Advances in PDF modeling for inhomogeneous turbulent flows

Probability density function (PDF) models which are based on an exact representation of rapidly distorting homogeneous turbulence are applied to a free shear flow, the temporal mixing layer. These velocity wave-vector models were constructed in a previous paper by Van Slooten and Pope [Phys. Fluids 9, 1085 (1997)], but were only tested in cases of homogeneous turbulence. At the edges of free shear flows both turbulent–nonturbulent intermittency and pressure transport are demonstrated to play a significant role in the behavior of the flow. A natural treatment of intermittency is obtained by extending the PDF formulation to include a model for the turbulent frequency following a fluid particle. A model for the pressure transport is also constructed via a scaling analysis. The resulting velocity wave-vector turbulent-frequency PDF model with the pressure transport model yields a good comparison with the available direct numerical simulation data for the temporal shear layer.

[1]  T. Gatski,et al.  Modelling the pressure–strain correlation of turbulence: an invariant dynamical systems approach , 1991, Journal of Fluid Mechanics.

[2]  S. Pope,et al.  Modeling of extinction in turbulent diffusion flames by the velocity-dissipation-composition PDF method☆ , 1995 .

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

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

[5]  Thomas D. Dreeben,et al.  Wall-function treatment in pdf methods for turbulent flows , 1997 .

[6]  J. Bell,et al.  Development of a two-stream mixing layer from tripped and untripped boundary layers , 1990 .

[7]  Z. Warhaft,et al.  The shearless turbulence mixing layer , 1989, Journal of Fluid Mechanics.

[8]  Stavros Kassinos,et al.  A Structure-Based Model for the Rapid Distortion of Homogeneous Turbulence. , 1995 .

[9]  R. Moser,et al.  The three-dimensional evolution of a plane mixing layer: the Kelvin–Helmholtz rollup , 1992, Journal of Fluid Mechanics.

[10]  B. Launder,et al.  Mathematical Models of turbulence , 1972 .

[11]  Peter Bradshaw,et al.  The effect of initial conditions on the development of a free shear layer , 1966, Journal of Fluid Mechanics.

[12]  B. Launder,et al.  Numerical Prediction of Axisymmetric Free Shear Flows with a Reynolds Stress Closure , 1979 .

[13]  Stephen B. Pope,et al.  Application of PDF methods to compressible turbulent flows , 1997 .

[14]  S. Fu.  Modelling of the pressure-velocity correlation in turbulence diffusion , 1993 .

[15]  B. G. Jones,et al.  Statistical investigation of pressure and velocity fields in the turbulent two-stream mixing layer , 1971 .

[16]  A. M. Oboukhov.  Some specific features of atmospheric tubulence , 1962, Journal of Fluid Mechanics.

[17]  S. Pope.  PDF methods for turbulent reactive flows , 1985 .

[18]  M. Rogers,et al.  On modeling pressure diffusion in non-homogeneous shear flows , 1996 .

[19]  S. Pope,et al.  Lagrangian statistics from direct numerical simulations of isotropic turbulence , 1989, Journal of Fluid Mechanics.

[20]  M. Ohtsuka.  Numerical analysis of swirling non-reacting and reacting flows by the Reynolds stress differential method , 1995 .

[21]  P. Dimotakis.  Turbulent Free Shear Layer Mixing and Combustion , 1991 .

[22]  P. Durbin,et al.  Role of pressure diffusion in non-homogeneous shear flows , 1994 .

[23]  J. Lumley,et al.  The return to isotropy of homogeneous turbulence , 1977, Journal of Fluid Mechanics.

[24]  Steven A. Orszag,et al.  Direct numerical simulations of chemically reacting turbulent mixing layers , 1986 .

[25]  I. Wygnanski,et al.  The two-dimensional mixing region , 1970, Journal of Fluid Mechanics.

[26]  Charles G. Speziale,et al.  ANALYTICAL METHODS FOR THE DEVELOPMENT OF REYNOLDS-STRESS CLOSURES IN TURBULENCE , 1990 .

[27]  S. Pope.  Application of the velocity‐dissipation probability density function model to inhomogeneous turbulent flows , 1991 .

[28]  E. T. Curran,et al.  High-Speed Flight Propulsion Systems , 1991 .

[29]  A. Townsend.  The Structure of Turbulent Shear Flow , 1975 .

