Active Noise Control of Supersonic Impinging Jets

Using a Physical Model

J. Choi∗ D. Wee∗ A. M. Annaswamy†

Massachusetts Institute of Technology, Cambridge, MA, 02139

F. S. Alvi‡

Florida A & M University and Florida State University, Tallahassee, FL

Supersonic impinging jets produce a highly unsteady flowfield leading to a noisy en-vironment with high dynamic pressure loads on nearby surfaces. In prior work, it wasdemonstrated that microjet injection along the circumference of the main jet nozzle di-rectly into the shear layer of the main jet disrupts the feedback loop inherent in high-speedimpinging jet flows, thereby significantly reducing the adverse effects produced. The mi-crojet action was due to steady blowing whose flow rate was either uniform along thecircumference or varied using the eigenmode of the flow. While these methods yieldedsome successes, uniform reduction of all operating conditions was not obtained. In orderto obtain an improved reduction of the unsteadiness, a new model of the impinging jet flowfield is suggested in this paper based on a collision model of two identical vortices. Theintroduction of the microjet appears to cause a weakening of this vortical structure andleading to noise reduction. The vortical structure seems to be destroyed effectively whenthe microjet injection is pulsed, thereby leading to uniform suppression of impinging jetnoise.

Nomenclature

d Nozzle diameter of mainjet, mD Diameter of lift plate, mh Distance from lift plate to ground plane, mm Mass flow rate, kg/sρ Density of air, kg/m3

U0 Mean velocity of microjet, m/sA Cross sectional area of microjet, m2

B Amplitude of velocity fluctuation, m/s

I. Introduction

The interaction between the ground and the high speed jet emanating from a STOVL aircraft nozzlegenerates discrete, high-amplitude acoustic tones. Such discrete tones cause high levels of noise and acousticfatigue of nearby structures and are also the cause of lift loss and ground erosion. Suppression of these tonesrequires destabilizing the feedback loop,1 which can be realized by suitably disturbing the shear layer nearthe nozzle exit. Two methods of unsettling the shear layer, which include using coaxial flow2 and counterflow,3 have showed a moderate reduction in noise level. A more flexible way of affecting the shear layerthat has been attempted in reference[1] is to introduce microjets along the periphery of the nozzle exit. Due

∗Graduate Research Assistant†Senior Research Scientist, Member AIAA‡Associate Professor, Senior Member AIAA

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11th AIAA/CEAS Aeroacoustics Conference (26th AIAA Aeroacoustics Conference)23 - 25 May 2005, Monterey, California

AIAA 2005-2893

Copyright © 2005 by Annaswamy. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

to their small size, these microjets can be optimally distributed along the circumference and can also beswitched on and off on-demand.

While it has been shown in the previous work1 that an open-loop control strategy that employs themicrojets is effective in suppressing the impingement tones, the amount of suppression is dependent to alarge extent on the operating conditions. Since in practice, the flow conditions are expected to changedrastically, a more attractive control strategy is one that employs feedback and has the ability to controlthe impingement tones over a large range of desired operating conditions. Recently, a closed-loop controlmethod was introduced4 to suppress the tones under various operating conditions based on ‘proper orthogonaldecomposition’ and produced additional noise reduction compared to open-loop control strategy. But theperformance is still sensitive to changes in operating conditions such as the distance between nozzle exit andthe impinging region. We attribute the result which is highly dependent to operating condition not only tothe improper actuation scheme but to the lack of information about noise generation mechanism. Hence, weneed to devise new methods to obtain consistent noise reduction under various jet operating conditions aswell as impinging jet model.

In this paper, it is proposed that the main source for generating noise is the impingement of a large scalevortical structure whose intensity is proportional to the vortex strength. This impingement is modeled asa head-on collision between two vortex rings of identical strength5. It is well known that unsteady motionof vortices emits acoustic waves called “vortex sound”.5 In his classical paper in reference[6], Powell showedthat an acoustic wave is excited by the vortex acceleration term (ω×υ). The theory of vortex sound wasfurther expanded in refs. (Mohring,7 Obermeier,8 and Kambe9). Of particular interest to the topic underconsideration in this paper is reference [5] (Kambe and Minota, 1983) since their analytic model takes intoconsideration the compressibility and viscous effects. These two effects play a major role in our problem dueto the fact that the flow is supersonic, and in an impinging jet, vortices formed are sufficiently close to theground, respectively. Using this collision mechanism, we develop a new model in this paper that explainsthe acoustics due to impinging jets. The impinging tone frequencies are determined in a manner similarto that in reference[10], and are shown to capture the staging phenomena quite well. Then the model isderived using the wave equation, colliding vortices of a certain strength, and Green’s function. This modelis compared with experimental results obtained in the FMRL, FSU, and is shown to match the data quitewell. In particular, it is shown that the noise intensity is found to be increasingly proportional to the vortexstrength.

