Effects of pulsed and continuous jet vortex generators in a turbulent boundary layer flow – an investigation using two high-speed stereo PIV systems

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Effects of pulsed and continuous jet vortex generators in a turbulent boundary layer flow – an investigation using

two high-speed stereo PIV systems

A. Schröder, A. Gilliot, R. Geisler, J.C. Monnier, D. Schanz, D. Pallek, M.

Pruvost, J. Delva

To cite this version:

A. Schröder, A. Gilliot, R. Geisler, J.C. Monnier, D. Schanz, et al.. Effects of pulsed and continuous jet vortex generators in a turbulent boundary layer flow – an investigation using two high-speed stereo PIV systems. 2015. �hal-01110707�

Effects of pulsed and continuous jet vortex generators in a turbulent boundary layer flow – an investigation using two high-speed stereo PIV systems

A. Schröder¹, A. Gilliot², R. Geisler¹, J.C. Monnier², D. Schanz¹, D. Pallek¹, M. Pruvost² and J. Delva²

Abstract Two high-speed stereo PIV systems have been used for the characterization of pulsed and continuous jet actuators in the turbulent boundary layer wind tunnel at ONERA Lille. The test aimed at generating an aerodynamic database useful for the characterization of (unsteady) vortical structures responsible for the wall-normal fluid exchange which enable an increase of wall-shear stress in the wake of the jet actuator row. Averaging over all velocity measurements of the data-set without regarding the different cycle-phases of the jet pulses and calculating the respective scalars and RMS values is the first step in the analysis of the time series of velocity fields. The second step is averaging the different phase-locked positions per cycle so that a quasi-time-resolved reconstruction of the phase average induced vortical wake flow could be realized. Then, a comparison between continuous and pulsed jets through several criteria and an estimation of the minimal number of independent samples in a typical turbulent boundary layer were performed. This work has been realized in close collaboration between ONERA DAAP in Lille, France and DLR-AS-EXV in Göttingen, Germany.

The paper is based on work that was presented at the 16^th International Symposium on Applications of laser Techniques to Fluid Mechanics, 09-12 July 2012, Lisbon, Portugal.

1A. Schröder, R. Geisler, D. Schanz, D. Pallek German Aerospace Centre (DLR), Institute of Aerodynamics and Flow Technology, Department of Experimental Methods, Germany

Email: [email protected]

2A. Gilliot, J.C. Monnier, M. Pruvost, J. Delva ONERA, The French Aerospace Lab, Lille, France Email : [email protected]

Keywords Flow control . Air jet vortex generator . Fluidic jet . HS-PIV. Turbulent boundary layer List of symbols

cf Skin friction coefficient

d Diameter of the actuator holes [mm]

dp Particle diameter [µm]

F Acquisition frequency [kHz]

f# Aperture number

H Form factor

K Fluctuating kinetic energy [m²/s²] M Magnification [pix/mm]

Nsamples Number of PIV images Q Vortex Criterion [s^-2]

Reδ Boundary-layer thickness Reynolds number

Reθ Momentum thickness Reynolds number Ti Integral time scale [s]

U∞ Freestream Velocity [m/s]

Uj Maximum of jet velocity [m/s]

u, v, w Velocity vector components in x, y and z directions

u’,v’,w’ RMS components of the velocity in x, y and z directions

uτ Skin friction velocity [m/s]

VR Velocity ratio Uj/ U∞

X, Y, Z Streamwise, wall normal and spanwise coordinate

α, β Jet angle of incidence and yaw [°]

Г2 Vortex Criterion

δ Boundary-layer thickness [mm]

δ1 Displacement thickness [mm]

Δ_v² Wall normal Fluid transport [m²/s²] θ Momentum thickness [mm]

λ Laser wavelength [nm]

ν Kinematic viscosity [m²/s]

ρ Density of air [kg/m³]

τ Time separation b/w 2 PIV frames [µs]

ωx Vorticity [s^-1]

1. Introduction and Motivation

Continuous and pulsed jet vortex generators are well known for their capability of inhibiting flow separation due to enhanced mixing in turbulent boundary layer (TBL) flows (see Johnston and Nishi 1990) but the transient nature of the flow organisation in the wake of pulsed jet vortex generators is still not well understood. Jet vortex generators of adequate geometries produce streamwise vorticity which, in interaction with the TBL, increases the wall normal fluid transport. For a given ideal configuration, this transport depends on the ratio between jet and bulk velocity, but with a moderate jet velocity - especially in a pulsed mode - the wall normal fluid exchange can be organized more efficiently. Especially the shifts of high momentum fluid towards the wall produce regions of higher wall-shear stress in comparison with the situation without jet interaction (see Godard and Stanislas 2006, Ortmanns et al. 2008, Costas et al 2007). This is a favourable condition for TBL flows with adverse pressure gradients, e.g.

wings or flaps of high-lift-configurations to remain attached to the wall (see Magill and McManaus 2001). The efficiency of producing wall-shear stress by means of induced streamwise vorticity has been found to be increased for small and average distances of the vortex core to the wall (see Ortmanns et al. 2008). Elaborated DNS of a jet vortex generator in a turbulent boundary layer flow at a moderate Reynolds number (see Selent and Rist 2010) shows the complex interaction between the streamwise vorticity producing jet flow wake and the new formation of turbulent structures in the further development of the TBL. Nevertheless, for most relevant cases, the role of the coherent structures for the temporal evolution of the wall normal momentum exchange for continuous and pulsed jet vortex generators in TBLs is still an open issue in the scientific community.The present work deals with the fluid dynamic principles and the spatial and temporal organisations of the induced flow topologies downstream of a jet actuator row in a relatively high Reynolds number TBL flow (Reδ

~ 68000 for U∞ = 30 m/s).

