Numerical simulation of vortex shedding flows past moving obstacles using the k-£ turbulence model on unstructured dynamic meshes

Authors

  • Hai Tran Department of Aerospace Engineering Sciences and Center for Aerospace Structures University of Colorado, Campus Box 429 Boulder; CO 80309-0429, USA
  • Bruno Koobus Department of Aerospace Engineering Sciences and Center for Aerospace Structures University of Colorado, Campus Box 429 Boulder; CO 80309-0429, USA
  • Charbel Farhat Department of Aerospace Engineering Sciences and Center for Aerospace Structures University of Colorado, Campus Box 429 Boulder; CO 80309-0429, USA

Keywords:

finite element/finite volume method, dynamix meshes, k-e turbulence model, vortex shedding flows

Abstract

>p>We consider the numerical solution on unstructured dynamic meshes of the averaged Navier-Stockes equations equipped with the k-e turbulence model and a wall function. We discuss discretization issues pertaining to moving grids and numerical dissipation, and present a robust spring analogy method for constructing dynamic meshes. We validate our implementation of this two-equation turbulence model and justify its usage for a class of vortex shedding problems by correlating our computational results with experimental data obtained for a flow past a square cylinder. We also apply our solution methodology to the twodimensional aerodynamic stability analysis of the Tacoma Narrows Bridge, and report nwnerical results that are in good agreemellt with observed data.

 

Downloads

Download data is not yet available.

References

J. W. Edwards and J. B. Malone, Current Status of Computational Methods for

Transonic Unsteady Aerodynamics and Aeroelastic Applications, Comput. Sys.

Engrg. 1992, 3:545-569.

E. Simiu and R.H Scanlan, Wind Effects on Structures, John Wiley & Sons, 2nd

Edition, 1986.

Y. C. Fmg, An Introduction to the Theory of Aeroelasticity, Dover Publications,

Inc., 1969.

M. Xia and G.E. Karniadakis, The Spectrum of the Turbulent Near- Wake: a

Comparison of DNS and LES, Proc. 1st AFOSR Int. Conference on DNS/LES,

Ruston, LA, 1997.

B. E. Launder and D. B. Spalding, The Numerical Computation of Turbulent

Flows, Comput. Meths. Appl. Mech. Engrg. 1974, 3:269-289.

J. Donea, An Arbitrary Lagrangian-Eulerian Finite Element Method for Transient

Fluid-Structure Interactions, Comput. Meths. Appl. Mech. Engrg. 1982,

: 689-723.

R. Franke and W. Rodi, Calculation of Vortex Shedding Past a Square Cylinder

With Various Turbulence Models, Eighth Symposium on Turbulent Shear Flows,

Technical University of Munich, 1991.

C. Farhat, M. Lesoinne and N. Maman, Mixed Explicit/Implicit Time Integration

of Coupled Aeroelastic Problems: Three-Field Formulation, Geometric Conservation

and Distributed Solution, Intemat. J. Numer. Meths. Fluids 1995, 21:

-835.

T. Tezduyar, M. Behr and J. Liou, A New Strategy for Finite Element Computations

Involving Moving Boundaries and Interfaces - The Deforming Spatial

Domain/Space- Time Procedure: I. The Concept and the Preliminary Numerical

Tests, Comput. Meths. Appl. Mech. Engrg. 1992, 94: 339-351.

A. Masud, A Space-Time Finite Element Method/or Fluid Structure Interaction,

Ph. D. Thesis, Stanford University, 1993.

M. Jaeger and G. Dhatt, An Extended k- ~ Finite Element Model, Intemat. J.

Numer. Meths. Fluids 1992, 14:1325-1345.

C. Farhat, L. Fezoui and S. Lanteri, Two-Dimensional Viscous Flow Computations

on the Connection Machine: Unstructured Meshes, Upwind Schemes, and

Massively Parallel Computations, Comput. Meths. Appl. Mech. Engrg. 1993,

:61-88.

P. L. Roe, Approximate Reimann Solvers, Parameters Vectors and Difference

Schemes, J. Comp. Phys. 1981, 43:357-371.

J. Steger and R. F. Warming, Flux Vector Splitting/or the Inviscid Gas Dynamic

with Applications to Finite-Difference Methods, J. Comp. Phys. 1981, 40:263-293.

B. Van Leer, Towards the Ultimate Conservative Difference Scheme V: a SecondOrder

Sequel to Godounov's Method, J. Comp. Phys. 1979, 32:361-370.