[30]  F. R. Menter,et al.  Influence of freestream values on k-omega turbulence model predictions , 1992 .

[31]  George L. Mellor,et al.  A survey of the mean turbulent field closure models. , 1973 .

[32]  A. Kolmogorov.  A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number , 1962, Journal of Fluid Mechanics.

[33]  J. Lumley.  Whither Turbulence? Turbulence at the Crossroads , 1990 .

[34]  Stephen B. Pope,et al.  PDF modeling for inhomogeneous turbulence with exact representation of rapid distortions , 1997 .

[35]  N. Sandham,et al.  Some Inlet-Plane Effects on the Numerically Simulated Spatially-Developing Mixing Layer , 1989 .

[36]  Y. Pao,et al.  On the two-dimensional mixing region , 1976, Journal of Fluid Mechanics.

[37]  S. Pope,et al.  PDF calculations for swirling flows , 1993 .

[38]  John L. Lumley,et al.  Computational Modeling of Turbulent Flows , 1978 .

[39]  Brian Launder,et al.  Phenomenological modelling : Present .... and future? , 1990 .

[40]  Franz Durst,et al.  Turbulent Shear Flows I , 1979 .

[41]  B. Mandelbrot.  Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier , 1974, Journal of Fluid Mechanics.

[42]  J. R. Ristorcelli,et al.  A rapid-pressure covariance representation consistent with the Taylor—Proudman theorem materially frame indifferent in the two-dimensional limit , 1995, Journal of Fluid Mechanics.

[43]  B. Launder,et al.  Progress in the development of a Reynolds-stress turbulence closure , 1975, Journal of Fluid Mechanics.

[44]  Brian Launder,et al.  A Reynolds stress model of turbulence and its application to thin shear flows , 1972, Journal of Fluid Mechanics.

[45]  J. Rotta,et al.  Statistische Theorie nichthomogener Turbulenz , 1951 .

[46]  A. Johansson,et al.  Modelling of rapid pressure—strain in Reynolds-stress closures , 1994, Journal of Fluid Mechanics.

[47]  Stephen B. Pope,et al.  The velocity‐dissipation probability density function model for turbulent flows , 1990 .

[48]  Robert D. Moser,et al.  Self-similarity of time-evolving plane wakes , 1998, Journal of Fluid Mechanics.

[49]  Franz Durst,et al.  Turbulent Shear Flows 6 , 1989 .

[50]  Francis H. Harlow,et al.  Transport Equations in Turbulence , 1970 .

[51]  Robert D. Moser,et al.  Direct Simulation of a Self-Similar Turbulent Mixing Layer , 1994 .

[52]  Stephen B. Pope,et al.  A generalized Langevin model for turbulent flows , 1986 .

[53]  D. Wilcox.  Turbulence modeling for CFD , 1993 .

[54]  Stephen B. Pope,et al.  Calculations of Swirl Combustors Using Joint Velocity-Scalar Probability Density Function Method , 1997 .

[55]  C. G. Speziale.  A REVIEW OF REYNOLDS STRESS MODELS FOR TURBULENT SHEAR FLOWS , 1995 .

[56]  R. Moser,et al.  The three-dimensional evolution of a plane mixing layer: pairing and transition to turbulence , 1993, Journal of Fluid Mechanics.

[57]  Stephen B. Pope,et al.  On the relationship between stochastic Lagrangian models of turbulence and second‐moment closures , 1994 .

[58]  S. Pope.  Lagrangian PDF Methods for Turbulent Flows , 1994 .

[59]  Stavros Kassinos,et al.  One-point modelling of rapidly deformed homogeneous turbulence , 1995, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[60]  W. C. Reynolds,et al.  Effects of rotation on homogeneous turbulence , 1989 .

[61]  Paul A. Durbin,et al.  Realizability of second-moment closure via stochastic analysis , 1994, Journal of Fluid Mechanics.

[62]  R. G. Batt,et al.  Turbulent mixing of passive and chemically reacting species in a low-speed shear layer , 1977, Journal of Fluid Mechanics.

[63]  W. P. Jones,et al.  Calculation of Confined Swirling Flows With a Second Moment Closure , 1989 .

[64]  T.W.J. Peeters,et al.  On the existence of a Generalized Langevin model representation for second‐moment closures , 1996 .