Two high-speed stereo PIV (HS-SPIV) systems are used for characterization of pulsed and continuous jet actuators in the turbulent boundary layer wind tunnel at ONERA Lille (SCL). The work is realized in close collaboration between ONERA DAAP in Lille, France and DLR-AS-EXV in Göttingen, Germany (see Gilliot et al. 2011).

First, the wind tunnel description is provided. Next, calibration and characterisation of the actuators and the flow in the test section are carried out. Then, results about convergence, vortex detection criteria and instantaneous and phase-locked average PIV fields are presented.

2. Wind tunnel description

All the tests are realized in the turbulent boundary layer wind tunnel of ONERA – Lille (Fig. 1) which is an Eiffel type wind tunnel in suction mode with a low turbulence level (0.4%).

The size of the test section is 0.3 m x 0.3 m and the length of the wind tunnel is 2.64 m.

The flow velocity can vary from 0 to 40 m/s. It is a metallic wind tunnel with glass windows. The collector and the diffuser are in wood. The contraction ratio is 10. A seeding device is added upstream of the collector. Adequate optical access is easily obtained using the modularity of the test section components. The five actuators are implemented on a specific plate, which can be placed at different locations on the vertical wall.

Five electro pneumatic valves which are mounted on a flat plate are used to generate five continuous or pulsed jets. The actuators are localised at 2100 mm downstream the wind tunnel collector. The distance between each actuator in spanwise direction is Z=20mm in order to limit the interaction between the induced vortices. The geometric characteristics of the actuators are the following: the diameter of each hole is d=3mm and the jet direction is oriented with two angles, in incidence (α=30°) and in yaw (β=60°) as depicted in Fig. 2.

Fig. 2 Geometric characteristics of the actuators Front view / Side view of the plate

2100 mm

Actuator row localization (X=0)

Fig. 1 Sketch of the turbulent boundary layer wind tunnel of ONERA – Lille Wind

X

2100 mm

Actuator row localization (X=0)

2100 mm

Actuator row localization (X=0)

2100 mm

Actuator row localization (X=0)

Wind Wind

Y

Z Y X

Z Y X

Z

In previous studies, it was shown by Zhang 2000 that yaw angles between 45° and 75° generate stronger vortices than others and a sensitivity analysis has been undertaken by Garnier 2011 to document the effects of the jet blowing velocity, jet sideslip angle and jet diameter for Air Jet Vortex Generator (AJVG).

3. Actuator calibration and characterization procedure

The actuators (feeding system+valve+drilled flat plate) have been calibrated on a specific bench before the wind tunnel tests (Fig. 3). The objectives of the calibration were to identify the jet velocities and the response times at opening and closing of the valves in a quiescent medium. The hot wire technique has been used. A specific calibration procedure of the hot wire has been developed at ONERA-Lille for micro-jets, in order to deal with the smaller size of the jet with respect to the sensor length.

It consists in establishing the relation between the hot wire signal localized at 1 mm from the hole exit, and the jet total pressure, measured in the hole exit with a tiny pressure probe. This is done first with a continuous jet, corresponding to an actuator frequency = 0 Hz, for various jet velocities (variable feeding pressure). Assuming an incompressible flow, the flow velocity is derived from the total pressure applying Bernoulli equation.

The relation is then employed in pulsating conditions to derive the flow velocity from the hot wire measurement, the relative position between the hole exit and the hot wire probe being kept rigorously identical to the one used for the calibration. Details of the instrumentation used is mentioned below:

- Multi-channel system from DANTEC - Temperature sensor

- CTA Conditionnement Hot wire - Conditionnement for Keller sensors - Keller sensor K5

- Furness FCO 510 Micromanoter - Atmospheric pressure sensor

Fig. 3 Hot wire probing during calibration of each jet

In pulsed mode, Festo valves are connected to a 24 Volt power supply large capacity (32 Volts, 16 Amperes) via a system developed by ONERA/DMS. This system will simultaneously control the five Festo valves by a TTL signal which is generated at the desired frequency by the acquisition card of the PC dedicated to measurements. In pulsed mode, only the central actuator was qualified by a hot wire (see Pruvost 2010).

