A realisable non-linear eddy viscosity/diffusivity model for confined swirling flows

A non-linear eddy viscosity/diffusivity model for turbulent flows is presented, featuring quadratic constitutive relationships for both Reynolds stresses and scalar fluxes. Model coefficients are defined by enforcing compliance with fundamental experimental evidence, and realizability of both the velocity and scalar fields, which is achieved by making coefficients depend upon an appropriately defined strain parameter. The model is also shown to satisfy joint-realizability. The model is extensively tested against experimental results for confined swirling flows, encompassing a wide range of values of the swirl number, momentum and density ratios. The results unambiguously indicate a remarkable, uniform improvement over standard modelling. Further, previous work on the subject of nonlinear models is reviewed.

[1]  E. Dick,et al.  A Quasi-Realizable Cubic Low-Reynolds Eddy-Viscosity Turbulence Model with a New Dissipation Rate Equation , 2001 .

[2]  Bengt Sundén,et al.  Calculation of turbulent fluid flow and heat transfer in ducts by a full Reynolds stress model , 2003 .

[3]  Dan S. Henningson,et al.  Turbulence and Transition Modelling , 1996 .

[4]  T. Schwartzkopff,et al.  A Numerical Investigation of the Heat Transfer in a Parallel Plate Channel With Piecewise Constant Wall Temperature Boundary Conditions , 2002 .

[5]  P. Libby,et al.  Measurements in the turbulent boundary layer with slot injection of helium , 1977 .

[6]  Joseph H. Morrison,et al.  Turbulence Model Predictions of Strongly Curved Flow in a U-Duct , 2000 .

[7]  S. Girimaji.  Lower-Dimensional Manifold (Algebraic) Representation of Reynolds Stress Closure Equations , 2001 .

[8]  W. L. Chen,et al.  Low-Reynolds-Number Eddy-Viscosity Modelling Based on Non-Linear Stress-Strain/Vorticity Relations , 1996 .

[9]  C. G. Speziale.  Comparison of Explicit and Traditional Algebraic Stress Models of Turbulence , 1997 .

[10]  Hyung Jin Sung,et al.  Development of a nonlinear near-wall turbulence model for turbulent flow and heat transfer , 2001 .

[11]  Hyung Jin Sung,et al.  A nonlinear low-Reynolds-number κ-ε model for turbulent separated and reattaching flows—I. Flow field computations , 1995 .

[12]  Rhj Sellin,et al.  Engineering Turbulence - Modelling and experiments 3 , 1996 .

[13]  Prediction of Strongly Curved Turbulent Duct Flows with Reynolds Stress Model , 1997 .

[14]  Strategies for turbulence modelling and simulations , 2000 .

[15]  Kazuhiko Suga,et al.  Predicting turbulence and heat transfer in 3-D curved ducts by near-wall second moment closures , 2003 .

[16]  W. Jones,et al.  The prediction of laminarization with a two-equation model of turbulence , 1972 .

[17]  János M. Beér,et al.  Combustion in swirling flows: A review , 1974 .

[18]  K. Rajagopal,et al.  On a generalized nonlinearK-ɛ model for turbulence that models relaxation effects , 1996 .

[19]  Arne V. Johansson,et al.  An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows , 2000, Journal of Fluid Mechanics.

[20]  B. Launder,et al.  The numerical computation of turbulent flows , 1990 .

[21]  W. K. Anderson,et al.  Isolating curvature effects in computing wall-bounded turbulent flows , 2001 .

[22]  F. Mashayek,et al.  TURBULENT GAS-SOLID FLOWS, PART II: EXPLICIT ALGEBRAIC MODELS , 2002 .

[23]  Ken-ichi Abe,et al.  Towards the development of a Reynolds-averaged algebraic turbulent scalar-flux model , 2001 .

[24]  Makoto Nagaoka,et al.  Application of a Higher Order GGDH Heat Flux Model to Three-Dimensional Turbulent U-Bend Duct Heat Transfer , 2003 .

[25]  P. Durbin,et al.  On Algebraic Second Moment Models , 2000 .

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

[27]  T. Shih,et al.  Constitutive Relations and Realizability of Single-Point Turbulence Closures , 1996 .

[28]  N. A. Chigier,et al.  Experimental Investigation of Swirling Vortex Motion in Jets , 1967 .

[29]  P. Saffman,et al.  A model for inhomogeneous turbulent flow , 1970, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[30]  Saad A. Ahmed,et al.  Behaviour of carbon dioxide jets in a confined swirling flow , 1987 .

[31]  S. Corrsin,et al.  Experiments on nearly homogeneous turbulent shear flow , 1970, Journal of Fluid Mechanics.

[32]  Thomas B. Gatski,et al.  Predicting Turbulent Convective Heat Transfer in Fully Developed Duct Flows , 2001 .

[33]  H. C. Mongia,et al.  An experimental investigation of gas jets in confined swirling air flow , 1984 .

