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

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.

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Abbreviations

Reference axis :

(X, Y, Z):

Coordinates with origin considered at the leading edge of

ᅟ:

the flap

t :

Reduced time t = t U 0 / H s

Flow :

A sep :

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

L sep :

Length of the separation bubble

Re 𝜃 :

Reynolds number based on 𝜃

St :

Strouhal number St = f L 0 / U 0

U mean , V mean :

Mean streamwise and wall-normal velocity for the

ᅟ:

separated flow

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

Phase-averaged mean streamwise and wall-normal velocity

U 0 :

Reference freestream velocity of the flow at the leading

ᅟ:

edge

x R :

Position of the reattachment point

x S :

Position of the separation point

δ :

Boundary layer thickness

χ :

Backflow function

𝜃 :

Momentum thickness of the boundary layer

Ramp :

H s :

Step height

α R / β R :

Angles of the ramp configuration

Metrology (hot-films, PIV) :

EE 0 :

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

f o :

Lenses focal

f # :

Aperture

f PIV :

Frequency of phase-averaging PIV

px:

Pixel

Δt :

Time separation between two laser pulses

Actuators :

<c μ > :

Transient momentum coefficient

ᅟ:

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

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

ᅟ:

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

N j :

Number of actuators

U j :

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)

ΔX vg :

Distance between the vortex generators jets and the

ᅟ:

separation line

λ :

Span distance between two consecutive jets

ϕ :

Diameter of the jets

POD :

a i :

i th temporal mode for the Conditional Proper Orthogonal

ᅟ:

Decomposition

N m :

Number of modes for the Proper Orthogonal Decomposition

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

Phase-averaged streamwise velocity downstream the

ᅟ:

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

ᅟ:

Decomposition

Others :

N c :

Number of cycles used for the phase-averaging procedure

N p :

Number of phases during the transition

t d :

Delay time

t :

Time position compared to one actuation period

ᅟ:

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

τ r , τ s :

Characteristic reattachment/separation time

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

Reduced characteristic reattachment/separation time

ᅟ:

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

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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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Raibaudo, C., Stanislas, M. & Kerhervé, F. Transient Characterization of the Reattachment of a Massively Separated Turbulent Boundary Layer Under Flow Control. Flow Turbulence Combust 98, 1039–1063 (2017). https://doi.org/10.1007/s10494-016-9796-4

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Keywords

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