Investigation of transition to turbulence at low Reynolds numbers using Implicit Large Eddy Simulations with a Discontinuous Galerkin method

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, February 2011.

[1]  David L. Darmofal,et al.  Impact of Turbulence Model Irregularity on High-Order Discretizations , 2009 .

[2]  Miguel R. Visbal,et al.  High-fidelity simulations of moving and flexible airfoils at low Reynolds numbers , 2009 .

[3]  R. Mayle,et al.  Heat Transfer Committee and Turbomachinery Committee Best Paper of 1996 Award: The Path to Predicting Bypass Transition , 1997 .

[4]  Baron Kelvin William Thomson,et al.  Baltimore Lectures On Molecular Dynamics And The Wave Theory Of Light , 1901 .

[5]  Per-Olof Persson,et al.  RANS Solutions Using High Order Discontinuous Galerkin Methods , 2007 .

[6]  Richard E Kaplan,et al.  The stability of laminar incompressible boundary layers in the presence of compliant boundaries , 1964 .

[7]  M. Selig.  Summary of low speed airfoil data , 1995 .

[8]  Rolf Radespiel,et al.  Implementation and Extension of a Near-Wall Reynolds-Stress Model for Application to Aerodynamic Flows on Unstructured Meshes , 2008 .

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

[10]  F. Grinstein,et al.  Monotonically integrated large eddy simulation of free shear flows , 1999 .

[11]  D. K. Walters,et al.  A New Model for Boundary Layer Transition Using a Single-Point RANS Approach , 2004 .

[12]  Miguel R. Visbal,et al.  High-Fidelity Simulation of Transitional Flows Past a Plunging Airfoil , 2009 .

[13]  E. F. Kurtz,et al.  Computer‐Aided Analysis of Hydrodynamic Stability , 1962 .

[14]  D. Wilcox.  Simulation of Transition with a Two-Equation Turbulence Model , 1994 .

[15]  Tuncer Cebeci,et al.  Stability and Transition: Theory and Application , 2004 .

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

[17]  T. Tatsumi.  Theory of Homogeneous Turbulence , 1980 .

[18]  S. Scott Collis,et al.  The DG/VMS Method for Unified Turbulence Simulation , 2002 .

[19]  Nikolaus A. Adams,et al.  Direct modelling of subgrid scales of turbulence in large eddy simulations , 2002 .

[20]  Per-Olof Persson,et al.  Implicit Large Eddy Simulation of transition to turbulence at low Reynolds numbers using a Discontinuous Galerkin method , 2011 .

[21]  J. V. Ingen.  A suggested semi-empirical method for the calculation of the boundary layer transition region , 1956 .

[22]  Wei Shyy,et al.  Local and Global Stability Analysis on Flows around a SD7003 Airfoil , 2009 .

[23]  A. Srokowski,et al.  Mass flow requirements for LFC wing design , 1977 .

[24]  F. Grinstein,et al.  Large Eddy simulation of high-Reynolds-number free and wall-bounded flows , 2002 .

[25]  Chi-Wang Shu,et al.  The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems , 1998 .

[26]  Ewald Krämer,et al.  A parallel, high-order discontinuous Galerkin code for laminar and turbulent flows , 2008 .

[27]  J. Ferziger,et al.  Improved subgrid-scale models for large-eddy simulation , 1980 .

[28]  Daniel J. Garmann,et al.  High-Fidelity Simulations of Transitional Flow Over Pitching Airfoils , 2009 .

[29]  A. R. Wazzan,et al.  The Stability of Water Flow Over Heated and Cooled Flat Plates , 1968 .

[30]  Wei Shyy,et al.  Aerodynamics of Low Reynolds Number Flyers: Plate Section , 2007 .

[31]  C. W. Hirt.  Computer Studies of Time‐Dependent Turbulent Flows , 1969 .

[32]  W. Tollmien,et al.  Über die Entstehung der Turbulenz , 1930 .

