THRUST PERFORMANCE OF MICROMACHINED SYNTHETIC JETS

AIAA 2000-2404 THRUST PERFORMANCE OF MICROMACHINED SYNTHETIC JETS Michael O. Müller, Luis P. Bernal, Robert P. Moran, Peter D. Washabaugh Department of Aerospace Engineering

Babak Amir Parviz, T.-K. Allen Chou, Chunbo Zhang, Khalil Najafi Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor, MI 48109-2140

Fluids 2000 19-22 June 2000 / Denver, CO For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics 1801 Alexander Bell Drive, Suite 500, Reston, VA 20191

AIAA-2000-2404 THRUST PERFORMANCE OF MICROMACHINED SYNTHETIC JETS Michael O. Müller*, Luis P. Bernal †, Robert P. Moran*, Peter D. Washabaugh†, Babak Amir Parviz‡, Tsung-Kuan Allen Chou‡, Chunbo Zhang‡, Khalil Najafi§ University of Michigan Ann Arbor, MI 48109-2140

ABSTRACT The performance of synthetic jets produced by an electrostatically driven acoustic resonator is discussed. A reduced order model of the coupled membrane motion and acoustic field in the resonator is used to determine thrust and power consumption. The coupled system presents unique features depending on the pressure coupling parameter defined as the ratio of the pressure force on the membrane to its inertia. Thrust output increases as the pressure coupling parameter decreases and for stiffer membranes. Theoretical thrust performance of the order of 50 µN per resonator, and power to thrust ratio in the range 20-60 m/s could be achieved. We report also progress in the development of a micro propulsion system based on synthetic jets. Measurements of the membrane deformation and flow at the exit of the synthetic jets are reported. INTRODUCTION The development of high impulse momentum sources for application to micro propulsion and flow control remains a very difficult challenge. Recently zero-mass-flux synthetic jets have been 1,2 proposed as an actuator for flow control . Simple scaling arguments suggest that various performance parameters improve as the scale of the jets is reduced. For example as the scale is reduced the acoustic frequency increases * Graduate Research Assistant, Department of Aerospace Engineering, Member AIAA. † Associate Professor, Department of Aerospace Engineering, Senior Member AIAA. ‡ Graduate Research Assistant, Department of Electrical Engineering and Computer Science. § Professor, Department of Electrical Engineering and Computer Science.

Copyright © 2000 by Luis P Bernal, Published by the American Institute of Aeronautics and Astronautics, Inc. with permission

At Aex

Uex FIGURE 1: Micromachined ACoustic Ejector (MACE) concept, combining an ejector shroud with synthetic jets located at the throat. At is the throat area, Aex the ejector exit area, and Uex the exit velocity.

resulting in higher Reynolds number. Also, at small scales, the surface to volume ratio increases, which would improve mixing as long as the Reynolds number is kept relatively high. Coe et el 3 report an implementation of synthetic jets using Micro Electro-Mechanical Systems (MEMS) fabrication techniques. MEMS fabrication has several important advantages including integration with sensors for distributed flow control applications and batch processing for reliability and reduced cost. Our present efforts focus on the development of a micro propulsion system based on the synthetic jet concept4,5. The basic element of the proposed system is a Micromachined ACoustic Ejector (MACE) illustrated in figure 1. It consists of synthetic jets located at the throat of an ejector shroud that amplifies the thrust produced by the jets resulting in higher propulsion efficiency. A large number of these MACE devices are integrated to form an ACoustic Thruster (ACT) for

1 American Institute of Aeronautics and Astronautics

Table 1 Wafer-Integrated Resonator Parameters5 Cavity volume, VC (m3)

7.6 e-11

Number of throats, Nc

2

Throat length, Lt (m)

15 e-6

Throat width, W t (m)

1.4 e-3

Throat height, ht (m)

15 e-6 2

FIGURE 2: Photograph of micromachined wafer.

propulsion of Micro Airborne Platforms (MAP). The entire system is designed for MEMS fabrication and implemented on a single wafer containing over 900 individual resonators. A photograph of a wafer-integrated MACE thruster is shown in figure 2. The acoustic resonator used in this thruster is illustrated in Figure 3. It consists of a resonator cavity etched in a glass substrate bonded to a silicon wafer. The silicon wafer has two throats, a polysilicon membrane and a perforated electrode used to drive the resonator. The geometry of the resonator is given in Table 1. Electrostatic actuation was chosen because it is simpler to implement and provides larger actuation force at micro scales. However, it results in unique resonator dynamics that are not well understood. Throat

Boron-Doped Perforated Drive Electrode

Throat

Polysilicon Membrane

Resonant Chamber

Glass Substrate

FIGURE 3: Schematic diagram of acoustic resonator, showing the membrane, the electrode, the resonator cavity, and two nozzles.