Starting from such a vortex-collision model, we then proceed to the introduction of microjets which havebeen shown to lead to effective suppression in our earlier work.1,11 It is quite likely that the noise reductionmechanism due to microjets is because their action results in a weakening of the strength of vortex structurewhich is the key to suppress the noise level. The recent microjet control strategy introduced in reference[12],which is a pulsed microjet, which was shown to lead to a large noise reduction, is also perhaps due to thesame mechanism, in that a pulsed injection can generate a larger momentum than steady microjet injection,and hence makes a stronger impact on the impinging jet noise.

II. Acoustic Wave Radiated by Supersonic Impinging Jets

To develop a physical model of acoustic field generated by impinging jet is very difficult work due toseveral factors such as strong coupling with highly unsteady flow. Tam13 developed the vortex sheet modelto investigate the structure of the free jet. He approved the model by showing the nonexistence of helicalmode in the subsonic free jet. Motivated by the vortex sheet model, Annaswamy et al.11 introduced thereduced order model of impinging jet. This model gave insight on predicting the most dominant frequencyand its multiples, but it does not predict the trend of reducing amplitude at high frequency (see figure 1)because the reduced order model holds only near the nozzle exit but the author tried to expand the modelinto the downstream of the impinging jet. In this paper, we suggest a modification to the model in [11] usinga different approach.

A. Prediction of Impingement Frequencies

The most dominant frequency at a certain height was suggested by Neuwerth 10 to be

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

110

115

120

125

130

135

140

145

150

155

160

Hz

dB

Figure 1. Frequency content at h/d = 6.0, measured by pressure transducer near the nozzle exit using STOVLfacility of FRML in FSU

f =M

h

(1

Ca+

1Cv

) (1)

where f is the frequency, and h is the distance between the ground and the jet nozzle. Ca and Cv are thepropagation speed of vortex rings and the speed of sound, M is an integer. As we change h, the value of Mchanges, which leads to a discontinuous jump in the frequency of the dominant peak. The integer M whichis a function of h is chosen by fitting the above equation into the experimental data. Explicit prediction ofM is the first step for the impinging jet model, which is carried out below

d

U

Water Tank

Figure 2. Experimental schematics of reference14

Gharib et al.14 postulated that there exists a universal upper bound of the ‘formation number’ to form astable vortex ring by an impulsive piston motion. The formation number is defined as Nf = Ut

d where U isthe speed of the piston, and t is the time duration of the motion. d is the diameter of the piston apparatus.They found that one single vortex ring could be maintained, if Nf < N∗ and N∗ lies in the range of 3.6 ∼4.5. Although the case considered in [14] is pretty different from the mechanism of vortex ring formation inan impinging jet, where a supersonic jet is perturbed by the incident acoustic wave created by the collision

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of the jet at the ground, the dependence of the vortex formation on the foundation number in our case seemsto be similar. To use N∗ in our derivation, we define the Strouhal number as follows.

St =fd

Uj=

M

h

d

(Uj

Ca+

Uj

Cv

) =M

Ma + Uj/Cv

(h

d

)−1

(2)

Here, d is the exit diameter and Uj are the jet velocity. Uj/Ca is simply the Mach number of the jet (Ma).The convective velocity of the large scale vortical structure is around 50% of the main jet speed in [15], henceUj/Cv ∼ 2. Thus, St=M

Ma+2(hd )−1

.(2)Now, we assume that the circulation introduced by the jet within one period is contained in one single

vortex ring. Since the period t is the inverse of the frequency f , the formation number can be written asfollows.

