, Journal of Fluid Mechanics.

[29]  P. Dimotakis,et al.  Measurements of scalar power spectra in high Schmidt number turbulent jets , 1992, Journal of Fluid Mechanics.

[30]  James C. McDaniel,et al.  Quantitative investigation of compressible mixing - Staged transverse injection into Mach 2 flow , 1994 .

[31]  W.,et al.  Time Dependent Boundary Conditions for Hyperbolic Systems , 2003 .

[32]  S. Osher,et al.  A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method) , 1999 .

[33]  K. Thompson.  Time-dependent boundary conditions for hyperbolic systems, II , 1990 .

[34]  B. Geurts,et al.  Database-analysis of errors in Large-Eddy Simulation , 2003 .

[35]  Robert W. Bilger,et al.  A Note on Favre Averaging in Variable Density Flows , 1975 .

[36]  P. Moin,et al.  Large-eddy simulation of turbulent confined coannular jets , 1996, Journal of Fluid Mechanics.

[37]  S.N.B. Murthy,et al.  Turbulent Free Shear Layer Mixing and Combustion , 1991 .

[38]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[39]  P. Moin,et al.  A dynamic subgrid‐scale model for compressible turbulence and scalar transport , 1991 .

[40]  S. Ghosal.  Mathematical and Physical Constraints on Large-Eddy Simulation of Turbulence , 1999 .

[41]  Z. Warhaft.  Passive Scalars in Turbulent Flows , 2000 .

[42]  B. Kosović,et al.  Subgrid-scale modeling for large-eddy simulations of compressible turbulence , 2002 .

[43]  S. Ghosal.  An Analysis of Numerical Errors in Large-Eddy Simulations of Turbulence , 1996 .

[44]  T. Poinsot.  Boundary conditions for direct simulations of compressible viscous flows , 1992 .

[45]  A. Roshko,et al.  The compressible turbulent shear layer: an experimental study , 1988, Journal of Fluid Mechanics.

[46]  Chi-Wang Shu,et al.  Strong Stability-Preserving High-Order Time Discretization Methods , 2001, SIAM Rev..

[47]  P. Dimotakis.  Two-dimensional shear-layer entrainment , 1986 .

[48]  A. Roshko,et al.  On density effects and large structure in turbulent mixing layers , 1974, Journal of Fluid Mechanics.

[49]  Steven A. Orszag,et al.  Intermittent vortex structures in homogeneous isotropic turbulence , 1990, Nature.

[50]  Edward E. Zukoski,et al.  Secondary injection of gases into a supersonic flow , 1964 .

[51]  S. Pope.  Ten questions concerning the large-eddy simulation of turbulent flows , 2004 .

[52]  D. Pullin.  A vortex-based model for the subgrid flux of a passive scalar , 2000 .

[53]  Paul E. Dimotakis,et al.  Effects of heat release in a turbulent, reacting shear layer , 1989, Journal of Fluid Mechanics.

[54]  Feng Gao,et al.  A large‐eddy simulation scheme for turbulent reacting flows , 1993 .

[55]  T. Lundgren,et al.  Strained spiral vortex model for turbulent fine structure , 1982 .

[56]  Michel Riondet,et al.  The cavitation instability induced by the development of a re-entrant jet , 2001, Journal of Fluid Mechanics.

[57]  John Harrison Konrad,et al.  An Experimental Investigation of Mixing in Two-Dimensional Turbulent Shear Flows with Applications to Diffusion-Limited Chemical Reactions , 1977 .

[58]  C. Bretherton,et al.  Effects of Domain Size and Numerical Resolution on the Simulation of Shallow Cumulus Convection , 2002 .

[59]  D. I. Pullin,et al.  Reynolds stresses and one‐dimensional spectra for a vortex model of homogeneous anisotropic turbulence , 1994 .

[60]  Carlos Pantano,et al.  Verification of a fluid-dynamics solver using correlations with linear stability results , 2008, J. Comput. Phys..

[61]  W. Rodi,et al.  Experimental investigation of jets in a crossflow , 1982, Journal of Fluid Mechanics.

[62]  B. Strand.  Summation by parts for finite difference approximations for d/dx , 1994 .

[63]  J. Wyngaard,et al.  Resolution Requirements for the Simulation of Deep Moist Convection , 2003 .

[64]  Paul E. Dimotakis,et al.  Turbulent shear-layer mixing: growth-rate compressibility scaling , 2000, Journal of Fluid Mechanics.

[65]  A. Leonard.  Energy Cascade in Large-Eddy Simulations of Turbulent Fluid Flows , 1975 .

