[american institute of aeronautics and astronautics 31st aiaa applied aerodynamics conference - san...

American Institute of Aeronautics and Astronautics

1

Flow Over a Backward Facing Step Subjected to Multiple

Synthetic Jet Actuators

31st AIAA Applied Aerodynamics Conference

Active and Passive Flow Control

Aaron M. Sassoon1 and Dr. James E. Hubbard, Jr.

2

University of Maryland, College Park, Maryland, 20740

Dr. Alison Flatau3


and

Zohaib Hasnain4


The ability of synthetic jet actuators to leverage natural instabilities in the flow field due to

separation is reviewed for applications towards virtual shape change. The separating flow over

a backward facing step of height h is studied under the influence of an actuator upstream and

downstream of separation. Experimental tests were conducted in a wind tunnel using particle

imaging velocimetry and time averaged static pressure data to measure and analyze the affected

flow fields and pressure distribution. Results show a single actuator placed upstream of

separation is capable of diminishing the separation region by up to 55%. By placing a second

actuator downstream of separation, the ability to influence the pressure distribution has been

shown. The two actuators demonstrated the ability to affect and

in the region from 0 - 6h

after the step. The location of the second actuator downstream was also shown to be no longer

effective in influencing the pressure distributions after a distance of 4.67h downstream from the

step.

Nomenclature

b = Orifice width of synthetic jet actuator

c = Characteristic length scale

= Pressure coefficient

= Momentum coefficient

FFP = Forward flow probability

h = Step height

L/ = Lift over pressure drag

p = Static wall pressure

= Reynolds Number with respect to step height

1 Graduate Research Assistant, Department of Aerospace Engineering, 3181 Glenn L. Martin Hall Bldg #088

University of Maryland College Park, MD 20742 2 Langley Distinguished Professor, Department of Aerospace Engineering, National Institute of Aerospace, 100

Exploration Way, 23666 Hampton VA, Fellow AIAA 3Professor, Department of Aerospace Engineering, 3184 Glenn L. Martin Hall, AIAA Senior Member.

4 Graduate Research Assistant, Department of Aerospace Engineering, 3181 Glenn L. Martin Hall Bldg #088

University of Maryland College Park, MD 20742

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31st AIAA Applied Aerodynamics Conference

June 24-27, 2013, San Diego, CA

AIAA 2013-3166

Copyright © 2013 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Fluid Dynamics and Co-located Conferences


2

= Strouhal Number of actuator

= Strouhal Number of separated flow

= Free stream velocity reference upstream of step

= Average peak velocity of synthetic jet actuator

u = Stream wise velocity component

x = Distance along the step

= Spanwise distance of actuator in reference to the step

ρ = Freestream fluid density

δ = Boundary layer height

n the aerospace industry there is always an effort to find new ways to fly faster, farther and more efficiently.

Active flow control offers the ability to revolutionize aircraft design, improving performance capability by

simplifying complex control surfaces, and reducing weight. The study of flow control involves manipulating flow

fields in order to modify their aerodynamic characteristics and satisfy a selected performance metric. Over the past

few decades, research and technology advancements have paved the way for the use of an active flow control device

called a synthetic jet actuator (SJA) (Glezer 2011). SJAs or zero net mass-flux devices are small lightweight devices

that can be described in the simplest terms, as a sealed cavity with an oscillating diaphragm and a small opening on

one side of the cavity. As the diaphragm moves up and down, the change in cavity volume induces an expulsion and

ingestion of air through the orifice. With careful design of the orifice for operational parameters (e.g. frequency,

displacement) a vortex pulse train through the orifice is created that coalesces into a jet of air.

During the late 90’s and on through to the early 2000’s there have been numerous review articles regarding the

function and application of SJAs (Greenblatt and Wygnanski 2000, Glezer and Amitay 2002, Glezer 2011).