Fig. 4a Temporal evolution of exit velocity at 75Hz for 60 m/s jet velocity - Square command signal

Fig. 4b Temporal evolution of exit velocity at 150 Hz (right) for 60 m/s jet velocity square command signal

Velocity signals for F = 75Hz and F = 150 Hz are shown in Fig. 4a/b. At both frequencies, the flow reaches the required Uj = 60 m/s jet velocity at about one millisecond after the valves opening starts, while the top hat signal form shows values with low variations during opening. During the HS- SPIV measurements, jets have been activated in a continuous or pulsed mode. When using normalized amplitudes and time scales for the different values of the jet frequencies and velocities, all signals are superimposed.

4. Flow characterisation in the test section In order to characterize the turbulent boundary layer flow at U∞ = 15 m/s and U∞ = 30 m/s, hot wire measurements were performed beforehand of the PIV campaign.

Table 1 Characteristics of the Turbulent Boundary Layer in the test section

U∞ [m/s] δ [mm] δ₁ [mm] θ [mm] H Reθ cf uτ [m/s]

15 31 3.64 3.05 1.19 2920 0.0035 0.60

30 34 4.47 3.27 1.37 6570 0.0029 1.16

Fig. 5 and 6 present the velocity and turbulence level profiles obtained for both free stream velocities.

The classical King formula has been used to derive the flow velocity. The hot wire probe has been calibrated in-situ, so that environmental effects (flow conditions, interaction with the support etc.) are reduced as far as possible.

0 0,25 0,5 0,75 1 1,25 1,5

0,6 0,7 0,8 U/U∞ 0,9 1 1,1

y/δ

30m/s 15 m/s

Fig. 5 Velocity profiles at 15 m/s and 30 m/s

0 0,25 0,5 0,75 1 1,25 1,5

0% 1% 2% 3% 4% 5% 6% 7% 8%

u'/U∞

y/δ

30 m/s 15 m/s

Fig. 6 Turbulence level profiles at 15 m/s and 30m/s

The turbulence ratio (u’/ U∞) measured outside the boundary layer in the wind tunnel is 0.42 % for U∞

= 30 m/s and 0.46 % for U∞ =15 m/s (Fig. 6). The first point was measured at Y = 0.3 mm and the last point at Y = 38.5 mm from the wall. The thickness of the boundary layer was identified during these preliminary tests. A value of δ = 34 mm for U_∞ = 30 m/s (U(δ) = 99 % U∞) and δ =31 mm for U_∞ = 15 m/s has been found. Table 1 presents the characteristic values of the boundary layer for both free stream velocities (see Hoyez 1990).

With:

(

)

U

− ∞

=∫0 ¹ 1

δ δ

(

)

U U

U

∞

∞ −

=∫0 ¹

θ δ (1)

v U_∞

=θ⋅

Reθ τ = ₂¹ρ⋅C_f ⋅U_∞² (2)

2 Cf

U

u_τ = _∞⋅ (3)

5

Re 1

0172 .

0 ⋅ ⁻

= _θ

cf (Clauser formula ) (4)

5. PIV Experimental measurements

The experimental set-up is shown in Fig. 7 and 8.

The set-up consists of a combination of two synchronized stereoscopic HS-PIV systems, one supported by ONERA and one by DLR. Both light sheets are introduced perpendicular to the mean flow direction.

Fig. 7 front view of the set-up of two HS-SPIV systems around the test section of the turbulent boundary layer wind tunnel at ONERA, Lille including the jet actuator row.

Fig. 8 Two synchronized HS-SPIV systems at the SCL wind tunnel at ONERA, Lille. Support and valves of the (pulsed) jet actuator row are marked by red ellipse. Flow from right to left.

For the ONERA as well as DLR systems, the light sources for illumination of the tracer particles are pulsed lasers with two oscillators each supplying two consecutive pulses at 1kHz frequency with about 20mJ per pulse at slightly different wavelengths. ONERA used a frequency-doubled Nd :YLF laser (at λ = 527 nm) manufactured by

Quantronix while DLR used a Nd :YAG laser (at λ

= 532 nm) manufactured by LEE Laser Inc. The time interval between each of the two pulses has been adjusted in the frame straddling mode according to the measured flow dynamics. In order to obtain a proper light sheet, the light beam emitted by each laser passes through a set of spherical and cylindrical lenses. The laser sources are placed outside the test section. The light sheets are directed towards the measurement areas through glass window on the test section walls by means of mirrors. The DLR system was mounted on a displacement bench to allow an easy translation of the whole optical arrangement between the different measurement planes.

For the recording of PIV images, high resolution CMOS cameras (1024 x 1024 pix², full frame rate at 3 kHz with 10 bits) APX-RS from Photron with 8 GB memory on-board have been used. Each camera has been equipped with Nikkor lenses (f = 105 mm) adapted to Scheimpflug mounts operating at an aperture number of f# = 8 in order to achieve in- focus particle image diameter of ~ 3 pixels for diminishing the peak-locking effect at 17 µm pixel width of the used CMOS sensor. All cameras have been reduced in the spatial resolution to 1024 x 768 pixels in z and y direction for achieving 4 kHz framing rate. Each camera has been connected to its own dedicated computer on which the recorded frames from the camera RAM have been stored after each measurement point.