[34]  Michael A. Leschziner,et al.  Computation of highly swirling confined flow with a Reynolds stress turbulence model , 1989 .

[35]  S. Fu,et al.  Development of Curvature Sensitive Nonlinear Eddy-Viscosity Model , 2002 .

[36]  Arne V. Johansson,et al.  Modelling streamline curvature effects in explicit algebraic Reynolds stress turbulence models , 2002 .

[37]  P. Spalart,et al.  On the sensitization of turbulence models to rotation and curvature , 1997 .

[38]  R. Bilger,et al.  Further velocity measurements in a turbulent diffusion flame with moderate swirl , 1989 .

[39]  T. B. Gatski,et al.  Nonlinear eddy viscosity and algebraic stress models for solving complex turbulent flows , 2000 .

[40]  H. Sung,et al.  Development of a near-wall turbulence model and application to jet impingement heat transfer , 2000 .

[41]  K. Hanjalic.  ACHIEVEMENTS AND LIMITATIONS IN MODELLlNG AND COMPUTATION OF BUOYANT TURBULENT FLOWS AND HEAT TRANSFER , 1994 .

[42]  S. Chakravarthy,et al.  Predictions of Axial and Transverse Injection into Supersonic Flow , 2001 .

[43]  W. Rodi.  A new algebraic relation for calculating the Reynolds stresses , 1976 .

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

[45]  Gilmar Mompean,et al.  On predicting abrupt contraction flows with differential and algebraic viscoelastic models , 2002 .

[46]  R. Thompson,et al.  A general transformation procedure for differential viscoelastic models , 2003 .

[47]  L. Zhou,et al.  Simulation of swirling gasparticle flows using a nonlinear k e k p two-phase turbulence model , 2002 .

[48]  David G. Lilley,et al.  Swirl Flows in Combustion: A Review , 1977 .

[49]  S. Girimaji.  Fully explicit and self-consistent algebraic Reynolds stress model , 1995 .

[50]  Minh Hieu Ha,et al.  The impact of turbulence modelling on the numerical predictions of flows , 1993 .

[51]  C. G. Speziale.  On nonlinear K-l and K-ε models of turbulence , 1987, Journal of Fluid Mechanics.

[52]  J. Lumley,et al.  A Realizable Reynolds Stress Algebraic Equation Model , 1993 .

[53]  Brian Launder,et al.  On the Computation of Convective Heat Transfer in Complex Turbulent Flows , 1988 .

[54]  Paul Batten,et al.  Modelling Shock/Boundary-Layer Interaction with Nonlinear Eddy-Viscosity Closures , 1998 .

[55]  Andreas Abdon, Bengt Sundén,et al.  NUMERICAL INVESTIGATION OF IMPINGEMENT HEAT TRANSFER USING LINEAR AND NONLINEAR TWO-EQUATION TURBULENCE MODELS , 2001 .

[56]  K. Hutter,et al.  On Euclidean invariance of algebraic Reynolds stress models in turbulence , 2003, Journal of Fluid Mechanics.

[57]  P. Vimala,et al.  Accounting for Buoyancy Effects in the Explicit Algebraic Stress Model: Homogeneous Turbulent Shear Flows , 2002 .

[58]  William W. Liou,et al.  Modeling of Turbulent Swirling Flows , 1997 .

[59]  R. Bilger,et al.  Joint measurements of velocity and scalars in a turbulent diffusion flame with moderate swirl , 1988 .

[60]  J. Lumley.  Stochastic tools in turbulence , 1970 .

[61]  H. Weinberger,et al.  Maximum principles in differential equations , 1967 .

[62]  J. Lumley,et al.  Remarks on turbulent constitutive relations , 1993 .

[63]  D. Taulbee,et al.  A Nonlinear Stress-Strain Model for Wall-Bounded Turbulent Flows , 1999 .

[64]  J. A. H. Graham,et al.  Further experiments in nearly homogeneous turbulent shear flow , 1977, Journal of Fluid Mechanics.

[65]  Wolfgang Rodi,et al.  The prediction of free turbulent boundary layers by use of a two-equation model of turbulence , 1973 .

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

[67]  Timo Siikonen,et al.  Modifications for an explicit algebraic stress model , 2001 .

[68]  Brian Launder,et al.  Second-moment closure: present… and future? , 1989 .

[69]  Michael A. Leschziner,et al.  An investigation of wall-anisotropy expressions and length-scale equations for non-linear eddy-viscosity models , 2003 .

[70]  T. Gatski,et al.  On explicit algebraic stress models for complex turbulent flows , 1992, Journal of Fluid Mechanics.

[71]  Farzad Mashayek,et al.  A FOUR-EQUATION MODEL FOR PREDICTION OF GAS-SOLID TURBULENT FLOWS , 2002 .

[72]  B. Launder,et al.  Development and application of a cubic eddy-viscosity model of turbulence , 1996 .

[73]  J. Lumley,et al.  A new Reynolds stress algebraic equation model , 1994 .