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33rd AIAA Fluid Dynamics Conference and Exhibit23-26 June 2003, Orlando, Florida
* Graduate Student ** Senior lecturer, Associate Fellow AIAA Copyright (c) by the authors. Published by the AIAA with permission.
1
Boundary Condition Effects on Oscillatory Momentum Generators
Tal Yehoshua* and Avi Seifert**
Dep. of Fluid Mechanics and Heat Transfer Faculty of Engineering, Tel-Aviv University, Ramat-Aviv 69978, ISRAEL
Abstract
The effects of boundary conditions on the performance of compact oscillatory momentum generators were studied experimentally. The boundary conditions included: unrestricted and restricted entrainment, relative directions between the excitation and the surface, and the effect of an incoming laminar boundary layer. The excitation signals included a pure sine wave or an amplitude modulated sine wave, in order to generate low frequency excitation through non-linearity.
When the actuator operates in still air, a quasi-2D vortex pair is generated due to the extreme shear at the edges of the ejected flow during the blowing stage of the cycle. A threshold slot exit velocity was identified, under which the vortices are either sucked back into the actuator’s cavity or canceled due to the opposite shear generated during the suction portion of the cycle. The vorticity flux exiting the slot determines the resulting vortex circulation, while the vortex convection speed approximately scales with the peak velocity at the slot exit.
Vortex pairing was identified for amplitude modulated signals, when faster, larger circulation vortices accelerate and catch-up with slower, weaker ones and the far-field only senses the low frequency modulation.
When even a very short extension is attached to one “lip” of the actuator exit, operating in still air, the jet is deflected in the direction opposite the extended lip, due to the restriction on the entrainment process. When a long extension is attached, the coherence of the vortices increases, their phase speed and magnitude decrease.
The effects of high-frequency excitation, ejected perpendicular to the wall into a laminar boundary layer for active tripping, were investigated. It was found that shallow angle downstream excitation is more effective for transition promotion, as well as for increasing the skin friction, than wall-normal excitation.
Detailed PIV measurements of excitation-laminar boundary layer (LBL) interaction reveal that unsteady vortices are being shed and convected downstream, as long as the actuation magnitude is supercritical. The “mean bubble” identified using simple averaging does not represent the flow at any given time. A “bubble” of separated flow exists for only a fraction of the cycle and is convected downstream while the boundary layer is completely “washed away” at other times.
The mechanism by which amplitude modulated signals generate low frequency at a distance of only several slot widths or LBL thicknesses was demonstrated and explained.
Nomenclature
Ai slot exit area, =hb Ar reference area b actuator and LBL span
H=δ∗/θ h slot height, Lc reference length of controlled flow Le extension length of one actuator
“lip” (Fig. 1c) Ls length of separated flow region L0 stroke length, defined in text
Q in-plane velocity magnitude; 22 vu + Re BL Reynolds number, νθ eU= Vac RMS excitation voltage Tm input signal modulation period Tr period of actuators’ sine wave Ue free-stream tunnel velocity W actuator input power [Watt] fr actuators resonance frequency fm modulating frequency f excitation frequency. Either fm or fr
depends on excitation type n number of excitation cycles p instantaneous local pressure u ̀ R.M.S of velocity fluctuations Up peak slot exit velocity u,v,w velocity components in the x,y,z directions x,y,z Cartesian coordinates. see Fig. 9 θ boundary layer momentum thickness
δ∗ boundary layer displacement thickness
ν kinematic viscosity
ϕ phase angle of excitation cycle …
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1. Introduction 1.1 Overview, scope and motivation Zero-Net-Mass-Flux oscillatory momentum generators (OMJ, known recently as “Synthetic jets”) are being used as a versatile tool for active flow control for the past decade with applications like separation control, thrust vectoring, mixing and heat transfer enhancement, and more (Ref. 1-7). Typically, these devices are used to generate large coherent structures in shear flows, promoting transition, introducing unsteady harmonic or pulsating motion into a turbulent shear flow, or even generating turbulent jets through entrainment of still fluid (in the latter application it is physically relevant to use the term “synthetic jets” (Ref 4 ). From the time that Crow and Champagne (Ref. 8) investigated the orderly structures in turbulent jets, the dynamics of artificially excited jets generated great interest in the scientific community. Pulsed jets were also used in industrial applications in internal combustion engines for improving the mixing of fuel and air (Ref. 2). The separation of boundary layers from lifting bodies could be delayed, thereby generating higher lift when oscillatory momentum was introduced to the flow, like in the experiments described in Refs 3,6. It was demonstrated that periodic excitation is a useful tool for Active Flow Control (AFC), but the understanding of the physical mechanism governing the interaction of periodic excitation with ambient, stagnant or flowing fluid is far from being complete. Only partial understanding of how large amplitude periodic excitation creates coherent structures in common flows, the receptivity problem, exists (Ref. 9). The effects of the boundary conditions on the actuator performance and features of the resulting coherent structures are not thoroughly documented or understood to date. The aim of this study was to demonstrate and attempt to explain flow features generated by an oscillatory momentum generator using several types of input excitation signals and a range of relevant exit slot boundary conditions. The manner in which the boundary conditions affect the resulting slug and vortices, and their interaction with the surrounding still or flowing fluid were studied. Particle Image Velocimetry (PIV),
Hot-wire anemometry and unsteady pressures were the main measurement tools. 1.2 Cavity based fluidic actuators Oscillatory momentum generator is a zero-mass flux fluidic actuator, typically containing three components: Active materials (such as Piezo ceramics) bonded to a membrane, a cavity and a slot, communicating the cavity and the surrounding fluid. Several configurations were tested and reported in the literature, and a schematic of an compact design is shown in Fig. 1. When the Piezo element is driven by an AC voltage, the membrane oscillates between two extreme conditions as shown schematically (and in an exaggerated manner) in Fig. 1. The Piezoelectric ceramic material responds to the input voltage signal by contracting or expanding, thereby causing the membrane to oscillate, thus altering the volume of the cavity at the excitation frequency and creating pressure oscillations. Consequently, velocity oscillations result at the actuator’s exit slot. This dynamic process creates a phase lag between the applied voltage, the membrane’s deformation, the pressure and the velocity oscillations at the slot, therefore peak applied voltage does no imply peak velocity at the slot. Furthermore, applying a certain type of excitation voltage does not guarantee a similar response of the slot velocity signal, due to the dynamics and non-linearities of each component of this complex system (Ref. 10, 11). Typically, the membrane deflections are on the order of 10-100µm and the Helmholz acoustic resonance enables the generation of larger velocities than one could obtain only due to volumetric cavity changes, but over a narrow frequency range. During the suction stage (phases 180°-360°), fluid is drawn into the cavity from the surrounding fluid, stagnant in this case, as shown in Fig. 2b, when using the compact actuator (Fig.1, Le/h=0 Up=43m/s). While during the latter part of the blowing stage (Fig. 2a, phases 90°-180°), strong shear layers are formed between the exhaled and the surrounding still air. In the absence of external flow, and as a consequence of the vorticity flux of the strong shear layers ejected from the actuator’s slot, two counter rotating vortices (which are, after all, a part of an elliptic vortex ring, see Fig. 3 for vorticity contours corresponding to the velocity data of Fig. 2) are created at the "lips" of the slot, and propagate downstream alongside the high velocity slug ejected during the blowing stage of the cycle. By the time the suction stage begins, and for sufficiently large slot peak velocities (to be defined later), the vortex pair has already moved far
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enough not to be inhaled into the slot. This condition is satisfied provided the vortex ring advection velocity, Uc, is greater than the suction velocity at the vortex core location at any given time. The time periodic reversal in the flow direction creates a stagnation point in the vicinity of the slot (that would lay on the centerline of a symmetric actuator operating in still air) and the location of this stagnation point varies with time when considering a phase-locked averaged velocity field (clearly shown at x/h=0 and y/h=1.5 in the later phases of Fig. 2) and will depend on Up and other BC’s, especially in cross-flow. It was, demonstrated (Ref. 4) that the distance of the stagnation point from the slot increases with
hL0 (excitation amplitude). The use of stroke length as an amplitude parameter is somewhat artificial for devices that do not have a piston as the motion of the membrane is next to impossible to describe in full. It is therefore useful to establish a connection between the momentum coefficient,
µC , and the stroke length, hL0 . The latter
parameter was developed for a piston moving at a fixed speed for a distance L0 to form a vortex pair (an analogy to the 2D case is used here). The analysis equates the mass ejected from a 2D piston to that of a fluidic actuator with a uniform exit velocity and harmonic time signal. During the ejection stage of the cycle, one obtains
fUL p π20 = . The relationship to the
momentum coefficient (where an external boundary layer interacts with the actuator’s output) is:
20
2
23
2
20
2
2 )2()2(
===hL
Ufh
UfLh
U
UhC
eee
p πθ
πθθµ
For the data shown in Fig. 2 and Fig. 3, hL0 ≈4.6, using the above assumption. Note that the momentum thickness is used here as the BL scaling argument rather than the accepted chord length -scale for airfoil separation control (i.e., length of separated region, Ref. 1).