Synthetic jet actuators have been used for flow control applications such as boundary layer separation control and

virtual aerodynamic shaping. Boundary layer separation control through periodic excitation has been an interest of

many researchers since the 1980’s. Experiments have shown that acoustic excitation of the separating shear layer at

a forcing frequency that is close to the natural shedding frequency Stact~O(Sts), will delay the onset of separation and

stall at high angles of attack (Greenblatt & Wygnanski 2000). Subsequently, Glezer and Amitay proposed excitation

at a frequency that is at least an order of magnitude higher than the natural shedding frequency of the flow,

Stact~O(10 ). They noted that forcing close to the natural shedding frequency of the shear layer can cause

instabilities in the flow field resulting in unsteady aerodynamic forces (Glezer & Amitay 2002). By forcing at a

frequency Stact~O(10 ), the forcing frequency no longer remains coupled to any resonant frequency in the flow,

avoiding any instability that may arise as a result. This also eliminates the limited bandwidth associated with forcing

near the characteristic frequency of the flow. When at ~10Sts or higher, an interaction domain develops between the

jet and the cross flow which results in a closed form recirculation region upstream of separation. This recirculation

region alters the streamwise pressure gradient to delay or suppress any flow detachment that would have otherwise

occurred (Honohan 2000 & Glezer et al 2003). The closed form recirculation that develops acts like a virtual shape,

displacing the local streamlines.

Virtual shaping of airfoils has been an interest of researchers for many years. Synthetic jet actuators can also be

used to virtually shape the airfoil thus increasing performance metrics and extending the aerodynamic profile

without adding additional structural weight. Chatlynne et al. demonstrated the use of synthetic jet actuators for

fluidic shape modification on a Clark-Y airfoil at low angles of attack, yielding a small reduction in pressure drag.

Placing a synthetic jet actuator directly downstream of a passive obstruction creates a recirculation region next to the

surface of the airfoil. The synthetic jet actuator with a miniature obstruction was located on the suction side of a

Clark-Y airfoil. Similarly a study by Chen and Beeler showed that a reduction in lift occurs on the airfoil compared

to the baseline case for a NACA 0015 using only a synthetic jet actuator and no obstruction. Desalvo and Glezer

were able to demonstrate an increase in lift and a reduction in pressure drag with a wedge like obstruction in

combination with a synthetic jet. By placing one of these ‘hybrid’ actuators near the leading edge and another one

by the trailing edge on the pressure side of the airfoil, they were able to trap vortex concentrations close to the

surface, which was then used to alter the Kutta condition of the airfoil. They were also able to show increases in

L/Dp using this method. Shea et al. produced similar results using a synthetic jet actuator behind a gurney flap to

modify the wake of the gurney flap and consequently alter the Kutta condition.

The works cited above on virtual shaping have all focused on altering the shape of current airfoil designs;

however, none have explored the notion that with virtual shaping, airfoil design can transition away from being a

compromise and move towards a fundamentally novel kind of airfoil. An airfoil that is designed from the start using

flow control instead of current airfoils which historically are designed as a compromise between operations at

different flight regimes. Looking forward, aircraft designers eliminate such compromises by employing an active

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flow control device to change the airfoil shape on demand. In order to do so, there needs to be a more

comprehensive understanding of virtual shaping using synthetic jet actuators. Given the brief literature review

presented above, it is evident that some mechanism, either fluidic or geometric, is necessary to displace the local

streamlines to cause separation using a synthetic jet actuator placed behind it to create a region of recirculation. The

simplest and most widely studied geometry of separated flow is the backward facing step. Flow over a backward

facing step will always separate at the step and reattach some distance downstream (Spazzini 2001). Studies as far

back as the 1950’s, have researched the prospects of introducing local forcing to reduce the size of the separated

region (Greenblatt & Wygnanski 2000). A recent study (Yamada et al. 2007) demonstrated the use of synthetic jet

actuators directly upstream of the step in order to control the location of reattachment. However, all of these studies

have focused on forcing close to the natural frequency of shedding shear layer Stact~O(Sts) (Spazzini 2002 &

Yamada et al. 2007).