Nf =Ujt

d=

Uj

fd= St−1 (3)

which implies that the formation number is simply the inverse of the Strouhal number under this assumption.If we extrapolate the result in [14], this leads to the following conclusion: there exists a universal lower boundon the Strouhal number for impinging tones, which we predicted in Ref [14] to 4. Hence we set Nf < N∗ ∼4.Table 1 contains Nf computed from St for various values of h/d and M . The Mach number of the jet waschosen to be 1.5, which is the experimental condition reported in [11]. Note that Nf should be less than N∗

in order to contain the circulation introduced by the jet in one single vortex ring. The bold-faced numberindicates the largest formation number(Nf ) satisfying this condition for each value of h/d. We expect thatthe dominant impinging tone must occur at this largest formation number, since each vortex ring containsthe largest possible circulation at this condition. Table 2 contains the corresponding frequency in Hz.

The existence of the largest possible Strouhal number seems to be a valid assumption for h/d between 3and 6 from the data given in [11] Also, the frequency predicted in Table 2 seems to be reasonably accuratefor the range.

Table 1. The formation number (Nf ) corresponding M at each height (h/d) condition

M = 1 2 3 4 5 6 7h/d = 3.0 10.500 5.250 3.500 2.625 2.100 1.750 1.500

4.0 14.000 7.000 4.667 3.500 2.800 2.333 2.0004.5 15.750 7.875 5.250 3.938 3.150 2.625 2.2505.0 17.500 8.750 5.833 4.375 3.500 2.917 2.5006.0 21.000 10.500 7.000 5.250 4.200 3.500 3.000

Table 2. The frequency (f) corresponding formation number(Nf ) at each height (h/d) condition. ∗ denotesthe value closest to experimental data

M = 1 2 3 4 5 6 7h/d = 3.0 1916.01 3832.02 5748.03∗ 7664.04 9580.05 11496.06 13412.07

4.0 1437.01 2874.02 4311.02 5748.03∗ 7185.04 8622.05 10059.064.5 1277.34 2554.68 3832.02 5109.36 6386.70∗ 7664.04 8941.385.0 1149.61 2299.21 3448.82 4598.43 5748.03∗ 6897.64 8047.246.0 958.00 1916.01 2874.02 3832.02 4790.03 5748.03∗ 6706.04

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B. Collision of Two Identical Vortices

The highly unsteady behavior of the jet and the resulting impinging tones is governed by a feedback mech-anism, between the instability waves in the jet that originate at the nozzle and grow as they propagatedownstream towards the impingement surface, and the acoustic waves that are produced upon impingementwhich then travel upstream and excite the nascent shear layer near the nozzle exit. The main source for thenoise generation of impinging jet is the impingement of the large scale vortical structure which was formedby the evolution of the instability triggered by acoustic wave near the nozzle. In this paper, we model theimpingement of the large scale vortical structure on the wall by viewing it as a head-on collision of twoidentical vortices. Seen in figure 3(b), the acoustic field of impinging vortex is composed of two acousticwave equations (i) a wave produced by impingement of jet travels directly toward the nozzle exit, and (ii)the other bouncing from the wall which also travels toward the nozzle. Similar to this, the acoustic field bythe colliding vortices is the superposition of two wave equations produced by each vortex in figure 3(a). Ifwe assume that the acoustic energy of bouncing wave is perfectly conserved while reflecting from the wall,the colliding model is quite analogous to the impinging tone generation mechanism.

(a) (b)

Figure 3. Acoustic field generated by (a) head-on collision of two identical vortices and (b) vortex impingingon the wall

In the reference,5 the far field acoustic equation generated by the colliding vortex is(∇2 − 1

c2

∂2

∂t2

)p = −ρF (x, t) (4)

where

F (x, t) = ∇ · L +1c2

∂2

∂t2υ2 +

∂

∂t

(1cp

D

Dts

)+

1c2

∂

∂t(υ · ∇)

12υ2 − ν

c2

∂

∂t(υ∇ : e) +

43ν∇2(∇ · υ) (5)

This equation is obtained from the basic mass, momentum and energy conservation equation for a viscousfluid, where x = (x1,x2,x3), r = |x|. Solving the equation using Green function, the acoustic pressure wavep is expressed as

p(x, t) =ρ

c2

xixj

r3Q′′′ij (t− r/c) +

ρ

15πc2

1rK′′(t− r/c) (6)

whereQij(t) =

112π

∫xi(x× ω(x, t))jdx (7)

andK(t) =

12

∫υ2(x, t)dx. (8)