One could also think of the following operation principle. During the blowing stage, the flow emerging from the device is similar to a jet flow, due to the strong shear layers created and the jet spreading phenomena (at a streamwise distance where reverse flow disappears). While in the suction stage, the flow near the slot resembles a potential sink placed at the slot, creating a velocity field with a typical 1/r decay (this also holds for regions not affected by the jet flow at all times). Hence, as explained earlier, if the slug of high velocity has moved far enough from the slot not to be dominated by the suction stage due to its 1/r decay, it will be sensed in the far-field. The same mechanism determines the motion of the counter-rotating vortices created in the blowing stage. It is
clear that the magnitude of this asymmetry between the blowing and suction stages of the actuator operation increases with the peak slot velocity (L0/h) and could be considered a non-linearity of the system (Ref. 12, 3) leading also to thrust generation. 1.3 Dimensional analysis The problem at hand (“system”) contains four major components leading to the following four groups of parameters: 1. The actuator geometry, 2. Actuator operating conditions, 3. The laminar boundary layer, and 4. Interaction conditions. The geometry of the cavity is of lesser importance for the current study, but the neck geometry is (Ref. 13) important, determining the shape of the slot exit velocity profile. As will be shown later, the slot vorticity flux during the blowing stage is crucial. An application dependent optimum should be found between maximum ejection velocity and maximum vorticity at the slot exit. The excitation parameters are: membrane amplitude, frequency, actuator acoustic and mechanical resonant frequencies, modulation frequency, resulting cavity pressure fluctuations (assuming cavity dimensions much smaller than acoustic wavelength) and slot Stokes number (determining viscous boundary layer penetration into slot exit slug flow). The slug Reynolds number is probably the least representative Reynolds number of the problem at hand. Density variations might be important in compressible operating conditions. The relevant boundary layer parameters are: momentum or displacement thickness Reynolds number, the boundary layer characteristic thickness, the free-stream velocity and turbulence levels, shape factor, pressure gradient (for non-similar BL), the BL origin and history details. The present study is limited to laminar flow. Finally, the interaction parameters are: fundamental and modulation frequencies, peak exit velocity, time-history waveform, slot exit velocity profile and excitation injection angle. These could be combined into several dimensionless parameters, of which the vorticity flux ratio will be discussed in detail later. 1.4 Purpose of the study and Layout of Paper The main research questions to be discussed in the current study are the following. Vortex rings or pairs are an exciting part of the flow field generated by oscillatory momentum or vorticity flux generators, but how relevant are the
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dynamics of the latter to the evolution of the excited flow? More fundamentally: are we using the oscillatory momentum or vorticity flux out of these devices? Is the mean flow measured and calculated by many relevant at all to understanding the unsteady flow physics? We would like to identify effective configurations for actuator-LBL interaction leading to effective transition promotion, separation delay and separated flow reattachment. We would like to explore the physics of the de-modulation mechanism allowing low frequency generation from the high frequency excitation of the actuator, in still air and in cross-flow. In the present work, effects of different boundary conditions on the performance and flow field evolution of oscillatory momentum generators will be investigated. First, the compact actuator with different asymmetric extensions will be tested, and the flow field generated in each configuration explored by PIV and HW, using two modes of excitation (Pure sine and Amplitude Modulation). Once the database is described, the interaction of the excitation imposed by actuators using several types of boundary conditions with an incoming cross flow LBL will be studied and discussed. The paper is divided into the following sections. The experimental set-up is described in Sec. 2, results are provided in Sec. 3, where the effects of slot extensions are discussed in 3.1, the effects of wall-normal excitation ejected into still air in 3.2, the effects of pure sine excitation – laminar boundary layer interaction in sec. 3.3 and the effects of amplitude modulation in sec. 3.4. Conclusions are provided in Sec. 4.
2. Experimental set-up
2.1 Actuators
Experiments were preformed on three types of actuators. The isolated actuator experiments were performed on a compact, anodized, metallic actuator having dimensions of 46mm x 48mm and 4mm thickness (as shown schematically in Fig. 1). A slot of 1mm x 39mm connects the cavity with the external fluid. This actuator was fitted with several extensions, elongating one “lip” of the slot. The elongations were 1mm, 5mm and 23 mm long (Fig. 1c).
Additional actuators were designed, fabricated and characterized for the excitation-boundary layer interaction experiments. These actuators had a span uniform cavity driven at the acoustic resonant frequency (about 1kHz) by six Piezo actuators. The slots were 1mm wide by 135mm long. One actuator ejected the excitation normal to
the wall on which it was installed while the other could be installed at an angle of 30° or 150° with respect to the wall, and therefore to the incoming laminar boundary layer (currently only the 30° data set is presented and compared to the 90° case). Fig. 4a shows a picture of the 90° actuator installed in the small wind tunnel test section (to be described next). Note that there is a major difference between the boundary conditions of the compact actuator and the plate inserted actuators, namely a 360° vs. 180° in-plane suction into the slot and fluid entrainment capability during the ejection stage.
Unsteady pressure and temperature were measured in the actuators’ cavities. Indications of the actuator membrane displacements were measured for health monitoring purposes.
2.2 Actuator wind tunnel
Actuator-boundary layer interaction experiments were conducted in a small open-loop wind tunnel (Fig. 4).
Two sets of four DC fans were followed by a honeycomb to remove flow swirl that were followed by a dense screen, situated at the entrance to a contraction (cross sections: 600mm x 600mm entrance and 150mm x 50mm exit, 5th order polynomial). A laminar rectangular jet with mean speeds of 2m/s to 18m/s and turbulence level less than 0.2% is formed at the exit of the contraction.
A transparent test section with dimensions of 150 mm wide, 50mm high and 300mm long (two interchangeable chambers, 150mm long each) was fitted at the end of the contraction section. A laminar boundary layer developed on the walls of the test section. The upper boundary layer was used for the actuator-BL interaction studies (Fig. 4a). The 90° and 30° actuators were installed such that the exit slots were located 193mm and 203.5 mm from the entrance to the test section, respectively (43mm and 53.5mm from the entrance to the second chamber, respectively).
A hot-wire mounted on a 3D traverse system (Fig. 4b) allowed scanning the entire domain with improved time and space resolutions with respect to the PIV, but with other known limitations. Boundary layer profiles measured by HW and PIV on the test wall upstream of the excitation slot verified the laminar nature of the boundary layer and documented its features. The momentum thickness at the slot was 1.04mm at Ue≈10m/s and the shape factor, H≈2.4±0.05, corresponds to a Falkner-Skan flow with β≈0.1±0.05, i.e. slightly accelerating boundary layer. The virtual origin of
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the LBL was found to be at about 100mm upstream of the test section entrance.
2.3 Particle Image Velocimetry (PIV) Set-up
The flow fields generated by the actuators was measured using a two-component PIV system, with a double pulsed Nd:Yag laser, operating below the maximum output of 200mJ/pulse. The laser wavelength was 532nm with a maximum repetition rate of 15Hz. Light-sheet thickness was about 1mm.
The images were acquired using a double exposure CCD camera with a resolution of 1300 x 1030 pixels and a maximum sampling rate of 12 Hz. The camera was placed perpendicular to the light-sheet. A schematic description of the experimental setup for measuring the compact actuator in still air is shown in Fig. 5. The dimensions of the glass container were 450mm x 450mm x 500mm (height).
