Double penalisation method for porous-fluid problems and numerical simulation of passive and active control strategies for bluff-body flows

Size: px

Start display at page:

Download "Double penalisation method for porous-fluid problems and numerical simulation of passive and active control strategies for bluff-body flows"

Jane Powell
6 years ago
Views:

1 Double penalisation method for porous-fluid problems and numerical simulation of passive and active control strategies for bluff-body flows Iraj Mortazavi Institut Polytechnique de Bordeaux INRIA Bordeaux Sud-Ouest - Projet MC2 Institut de Mathématiques de Bordeaux UMR CNRS 5251 In Collaboration with: C.-H. Bruneau (Université Bordeaux 1), E. Creusé (INRIA Lille), D. Depeyras (INRIA Bordeaux), & P. Gilliéron (Renault) January 29, 2010

2 Introduction Flow problems essentially rised from industrial needs To explore efficient modelling approaches related to them To choose, design and fit appropriate numerical methods To build efficient control techniques to improve some undesirable behaviours. In this talk: Penalization method and coupled active/passive control Applications to risers and simplified car models

3 Targets... and the main tool to postpone the transition from laminar to turbulent flow, to delay separation, to reduce the vortex induced vibrations (VIV), to reduce the skin friction drag. Active or passive control? Answer: Passive control doesn t need a regular energy supply (Previous works: Bearman, Bottaro, Carpenter, Luchini...). Nevertheless, it is not always efficient. 1st tool: passive control is achieved introducing a porous interface between the solid body and the flow in order to reduce the vorticity production of the boundary layer.

4 Targets... and the main tool to postpone the transition from laminar to turbulent flow, to delay separation, to reduce the vortex induced vibrations (VIV), to reduce the skin friction drag. Active or passive control? Answer: Passive control doesn t need a regular energy supply (Previous works: Bearman, Bottaro, Carpenter, Luchini...). Nevertheless, it is not always efficient. 1st tool: passive control is achieved introducing a porous interface between the solid body and the flow in order to reduce the vorticity production of the boundary layer.

5 Targets... and the main tool to postpone the transition from laminar to turbulent flow, to delay separation, to reduce the vortex induced vibrations (VIV), to reduce the skin friction drag. Active or passive control? Answer: Passive control doesn t need a regular energy supply (Previous works: Bearman, Bottaro, Carpenter, Luchini...). Nevertheless, it is not always efficient. 1st tool: passive control is achieved introducing a porous interface between the solid body and the flow in order to reduce the vorticity production of the boundary layer.

6 Targets... and the main tool to postpone the transition from laminar to turbulent flow, to delay separation, to reduce the vortex induced vibrations (VIV), to reduce the skin friction drag. Active or passive control? Answer: Passive control doesn t need a regular energy supply (Previous works: Bearman, Bottaro, Carpenter, Luchini...). Nevertheless, it is not always efficient. 1st tool: passive control is achieved introducing a porous interface between the solid body and the flow in order to reduce the vorticity production of the boundary layer.

7 ...Targets Computing efficiently the flow in solid-porous-fluid media. To explore a tool to perform simultaneously all computations: Low computational tasks; Low complexity of the method; Useful to solve different industrial problems.

8 Physical description y u 0 Fluid domain u i u D Porous layer Solid body x Thus, we have to solve a problem involving three different media, the solid body, the porous layers and the incompressible fluid.

9 ...physical description From the solid to the main fluid (Vafai 81, Nield & Bejan 99): the boundary layer in the porous medium close to the solid wall has a thickness thickness order of k 1/2, the homogeneous porous flow with the very low Darcy velocity u D, the porous interface region with the fluid velocity from u D to u i at the boundary and the thickness about k 1/2, the boundary layer in the fluid close to the porous frontier that grows from the interface velocity u i instead of zero, the main fluid flow with mean velocity u 0.

