IMPLEMENTATION AND VALIDATION OF THE HYBRID TURBULENCE MODELS IN AN UNSTRUCTURED GRID CODE

OF THESIS IMPLEMENTATION AND VALIDATION OF THE HYBRID TURBULENCE MODELS IN AN UNSTRUCTURED GRID CODE Since its introduction in 1997, the use of Detached Eddy Simulation (DES) and similar hybrid turbulence techniques has become increasingly popular in the field of CFD. However, with increased use some of the limitations of the DES model have become apparent. One of these is the dependence of DES on grid construction, particularly regarding the point of transition between the Reynolds-Averaged NavierStokes and Large Eddy Simulation models. An additional issue that arises with unstructured grids is the definition of the grid spacing in the implementation of a DES length scale. To lay the ground work to study these effects the Spalart-Allmaras oneequation turbulence model, SA based DES hybrid turbulence model, and the Scale Adaptive Simulation hybrid turbulence model are implemented in an unstructured grid CFD code, UNCLE. The implemented SA based DES model is validated for flow over a three-dimensional circular cylinder for three different turbulent Reynolds numbers. Validation included studying the pressure, skin friction coefficient, centerline velocity distributions averaged in time and space. Tools to output the mean velocity profiles and Reynolds stresses were developed. A grid generation code was written to generate a two/three dimensional circular cylinder grid to simulate flow over the cylinder in UNCLE. The models implemented and validated, and the additional tools mentioned will be used in the future.

[1]  A. Tsinober An informal introduction to turbulence , 2001 .

[2]  G. S. Patterson,et al.  Numerical Simulation of Three-Dimensional Homogeneous Isotropic Turbulence , 1972 .

[3]  F. Menter Two-equation eddy-viscosity turbulence models for engineering applications , 1994 .

[4]  K. Lilly On the application of the eddy viscosity concept in the Inertial sub-range of turbulence , 1966 .

[5]  Walter Tollmien,et al.  Über ein neues Formelsystem für die ausgebildete Turbulenz , 1961 .

[6]  E. Achenbach,et al.  Distribution of local pressure and skin friction around a circular cylinder in cross-flow up to Re = 5 × 106 , 1968, Journal of Fluid Mechanics.

[7]  B. Launder,et al.  Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc , 1974 .

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

[9]  Eduard Naudascher,et al.  Flow-Induced Structural Vibrations , 1974 .

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

[11]  Philippe R. Spalart,et al.  Detached-Eddy Simulations Past a Circular Cylinder , 2000 .

[12]  R. Kraichnan Eddy Viscosity in Two and Three Dimensions , 1976 .

[13]  P. Libby,et al.  Analysis of Turbulent Boundary Layers , 1974 .

[14]  C. Norberg An experimental investigation of the flow around a circular cylinder: influence of aspect ratio , 1994, Journal of Fluid Mechanics.

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

[16]  O. Reynolds III. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels , 1883, Proceedings of the Royal Society of London.

[17]  U. Piomelli High Reynolds number calculations using the dynamic subgrid‐scale stress model , 1993 .

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

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

[20]  Urmila Ghia,et al.  Higher-Order Accurate Solution for Flow Past a Circular Cylinder at Re = 13,400 , 2005 .

[21]  Saurabh Gupta,et al.  PERFORMANCE EVALUATION AND OPTIMIZATION OF THE UNSTRUCTURED CFD CODE UNCLE , 2006 .

[22]  R. M. Traci,et al.  A complete model of turbulence , 1976 .

[23]  Leslie M. Smith,et al.  Renormalization group analysis of turbulence , 2003 .

[24]  L. Prandtl 7. Bericht über Untersuchungen zur ausgebildeten Turbulenz , 1925 .

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

[26]  T. Kármán,et al.  Mechanische Ahnlichkeit und Turbulenz , 1930 .

[27]  J. Anderson,et al.  Computational fluid dynamics : the basics with applications , 1995 .

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

[29]  K. Lilly The representation of small-scale turbulence in numerical simulation experiments , 1966 .

[30]  F. Menter,et al.  Adaptation of Eddy-Viscosity Turbulence Models to Unsteady Separated Flow Behind Vehicles , 2004 .

[31]  V. M. Tikhomirov,et al.  Equations of Turbulent Motion in an Incompressible Fluid , 1991 .

[32]  J. Deardorff Three-dimensional numerical study of the height and mean structure of a heated planetary boundary layer , 1974 .

[33]  A. Roshko Experiments on the flow past a circular cylinder at very high Reynolds number , 1961, Journal of Fluid Mechanics.

