Turbulence modeling for complex shear flows

The turbulence models available for the prediction of complex turbulent shear layers are reviewed in this paper, concentrating mainly on three-dimensional flows, flows subjected to curvature and body rotation, separated flows, and vortex flows. A critical review of zero-equation, one-equation, two-equation, algebraic Reynolds stress, and full Reynolds stress models are carried out, with a specific emphasis on their applicability to complex flows. It is concluded that algebraic eddy viscosity models and kappa-epsilon/kappa-omega models, with a constant value of coefficients, are not adequate for complex flows. The models which include a description of stresses, either through an algebraic Reynolds stress model or a full Reynolds stress model, are essential for adequate prediction of these flows. It is recommended that systematic experimental investigations be carried out to isolate various complex interactions in order to understand and model the various effects and to carry out an extension of the present models to include complex flows.

[1]  T. Lin,et al.  Turbulence Models for High-Speed, Rough-Wall Boundary Layers , 1982 .

[2]  J. Weinstock,et al.  Theory of pressure-strain-rate correlation for Reynolds-stress turbulence closures. Part 1. Off-diagonal element , 1981, Journal of Fluid Mechanics.

[3]  D. C. Wilcox,et al.  Streamline curvature effects on turbulent boundary layers , 1976 .

[4]  H. Lomax,et al.  Thin-layer approximation and algebraic model for separated turbulent flows , 1978 .

[5]  C. Rhie,et al.  Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation , 1983 .

[6]  Wolfgang Rodi,et al.  Calculation of Turbulent Wall Jets With an Algebraic Reynolds Stress Model , 1980 .

[7]  I. Watanabe,et al.  Stabilizing and Destabilizing Effects of Coriolis Force on Two-Dimensional Laminar and Turbulent Boundary Layers , 1979 .

[8]  B. Lakshminarayana,et al.  A space-marching method for viscous incompressible internal flows , 1986 .

[9]  T. J. Coakley,et al.  Effects of turbulence model selection on the prediction of complex aerodynamic flows , 1979 .

[10]  P. A. Smith,et al.  Prediction of the effect of streamline curvature on turbulence , 1975 .

[11]  Toshi Kubota,et al.  An experiment on the adiabatic compressible turbulent boundary layer in adverse and favourable pressure gradients , 1972, Journal of Fluid Mechanics.

[12]  B. Launder,et al.  PREDICTION OF FLOW AND HEAT TRANSFER IN DUCTS OF SQUARE CROSS-SECTION , 1973 .

[13]  W. Rod,et al.  Examples of Turbulence Models for Incompressible Flows , 1982 .

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

[15]  Jean-Pierre Bertoglio,et al.  Homogeneous Turbulent Field within a Rotating Frame , 1980 .

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

[17]  F. Durst,et al.  Theoretical and Experimental Investigations of Turbulent Flows with Separation , 1979 .

[18]  Klaus Bremhorst,et al.  A Modified Form of the k-ε Model for Predicting Wall Turbulence , 1981 .

[19]  P. Saffman MODEL EQUATIONS FOR TURBULENT SHEAR FLOW , 1974 .

[20]  D. A. Johnson,et al.  A new turbulence closure model for boundary layer flows with strong adverse pressure gradients and separation , 1984 .

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

[22]  H.-P. Kreplin,et al.  Influence of Freestream Turbulence on Boundary-Layer Development , 1980 .

[23]  W. Reynolds Computation of Turbulent Flows , 1975 .

[24]  C. C. Horstman,et al.  Investigation of a Three-Dimensional Shock Wave Separated Turbulent Boundary Layer , 1980 .

[25]  J. Douglas Faires,et al.  Numerical Analysis , 1981 .

[26]  P. Bernard,et al.  Limitations of the near-wall k-epsilon turbulence model , 1986 .

[27]  Otto Zeman,et al.  Modeling Buoyancy Driven Mixed Layers , 1976 .

[28]  C. Hah,et al.  Prediction of Two- and Three-Dimensional Asymmetrical Turbulent Wakes, Including Curvature and Rotation Effects , 1980 .

[29]  F. Lockwood,et al.  The Prediction of Axisymmetric Turbulent Swirling Boundary Layers , 1974 .

[30]  B. E. Launder,et al.  A generalized algebraic stress transport hypothesis , 1982 .

[31]  Wolfgang Rodi,et al.  Computation of strongly swirling axisymmetric free jets , 1984 .

[32]  B. Lakshminarayana,et al.  Turbulence Characteristics in the Near Wake of a Compressor Rotor Blade , 1979 .

[33]  James P. Johnston,et al.  Effects of spanwise rotation on the structure of two-dimensional fully developed turbulent channel flow , 1972, Journal of Fluid Mechanics.

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

[35]  R. So A turbulence velocity scale for curved shear flows , 1975, Journal of Fluid Mechanics.

[36]  B. E. Launder,et al.  Stress Transport Closures — Into the Third Generation , 1979 .

[37]  Brian Launder,et al.  Fully developed asymmetric flow in a plane channel , 1972, Journal of Fluid Mechanics.