Recent work by Desalvo et al. (2011) showed a positive influence of multiple actuators adjacent to each other in

affecting flow reattachment over a drooped flap. Building upon this notion, the main objective of this paper is to

study the behavior of the quasi-steady recirculation region that develops over a backward facing step when subjected

to multiple synthetic jet actuators before and after the step. This paper studies the effect of synthetic jet actuators

on the flow over a backward facing step at forcing frequencies which are an order of magnitude higher than the

natural frequency Stact~O(10Sts), investigating the interacting flow domain between two synthetic jet actuators and a

backward facing step. A single actuator placed upstream of separation has been shown to alter the streamwise

pressure gradient in a manner to delay separation (Glezer et al 2003). The purpose of this study is to investigate the

influence of a second actuator placed downstream of the step on the region of separated flow. Wind tunnel

experiments were conducted using Particle Image Velocimetry (PIV) and static pressure ports to study this

interaction between the two jets and the separated flow in the wake of the step. The pressure distribution in the wake

of the step is studied to assess the effect of the two actuators on altering this distribution. The parameters

investigated were the actuator distance from the step and jet momentum coefficient.

I. Experimental Setup

Two separate sets of experiments were conducted. The first set studied the effect of actuator placement upstream

of the step on the flow reattachment length. The objective of this was in order to establish a baseline flow which a

second actuator placed downstream of the step could influence and thus create an interaction domain. The second

study was initiated to observe the combined influence of two actuators on the flow. The first actuator, placed

upstream of the step will be referred to as SJA1; the second actuator, placed downstream of the step will be referred

to as SJA2.

A. Synthetic Jet Actuators

The synthetic jet actuators used in the experiments were based on a NASA design (Rumsey 2004). Each of the

actuators consists of two individual synthetic jet actuators separated by a small distance shown in Fig. 1a. The

spacing between the two actuators was two and a half times the orifice width or 1.27mm. The actuator orifice

measures .5mm x 28mm which yields an aspect ratio of 56. The

piezoelectric disk measured 41mm in diameter. The actuators were

assembled using a torque screwdriver to .5Nm to ensure consistent

boundary conditions.

The frequency response of the actuators was characterized using

bench top hotwire tests. The resonant frequency of the actuators vary

from 1700Hz – 1800Hz due manufacturing variations of the

piezoelectric disc and aluminum housings. Hot wire tests and PIV

measurements in quiescent flow were used to characterize each of the

actuators. A photograph of the PIV tests in quiescent flow is shown in

figure 1b. A single channel hot wire probe was placed 5mm above the

center of the jet orifice and mean velocities were recorded. PIV

measurements were used to characterize the velocity profile of each

jet, under quiescent flow conditions, and to match the velocities for

the pairs of closely spaced actuators. Hasnain (2012) and Smith and

Glezer (2005) showed that the jet profiles of two closely spaced actuators, operated in phase and with matched

velocities, will merge to form a single jet. It is desirable to consider, for the purpose of this paper, the two closely

Figure 1. (a) 3D model of two closely spaced

actuators which was considered a single ‘blackbox’

actuator. (b) Photograph of PIV testing with

actuator in quiescent flow conditions.

a) b)

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spaced actuators as a ‘blackbox’ forming a single synthetic jet actuator. From here on they will be referred to as

such.

B. Wind Tunnel and Step Model

The experiments were conducted in an aerolab wind tunnel at the University of Maryland which has a test

section of .71m x .5m x 1.2m. The floor of the test section was modified with an external ramp and platform in order

to create a step geometry inside of the test section. To maintain the 2-D dimensionality of the flow, the ramp and

platform spanned the entire width of the test section. Fig. 2a and 2b shows a 3-D model of setup in the test section.

The synthetic jet actuators are placed along the centerline of the tunnel as shown in Fig. 2b.

C. Backward Facing Step with SJA1

The first set of tests consisted of using SJA1 to study the effect of the actuator positioned with respect to the step

and its influence on the separation bubble. The step height for these tests was set to 14mm and the cross flow

velocity was set to 8.75m/s which corresponds to a ≈ 7800. The actuation frequency of the jets was kept constant

at 1750Hz and a drive voltage of 108V.

