American Institute of Aeronautics and Astronautics1

An Experimental and Numerical Investigation on FluidicOscillators For Flow Control

Ciro Cerretelli* and Emad Gharaibah.†

GE Global Research Europe, Munich, Germany

Fluidic oscillators are actuators that are essentially constituted of a flow vane with nomoving parts. They are very effective in generating an oscillating velocity field, and becauseof their robustness they have the potential to meet most application requirements. In thiswork we investigate the flow field within the oscillator and the basic physical laws thatgovern the behavior of such actuators. We develop a simple analogy based on the LumpedModeling theory for fluidic components, where the oscillator is essentially modeled as a R-C-R circuit. With this theory we are able to predict the frequency of oscillation. Ourpredictions compare very well with experimental data from Hot-Wire Anemometry and withUnsteady Numerical Simulations, which can be employed as a powerful design tool when theinfluence of the vorticity dynamics on the effectiveness of the oscillator is better understood.This study also shows that it is possible to achieve high values of fluctuating (RMS) velocitycomponents at reasonable jet efficiency.

I. Introductionlow control actuators are devices that are capable of enacting large-scale changes in a flow field by employingonly a small amount of such flows. The implementation of these changes is usually done with the intention to

improve the performance of a fluid-based device whether it is a flying vehicle, a home appliance or aturbomachinery component. In practical terms this translates into increasing thermodynamic efficiency, reducingfuel consumption, reducing drag, enhancing lift, abating noise or suppressing combustion dynamics. A greatemphasis has recently been placed on assessing the merits of flow control in overcoming boundary layerseparation.1-5 Separation is often limiting performance and efficiency and presents itself in a variety of situationsranging from external aerodynamic flows to internal flows. For example, separation can occur throughout thecompression system of aircraft engines and power system turbines, especially in highly loaded turbomachinerypassages and transition ducts.1

Flow control actuators are employed to inject small amounts of air taken from high-pressure sources into thenear wall region upstream of a separated flow. In this way, the boundary layer may be sufficiently energized toovercome the downstream adverse pressure gradient and avoid flow separation. Because the extraction of this high-pressure air results in a penalty on the overall system performance, it is necessary to implement boundary layerinjection as efficiently as possible and to minimize the flow requirements of steady blowing or suction in order toachieve a net positive cycle impact.

There has been an extensive amount of research in this field during the previous two decades.6-9 This researchhas provided great insight into the physics of large coherent structures. It also achieved impressive results in thecontrol, or rather the manipulation, of turbulent shear flows, with reduction of more than two orders of magnitude inthe required massflow to repair flow separation. The vast majority of these studies, however, employ a range ofmechanical or piezoelectric actuators such as pulsed jets, synthetic jets, Hartmann tubes or plasma actuators. Thesedevices are often large in size, employ numerous moving parts, have reliability issues and limited lifetime and areextremely difficult to implement in high temperature components. Therefore, in recent years there has been arenewed interest in the field of fluidics,10-11 in particular in fluidic oscillators for flow control application. Thesefluidic actuators have the advantage of a high frequency bandwidth, small mass flow requirements and areessentially constituted by a flow vane with no moving parts. For this reason, they have the potential to meet mostapplication requirements.

* Research Scientist, Energy and Propulsion Technologies, AIAA Member, <ciro.cerretelli@ge.com>.† Research Scientist, Energy and Propulsion Technologies, <emad.gharaibah@ge.com>.

F

37th AIAA Fluid Dynamics Conference and Exhibit25 - 28 June 2007, Miami, FL

AIAA 2007-3854

Copyright © 2007 by General Electric. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

American Institute of Aeronautics and Astronautics2

In a recent study, Cerretelli & Kirtley12 have successfully demonstrated fluidic oscillators in a hump diffuser asmeans of preventing boundary layer separation due to an adverse pressure gradient.However, there have been otherattempts13 to incorporate these devices in turbomachinery components such as stator vanes, with results that havenot been entirely positive up to this point. The reasons for this are probably related to the high-pressure drop thatthese actuators require in order to generate unsteadiness. It is necessary to operate these devices close to the point oftheir maximum efficiency, which is strongly dependant on the specific requirements of each application and in away that is the most effective on repairing the separated boundary layer flow. Due to often highly complicatedgeometries and associated narrow spaces, designing the proper fluidic oscillator that can fit in the available space ismost certainly not a trivial exercise.