Seeding particles for the still air experiments of the compact actuator were produced by an Atomizer, creating water droplets on the order of
mµ1 . The particles were fed to the test chamber, and once the required density and distribution were achieved the seeding was stopped and was not operated during data acquisition in order not to affect the flow field. The other two types of actuators were tested as installed in the plate test section on which the LBL developed. These were characterized also in still air, in which seeding was provided by a theatrical smoke generator, used also for the LBL-excitation interaction experiments. The smoke source was positioned at the entrance to the small wind tunnel (on the left of Fig. 4). PIV data was processed using commercial software using a rectangular grid. 2.4 Actuator Characterization A comprehensive bench-top calibration was performed, in order to evaluate the fluidic momentum output of the actuators. These tests included frequency response at several excitation levels using either a pure sine or frequency sweep signals and amplitude scans at selected frequencies. The mechanical resonant frequencies of each active element were easily identified using a feed-back sensor that was a part of the Piezo element. The 150mm long actuators also included a thermocouple and an unsteady pressure sensor installed at the bottom of the cavity, opposite the exit slot and at mid span. A hot-wire was placed in the core region of each slot, and the velocity signal was measured for the relevant range of excitation frequencies, typically between 0.3kHz to 2.5kHz. Fig. 6a shows a frequency scan conducted at five z locations
(x=y=0) of the 90° actuator. The peak exit velocities are plotted along with the cavity pressure fluctuations (right side ordinate) against the excitation frequency. Two resonance frequencies can be identified, the lower one corresponds to the Helmholz resonance while the higher to the active element’s mechanical resonance. Note the better spanwise uniformity, though at lower peak exit velocities, of the acoustic frequency. Due to its superior 2D performance it was selected as the working frequency. Fig. 6b presents amplitude scans of the 90° actuator at the same locations as in Fig. 6a, performed at the acoustic resonance frequency of 1060Hz. One can note two slopes for the peak velocity to cavity pressure amplitude. The slope change occurs at Up≈12m/s. Similar behavior was observed previously in Refs. 12 and 3. The spanwise uniformity of the excitation is better than ±10%, including hot-wire and positioning uncertainty. The 30° actuator was calibrated in a similar manner. Its acoustic frequency was 1040Hz and a typical slot velocity-pressure curves for x=y=z=0 is shown in Fig. 6c, compared to that of the 90° actuator at the same location. The good agreement between the performance curves of the two actuators speaks for itself. Due to the similar correlations for both actuators, the cavity pressure was used as an output magnitude indicator throughout. In addition to a pure sine input excitation voltage signal, the following waveforms were tested: (i), amplitude modulation, (ii) burst mode. Fig. 7 (taken from Ref. 11) shows the excitation, pressure and de-rectified slot exit velocity signal. As noted before (Ref. 11), the velocity signals do not follow exactly the excitation signals, due to the 2nd order dynamic system features. Only pure sine and AM signals will be presented in what follows. 2.5 PIV vs. Hot-wire measurements
In order to evaluate the resolution and uncertainty of the PIV data, a comprehensive comparison between velocity data measured with a single hot-wire (HW) and that of the PIV system was conducted. A HW was calibrated in the velocity range 0.5m/s to 50m/s with uncertainty of 2% (full scale above 10m/s and 5% for lower speeds), and was placed at the slot exit with its long dimension along the long axis of the slot. The exact initial streamwise location was determined by monitoring the rectified HW signal and obtaining the same peak voltage for the blowing and suction stages. This location was used to acquire the slot peak exit velocity used throughout this investigation to characterize the actuator’s output. Then, the HW was traversed in the streamwise direction and velocity data was recorded for 1 sec at a rate of 150kHz. The peak velocity measured
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at the slot exit (for the conditions shown in Figs. 2, 3) was about 43m/s. It was fixed for the 2 mm closest to the slot exit (h=1mm, Fig. 8). The peak velocity decays almost linearly for 2.5<y/h<4.5 and then a slower logarithmic decay rate can be observed. Fig. 8 shows the peak velocities calculated from the 16 phases acquired by PIV for the same flow conditions (PIV data of Figs. 2). The spatial resolution of the PIV is about 0.5mm x 0.5mm (with 50% overlapping in the interrogation process for this data set) and it results in a significant difference of the peak velocities for x<3mm from the slot between the PIV and the HW data. An additional source for the lower averaged peak PIV measured velocity could be the rather low phase resolution at which the PIV images were acquired (16 per cycle). For x>3mm a difference of less than 5% (or max of 2 m/s) provides mutual validation for the PIV and HW data. Special care was taken to minimize reflections from all solid boundaries, but still no valid data was obtained for distances smaller than 0.5mm from the exit of the compact actuator, using the set-up described in Fig. 5. Subsequent improvement enabled reliable data to be measured at distances as small as 0.25mm from the wall on which the excitation-LBL interaction took place.
3. Results
3.1 The effects of exit slot restrictions in still air The evolution of unrestricted excitation in still air was discussed in the introduction and is presented in Figs. 2, 3. The current discussion will focus on several types of restrictions at the slot exit, shown schematically in Fig. 1c.
A number of simplified experimental installations of oscillatory momentum generators, are shown in Fig. 9. The entrainment of ambient fluid is relatively restricted in comparison to the symmetrical compact actuator boundary conditions shown in Fig. 1, which enables in-plane unrestricted suction into the slot and entrainment into the exiting jet. However, an important custom application might require changing the boundary conditions of these actuators, with and without boundary layer interaction (Ref. 5, 7). The configurations shown in Fig. 9 and might be useful to inject oscillatory momentum and unsteady vorticity flux in different directions (other than perpendicular to the surface, and to the flow direction such as shown in Fig. 9 as well), with and without an interaction with a cross-flow. One should bear in mind that the current interest is in generating unsteady and unstable vortical motion in the boundary layer, preferably with identical sign vorticity as that of the mean BL shear and
enhancing it, due to efficiency considerations and not just attempting to inject steady momentum in a method different from steady blowing. A numerical investigation was performed (Ref. 14, 15) of an oscillatory momentum generator interacting with a boundary layer, when the direction of the oscillating momentum was perpendicular to the boundary layer flow direction (as in Fig. 9c, 90° actuation in the current terminology) and reported actuator’s cavity as well as external flow ejected into still air and into cross-flow laminar boundary layer. The interaction between a TBL and 90° excitation was studied experimentally (Ref. 16), sowing the resulting coherent structures and a reduction in mean skin friction. It was shown (Ref. 15) that the wall-normal injected oscillatory momentum could form a mean re-circulating bubble that essentially modifies the external flow streamlines, hence the pressure distribution over the surface. It was also shown, that the size of the bubble (characterized by its length) is linearly proportional to the injected momentum coefficient, µC . The interaction of a
fluidic actuator with a boundary layer has significant practical importance when one is interested in the delay of boundary layer separation or in the promotion of flow reattachment to a solid surface. Note that much lower frequencies will be required for the latter since the effective frequencies were shown to scale with the length of the separated region (Ref. 1) and not with a typical shear-flow thickness as in the former. Separation over an airfoil is typically an unsteady process, involving the formation of large-scale vortices in the separated shear layer, with typical vortex shedding features. It was shown (Ref. 1), that exciting the separated shear layer with unsteady vortices with a typical characteristic frequency on the order of
s
eL
UO 2 , helps to regulate the large coherent
structures that transport high momentum fluid to the vicinity of the wall. Periodic excitation can also assist in transitioning laminar boundary layers into turbulent ones. This mechanism can also delay boundary layer separation, since turbulent boundary layers are more resistant to separation than their laminar counterpart. It is desired to determine the optimal excitation configuration that would lead to required results using the lowest actuation energy expenditure and understand the responsible mechanism. Studies about these questions have not been conducted, to the best knowledge of the authors.
