Direct numerical simulation and control of the flow over a · PDF fileDirect numerical...

Direct numerical simulation and control ofthe flow over a backward facing ramp

Ch-H. Bruneau, M.Jedouaa, K.Khadra, I. Mortazavi2

1IMB Université de Bordeaux, France

2IMB Institut polytechnique de Bordeaux,France

Inria Bordeaux Sud Ouest MC2 project

3rd GDR “Contrôle des décollements”Symposium

Numericalsimulation and

control of the flowover a backward

facing ramp

Ch-H. Bruneau,M.Jedouaa,K.Khadra,

I. Mortazavi

Motivations

Computationaldomain andnumerical tools

Analysis of theuncontrolled flow

Active control

Conclusion

Outline

Motivations

Computational domain and numerical tools

Analysis of the uncontrolled flow

Active control

Conclusion



facing ramp


I. Mortazavi

Motivations



Active control

Conclusion

Outline

Motivations



Active control

Conclusion



facing ramp


I. Mortazavi

Motivations



Active control

Conclusion

Motivations

On a ground vehicle the rear window is responsible for:

• 30 to 45 % of the total vehicle drag→ Real impact on fuel consumption and CO2 emission.

I Focus on the recirculation zone behind a car rear-windowusing a two -dimensional backward facing ramp which is abenchmark of GDR “Contrôle des décollements”

Aim of the study :

I Simulation and analysis of the flow behaviour over thebackward facing ramp

I Control the flow using active procedures



facing ramp


I. Mortazavi

Motivations

Computationaldomain andnumerical toolsMathematical Modelization

Numerical algorithms

Numerical data


Active control

Conclusion

Outline

Motivations



Active control

Conclusion



facing ramp


I. Mortazavi

Motivations



Numerical data


Active control

Conclusion

Computational domain Ω

I Ω = (20× 5)

I Height of the step h = 1I Inclination angle α = 25

I The solid body stay stillI The fluid is supposed to be incompressible



facing ramp


I. Mortazavi

Motivations



Numerical data


Active control

Conclusion

Adimensional Navier-Stokes (u,p) incompressible +penalisation1:

∂tU + (U · ∇)U − 1Re

∆U +UK

+∇p = 0 in ΩT

div U = 0 in ΩT

U(0, .) = U0 in Ω

where K is the non dimensional coefficient of permeability ofthe medium without gravity,Re = U∞h

µ is the non dimensional Reynolds number, Ω is thefull domain including the solid body, I = (0,T), ΩT = Ω× I.Numerically:

I In the fluid: K = 1016,I In the solid body: K = 10−8.

1Bruneau and Angot [99]



facing ramp


I. Mortazavi

Motivations



Numerical data


Active control

Conclusion

Boundary conditions

I U = U∞ = (u∞, 0) on the entrance section ΓD

I U = 0 on Γ0

I σ(U, p)n + 12(U · n)−(U − Uref ) = σ(Uref , pref )n on the

artificial frontiers2 ΓN ,where σ(U, p) = 1

Re(∇U +∇Ut)− pI n is the unitnormal pointing outside of the domain and (Uref , pref ) is areference flow.

I The no-slip boundary layers on the solid are obtainedusing the penalisation method

2Bruneau [2000]



facing ramp


I. Mortazavi

Motivations



Numerical data


Active control

Conclusion


I The space discretization is performed on staggered gridswith strongly coupled equations.

I Second-order Gear scheme in time.I Second-order centered finite differences are used for the

linear terms→ the divergence-free equation isdiscretized on the pressure points.

I The convection terms are approximated by an upwindthird order scheme.

I The resolution is achieved by a V-cycle multigridalgorithm coupled to a cell-by-cell relaxationprocedure.



facing ramp


I. Mortazavi

Motivations



Numerical data


Active control

Conclusion

Numerical data

I Height of the step h = 1↔ h = 0.1m

I Upstream velocity U∞ = 1↔ U∞ = 20m/s

I Reynolds number: Re = 1, 23.105



facing ramp


I. Mortazavi

Motivations


Analysis of theuncontrolled flowGrid convergence

Behaviour of the solution

Study of the mean flow

Active control

Conclusion

Outline

Motivations



Active control

Conclusion



facing ramp


I. Mortazavi

Motivations





Active control

Conclusion

Grid convergence

I Simulation time T = 1000I Three different grids:

• G7: (1280× 320) → δx = 1.5625.10−2

• G8: (2560× 640) → δx = 7.8125.10−3

• G9: (5120× 2560) → δx = 3.90625.10−3

Resolution Mean kinetic energy Recirculation lengthG7 85 5.6G8 78 5.1G9 76 4.9

Table: Mean kinetic energy and recirculation length



facing ramp


I. Mortazavi

Motivations





Active control

Conclusion

Grid convergence

Mean velocity isolines Mean pressure isolines

G7

G8

G9

→ The grid used for the simulations is G8 (δx = 7.8125.10−3)



facing ramp


I. Mortazavi

Motivations





Active control

Conclusion


T = 50 T = 60

T = 70 T = 80

T = 90 T = 100

Figure: Evolution of vorticity field for uncontrolled flow.



facing ramp


I. Mortazavi

Motivations





Active control

Conclusion


Mean pressure field.

Mean vorticity field.



facing ramp


I. Mortazavi

Motivations





Active control

Conclusion

Study of the mean flowMean velocity streamlines

Numerical results

Experimental results( R.Joussot and A.Tracker. Orléans)

→ Recirculation length:I Numerical results :5.1I Experiments: 5.3



facing ramp


I. Mortazavi

Motivations





Active control

Conclusion


Mean velocity profiles for the uncontrolled flow.

→ The boundary layer thickness at X/h = 10 (the top edge ofthe step) is 0.031 (3.1mm).



facing ramp


I. Mortazavi

Motivations



Active controlControl with continuous jets

Control with synthetic jets

Synthesis

Conclusion

Outline

Motivations



Active control

Conclusion



facing ramp


I. Mortazavi

Motivations





Synthesis

Conclusion

Active Control

I Two types of jets studied:

Continuous jets→ Uj = AU∞ Synthetic jets → Uj = AU∞sin(2πfT)

where:

• Uj 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 with50Hz)

I Three different configurations of jets:

vertical jet normal jet horizontal jet



facing ramp


I. Mortazavi

Motivations





Synthesis

Conclusion

Active ControlControl with continuous jets

Vertical jet control

Normal jet control

Horizontal jet control

Figure: Mean velocity streamlines



facing ramp


I. Mortazavi

Motivations





Synthesis

Conclusion

Active ControlControl with continuous jets

Figure: Mean velocity profile at line X/h = 11 for uncontrolled (blueline) and controlled flows using uniform jets (black for horizontal jetcontrol, red for vertical jet control and green for normal jet control).



facing ramp


I. Mortazavi

Motivations





Synthesis

Conclusion

Active ControlControl with synthetic jets


Normal jet control


Figure: Mean velocity streamlines



facing ramp


I. Mortazavi

Motivations





Synthesis

Conclusion

Active ControlControl with synthetic jets


Normal jet control


Figure: Mean vorticity fields



facing ramp


I. Mortazavi

Motivations





Synthesis

Conclusion

Active ControlSynthesis

Vertical Normal HorizontalLr for continuous jet control 3.7 3.2 2.8Lr for synthetic jet control 4.4 3.1 2.6

Recirculation length Lr for various controls (This length for thenatural flow is 5.1).

Vertical Normal HorizontalFp for continuous jet control 0.10 0.09 0.09Fp for synthetic jet control 0.14 0.09 0.09

Mean pressure force on the back wall Fp for various controls (Thispressure force is equal to 0.14 for the natural flow ).

→ Horizontal and normal jets are the most efficient



facing ramp


I. Mortazavi

Motivations



Active control

Conclusion

Outline

Motivations



Active control

Conclusion



facing ramp


I. Mortazavi

Motivations



Active control

Conclusion

ConclusionI The main characteristics of the uncontrolled flow are well

capturedI Two types of jets studied:

• Continuous jet

• Synthetic jet

→ Similar results except for the vertical jet

I 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 ofthe recirculation zone



facing ramp


I. Mortazavi

Motivations



Active control

Conclusion

Philippe Angot, Charles-Henri Bruneau, Pierre FabrieA penalization method to take into account obstacles inincompressible viscous flowsNumerische Mathematik,1999

C.H. Bruneau, P. Gillieron ,I. MortazaviFlow manipulation around the Ahmed body with a rearwindow using passive strategiesCompte Rendu Acad. des Sciences, 2007

Charles-Henri Bruneau, Emmanuel Creuse, DelphineDepeyras, Patrick Gillieron, Iraj MortazaviActive procedures to control the flow past the Ahmed bodywith a 25 rear windowInt. J. of Aerodynamics,2011

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