LES Study of Synthetic Jet Frequency and Amplitude Effects on a Separated Flow

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2 LES Study of Synthetic Jet Frequency and Amplitude Effects on a Separated Flow ONERA Applied Aerodynamic Department Pierre-Yves Pamart, Julien Dandois, Eric Garnier, Pierre Sagaut 2

3 Introduction Separated flow LES computations Synthetic jet actuator LES computations of active separation control by synthetic jet 3

4 Introduction But Optimal frequency? Optimal amplitude? On which criteria? 4

5 Bibliography Bhattacharjee et al. (1986) Chun & Sung (1996) Yoshioka et al. (2001) Wengle et al. (2001) Dejoan & Leschziner (2004) Neumann & Wengle (2004) Optimal Strouhal equal to 0.2 for the reduction of separation length Seifert & Pack (2002): F + opt =1.6 Darabi & Wygnanski (2004): F + opt =1.5 Amitay & Glezer (2002) Glezer et al. (2005) High frequency = increase of the lift 5

6 Outline I Flow Configuration A Ramp topology B Actuator II Numerical methods III Results A Uncontrolled cases B Controlled cases C Actuator validation D Frequency and amplitude effects Conclusion 6

7 Outline I Flow Configuration A Ramp topology B Actuator II Numerical methods III Results A Uncontrolled cases B Controlled cases C Actuator validation D Frequency and amplitude effects Conclusion 7

8 I Ramp Topology Configuration Dandois et al. (2007) topology + extensions Step height h 20 mm Maximum slope 35 P Pa T 281 K M 0.33 δ BL at x/h = h Re θ 1510 Re h

9 I Actuator Actuator design criteria Frequency range F + [0.1,10] Amplitude range C µ [0.33%,1%] Synthetic jet formation Stroke length (Holman et al., Schuster et al.) Minimal stokes number (Holman et al., Schuster et al.) F + = f L UC U C µ = ρ j dv RMS 2 ρ L UC U 2 Resonance frequency far enough of F + max Dimension Slot width Slot height Cavity width Cavity height Value 0.55 mm 0.55 mm 2 x 0.55 mm 0.5 x 0.55 mm 9

10 Outline I Flow Configuration A Ramp topology B Actuator II Numerical methods III Results A Uncontrolled cases B Controlled cases C Actuator validation D Frequency and amplitude effects Conclusion 10

II Numerical Methods Numerical methods FLU3M code Finite volume Compressible Navier-Stokes LES + selective mixed scale model (Sagaut (2005)) Time step dt = 0.

11 II Numerical Methods Numerical methods FLU3M code Finite volume Compressible Navier-Stokes LES + selective mixed scale model (Sagaut (2005)) Time step dt = h/u Spatial scheme of Mary & Sagaut (2002) Mesh Computation domain length: 24h Spanwise extent: 4h Height extent on the inflow plane: 10h 12x10 6 cells Δx + max = 50, Δy+ min =0.5 and Δz+ = 18 Inflow condition of the turbulent boundary layer 11 Modified Synthetic Eddy method of Pamiès et al. (2009)

12 Outline I Flow Configuration A Ramp topology B Actuator II Numerical methods III Results A Uncontrolled cases B Controlled cases C Actuator validation D Frequency and amplitude effects Conclusion 12

13 III Uncontrolled case Unsteady 13

14 III Uncontrolled case Statistics 14 Result Value Separation position x s /h 0.48 Reattachment position x r /h 4.89 Separation length L UC /h 4.41 Mean bubble surface S UC /(L UC h) 0.39 F + = Hz St bh = Hz

15 III Uncontrolled case Spectral analysis U umin (x) Fkh (x) = δω (x) U umin (x) δω (x) = u (x, y) max y y 15

16 III Controlled cases F St bh Cµ 0 Cµ Cµ Α Cµ Β 3 amplitudes cases: Cµ 0 = 0.33 % V jet = 39.9 m.s -1 Cµ A = 0.66 % V jet = 56.5 m.s -1 Cµ B = 1.00 % V jet = 69.2 m.s -1 16

17 III Actuator validation Actuator validation: V rms constant on F + [0.1;10] Limited resonance effect V rms profiles Synthetic jet formation Results: V rms quasi constant on F + [1;6] for each amplitude Small resonance effect for F + =10 Viscous effects for F + <1 ( Stokes <10, see Zhou et al. (2009)) 17

18 III Actuator validation Synthetic jet formation: F + = 0.5 F + = 10 18

III Forcing Results Separation and reattachment positions Optimization criterion: To minimize the reattachment point position To delay the separation point position Criterion estimation: Wall