In this paper we discuss the present state of the development of these synthetic jet actuators. We present first an analysis of the performance of electrostatically driven resonators and discuss their thrust performance. We present also experimental characterization of micromachined devices, and in particular, we describe the

Membrane area, AD (m )

1.44 e-6

Membrane thickness, tD (m)

1.36 e-6

Electrode/Membrane Gap, ho (m) development of experimental testing at micro scales.

3 e-6

techniques

for

ANALYSIS The present analysis is based on the reduced order model described by Muller et al 6. The resonator performance is described in terms of the resonator cavity pressure and the exit flow velocity given by equations due 1 p ue2 µ ue L v = − −8 , ue ≥ 0 ..........(1) 2 dt LE ρ 2CD LE ρ h2T LE dp dρ u A 1dV = a2 = −ρ a 2 e E − ρ a 2 , ue ≥ 0 ....(2) dt dt V V dt due 1 p ue2 µ ue L v , ue < 0 ...(3) = + −8 2 d t LE ρamb 2CD LE ρamb h2T LE dp dρ uA 1 dV = a2 = −ρamba 2 e E − ρ a 2 , ue < 0 ....(4) dt dt V V dt

where: ue(t) is the maximum velocity at the exit plane of the resonator, a

is the speed of sound,

p(t) = pc - pamb is the relative pressure in the resonator cavity, ρ(t) is the air density in the resonator cavity, ρamb is the ambient air density, µ

is the air viscosity,

hT is the resonator throat height,


LE

is the equivalent inertia length of the throat, AE is the effective area of the throat, Lv is the equivalent viscous length of the throat, CD is a flow coefficient associated with the streamline curvature at the exit plane of the throat.

V(t) is the cavity volume The cavity volume for a sinusoidal deformation of the membrane,  πx   πy  η(x,y,t) = hD (t) sin   sin   ,...................... (5)  LD   LD  is given by 4 V(t) = VC − 2 ADhD (t) , .................................... (6) π and

membrane stress. The driving force is the electrostatic pressure pe given by equation, ε E pe =   2  ho 

h  1 1 dx dy f D  = ∫∫ . .............(11) 2  ho  0 0  hD   1 + h sin ( πx ) sin ( πy )   o  The function f(hD/ho) is plotted in Figure 4. The integral (11) was evaluated numerically and the result approximated by the equation h  1 f D  = .......................................(12) 0.846 h  o   hD  1 + h   o  10

10

10

AE .................................................... (8) LE Vc

with ωo in rad/s. In the present investigation we consider the coupled system formed by the acoustic resonator and the electrostatically driven membrane. If structural damping is ignored, the membrane position is given by the equation, ρD t D

 4AD  d2hD + ωD2 hD  = −pAD − p e A D , ................ (9)  π 2  dt 2 

where the factor on the left hand side of the equation accounts for the varying acceleration at 2σ different points on the membrane, ωD = π ρD AD is the membrane’s structural resonant frequency in rad/s, ρD is the membrane density, and σ is the

2

1

f(h)

10

In reference [6] these equations were solved for a prescribed membrane time history hD(t). The results showed that the maximum thrust is obtained at the acoustic resonant frequency given by ωo = a

h  f  D  ,.....................................(10)  ho 

with ho the distance between the electrode and membrane, E is the drive voltage, ε is the permittivity of air, and

dV 4A dh = − 2D D .............................................. (7) dt π dt where Vc is the resonator cavity volume, hD(t) is the membrane displacement at the center, and AD = L2D is the area of the membrane.

2

0

-1

10

-2

10

-1

10

0

10

1

1 + h

FIGURE 4: f(h) as a function of 1+h. Open symbols numerical evaluation of equation (11). Solid line, equation (12).