Stereoscopic PIV measurements were taken to obtain quantitative measurements of the flow field and in

particular to measure the effect of the actuator on the separation bubble and shear layer at the step. Two 1MPx

Phantom V311 high speed cameras with a resolution of 1280 x 800 px and a Litron LDY300 ND:YLF laser were

used to capture the stereo PIV images. Figure 3 is a photograph of the test setup in the wind tunnel. A laser sheet

was oriented along the centerline of the actuators. The flow was seeded using mineral oil and a TSI 6 jet atomizer.

Double frame PIV images were captured at 1750Hz, the same as the operating frequency of the synthetic jet

actuators. For each test, 525 image pairs were captured by each camera and processed using the Davis 8.1 software

suite by Lavision Inc. A stereo cross-correlation was used with a multi-pass interrogation window size of 32 x 32

down to a window of 16x16 with a 50% overlap on each pass. A median filter was applied using universal outlier

(a) (b)

b) a)

𝑼

SJA1

SJA2

𝑈

Figure 2. (a) Experimental setup inside of the wind tunnel with laser sheet. (b) Enlarged view of actuator location before and

after step.

SJA1

SJA2

Step Location

Width: .71m

Height: .5m

High Speed

Cameras

𝑼

Figure 3: Photograph of experimental setup installed inside the test section of the wind

tunnel. High speed camera location and actuator locations are denoted in the figure.

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Figure 5. 3-D CAD model of

plastic pressure port plates

illustrated with synthetic jet

actuator.

SJA1

[…] [ …

[…]

SJA2

Ports 11-

21

4mm

spacing

Ports 22-34

5mm

spacing

Ports 35-45mm

10mm spacing

Ports 47 &

48mm Located

310 and 350mm

downstream of

step

20mm

Figure 4. (Top view) Step model with layout of wall static pressure ports.

Ports 1-10

detection for post processing purposes using Davis. All the PIV data presented in this paper represent time averaged

results.

D. Backward Facing Step with SJA1 and SJA2

The second set of tests investigated the interaction between the separated flow over the step and the two

actuators, SJA1 and SJA2. In order to test SJA2 at a point <1h from the step, it was necessary to increase the step

height to 20mm. The free stream velocity was held constant at 7.2m/s, which corresponds to a freestream Reynolds

of ≈9000. The actuators were operated at a constant frequency of 1500Hz. It is important to note that this

frequency differs slightly from the previous test. This was done to mitigate the risk of damaging the piezoelectric

disks during tests by operating at or close to resonance. The disks were driven at voltages between 40V-120V.

The step model was outfitted with 48-

static pressure ports, along its center-line.

The pressure port arrangement on the step

model is illustrated in Fig. 4. The first ten

ports were placed upstream before the SJA1

in order to reference the upstream

conditions. The remainder of the ports were

located downstream of the step as far as

350mm or 17.5h.

The two parameters of interest were the

distance of SJA2 from the step and the

momentum coefficient of each jet, .

As the location of SJA2 was moved

downstream, it was necessary to alter the

locations of the pressure ports alongside it.

Thus a simple, easily maneuverable method was needed to complete the setup for each subsequent change of

location of SJA2. To solve this, a set of plastic plates dimensioned to match the width of the actuator were used with

the pressure ports printed along the center line. For example, for the first location for SJA2, the actuator is located

between 0-1h and the first plastic plate is located between 1h-2h. As the actuator is moved downstream h, the first

plastic plate is moved to 0-1h while the actuator is between 1h-2h. Fig. 5 contains a 3-

D CAD model of the actuators and plastic inserts. The plastic pressure port inserts

were printed using an objet polyjet rapid prototype printer with layer resolution of

16 m.

The tests were conducted using a 48-channel scanivalve with a Sensor-Technics

differential low pressure sensor with a range of 0-50 Pa. The data was acquired using a

National Instruments data acquisition unit. To obtain sufficient time averaged pressure

measurements, 1000 samples were acquired over 10 seconds for each port.

A 2-D CFD study was also initiated to verify the experimental pressure

measurements. The flow over a backward facing step is one of the most widely studied

flow phenomenon in CFD. A baseline CFD study was modeled to compare the experimental baseline with a

numerical model. The numerical modeling was performed using commercial software, Comsol multiphysics. The

CFD model was done using RANS with a k-ε turbulence model. The upstream and downstream boundary conditions

were taken from the experimental data.

