LARGE EDDY SIMULATION AND FLOW CONTROL OVER A 25 RAMP MODEL

Transcription

1 LARGE EDDY SIMULATION AND FLOW CONTROL OVER A 25 RAMP MODEL 09/11/2017 Paolo Casco Stephie Edwige Philippe Gilotte Iraj Mortazavi

2 LES and flow control over a 25 ramp model : context 2 Context Validation of flow control simulation with Acusolve LES solver on a fully characterized experimental detached flow on a ramp inclined at 25 Comparison with an active flow control experiments performed with synthetic jets by the PRISME Institute for the GDR Contrôle des Décollements Effect of the synthetic jet frequencies on the flow with a Sparse Promoting DMD analysis. Work initiated with a master training partially supported by the GDR

3 CONTENTS Context Numerical setup Uncontrolled wake flow Flow control DMD Conclusions and perspectives

4 LES and flow control over a 25 ramp model : experimental setup 4 GDR ramp model in PRISME Malavard wind tunnel (Orléans) 25 Ramp flow experimental analysis with synthetic jet actuator at x=0 15 h 2 h 18 h PIV and LDV probe for velocity measurements and pressure acquisition on longitudinal and transversal monitoring points 20 h

5 LES and flow control over a 25 ramp model : numerical setup 5 Numerical domain : Boundary layer length reduction of the numerical domain : 4h instead of 15h Introduction of the measured inflow condition Width reduction with periodic condition on lateral sides : 4h instead of 20h Inlet velocity profile Computational domain

6 LES and flow control over a 25 ramp model : numerical setup 6 Inflow boundary layer conditions at x = -4 h Introduction of the experimental velocity and turbulence intensity profiles Velocity profile at X = -4 h Longitudinal turbulent intensity at X = -4 h (estimated from DNS of Schlatter) Modeled eddy viscosity Friction coefficient C f = u τ 0.5ρU 2 Close to PRISME measurements of C f = (*) = corresponds at inflow to the imposed gradient (*) Stella F, Mazellier N, Kourta A. (2017) Scaling of separated shear layers: An investigation of mass entrainment. Journal of Fluid Mechanics, 826,

7 LES and flow control over a 25 ramp model : numerical setup 7 Modeled boundary layer at -2.5 h : with wall function In the first layer, C f = , computed with a laminar viscous sub layer model, corresponding to a u τ = 0.34m/s for a first layer at 0.2mm With a more refined mesh, C f = 1, with u τ = 0.6 m/s for a first layer at 0.06 mm and with Y + = 3 which is still lower than the measurement value of 1.1 m/s Experiment 60 millions cells mesh 100 millions cells mesh Velocity profile at X = -2,5H velocity normalized with the experimental friction velocity No resolved U rms in the boundary layer due to the wall function

8 LES and flow control over a 25 ramp model : numerical setup 8 Modeled boundary layer at -2.5 h : without wall function With a more refined mesh, without wall model, C f = with u τ = 0.9 m/s for a first layer at 0.06 mm and which is closer to the measurement value of 1.1 m/s With turbulence wall model Without turbulence wall model Impact of the turbulence wall model on the friction coefficient (Green curve gives the best results) Comparison of longitudinal fluctuations with turbulence wall model and without wall model (No Urms with or without wall function coming from the boundary layer) No resolved U rms above the high cutoff frequency of the dynamic Smagorinsky model corresponding to the fine mesh size below 1mm in the boundary layer and at the detachment edge

9 LES and flow control over a 25 ramp model : numerical setup 9 Modeled boundary layer at -2.5 h : without wall function In the first layer, C f = , computed with a laminar viscous sub layer model, corresponding to a u τ = 0.34m/s for a first layer at 0.2mm With a more refined mesh, without wall model, C f = with u τ = 0.9 m/s for a first layer at 0.06 mm and which is closer to the measurement value of 1.1 m/s Experiment 100 millions cells mesh without wall model Velocity profile at X = -2,5H velocity adimensioned with the experimental friction velocity Low impact on shear layer momentum thickness

10 LES and flow control over a 25 ramp model : numerical setup 10 Numerical model 60 millions tetrahedral elements 0.7seconds of simulation with a sampling frequency of 2000Hz 60 millions cells mesh

11 25 ramp flow simulation : Numerical setup 11 LES numerical model with a turbulence subgrid scale model Filtered Navier-Sokes equations solved with a finite element solver based on Least Square Galerkin approximation (AcuSolve) with respect to a grid cutoff frequency Δ of 1mm (see table) ρ u t + ρ u u = p + μ u + u = 0 1 ρ τ + ρf Eq. 1 ν t = C s Δ 2 2S ijs ij Eq. 2 With u, p grid filtered velocity and pressure variables τ = 2μ t S the subgrid scale stress term S = S ij = 1 2 ju i + i u j the strain rate tensor C s = 0.3 Smagorinsky constant Turbulent characteritics of 25 ramp detached flow Characteristic parameters Definition Values H [m] 1,00E-01 U [m/s] 3,00E+01 Re H [-] 2,06E+05 Dissipation rate [m 2 /s 3 ] eps = U^3/H 2,70E+05 Kolmogorov length scale [m] L kolm = H*ReH^-3/4 1,03E-05 Dissipation length scale [m] Ldi = 60*L kolm 6,20E-04 Dissipation velocity [m/s] U Ldi = B115(eps*Ldi)^(1/3) 5,51E+00 Time of dissipation scales [s] T Ldi =(nu/eps)^0,5 = Ldi/U Ldi 1,12E-04 Frequency of dissipation scales [Hz] F Ldi = 1/T Ldi 8,89E+03