The intent this study is to investigate the physical mechanism and the scaling laws for flows in fluidic oscillatorsin order to tune their performance in terms of oscillation frequency and mass flow. We perform this investigation bymeans of experiments and CFD analysis.

II. Theoretical ApproachFluidic oscillators have been employed for the past four decades, and a review of the most common

configurations can be found in Campagnuolo & Lee.14 A feedback oscillator constitutes the core of the no-moving-part actuator examined in this study. The working mechanism of such oscillators is shown in Fig. 1. This deviceconsists of a high-gain bistable fluid amplifier in which part of each output signal is fed back and applied as anegative signal at the amplifier's control port to switch the jet. The operation of the oscillator can thus be analyzed intwo parts: the switching of the bistable amplifier, and the response of the feedback network. The switching time ofthe amplifier is typically negligible compared with the transport time of the network, therefore the frequency of theoscillator is basically determined by the network itself.

In order to obtain the working equation for the oscillator we make use of the lumped parameter analysis firstdescribed by Deadwyler.15 For the system described in Fig. 1 the feedback network can be modeled as a R-C-Requivalent circuit where the feedback line, the entrance and exit orifices act as Resistors while the feedback volumesact as Capacitors (Fig. 2). A fluid Resistor and Capacitors can be written as as:

m

P

flow

potentialR

&

ρ/∆== (1)

RT

VC

γρ= (2)

where ∆P is the pressure drop, ρ is the density, m& is the mass flow, V is the capacitor volume, T is the temperature, γis the polytrophic coefficient and R is the gas constant. For a bistable fluid amplifier the switching of the power jetoccurs when the differential flow across the power jet at the control nozzles reaches a critical value

(a) (b) (d)(c)

PS

(a) (b) (d)(c)(a) (b) (d)(c)

PS

Figure 1.Feedback fluidic oscillator: switching mechanism. PS indicates the supply plenum pressure.

American Institute of Aeronautics and Astronautics3

21 SSS mmm &&& −=∆ where 1Sm& and 2Sm& are the mass flow at the switch- enacting branch and receiving branch

respectively. When the jet is flowing in the left outlet and will eventually switch to the right outlet, the differentialflow can be computed as the rising control low from the left feedback minus the decaying control flow from theright feedback, which can be written as:

( )

tCRR

RR

SR

tCRR

RR

S

tCRR

RR

L

emm

emeRR

Pm

+−

+−

+−

=

+

−

+∆=

21

21

1

21

21

221

21

21

1

&&

&&ρ

(3)

The difference flow for the network can thus be easily obtained as RL mmm &&& −=∆ which yields the following

operating equation:

( ) ( )t

CRR

RR

S emRR

P

RR

Pm

+−

∆+

+∆

−+∆=∆ 21

21

2121

&&ρρ

(4)

Switching occurs when the differential flow reaches the critical value Sm&∆ and the switching time St can then be

obtained from equation (4) when Smm && ∆=∆ . Since the switching process from right to left outlets is exactly

identical, the full period of the oscillator will be twice the switching time and the frequency of oscillation is thengiven by:

( ) ( )

∆−

+∆

∆++∆

+

==

SSS m

RR

Pm

RR

P

RR

CRRtf

&&ρρ 212121

21 ln2

1

2

1(5)

From equation (5) it ispossible to determine thegeometrical parameters that arenecessary to obtain the desiredfrequency, which are feedbackvolume, orifices and length. It isindeed possible to design fluidicoscillators that are almostpressure-insensitive, and fluidic oscillator that are pressure-controlled. Depending on the requirements of thespecific application, one of these two solutions would be preferred.

III. Pressure-Insensitive and Pressure-ControlledOscillators

Following the theoretical considerations discussedabove, two different feedback oscillators (A) and (B) havebeen designed for our experiments (see Table 1). Thefluid amplifier is identical in both devices, but thefeedback path geometry differs, thus changing frequencycharacteristic between the two. Oscillator (A) operates ata constant frequency f ≈ 500 Hz, and oscillator (B)operates at a pressure-controlled frequency ranging from500Hz ≤ f ≤ 2500Hz. Examples of the unsteady velocitywaveforms measured with a hotwire anemometer at theoutput of the oscillators are given in Fig. 3 and Fig. 4,

21 mm && +

21m&

21m&

2m& 2R

1R

ρ/P∆

21 mm && +

2m&1m&

Figure 2.R-C-R Fluidic Network.

Oscillator A OscillatorBNozzle Width 0.050 in. 0.050 in.Nozzle Depth 0.120 in 0.120 inExit channel Width 0.055 in 0.055 inCapacitor Volume 0.320 in3 0.016 in3

Table 1. Features of the fluidic oscillator.