[38]  C. Hah Turbulence Closure and Prediction of the Wake in a Rotating Wall Shear Layer , 1982 .

[39]  C. Hah,et al.  Numerical Analysis of Turbulent Wakes of Turbomachinery Rotor Blades , 1980 .

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

[41]  D. A. Johnson,et al.  A Comprehensive Comparison Between Experiment and Prediction for a Transonic Turbulent Separated Flow , 1980 .

[42]  A. Townsend THE UNIFORM DISTORTION OF HOMOGENEOUS TURBULENCE , 1954 .

[43]  Wolfgang Rodi,et al.  Prediction of Horizontal and Vertical Turbulent Buoyant Wall Jets , 1981 .

[44]  George L. Mellor,et al.  Turbulent boundary layers with large streamline curvature effects , 1978 .

[45]  J. Gillis,et al.  Experimental data and model for the turbulent boundary layer on a convex, curved surface , 1981 .

[46]  B. R. Ramaprian,et al.  The structure of turbulent boundary layers along mildly curved surfaces , 1978, Journal of Fluid Mechanics.

[47]  B. Lakshminarayana,et al.  An Experimental Study of Three-Dimensional Turbulent Boundary Layer and Turbulence Characteristics Inside a Turbomachinery Rotor Passage , 1978 .

[48]  Charles G. Speziale,et al.  Second-order closure models for rotating turbulent flows , 1987 .

[49]  Stephen B. Pope,et al.  The calculation of near-wake flows , 1976, Journal of Fluid Mechanics.

[50]  B. I. Sharma Computation of flow past a rotating cylinder with an energy-dissipation model of turbulence , 1977 .

[51]  Hans Edelmann,et al.  Vier Woodbury-Formeln hergeleitet aus dem Variablentausch einer speziellen Matrix , 1976 .

[52]  M. M. Gibson An algebraic stress and heat-flux model for turbulent shear flow with streamline curvature , 1978 .

[53]  S. Eskinazi AN INVESTIGATION OF FULLY DEVELOPED TURBULENT FLOW IN A CURVED CHANNEL , 1954 .

[54]  A. Baker,et al.  An interaction algorithm for three-dimensional turbulent subsonic aerodynamic juncture region flow , 1983 .

[55]  I. Castro Time-domain measurements in separated flows , 1985, Journal of Fluid Mechanics.

[56]  P. Chou On velocity correlations and the solutions of the equations of turbulent fluctuation , 1945 .

[57]  K. Kirtley,et al.  Computation of internal incompressible separated flows using a space-marching technique , 1985 .

[58]  Brian Launder,et al.  Contribution towards a Reynolds-stress closure for low-Reynolds-number turbulence , 1976, Journal of Fluid Mechanics.

[59]  M. Visbal,et al.  The Baldwin-Lomax Turbulence Model for Two-Dimensional Shock-Wave/Boundary-Layer Interactions , 1984 .

[60]  D. Naot,et al.  Two‐point correlation model and the redistribution of Reynolds stresses , 1973 .

[61]  Coleman duP. Donaldson,et al.  Decay of an Isolated Vortex , 1971 .

[62]  B. Lakshminarayana,et al.  Structure and decay characteristics of turbulence in the near- and far-wake of a moderately loaded compressor rotor-blade , 1981 .

[63]  D. M. Bushnell,et al.  Numerical computations of turbulence amplification in shock wave interactions , 1984 .

[64]  C. Hah,et al.  The prediction of two- and three-dimensional asymmetrical turbulent wakes - A comparision of the performance of three turbulence models for the effects of streamline curvature and rotation , 1979 .

[65]  Robert P. Lohmann,et al.  The Response of a Developed Turbulent Boundary Layer to Local Transverse Surface Motion , 1976 .

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

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

[68]  P. Bradshaw Calculation of boundary-layer development using the turbulent energy equation , 1967, Journal of Fluid Mechanics.

[69]  Contribution to the Reynolds stress model as applied to near-wall region , 1984 .

[70]  R. Raj Pressure gradient‐velocity correlations for flows with two‐and three‐dimensional turbulence , 1977 .

[71]  S. Biringen Calculation of axisymmetric jets and wakes with a three-equation model of turbulence , 1978, Journal of Fluid Mechanics.

[72]  Joseph G. Marvin,et al.  Turbulence modeling for computational aerodynamics , 1982 .

[73]  B. Ramaprian,et al.  Turbulence Measurements in Boundary Layers Along Mildly Curved Surfaces , 1978 .

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

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

[76]  E. Eichelbrenner,et al.  Three-Dimensional Boundary Layers , 1973 .

[77]  C. Donaldson,et al.  A theoretical study of the generation of atmospheric clear air turbulence , 1970 .

[78]  Wolfgang Rodi,et al.  Calculation of Annular and Twin Parallel Jets Using Various Discretization Schemes and Turbulence-Model Variations , 1981 .

[79]  A. Gosman,et al.  The Calculation of Two-Dimensional Turbulent Recirculating Flows , 1979 .