The parameters used to characterize the performance of the resonator are the thrust and the power to thrust ratio. As discussed in reference [6] the average thrust is given by J=

1 1 ρu2 dAdt = ρue2 A JE dt .................(13) ∫ ∫ T ue > 0 A T T ue∫> 0

The power to thrust ratio is derived from the electrical power used by the resonator which is given by We = Ñ ∫E

dQ d(CE) dt = Ñ E dt , .........................(14) ∫ dt dt


where Q is the charge and C the capacitance of the resonator. The capacitance is given by,

ρD t D

h  εA C = c  D  D ................................................. (15)  ho  ho

or using (12),

with h c D  ho

 dx ' dy ' ................ (16)  = ∫∫ h  0 0 1 + D sin ( πx ' ) sin ( πy ' ) ho 1 1

The function c(hD/ho) is plotted in figure 5. The integral (16) was evaluated numerically and the result approximated by the expression h   h  c  D  = 1 + D   ho   ho 

 h  −0.4047 − 0.0317log 1+ D   ho 

.................... (17)

2.6

2.4

2.2

2

c(hD/ho)

1.8

1.6

hD  hD  1+  ho  ho 

0.846

=−

E π2 εo  2  8ρD tDho ωD  ho 

2

h  f  D  A D ...(18)  ho 

2

.................(19)

The left hand side has a minimum at hD/ho = -0.5417. Hence there are no equilibrium solutions for E > Ec, with Ec =

1.5 ωD π

ρD t Dh3o .........................................(20) εo

Ec is readily identified as the collapse voltage. Thus the maximum stable membrane deflection is hDmx = −0.5417ho (the negative value indicates a displacement of the membrane toward the electrode). The collapse voltage, Ec, provides a simple way to characterize the tension/stiffness of the membrane. From a practical point of view, Ec gives a good estimate of the magnitude of the voltage required to drive the membrane at the large deflections needed for thrust generation. The second important feature of interest is the coupling between the membrane motion and the acoustic cavity. Equation (9) can be written in non-dimensional form as

1.4

1.2

1

0.8

0.6 -1

ε E 4AD 2 ωD hD = −p e A D = − o   2 π 2  ho 

-0.8

-0.6

-0.4

-0.2

0 hD/ho

0.2

0.4

0.6

0.8

1

FIGURE 5: Plot of c(hD/ho) as a function of hD/ho. Symbols, numerical evaluation using equation (16). Solid line, equation (17).

d2h * * ..................................(21) + ω*2 D h = −K D p + p e dt *2

(

)

where h=hD/ho, t* = ωot, ωD* = ωD / ωo , p*=p/(ρ a2), pe*=pe/(ρ a2), and 2

Results The membrane equation (9) captures the more important dynamical features of electrostatically driven resonators. First, the membrane collapse phenomenon is included in the equation. The membrane collapse is associated with a structural instability of the system7,8. As the voltage increases the membrane deflects closer to the electrode, thus increasing the electrostatic load acting on the membrane. The instability is reached when the tension on the membrane is no longer able to balance the increasing elestrostatic load and the membrane quickly collapses against the electrode. The equilibrium position of the membrane is given by the steady solutions of equation (9),

π2 ρ  a  1 KD = .....................................(22)   4 ρD  ωo  tD ho The non-dimensional parameter KD is the ratio of the pressure load acting on the memebrane to the inertia of the membrane. For large values of KD there is strong coupling between the acoustic field and the membrane motion. The system behavior must be derived from the solution of the coupled system of equations. If KD is small the membrane inertia is large enough to decouple the membrane motion from the acoustic field in the cavity. In this case the solution could be described in terms of two weakly coupled resonators. The performance of the resonator was determined by numerically solving the coupled system of equations (1) to (4) and (9) for a sinusoidal drive


70

10 60

50

6

Thrust X 10 (N)

6

Thrust x 10 (N)

8

6

4

40

30

20

10

2 0 0

0 20

30

40

50

60

70

80

90

100

110

20

40

60 frequency (kHz)

80

100

120

120

frequency (kHz)