II. Results and Discussion

A. Backward Facing Step with Single Actuator Upstream of Step

The output velocity of SJA1 was measured before and after the tests using stereoscopic PIV to ensure the

actuator output remained constant throughout the testing. The averaged velocity profile of the actuator used in

the tests can be seen in Fig. 6, with an average peak velocity of 13m/s. The momentum coefficient, which is

denoted as , defined as follows:

(1)

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where and are the jet and freestream fluid densities, b is the orifice width of

the actuators, is the average peak velocity of the jets, the cross flow velocity, and

c a characteristic length, which for these experiments was set equal to h (Ugrina

2007). The momentum coefficient was kept constant at .31 for this set of tests.

The location of SJA1 upstream of the step was varied from 1.07h – 7.14h (15mm-

100mm). The baseline case without actuation is pictured in Fig. 7a. Note the blacked

out areas in Fig. 7 correspond to masked areas where there was a strong reflection

from the step and the grey rectangle corresponds to the floor of the tunnel. From these

results, the boundary layer height before separation was calculated, based on .99 , to be δ=11.08mm. The step height is thus 1.26δ. It should be noted that according to

classical laminar boundary layer theory, the boundary layer height before the step was

estimated to be 6mm; however, the boundary layer is a turbulent layer as it is twice

the thickness of the estimation. Upon further investigation, it was discovered that the

experimental setup, namely the ramp geometry, tripped the flow upstream of the step

resulting in a turbulent boundary layer. In most real world applications, the boundary

layer is rarely laminar. In addition, many studies have shown that tripping the

boundary layer upstream of separation results in a positive influence on reducing the

separation length.

Results from the tests are shown in Fig. 7a-e. As mentioned earlier, Fig. 7a illustrates the baseline case

without actuation for which decreases in the reattachment length will be assessed from. In Fig. 7b, the actuator is

placed 1.07h upstream and the drastic effect the presence of the actuator has on the step can clearly be seen.

Immediately downstream of the actuator there is a small recirculation region located at the edge of the step which

alters the streamwise pressure gradient, pulling the boundary layer down towards the floor and promoting mixing of

the shear layer. In Fig. 7c-7e. the actuator is moved further upstream and the effect is slightly diminished; however,

there is still a noticeable reduction. This can be attributed to the increase in turbulence upstream of the step as a

result of the actuators located there.

The location of reattachment is time dependent. For this reason, a statistical method (the forward flow

probability or FFP) was used to assess the mean point of reattachment. The forward flow probability is a measure of

how often a vector is facing downstream versus upstream. It can be defined as :

∑

| | (2)

where N represents the number of images evaluated over and u is the x-component of the velocity vector. The y-

component is not of importance as the direction of x-component can be assessed independently of the vertical

component. FFP=1 corresponds to velocity vectors facing downstream 100% and FFP=0 to velocity vectors facing

downstream 0%. It can also be considered as a method to assess the unsteadiness of the x-component of velocity. In

order to determine the reattachment point, it was desirable to evaluate the location of mean reattachment which

corresponds to FFP=.5. Note that for flow over a backward facing step there are often two locations along the wall

for which FFP=.5, the first location is the point the separates the primary and secondary recirculation regions and the

second location is the point of mean reattachment. The results of this can be seen in Table 1. Analyzing Table 1, the

effect of the actuator closest to the step is almost twice the effect of the other actuator locations. It is notable that

actuation as far upstream as 7.14h is still felt at the step.

Figure 6. Average

magnitude of velocity

profile of synthetic jet

actuators

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a)

b)

e)

d)

c)

𝑼

𝑼

𝑼

𝑼

𝑼

Table 1. Reduction in separation length for different values of SJA1 location,

Baseline =1.07h =2.14h =4.28h =7.14h

Separation Length 5.8h 2.6h 4.1h 4.2h 4.4h

Percent change in

separation length N/A 55 % 29% 28% 24%

Figure 7 a-e. Average PIV velocity magnitude plots ≈7800 (a) Baseline case without

actuation (b) actuator distance = 1.07h (denoted by white arrow). (b) actuator distance

=2.14h (denoted by white arrow). (c) actuator distance =4.28h. (d) actuator distance

=7.14h.