As a matter of fact, both systems acquired double- images at 1kHz with a phase shift of 500 μs in between the acquisition of the two HS-SPIV systems, while the jet actuator valves control electronics delivers the trigger signals for the master clock in order to enable phase locked HS- SPIV measurements: At 50Hz jet frequency, each system measures the instantaneous velocity vector fields at 20 fixed phase positions, in time-dependant series of each pulsed cycle. At 100 Hz, there are 10 phase positions. The synchronisation of the whole measurement system has been realised by a programmable sequencer V5.1 from Hard soft (Fig.

9/Fig. 10).

Trig Pos Manual Arm Control Panel

Laser 2 Quantronix

TTL Driver

Trig Pos

Trig Pos

Trig Pos Cam Sync Pos

Cam Sync Pos

Cam Sync Pos 2

Camera 4 Photron APX

Camera 3 Photron APX

Camera 2 Photron APX Sequencer

Function Generator

2

Trigger 1/2 Trigger

Trigger 1/2 Jet Actuator

Laser 1 LEE

Camera 1 Photron APX Cam Sync Pos

Rec Pos

Fig. 9 Trigger electronics scheme for synchronization of two HS-SPIV systems and valves of the pulsed fluidic actuator row

τ 250 μs

τ Laser 2b

Laser 2a Laser 1b Cameras

Jet Laser 1a

Frame 2

Frame 1 Frame N Frame N+1

Frame 0 Frame 3 Frame 4

Fig. 10 Timing diagram of the trigger events for synchronization of HS-cameras (black) and two laser systems (green and blue) and initiating the valves of the pulsed fluidic actuator row (red) Olive oil particles have been used as tracers with an average diameter of dp ≈ 1 µm. They were generated by a multi-Laskin nozzle device connected to a special seeding rake which was placed at the intake of the wind tunnel. With this seeding system a sufficient and homogeneous concentration of tracers in the test section has been reached reliably. However, the pressurized air supply of the jet vortex generators could not be pre- seeded with such particles, which had an unfavourable impact on the seeding distribution for PIV evaluation schemes within the immediate jet wake, especially in the first two measurement planes downstream where additionally strong velocity gradients in streamwise and spanwise directions are present.

6. Test Schedule

Table 2 presents the test program of the PIV campaign. The distances between the two light sheets have been varied during the test campaign.

The first measurement plane is at a fixed position:

0.5*δ or 0.55*δ (depending of the value of the freestream velocity) downstream of the spanwise row of jet vortex actuators. The second measurement plane is placed at three different positions: 1*δ (U_∞ = 30 m/s) or 1.1*δ (U_∞ = 15 m/s); 2*δ (U_∞ = 30 m/s); 3.5*δ (U_∞ = 30 m/s) or 3.84*δ (U∞ = 15 m/s) downstream of the actuator row.

The PIV acquisition frequency was 1 kHz for all experiments listed in Table 2. Two freestream velocities U∞ are tested: 15 m/s and 30 m/s, while the velocity ratio VR= Uj /U∞ was fixed at 2. For pulsed configurations, two frequencies of pulsed jets are investigated: 50 Hz (at U∞ = 15 and 30 m/s) and 100 Hz (at U∞= 30 m/s). Measurements with continuous jets were carried too for U∞ = 30 m/s; in this case Uj was constant at 60 m/s.

Table 2 Testing program (flow conditions, jet velocities, frequencies and measurement plane distances) X Position (mm) U∞ [m/s]

Freestream Velocity

Uj [m/s]

Jet

Velocity VR

Jet frequency

[Hz]

δ [mm]

Boundary Layer

thickness 17 34 68 119

15 0 0 0 31 0.55δ 3.84δ

15 30 2 50 31 0.55δ 1.1δ 3.84δ

30 0 0 0 34 δ/2 δ 2δ 3.5δ

30 60 2 50 34 δ/2 δ 2δ 3.5δ

30 60 2 0 34 δ/2 δ 2δ 3.5δ

30 60 2 100 34 δ/2 δ 2δ 3.5δ

7. PIV calibration and processing

Calibration of both stereo camera systems has been achieved using a 2 mm thick transparent glass target. The plane target has regular grid lines printed on one side placed in the corresponding light-sheet plane and attached to the wall. After mapping of the particle images, a disparity correction procedure has been applied in order to correct for the errors in positioning the calibration target and induced by the refractive index changes of the oblique viewing through the glass target from one camera side. The magnification factor was fixed at M = 18 px/mm at a mapped field-of-view of 1380 x 770 pixels.

For the processing of the time dependent series of particle images acquired in frame straddling mode, a local iterative multi-grid cross-correlation algorithm with image deformation scheme has been applied to the image numbers 1 and 2, 5 and 6, 9 and 10 and so on for the DLR PIV system and the respective intermediate image numbers for the ONERA PIV system (3 and 4, 7 and 8, 11 and 12 and so on), avoiding background light in all double- frames from light reflection interferences. By this method, 2048 instantaneous velocity vector fields per case and HS-SPIV system have been calculated.

A final window size of 20 x 20 pixels at 6 pixels step width in y- and z- directions corresponding to a spatial resolution of 1.11 mm at 0.33 mm grid spacing between two neighbouring velocity vectors has been reached.