FIGURE 6: Resonator thrust as a function of drive frequency at constant input voltage for large pressure coupling coefficient, KD = 69. , High stiffness diaphragm, Emx = 30 v. , Low stiffness diaphragm Emx = 20 v

voltage using a standard ODE solver. As the amplitude of the driving voltage is increased the membrane collapses. A detailed model of the collapse and release of the membrane would be required for an accurate solution in this case. In all the cases reported below the voltage amplitude was less than the value required to collapse the membrane. Figures 6 and 7 show typical thrust performance results calculated using the model. The resonator parameters are listed in Table 1. These approximately correspond to the design conditions for the wafer-integrated MACE device. However in order to characterize the coupling effect discussed earlier calculations were conducted at several other conditions. The results were obtained for high and low membrane stiffness. The stiffness of the membrane is characterized by the structural resonant frequency, ωD. The high stiffness case corresponds to a structural frequency equal to the acoustic resonant frequency, ωo, and the low stiffness case corresponds to ωD = ωo / 2 . In all these cases the acoustic resonant frequency is 120 kHz. Figure 6 is a plot of the thrust produced by the resonator as a function of drive frequency for a relatively high pressure coupling parameter (KD = 69). The calculations were conducted at constant amplitude equal to the largest voltage that did not result in membrane collapse over the entire frequency range considered. This maximum voltage increases as the structural resonant frequency (structural stiffness) is increased. The thrust has two peaks at approximately 30 and 100

FIGURE 7: Plot of the thrust as a function of drive frequency for constant input voltage for small pressure coupling coefficient, KD = 7.6. , High stiffness diaphragm Emx = 304 v. , Low stiffness diaphragm Emx = 149 v

kHz for the high stiffness membrane. In contrast there is only one peak at approximately 95 kHz for the low stiffness membrane. The maximum thrust is 2 and 9 µN for the low and high stiffness membranes respectively. The corresponding values of the power to thrust ratio are 30 and 47 m/s. This spectral response is markedly different than the resonator response found in [6] which did not include the effect of electrostatic forcing. In that case a single peak at the acoustic resonant frequency characterizes the frequency response, and the predicted thrust is an order of magnitude larger than in the present calculations. Examination of the cavity pressure and membrane displacement time series shows smaller displacement amplitudes, which suggests that the relative phase between the cavity pressure and the membrane displacement determines the location of the spectral peaks. It should be noted that these thrust results are expected to be a lower bound of the actual values because the membrane is not collapsing. Figure 7 is a plot of the thrust produced by the resonator as a function of drive frequency for KD = 7.6. The reduced pressure coupling parameter was obtained by increasing the electrode-to-membrane gap and the thickness of the membrane each by a factor of 3. The resonator acoustic parameters were not changed. The increased gap results in much larger voltage amplitude for membrane collapse as indicated. The maximum voltage also increases with membrane stiffness. Two spectral peaks are found for both the low and high stiffness membranes. For the low stiffness membrane the spectral peaks


occur at, approximately, 20 and 75 kHz, the thrust is 10 and 5 µN and the power to thrust ratio is 60 and 25 m/s, respectively. For the high stiffness membrane the spectral peaks occur at, approximately, 30 and 78 kHz, the thrust is 50 and 62 µN, respectively, and the power to thrust ratio is 65 m/s at both peaks. Clearly the pressure coupling parameter plays a key role in the performance of the resonators.

1.E-01

1.E-02

A1

Amplitude 1.E-03

A3

A2 1.E-04

1.E-05 0

25

EXPERIMENTAL RESULTS To characterize the performance of the micromachined synthetic jets, structural and fluidic tests were performed. First, knowledge of the structural behavior of the membrane is desired. To this end, detailed device current measurements are carried out to determine the resonant frequency, and interferometry is conducted to accurately determine the dynamic membrane shape. Secondly, the flow structure of the resulting synthetic jet needs to be quantified. This is done by flow visualization using small particles, and hot wire anemometry. All the tests are conducted in a wafer-integrated MEMS-fabricated devices (see figure 2). Each device has four electrically independent quadrants with 280 resonators each.

The design of the synthetic jet propulsion device is effectively a non-linear capacitor. It consists of a grounded, moving, membrane, and an electrode, to which a sinusoidal voltage is applied. Thus, the capacitance of the system consists of a mean value, plus additional, varying, capacitance caused by the motion of the membrane relative to the electrode. When the membranes are moving at their lowest structural resonant frequency, their displacement will be at a maximum for a given supply voltage. Thus, the varying capacitance will be at a maximum at this resonance. This maximum can be determined by measuring the spectrum of the current flow, as follows: For a given drive voltage to the electrodes: E=