The properties ρ and c are the density and sound speed in the undisturbed medium. The prime denotesdifferentiation with respect to time. The first term Qij(t) is derived as Mohring’s quadrupole, and the secondterm is the monopole representing the change in the total kinetic energy. When the vortices are far fromeach other, they are inviscid and the kinetic energy (K) is conserved. As they come closer, the viscous effectis not negligible and hence neither the kinetic energy nor the vorticity is conserved. Taking advantage of the

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axisymmetric property (Q′′′ij = Q

′′′ji) of circular vortex-lines, the far-field acoustic pressure of equation 6 is

reduced to the following form

p(r, θ, t) =ρ

4c2

1r

(cos2θ − 1

3

)Q′′′

(t− r/c) +ρ

15πc2

1rK′′(t− r/c), (9)

where r is the distance from the observation point to the center of vortex ring, θ is its polar angle from thez-axis seen in figure 4 and the function Q(t) is defined by

Q(t) =∫ ∫

R2zωdRdz, (10)

where z, R are the axial and radial coordinate respectively in the cylindrical coordinate system. The factorωdRdz in the equation (10) can be replaced by dΓ. Hence the appropriate Q(t) form from N discrete vorticescan be written as

Q(t) =N∑

i=1

R2i ZiΓi, (11)

where Ri, Zi and Γi are the radius, axial position and strength of the ith vortex respectively.

Z

R

O

Γ -Γ

P

θ

r

Figure 4. The diagram of colliding vortices

As seen in figure 4, the head-on collision case is composed of two identical circular vortices whose commonaxis coincides with the z-axis with the same circulation but opposite direction. Incorporating the propertyof R1 = R2 ≡ R, Z1 = −Z2 ≡ Z(> 0), −Γ1 = Γ2 ≡ Γ(> 0), into the equation ( 11). We obtain

Q(t) = −2ΓR2Z, (12)

and the corresponding total kinetic energy K is represented as follows

K = Γ2R (ln 8R/δ − 7/4)− Γ2Φ(Z,R) . (13)

The trajectory of R and Z can be calculated from the following equation.

dZ

dt= −Us +

Γ4πR

∂Φ∂R

(14)

dR

dt= − Γ

4πR

∂Φ∂Z

, (15)

where R,Z and Γ are defined above 12 and

Φ(Z,R) = Φ(R; k) = R[(2/k − k)F (k)− (2/k)E(k)] (16)

with k = R/√

R2 + Z2. The F(k) and E(k) in equation 14 are the complete elliptic integral of the firstand second kinds respectively.

F (k) =∫ π/2

0

dψ√1− k2 sin2 ψ

(|k| < 1), (17)

E(k) =∫ π/2

0

√1− k2 sin2 ψdψ (|k| < 1), (18)

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Us in the equation ( 14) represents the self-speed of a single vortex ring without interaction

Us =Γ

4πR

(ln

8R

δ− 1

4

), (19)

where δ is the effective size of the vortex core which is much less than the ring radius R. As R changes, thecore is assumed to satisfy the condition Rδ2 = R0δ

20 . Considering the viscous effect, the vortex strength Γ(t)

is no more conserved and assumed to be given by

Γ(t) = Γ0erf(Z/ε), (20)

where

ε2(t) = (R0/R)(ε20 + 4ντ),

τ = α

∫ t

0

exp

(2

∫ s

0

∣∣∣∣∣Z′(t)

Z(t)

∣∣∣∣∣ dt

)ds. (21)

Here ε is the second core size which represents as in equation ( 20), while the first core size δ determinesthe kinematic motion of the vortex center. The impingement model proposed in this paper can therefore besummarized thus: The pressure field is given by Equation ( 9) where the functions K and Q are determinedby equations ( 14)∼( 21).