First we studied the flow field generated by an oscillatory momentum generator configured as in Fig. 9a and compared it to that generated by the
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device scheme shown in Fig. 1 (Le/h=0). The presence of a wall is expected to reduce the shear, the peak velocity and the vorticity flux leaving the actuator, due to the no slip condition at the extended wall, and eliminate entrainment on the restricted side. Therefore, the major expected effect of viscosity is to nullify the streamwise velocity at the extended lip, instead of the maximum that was present there in the unrestricted actuator case, due to the slug exiting the actuator’s slot during the blowing stage of the cycle. (An analogy between h wide unrestricted actuator and 2h wide restricted actuator as in Fig. 9a is drawn here) Data that was acquired with an Le/h=23 (h=1mm, fig. 1c) extension of the lower slot lip is shown in Fig. 10. Note that the vorticity scale was limited to 10ms -1 for clarity. The major difference between the oscillatory wall-jet and the data of the free oscillatory jet of Figs. 2, 3, is that one can clearly observe two coherent vortices at the upper edge of the wall jet. The wall boundary layer is clearly seen as negative vorticity near the wall, rather than isolated vortices in the upper edge of the oscillatory jet. The peak streamwise velocity at a distance of 3mm from the slot exit is now 42 m/s with respect to 43 m/s for the free oscillatory jet, using the same excitation voltage. The convection speed of these vortices is about Uc=8.5 m/s or Uc/Up≈0.20 as compared to Uc/Ue≈0.29 for the data shown in Figs. 2, 3. As seen before in Ref. 7, even a very short restriction on one side of the slot exit can significantly affect the evolution of the entrained flow. Fig. 11 compares a free oscillatory jet with a restricted jet (with lower side extension of Le/h=1, h=1mm, Fig. 1c). Comparing the vorticity at a phase of 225°, indicates that the jet is tilted up and that the vortex on the lower side is convected downstream faster (Figs. 11a, 11b). A comparison of the mean velocity profiles corresponding to the above conditions at y/h=21 is shown in Fig. 11c. A vectoring of the mean entrained flow upwards can clearly be seen to take place due to the small extension of the lower side of the exit slot. The effect of a lower side restriction with Le/h=5 (h=1mm) is to cause significant asymmetry in the vertical velocity component and significant vectoring of the resulting jet to the upper side. The coherence of the structures is maintained for larger distances from the slot, and at least two vortices were identified in each phase. The effect on the convection speed of the vortices over the extension and in free air is under investigation. The main difference between the symmetric and the asymmetric actuator exit BC discussed, is the entrainment process. However this process is
expected to be extremely sensitive to the external flow as well, once present.
3.2 The evolution of wall-normal excitation in still air Figs. 12a-12d present four phases of the flow field generated by the actuator operated by pure sine excitation at 1060Hz and peak exit velocity Up=18m/s alongside a schematic of the signal time history (Fig. 12a, indicating the phase of each of the flow fields presented in Figs. 12b through 12e. Fig. 12b shows the velocity vectors when the slot exit velocity is zero. The velocity slug and the accompanying vortices, associated with the previous cycle, traveled about 3.5h downstream and the fluid at the vicinity of the slot is quiescent. At the maximum blowing phase (ϕ=90°, Fig. 12c), a strong fluid slug is ejected from the slot, accompanied by a pair of counter rotating vortices situated at the sides of the strong shear layers. In the following presented phase ((ϕ=180°, Fig. 12d), the slot exit velocity nullifies again and a massive entrainment process takes place between the velocity slug, the vortices (now at y/h≈1.4) and the slot. In the last presented phase ((ϕ=270°, Fig. 12e), the slug and vortices traveled to y/h ≈3.4, the slug velocity and magnitude of vortices have been reduced. A stagnation point flow (as seen in Ref. 5) can be identified in the region bounded by the slot exit and the stagnation point. The slot region is dominated by the suction induced sink like flow. Figs. 13, 14 show the corresponding vertical velocity and out-of-plane vorticity contours of the flow field presented in figs. 12. The first thing to note about Figures 13, 14 is the parallel motion of the ejected slug and the accompanying vortices. The vortices start to form with some phase lag behind the ejected velocity. Fig. 14c demonstrates very nicely and clearly that the vorticity ejected from the slot (as a result of the in-slot shear) accumulates and forms the vortices. Opposite direction vorticity could be seen parallel to the plate in later phases (Fig. 14c, 14d) and it is sucked back into the slot. The flow fields associated with smaller Up, but still greater than Up≈12 m/s are similar in overall features to that shown in Figs. 12-14. However, when the peak exit slot velocity is reduced below 12m/s, a different flow field was measured. Figs 15, 16 show the vertical velocity and vorticity at the same phases as those of Figs. 12-14 but for Up=9m/s. Naturally, much smaller velocities were measured for the ejected slug and suction stages of the cycle. The slug did not seem to significantly propagate away from the slot before being dissolved. Two weak vortices were generated, but are sucked back into the slot. Therefore, the far field would not sense the effect of the excitation at this sub-critical level. The difference between the
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flow fields presented in Figs. 14, 15 could be perhaps best appreciated when comparing phases of 90° and 270° for both Up’s. While in Fig. 14b the vortex-pair started forming and in Fig. 14d it convected away from the slot, in Fig. 16b and 16d we see completely different flow fields in the corresponding phases. Figs 16b, 16d are almost mirror images one of the other, i.e. symmetric-linear flow. The resulting mean vertical velocity at y/h=8 and x/h=0 is practically zero for Up=9m/s while it is 3.2 m/s for Up=18m/s. The corresponding mean velocity was 12m/s for Up=43m/s for the compact actuator data shown in Fig. 2. To better identify the conditions allowing the “escape” of the slug flow and associated vortices from the suction effect, four flow fields measured at time corresponding to the maximum suction velocity at the slot are plotted in Fig. 17. This data set indicates that for the maximum suction phase, the vortices have been sucked back into the slot for Up<12m/s. The vortices escape the suction effect and travel an increasingly larger distance away from the slot as the Up increases (Figs. 17d , 17e). This feature is indicative of the highly non-linear and asymmetric nature of the wall-normal excitation resulting flow field, in otherwise still air. Before proceeding with data presentation and discussion, we should introduce the methods used to identify a vortex and calculate its features. Even the definition of a vortex is under some controversy, all the more, its identification method. Historically, it was performed using dye or smoke flow visualization and the relationship to vorticity dynamics was through HW data and Taylor’s hypothesis. Intuitive vortex identification is straightforward when the vortex is circular and its convection speed have been removed (Ref. 18). Currently, the vortices move in space and significantly change in time, but when coherent, they are easily identifiable either at the peak angular momentum (Ref. 19) or by the location of peak vorticity. The angular momentum was calculated for each point in the flow in four layers that were summed according to the method described in Fig. 18. Fig. 18 presents a typical vortex associated flow field. Its center, as defined by the angular momentum method (AMM), is depicted by a triangle, while the location of the out-of-plane peak vorticity is indicated by the circle. It is clear that the vortex center according to the AMM better corresponds to the intuitive vortex center location. It is also indicated that using the current resolution (25% slot width), four layers of the AMM is appropriate. Also note that the distance between the AMM vortex center and the peak vorticity increased in certain cases. Unless otherwise noted, the vortices were identified using the AMM (Ref. 19).
The vortex core locations were identified and are plotted in Fig. 19a for the three slot exit velocities (i.e., Up=9m/s, 14m/s and 18m/s, Lo/h≈1.5, 2.3 and 3.0, respectively) and for the 90°, plate embedded wall-normal, actuator operating in still air. The vortex core locations are plotted for all the phases (16 per cycle were measured) in which a vortex was identified in the 3mm wide by 4mm long area closest to the slot. The first thing to note is the symmetry of the vortex core locations with respect to the x=0 axis. Vortices were first identified for the three slot exit velocities at y/h≈0.25 and at x/h≈±0.75. Each data point represents a phase increment of 22.5°. The vortices for Up=9m/s do not propagate away from the slot, rather they are ingested into the slot. As Up increases and becomes supercritical, the vortices propagate downstream to increasing distances that are proportional to Up. The vortices initially (for t/T<0.5) move closer to each other due to three possible mechanisms. The first mechanism might be related to lower static pressure at the centerline due to acceleration downstream of the stagnation point located between the slot and the velocity slug. The second mechanism might be related to induced force acting on a vortex in streaming flow according to potential flow considerations. Another possible mechanism offered is a “vena-contracta” effect, considering the vortices as passive attendants of the narrowing slug flow ejected from the slot. The vortices are moving away from the x=0 axis as they lose coherence and transition to turbulence, towards the end of the first cycle. The motion is then explained by entrainment considerations. Fig. 19b presents the vortices y/h locations vs. time in the cycle. Note that the constant slope of the fitted lines, indicating fixed streamwise convection velocities, result in Uc=3.0m/s and 4.2m/s for Up=14m/s and 18m/s, respectively. When normalizing Uc by Up, we obtain 0.23 and 0.21, for Up=14m/s and 18m/s, respectively (for the unrestricted compact actuator with Up=43m/s, Uc/Up=0.29, so the convection speed does not simply scale with the slot peak exit velocity). Since only two Up levels were measured for the plate normal excitation using supercritical Up, it is impossible to determine if there is a trend of Uc/Up or if the difference is due to experimental uncertainty. Also plotted in Fig. 19b are the velocity slug core locations on the x=0 axis. It is practically impossible to distinguish these from vortex core streamwise locations. The latter finding indicates that the models attempting to explain the evolution of these type of flows using only the vorticity dynamics might not be as relevant. Alternative, the vortex might be a passive attendant resulting from roll-up of the intense slug flow high-shear layers.
