Advertisement

Unsteady Behavior of a Backward-facing Step in Forced Flow

  • Camila Chovet
  • Marc Lippert
  • Laurent Keirsbulck
  • Jean-Marc Foucaut
Article

Abstract

The unsteady behaviour of a turbulent flow (Reh = 30450) over a backward-facing step was investigated under sinusoidal actuation. Non-time-resolved Piv and time-resolved pressure measurements were done simultaneously to analyse the dynamical aspects. Initial measurements were made varying the periodic forcing (Strouhal number) based on the step height, \(St_{a}\), from 0.045 to 0.453. Results suggest that an excitation at \(St_{a}= 0.226\), associated to the shedding frequency, leads to a decrease of the external reattachment length \(L_{r}\) and an increase of the internal separation length \(X_{r}\). A further study of both, the natural and optimal frequency (among the tested) cases is done using modal decomposition techniques; this method separates the dominant spectral contributions. The spectral decomposition showed an increasing peak related to the shedding phenomena. Comparative results highlighted the dynamical flow mechanism involved in forced flow and underlined that the energetic flow structure interactions is due to a periodic actuation close to the natural shedding frequency. This dynamical behaviour is finally confirmed with a phase averaging of the stochastic flow reconstruction showing convective structures induced by periodic forcing.

Keywords

Forcing frequency flow control Spectral analysis Pulsed micro-blowers Backward-facing step 

List of sympols

Ar

Recirculation area [m2]

Ar

Aspect ratio of the backward-facing step

Cp

Mean pressure coefficient

Cprms

Rms Pressure coefficient

Cμ

Momentum coefficient

δ99 %

Incoming boundary layer thickness [m]

Er

Expansion ratio of the flow configuration

fa

Actuation frequency [Hz]

Φn

nth Spatial Pod eigenfunction [m]

an

nth Pod temporal coefficient [s]

λn

nth Pod eigenvalue

E(f)

Psd of the wall pressure fluctuation

h

Step height [m]

Lr

External reattachment length [m]

Reδ

Reynolds number based on \(\delta \)

Reθ

Reynolds number based on \(\theta \)

Reh

Reynolds number based on h

Sjet

Cross-section of the micro-jets [m2]

Sref

Reference surface of the Bfs [m2]

Sta

Actuation Strouhal number based on h

Stθ

Actuation Strouhal number based on \(\theta \)

St

Strouhal number based on \(L_{r}\)

θ

Momentum thickness [m]

U0

Free-stream velocity [m/s]

ujet

Jet velocity [m/s]

Vjet

Jet velocity amplitude [m/s]

Xr

Internal separation length [m]

x, y, z

Spatial coordinates [m]

wz

Spanwise fluctuation vorticity [s− 1]

Ve

Actuation power supply [Volts]

VR

Velocity ratio

Aij, \(B_{ijk}\)

Stochastic estimation coefficients

Notes

Acknowledgements

This work was carried out within the framework of the CNRS Research Federation on Ground Transports and Mobility, in articulation with the Elsat2020 project supported by the European Community, the French Ministry of Higher Education and Research, the Hauts de France Regional Council. The authors gratefully acknowledge the support of these institutions.The authors declare that they have no conflict of interest.