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 10-3

-800

-600

-400

-200

0

200

400

600

t

p' (

pasc

al)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 10-3

-400

-300

-200

-100

0

100

200

300

400

t

p' (

pasc

al)

(a) (b)

t (sec) t (sec)

p (p

asca

l)

p (p

asca

l)

Figure 5. The time series of the acoustic pressure (a) produced by head-on collision of two identical vorticespcycle,(b) reconstructed repeating head-on collision data, preconst

The figure 5(a) is the pressure signal(pcycle) plot predicted from the equation 9 with respect to time.This plot is based on the data simulated at the same position where microphone is located in experimentaltest which will be mentioned in the next section in detail. h/d = 4, ρ = 1.23kg/m3 and with the initialcondition of δ0/R0 = 0.3. Alternately, the impinging tone data can be reconstructed by repeating one cycleof pressure signal seen in the figure 5(a) to the most dominant frequency (f) obtained from equation 1 withpredicted integer M using the criterion mentioned at the previous section.

preconst(t) =∞∑

n=1

pcycle (t− n/f) (22)

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where pcycle is the data obtained from the equation 9, f is the most dominant peak frequency calculatedfrom the equation 1, n is integer. The reconstructed data presented in the figure 5(b) is simulated at h/d =4.0, f = 6048 Hz.

As mentioned in the introduction, the impingement model proposed in our earlier work in reference[11]was accurate in its frequency prediction but poor in its amplitude prediction. The experimental data fromthe impinging jet shows several distinct peaks (figure 1), at 6, 12, and 18 kHz. In this section, we havepresented a model which attributes the noise generation to creation of vortices that collide with the ground.The simplest possible explanation for the peaks in figure 1 using these colliding vortices is to say that thehigh amplitude peaks at 6 kHz may be due to the impingement of slow but strong vertical structures, whereasthe low amplitude peaks at 12 and 18 kHz may be caused by fast but weak vortices with the vortex intensitygiven by (ω = ∇ × υ). However, this is not necessarily the case but is instead due to the impingement ofa single vortical structure at the dominant frequency of 6 kHz. As shown by the vortex-collision model inEquation ( 9) and Figure 5(a), this impingement causes a pressure time-trace that is not perfectly sinusoidaland hence can produce peaks at multiple frequencies. Indeed this is corroborated by Figure 6 which containsthe FFT of the predicted pressure from the collision model.

0 0.5 1 1.5 2 2.5 3 3.5

x 104

80

90

100

110

120

130

140

150

Hz

dB

Experimental Result

Prediction from Model

Figure 6. The frequency content of experimental result and prediction. h/d = 4.0

Several points should be made in reference of figure 6. First of all, the frequency content shows not onlya dominant peak but also harmonics of the frequency which was expected above. Secondly, similar to theexperimental result, the amplitude of each peak also tends to decrease at high frequency, which was notpredicted by the previous model.11 Third, the amplitude of the peak matches to the value obtained fromexperiment. However, the overall amplitude predicted is in general much less than that of experiment data,which is due to the fact that we considered only the impinging vortex as the noise generation source. Inreality, the actual signal contains broadband noise which is produced by mixing noise, edge tone and etc.Once we take into consideration of these sound sources, we could obtain closer predictions to the experiment.

III. Control of Supersonic Impinging Tone Using Modulated Microjets

For a given mass flow rate m = ρAU0, the force induced by steady microjet injection is given by therate of momentum change in time. Using the same mass flow rate, unsteady injection can exert more forceon the shear layer of the flow than steady injection, in an average sense. Equation ( 23) described below

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shows that, if the unsteady flow is represented in sinusoidal form, the additional force increase is realized byρA

(B2/2

):

Fsteady =d

dt(mU0) = mU0 = ρAU2

0

Uunsteady = U0 + B sin(ωt)

F (t) = mUunsteady = ρA (U0 + B sin(ωt))2

F (t) =1T

∫ T

0

mUunsteaydt = ρA

(U2

0 +B2

2

)(23)

Because the increased forcing strength is expected to cause stronger impact on the noise reduction mechanism,a suitable pulsing strategy is sought for the new actuation scheme. Two different methods for introducingpulsing are explored. One method is to use a high speed valve that modulates the flow from upstream. Theother method is to use a rotating cap actuator that generates pulsing directly at the microjet exit. Theseactuation schemes are discussed in the following section in detail.

