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GDR 2902, 26-27 Septembre, Sophia-Antipolis

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GDR 2902, 26-27 Septembre, Sophia-Antipolis

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  1. APPLICATION DE LA MÉTHODE DE MAILLAGES DYNAMIQUES POUR LAPRÉDICTION D’ÉCOULEMENTS AUTOUR D’UN PROFIL D’AILEOSCILLANT DANS LE CONTEXTE DE L’INTERACTIONFLUIDE-STRUCTURESébastien Bourdet,Marianna BrazaInstitut de Mécanique des Fluides de Toulouse, Unité Mixte de Recherche CNRS/INPT UMR N° 5502, Allée du Prof. Camille Soula, 31400 Toulouse GDR 2902, 26-27 Septembre, Sophia-Antipolis

  2. Introduction Applications Biomechanic Blood and breath flows Civil engineering Flutter on the Tacoma bridge (1940) • Nuclear engineering : cooling system. • Naval architecture : dykes construction, offshore petroleum platforms. • Naval hydrodynamic : ship hulls conception. Aeronautical field

  3. Introduction • Drag increase • Vibrations Structure destruction Sudden lift loss • Structure enforcement • Velocity reduction • Manoeuvrability limitation • Velocity reduction (helicopter) • materials fatigue • Reduction of the range of operation Aeronautical field Buffeting Flutter phenomenon Dynamic stall

  4. Introduction Spontaneous development : von Kármán rows alley. Local injection of perturbations. Boundary motion : deformation, pitching, plunging etc. Unsteady flows Natural unsteadiness Forced unsteadiness Understanding of unsteady phenomenon. Appearance mechanisms. Major interest

  5. Equations & Numerical Schemes Spatial scheme Finite Differences Convective term Diffusion term Centered differences Precision O(2) 1Monotonic Upstream Scheme for Conservation Law Roe Upwind Scheme MUSCL1 Approach Navier-Stokes equation Temporal scheme Explicit Three-StagesRunge-Kutta Precision O(3) • Unsteady, Viscous, Compressible equation system • Dimensionless, under strong conservative form • General, non-orthogonal, curvilinear coordinates system

  6. Inflow and Outer boundaries Free stream conditions Outflow boundary First order extrapolation for unknown variables Wake line Averaging of variables above and below the wake line • Wall • Non-slip condition • Neumann condition for temperature,density and energy • Pressure : Resolution of NS equations with non-slip condition Flow domain configuration NACA0012 Airfoil Flow parameters : Re 10000 5000 M [0.1,0.4] M= 0.4,0.5 Incidence 0° variable Meshes parameters : Structured C-Type grid (2D) Initial conditions: Uniform fields from inflow conditions

  7. Dynamic mesh method Displacement field Static mesh Lagrangian or Eulerian formulation Dynamic mesh Generalized formulation : Mesh velocity field Equation formulation Instant t0 Instant t0+t Continuity equation : J(t) : time dependent Jacobian

  8. Geometric conservation law(GCL) 1 p : Roe’s scheme constant Metrics compatibility relations : 2 Centered, second order derivative Conservative character Conservative character of continuous equations Numerical conservation ? Thomas & Lombard (1979) 2D local form : : Contravariant mesh velocities Consistent scheme Numerical discretisation of the GCL ? Injection of a constant solution in the numerical scheme

  9. Mesh actualization On each node : Spring analogy • Compatibility nodes-walls • Mesh integrity (avoid ill-conditioned cells) Computational mesh movement Linear tension springs • : global parameter  : local function

  10. Mesh actualization Spring analogy Torsional springs Stiffness : Iterative solver Flat plate oscillation

  11. Validation Geometric conservation law Oscillation of a fictitious flat plate • Re=104 • M∞=0.5 • = 2 max =+/- 15 ° Constant solution for fluid Comparison of two simulations Without GCL With GCL Longitudinal velocity field

  12. Validation Pitching case Barakos & Drikakis (1999) • No mesh motion • Harmonic oscillation of the airfoil : Comparison of lift and moment coefficients Comparison of the Dynamic Stall Vortex (DSV) convection velocity (Guo et al, 1994 ; Chandrasekhara & Carr, 1990)

  13. Validation Dynamic stall : 19,3° CL, CM coefficients Barakos & Drikakis Present study Coherent amplitude, hysteresis Different stall Vortex dynamic

  14. Validation Vortex dynamic Streamlines Temporal evolution of the Lift coefficient

  15. Validation Dynamic Stall Vortex Convection Velocity density contours Barakos & Drikakis Q-criterion, present study

  16. Validation Pitching Simulation Vorticity contours White: positive vorticity, black: negative vorticity

  17. Conclusions - Perspectives Dynamic mesh Conclusion • Numerical code using dynamic mesh • Mesh actualization • Independence of physical results on mesh motion (GCL) • Realistic vortex dynamic Perspectives • Others test-cases, experimental datas • Second step … Two degrees of freedom Numerical coupling

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