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Next, the circulation of the vortices was calculated, using a surface integral of the vorticity. The integration was performed around the identified vortex cores (using the AMM), down to the lowest closed vorticity contour level. The vorticity is plotted in Fig. 19c against the time in the first vortex cycle for the three Up tested using the 90°, plate embedded, actuator. The vortices are forming for t/T<0.3. Note that the formation distance would be a strong function of Up, since Uc roughly scales with Up. For t/T>0.3 the circulation decays, while for Up=9m/s the vortex-pair is simply ingested into the slot with diminished circulation. It seems that the circulation decay rate scales also with Up, but more data and additional processing is needed to validate this trend. The scaling of the circulation with the slug properties is justified following the accepted norms for vortex rings formation. The slug model (Ref. 21) predicts the vortex circulation as a result of the vorticity flux ejected from the neck boundary layers during the ejection period. The vorticity flux during the blowing stage of the cycle was calculated and it was found that for the Up=18m/s case, the slot exit vorticity flux, calculated from the PIV data at x/h≈0.4, was 0.046m2s-1 while from the vorticity surface integral, the maximum calculated vorticity was 0.038m2s-1. This finding indicates that indeed, as also seen in the PIV clips (e.g., Fig. 14c), the slot exit boundary layer vorticity rolls up to form the vortices. The fact that the circulation did not saturate (for the compact actuator with Up=43m/s the maximum circulation was 0.13m2/s) as in vortex ring studies (Ref. 23) is encouraging for flow control applications and calls for further study to explore the differences.
3.3 Pure sine excitation – LBL Interaction
The LBL The laminar boundary layer with which the excitation interacted developed on the upper surface of the test section. It originated directly from the contraction with no treatment. The LBL characteristics in the first test section were measured at several x locations upstream of the excitation slot. The displacement thickness was about 1mm while the shape factor was H=2.4±0.05, indicating a slightly favorable pressure gradient and a (linear stability) critical displacement thickness Reynolds number of about 1000. A comparison between HW and PIV measured mean velocity profiles is provided in Fig. 20a. This data was measured 6mm downstream of the 90° slot. Besides the very good agreement between the two measurement methods, this data shows that the presence of the slot did not trip the LBL, and the shape factor was not significantly altered from its value at x/h<0.
Wall-normal (90°) Excitation – LBL Interaction
Fig. 21 shows eight phases of out-of--plane vorticity calculated from PIV measured velocity data in the immediate vicinity of the excitation slot, ejecting the excitation in the wall-normal direction. The peak slot exit velocity was Up=18m/s while the free stream LBL velocity was Ue=8.3m/s. Note that the mean BL vorticity is negative and the vorticity contours are plotted only between ±10m/s. The LBL vorticity flux is of order Ue(dUe/dy) while the excitation vorticity flux is of order Up(dUp/dx) across the slot. The ratio of the excitation to LBL vorticity fluxes is therefore about 4.7, while the impulse ratio ( 22 / ep UhU θ ) is about
2.1. The vorticity contours shown in Fig. 21 indicate that the upstream vortex, with sign opposite to that of the LBL vorticity, is partly cancelled by the incoming LBL vorticity. The remaining positive circulation vortex is ejected into the free-stream and dissolves when convected downstream. The negative vorticity-sign vortex on the other hand, survives and is convected downstream, one vortex per period. As expected, the effects on the incoming LBL are dramatic. The corresponding streamwise velocity contours are shown in Fig. 22a and the mean velocity and streamlines are shown in Figs. 22b, 22c. These figures show a significant redistribution of the streamwise momentum in the BL. The mean velocity field shows what appears to be a tiny separation bubble with a small mean reverse flow region. The bubble is located at x/h≈1. Its size is about 1h long and 2h/3 high. However, what appears to be a mean bubble is irrelevant since there is no point in the flow in which reverse flow exists all the time, as predicted by computations (e.g. those presented in Ref. 15 Fig. 3c, but for slightly different conditions). The temporal bubble seen for the first time downstream of the slot at ϕ=135° (Fig. 22a) is steadily convected downstream with an approximate convection speed of 0.5Ue in a parallel manner to the negative sign vortex (blue in Fig. 21). One of the major candidate applications of periodic excitation is the promotion of LBL transition. It is well known that TBLs are more resistant to adverse pressure gradient and that convection heat transfer significantly increases in a TBL versus its laminar counterpart. This is especially important in low sub-critical Reynolds numbers, in which natural transition does not take place. To quantify transition promotion through excitation, long time-histories of hot-wire measured, near-wall velocity signals were acquired at x/h=30, 75 and 110 downstream of the 90° and 30° plate emanating excitation. Two free-
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stream velocities of Ue=5.5 and 10.5m/s were used in these experiments. Intermittency factors, defined as the time fraction the flow is turbulent, were then calculated for the measured time-histories. The intermittency was calculated using a short-time standard deviation in windows of 0.01s or 0.02s for Ue=5.5 and 10.5 m/s, respectively. A threshold level of 2% Ue was selected for turbulent flow detection. Both the duration of the time window and threshold level were carefully selected such that the results would be only marginally dependent on the selected values of the turbulence threshold and time window duration. Fig. 23a shows a flow visualization picture acquired with the 30° actuator operating at Up/Ue=2.5. The LBL velocity is Ue=8.5m/s and it flows from right to left. The LBL significantly accelerates towards the slot at its upstream side. Downstream of the slot, large structures appear to mix between the layered smoke pattern flowing from right. Figs. 23b-e present intermittency factors vs. normalized peak excitation velocity for the two free-stream velocities (5.5 and 10.5m/s) and for the three x stations (x/h=30, 75 and 100) considered, using two slot orientations, 90° and 30°. The overall conclusion that could be drawn from Fig. 23, is that the shallow angle (30°) downstream introduction of the excitation is more effective for transition promotion. For Ue=10.5m/s (Figs. 23b-23c) and x/h>75 both excitation directions promote a fully turbulent flow, while the 30° excitation does that at 65% the amplitude required for the 90° excitation to achieve the same effect. For a free-stream velocity of 5.5m/s (Figs. 23d-23e) and the 90° excitation, the flow turns turbulent between x/h=30 and 75 (within the measured locations) requiring roughly twice the Up/Ue it required at Ue=10.5m/s at otherwise similar conditions. The 30° excitation at Ue=5.5m/s is capable of promoting the establishment of turbulent flow at a much closer x distance from the introduction of the excitation, but again at roughly twice the Up/Ue required for transition promotion at Ue=10.5m/s. In order to analyze the flow features, determined turbulent by the intermittency criteria at x/h=30 for the 30° excitation with Ue=5.5m/s, we examine the velocity spectra at the near-wall region for a range of Up (Fig. 24a, Ue=10.5m/s for this data). The arrow superimposed on the chart implies increasing Up. The fundamental excitation frequency and its higher harmonics dominate the spectra, but the peaks widen and the gaps between the excitation related peaks fill-up as Up increases. The magnitude of the excitation related peaks significantly attenuate as one progresses from x/h=30 to x/h=75 (Fig. 24b) and the spectra resembles a turbulent one. Same features were identified for the Ue=5.5m/s spectra (not shown),
with the major difference being that lower than the fundamental frequencies become active in the transition process, implying a different mechanism. Fig. 24c presents mean velocity profiles measured at x/h=75 with 30° and 90° excitation and without excitation (baseline). The excited profiles for the 90° excitation resemble turbulent profiles, with H=1.55, that is expected for Reθ≈300, and a logarithmic region, but with somewhat different constants than the accepted “law of the wall” constants for zero-pressure-gradient developed turbulent boundary layer. This is expected since this highly energetic artificially tripped BL has not reached equilibrium state yet. While the 90° excitation significantly increased the momentum thickness, the 30° excitation significantly reduced it, while the shape factor was reduced to 1.79 (from 2.42 in the baseline).