The processing procedure results in an array of 237 x 127 instantaneous 3-component velocity vectors (including masked areas at the wall) per measurement field. A specific filter is applied to deal with the above mentioned problematic of the strong velocity gradients and inhomogeneous seeding distribution immediately downstream of the (not-seeded) jet actuator row, where mixing of particles and reduction of gradients dampened the problems. At X=17 mm downstream of the actuator, filtering averages outlier ratio up to ~ 4 % and at X=119 mm less than 1%. The outlier ratio is

detected by a normalised median filter with a value of 1.9 and an absolute velocity histogram filter.

Velocity components have been interpolated from neighbouring vectors, which induced aconvergence problem and bias shift towards smaller values in the areas of the immediate jet wakes. In a convergence study, the difference of the average over 1000 instantaneous velocity vector fields divided by the overall average over 2048 velocity fields still leaves local differences up to 5 % within the above mentioned regions (see details in session 10).

Due to the local convection velocity (assuming ~ 0.7*U∞ for the jet wake area) two subsequently measured velocity vector fields in a plane perpendicular to the mean flow with 1 ms increments in time enable to capture only relatively large coherent flow structures greater than 0.6*δ for U∞ = 30 m/s and greater than 0.3*δ for U_∞ = 15 m/s. The induced spatial and temporal behaviour of the streamwise jet wake vorticity of both jet actuator modes have been the main focus of the present investigation.

The corresponding lengths of the evolving coherent vortical structures are penetrating all measurement planes at certain phase positions of the cycle. The effects of the pulsed jet wake vortices within the TBL flow is then analysed in the chapter 9.

8. Convergence study

Bruun 1995 proposes a way to estimate the minimal number of independent samples in a typical turbulent boundary layer in order to check the convergence of the averaged data. To calculate this number, we have to determine first the integral time scale Ti and the number of samples Nsamples.

∞

=U T_i δ

;

i

s F T

N N

* 2

*

PIVimages

sample = (5) We obtain in our case: Ti = 0.00113 sec. Hence, with NPIVimages=2048 the minimal number of independent samples should be Nsamples= 904 based on this criterion.

A convergence analysis is carried out to check if average data were converged.

This study is made at X= 0.5·δ (X = 17 mm) from the actuators with continuous jets. For this study, four packages of 250 images, four packages of 500 images, three packages of 1000 images, three packages of 1250 images and three packages of 1500 images were analysed. The average reference velocity component and velocity rms were calculated with 2048 PIV images. In Figures 11 to 16, the velocity components (resp. rms) minus the reference velocity (resp. reference rms) components, normalized by the freestream velocity U∞ (resp. square of the free stream velocity U∞²) are plotted.

As expected, results on the velocity components and on the rms of the velocity show a large discrepancy for the case where the average is calculated with a number of samples less than one thousand images. For the velocity components (resp. the velocity rms), this discrepancy decreases for a number of samples higher than one thousand and is less than 0.5% (resp. 0.05%) for a number of samples equals to 1500.

0%

1%

2%

3%

4%

0 200 400 600 800 1000 1200 1400 1600

Nsamples

Delta u/U∞

Average

Fig. 11 Effect of the images number on the u component of the velocity. Delta u = uNsamples-u2048

0%

1%

2%

3%

4%

0 200 400 600 800 1000 1200 1400 1600

Nsamples

Delta v/U∞

Average

Fig. 12 Effect of the images number on the v component of the velocity. Delta v = vNsamples-v2048

0%

1%

2%

3%

4%

0 200 400 600 800 1000 1200 1400 1600

Nsamples

Delta w/U∞

Average

Fig. 13 Effect of the images number on the w component of the velocity. Delta w = wNsamples-w2048

0,0%

0,1%

0,2%

0,3%

0 200 400 600 800 1000 1200 1400 1600

Nsamples

Delta u'²/U∞² Average

Fig. 14 Effect of the images number on the u’

velocity correlation. Delta u’² = u’²Nsamples-u’²2048

0,0%

0,1%

0,2%

0,3%

0 200 400 600 800 1000 1200 1400 1600

Nsamples

Delta v'²/U∞² Average

Fig. 15 Effect of the images number on the v’

velocity correlation. Delta v’² = v’²Nsamples-v’²2048

0,0%

0,1%

0,2%

0,3%

0,4%

0 200 400 600 800 1000 1200 1400 1600

Nsamples

Delta w'²/U∞² Average

Fig. 16 Effect of the images number on the w’

velocity correlation. Delta w’² = w’²Nsamples-w’²2048

To conclude, for the velocity components (resp. the rms components), with a number of samples higher than 1500, the results show an asymptotic tendency towards a number lower than 0.5% (resp. 0.05%).

Pulsed jets configurations where the frequency of the jets was 50 Hz or 100 Hz did not justify this criterion because less than one thousand images were acquired.