[66]  Paul E. Dimotakis,et al.  TURBULENT MIXING , 2004 .

[67]  M. Lesieur,et al.  New Trends in Large-Eddy Simulations of Turbulence , 1996 .

[68]  Parviz Moin,et al.  Higher entropy conservation and numerical stability of compressible turbulence simulations , 2004 .

[69]  M. Rai.  A conservative treatment of zonal boundaries for Euler equation calculations , 1984 .

[70]  Tobias Voelkl,et al.  A physical-space version of the stretched-vortex subgrid-stress model for large-eddy simulation of incompressible flow , 2000 .

[71]  B. D. Pratte,et al.  Profiles of the Round Turbulent Jet in A Cross Flow , 1967 .

[72]  Andrew W. Cook,et al.  The mixing transition in Rayleigh–Taylor instability , 2004, Journal of Fluid Mechanics.

[73]  P. Moin,et al.  A dynamic subgrid‐scale eddy viscosity model , 1990 .

[74]  P. Wesseling.  Principles of Computational Fluid Dynamics , 2000 .

[75]  M. Mungal,et al.  Quantitative scalar measurements in compressible mixing layers , 1996 .

[76]  J. Lumley,et al.  A First Course in Turbulence , 1972 .

[77]  Caskey,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS I . THE BASIC EXPERIMENT , 1962 .

[78]  J. O N A T H A,et al.  Compressibility effects in a turbulent annular mixing layer . Part 1 . Turbulence and growth rate , 2022 .

[79]  H. C. Hottel,et al.  The nozzle-fluid concentration field of the round, turbulent, free jet , 1967, Journal of Fluid Mechanics.

[80]  M. Mungal,et al.  Mixing, structure and scaling of the jet in crossflow , 1998, Journal of Fluid Mechanics.

[81]  David H. Rudy,et al.  Boundary conditions for subsonic compressible Navier-Stokes calculations , 1981 .

[82]  P. Dimotakis,et al.  Molecular Mixing and Flowfield Measurements in a Recirculating Shear Flow. Part I: Subsonic Flow , 2009 .

[83]  Michael B. Johnson.  Aerodynamic control and mixing with ramp injection , 2005 .

[84]  J. Riley,et al.  A subgrid model for equilibrium chemistry in turbulent flows , 1994 .

[85]  B. Stratford.  The prediction of separation of the turbulent boundary layer , 1959, Journal of Fluid Mechanics.

[86]  Roger E. A. Arndt,et al.  Advances in Turbulence , 1988, Lecture Notes in Mechanical Engineering.

[87]  Ugo Piomelli,et al.  Large-eddy simulation: achievements and challenges , 1999 .

[88]  P. Dimotakis,et al.  Some consequences of the boundedness of scalar fluctuations , 1990 .

[89]  R. Bilger.  Comment on "Structure of Turbulent Shear Flows: A New Look'' , 1977 .

[90]  Bernardus J. Geurts,et al.  COMPARISON OF NUMERICAL SCHEMES IN LARGE-EDDY SIMULATION OF THE TEMPORAL MIXING LAYER , 1996 .

[91]  Noel T. Clemens,et al.  Large-scale structure and entrainment in the supersonic mixing layer , 1995, Journal of Fluid Mechanics.

[92]  T. Lundgren,et al.  Axial motion and scalar transport in stretched spiral vortices , 2001 .

[93]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[94]  Gregory C. Burton.  Scalar-energy spectra in simulations of Sc⪢1 mixing by turbulent jets using the nonlinear large-eddy simulation method , 2008 .

[95]  T. A. Zang,et al.  On the rotation and skew-symmetric forms for incompressible flow simulations , 1991 .

[96]  Sutanu Sarkar,et al.  Large Eddy Simulation of Evolution of a Passive Scalar in Plane Jet , 2001 .

[97]  Manoochehr Koochesfahani,et al.  Mixing and chemical reactions in a turbulent liquid mixing layer , 1986, Journal of Fluid Mechanics.

[98]  Jeffery L. Hall.  An experimental investigation of structure, mixing and combustion in compressible turbulent shear layers , 1991 .

[99]  C. Bond.  Reynolds number effects on mixing in the turbulent shear layer , 1999 .

[100]  P. Moin,et al.  A dynamic model for subgrid-scale variance and dissipation rate of a conserved scalar , 1998 .

[101]  C. Meneveau,et al.  Scale-Invariance and Turbulence Models for Large-Eddy Simulation , 2000 .

[102]  Ralf Deiterding,et al.  Parallel adaptive simulation of multi-dimensional detonation structures , 2003 .