Epp 2

sin ωt .................................................. (22)

and, for a capacitance given by the sum of a mean capacitance and the varying capacitance due to the moving membrane: C = C0 + Cp sin2ωt .......................................... (23)

75

100

FIGURE 8: Typical spectrum of current signal. A1, A2, and A3 indicate the amplitude of the spectrum components at the drive frequency of 25 kHz, and two and three times the drive frequency, respectively.

where Cp is the amplitude of the fluctuating capacitance of the membrane. Note that the frequency of the varying capacitance is twice that of the drive voltage. This is because the effective electrostatic load on the membrane is attractive for both the positive and the negative part of the cycle. Thus, the charge of the capacitor is: Q = CE =

Membrane Structure

50

Frequency (kHz)

=

C0Epp 2

C0Epp 2

sin ωt +

sin ωt +

CpEpp 2

sin 2ωt sin ωt

CpEpp  1 1  cos ωt − cos3ωt  .....(24)  2 2 2 

Finally, the current is given by: i=

d(CE) C0Epp ω cos ωt = dt 2 ......................(25) C E ω1 3  − p pp  sin ωt − sin3ωt  2 2 2 

Hence the spectrum of the current is expected to have peaks at one and three times the driving frequency, ω. A peak in the component at three times the drive frequency is expected at the maximum Cp, or when the membrane deflection is at a maximum. Additionally, if the device acts as a pure capacitor, with infinite resistance between the electrode and membrane layers, we expect the amplitude of the spectral peak at the drive frequency to increase linearly with frequency. Experimentally, the current is computed by measuring the voltage drop across a resistor in series with the device. The resistor value is 33 Ω, and the capacitance of the device is of order 1 nF.


300 0.006 Atm 1 Atm 200

A1 (mV) 100

0 0

10

20

30

40

(a)

50

Drive Frequency (kHz)

FIGURE 9: Plot of A1 at varying frequency.

The spectrum of the current is measured using a spectrum analyzer. Figure 8 shows a typical spectrum. The A1, A2 and A3 spectral peaks correspond to one, two and three times the drive frequency, respectively. Spectra are taken at both ambient pressure, and very low pressure; 0.006 Atm. At low pressure, air damping is greatly reduced, so the membrane displacement should increase, and the A3 curve should have a more pronounced peak. Figure 9 shows the amplitude of the A1 spectral peak at varying frequency, at low pressure (0.006 Atm) and at ambient pressure. It can be seen that A1 does not follow the expected linear behavior. This is believed to be due to the inductance in the lead wires to the device. Figure 10 shows the amplitude of A3 at varying frequency, again at low and ambient pressures.

0.006 Atm 1 Atm

A3 / A1 0.010

0.000 0

10

The figure shows a peak, and thus structural resonance, at 28 kHz drive frequency; or 56 kHz membrane frequency (the doubling due to the attractive force for both positive and negative voltage applied to the electrode). Optical interferometry is used to determine the characteristic membrane response time, for both the collapse and the restorative part of the cycle. There are three loads acting on the membrane: the deforming pressure field due to the electrostatic attraction of the electrode, the restorative loads of the membrane tension and curvature, and the pressure associated with air damping.

0.030

0.020

(b) FIGURE 11: Interferograms of the membrane. The menbrame is inside the square feature in the center of the image. Each fringe corresponds to a displacement of 244 nm. (a) Membrane in a fully collapsed state. (b) Membrane in a fully released state.

20

30

40

Drive Frequency (kHz)

FIGURE 10: Plot of the amplitude ratio A3 / A1 as a function of frequency.

Using a 488 nm wavelength collimated laser beam, membrane position is known to a quarter micron; providing sufficient resolution for the expected 3 micron deflection of the membrane. The surface is imaged through the glass substrate shown in Figure 3, using a 100:1 magnification microscope. A high-speed digital camera capable of 2 µs exposures is used to freeze the membrane


motion. This test is conducted both at low pressure (0.006 Atm) and ambient pressure conditions, to determine the effects of the air damping. Figure 11 shows typical interferograms. Figure 11a shows the membrane in the fully collapsed position, and figure 11b shows the membrane in the released state. Both images clearly show the 1200 µm square outline of the membrane. Fringes on the membrane in figure 11b indicate that the membrane is not perfectly flat in the released state; this is likely a result of the manufacturing process.

frequency indicated by the current spectrum. Note that the current spectrum indicates the same resonant frequency, regardless of pressure.