A. Experimental Facility and Test Configuration

The experiments were carried out at the STOVL supersonic jet facility of the Fluid Mechanics ResearchLaboratory (FMRL) located at the Florida State University. A schematic of the test geometry with a singleimpinging jet is shown in Figure 7. This facility is used primarily to study jet-induced phenomenon onSTOVL aircraft hovering in and out of the ground effect. Further facility details can be found in Krothapalliet al.15

h (variable)

Lift Plate

Ground Plate

Nozzled

Dz

Microphone

Figure 7. Test geometry

The measurements were conducted using an axisymmetric, convergent-divergent (C-D) nozzle with adesign Mach number of 1.5. The throat and exit diameters (d, de) of the nozzle are 2.54cm and 2.75cm (seeFigure 7& 8). The divergent part of the nozzle is a straight-walled conic section with a 3◦ divergence anglefrom the throat to the nozzle exit. Although tests were conducted over a range of Nozzle Pressure Ratios(NPR, where NPR = stagnation pressure/ambient pressure), the results discussed in the present paper arelimited to NPR = 3.7 that corresponds to an ideally expanded Mach 1.5 jet, A circular plate of diameterD (25.4 cm∼10d) was flush mounted with the nozzle exit and, henceforth referred to as the ‘lift plate’,represents a generic aircraft planform. A 1m x 1m x 25 mm aluminum plate serves as the ground plane andis mounted directly under the nozzle on a hydraulic lift.

Active flow control was implemented using sixteen microjets, flush mounted circumferentially around themain jet as shown in figure 8a. The jets were fabricated using 400 µm diameter stainless tubes and areoriented at approximately 30◦ with respect to the main jet axis. The supply for the microjets was providedby compressed nitrogen cylinders through a main and four secondary plenum chambers. In this manner, thesupply pressures to each bank of microjets could be independently controlled. The microjets were operated

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Microjets (dm =400µm)

de =27.5 mm

Lift plate

Kulite 1

2

3

45

6

(a)

Secondary plenumchambers

To microjets

Control valves

Primary Plenum

(b)

Figure 8. (a) Lift plate/microjet layout, (b)Microjet feed assembly

over a range of NPR = 5 to 7 where the combined mass flow rate from all the microjets was less than 0.5%of the primary jet mass flux.

Near-field noise was measured using B&K TM microphones placed approximately 25 cm away fromthe jet. The distribution of unsteady loads on the lift plate was measured by six high frequency responseminiature KuliteTM pressure transducers, placed symmetrically around the nozzle periphery plate, at r/d=1.3 from the nozzle centerline (figure. 8). The transducer outputs were conditioned and simultaneouslysampled using National Instruments digital data acquisition cards and LabV iewTM software. Standardstatistical analysis techniques were used to obtain the spectral content and the Overall Sound Pressure Level(OASPL) from these measurements.

B. Modulated Microjet - Rotating Cap

To make flow modulation, direct modulation from the exit was tried, where the pulsing device was collocatedat the microjet exit. This device was chosen to be a rotating cap, designed so as to interrupt the microjetstreaks. In particular, if a rotating cap is placed at the exit as shown in figure 9, the tooth inside thecap, while rotating, periodically blocks the microjet hole. By continuing the rotation, a pulsing action ofmicrojets is achieved.

Rotating Cap

Figure 9. Conceptual diagram for rotating cap actuator

Figure 10 shows the design of the rotating cap and its installation in the experimental setup. The rotatingcap is assembled into the small lift plate connected with the slim bearing(Kaydon, KAA15AG0) whose inner

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and outer race are tightly fitted to the small lift plate and rotating cap respectively. Because the pulsingactuator should be installed, the design of the lift plate is slightly changed to install the rotating cap actuator.As seen in figure 11, the lift plate is composed of two parts, a small lift plate and a big lift plate. The smalllift plate assembled with the rotating cap is fixed at the center of the big lift plate. A motor mounted onthe lift plate drives the rotating cap connected by a belt. Finally, the lift plate is supported by three armsattached at the end of the holder grabbing the nozzle side firmly. Figure 12 shows the installation of liftplate into the nozzle.