10 Reduction of the porous layer to a boundary condition From the Darcy law, Beavers and Joseph (1972) derived the ad hoc boundary condition u y = α k 1/2 (u i u D ) ; v = 0 with α: a slip coefficient. Modified boundary condition (Jones 1973) ( v x + u y ) = α k 1/2 (u i u D ) ; v = 0 Normal transpiration (Perot & Moin 1995) v u = 0 ; = 0 or u = 0 ; v = βp y with β: the porosity coefficient; p = p G(t)x: fluctuation of the wall pressure versus the mean pressure gradient.

11 Coupling of Darcy equations with Fluid equations Modelling both the porous medium and the flow µ p k U + p = 0 ; div U = 0 t U ν U + p = 0 ; div U = 0 Boundary condition at the interface (Das et al. 2002, Hanspal et al. 2006, Salinger et al. 1994): Darcy equation as a boundary condition for the fluid Beavers & Joseph type condition and Brinkman equation Interface velocity continuous with a stress jump µ p ( u i y ) porous µ( u i y ) fluid = γ k 1/2 u i where γ is a dimensionless coefficient of order one.

12 A 3rd approach: Penalisation method Arquis & Caltagirone (88), Angot et al. (99), Kevlahan & Ghidaglia (99), Bruneau & Mortazavi (01, 04, 06, 07, 08). Brinkman s equation (valid only for high porosities close to one) obtained from Darcy s law by adding the diffusion term: p = µ ΦU + µφ U k adding the inertial terms with the Dupuit-Forchheiner relationship, the Forchheiner-Navier-Stokes equations: ρ t U + ρ (U ) U + p = µ ΦU + µφ U k where k: intrinsic permeability, µ: Brinkman s effective viscosity and Φ: porosity. As Φ is close to 1 we have µ close to µ/φ: ρ t U + ρ (U ) U + p = µ ΦU + µ U k

13 Double penalisation method Nondimensionalisation using the mean fluid velocity U and the obstacles heigh H: U = U U ; x = x H ; t = t /U. Penalised non dimensional Navier-Stokes equations adding U/K to incompressible NS equations (K = ρkφu µh non dimensional permeability coefficient of the medium): t U + (U )U 1 Re U + U K + p = 0 divu = 0 U(0,.) = U 0 U = U U = 0 σ(u, p) n (U n) (U U ref ) = σ(u ref, p ref ) n in Ω T in Ω T in Ω on Γ D I on Γ W I on Γ N I Solid: K = 10 8, Fluid: K = 10 16, Porous layer: K = 10 1 Specific interpolations needed in the fluid-porous interface.

14 Outline of the numerical simulation Second-order Gear scheme in time. The space discretization is performed on staggered grids with strongly coupled equations. Second-order centred finite differences are used for the linear terms - The location of the unknowns enforce the divergence-free equation which is discretized on the pressure points. The convection terms are approximated by a third order Murman-like scheme. The resolution is achieved by a V-cycle multigrid algorithm coupled to a cell-by-cell relaxation procedure. There is a sequence of grids from a coarse cells grid to a fine cells grid for instance.

15 Applications to control: Functionals to be minimized As the pressure is computed inside the solid body, the drag and lift forces are computed by integrating the penalisation term on the volume of the body: F D F L = body x1p dx + body = body x2p dx + body 1 Re u dx 1 Re v dx body body Important quantities to quantify the control effect: C p = 2(p p 0 )/(ρ U 2 ) C D = 2F D H ; C L = 2F L H 1 T C Lrms = CL 2 T dt ; Z = 1 ω 2 dx 2 0 Ω u K dx(1) v K dx.(2)

16 Passive control around a riser using a porous ring Flow simulation behind a circular bluff body with a size D = 0.16, located at the position (1.1, 1) in an open computational domain. The pipe is surrounded by a solid (larger diameter), a porous or a fluid sheath (smaller diameter): δd = 0.2. The Reynolds number based on the pipe diameter D is R D = for the solid case. The control target is to reduce the VIV (Vortex Induced Vibrations) around the riser.

17 Vorticity field for a fluid (bottom) and a porous (top) sheath for the same time at R D =

18 Mean values of the enstrophy and the drag coefficient and asymptotic value of the CLrms for R D = Grid K Enstrophy Drag C Lrms E E A patent in 2005 on the passive control of VIV around riser pipes using porous media with IFP.