9. Results

9.1. Criteria Comparison

Jet vortex generators of adequate geometries produce streamwise vorticity which, in interaction with the TBL, increase the wall normal fluid transport. For a given ideal configuration, this transport depends on the ratio between jet and bulk velocity, but with a moderate jet velocity, especially in a pulsed mode, the wall normal fluid

exchange can be organized more efficiently. That’s why a comparison between continuous and pulsed jets was made through several criteria: The vorticity ωx, the Q criterion and the Γ2 criterion (see Hunt and al 1988, Michard and al 2001). The main results obtained on this criteria comparison have been presented by Gilliot and al 2011 and Schröder and al 2012. For this comparison, the velocity of the wind tunnel U∞ is equal to 30 m/s, the velocity of the continuous and pulsed jets is fixed at 60 m/s and the frequency of the pulsed jets is fixed at 100 Hz. All the calculations have been obtained from 2048 instantaneous PIV images. The ωx (vorticity), Q and Γ2 criteria, in 2D, can be written as:

y U z U_{y z}

x ∂

−∂

∂

=∂

ω (6)

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡ ⎟

⎠

⎜ ⎞

⎝

⎛

∂

⎟⎟ ∂

⎠

⎜⎜ ⎞

⎝

⎛

∂ + ∂

⎟⎟⎠

⎜⎜ ⎞

⎝

⎛

∂ + ∂

⎟⎠

⎜ ⎞

⎝

⎛

∂

− ∂

= z

v y w y

v z

Q w 2

1 ^{2 2} ₍₇₎

( )

(

)

U U PM

Z U U PM P S

P M

P M S

M r r

r r r

−

−

= ∧

Γ^{2 1} ∫ ^∈ _. ^{. (8)}

Where S is an area of the PIV map, P a reference point in the area S, M is an ensemble of discrete points around the point P and UP is a local convection velocity around P. The criterion Γ2

computes the local orientation of the velocity field relative to a reference point P of the PIV map.

Fig. 17 and Fig. 18 show a comparison of all these criteria in terms of vortex centre location coordinates.

Continuous jets:

0 2 4 6 8

-15 -10 -5 0 5 10 15 20

Z(mm)

Y(mm)

ω Q Γ2 Pulsed jets: ω Q Γ2

Fig. 17 Vortex centre coordinates at X= 17 mm obtained with different criteria

Continuous jets:

0 2 4 6 8

-15 -10 -5 0 5 10 15 20

Z(mm)

Y(mm)

ω Q Γ2 Pulsed jets: ω Q Γ2

Fig. 18 Vortex centre coordinates at X= 34 mm obtained with different criteria

The Z positions of the vortex centres obtained with all the criteria are similar but some differences appear on the Y coordinate (direction normal to the wall) in the plane X=17 mm. It is noticed that in this plane, plane localized just downstream of the actuators, the discrepancy in Y positions obtained from all the criteria is much higher than in the plane X=34 mm. This result could be explained by the sensitivity of the various criteria calculated in this work to the levels of unsteadiness and of the velocity gradients, as explained below.

The vorticity criterion is only based on the velocity gradients and presents the major drawback to not distinguish between shear and swirl.

Comparatively, the Q criterion defines the swirls as the area where the flow is dominated by the rotation tensor. Consequently, the vortex structures are identified by a representation of the positive Iso- values of Q whereas their centres are determined by the maximum values of Q. On the other hand, the Γ₂ criterion is used to localise the centre and the vortex border by considering only the topology of the velocity field without its intensity.

Nevertheless, one can see the progressive side displacement of the vortices in positive Y-direction and in negative Z-direction due to the blowing direction of the jets with α=30° incidence angle and β=60° yaw angle. All the criteria show a more important efficiency of the pulsed jets on the vortex transportation.

9.2. Instantaneous fields

Fig. 19 presents for U∞ = 30 m/s and a jet pulse frequency of f = 100 Hz and a VR= Uj/U∞= 2 (Z = 0 at the middle of five actuator positions), the instantaneous 3-component velocity vector fields at all measured planes at the same phase position of the jet pulse cycle. Red arrows on the figure show the positions of the five actuators.

A turbulent boundary layer profile is visible with large coherent areas of u-velocity fluctuations typical for the outer part of the boundary layer above the logarithmic region. The wakes of the pulsed jets are affecting the region below y = 10 mm and are still quite significant at this phase position for the two downstream planes, although the velocity fluctuations from the TBL flow is almost of the same amplitude. At the first two planes, the re-organised TBL flow is represented with no direct jet wake interaction.

Fig. 19 Instantaneous velocity vector fields out of 1 kHz time series at all investigated planes at U∞ = 30 m/s and 100 Hz jet pulse frequency (all planes at the same jet pulse phase position).

9.3. Phase locked averaged fields

Averaging over all velocity measurements of the data-set without regarding the different cycle- phases of the jet pulses and calculating the respective scalars and RMS values was the first step in the analysis of the time series of velocity fields.

The second step was averaging the different phase- locked positions per cycle so that a quasi-time- resolved reconstruction of the phase average induced vortical wake flow could be realized. For the averaging of the velocity vector fields of the pulsed jet case at f = 50 Hz, 102 samples for each of the 20 different phase-locked positions have been used, while for the f = 100 Hz case 204 samples for 10 different phase-locked positions were present. From this point, a triple decomposition could enable the calculation of periodic and non-periodic parts of the Reynolds stresses, but due to the small number of samples, we focus our analysis in the present work onto the time dependent phase-locked averages.