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B. Actuator upstream and downstream of step

The second set of tests involved the study of two actuators, one located before and the other after a backward

facing step, using time averaged static pressure data. It was shown in the previous section that the actuator location

closest to the step had the largest influence on the separated flow at the step. Using these results, SJA1 for this study

was placed 15mm (.75h) before the step, which corresponds to the same physical location used in the previous study

discussed above, except for the change in step height. The location of SJA1 was held constant. The location of

SJA2 was then varied in increments of ~20mm from .75h – 4.625h (15mm – 92.5mm) downstream of the step. For

all subsequent results, the location of SJA2 will be referred to as X1-X5, X1 being the closest to the step, X5 the

furthest away.

The momentum coefficient for SJA1 and SJA2 were varied as well. In the previous test case, the momentum

coefficient of SJA1 was considered to be too large to achieve any noticeable interaction between the downstream

actuator. For this set of tests, the momentum coefficient for SJA1 was varied between . The

momentum coefficient for SJA2 was varied between . The results are presented below in Fig. 8-

10 to represent SJA2 location at X1, X3, and X5 respectively.

The results from the 2-D numerical simulation for the baseline case of flow over a backward facing step are

included in Fig. 8-10 as well. The model shows a good agreement with the experimental data except that the

numerical model under predicted the pressure directly after the step. The numerical model also under predicted the

minimum value that occurs the in the experimental baseline at x/h=2.5. Overall, the numerical model performed well

in its ability to capture the overall shape as well as, to a high degree, the physical values that are represented in the

experimental data presented below. The data is presented below along with the rest of the experimental data as a

reference to the numerical model that was used to verify the experimental baseline case.

Note that, the data presented represents only the downstream pressure data from 0-8.5h as the upstream pressure

measurements were only used for reference. The time averaged pressure plots presented in Fig. 8-10 have been

curve fitted as well as non-dimensionalized using which can be defined as:

(3)

where here was chosen based on an average value obtained from the upstream pressure data.

Each of the figures contain two plots which correspond to the lowest (top plot) and highest (bottom plot)

momentum coefficient of SJA1, , respectively. Note, the location of the downstream

actuator is denoted by a dashed red line and labeled SJA2. The line denotes the center of the actuator; however the

actuator spans ±.5h of this dashed line. As a result, in Fig. 8, there is no pressure data up until around 1.5h. In all

three figures it is clear that there are three distinct regions in the pressure data for which the effect of the two

actuators can be assessed. The first region, Region I, is the region from 0-2.5h, Region II is from 2.5-6h, and Region

III, from 6.5h-8.5h.

a) Region I:

In Fig. 8a-b, there is a difference in the curves compared to the baseline when both actuators are on. The case

with only SJA1 on, =0, is first explored in detail to identify the effects of the single actuator case on before

doing so for the two actuator case. Focusing first on the lowest momentum coefficient of SJA1, it is

difficult to come to any conclusion from Fig. 8a as the data is limited in this region due to the location of SJA2. The

same test case can be viewed more effectively in Fig. 9a & 10a which both show that in Region I, has

very little effect on altering the flow compared to the baseline. Shifting now to study the case with highest

momentum coefficient, it is perhaps more obvious looking at Fig. 8b,9b, and 10b as the effect of SJA1

on altering the pressure curves in Region I is more pronounced. In all three figures, the value of has become more

negative, which connotes the effect of the SJA1 has resulted in an increase in suction in Region I. Based on the

results of the previous section, this helps to explain Fig. 7b from the PIV results.