19 III Forcing Results Separation and reattachment positions Optimization criterion: To minimize the reattachment point position To delay the separation point position Criterion estimation: Wall friction cancellation τ y= 0 (x) = µ u(x,0) y Results: + v(x,0) x y= 0 Criteria Cµ0 CµA CµB Separation point position F + = 0.1 St bh = 0.02 Reattachment point position F + = 1.2 St bh = 0.20 F + = 1.2 St bh = 0.25 F + = 1.5 St bh = 0.25 For F + 2 appearance of a secondary bubble For C µ Cµ B and for F + 3 appearance of a third bubble 19

20 III Forcing Results Separation length Optimization criterion: To minimize the separation length Criterion estimation: Difference between the last reattachment and the first separation points positions Results: Case F + opt. St bh opt. L/L UC min. Cµ % Cµ A % Cµ B % Amplitude saturation: C µ Cµ A for F

21 III Forcing Results Mean bubble surface Optimization criterion: To minimize the separation bubble area Criterion estimation: Surface given by the zero-mass-flux line Results: Case F + opt. St bh opt. S/S UC min. Cµ % Cµ A % Cµ B % Amplitude saturation: C µ Cµ A for F

22 III Forcing Results Mean bubble surface Frequency effect: 22 Uncontrolled flow F+ = 0.5 Cµ0 F+ = 1.5 Cµ0 F+ = 10 Cµ0

23 III Forcing Results Mean bubble surface Amplitude effect: Uncontrolled flow F + = 1.5 Cµ 0 F + = 1.5 Cµ A F + = 1.5 Cµ B 23

III Forcing Results Wall Pressure Coefficient Optimization criterion: To maximize the wall pressure coefficient Criterion estimation: Local wall

24 III Forcing Results Wall Pressure Coefficient Optimization criterion: To maximize the wall pressure coefficient Criterion estimation: Local wall pressure C p (x) coefficient given by Results: C p (x) = p(x,0) p 1 2 ρ 2 U Case F + opt. St bh opt. Cµ Cµ A Cµ B

III Forcing Results Integral of Pressure Fluctuations Optimization criterion: To minimize the integral of pressure fluctuations Criterion estimation: Local integral

25 III Forcing Results Integral of Pressure Fluctuations Optimization criterion: To minimize the integral of pressure fluctuations Criterion estimation: Local integral of pressure fluctuations C prms (x) given by: Results: Case F + opt. St bh opt. C Prms (x) = y max y wall p rms (x, y) p dy Cµ Cµ A Cµ B

III Forcing Results Integral of Turbulence Level Optimization criterion: To minimize the integral of turbulence level Criterion estimation: Local integral of turbulence C Tu (x) level

26 III Forcing Results Integral of Turbulence Level Optimization criterion: To minimize the integral of turbulence level Criterion estimation: Local integral of turbulence C Tu (x) level given by Results: with Tu(x, y) = 1 U 2 and 3 k(x, y) k = u rms C Tu (x) = v rms 2 y max y wall Tu(x, y)dy 2 + w rms Case F + opt. St bh opt. Cµ Cµ A Cµ B

III Forcing Results Maxima of Turbulent Kinetic Energy Optimization criterion: To minimize the maxima of turbulent kinetic energy Criterion

27 III Forcing Results Maxima of Turbulent Kinetic Energy Optimization criterion: To minimize the maxima of turbulent kinetic energy Criterion estimation: Maximum of the turbulent kinetic energy given by max y (Tu(x, y)) Results: Case F + opt. St bh opt. Cµ Cµ A Cµ B

28 III Forcing Results Drag Pressure Optimization criterion: To minimize the pressure drag for -2 x/h 10 Criterion estimation: Integration of the local pressure coefficient C p (x) on the interval x/h [-2;10] + projection on the x axis Results: Case F + opt. St bh opt. Cx p /Cx p UC min. Cµ % Cµ A % Cµ B % Amplitude effect for: C µ > Cµ A 28

29 III Forcing Results Recapitulation Criteria Cµ 0 Cµ A Cµ B Observations Separation point position F + = 0.1 For F + 2 appearance of a secondary bubble For C µ Cµ B and for F + 3 appearance of a third bubble Reattachment point position F + = 1.2 F + = 1.2 F + = 1.5 Separation length F + = 1.2 F + = 1.2 F + = 1.5 Amplitude effect on optimal frequency Separation bubble area F + = 1.5 F + = 1.5 F + = 1.5 Amplitude saturation for C µ Cµ A and F + 2 Wall pressure coefficient F + = 1.5 F + = 1.5 F + = 1.5 Integral of turbulence level F + = 3.0 F + = 1.2 F + = 1.2 Amplitude effect on optimal frequency Pressure fluctuation profile F + = 1.2 F + = 1.2 F + = 1.2 Maxima of TKE F + = 3.0 F + = 2.0 F + = 2.0 Amplitude effect on optimal frequency Pressure drag F + = 3.0 F + = 3.0 F + = 3.0 Amplitude effect for C µ > Cµ A Mean bubble circulation F + = 1.5 F + = 1.5 F + = 1.5 Amplitude saturation for C µ Cµ A and F