Pulley

Kulite

Motor

Rotating Cap

Small Lift Plate

Microjets

Bearing

Main jet

Tooth

Figure 10. Rotating cap design

In figure 13, unsteady pressure data measured by Kulite shows a well modulated flow velocity withrespect to time. The FFT plot also indicates the exact pulsing frequency of the microjet. In additionto providing a direct method of pulsing the microjet flow, the rotating cap technique is also amenable toachieving parametric changes in the pulsed flow. Several properties including the amplitude, frequency, andduty cycle of the pulsing can be changed by varying the design parameters of the pulsing cap. For example,the duty cycle of this pulsing defined as the ratio of valve opening time to pulsing period is decided by thesize of tooth in the cap as shown in figure 14, while both the duty cycle and the magnitude of fluctuation isdetermined by the supply pressure delivered to microjet chamber. Pulsing speed is solely controlled by therotation speed of the cap.

C. Experimental Result using Modulated Microjet

The results obtained using the collocated rotating cap for impingement control are shown in Figure 15. Thenoise level is measured by the microphone located at 25 cm away from the nozzle axis because it was observedthat the Kulite transducer mounted on the lift plate does not capture the correct signal due to the vibrationof the motor. The signals sampled at 70kHz were feeded into the low pass filter whose cut off frequency is33kHz. In figure 15, steady microjet injection case was also compared to check the pulsing efficacy under thesame experimental condition. The supply pressure to the microjets was set to 115psi during the operation.Under the same supply pressure, the peak value of flow modulation due to pulsing corresponds to the flowexit speed during steady injection, hence the duty cycle of pulsing determines the relative mass flow rate dueto pulsing as compared to the steady injection case. The speed of pulsing is determined by the motor speed,size of rotating cap and number of teeth in the cap. Here the resultant pulsing speed by the rotating capwas set to 121.09 Hz, which is a moderate speed and does not lead to a broadband noise increase. Figure 15-(a) illustrates that pulsing of microjets using the collocated rotating cap can generate an acceptable levelof noise reduction. Another attractive feature of this actuator is that the noise reduction shown in figure15-(a) was achieved using 42% of the mass flow rate of the steady microjet injection case. As the dutycycle was increased, it was observed that the pulsed injection completely destroyed the distinct impingingtone for almost all distance conditions, and is shown in figures 15-(b). For example, the frequency contentin figure 15-(b) shows that the impingement tone has been eliminated at height h/d = 3.5 because of the

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1. Holder

2. Arm

3. Small Lift Plate

4. Bearing

5. Rotating Cap

6. Big Lift Plate

7. Nozzle

Figure 11. Assembled feature of lift plate and nozzle

Figure 12. Experimental setup installed with lift plate

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13.5

14

14.5

15

15.5

16

16.5

17

17.5

0 0.02 0.04 0.06 0.08 0.1

psi

Steady flow

13.5

14

14.5

15

15.5

16

16.5

17

17.5

0 0.02 0.04 0.06 0.08 0.1

psi

304.74 Hz

(a) (b) (c)

0 50 100 150 200 250 300 350 400 450 50020

30

40

50

60

70

80

90

100

Hz

dB

304.74 Hz

Figure 13. Performance of collocated rotating cap actuator; Total pressure data in time series (a) Case ofsteadily injecting microjet (b) Case of pulsing microjet at the speed of 304.74Hz (c) FFT plot of pulsingmicrojet

42% duty cycle

74% duty cycleHole

Microjet

Figure 14. Modification of duty cycle by changing hole size

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pulsed injection. Moreover, the required mass flow rate is less than the steady injection case (74%). Theseresults are encouraging because this technique has resolved the long-cherished problem of “uneven reductionfor different height.”

h/d = 3.5

142

144

146

148

150

152

154

3 3.5 4 4.5 5 5.5 6

h/d

OA

SP

L(d

B)

0 0.5 1 1.5 2 2.5 3 3.5

x 104

100

110

120

130

140

150

142

144

146

148

150

152

154

3 3.5 4 4.5 5 5.5 6h/d

OA

SP

L

0 0.5 1 1.5 2 2.5 3 3.5

x 104

100

110

120

130

140

150

h/d = 4.0

No ControlSteadyPulsing

X 104X 104

(a) (b)

Figure 15. Experimental result using synchronous pulsing scheme (a) Case of 42% duty cycle (b) Case of 74%duty cycle

IV. Conclusion

In this paper, a physical model which describes the acoustic field produced by supersonic impingingjet is presented. This is motivated by colliding vortex model5 because the vortex impinging on a wall mayexperience similar annihilation process to the head-on collision of two identical vortices. Seen in figure 6, thismodel successfully predicts the major characteristics of experimental result such as (i) both the dominantpeak and its harmonics, (ii) decreasing amplitude at higher frequency, (iii) peak amplitude at dominantfrequency .