[33]  A. Kolmogorov.  Dissipation of energy in the locally isotropic turbulence , 1941, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[34]  A. Gosman,et al.  A comparative study of subgrid scale models in homogeneous isotropic turbulence , 1997 .

[35]  R. Jordinson,et al.  The flat plate boundary layer. Part 1. Numerical integration of the Orr–-Sommerfeld equation , 1970, Journal of Fluid Mechanics.

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

[37]  Rolf Radespiel,et al.  Numerical Aspects of Transition Prediction for Three- Dimensional Configurations , 2005 .

[38]  Hassan Hassan,et al.  A Transition Closure Model for Predicting Transition Onset , 1998 .

[39]  Ridha Abid,et al.  Evaluation of two-equation turbulence models for predicting transitional flows , 1993 .

[40]  W. Saric,et al.  STABILITY AND TRANSITION OF THREE-DIMENSIONAL BOUNDARY LAYERS , 2003 .

[41]  Feng Liu,et al.  Turbulent transition simulation using thek-ω model , 1998 .

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

[43]  Jay P. Boris,et al.  On large eddy simulation using subgrid turbulence models Comment 1 , 1990 .

[44]  Edward N. Tinoco,et al.  Data Summary from Second AIAA Computational Fluid Dynamics Drag Prediction Workshop , 2003 .

[45]  R. Mayle,et al.  The Path to Predicting Bypass Transition , 1996 .

[46]  Guy Chavent,et al.  The local projection P 0 − P 1 -discontinuous-Galerkin finite element method for scalar conservation laws , 2009 .

[47]  Victor Lee,et al.  New Trends in Large-Eddy Simulations of Turbulence , 2011 .

[48]  M. Giles,et al.  Viscous-inviscid analysis of transonic and low Reynolds number airfoils , 1986 .

[49]  A. Bressan.  Hyperbolic Systems of Conservation Laws , 1999 .

[50]  R. Liebeck,et al.  A Comparison Between Boundary Layer Measurements in a Laminar Separation Bubble Flow and Linear Stability Theory Calculations , 1989 .

[51]  L. Margolin,et al.  From Numerical Analysis to Implicit Subgrid Turbulence Modeling (Invited) , 2003 .

[52]  S. Rebay,et al.  A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier-Stokes Equations , 1997 .

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

[54]  Wei Shyy,et al.  Laminar-Turbulent Transition of a Low Reynolds Number Rigid or Flexible Airfoil , 2006 .

[55]  R. Jordinson.  Spectrum of Eigenvalues of the Orr Sommerfeld Equation for Blasius Flow , 1971 .

[56]  E. Dick,et al.  Modelling of bypass transition with conditioned Navier-Stokes equations coupled to an intermittency transport equation , 1996 .

[57]  D. Arnal,et al.  Linear Stability Theory Applied to Boundary Layers , 1996 .

[58]  Neil D. Sandham,et al.  Direct numerical simulation of ‘short’ laminar separation bubbles with turbulent reattachment , 2000, Journal of Fluid Mechanics.

[59]  H. Schlichting.  Zur Enstehung der Turbulenz bei der Plattenströmung , 1933 .

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

[61]  Michael Ol,et al.  Comparison of Laminar Separation Bubble Measurements on a Low Reynolds Number Airfoil in Three Facilities , 2005 .

[62]  S. Zalesak.  Introduction to “Flux-Corrected Transport. I. SHASTA, A Fluid Transport Algorithm That Works” , 1997 .

[63]  Andreas Krumbein,et al.  Automatic Transition Prediction and Application to 3D Wing Configurations – Current Status of Development and Validation , 2005 .

[64]  Jay P. Boris,et al.  Implicit Large Eddy Simulation: More for LES: A Brief Historical Perspective of MILES , 2007 .

[65]  P. Roe.  Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[66]  Dirk Nürnberger,et al.  Numerical Investigation of Unsteady Transitional Flows in Turbomachinery Components Based on a RANS Approach , 2002 .