American Institute of Aeronautics and Astronautics4

together with the frequency response curve as a function of the driving pressure. The hotwire probe was placed onenozzle diameter downstream of the exit surface. The modulation is very strong, with the RMS velocity componentranging from 35% to 60% of the average value of the outlet velocity, as it is shown in Fig. 5.

It is somewhat difficult to quantify the "pressure drop" and the "efficiency" of a fluidic oscillator, since it is anunsteady device and it requires pressure ratio significantly greater than 1 to operate in the bistable mode. An idealoscillator would have a maximum velocity equal to the ideal frictionless velocity, a minimum velocity equal to zero

(complete shutoff) and a RMS velocity component of 21 of the average value. In practice, oscillators can never

attain complete shutoff because of the inherent leakage that is present in any fluidic bistable switch.16 Figure 6 gives

t [s]

v[m

/s]

0 0.002 0.004 0.006 0.008 0.010

100

200

pS/p0

f[H

z]

1 1.2 1.4 1.6 1.8 2 2.20

100

200

300

400

500

600

Figure 3.Feedback fluidic oscillator A, f≈550 Hz. a)Velocity waveform as measured by the HWA. b)Frequency response as a function of supply pressure.

t [s]

v[m

/s]

0 0.002 0.004 0.006 0.008 0.010

100

200

pS/p0

f[H

z]

1 1.2 1.4 1.6 1.8 2 2.20

500

1000

1500

2000

2500

3000

Figure 4.Feedback fluidic oscillator B, 500Hz ≤ f ≤2500Hz. a) Velocity waveform as measured by theHWA. b) Frequency response as a function of supplypressure.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

p/p0

Vrm

s/V

ave

osc. A

osc. B

Figure 5.RMS velocity component for oscillatorsA and B as a function of the supply pressure.

pS/p0

v[m

/s]

1 1.2 1.4 1.6 1.8 20

100

200

300

400Ideal NozzleMin Velocity, AMax velocity, AMin Velocity, BMax velocity, B

Figure 6.Frictionless nozzle velocity, oscillator maximumand minimum velocity as a function of the supplypressure.

American Institute of Aeronautics and Astronautics5

an indication of the efficiency of the oscillators employed in this work, by plotting the velocity of an idealfrictionless nozzle, the maximum velocity and the minimum velocity from the oscillator outlets. It can be noticedthat the devices have a relatively small minimum velocity and the maximum velocities often exceed 80% of theideal values. Further experiments are currently in process in order to establish the influence of geometricalparameters such as splitter distance, aspect ratio and splitter divergence angle on the output signal of the oscillator interms of minimum and maximum velocities and frequency.

IV. Scaling laws: effect of scale and fluid density changesFluidic Oscillators can be used in a variety of applications. In order to test the validity of our design laws, we

performed experiments to investigate the effect of size and medium change on the frequency of oscillation. In thefirst experiment we built an oscillator identical to oscillator (B) described in Table 1, but scaled-up by a factor of 10.The result for the frequency characteristics are described in Fig. 7a, while the frequency scaling is depicted in Fig7b. It is possible to see that when the plenum pressure is high enough, the scaling of the frequency stabilizes at8.263, which is below the factor of 10 that simple dimensional reasoning would suggest. But in fact, when equation

(5) is considered it is clear that the logarithmic term does not remain constant after scaling, and that thereforeintroduces a factor of about 0.83 to the simple algebraic multiplier.

In the second experiment we tested both oscillators A and B with different media, namely Helium and Neon. Theresults are shown in Fig. 8 and indicate that for He and Ne the frequencies relative to Air scale respectively as

73.2/ =AirHe ff and 26.1/ =AirNe ff . These scaling factors are smaller than the ones due to purely transport

phenomena that would be merely given by changes in the sound speed:

86.1//

16.4//

====

AirNeAirNe

AirHeAirHe

aaff

aaff(6)

This would occur if the feedback circuits were constituted by transport lines only, with no capacitors. The effect ofthe capacitors can then be quantified as:

( ) ( )( ) ( ) 68.0//

66.0//

==

AirNemeasuredAirNe

AirHemeasuredAirHe

aaff

aaff(7)

p/p0

f Scal

e=1

/fSc

ale=

10

1 1.2 1.4 1.6 1.80

2

4

6

8

10

p/p0

f[H

z]