30 Outline I Flow Configuration A Ramp topology B Actuator II Numerical methods III Results A Uncontrolled cases B Controlled cases C Actuator validation D Frequency and amplitude effects Conclusion 30

31 Conclusion LES computations for studying the frequency and amplitude effect Actuator well designed Optimal frequency is relative to the chosen criterion No frequency is optimal for every chosen criterion In the vicinity of F + =1.2~1.5 (St bh =0.2~0.25): most of criteria minimized Validated by the literature Amplitude effect seems to be monotonic between Cµ 0 and Cµ A Nonlinearities may appear for Cµ > Cµ A : saturation, optimal frequency shift,... Frequency first parameter to set 31

32 Perspectives Understand the physics phenomenon of control on this separation Closed-loop control 32

33 References Amitay, M., and Glezer, A., Role of actuation frequency in controlled flow reattachment over stalled airfoil, AIAA Journal, Vol. 40, No. 2, 2002, pp Bhattacharjee, S., Scheelke, B., and Troutt, T.R., Modification of vortex interactions in a reattaching separated flow, AIAA Journal, Vol. 24, No. 4, 1986, pp Chun, K.B., and Sung, H.J., Control of turbulent separated flow over a backward facing step by local forcing, Experiments in fluids, Vol. 21, No. 6, 1996, pp Dandois, J., Garnier, E., and Sagaut, P., Numerical simulation of active separation control by synthetic jet, Journal of fluid mechanics, Vol. 574, 2007, pp. 25, 58. Darabi, A., and Wygnanski, I., Active management of naturally separated flow. Part 1: the forced reattachment process, Journal of fluid mechanics, Vol. 510, 2004, pp. 105, 129. Darabi, A., and Wygnanski, I., Active management of naturally separated flow. Part 2: the separation process, Journal of fluid mechanics, Vol. 510, 2004, pp Dejoan, A., and Leschziner, M.A., Large eddy simulation of periodically perturbed separated flow over a backwardfacing step, International Journal of Heat and Fluid Flow, Vol. 25, 2004, pp Glezer, A., Amitay, M., and Honohan, A.M., Aspects of low and high frequency aerodynamic flow control, AIAA Journal, Vol. 43, No. 7, 2005, Holman, R., Utturkar, Y., Mittal, R., Smith, B.L., and Cattafesta, L., Formation criterion for synthetic jets, AIAA Journal, Vol. 43, No. 10, 2005, pp Lund, T.S., Wu, X., and Squires, K.D., Generation of turbulent inflow data for spatially developing turbulent boundary layer simulations, Journal of computational physics, Vol. 40, No. 2, 1998, pp Mary, I. and Sagaut, P., Large eddy simulation of a flow around an airfoil near stall, AIAA Journal, Vol. 40, No. 6, 2002, pp Neumann, J., and Wengle, H., Coherent structures in controlled separated flow over sharp edged and rounded steps, Journal of Turbulence, Vol. 5, 2004, pp Pamiès, M., Weiss,.P.E., Garnier, E., Deck, S., and Sagaut, P., Generation of synthetic turbulent inflow data for large eddy simulation of spatially evolving wall bounded flows, Physics of fluids, Vol. 21, No. 4, 2009, pp

34 References Sagaut, P., LargeEddy Simulation for Incompressible Flows, An Introduction, 3rd ed, Springer, Berlin, Schuster, J.M., and Smith, D.R., A Study of the formation and scaling of a synthetic jet, 42nd AIAA Aerospace Sciences Meeting and Exhibit, Vol200490, AIAA,2004. Seifert, A., Bachar, T., Koss, D., Shepshelovich, M., and Wygnanski, I, Oscillatory blowing: a tool to delay boundary layer separation, AIAA Journal, Vol. 31, No. 11, pp Seifert, A., and Pack, L.G., Active flow separation control on wall mounted hump at high Reynolds numbers, AIAA Journal, Vol. 40, No. 7, 2002, pp Wengle, H., Huppertz, A., Bärwolff, G., and Janke, G., The manipulated transitional backward facing step flow: an experimental and direct numerical simulation investigation, European journal of mechanics. B, Fluids, Vol. 20, No. 1, 2001, pp Yoshioka, S., Obi, S., and Masuda, S., Organized vortex motion in periodically perturbed turbulent separated flow over a backward facing step, International Journal of Heat and Fluid Flow, Vol. 22, 2001, pp Yoshioka, S., Obi, S., and Masuda, S., Turbulence statistics of periodically flow over a backward facing step, International Journal of Heat and Fluid Flow, Vol. 22, 2001, pp. 393, 401. Zhou, J., Tang, H., and Zhong, S., Vortex rollup criterion for synthetic jets, AIAA Journal, Vol. 47, No. 5, 2009, pp

35 Questions? 35

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