12 LES and flow control over a 25 ramp model : numerical setup 12 Dynamic LES numerical model : Local level of turbulence C s x, t is introduced into ν t thanks to an additional test filter with a higher frequency Δ equal to 2Δ as proposed by Germano ν t = C s x, t Δ 2 2S ijs ij Eq. 1 The dynamic Smagorinsky coefficient is obtained thanks to the Germano identity involving the Leonard tensor L = T τ with T the stress tensor associated to the Δ filter and τ the stress tensor associated to the Δ Replacing the Smagorinsky formulation in both T and τ, the Leonard tensor can be expressed as : L ij S ij = 2C s x, t Δ 2 S S ij S ij Δ 2 S S ij S ij Eq. 2 which leads to the value of C s x, t Resolved and modeled scale with Dynamic LES

13 PSD[Vx] U 2 LES and flow control over a 25 ramp model : numerical setup 13 LES numerical model discussion : On the opposite of the classical Smagorinsky model, the Dynamic Samgorinsky model will increase the transfer of energy at the grid cutoff Δ based on local turbulent resolved scale below Δ This dissipated turbulence energy level at the cutoff frequency Δ will be upper than in the constant Smagorinsky model The iterative procedure for the normalization of the dissipation rate will induce higher resolved fluctuations Classical Smagorinsky Classical Smagorinsky Dynamic Smagorinsky Dynamic Smagorinsky Longitudinal turbulence intensity PSD of Vx in shear turbulent region

14 PSD Vx. Δf U rms LES and flow control over a 25 ramp model : uncontrolled wake flow 14 Wake flow longitudinal velocity fluctuations level validation: The normalized power energy spectra has been computed with the same average acquisition frequency used in experiment According to spectra comparison, the numerical dissipating value are to the experiment below St = 3 Experiment Vx experiment [Thacker] Vx Dynamic Smagorinsky Numerical result Longitudinal turbulence intensity St = f. x r /U PSD of Vx in shear turbulent region The computed velocity fluctuations at detached edge is underestimated due to the modeled boundary layer

15 LES and flow control over a 25 ramp model : uncontrolled wake flow 15 Time average wake flow validation: Similar reattachment value between experiment and numerical result (left) Same level of pressure on Y0 wall profile but higher gradient on the top ridge (right) : Influence of the small shear layer fluctuations? Experiment Numerical result Cp = P P ref 0.5ρV 2 ref Time average velocity magnitude Time average pressure coefficient distribution and profile in Y0 cut plane

16 LES and flow control over a 25 ramp model : flow control 16 Flow control Synthetic jet actuator of 1mm width at 1mm from ramp edge Synthetic control (C mu = 0. 04; F + = 0. 2 ) V jet F + = f. h U ref Monitoring point C Wall Cp value at the monitoring point C and integrated ramp force in x direction Selected configuration C μ = 0.04 ; F + = 0.2 ΔCp ΔC Xp Joseph P, Stéphane Loyer S, Mazellier N, Azeddine Kourta A, (2016) Control of GDR ramp separation with synthetic jet, presentation PRISME, journée du GDR

17 LES and flow control over a 25 ramp model : flow control 17 Flow control results on C Xp Same C Xp reduction of 0.05 obtained on integrated ramp at F + = 0.2 ΔC Xp Uncontrolled flow AFC (C mu = 0. 04; F + = 0. 2 ) C Xp = 0.1 C Xp = 0.05 Time average Cp in Y0 cut-plane Important change of fluctuation energy at detachment point Uncontrolled flow AFC (C mu = 0. 04; F + = 0. 2 ) Longitudinal turbulence intensity

18 LES and flow control over a 25 ramp model : flow control 18 Flow control results on Cp Gain on Cp of 0.13 in numerical result lower than experimental gain of ΔCp From now, the analysis will focus on control at F + = 0.2 (best reduction) C p = 0.03 C p ref = 0.1 C p = 0.15 C p ref = 0.12 Numerical time average Cp profiles Experimental time average Cp (*) (*) Joseph P, Stéphane Loyer S, Mazellier N, Azeddine Kourta A, (2016) Control of GDR ramp separation with synthetic jet, presentation PRISME, journée du GDR