1 1.2 1.4 1.6 1.8 20

500

1000

1500

2000

2500

3000

Oscillator B, Scale=1Oscillator B, Scale=10

Figure 7.Scale effect on the oscillation frequency for oscillator (B)

American Institute of Aeronautics and Astronautics6

V. Numerical SimulationsIn order to develop a valid predictive tool and to gain invaluable insight into the flow physics and the vortex

dynamics governing the behavior of the oscillators, we have performed numerical simulation for the geometries (A)and (B) described in Table 1. Figure 9 shows a comparison between a typical experimental waveform and the CFDdata; it is possible to see that the velocity signal is reproduced in good detail; predictions are good for the peak andminimum velocities. It is possible to see that the bimodal behavior in the peak region is captured very well with twodistinct local maxima. The slight shift in the velocity waveforms is symptomatic of a small difference in theprediction of the frequency. Figure 10 shows the pressure-to-frequency characteristic of the oscillators: the unsteadyCFD results are able to predict the operating frequency with an error of less that 10% for both geometries. Theswitching phase of the nozzle jet that is caused by the lateral jets from the feedback capacitors is shown in details for(B) in Fig. 11. In particular, it is possible to see that the second local maximum in the velocity waveform isassociated with the highly distorted vena that ensues when the jet from the nozzle is switching. This is also coupledwith an interesting vortex structure, comprising two strong counter-rotating vortices developing in the outlet fromwhere the flow has switched. These vortex structures are very likely to have a strong influence on the minimumvelocity (leak) out of the oscillator.

Figure 12 shows the peculiar vorticity dynamics that ensues in the feedback capacitors of oscillator (A). Due tothe relative large size of such feedback, the feedback flow to the control port induces large vortices that are presentduring the whole switching cycle, both when the flow is attached to the respective wall side or detached from it. Thecapacitor flow becomes strongly two-dimensional and is substantially different from the one-dimensional flow thatcharacterizes a small capacitor, such as the one in oscillator (A). It is very likely that such large vortices stabilize theflow and play a definite role in generating the quasi-flat frequency response.

t [s]

v[m

/s]

0.002 0.0025 0.003 0.0035 0.004 0.0045 0.000

100

200

ExperimentsCFD

Figure 9.Data-CFD comparison of the velocitywaveforms at oscillator exits and of the frequencycharacteristic law as a function of the supply pressure

0

0.5

1

1.5

2

2.5

3

3.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

p/p0

f/f a

ir

fHe/fAir, A

fNe/fAir, A

fHe/fAir, B

fNe/fAir, B

Figure 8.Frequency of Oscillation for oscillator A andB operating with Helium and Neon

pS/p0

f[H

z]

1 1.2 1.4 1.6 1.8 2 2.20

500

1000

1500

2000

2500

3000

ExperimentsCFD

pS/p0

f[H

z]

1 1.2 1.4 1.6 1.8 2 2.20

100

200

300

400

500

600

700

ExperimentsCFD(A) (B)

Figure 10. Data-CFD comparison of the frequency characteristic law as a function of the supply pressurefor oscillator inserts (A) and (B).

American Institute of Aeronautics and Astronautics7

Figure 11. Velocity and vorticity flow fields of the switching phase of the nozzle jet as computed by ourCFD methods for oscillator (B). a) End of one semi-cycle, jet is attached to right wall. b) Beginning ofswitching, overpressure builds at right control port. c) Overpressure at control port reached the criticalvalue. d) Switching begins. e) Switching proceeds. f) Switching is almost complete, note the system ofcounter-rotating vortices which develops in the left passive branch

American Institute of Aeronautics and Astronautics8

The very good agreement between the experimental result and numerical simulation for frequency and velocitydata indicates that at this stage our CFD tools can indeed be used for designing fluidic actuators. However, aseparate study would be needed in order to fully understand and better quantify the effect of the vortex dynamics onthe various design parameters in order to allow for the design of more efficient and better controlled oscillators.

