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Unsteady Behavior of a Backward-facing Step in Forced Flow

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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.

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Abbreviations

A r :

Recirculation area [m2]

Ar :

Aspect ratio of the backward-facing step

Cp :

Mean pressure coefficient

Cp r m s :

Rms Pressure coefficient

C μ :

Momentum coefficient

δ 99 % :

Incoming boundary layer thickness [m]

Er :

Expansion ratio of the flow configuration

f a :

Actuation frequency [Hz]

Φn :

nth Spatial Pod eigenfunction [m]

a n :

nthPod temporal coefficient [s]

λ n :

nthPod eigenvalue

E(f):

Psd of the wall pressure fluctuation

h :

Step height [m]

L r :

External reattachment length [m]

Re δ :

Reynolds number based on \(\delta \)

Re θ :

Reynolds number based on \(\theta \)

Re h :

Reynolds number based on h

S j e t :

Cross-section of the micro-jets [m2]

S r e f :

Reference surface of the Bfs [m2]

St a :

Actuation Strouhal number based on h

St θ :

Actuation Strouhal number based on \(\theta \)

St :

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

θ :

Momentum thickness [m]

U 0 :

Free-stream velocity [m/s]

u j e t :

Jet velocity [m/s]

V j e t :

Jet velocity amplitude [m/s]

X r :

Internal separation length [m]

x, y, z :

Spatial coordinates [m]

w z :

Spanwise fluctuation vorticity [s− 1]

V e :

Actuation power supply [Volts]

V R :

Velocity ratio

A ij, \(B_{ijk}\) :

Stochastic estimation coefficients

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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.

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Authors and Affiliations

  1. Lamih Umr8201, Department of Mechanical Engineering, 59313, Valenciennes, France

    Camila Chovet, Marc Lippert & Laurent Keirsbulck

  2. Lml Umr8107, 59650, Villeneuve d’Ascq, France

    Jean-Marc Foucaut

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  1. Camila Chovet
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Chovet, C., Lippert, M., Keirsbulck, L. et al. Unsteady Behavior of a Backward-facing Step in Forced Flow. Flow Turbulence Combust 102, 145–165 (2019). https://doi.org/10.1007/s10494-018-9944-0

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