19 Drag reduction for a simplified car model (collaboration with Renault) Γ D z Γ N O Ω α A y x Γ 0 Computational domain for the Ahmed body without or with a rear window on top of a road (distance from the road = h).

20 New experimental set-up z y x Domain definition

2D and 3D Simulations Comparison of the two-dimensional

and side section (right) streamlines in the near wake of

2D studies have a physical sense for this geometry.

21 2D and 3D Simulations Comparison of the two-dimensional (left) with the three-dimensional middle section (middle) and side section (right) streamlines in the near wake of the square back Ahmed body (Computations with a fine mesh): 2D studies have a physical sense for this geometry. Also to see: Gilliéron & Chometon 01, Krajnovic & Davidson 06, Roméas 07.

22 Drag history for uncontrolled flow Drag coefficient Cd 0,18 0,16 0,14 0,12 standard deviation = average 0,1 0, Time Instantaneous C d during two shedding cycles

23 Evolution of the pressure field during two shedding cycles

24 Evolution of the vorticity field during two shedding cycles

25 Passive control: square-back Ahmed body Porous layer on the roof (after a parametric study): Average static pressure coefficient contours (h = 0.6): Average drag coefficients : Case C Dfront C Dback C D Var. C D Ref Pas (+5.3%) ( 37.6%) %

26 Passive control: square-back Ahmed body Porous layer on the roof & the bottom (after a parametric study): Average static pressure coefficient contours (h = 0.6): Average drag coefficients : Case C Dfront C Dback C D Var. C D Ref Pas (+7%) ( 45%) %

27 Active control set-up U j = U jav (1 β(p sensor P sensor )) with U jav the jet mean amplitude, β the normalizing coefficient to get the limit values U j = 0 et U j = 2U jav (here β = 1.5 for the square back), P sensor the instantanous sensor pressure at time t for only one sensor or (P sensor = min(p sensor1, P sensor2 ) for 2 sensors) & P sensor the average pressure value at that point.

28 Accurate modelling of actuators Adding proper velocities on the actuator mesh points Local change of the divergence-free condition (mathematically demonstrated Bruneau & Mortazavi 10) U = U j δx (3)

29 Control C dup Var. C ddown Var. C d Var. No Steady % % % Pulsed % % % Closed-loop % % % Comparison of the mean drag coefficients for active controls with a middle actuator (SBAB). Two sensors are placed at the distance H/10 from the back wall edges of the body.

30 Active control: square-back Ahmed body Non intrusive closed-loop control with pressure sensor and distance to road of h = 0.6 (middle jet & 0 act 0.6V 0 ): sensor act Average static pressure coefficient contours: Average drag coefficients: Case C Dfront C Dback C D Var. C D Ref Act ( 17%) ( 22.5%) %

6U 0 Two sensors at the distance H/10 from the edges

31 Square back: Closed-loop active control actuator in the center with an average velocity U jmoy = 0.6U 0 Two sensors at the distance H/10 from the edges of the back wall Average velocity vectors in the near wake:

32 Active control: square-back Ahmed body Non intrusive closed-loop control with pressure sensor and distance to road of h = 0.6 (down jet & 0 act 0.6V 0 ): sensor act Average static pressure coefficient contours: Average drag coefficients: Case C Dfront C Dback C D Var. C D Ref Act ( 6.0%) ( 4.0%) %

33 Coupled control: square-back body Closed-loop control with pressure sensor (down jet & 0 act 0.6V 0 ) and porous surface on the roof: Average static pressure coefficient contours (h = 0.6): Average drag coefficients: Case C Dfront C Dback C D Var. C D Ref Coup ( 15.8%) ( 47.6%) %

34 Flow control around the Square Back Ahmed Body: C p profiles 1 z (0 at the bottom of the body) 0,8 0,6 0,4 0,2 Reference Case 0 + Uj middle Case 0 + Uj down Case 1 Case 1 + Uj down ,8-1,6-1,4-1,2-1 Cp C p profiles on the back for: the uncontrolled case, the passive control, the closed-loop active controls (with middle & down actuators) and the coupled passive-active control.