A. Dervieux, Steady Euler Simulations Using Unstructured Meshes, Von Karman

Institute Lecture Series, 1985.

G. D. van Albada, B. van Leer and W. W. Roberts, A Comparative Study of Computational

Methods in Cosmic Gas Dynamics, Astron. Astrophys. 1982, 108:76-

E. Thrkel, Precondition ned Methods for Solving the Incompressible and Low-Speed

Compressible Equations, J. Comp. Phys. 1987, 72:277-298.

B. Larrouturou, How to preserve the mass fraction positivity when computing

compressible multi-component flows, J. Comp. Phys. 95, 1:59-84.

B. Koobus and C. Farhat, Second-Order Time-Accurate and Geometrically

Conservative Implicit Schemes for Flow Computations on Unstructured Dynamic

Meshes, Comput. Meths. Appl. Mech. Engrg., (submitted for publication).

Also published as Technical Report CU-CAS-97-12, College of Engineering, The

University of Colorado at Boulder, June 1997.

(21] M. Lesoinne and C. Farhat, Geometric Conservation Laws for Aeroelastic Computations

Using Unstructured Dynamic Meshes, AIAA Paper 95-1709, 12th

AIAA Computational Fluid Dynamics Conference, San Diego, June 19-22, 1995.

M. Lesoinne and C. Farhat, Geometric Conservation Laws for Flow Problems

with Moving Boundaries and Deformable Meshes, and Their Impact on Aeroelastic

Computations, Comput. Meths. Appl. Mech. Engrg. 1996, 134:71-90.

B. Koobus and C. Farhat, Time-Accurate Algorithms for the Evaluation of

the Viscous Fluxes Associated with Unsteady Flows and Unstructured Moving

Meshes, AIAA Paper 96-2384, 14th AIAA Applied Aerodynamics Conference,

New Orleans, Louisiana, June 18-20, 1996.

J.-A Desideri and P. W. Hemker, Convergence Analysis of the Defect-Correction

Iteration for Hyperbolic Problems, SIAM J. Sci. Comput. 1995, 16:88-118.

K. Bohmer, P. Hemker, and H. Stetter, The Defect Correction Approach, Comput.

Supp. 1984, 5:1-32.

(26] R. Martin and H. Guillard, A Second-Order Defect Correction Scheme for Unsteady

Problems, Comput. and Fluids 1996, 25:9-27.

J. T. Batina, Unsteady Euler Airfoil Solutions Using Unstructured Dynamic

Meshes, AIAA Paper No. 89-0115, AIAA 27th Aerospace Sciences Meeting,

Reno, Nevada, January 9-12, 1989.

(28) S. R. Chakravarthy and K. Y. Szema, Computational Fluids Dynamics Capability

for Internally Carried Store Separation, Rockwell Inti. Corp. Rep. SC-71039-TR,

Science Center, Thousand Oaks, CA, 1991.

C. Farhat, C. Degand, B. Koobus and M. Lesoinne, Torsional Springs for TwoDimensional

Dynamic Unstructured Fluid Meshes, Comput. Meths. Appl. Mech.

Engrg. (submitted for publication). Also published as Technical Report CU-CAS-

-03, College of Engineering, The University of Colorado at Boulder, January

R. H. Scanlan and J. J. Tomko, Airfoil and Dridge Deck Flutter Derivatives, J.

Engrg. Mech. 1971, 97:1717-1737.

S. Piperno, C. Farhat and B. Larrouturou, Partitioned Procedures for the Transient

Solution of Coupled Aeroelastic Problems- Part I: Model Problem, Theory,

and Two-Dimensional Application, Comput. Meths. Appl. Mech. Engrg. 1995,

:79-112.

T. J. R. Hughes, The Finite Element Method, Prentice-Hall, Inc., 1987.

D. Amsler, Etude Theorique et Experimentale des Ponts a Cables de Tres Grande

Portee: Ponts Suspendus et Ponts Hybrides, These No. 1290, Ecole Polytechnique

Federale de Lausanne, 1994.

Downloads

Published

1997-02-19

How to Cite

Tran, H. ., Koobus, B. ., & Farhat, C. (1997). Numerical simulation of vortex shedding flows past moving obstacles using the k-£ turbulence model on unstructured dynamic meshes. European Journal of Computational Mechanics, 6(5-6), 611–642. Retrieved from https://journals.riverpublishers.com/index.php/EJCM/article/view/3427

Issue

Section

Original Article