[80]  M. Wolfshtein,et al.  Theoretical Study of the Reynolds Stress Equations , 1979 .

[81]  S. V. Patankar,et al.  Flow Prediction in Rotating Ducts Using Coriolis-Modified Turbulence Models , 1980 .

[82]  W. Rodi Turbulence models for environmental problems , 1979 .

[83]  B. Lakshminarayana,et al.  Computation of three-dimensional viscous flows using a space-marching method , 1984 .

[84]  P. Morris Modeling the pressure redistribution terms , 1984 .

[85]  D. Wilcox Multiscale model for turbulent flows , 1986 .

[86]  J. Lumley Pressure‐strain correlation , 1975 .

[87]  B. S. Rao,et al.  Structure and Mean Flow Similarity in Curved Turbulent Boundary Layers , 1983 .

[88]  A. Sugavanam Evaluation of low Reynolds number turbulence models for attached and separated flows , 1985 .

[89]  C. H. Priddin,et al.  The calculation of turbulent boundary layers on spinning and curved surfaces , 1977 .

[90]  K. Chien,et al.  Predictions of Channel and Boundary-Layer Flows with a Low-Reynolds-Number Turbulence Model , 1982 .

[91]  H. Thomann,et al.  Effect of streamwise wall curvature on heat transfer in a turbulent boundary layer , 1968, Journal of Fluid Mechanics.

[92]  E. Behrens Reply by Author , 1968 .

[93]  Tuncer Cebeci,et al.  A general method for calculating three-dimensional compressible laminar and turbulent boundary layers on arbitrary wings , 1977 .

[94]  J. P. Johnston,et al.  THE INFLUENCE OF ROTATION ON FLOW IN A LONG RECTANGULAR CHANNEL: AN EXPERIMENTAL STUDY, , 1967 .

[95]  John L. Lumley,et al.  Toward a turbulent constitutive relation , 1970, Journal of Fluid Mechanics.

[96]  Farzad Pourahmadi,et al.  Prediction of curved channel flow with an extended k-epsilon model of turbulence , 1983 .

[97]  Numerical solution of the Reynolds stress equations in a developing duct flow , 1983 .

[98]  P. Bradshaw,et al.  The turbulence structure of a highly curved mixing layer , 1976, Journal of Fluid Mechanics.

[99]  P. Wesseling,et al.  Measurements in an incompressible three-dimensional turbulent boundary layer, under infinite swept-wing conditions, and comparison with theory , 1974, Journal of Fluid Mechanics.

[100]  B. Lakshminarayana,et al.  Turbulence modeling for three-dimensional shear flows over curved rotating bodies , 1984 .

[101]  B. Lakshminarayana,et al.  Computation of turbulent rotating channel flow with an algebraic Reynolds stress model , 1986 .

[102]  G. Mellor,et al.  Experiment on convex curvature effects in turbulent boundary layers , 1973, Journal of Fluid Mechanics.

[103]  C. Hah,et al.  Measurement and prediction of mean velocity and turbulence structure in the near wake of an airfoil , 1982, Journal of Fluid Mechanics.

[104]  Wolfgang Rodi,et al.  A Reynolds-stress closure model of turbulence applied to the calculation of a highly curved mixing layer , 1981, Journal of Fluid Mechanics.

[105]  Robert N. Meroney,et al.  An algebraic stress model for stratified turbulent shear flows , 1976 .

[106]  D. A. Johnson,et al.  Prediction of Transonic Separated Flows , 1984 .

[107]  B. Lakshminarayana,et al.  On the Investigation of Cascade and Turbomachinery Rotor Wake Characteristics. , 1975 .

[108]  K. Hanjalic,et al.  Turbulent Transport Modelling of Separating and Reattaching Shear Flows , 1982 .

[109]  A. F. Emery,et al.  A Reynolds Stress Model for Turbulent Corner Flows—Part I: Development of the Model , 1976 .

[110]  P. Bradshaw,et al.  The analogy between streamline curvature and buoyancy in turbulent shear flow , 1969, Journal of Fluid Mechanics.

[111]  D. A. Johnson,et al.  Comparison Between Experiment and Prediction for a Transonic Turbulent Separated Flow , 1982 .

[112]  John L. Lumley,et al.  Computational Modeling of Turbulent Transport , 1975 .

[113]  C. Horstman Prediction of separated asymmetric trailing-edge flows at transonic Mach numbers , 1983 .

[114]  J. C. Rotta,et al.  A Family of Turbulence Models for Three-Dimensional Boundary Layers , 1979 .

[115]  H. Fernholz,et al.  Measurements in an axisymmetric turbulent boundary layer with weak and strong three-dimensional disturbances , 1978 .

[116]  J. P. Johnston The Effects of Rotation on Boundary Layers in Turbomachine Rotors , 1974 .

[117]  P. Bradshaw Effects of Streamline Curvature on Turbulent Flow. , 1973 .

[118]  W. Rodi,et al.  Calculation of curved shear layers with two‐equation turbulence models , 1983 .