[67]  Per-Olof Persson,et al.  Scalable parallel Newton-Krylov solvers for discontinuous Galerkin discretizations , 2009 .

[68]  Ulrich Rist,et al.  Investigations on controlled transition development in a laminar separation bubble by means of LDA and PIV , 2004 .

[69]  B. J. Abu-Ghannam,et al.  Natural Transition of Boundary Layers—The Effects of Turbulence, Pressure Gradient, and Flow History , 1980 .

[70]  Roddam Narasimha,et al.  Some properties of boundary layer flow during the transition from laminar to turbulent motion , 1958, Journal of Fluid Mechanics.

[71]  Miguel R. Visbal,et al.  Implicit Large Eddy Simulation of Low Reynolds Number Flow Past the SD7003 Airfoil , 2008 .

[72]  P. Spalart.  Strategies for turbulence modelling and simulations , 2000 .

[73]  L. Rayleigh.  On the Stability, or Instability, of certain Fluid Motions , 1879 .

[74]  Lei Tang.  RANS Simulation of Low-Reynolds-Number Airfoil Aerodynamics , 2006 .

[75]  N. Krimmelbein,et al.  Transition prediction for three-dimensional flows using parallel computation , 2009 .

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

[77]  William J. Rider,et al.  Implicit Large Eddy Simulation: Numerical Regularization: The Numerical Analysis of Implicit Subgrid Models , 2007 .

[78]  Per-Olof Persson,et al.  The Compact Discontinuous Galerkin (CDG) Method for Elliptic Problems , 2007, SIAM J. Sci. Comput..

[79]  Ewald Krämer,et al.  A Parallel Discontinuous Galerkin Code for the Navier-Stokes Equations , 2006 .

[80]  Per-Olof Persson,et al.  Newton-GMRES Preconditioning for Discontinuous Galerkin Discretizations of the Navier--Stokes Equations , 2008, SIAM J. Sci. Comput..

[81]  Raytcho D. Lazarov,et al.  Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems , 2009, SIAM J. Numer. Anal..

[82]  A. Kolmogorov,et al.  The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[83]  Edward N. Tinoco,et al.  Abridged Summary of the Third AIAA Computational Fluid Dynamics Drag Prediction Workshop , 2008 .

[84]  J. Spurk.  Boundary Layer Theory , 2019, Fluid Mechanics.

[85]  Bo Dong,et al.  A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems , 2008, Math. Comput..

[86]  焦予秦,et al.  Detached—Eddy Simulation方法模拟不同类型翼型的失速特性 , 2005 .

[87]  Rolf Radespiel,et al.  Transition Prediction for 3D Flows Using a Reynolds-Averaged Navier-Stokes Code and N-Factor Methods , 2003 .

[88]  N. Gregory,et al.  On the stability of three-dimensional boundary layers with application to the flow due to a rotating disk , 1955, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[89]  P. Yeung,et al.  On the Universality of the Kolmogorov Constant in Numerical Simulations of Turbulence , 1997 .

[90]  Tuncer Cebeci,et al.  Essential ingredients of a method for low Reynolds-number airfoils , 1989 .

[91]  John A. Ekaterinaris,et al.  Computation of Separated and Unsteady Flows with One- and Two-Equation Turbulence Models , 1994 .

[92]  J. Koseff,et al.  A dynamic mixed subgrid‐scale model and its application to turbulent recirculating flows , 1993 .

[93]  Rolf Radespiel,et al.  Propulsive Efficiency of a Moving Airfoil at Transitional Low Reynolds Numbers , 2008 .

[94]  Marco Luciano Savini,et al.  Discontinuous Galerkin solution of the Reynolds-averaged Navier–Stokes and k–ω turbulence model equations , 2005 .

[95]  The Stability or Instability of the Steady Motions of a Perfect Liquid and of a Viscous Liquid. Part I: A Perfect Liquid , 2008 .