References

  1. 1.
    Roos, F.W., Kegelman, J.T.: Control of coherent structures in reattaching laminar and turbulent shear layers. AIAA J. 24, 1956–1963 (1986)CrossRefGoogle Scholar
  2. 2.
    Barros, D., Borée, J., Noack, B.R., Spohn, A., Ruiz, T.: Bluff body drag manipulation using pulsed jets and Coanda effect. J. Fluid Mech. 805, 422–459 (2016)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Englar, R.J.: Advanced aerodynamic devices to improve the performance, economics, handling and safety of heavy vehicles. Tech. Rep. SAE Tech Paper 2001-01-2072 (2001)Google Scholar
  4. 4.
    Schmidt, H.J., Woszidlo, R., Nayeri, C.N., Paschereit, C.O.: Drag reduction on a rectangular bluff body with base flaps and fluidic oscillators. Exp. Fluids 56(7), 1–16 (2015)CrossRefGoogle Scholar
  5. 5.
    Cattafesta, L.N., Sheplak, M.: Actuators for active flow control. Annu. Rev. Fluid Mech. 43, 247–272 (2011)CrossRefzbMATHGoogle Scholar
  6. 6.
    Garrido, P.: Active Control of the Turbulent Flow Downstream of a Backward Facing Step with Dielectric Barrier Discharge Plasma Actuators. Thèse Mécanique Des Fluides. Université de Poitiers, Poitiers (2014)Google Scholar
  7. 7.
    Aubrun, S., McNally, J., Alvi, F., Kourta, A.: Separation flow control on a generic ground vehicle using steady microjet arrays. Exp. Fluids 51(5), 1177–1187 (2011)CrossRefGoogle Scholar
  8. 8.
    Rouméas, M., Gilliéron, P., Kourta, A.: Drag reduction by flow separation control on a car after body. Int. J. Num. Meth. Fluids 60(11), 1222–1240 (2009)CrossRefzbMATHGoogle Scholar
  9. 9.
    Yoshioka, S., Obi, S., Masuda, S.: Turbulence statistics of periodically perturbed separated flow over a backward-facing step. Int. J. Heat Fluid Flow 22, 393–401 (2001)CrossRefGoogle Scholar
  10. 10.
    Dejoan, A., Leschziner, M.A.: Large eddy simulation of periodically perturbed separated flow over a backward-facing step. Int. J. Heat Fluid Flow 25, 581–592 (2004)CrossRefGoogle Scholar
  11. 11.
    Glezer, A., Amitay, M., Honohan, A.M.: Aspects of low-and high-frequency actuation for aerodynamic flow control. AIAA J. 43(7), 1501–1511 (2005)CrossRefGoogle Scholar
  12. 12.
    Joseph, P., Amandolese, X., Edouard, C., Aider, J.-L.: Flow control using MEMS pulsed micro-jets on the Ahmed body. Exp. Fluids 54(1), 1–12 (2013)CrossRefGoogle Scholar
  13. 13.
    Park, H., Cho, J.-H., Lee, J., Lee, D.-H., Kim, K.-H.: Aerodynamic drag reduction of Ahmed model using synthetic jet array. SAE Int. J. Passeng. Cars - Mech. Syst. 6(1), 1–6 (2013)CrossRefGoogle Scholar
  14. 14.
    Yoshioka, S., Obi, S., Masuda, S.: Organized vortex motion in periodically perturbed turbulent separated flow over a backward-facing step. Int. J. Heat Fluid Flow 22, 301–307 (2001)CrossRefGoogle Scholar
  15. 15.
    Nishri, B., Wygnanski, I.: Effects of periodic excitation on turbulent flow separation from a flap. AIAA J. 36, 547–556 (1998)CrossRefGoogle Scholar
  16. 16.
    Seifert, A., Pack, L.G.: Oscillatory control of separation at high Reynolds numbers. AIAA J. 37, 1062–1071 (1999)CrossRefGoogle Scholar
  17. 17.
    Berk, T., Medjnoun, T., Ganapathisubramani, B.: Entrainment effects in periodic forcing of the flow over a backward-facing step. Phys. Rev. Fluids 2, 074605 (2017)CrossRefGoogle Scholar
  18. 18.
    Chun, K.B., Sung, H.J.: Control of turbulent separated flow over a backward-facing step. Exp. Fluids 21, 417–426 (1996)CrossRefGoogle Scholar
  19. 19.
    Dandois, J., Garnier, E., Sagaut, P.: Numerical simulation of active separation control by a synthetic jet. J. Fluid Mech. 574, 25 (2007)CrossRefzbMATHGoogle Scholar
  20. 20.
    Bhattacharjee, S., Scheelke, B., Troutt, T.R.: Modification of vortex interactions in a reattaching separated flow. AIAA J. 24, 623–629 (1986)CrossRefGoogle Scholar
  21. 21.
    Hasan, M.A.Z.: The flow over a backward-facing step under controlled perturbation : laminar separation. J. Fluid Mech. 238, 73–96 (1992)CrossRefGoogle Scholar
  22. 22.
    Chun, K.B., Sung, H.J.: Visualization of a locally-forced separated flow over a backward-facing step. Exp. Fluids 25, 133–142 (1998)CrossRefGoogle Scholar
  23. 23.
    Wengle, H., Huppertz, A., Bärwolff, G., Janke, G.: The manipulated transitional backward-facing step flow: an experimental and direct numerical simulation investigation. Eur. J. Mech. B. Fluids 20, 25–46 (2001)CrossRefzbMATHGoogle Scholar
  24. 24.
    Hung, L., Parviz, M., John, K.: Direct numerical simulation of turbulent flow over a backward-facing step. J. Fluid Mech. 330, 349–374 (1997)CrossRefzbMATHGoogle Scholar
  25. 25.
    Simpson, R.L.: Aspects of turbulent boundary-layer separation. Prog. Aerosp. Sci. 32, 457–521 (1996)CrossRefGoogle Scholar
  26. 26.
    De Brederode, V., Bradshaw, P.: Influence of the side walls on the turbulent centerplane boundary-layer in a squareduct. Trans. ASME I: J. Fluids Eng. 100, 91–96 (1978)Google Scholar
  27. 27.
