Unsteady Behavior of a Backward-facing Step in Forced Flow

  • Camila ChovetEmail author
  • Marc Lippert
  • Laurent Keirsbulck
  • Jean-Marc Foucaut


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.


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

List of sympols


Recirculation area [m2]


Aspect ratio of the backward-facing step


Mean pressure coefficient


Rms Pressure coefficient


Momentum coefficient

δ99 %

Incoming boundary layer thickness [m]


Expansion ratio of the flow configuration


Actuation frequency [Hz]


nth Spatial Pod eigenfunction [m]


nth Pod temporal coefficient [s]


nth Pod eigenvalue


Psd of the wall pressure fluctuation


Step height [m]


External reattachment length [m]


Reynolds number based on \(\delta \)


Reynolds number based on \(\theta \)


Reynolds number based on h


Cross-section of the micro-jets [m2]


Reference surface of the Bfs [m2]


Actuation Strouhal number based on h


Actuation Strouhal number based on \(\theta \)


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


Momentum thickness [m]


Free-stream velocity [m/s]


Jet velocity [m/s]


Jet velocity amplitude [m/s]


Internal separation length [m]

x, y, z

Spatial coordinates [m]


Spanwise fluctuation vorticity [s− 1]


Actuation power supply [Volts]


Velocity ratio

Aij, \(B_{ijk}\)

Stochastic estimation coefficients



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.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

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

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