It is worthwhile to discuss this single actuator case a little more in depth as it provides insight into the overall

fluid physics of this study. From Fig. 7b, the jet core can be seen clearly as the trajectory of the jet is turned into the

crossflow, essentially creating a virtual shape change through the displacement of the local streamlines. There is also

a change in the streamwise pressure gradient which has implications towards flow separation. This modification of

the streamwise pressure gradient upstream of separation using synthetic jets has been shown by others to delay or

suppress separation (Honohan 2000, Glezer et al 2003). From Fig. 7b it can be seen that the flow is pulled down

towards the step in a shorter distance essentially causing a suppression in the separation length. For the case with

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only SJA1 on, it can be said that the momentum coefficient of is not large enough to cause a sizeable

change in the streamwise pressure gradient. This helps to understand why there is little difference between the curve

in Region I and the baseline case. As stated earlier, the effect of is to cause an increase in the suction. It

follows that the momentum coefficient of is high enough for a meaningful change in the streamwise

pressure gradient upstream of separation leading to an increase in suction in Region I.

Proceeding to the cases with both of the jets on in Fig. 8-10 a-b, there is a modification in the values of for

all cases compared to the baseline. There is a change in the slope,

, compared to the baseline case. From

conservation of momentum, larger equates to a larger change in velocity. Applying this to the change in

means there is an increase in the local flow velocity in Region I. This increase in velocity can be attributed to a

region of circulation close to the step, perhaps the formation of a coherent structure close to the step (a PIV study

could be done to confirm this). It is noted that in Fig. 8a-b, for the increasing values of there is a small local

change in

, the cause of this is due to the local effects of the synthetic jet actuator. There is, however, a large

difference between =0 and ≠0 which is sufficient to say that the presence of the second jet is affecting the

flow beyond any local effects. As a result, the large change that is seen in

stems from an interaction between the

two jets and the separated shear layer. By increasing as done in Fig. 8b there is an increase in

compared to

the lower value shown in Fig. 8a. An additional study is needed in order to better understand this.

The results of moving SJA2 to X3 or 2.67h downstream from the step can be seen in Fig. 9. In both Fig.9a-b the

effect of having both SJA1 and SJA2 on, results in an increase in suction in Region I. The variations in as a result

of increasing is not significant enough to cause the increase in suction that appears in Fig. 9. The same effect

that was noted above for SJA2 located at X1 does not apply here. For SJA2 at X3 increasing while ≠0 results

in a larger increase in suction. There is also a shift between 1.5h-2h where

begins to increase. Lastly, Fig. 10

represents the extreme case of SJA2 located at X5 (4.67h from the step). In Fig. 10a-b, the curves do not appear

to vary with altering and thus are independent of .

b) Region III: Before discussing Region II it is desirable to briefly discuss Region III. Region III represents the far field flow in

which reattachment of the baseline case flow over a backward facing step with actuation has occurred in the time

averaged flow field. Analyzing the results of Region III in Fig. 8-10, for all cases, is invariant to both and

. The conclusion from this is that flow in Region III for all cases is considered statistically stationary. It should

be noted that for ≠0 in Fig. 8b, there is a downward shift in the value of the that is inconsistent with all the

other data sets; the reason behind this is currently unclear.

c) Region II:

We now consider Region I and Region III as simply boundary conditions for the solution represented by the data

in Region II to satisfy. The boundary of Region III is invariant for all cases while the effects of the SJA1 & SJA2 in

Region I have a direct effect on the flow downstream in Region II. Thus, any alteration in the shape of the curve

in Region I will have an impact on the shape of the curve entering Region II. This however does not draw a clear

picture of what is physically occurring in Region II. To start, in Figure 8a-b the effect is again clear, it is seemingly a

continuation of the effects discussed in the previous section of Region I. The slope,

, is distinctly larger compared

to the baseline case and the case without SJA2 on. Again, there seems to be very little variation in the curves for

different values of . Increasing causes an increase in the slope of the curve. Figure 9a-b show similar

results, though not as pronounced a change as seen in Fig 8. There is a point the curves all converge towards the

single actuator case. There is a shift in this point for the different values of . This is also seen in Fig. 9a-b. There

is a similarity in this point of interest between Fig. 8 & 9. Figure 8a & Figure 9a both converge back to the single

actuator case in the same manner, the same is true for Fig. 8b & Fig. 9b. A further study is necessary in order to

understand what this means physically. Lastly, the case where SJA2 is located downstream at X5 in Fig. 10a-b is

distinctly different than the cases depicted Fig.8 & Fig. 9 namely that the effect of the jet location at X5 does not

have any influence on the curve in Region II except in the close vicinity to the jet. This final result is significant, as

it represents the case where the two jets are acting independent of one another. It signifies that as SJA2 is moved as

far downstream as 4.67h it no longer interacts with SJA1.

