Direct numerical control of the flow 2 1 IMB Université de Bordeaux, France 2 IMB Institut polytechnique de Bordeaux,France Inria Bordeaux Sud Ouest MC2 project 3rd GDR Contrôle des décollements Symposium
Outline
Outline
On a ground vehicle the rear window is responsible for: 30 to 45 % of the total vehicle drag Real impact on fuel consumption and CO 2 emission. Focus on the recirculation zone behind a car rear-window using a two -dimensional backward which is a benchmark of GDR Contrôle des décollements Aim of the study : Simulation and analysis of the flow behaviour over the backward Control the flow using active procedures
Mathematical Modelization Numerical algorithms Numerical data Outline
domain Ω Mathematical Modelization Numerical algorithms Numerical data Ω = (20 5) Height of the step h = 1 Inclination angle α = 25 The solid body stay still The fluid is supposed to be incompressible
Mathematical Modelization Numerical algorithms Numerical data Adimensional Navier-Stokes (u,p) incompressible + penalisation 1 : t U + (U )U 1 Re U + U K + p = 0 in Ω T div U = 0 U(0,.) = U 0 in Ω T in Ω where K is the non dimensional coefficient of permeability of the medium without gravity, Re = U h µ is the non dimensional Reynolds number, Ω is the full domain including the solid body, I = (0, T), Ω T = Ω I. Numerically: In the fluid: K = 10 16, In the solid body: K = 10 8. 1 Bruneau and Angot [99]
Boundary conditions Mathematical Modelization Numerical algorithms U = U = (u, 0) on the entrance section Γ D Numerical data U = 0 on Γ 0 σ(u, p)n + 1 2 (U n) (U U ref ) = σ(u ref, p ref )n on the artificial frontiers 2 Γ N, where σ(u, p) = 1 Re ( U + Ut ) pi n is the unit normal pointing outside of the (U ref, p ref ) is a reference flow. The no-slip boundary layers on the solid are obtained using the penalisation method 2 Bruneau [2000]
Numerical algorithms Mathematical Modelization Numerical algorithms Numerical data The space discretization is performed on staggered grids with strongly coupled equations. Second-order Gear scheme in time. Second-order centered finite differences are used for the linear terms the divergence-free equation is discretized on the pressure points. The convection terms are approximated by an upwind third order scheme. The resolution is achieved by a V-cycle multigrid algorithm coupled to a cell-by-cell relaxation procedure.
Numerical data Mathematical Modelization Numerical algorithms Numerical data Height of the step h = 1 h = 0.1m Upstream velocity U = 1 U = 20m/s Reynolds number: Re = 1, 23.10 5
Grid convergence Behaviour of the solution Study of the mean flow Outline
Grid convergence Behaviour of the solution Study of the mean flow Grid convergence Simulation time T = 1000 Three different grids: G 7 : (1280 320) δ x = 1.5625.10 2 G 8 : (2560 640) δ x = 7.8125.10 3 G 9 : (5120 2560) δ x = 3.90625.10 3 Resolution Mean kinetic energy Recirculation length G 7 85 5.6 G 8 78 5.1 G 9 76 4.9 Table: Mean kinetic energy and recirculation length
Grid convergence Mean velocity isolines Mean pressure isolines G7 Grid convergence Behaviour of the solution Study of the mean flow G8 G9 The grid used for the simulations is G8 (δ x = 7.8125.10 3 )
Behaviour of the solution Grid convergence Behaviour of the solution Study of the mean flow T = 50 T = 60 T = 70 T = 80 T = 90 T = 100 Figure: Evolution of vorticity field for.
Study of the mean flow Grid convergence Behaviour of the solution Study of the mean flow Mean pressure field. Mean vorticity field.
Study of the mean flow Mean velocity streamlines Numerical results Grid convergence Behaviour of the solution Study of the mean flow Experimental results( R.Joussot and A.Tracker. Orléans) Recirculation length: Numerical results :5.1 Experiments: 5.3
Study of the mean flow Grid convergence Behaviour of the solution Study of the mean flow Mean velocity profiles for the. The boundary layer thickness at X/h = 10 (the top edge of the step) is 0.031 (3.1mm).
Control with continuous jets Control with synthetic jets Synthesis Outline
Control with continuous jets Control with synthetic jets Synthesis Active Control Two types of jets studied: Continuous jets U j = AU Synthetic jets U j = AU sin(2πft) where: U j the velocity of the jet The amplitude of the jet A = 0.6 The simulation time T = 1000 The frequency of the jet f = 20Hz (similar results with 50Hz) Three different configurations of jets: vertical jet normal jet horizontal jet
Active Control Control with continuous jets Vertical jet control Control with continuous jets Control with synthetic jets Synthesis Normal jet control Horizontal jet control Figure: Mean velocity streamlines
Active Control Control with continuous jets Control with continuous jets Control with synthetic jets Synthesis Figure: Mean velocity profile at line X/h = 11 for uncontrolled (blue line) and controlled flows using uniform jets (black for horizontal jet control, red for vertical jet control and green for normal jet control).
Active Control Control with synthetic jets Control with continuous jets Control with synthetic jets Synthesis Vertical jet control Normal jet control Horizontal jet control Figure: Mean velocity streamlines
Active Control Control with synthetic jets Vertical jet control Control with continuous jets Control with synthetic jets Synthesis Normal jet control Horizontal jet control Figure: Mean vorticity fields
Active Control Synthesis Vertical Normal Horizontal L r for continuous jet control 3.7 3.2 2.8 L r for synthetic jet control 4.4 3.1 2.6 Recirculation length L r for various controls (This length for the natural flow is 5.1). Control with continuous jets Control with synthetic jets Synthesis Vertical Normal Horizontal F p for continuous jet control 0.10 0.09 0.09 F p for synthetic jet control 0.14 0.09 0.09 Mean pressure force on the back wall F p for various controls (This pressure force is equal to 0.14 for the natural flow ). Horizontal and normal jets are the most efficient
Outline
The main characteristics of the are well captured Two types of jets studied: Continuous jet Synthetic jet Similar results except for the vertical jet Three different configurations of jet: Vertical jet just before the corner Normal to the ramp Horizontal to the ramp Horizontal and normal jets reduces drastically the size of the recirculation zone
Philippe Angot, Charles-Henri Bruneau, Pierre Fabrie A penalization method to take into account obstacles in incompressible viscous flows Numerische Mathematik,1999 C.H. Bruneau, P. Gillieron, Flow manipulation around the Ahmed body with a rear window using passive strategies Compte Rendu Acad. des Sciences, 2007 Charles-Henri Bruneau, Emmanuel Creuse, Delphine Depeyras, Patrick Gillieron, Iraj Mortazavi Active procedures to control the flow past the Ahmed body with a 25 rear window Int. J. of Aerodynamics,2011