Shallow angle excitation emanating from a plate
Figs. 25a-25c present phase-locked data for the shallow angle of 30° introduction of periodic excitation from the wall embedded actuator ejected into still air, with up=18m/s, fr=1040Hz. In the vorticity data, shown in Fig. 25a, the vortex pair was significantly distorted by the broken symmetry and resembles an unsteady wall-jet flowing to the left, as can be nicely viewed from the s lot tangent velocity component, shown in Fig. 25b, for the same phases and flow conditions as the vorticity data shown in Fig. 25a. The phase-locked, slot perpendicular velocity component (Fig. 25c), shows that in all but the first phase, strong entrainment from upstream of the slot takes place. Even the downstream side of the slot (i.e. x>0) is dominated by wall directed flow, feeding entrained fluid to form the unsteady wall jet. Returning to the vorticity data (Fig. 25a) one can note that the vorticity with sign equal to that of the BL, is residing at all times near the wall, both upstream but more so downstream of the slot. The combined effects of the velocity fluctuations and near-wall vorticity indicate the great effectiveness of this mode of excitation for the delay of boundary layer separation, due to enhanced near-wall vorticity. The vortex with positive vorticity sign is convected to the left, initially rather fast (for ϕ=45° to 135°), but is significantly slowed down by the slot tangent suction velocity during ϕ=180°-270°. During this period (ϕ=180°-270°), the circulation of the positive vorticity vortex is substantially reduced. The dynamics of this vortex should have an important role in unstable, separating boundary layers and perhaps in inducing near-wall motion as in the numerical simulation (Ref. 24). Fig. 26 presents data relevant to the interaction between the 30° excitation ejected from the wall in
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the downstream direction and the LBL with Ue=8.3m/s when Up/Ue=2.2. Note that the field of view is about twice as large, compared to that of Fig. 15. The major effect of the cross-flow LBL is the streamwise acceleration of the vortex pair as compared to the still air case (Fig. 25), allowing the vortex to escape the suction effect, therefore maintaining larger circulation for both negative and positive sign vortices. Several striking differences could be identified when comparing the wall-normal (Fig. 21) and the shallow downstream introduction of the excitation (Fig. 26), when the two types of excitation interact with a LBL in otherwise identical conditions. The circulation of the positive signed vortex created by the wall-normal excitation is eroded by the opposite sine vorticity flux of the incoming LBL (Fig. 21, ϕ=135°-225°), while the positive directed vortex escaping the suction effect in the same phases in Fig. 26, is less affected by the incoming LBL with opposite vorticity flux, due to its positive streamwise velocity, lowering the effective vorticity flux. The wall normal excitation also ejects a pocket of negative vorticity into the free-stream (ϕ=45°-180°, Fig. 21, that is partly responsible for the cancellation of the positive sign vortex, disappeared for ϕ>315°, Fig. 21) and partly for the maintenance and enhancement of the negative vortex. In any event, both sign vortices were identified for the shallow angle downstream directed excitation (Fig. 26) while only a negative sign vortex survived downstream of the wall-normal excitation-LBL interaction (Fig. 21). Moreover, the downstream convection speed of the negative vortex is about twice as large in Fig. 26 as compared to that of Fig. 21, i.e., Uc≈Ue for the shallow downstream excitation and Uc≈0.5Ue for the wall-normal excitation. 3.4 The effects of Amplitude Modulation
Typically, the mechanical and acoustical resonant frequencies of the actuator are at much higher frequencies than the unstable frequencies of the base flow to be controlled, at least in low speeds and large dimensions. In order to efficiently excite the flow, it is desirable to create excitation at these low unstable frequencies. It is possible to use amplitude modulation or burst mode (pulsed modulation, Ref. 6) as an excitation input. It was recently shown (Ref. 11, 22) that burst mode, using extremely low duty cycles, therefore minute momentum coefficients, are very effective for flow control applications. It was hypothesized that a wide excited spectrum is obtained due to the pulsatile nature of the excitation. Therefore, it becomes feasible for the base flow to amplify the frequencies it is most unstable to and be efficient. The evolution of amplitude modulated, burst mode and other complex voltage input signals used to operate oscillatory momentum generators have not been studied previously, according to the
knowledge of the authors. Therefore, detailed flow fields were measured, for the three actuators used in still air and in the presence of a cross-flow BL, in order to gain insight as to the physical mechanism allowing low frequency generation through demodulating of the amplitude modulated high-frequency signal used to drive the actuators. Figs. 27b-27f present vorticity fields corresponding to the peak ejection speed (marked by circles on the excitation signal shown in Fig. 27a) for each high frequency cycle in the 5:1 frequency ratio used in this AM case. In agreement with current findings, as Up increases, stronger and faster vortices are generated. The hypothesis is that the stronger and faster vortices would accelerate and catch-up with the weaker-slower vortices and either pass through or amalgamate with them to generate larger circulation vortex. In any event, the result would be that the far field would only sense the low frequency content due to the capability of the larger circulation vortices with larger convection speeds to survive for longer distances from the actuator’s slot. The vorticity data shown in Fig. 27 corroborates the hypothesis that as the excitation magnitude increases during the cycle, the resulting vortices would be stronger (compare Figs 27a-27c) and that the y/h distance between two vortex pairs increases as well as Up increases between Figs. 27a, 27c. The coherence of the vortices is rather poor due to the large slot exit velocity (Up=35m/s for this case) promoting transition as well as the additional unsteady effects due to the AM signal. To validate the hypothesis regarding pairing, additional data was acquired with the compact actuator operating in still air, at a frequency ratio of 1:10. The phases to be considered can be depicted by the circles plotted on the excitation signal in Fig. 28a. The corresponding vorticity contours are plotted in Figs. 28b-28f. At T1, a vortex pair (marked 1) could be seen at y/h=3 (Fig. 28b). By T2 it propagated to y/h=4 and a new, stronger and faster, vortex pair (marked 2) can be seen at y/h=1 (Fig. 28c). In the following time frame (T3, Fig. 28d), vortex one started decaying and moved to y/h=5 while vortex two moved to y/h=1.5 and gained circulation. Still two closed and separated contours of vorticity could be identified for each vorticity sign vortex in Fig. 28d. At the next time frame (T4, Fig. 28e) the vortices paired to form a single vortex on each side of the x axis, marked by significantly larger circulation, but the core of the new vortex (marked by 2’) did not propagate downstream. At T5, the merged vortex (2’, Fig. 28f) propagated downstream and maintained high circulation. Next we consider AM (sine envelope) signal emanating from the 90° actuator embedded in a plate and operating in still air. Note that in this
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case, sub-critical vortices are sucked back into the actuator, adding an additional mechanism for low frequency generation in the far field, besides the vortex pairing seen in the previous section for the compact actuator. Figs 29a-29e present vorticity contours corresponding to the peak vorticity seen at the proximity of the slot for each high frequency (“fast”) cycle (ϕ=225°). The magnitude of the vortices increases from the first through the third (fast) cycles (Figs 29a-29c). For the first, fourth and fifth cycles, the vortices do not escape the suction effect and are ingested back into the slot (this would occur at ϕ≈270°, see Fig. 17). Indeed only the vortex pair next to the slot can be seen in Figs. 29a, 29b. In Fig. 22c we see the strongest vortex pair just forming and about to amalgamate with the previous vortex (formed in Fig. 22b, second cycle of low frequency, seen now at 2<y/h<2.5). The merged vortex moved to y/h=3 in the next slow cycle (Fig. 29d) and a weaker vortex can be seen next to the slot. The vortices from cycles 3 and 4 can be seen in the 5th cycle being convected away from the slot, while a new, weak vortex was formed at the slot but is about to be sucked back into it (Fig. 29e). Fig. 29f presents the evolution of the HW spectra for y/h>1.5 on x=0, where the velocity is always directed downstream. The data clearly shows that the AM envelope frequency (fm=212Hz) dominates the far-field spectra together with its harmonics. The excitation frequency (fr=1060Hz) and its side bands (fr±fm), and their harmonics (in agreement with the conclusion drawn from Fig. 29e) can be seen as well. Fig. 30a presents 90° wall-emanating, 1:5 frequency ratio AM excitation (Up=14m/s) interacting with a LBL at Ue=8.3m/s, at otherwise identical conditions as in Fig. 29. Presented are five phases of vorticity contours, corresponding to the first instance a vortex appeared at each high frequency (“fast”) cycle next to the slot. One can note that the positive vortex is partially cancelled due to the opposite sign vorticity of the LBL and partly due to slot suction, allowing the positive vorticity to survive in only two out of the five fast cycles. Eventually, for these three cycles (seen in Figs. 30a, 30d and 30e), the negative vortex is sucked back into the slot as well. Only the two strongest negative vortices are shed downstream as a single negative vortex for each cycle of the low (envelope) AM frequency. The mechanism is such that the negative vortex created during the second “fast” cycle is just supercritical, i.e. it neither shed nor ingested back into the slot. During the third “fast” cycle it gathers enough circulation to be convected downstream (or due to the supercritical Up it moves slightly farther away from the slot not to be affected from the suction) and begins to move downstream at the BL edge.
