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Flow, Turbulence and Combustion

, Volume 98, Issue 4, pp 1039–1063 | Cite as

Transient Characterization of the Reattachment of a Massively Separated Turbulent Boundary Layer Under Flow Control

  • C. RaibaudoEmail author
  • M. Stanislas
  • F. Kerhervé
Article
  • 256 Downloads

Abstract

The transient dynamics of a high Reynolds number separated flow over a two-dimensional ramp submitted to pulsed fluidic control is investigated. A spanwise array of 22 round jets, located upstream of the flap leading edge, is used as actuator to generate co-rotating vortical structures. Simultaneous measurements of wall friction using hot-film anemometry and phase-averaged velocity using 2D2C PIV are conducted. The PIV plane encompasses the incoming boundary layer upstream the flap leading edge, the separation bubble and the natural reattachment region. The dynamics of the separated flow is studied for successive sequences of pulsed actuation. Pockets of turbulence are periodically generated by the separation process and pushed downstream. After the transition period, the controlled flow shows large amplitude oscillations around a steady mean, particularly for the separation area. The transient dynamics of the flow at the actuation activation is also studied. The separated flow is strongly modified by the actuation from the first pulse. Characteristic times of the transient dynamics can be determined by fitting a first-order model with delay on the data. For the reattachment, the dimensionless characteristic rising times defined as \(\tau _{r}^{+} = \tau _{r} ~ U_{0} ~/~ L_{sep}\) of 11.7 for the friction gain, 4.8 for the separation length and 4.1 for the first mode of a Conditional Proper Orthogonal Decomposition analysis of the phase-averaged velocity fields were found. These values are in good agreement with previous studies and are of particular interest for modeling the transients and for further closed-loop control applications.

Keywords

Boundary layer Turbulence Adverse pressure gradient Flow Control Pulsed jets Transient dynamics POD 

List of symbols

Reference axis

(X, Y, Z)

Coordinates with origin considered at the leading edge of

the flap

t

Reduced time t = t U 0 / H s

Flow

Asep

Area of the separation bubble

k

Turbulent kinetic energy \(k = \frac {1}{2} (u^{\prime 2} + v^{\prime 2})\)

\(\widehat {k}\)

Phase-averaged turbulent kinetic energy

Lsep

Length of the separation bubble

Re𝜃

Reynolds number based on 𝜃

St

Strouhal number St = f L 0 / U 0

Umean, Vmean

Mean streamwise and wall-normal velocity for the

separated flow

\(\widehat {U}, \widehat {V}\)

Phase-averaged mean streamwise and wall-normal velocity

U0

Reference freestream velocity of the flow at the leading

edge

xR

Position of the reattachment point

xS

Position of the separation point

δ

Boundary layer thickness

χ

Backflow function

𝜃

Momentum thickness of the boundary layer

Ramp

Hs

Step height

αR / βR

Angles of the ramp configuration

Metrology (hot-films, PIV)

EE0

Friction gain (E 0 friction of the flow without control)

fo

Lenses focal

f#

Aperture

fPIV

Frequency of phase-averaging PIV

px

Pixel

Δt

Time separation between two laser pulses

Actuators

<cμ >

Transient momentum coefficient

\(<c_{\mu }>= DC~ (N_{j} \rho _{j} {U_{j}^{2}} S_{j} ) ~/~ (0.5 \rho _{0} {U_{0}^{2}} \delta \lambda )\)

DC

Duty cycle

f

Frequency of actuation

F+

Reduced frequency of actuation F + = f L sep / U 0

\(F_{opt}^{+}\)

Reduced optimum frequency of actuation

\(F_{opt}^{+} = f_{opt}~L_{sep}~/~U_{0}\)

Nj

Number of actuators

Uj

Mean velocity of the jets

VG

Vortex generator

VR

Velocity ratio of the jets U j / U 0

α / β

Skew/pitch angles of the jets (around Z-axis/around X-axis)

ΔXvg

Distance between the vortex generators jets and the

separation line

λ

Span distance between two consecutive jets

ϕ

Diameter of the jets

POD

ai

i th temporal mode for the Conditional Proper Orthogonal

Decomposition

Nm

Number of modes for the Proper Orthogonal Decomposition

\(\widehat {U}_{b}\)

Phase-averaged streamwise velocity downstream the

leading edge \(\mathbf {\widehat {U}_{b}} (\mathbf {x},t_{p}) = \mathbf {\widehat {U}} (\mathbf {x}(X>0,Y),t_{p})\)

\(\widehat {\Phi }_{i}\)

i th spatial mode for the Conditional Proper Orthogonal

Decomposition

Others

Nc

Number of cycles used for the phase-averaging procedure

Np

Number of phases during the transition

td

Delay time

t

Time position compared to one actuation period

(\(0 \leqslant t^{\triangle } < T\))

τr, τs

Characteristic reattachment/separation time

\(\tau _{r}^{+}, \tau _{s}^{+}\)

Reduced characteristic reattachment/separation time

\(\tau _{\star }^{+} = \tau _{\star } ~ U_{0} ~/~ L_{sep}\)

Notes

Acknowledgments

The present work is supported by the Agence National de la Recherche (ANR) through the french ANR project SePaCode (ANR-11-BS09-0018) and by the CISIT International Campus through the Contraéro project. The authors are indepted to C. Cuvier for his help during the experiments and for the PIV images processing.

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Laboratoire de Mécanique de LilleCNRS, École Centrale de LilleVilleneuve d’Ascq CedexFrance
  2. 2.Department of Mechanical and Manufacturing Engineering, Schulich School of EngineeringUniversity of CalgaryCalgaryCanada
  3. 3.École Centrale de LilleVilleneuve d’Ascq CedexFrance
  4. 4.ENSMA, CEAT, Institut PPRIME, CNRSUniversité de PoitiersPoitiers CedexFrance

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