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

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

[36]  Ugo Piomelli,et al.  On the large‐eddy simulation of transitional wall‐bounded flows , 1990 .

[37]  P. Spalart A One-Equation Turbulence Model for Aerodynamic Flows , 1992 .

[38]  George Karypis,et al.  A Software Package for Partitioning Unstructured Graphs , Partitioning Meshes , and Computing Fill-Reducing Orderings of Sparse Matrices Version 5 . 0 , 1998 .

[39]  D. C. Wilcox,et al.  Turbulence-Model Predictions for Turbulent Boundary Layers , 1974 .

[40]  梶島 岳夫 乱流の数値シミュレーション = Numerical simulation of turbulent flows , 2003 .

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

[42]  J. W. G. van Nunen Pressures and Forces on a Circular Cylinder in a Cross Flow at High Reynolds Numbers , 1974 .

[43]  J. Deardorff A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers , 1970, Journal of Fluid Mechanics.

[44]  R. Rogallo Numerical experiments in homogeneous turbulence , 1981 .

[45]  A. S. Monin,et al.  Statistical Fluid Mechanics: The Mechanics of Turbulence , 1998 .

[46]  P. Moin,et al.  Numerical studies of flow over a circular cylinder at ReD=3900 , 2000 .

[47]  I. G. Currie Fundamental mechanics of fluids , 1974 .

[48]  P. Moin,et al.  Model consistency in large eddy simulation of turbulent channel flows , 1988 .

[49]  J. Chasnov Simulation of the Kolmogorov inertial subrange using an improved subgrid model , 1991 .

[50]  G. Chapman,et al.  Observations, Theoretical Ideas, and Modeling of Turbulent Flows—Past, Present, and Future , 1985 .

[51]  T. Barth,et al.  A one-equation turbulence transport model for high Reynolds number wall-bounded flows , 1990 .

[52]  P. Spalart Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach , 1997 .

[54]  Florian R. Menter,et al.  A Scale-Adaptive Simulation Model for Turbulent Flow Predictions , 2003 .

[55]  P. Moin,et al.  Numerical Simulation of Turbulent Flows , 1984 .

[56]  P. Spalart Direct simulation of a turbulent boundary layer up to Rθ = 1410 , 1988, Journal of Fluid Mechanics.

[57]  D. Wilcox Reassessment of the scale-determining equation for advanced turbulence models , 1988 .

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

[59]  P. Moin,et al.  DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research , 1998 .

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

[61]  D. C. Wilcox,et al.  Progress in Turbulence Modeling for Complex Flow F4eMs including Effects of Compressibility , 2022 .

[62]  U. Schumann Subgrid Scale Model for Finite Difference Simulations of Turbulent Flows in Plane Channels and Annuli , 1975 .

[63]  F. Menter Eddy Viscosity Transport Equations and Their Relation to the k-ε Model , 1997 .

[64]  E. Saiki,et al.  A subgrid-scale model based on the estimation of unresolved scales of turbulence , 1997 .

[65]  C. Leith,et al.  Developments in the theory of turbulence , 1973 .

[66]  Yang Moon Koh,et al.  Turbulent Flow near a Wall , 1991 .

[67]  Lewis F. Richardson,et al.  Weather Prediction by Numerical Process , 1922 .

[68]  P. Spalart,et al.  Physical and Numerical Upgrades in the Detached-Eddy Simulation of Complex Turbulent Flows , 2002 .

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

[70]  L. Lourenço,et al.  Characteristics of the Plane Turbulent Near Wake of a Circular Cylinder , 1993 .

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

[72]  A. Yakhot,et al.  Renormalization group formulation of large-eddy simulations , 1989 .

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

[74]  B. Cantwell,et al.  An experimental study of entrainment and transport in the turbulent near wake of a circular cylinder , 1983, Journal of Fluid Mechanics.

[75]  Raymond P. LeBeau,et al.  A Cell-Centered Pressure Based Method for Two/Three- Dimensional Unstructured Incompressible Navier-Stokes Solver , 2005 .

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

[77]  P. Moin,et al.  Numerical investigation of turbulent channel flow , 1981, Journal of Fluid Mechanics.

[78]  U. C. Goldberg,et al.  Derivation and testing of a one-equation model based on two time scales , 1991 .

[79]  P. Spalart,et al.  A New Version of Detached-eddy Simulation, Resistant to Ambiguous Grid Densities , 2006 .

[80]  W. Tollmien,et al.  Bericht über Untersuchungen zur ausgebildeten Turbulenz , 1961 .