The wall-normal velocity data, shown in Figs. 30b, in identical conditions to the data shown in Figs. 30a, demonstrates that only in the second and third “fast” cycles, does positive velocity (i.e., directed away from the slot) exists, that can explain and enable the vortex to “escape” from the vicinity of the slot, given that the vortex streamwise velocity is initially zero due to the wall-normal injection. Fig. 31 shows interaction of the 30° excitation with a LBL, at otherwise identical conditions to the 1:5 frequency ratio AM signal of Fig. 30. Note that the major difference between the wall normal (Fig. 30) and the downstream introduction of the vorticity flux (Fig. 31), is that the resulting vortices of the shallow downstream introduction have an initial velocity that enables them to “escape” the suction effect and therefore survive further downstream. The flow field associated with the 30°, AM excitation, is extremely rich in details (Fig. 31). The weak positive vortices (fast cycles one and five, Figs. 31a and 31e) are re-ingested into the slot, because they are formed upstream of the slot and are convected over it by the incoming LBL. On the other hand, the negative vortices, created to begin-with downstream of the slot are assisted by the LBL convection to escape the suction effect. As a result, all five negative vortices survive downstream. Their mutual effect is to continuously increase the skin friction. Only the two strongest positive vortices escape the suction effect and are convected downstream alongside the BL edge, with the corresponding negative vortex. A complex mutual induction and interaction with the free stream velocity dictates the vortices motion and interaction. The corresponding HW spectra measured at x/h=15 across the excited BL is presented in Fig. 32. The data shows a very rich spectrum, containing the excitation frequency and its higher harmonics, but dominated by the low AM frequency and its three harmonics. It is hypothesized that the resulting flow field would be extremely effective in separation delay, due to the increased skin friction.
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Conclusions Based on the findings of the current study, the term: ”Oscillatory Vorticity Flux Generator” seems more appropriate than other common terminology to describe the physical evolution of fluidic periodic excitation, either in still air or interacting with an incoming boundary layer. It was found that the vorticity flux from the source (excitation slot) determines the vortex circulation and its subsequent development. The peak exit velocity determines the (linear) convection speed of the vortices, which is identical to the convection speed of the velocity slug ejected from the slot into quiescent environment. It was also noted that the peak vorticity scales with the slug velocity, so it is impossible to distinguish the cause from the effect. A threshold peak slot velocity was identified for vortex “escape” from the suction effect and this level is very sensitive to the boundary conditions. The fluidic periodic excitation promotes laminar-turbulent transition of an incoming boundary layer very effectively, especially when directed downstream at a shallow angle. The evolution of the spectra from highly coherent at the excitation and its higher harmonics, to that similar to turbulent spectra was documented. When the interaction between the vortices emanating from the excitation slot and a laminar boundary layer was considered, it became evident that the excitation direction dictates the sign of surviving vortices. The wall shear stress was significantly increased by the shallow downstream excitation, making the boundary layer more resistant to separation. The mean wall-shear was reduced by high amplitude wall-normal excitation, but the surviving vortices are of the same sign as that of the incoming boundary layer, so a conclusion as to what would be the effect on a separating boundary layer awaits further study. The major effect related to the excitation direction, results from the initial downstream velocity of the vortices, ejected from the 30° actuators. It was found that low frequency excitation is generated in the interaction domain with a laminar boundary layer either through pairing, re-ingestion into the slot of weaker and slower vortices or decay of the slower-weaker vortices either in the viscous boundary layer or through dissipation in the shear-less free stream.
Acknowledgments
The authors would like to acknowledge the following individuals for the special support to this project: T. Miloh, E. Krinosh, M. Vassermann, A. Blas, S. Paster, I. Fono and T. Bachar of the Faculty of Engineering, Tel-Aviv University. Partial support by the Israeli Science Foundation –
equipment initiation fund, The Fleischmann, The Meadow, TAU Internal funds and other sources are gratefully acknowledged. Last but not least special support by T.Ami, L.A. is greatly appreciated.
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24. Luton, A, Ragab, S, and Telionis, D, “Interaction of spanwise vortices with a boundary layer”, Phys of Fluids, V7, N11, 1995, p. 2757.
Fig. 2: Phase locked averaged U contours. Pure sine excitation (1500Hz, Up=43m/s), Actuator exit slot is located at (0,0) with slot exit oriented at y=0 axis. Phase of ‘0’ is U=0, dU/dt>0 at x=0. Actuator “lips” shown at y<0. Compact actuator in still air, Le/h=0.
Fig. 3: Phase locked vorticity contours. Pure sine excitation (1500Hz, Up=43m/s), Actuator exit slot is located at (0,0) with slot exit oriented at y=0 axis. Phase of ‘0’ is U=0, dU/dt>0 at x=0. Actuator “lips” shown at y<0. Compact actuator in still air, Le/h=0. Vorticity level truncated for clarity.
ϕ=135o ϕ=315o
ϕ=270oϕ=90o
ϕ=0o ϕ=180o
ϕ=225oϕ=45o
Fig. 5 Compact Actuator PIV test set-up.
Fig. 4c General view of the small wind tunnel. Flow direction is to the left .
Optical SetupLaser
Atomizer
ActuatorLight sheet
Glass container
Camera
Fig. 4a Ninety deg actuator installed above small wind tunnel test section, flow is to the left. Laser and light sheet forming optics shown below.
Fig. 4b Small wind tunnel test section, flow is to the left. Contraction seen on right and hot-
wire set-up on left.
actuator
Fig. 6 Actuators calibration data. Frequency scan of the 90° actuator (a), Amplitude scan of the 90°actuator at x=y=0 and at the acoustic frequency, conducted at five spanwise locations (b), and Peak slot exit velocity from the 30° and 90° actuators operating in still air and at the acoustic resonance frequency plotted vs. the cavity pressure rms, x=y=z=0 (c).
(a)
(c)
(b)
Fig. 7 Actuator calibration response to different excitation signals (from Ref. 11).
(a)
(c)
(b) AM(AmplitudeModulation)
BM(Burst Mode)
Pure Sine
Input signal
Input signal
Velocity
Velocity
Input signal
Tm=1/Fm
No. of cycles
T [sec]
Velocity
Tm=1/Fm
Fig. 8: Averaged peak velocity comparison of HW and PIV data. Measured with the compact actuator, 1500Hz, Le/h=0, h=1mm.
Fig. 9: Several of the actuator BC used. Origin of axis system is at slot exit.
UeUeUeUeUeUe
y
x
(a)
(b) (c)
y/h
x/h
y/h
x/h
y/h
x/h
y/h
x/h
y/h
x/h
y/h
x/h
y/h
x/h
y/h
x/h
y/h
x/h
y/h
x/h
y/h
x/h
y/h
x/h
y/h
x/h
y/h
x/h
y/h
x/h
y/h
x/h
y/h
x/h
y/h
x/h
y/h
x/h
y/h
x/h
y/h
x/h
y/h
x/h
y/h
x/h
y/h
x/h
Fig. 10: Phase-locked averaged Vorticity contours of extended compact actuator (Le/h=23).Pure sine excitation (1500Hz, Up=45m/s). Vorticity scale was truncated to clarity.Black area covers actuator. The extension upper surface is at y=h/2, h=1mm.
ϕ=0o
ϕ=135o ϕ=315o
ϕ=270oϕ=90o
ϕ=180o
ϕ=45o ϕ=225o
Fig. 11a: Phase-locked averaged Vorticitycontours. 225deg phase of pure sine excitation, Compact actuator, Le/h=0.Note that the actuator slot is located at (0,0).