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Figure 8. SJA2 at location X1 - Pressure distribution downstream of step with varying momentum coefficient for

SJA2, 𝑪𝝁𝟐. (a) Constant momentum coefficient for SJA1, 𝑪𝝁𝟐=.02 (b) Constant momentum coefficient for SJA1,

𝑪𝝁𝟐=.094.

a)

b)

Figure 9. SJA2 at location X3 - Pressure distribution downstream of step with varying momentum coefficient for

SJA2, 𝑪𝝁𝟐. (a) Constant momentum coefficient for SJA1, 𝑪𝝁𝟐=.02 (b) Constant momentum coefficient for SJA1,

𝑪𝝁𝟐=.094.

a)

b)

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Conclusion

The above work is intended to provide insight into the ability of synthetic jet actuators to leverage natural

instabilities in the flow field due to separation for future applications of virtual shape change. Time averaged particle

image velocimetry measurements showed the effect of actuator placement upstream of the step on the flow

reattachment length. A single actuator placed upstream of separation has been shown to alter the streamwise

pressure gradient in a manner to reduce the length of separation. Actuation at Xr=1.07h reduced the reattachment

length by as much as 55%. Actuation as far upstream as 7.14h from the step was still shown to be effective at

diminishing the separation region by 24%. Time averaged pressure data showed the ability of a second actuator

placed downstream of the step to influence the pressure distribution in the wake of the step. The effect of the second

actuator on altering the downstream pressure distribution was shown to be sensitive to the location of the SJA2. It

has been demonstrated that once SJA2 is located 4.67h downstream from the step, the jet is no longer capable of

having an impact on the pressure distribution outside of the local effects of the jet. It has also been shown that an

increase in momentum coefficient of SJA1, results in an increase of suction in Region I. SJA2 was also shown to

cause an increase in suction in Region I and Region II for actuator locations X1 and X3. When SJA2 is located

closest to the step, an increase in

was demonstrated in Region I & Region II. This alludes to the formation of

flow structures close to the step; a future PIV study is needed to study this further.

Areas for future work include PIV studies to gain insight into the flow interactions in Region I & II under the

influence of SJA1 and SJA2. The effects of phase and frequency modulation were not addressed in this study,

however, both have been shown to be an important parameter and will also be an interest for future work.

Figure 10. SJA2 at location X5 - Pressure distribution downstream of step with varying momentum coefficient

for SJA2, 𝑪𝝁𝟐. (a) Constant momentum coefficient for SJA1, 𝑪𝝁𝟐=.02 (b) Constant momentum coefficient for

SJA1, 𝑪𝝁𝟐=.094.

a)

b)

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Acknowledgments

This project has been supported through the NSF Award # 1031077 GOALI: Phased Array Synthetic Jets for

Influencing Dynamics of Complex Flows, Dynamical Systems, Fluid Dynamics.

The authors would like to thank Dan Clingman, Associate Technical Fellow at the Boeing Company for all his

time and support assisting externally on this project. The authors would also like to acknowledge the willingness to

share resources of all members of Jones’ Labs at the University of Maryland College Park. Without their facilities

this study would have been considerably hard to perform. Also we would like to acknowledge the contributions of

Alexander Brown who laid the foundations of this project by authoring the NSF proposal that is funding it. Many

thanks to our friends and colleagues including Andrew H. Lind, Jose Mondragon, Samantha Walters, and Lauren

Trollinger for being more than willing to help with the experiments. We would also like to acknowledge the help of

Dr. Alan E. Winkelmann and Dr. Kenneth T. Kiger for their advice related to the experiments. Last but not least we

would like to thank our families without their support this would not have happened.

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