19 LES and flow control over a 25 ramp model : DMD 19 Sparse Promoting Dynamic Mode Decomposition : Method Data on Y0 cut plane ( nodes) in a frequency range of [2Hz 400Hz] Considering the matrices Ψ 0 = U 0 U N 1 and Ψ 1 = U 1 U N with U i snapshots at time step i Singular value decomposition Ψ 0 = UΣV (with Σ the singular values) From linearization formulation Ψ 1 = AΨ 0 and by projection of A in the proper orthogonal base, the DMD matrix is computed as : F dmd = U Ψ 1 VΣ 1 Resolution of the eigenvalues μ m and eigenvectors Y m of F dmd : F dmd Y m = μ m Y m Modes are obtained by projection in 3D space : Φ m x = UY m C (*) Schmid P.J. (2010). Dynamic mode decomposition of numerical and experimental data, J. Fluid. Mech., Cambridge University Press, Cambridge, UK, vol. 656, pp

20 LES and flow control over a 25 ramp model : DMD 20 Sparse Promoting Dynamic Mode Decomposition : characteristics The velocity Ψ 1 rec is reconstructed with Φ m and μ m such as : Reconstruction Ψ 1 rec = With frequency f m = I ln μ m 2πΔt ; Growth rate σ m = R ln(μ m) Δt ; The amplitude α m is the solution of the sparsity promoting problem minimizing the cost function J α = Ψ rec 1 Ψ 1 constraint to a maximization of zeros amplitudes modes (proposed in *) σ m ~0 Periodic behavior; σ m < 0 Decaying instability; σ m > 0 Energy production (*) Mihailo R. Jovanovic, Peter J. Schmid, Joseph W. Nichols. Sparsity-promoting dynamic mode decomposition, Physics of Fluids, American Institute of Physics, 26 (2), 2014.

21 LES and flow control over a 25 ramp model : DMD 21 Sparse Promoting optimization resolution with ADMM approach Augmented Lagrangian formulation for α optimization : L α, β, λ = J α + γg β λ α β + α β λ + ρ α β 2 2 Residual minimization J α = Ψ 1 rec Ψ 1 Sparsity promoting constraint : g β = β With γ : Weight of the sparsity promoting constraint λ : Vector of Lagrange multipliers ρ : Quadratic penalty coefficient (for convex problem) Alternating Direction Method of Multipliers to minimize L : Iterative algorithm using a dual ascend method Coupling of residual optimization with sparsity promoting problem : α β = 0 Optimal result J α Reconstruction residual

22 LES and flow control over a 25 ramp model : DMD 22 Uncontrolled flow modal analysis 2 periodic energetic modes at F + = 0.14 and F + = 0.46, corresponds to the best C p reduction 1 decaying turbulent instability at F+=0.6 corresponds to the best C Xp experimental reduction Non dimensional frequency : F + = f m.h V ref F + = 0.14 And σ Φ the standard deviation of mode Φ m Φ σ Φ F + = 0.46 F + = 0.59

23 LES and flow control over a 25 ramp model : DMD 23 Uncontrolled flow modal analysis Wake vortex impacting the ramp wall correlated to structures attached to the top of the ramp edge at F + = 0.14 Wake periodic fluctuations starting from the shear layer at F + = 0.46 Turbulent dissipating instability in the shear layer at F += 0.59 Φ z /σ Φ F + = 0.14 F + = 0.46 F + = 0.59 Vertical velocity component of DMD modes

24 LES and flow control over a 25 ramp model : DMD 24 Uncontrolled flow modal analysis Truncated reconstruction based on 30 pairs of modes ( 30 frequencies) DMD modes Modes for truncated reconstruction Reconstruction with truncated model DMD modes amplitudes Instantaneous computed snapshots vs reconstructed snapshots

25 LES and flow control over a 25 ramp model : DMD 25 Controlled flow at F + = 0.2 modal analysis Emergence of a decaying instability at F + = 0.22 Main modes of uncontrolled flow at at F + = 0.14 and F + = 0.59 has been damped Φ /σ Φ F + = 0.23 F + = 0.57

26 LES and flow control over a 25 ramp model : DMD 26 Work in progress DMD spectra is modified by AFC DMD spectra of uncontrolled flow DMD spectra of controlled flow at F + = 0.2 Reduced order model has to be consistent on the actuator frequency range DMD with control * System identification based on a preliminary simulation with a pseudo randomize boundary signal (large band frequency actuator ) Phase decomposition of the database combined with actuator signal to construct a reduce order model (*) Schmid P.J. (2010). Dynamic mode decomposition of numerical and experimental data, J. Fluid. Mech., Cambridge University Press, Cambridge, UK, vol. 656, pp

27 LES and flow control over a 25 ramp model : conclusions 27 Conclusions : Dynamic Smagorinky LES model enables to compute a satisfactory dissipative energy in the wake with a good agreement to experiment Controlled flow simulation is efficient especially at the most detailed case of F + = 0.2 SPDMD shows the influence of the controlled flow frequency, allowing to have a better understanding of the shear flow dynamics Perspectives : Even if the momentum thickness shear layer is well resolved, the upstream boundary layer resolution must be improved A system identification using DMD with flow control will be applied to the ramp model and to a simplified car model Final target is to perform closed-loop flow control on a real car model

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