In the later part of the paper, pulsed microjet injection was tried using rotating cap actuator. Synchronouspulsing at the frequency of 121.09 Hz resulted in noise reduction as steady injection while using only 42%mass flow rate of the steady case. But as in the case of steady injection, the efficacy of synchronous pulsing

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at low duty cycle is dependent on the nozzle-to-ground height. However, as the duty cycle was increased,it was observed that the pulsed injection completely destroyed the distinct impinging tone for almost alldistance conditions. Thus, we have resolved the long problem of “uneven noise reduction for different heightcondition” as shown in figures 15-(b), through high duty cycle pulsing strategy.

Acknowledgments

This work was supported by a grant from AFOSR, monitored by Dr. J. Schmisseur. We would liketo thank the staff of FMRL, for their invaluable help in conducting these tests. We are grateful to Mr.Choutapalli for his help in conducting the tests, and Robert Avant for his advice in designing the experimentalsetup. In addition, Bobby DePriest’s prompt support make it possible to implement several crucial tests.

References

1Alvi, F. S., Elavarasan, R., Shih, C., Garg, G., and Krothapalli, K., “Control of Supersonic Impinging Jet Flow UsingMicrojets,” 2000-2236, AIAA paper, 2000.

2Sheplak, M. and Spina, E. F., “Control of high-speed impinging-jet resonance,” AIAA Journal , Vol. 32, No. 8, 1994,pp. 1583–1588.

3Shih, C., Alvi, F. S., and Washington, D., “Effects of Counterflow on the Aeroacoustic Properties of a Supersonic Jet,”Journal of Aircraft , Vol. 36, No. 2, 1999, pp. 451–457.

4Lou, H., Alvi, F. S., Shih, C., Choi, J., and Annaswamy, A. M., “Active Control of Supersonic Impinging Jets: FlowfieldProperties and Closed-loop Strategies,” 2002-2728, AIAA paper, 2002.

5Kambe, T. and T.Minota, “Acoustic wave radiated by head-on collision of two vortex rings,” Proc. R. Soc. Lond., 1983.6Powell, A., “Theory of Vortex Sound,” J. Acoust. Soc. Am., Vol. 36, 1964.7W, M., “On vortex sound at low Mach number,” Journal of Fluid Mechanics, Vol. 85, 1978.8Obermeier, F., “Berechnung aerodynamisch erzeugter Shallfelder mittels der Methode der Matched Asymptotic Expan-

sions,” Acoustica, Vol. 18, 1967.9Kambe, T. and T.Minota, “Sound radiation from vortex systems,” J. Sound Vib., Vol. 74, 1981.

10Neuwerth, G., “Acoustic feedback of subsonic and supersonic free jet which impinges on an obstacle,” F-15719, NASATT, 1974.

11Annaswamy, A. M., Choi, J., and Sahoo, D., “Active-Adaptive Control of Acoustic Resonances in Supersonic ImpingingJets,” 2003-3565,, AIAA paper, 2003.

12Choi, J., Annaswamy, A. M., Egungwu, O., and Alvi, F. S., “Active Noise Control of Supersonic Impinging Jet UsingPulsed Microjets,” 2005-798, AIAA paper, 2005.

13Tam, C. K. W. and Ahujae, K. K., “Theoretical model of discrete tone generation by impinging jets,” J. Fluid Mech.,Vol. 214, 1990, pp. 67–87.

14Gharib, M., Rambod, E., and Shariff, K., “A Universal Time Scale for Vortex Ring Formation,” Journal of FluidMechanics, Vol. 360, 1998.

15Krothapalli, A., Rajakuperan, E., Alvi, F. S., and Lourenco, L., “Flow field and Noise Characteristics of a SupersonicImpinging Jet,” Journal of Fluid Mechanics, Vol. 392, 1999.

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