Post on 30-Mar-2015
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APPLICATION DE LA MÉTHODE DE MAILLAGES DYNAMIQUES POUR LA
PRÉDICTION D’ÉCOULEMENTS AUTOUR D’UN PROFIL D’AILEOSCILLANT DANS LE CONTEXTE DE L’INTERACTION
FLUIDE-STRUCTURE
Sébastien Bourdet, Marianna Braza
Institut 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
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BiomechanicBlood and breath flows
Civil engineeringFlutter on the Tacoma bridge
(1940)Nuclear engineering : cooling system.
Naval architecture : dykes construction, offshore petroleum platforms.
Naval hydrodynamic : ship hulls conception.
IntroductionIntroduction
Applications
Aeronautical field
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Aeronautical field
IntroductionIntroduction
Flutter phenomenonBuffeting
•Drag increase•Vibrations
• materials fatigue• Reduction of the range of operation
Structure destruction
•Structure enforcement
•Velocity reduction
Dynamic stall
Sudden lift loss
• Manoeuvrability limitation
•Velocity reduction (helicopter)
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IntroductionIntroduction
Unsteady flows
Natural unsteadiness
Forced unsteadiness
Spontaneous development : von Kármán rows alley.
Local injection of perturbations.
Boundary motion : deformation, pitching, plunging etc.
Understanding of unsteady phenomenon.Appearance mechanisms.
Major interest
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DiffusionpressureConvection
RGFE
t
q
Re
1
•Unsteady, Viscous, Compressible equation system
•Dimensionless, under strong conservative form
•General, non-orthogonal, curvilinear coordinates system
iep )1(
e
v
uJq
Equations & Numerical SchemesEquations & Numerical Schemes
Navier-Stokes equation
Spatial scheme
Finite Differences
Convective term
Diffusion term Centered differences
Precision O(2)
1Monotonic Upstream Scheme for Conservation
Law
Roe Upwind SchemeMUSCL1 Approach
Temporal scheme
Explicit
Three-Stages Runge-Kutta
Precision O(3)
Uc
Re
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Flow domain configurationFlow domain configuration
Flow parameters :
Re 100005000
M [0.1,0.4] M= 0.4,0.5Incidence 0° variable
Meshes parameters :Structured C-Type grid (2D)
NACA0012 AirfoilInflow and Outer boundariesFree stream conditions
Outflow boundaryFirst order extrapolation for unknown variables
Wake lineAveraging 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 Initial conditions: Uniform fields from inflow
conditions
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Dynamic mesh methodDynamic mesh method
Instant t0Instant t0+t
Static mesh
Lagrangian or Eulerian formulation
Dynamic mesh
Generalized formulation
Displacement field
Continuity equation :
J(t) : time dependent Jacobian
Equation formulation
: Mesh velocity field
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Geometric conservation lawGeometric conservation law (GCL)(GCL)
Conservative character
Conservative character of continuous equations
Numerical conservation ?
Thomas & Lombard (1979)
2D local form :
Consistent schemeNumerical discretisation of the GCL ?
Injection of a constant solution in the numerical scheme
: Contravariant mesh velocities
p : Roe’s scheme constant1
2 Metrics compatibilityrelations :
Centered, second order derivative
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Mesh actualizationMesh actualization
Spring analogy
Computational mesh movement• Compatibility nodes-walls• Mesh integrity (avoid ill-conditioned cells)
Linear tension springs
: global parameter : local functionOn each node :
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Mesh actualizationMesh actualization
Spring analogy
Torsional springs
Stiffness :
Flat plate oscillation
Iterative solver
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ValidationValidation
Geometric conservation law
Oscillation of a fictitious flat plate
Re=104
M∞=0.5= 2max =+/- 15 °
Constant solution for fluid
Comparison of two simulations
Longitudinal velocity fieldWithout GCL With GCL
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Pitching case
ValidationValidation
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)
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CL, CM coefficients
ValidationValidation
Barakos & Drikakis
Present study
Dynamic stall : 19,3°
Coherent amplitude, hysteresisDifferent stallVortex dynamic
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ValidationValidation
Vortex dynamicStreamlines
Temporal evolution of the Lift coefficient
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ValidationValidation
Dynamic Stall Vortex Convection Velocity
Q-criterion, present study
density contoursBarakos & Drikakis
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ValidationValidation
Pitching Simulation
Vorticity contoursWhite: positive vorticity, black:
negative vorticity
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Dynamic mesh
Conclusions - PerspectivesConclusions - Perspectives
Perspectives
• Others test-cases, experimental datas • Second step … Two degrees of freedomNumerical coupling
Conclusion
• Numerical code using dynamic mesh• Mesh actualization• Independence of physical results on mesh motion (GCL)• Realistic vortex dynamic