By using this data, a comparison can be presented between the influences of continuous and pulsed jets on the TBL flow. The average velocity contour fields and corresponding RMS fields presented in Fig. 20 are calculated with 2048 instantaneous SPIV images, each without using the phase information. Red arrows on the figure show the positions of the five actuators. The two average velocity contour fields show for both cases the decay of the aerodynamically relevant wall-normal (v-component) velocity of opposite sign with downstream positions. The positive v-velocity side (red colour coding) of the induced average vortices are slightly larger in the first three planes than the negative part (blue) as the jets are blowing mass flow away from the wall in the first instance.

Fig. 20 a

Fig. 20 b

Fig. 20 c

Fig. 20 d

Fig. 20 Average velocity contour plots at all four measurement planes with v-component (wall- normal) of velocity colour coded (Fig.20a/20b) and corresponding RMS contour fields with colour coded magnitude (Fig.20c/20d) of the continuous blowing jet actuator row (Fig.20a/20c) and the pulsed jet actuator row at 50 Hz averaged over all phase positions (Fig.20b/20d) both at U∞ = 30 m/s.

With respect to the fact that the v-velocity magnitude shown in the overall average contour field of the pulsed jet actuator in Fig. 20b/20d is based on ~50 % of the mass flow of the continuous jet actuator shown (Fig. 20a/20c) there seem to be no hint for higher efficiencies of the wall-normal fluid exchange for pulsed actuators. The presented positive and negative values for the v-velocity at the pulsed case are not significantly more than half of those at the continuous case.

The RMS contour fields in the Fig. 20c/20d show special features of both flow control types. While for the continuous case the maximum fluctuation is located close to the vicinity of the wake of the blowing jet at relative large distances from the wall, the maximum fluctuations for the pulsed jet are located with large values close to the wall in the direct vicinity wake of the intermediate blowing jet orifices. This might not be very surprising as the jet is pulsating, but large turbulent kinetic energy distributions close to the wall is also favourable for inhibiting flow separation. The analysis of the transient nature of the pulsed jet wakes explaining the large RMS values close to the wall are subject to future work.

A judgement on the efficiency of the two jet actuator methods at the measured velocities and jet frequencies can be determined on the basis of the relation between flow velocity deficits in the wake to the ratio of transported high momentum fluid towards the wall where velocity increases (see Schröder and al 2011).

In Fig. 21 the distribution of the overall average u- velocity differences to the undisturbed turbulent boundary layer flow are shown for the continuous (Fig.21a) and pulsating jet at f = 50 Hz (Fig 21b) actuator flow. Red arrows on the figure show the positions of the five actuators. It is clearly visible for both cases that high momentum fluid is guided around the single vortices closer to the wall (purple/red areas) leading to higher wall-shear stress. While with the opposite process low momentum fluid with a velocity deficit is transported away from the wall (blue regions) which remains visible as slightly elevated wakes of the original jet cross flow. While for the continuous jets the regions of velocity increase and deficit are located with pronounced maxima and minima in all measurement planes, the u-velocity differences for the pulsed jet are slightly wider distributed in spanwise directions especially for the planes further downstream.

Besides the amplification of slight artefacts of the velocity distribution due to the calculation of differences, the integral momentum increase close to the wall is of the same size for both actuator modes when taking into account the differences of

induced momentum of ~ 2:1 for the continuous to the pulsed jet with 50 % duty cycle.

In order to quantify the overall average effects of the continuous and pulsed jet vortex generators onto the wall-normal fluid transport in their wake flows, an integral calculation of the squared v- velocity component within the iso-vorticity contour area S consisting of values below ω_x = -400 s^-1 have been performed for all measurement planes according to equation (10). S corresponds to the mentioned vorticity area and v² the squared wall normal velocity component with and without jets.

Fig. 21a

Fig. 21b

Fig. 21 Average difference velocity contour plots between jet actuator and undisturbed turbulent boundary layer at all four measurement planes with Δ_u-component of velocity colour coded. Fig.21a:

Δ_u of continuous jets field and Fig.21b delta_u of the pulsed jets actuator row at 50 Hz, both at U∞ = 30 m/s.

ds v

v

v _{without jet}

S( with jets )

_ ² = ² _{_} − ² _{_}

Δ ∫ (9) In Fig. 22, the integral values of the average v²- velocity components within the areas of vorticity with values below ω_x = -400 s^-1 and normalized by the size of S have been displayed for all three jet actuator modes and measurement planes at U∞ = 30 m/s. Using normalization of the values, all decay- curves are very close to each other, which means that within the same amount of induced average x- vorticity the same amount of wall normal fluid transport can be organized. For overall averages

this result seems to be reasonable, but this calculation does not consider the transient phases of the pulsed jet wakes.

∫v²dy

0,000 0,001 0,002 0,003 0,004 0,005

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0

x/δ

Pulsed jets 50Hz Continuous jets Pulsed jets 100Hz

Fig. 22 Integral values of average v² velocity components within the areas of vorticity with values below ωx = -400 s^-1 and normalized by the size of S for all three jet actuator modes and measurement planes at U∞ = 30 m/s.