    Ma, X., Geisler, R., Schröder, A.: Experimental investigation of separated shear flow under subharmonic perturbations over a Backward-Facing step. Flow Turbul. Combust. 99, 71 (2017)CrossRefGoogle Scholar
  28. 28.
    Chovet, C., Lippert, M., Keirsbulck, L., Foucaut, J.-M.: Dynamic characterization of piezoelectric microblowers for separation flow control. Sensors and actuators: A Physical 249, 122–130 (2016)CrossRefGoogle Scholar
  29. 29.
    Gautier, N., Aider, J.-L., Duriez, T., Noack, B.R., Segond, M., Abel, M.: Closed-loop separation control using machine learning. J. Fluid Mech. 770, 442–457 (2015)CrossRefGoogle Scholar
  30. 30.
    Mahesh, K.: The interaction of jets with crossflow. Annu. Rev. Fluid Mech. 45, 379–407 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Lumley, J.L.: The structure of inhomogeneous turbulent flows. Atmospheric Turbul. and Radio Wave Propagation (A.M. Yaglom and V.I. takarski, eds.), Moscow: Nauka 25, 166–178 (1967)Google Scholar
  32. 32.
    Chovet, C., Lippert, M., Keirsbulck, L., Foucaut, J.-M.: Dynamical aspects of a backward-facing step flow at large Reynolds numbers. Exp. Fluids 58(11), 162 (2017)CrossRefGoogle Scholar
  33. 33.
    Adrian, R.J., Moin, P.: Stochastic estimation of organized turbulent structure-homogeneous shear-flow. J. Fluid Mech. 190, 531–559 (1988)CrossRefzbMATHGoogle Scholar
  34. 34.
    Naguib, M., Wark, C.E., Juckenhofel, O.: Stochastic estimation and flow sources associated with surface pressure events in a turbulent boundary layer. Phys. Fluids 13, 2611 (2001)CrossRefzbMATHGoogle Scholar
  35. 35.
    Guezennec, Y.G.: Stochastic estimation of coherent structures in turbulent boundary-layers. Phys. Fluids A-Fluid 1(6), 1054–1060 (1989)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Murray, E., Ukeiley, L.S.: Estimation of the flow field from surface pressure measurements in an open cavity. AIAA J. 41, 969 (2003)CrossRefGoogle Scholar
  37. 37.
    Hudy, L.M., Naguib, A., Humphreys, W.M.: Stochastic estimation of a separated-flow field using wall-pressure-array measurements. Phys. Fluids 19, 024103 (2007)CrossRefzbMATHGoogle Scholar
  38. 38.
    Kostas, J., Soria, J., Chong, M.S.: Particle image velocimetry measurements of a backward-facing step flow. Exp. Fluids 33, 838–853 (2002)CrossRefGoogle Scholar
  39. 39.
    Scarano, F., Riethmuller, M.: Iterative multigrid approach in PIV image processing with discrete window offset. Exp. Fluids 26, 513–523 (1999)CrossRefGoogle Scholar
  40. 40.
    Farabee, M., Casarella, M.J.: Measurements of fluctuating wall pressure for separated/reattached boundary layer flows. ASME. J. Vib., Acoust., Stress, Reliab. Des. 108, 301 (1986)CrossRefGoogle Scholar
  41. 41.
    Castro, P., Haque, A.: The structure of a turbulent shear layer bounding a separation region. J. Fluid Mech. 179, 439 (1987)CrossRefGoogle Scholar
  42. 42.
    Driver, D.M., Seegmiller, H.L., Marvin, J.G.: Time-Dependent Behaviour of a reattaching shear layer. AIAA J. 25, 914–919 (1987)CrossRefGoogle Scholar
  43. 43.
    Heenan, A.F., Morrison, J.F.: Passive control of pressure fluctuations generated by separated flow. AIAA J. 36, 1014–1022 (1998)CrossRefGoogle Scholar
  44. 44.
    Li, Z., Bai, H., Gao, N.: Response of turbulent fluctuations to the periodic perturbations in a flow over a backward facing step. Theor. Appl. Mech. Lett. 5(5), 191–195 (2015)CrossRefGoogle Scholar
  45. 45.
    Nadge, P.M., Govardhan, R.N.: High Reynolds number flow over a backward-facing step: structure of the mean separation bubble. Exp. Fluids 55, 1657 (2014)CrossRefGoogle Scholar
  46. 46.
    Spazzini, P.G., Iuso, G., Onorato, M., Zurlo, N., Di Cicca, G.M.: Unsteady behavior of back-facing step flow. Exp. Fluids 30, 551–561 (2001)CrossRefGoogle Scholar
  47. 47.
    Nguyen, T.D., CraigWells, J., Mokhasi, P., Rempfer, D.: Proper orthogonal decomposition-based estimations of the flow field from particle image velocimetry wall-gradient measurements in the backward-facing step flow. Meas. Sci. and Tech. 21, 115406 (2010)CrossRefGoogle Scholar
  48. 48.
    Piponniau, S., Collin, E., Dupont, P., Debieve, J.-F.: Simultaneous wall pressure-PIV measuremnts in a shock wake/turbulent boundary layer interaction. In: 7th International Symp. on Turbul and Shear Flow Phenomena (2011)Google Scholar
  49. 49.
    Duriez, T., Brunton, S., Noack, B.R.: Learning control — taming non-linear dynamics and turbulence. Fluid Mech. and Its Appli. 116. Springer, Berlin (2017)zbMATHGoogle Scholar
  50. 50.
    Chovet, C., Keirsbulck, L., Noack, B.R., Lippert, M., Foucaut, J.-M.: Machine learning control for experimental shear flows targeting the reduction of a recirculation bubble, pp 1–4. 20Th World Congress IFAC, Toulouse (2017)Google Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Lamih Umr8201, Department of Mechanical EngineeringValenciennesFrance
  2. 2.Lml Umr8107Villeneuve d’AscqFrance

Personalised recommendations