VI. ConclusionsFluidic oscillators are actuators that have the advantage of a high frequency bandwidth, small mass flow

requirements and are essentially constituted by a flow vane with no moving parts. They are very effective ingenerating an oscillating velocity field, and because of their robust design and lack of complicated actuationmechanism they are extremely reliable and have the potential to meet most application requirements. In this workwe develop a simple analogy based on the Lumped Modeling theory for fluidic components, where the oscillator isessentially modeled as a R-C-R circuit. With this theory we are able to predict the frequency of oscillation, and thuswe are able to design both pressure-controlled and pressure-insensitive oscillators. Our design predictions comparevery well with experimental data from Hot-Wire Anemometry, and allow us to achieve high level of unsteadiness,where values of the fluctuating (RMS) velocity are higher than 60% of the average velocity at reasonable jetefficiency. In order to further refine our design tools, we investigate the flow field within the oscillator and thebasic physical law that govern the behavior of such actuators with Unsteady Numerical Simulations. Thesecomputations show the presence of complicated vorticity structures, often in the form of counter-rotating vortexpairs, that are peculiar to the specific oscillator design. This work shows clearly that a deeper understanding of theinfluence of the vorticity dynamics on the oscillator flowfield would allow designers to employ unsteady CFD as apowerful deign tool in order to increase the RMS velocity to average velocity ratio and to allow a better tuning ofthe output frequency to the application requirements.

AcknowledgmentsWe are indebted to Ron Capello, whose technical skills and dedication actually made the measurements happen.

We have very much benefited from many discussions with Dr. Kevin Kirtley. General Electric Company’s financialsupport is gratefully acknowledged.

References1Lord, W.K., MacMartin, D.G., and Tillman, T.G., “Flow Control Opportunities in Gas Turbine Engines,” AIAA Fluids

Conference, AIAA, Reston, VA, 2000.2Jenkins, L., Althoff Gorton, S., and Anders, S., “Flow Control Device Evaluation for an Internal Flow with an Adverse

Pressure Gradient,” 40th Aerospace Sciences Meeting and Exhibit, AIAA, Reston, VA, 2002.3Lin, J.C., Howard, F.G., Bushnell, D.M., and Selby, G.V., “Investigation of Several Passive and Active Methods for

Turbulent Flow Separation Control,” 21st Fluid Dynamics, Plasma Dynamics and Lasers Conference, AIAA, Washington, D.C.,1990.

Figure 12. : Vorticity and velocity flow field characterizing the feedback capacitors of oscillator (A).

American Institute of Aeronautics and Astronautics9

4Walker, S., “Lessons Learned in the Development of a National Cooperative Program,” 33rd AIAA/ASME/SAE/ASEEJoint Propulsion Conference and Exhibit, AIAA, Reston, VA, 1997.

5Washburn, A.E., Althoff Gorton, S., and Anders, S., “Snapshot of Active Flow Control Research at NASA Langley,” 1stFlow Control Conference, AIAA, Reston, VA, 2002.

6Luedke, J., Graziosi, P., Kirtley, K. & Cerretelli, C., “Characterization of Steady Blowing for Flow Control in a HumpDiffuser,” AIAA Journal, Vol. 43, No. 8, pp. 1644-1652, 2005.

7Seifert, A. and Pack, L.G., “Active Control of Separated Flows on Generic Configurations at High Reynolds Numbers,”AIAA 99-3403, June – July 1999.

8Wignanski, I.“Boundary Layer and Flow Control by Periodic Addition of Momentum,” AIAA Paper 97-2117, 4th AIAAShear Flow Conference, June 29-July 2, 1997.

9Greenblatt, D. & Wignanski, I., “The control of Flow Separation by periodic addition of momentum,” Progress in AerospaceSciences, Vol. 36, pp.487-545, 2000.

10Gregory, J., Sullivan, J., Raman, G.& Raghu, S., "Characterization of a Micro Fluidic Oscillator for Flow Control", AIAA-2004-2692, 2nd AIAA Flow Control Conference, Portland, Oregon, June 28-1, 2004.

11Kim, B., Williams, D., Emo, S. & Acharya, M., "Large Amplitude Pneumatic Oscillator for Pulsed-Blowing Actuators",AIAA Paper 2002-2704

12Cerretelli, C. & Kirtley, K., "Boundary Layer Separation Control with Fluidic Oscillators", ASME Turbo Expo 2006,GT2006-90738.

13Culley, D.E., Prahst, P.S., Bright, M.M. & Strazisar, A.J., "Active Flow Separation Control of a Stator Vane using SurfaceInjection in a Multistage Compressor Experiment, ASME Paper GT2003-38863, Proceedings of ASME Turbo Expo 2003.

14Campagnuolo, C.J. and Lee, H.C.,"Fluidic oscillators", Instruments and Control Systems, pp. 99-103, June 1970.15Deadwyler, R, "Theory of temperature and pressure insensitive fluid oscillators". Harry Diamond Laboratories TR 1422,

1969.16Kirshner, J.M., Katz, S., "Design Theory of Fluidic Components", Academic Press, NY 1975.