Fig. 11b: Phase locked average Vorticitycontours. 225deg phase of pure sine excitation, Compact actuator with extended “lip”, Le/h=1. Note that the actuator slot is located at (0,0).
-15
-10
-5
0
5
10
15
-2 0 2 4 6 8 10Vel [m/s]
x/h
Uavg, L/h=0
Vavg, L/h=0Uavg, L/h=1
Vavg, L/h=1
Fig. 11c: A comparison of the mean velocity components at y/h=21, Up=43 and 45m/s for the Le/h=1 and 0, respectively. PIV data.
Fig. 12 Velocity vectors due to pure sine, wall-normal excitation (90° actuator) ejected into still air. Four phases along the excitation cycle are shown, fr=1040Hz, Up=18m/s.(a) Schematic velocity signal at slot, (b) ϕ=0o, (c) ϕ =90o, (d) ϕ =180o, (e) ϕ =270o.
(b) (c)
(e)(d)
(a)
(b)
(c)
(d)
(e)
Fig. 14: Up=18m/s, VorticityContours (Magnitude truncated).Conditions as in Fig. 12.
(a) ϕ=0o
Fig. 13: Up=18m/s, Normalized Vertical Velocity. Conditions as in Fig. 12.
(a) ϕ=0o
(b) ϕ=90o (b) ϕ=90o
(c) ϕ=180o (c) ϕ=180o
(d) ϕ=270o(d) ϕ=270o
(a) ϕ=0o (a) ϕ=0o
(b) ϕ=90o (b) ϕ=90o
(c) ϕ=180o (c) ϕ=180o
(d) ϕ=270o(d) ϕ=270o
Fig. 15: Up=9m/s, Normalized Vertical Velocity. Other conditions as in Fig. 12.
Fig. 16: Up=9m/s, VorticityContours (Magnitude truncated).Other conditions as in Fig. 12.
(b) Up=7.5m/s
Fig. 17: Flow fields measured at phase of maximum slot suction velocity (ϕ=270°) for the wall normal excitation in still air. Frequency 1060Hz.
(a) Schematic slot velocity signal showing ϕ=270°
(c) Up=10.0m/s
(d) Up=12.5m/s (e) Up=15.0m/s
Fig. 18: Vortex identification methods. Top: Peak angular momentum using four layersBottom: a typical vortex, triangle – peak AMM, circle – peak vorticity.
( )( )( )∑ ×
+=
i ii
ii
MurMur
Npf
212
1)(
Peak angular momentum Where:f(p) – Normalized angular momentum parameter.u(Mi)- Velocity vector at point Mi.ri – A vector connecting ‘p’ and ‘Mi’.(Michard et al. 1997)
Fig. 19 (left col.) Vortex core locations for the 90° actuator operating in still air and in Up’s as indicated in legend (a), y/h vortex core and velocity slug locations vs. the normalized time (b), and circulation of the vortices vs. the normalized time (c).
(a)
(c)
(b)
(c)
Fig. 20 A comparison between HW and PIV measured mean velocity profiles. x/h=6, Ue=8.3m/s.
Fig. 21: Phase-locked Vorticity due to interaction of LBL with wall-normal excitation.Up=18m/s (PS, f=1060Hz), Up/Ue=2.2. Phase indicated on each figure.
ϕ=0o
ϕ=45o
ϕ=90o
ϕ=135o
ϕ=180o
ϕ=225o
ϕ=270o
ϕ=315o
Fig. 22a: Phase-locked streamwise velocity during interaction of LBL with wall-normal excitation.Up=18m/s (PS, f=1060Hz), Up/Ue=2.2. Phase indicated on each figure.
ϕ=0o
ϕ=315o
ϕ=270o
ϕ=225o
ϕ=180o
ϕ=45o
ϕ=90°
ϕ=135°
Fig. 22b-c: Mean (averaged over all phases) streamwise velocity (left) and Streamlines (right) due to interaction between LBL and wall-normal excitation. Up=18m/s (PS, f=1060Hz), Ue=8.3m/s. Slot width=1mm, LBL Del*=1.04mm
0
25
50
75
100
0.0 0.5 1.0 1.5 2.0Up/Ue
γ [%
]
x/h=30
x/h=75
x/h=110
Ue
(a)
(c)
0
25
50
75
100
0.0 0.5 1.0 1.5 2.0Up/Ue
γ [%
]
x/h=30
x/h=75
x/h=110
(b) (d)
(e)
Fig. 23 Near-wall intermittency Factor vs excitation level for several x stations, excitation at 1040 or 1060hz.(a) Flow visualization, Ue=8.4m/s, slot orientation 30deg, Up/Ue=2.5(b) 90deg excitation at Ue=10.5m/s(c) 30deg excitation at Ue=10.5m/s(d) 90deg excitation at Ue=5.5m/s(e) 30deg excitation at Ue=5.5m/s. Note abscissa scale change for Ue=5.5m/s.
Fig. 25a: Phase locked vorticity due to 30o excitation ejected into still. Up=18m/s, (PS, fr=1040Hz). Phase shown above left side of figures.
ϕ=0o
ϕ=315o
ϕ=270o
ϕ=225o
ϕ=180o
ϕ=45o
ϕ=90o
ϕ=135o
Fig. 25b: Phase locked velocity along the slot axis (dashed-dotted line) due to 30o excitation ejected into still. Up=18m/s, (PS, fr=1040Hz). Phase shown above left side of figures.Positive directed velocity is away from the slot.
ϕ=0o
ϕ=315o
ϕ=270o
ϕ=225o
ϕ=180o
ϕ=45o
ϕ=90o
ϕ=135o
Fig. 25c: Phase locked velocity along the slot perpendicular direction (dashed-dotted line) due to 30o excitation ejected into still. Up=18m/s, (PS, fr=1040Hz). Phase shown above left side of figures.Positive directed velocity is away from the slot.
ϕ=0o
ϕ=315o
ϕ=270o
ϕ=225o
ϕ=180o
ϕ=45o
ϕ=90o
ϕ=135o
Fig. 26: Phase-locked vorticity due to 30o excitation interaction with LBL. Up=18m/s (PS, f=1040Hz), Up/Ue=2.2, phase shown on figures.
0
0
0
0
1
1
1
1
1
1
ϕ=0o
ϕ=315o
ϕ=270o
ϕ=225o
ϕ=180o
ϕ=45o
ϕ=90o
ϕ=135o
Fig. 27: Vorticity contours of compact actuatoroperated by 5:1 AM (1500Hz/300Hz) excitation in still air, Up=35m/s. Phases shown are at 225o of high frequency.
(a)
(b)
(c)
(d)
(e)
Fig. 28: Vorticity of compact actuator operated by 10:1 AM (1500Hz/150Hz) excitation signal in still air. Up=43m/s. ∆ϕ=90o (of 1500Hz) between images, showing vortex pairing.
Fig. 29: Wall normal (90o) excitation using 5:1 AM input signal (1060Hz/212Hz) Vorticity Contours, Up=14m/s operating in still air. Phases shown are at 225o of high frequency signal. Where (a) is the “weakest” vortex pair and (c) is the “strongest” vortex pair. The vortices at (a), (d) and (e) are sucked back into the slot. The HW spectra along the y/h axis is shown in (e). Note that for y/h<1.5 the spectra is distorted by HW rectification.
(a)
(b)
(c)
(d)
(e)
(f)fm fr
standing
Fig. 30a: Vorticity Contours during Interaction of 90o AM (1060Hz/212Hz) excitation with LBL. Up=14m/s. phases shown are at 225o of high frequency.
(a)
(b)
(c)
(d)
(e)
Fig. 30b: Vertical velocity during Interaction of 90o AM (1060Hz/212Hz) excitation with LBL. Up=14m/s. Phases shown are all at 225o of high frequency. Same conditions as in Fig. N23-1.
(a)
(b)
(c)
(d)
(e)
Fig. 31: Vorticity Contours due to 30o AM (1040Hz/208Hz) excitation interaction with LBL. Up=14m/s. All ϕ=225o of high freq cycle, time progresses from (a) to (e).
(a)
(b)
(c)
(d) (e)
Fig. 32: AM 30 deg excitation BL interaction HW velocity profile spectra measured at x/h=14.
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