6) Reynolds number Re = 30000 Streamlines

35 Three-dimensional Ahmed body Ahmed body with a rear window (25 ) on top of a road (h = 0.6) Reynolds number Re = Streamlines and iso-x-vorticity with C pi colors at the back:

36 Three-dimensional Ahmed body Ahmed body with a rear window (25 ) on the top of a road (h = 0.6) Reynolds number Re = Isosurface of total pressure coefficient Cpi = 1 with CP colors:

37 Active control of the 3D body with a rear window Two possible control strategies 1 (left) & 2 (right): blowing blowing suction blowing Steady jets: V act = 0.6V 0

38 3D active control with a rear window Mean C p profiles on the window, without (top) and with (down) longitudinal jets (control 1):

39 3D active control with a rear window Mean vortices on the half normal section of the window without (left) and with (right) longitudinal jets (control 1):

40 3D active control with a rear window Mean vorticity field with C p colors; without (left) and with (right) longitudinal jets (control 1, ω = ±5):

41 3D active control with a rear window Mean velocity field on the neighboring half surface of the rear window without (left) and with (right) parallel control jets (blowing & suction - control 2):

42 3D active control with a rear window Mean vorticity field with C p colors; without (left) and with (right) parallel control jets (blowing & suction - control 2, ω = ±8):

43 3D active control with a rear window Case C dfront C dback C dwindow C d NC ( 7%) ( 0%) ( 17%) ( 11%) ( 1%) ( 4%) ( 11%) ( 7%) Table: Mean drag coefficients comparison for the 3D active control

44 3D Control: Coupling methods Coupling two active controls 1 & 2 in order to reduce both the longitudinal vortices and the window recirculation zone. blowing blowing suction blowing Velocity vectors on a plane at 0.03H from the rear window:

45 3D Control: Coupling methods Average x-vorticity isosurfaces ω = ±5 colored with C Pi : Average drag coefficients: Cas C dav. C dcu. C dlun. C d Ref Coup ( 1%) ( 2%) ( 21%) ( 13%)

46 Conclusion Thanks to the double penalisation method a passive control procedure using porous interfaces between solid bodies and the fluid is easily handled; Strong regularization and VIV reduction for flows around riser pipes: life time of the risers will increase; Significant drag reduction for the square back Ahmed body with a good choice of the porous device locations; Divergence-free law was modified to better handle the actuators on the wall; Coupled active and passive devices improve the drag reduction of the square back body; Good results for various active controls of 3D Ahmed body with a rear window. Work on progress: 3D coupled active-passive studies to achieve a more efficient control around the Ahmed body (especially with a rear window).

47 Conclusion Thanks to the double penalisation method a passive control procedure using porous interfaces between solid bodies and the fluid is easily handled; Strong regularization and VIV reduction for flows around riser pipes: life time of the risers will increase; Significant drag reduction for the square back Ahmed body with a good choice of the porous device locations; Divergence-free law was modified to better handle the actuators on the wall; Coupled active and passive devices improve the drag reduction of the square back body; Good results for various active controls of 3D Ahmed body with a rear window. Work on progress: 3D coupled active-passive studies to achieve a more efficient control around the Ahmed body (especially with a rear window).

48 References C.-H. Bruneau & I. Mortazavi, C. R. Acad. Sci C.-H. Bruneau & I. Mortazavi, Int. J. Num. Meth. Fluids C.-H. Bruneau & I. Mortazavi, Int. J. Offsh. Polar Engg C.-H. Bruneau, P. Gillieron & I. Mortazavi, C. R. Acad. Sci., C.-H. Bruneau, P. Gillieron & I. Mortazavi, Journal of Fluids Engineering, C.-H. Bruneau & I. Mortazavi, Computers & Fluids, C.-H. Bruneau, D. Depeyras & I. Mortazavi, Computers & Fluids, under review.

Direct numerical simulation and control of the flow over a backward facing ramp

Direct numerical simulation and control of the flow over a backward facing ramp 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