9.4. Transient fields

The transient nature of the development of wall- normal velocity exchange for four phase-locked averages at different time instants after the valve trigger at f = 100 Hz and U∞ = 30 m/s is shown in Fig. 23. Due to the imaging frequency, the time increment is Δt = 1 ms for each plane, with a 0.5 ms delay for the upstream plane at x = 17 mm. Three subsequent v-velocity distributions of the pulsed jet wakes show the transient organisation of the flow in all planes. At x = 119 mm or 3.5*δ, the wake of the pulsed jet already produces slight wall normal velocities at an elevated position ~y = 15 mm only 6 ms after opening trigger of the valves. In the subsequent images, an increase of the v-velocity magnitude is visible while the corresponding vorticity structure moves at the same time closer to the wall and in negative z-direction, which is the blowing direction of the jets with β = 60 ° yaw angle. This behaviour explains the wider distribution of the u-velocity differences in figure 21 and might be advantageous for inducing wall- shear stress due to its moving character.

In Fig. 23a, the v-velocity phase average at t = 2 ms, resp. 2.5 ms after the valve trigger for initiating the opening, is shown. At that time instant a first effect in the induced v-velocity can be noticed here at plane x = 17 mm, while a small amount of v- velocity induced by the forerunning pulse is still present at x = 119 mm. In Fig 23c, at 7 ms after valve trigger a considerable amount of streamwise vorticity reaches the downstream plane at x = 119 mm. Assuming that the jet vortex actuator effect was present at x = 17 mm already at t = 2 ms due to the pronounced structures at t = 2.5 ms an average convection velocity for the induced streamwise vortices of ~ 20.4 m/s can be calculated, which corresponds to ~0.68 U.

23a 2.5 ms after valve trigger

23b 6.5 ms after valve trigger

23c 7.5 ms after valve trigger

23d 8.5 ms after valve trigger

Fig. 23 Transient development of wall-normal velocity exchange for four phase-locked averages (Fig.23a to Fig.23d; v-velocity colour coded). The last three v-velocity distributions are subsequent with Δt = 1 ms increments of the pulsed jet at f = 100 Hz and U∞ = 30 m/s.

For a few phase-averaged time instants where the wake flow has been fully established the v-velocity magnitude is even slightly larger for the pulsed jets in comparison to the continuous ones in the two intermediate planes at x = 34 and 68 mm. But especially at times when the jet wake vortices first reach the different planes in the pulsed mode, the continuous jets produce a larger v-velocity magnitude. So that as stated before, the overall wall normal momentum exchange is of the same order for both flow types considering the jet momentum differences. Only the transient character of the pulsed jet might have an advantageous effect to the wall shear stress enhancement due to its unsteady character as visible in the larger RMS values close to the wall in figure 20 and in the spanwise shifting of large vortical structures in time as shown in Fig.

23.

A detailed analysis of the temporal development of velocity fluctuation components convecting through the two successive time-resolved measurement planes could have been realised statistically using space-time-correlations. The only visible

“transient” effect is the stretching of the induced flow by the shear present in the boundary layer.

However, as a significant relative increase of wall normal fluid exchange is not visible in the normalised average vorticity area as shown in figure 23 there is no need for a further temporal analysis of transient effects in terms of judging on the efficiency of pulsed or continuous fluidic vortex generators.

10. Summary

The wake effect of a row of flush mounted continuous and pulsed air jet actuators onto a turbulent boundary layer flow has been investigated by means of two HS-SPIV systems. Time series of 3-C velocity vector fields in two planes at different distances to the actuator row and perpendicular to the mean flow have been measured at 1 kHz. The changes in u- and v-velocity in relation to the undisturbed TBL flow and in comparison of the continuous and pulsed jet modes have been investigated. Continuous and pulsed jets induce streamwise vortices which increase the u-velocities close to wall by wall-normal momentum exchange.

A comparison of the overall averages and differences in the u- and v-velocity distributions of both jet blowing modes shows no significant benefits for one of the working modes.

Nevertheless, a look on the transient character of the pulsed mode supports the idea of a more efficient production of wall-shear stress due to temporal spanwise shifts of the vortical structures and the overall unsteady flow behaviour.

A convergence analysis was carried out.

Continuous jets configuration with a number of samples higher than 1500 shows an asymptotic tendency for the velocity and the rms components.

So, to record 1500 images for all the configurations is necessary to obtain the convergence of all the average data.

A comparison of different criteria in terms of vortex centre location was performed. It seems that some differences appear on the Y coordinate (direction normal to the wall) in the plane X=17 mm, plane localized just downstream of the actuators. This result could be explained by the sensitivity of the various criteria calculated in this work to the levels of unsteadiness and of the velocity gradients.

Acknowledgments

This work is supported by the FEDER (Fonds Européen de Développement Economique et Régional) and the Nord Pas de Calais region in the CISIT (Campus International pour la Sécurité et l’Intermodalité des Transports) project.

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