[96]  P. K. Sweby,et al.  High resolution TVD schemes using flux limiters , 1985 .

[97]  T. Herbert.  Secondary Instability of Boundary Layers , 1988 .

[98]  Farzad Mashayek,et al.  Large-eddy simulation using a discontinuous Galerkin spectral element method , 2007 .

[99]  Bernardo Cockburn,et al.  An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations , 2009, Journal of Computational Physics.

[100]  W. H. Reed,et al.  Triangular mesh methods for the neutron transport equation , 1973 .

[101]  Chi-Wang Shu,et al.  Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems , 2001, J. Sci. Comput..

[102]  A. Nayfeh.  Stability of Three-Dimensional Boundary Layers , 1979 .

[103]  M. Maughmer,et al.  Simplified Linear Stability Transition Prediction Method for Separated Boundary Layers , 1992 .

[104]  Michael Gaster,et al.  A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability , 1962, Journal of Fluid Mechanics.

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

[106]  Jonathan W. Naughton,et al.  Development of a Spectral Element DNS/LES Method for Turbulent Flow Simulations , 2007 .

[107]  William S. Saric,et al.  BOUNDARY-LAYER RECEPTIVITY TO FREESTREAM DISTURBANCES , 2002 .

[108]  F. Menter,et al.  A Correlation-Based Transition Model Using Local Variables: Part I — Model Formulation , 2004 .

[109]  Srinivas Ramakrishnan,et al.  Multiscale Modeling for Turbulence Simulation in Complex Geometries , 2004 .

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

[111]  A. U.S.,et al.  Implicit Large Eddy Simulation of Transitional Flows Over Airfoils and Wings , 2009 .

[112]  Rolf Radespiel,et al.  Dynamics of laminar separation bubbles at low-Reynolds-number aerofoils , 2009, Journal of Fluid Mechanics.

[113]  J. Boris,et al.  Flux-Corrected Transport , 1997 .

[114]  R. Radespiel,et al.  Numerical and Experimental Flow Analysis of Moving Airfoils with Laminar Separation Bubbles , 2006 .

[115]  J. Peraire,et al.  Sub-Cell Shock Capturing for Discontinuous Galerkin Methods , 2006 .

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

[117]  R. Radespiel,et al.  Transition Predictions using Reynolds-Averaged Navier-Stokes and Linear Stability Analysis Methods , 1991 .

[118]  Chi-Wang Shu,et al.  The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws , 1988, ESAIM: Mathematical Modelling and Numerical Analysis.

[119]  Weixing Yuan,et al.  An Investigation of Low-Reynolds-number Flows past Airfoils , 2005 .

[120]  Michael S. Selig,et al.  Airfoils at low speeds , 1989 .

[121]  Engineering Application Oriented Discontinuous Galerkin Methods , 2007 .

[122]  D. J. Marsden,et al.  Separation bubble model for low Reynolds number airfoil applications , 1994 .

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

[124]  H. Stock,et al.  Airfoil Validation Using Coupled Navier-Stokes and e Transition Prediction Methods , 2002 .

[125]  S. Rebay,et al.  GMRES Discontinuous Galerkin Solution of the Compressible Navier-Stokes Equations , 2000 .

[126]  R. Radespiel,et al.  Computational and experimental investigations of low-Reynolds-number flows past an aerofoil , 2007, The Aeronautical Journal (1968).

[127]  L. Mack,et al.  Transition prediction and linear stability theory , 1977 .

[128]  L. Margolin,et al.  Implicit Large Eddy Simulation: A Rationale for Implicit LES , 2007 .

[129]  Werner Haase,et al.  Feasibility Study of e Transition Prediction in Navier-Stokes Methods for Airfoils , 1999 .

[130]  Y. Dubief,et al.  On coherent-vortex identification in turbulence , 2000 .

[131]  L. Mack,et al.  Transition and laminar instability , 1977 .