The collapse time in low pressure and at ambient pressure is the same: 20 µs. The release time at low-pressure conditions is 35 µs, and 50 µs at ambient pressure. At the ambient pressure condition, the membrane is critically, or over-, damped. At low-pressure conditions, the membrane oscillates for about 5 ms until it returns to its equilibrium position. Given that 20 µs are required for a full collapse followed by 35 and 50 µs for a full release, the corresponding maximum operating frequency for full deflection is 18 and 14 kHz. This is significantly lower than the resonant

The flow along the wall, parallel to the surface of the wafer, is visualized using small particles. The velocities of these particles, and thereby the fluid velocity, can be determined. For a quantitative analysis the choice of particle turns out to be very important: particles must be small enough to be entrained by the airflow, and particles must be

Air Particle

8

Air Velocity (m/s)

Flow Structure The structure of the flow exiting the throat is measured in two separate regions. The jet is normal to a wall, so there is entrained flow parallel to the wall, towards the throat. Secondly, there is the jet itself, which flows normal to the wall, above the throat.

0.016

4

0.008

0

0

(a)

(b)

(c)

(d)

(e)

(f)

Particle Velocity (m/s)

-0.008

-4 -8 0

90

180

270

-0.016 360

Phase (degrees)

(a) 0.04 0.02

Particle 0 Position (µm) -0.02 -0.04 0

90

180

270

360

Phase (degrees)

(b) FIGURE 12: Periodic particle response at the throat, at 80 kHz, based on a throat velocity calculated from the volume displaced by the diaphragm. (a) Comparison of air and particle velocities. (b) Corresponding particle displacement.

FIGURE 13: Sequence of six images following a typical particle moving from left to right, (marked by white arrowhead) due to entrainment at the throat. The electrode is the perforated region on left side of the image. Part of the curved throat is visible on the right side. Membrane frequency is 80 kHz. Each image is 1/30th of a second apart.


Figure 14 shows flow velocities for different pulse inputs. There is no observed DC shift in the hot wire signal, indicating that streaming is not occurring. For the voltage used in these test (≥50 V) the interferometry data shows that the membrane is fully collapsed. Thus the volume

Drive Voltage (V)

90

50

60

25

30

0

0 -1

-0.5

0

0.5

1

Time (ms)

(a)

Drive Voltage (V)

Voltage

HWA Trace

75

90

50

60

25

30

0 -2.5

0 -1.25

0

1.25

2.5

Time (ms)

(b)

Drive Voltage (V)

Voltage

HWA Trace

75

90

50

60

25

30

0 -2.5

HWA Trace (mm/s)

Hot wire anemometry is performed at the throat, to characterize the jet created at the resonator. Objectives for this test are twofold. First, to experimentally determine the air-flow characteristic time at the throat. This is to be compared to the membrane collapse and release times. Secondly, to determine if streaming exists, particularly at the previously determined membrane and cavity resonant frequencies, as well as at the maximum frequency where full deflection of the membrane still occurs. A 5µm diameter hot wire is placed at about 50 µm above the nozzle exit. However, the resonator has a curved throat, while the hotwire is straight, and only 15% of the hotwire is exposed. This results in a comparable decrease of the anemometer sensitivity. A linear correction is applied to the hotwire output to account for this effect.

HWA Trace

HWA Trace (mm/s)

The particle testing indicates a peak inlet velocity, and thus cavity resonance, at a membrane frequency of 80 kHz. From the sequence of images shown in figure 13, the peak entrainment velocity is 1.5 mm/s; the average from the electrode to the throat is about 0.5 mm/s. No particles are ejected from the nozzle, as could be expected. However, in some of the video sequences, particles can be seen to “buzz” in the vicinity of the throat.

Voltage 75

HWA Trace (mm/s)

conductive to reduce electrostatic stiction problems inherent in MEMS devices. 15 µm silvercoated hollow glass particles are used (specific gravity = 1.33). Based on a simple Stokes’ spheredrag analysis, these particles have a response time of 0.9 ms, which is sufficient to capture the mean flow along the device surface, but not fast enough to follow the high frequency oscillatory flow at the throat. Figure 12 demonstrates the expected response of the particles at the throat. There is a two orders of magnitude difference in peak particle and air velocity. The electrical properties of these particles do not completely eliminate stiction, but particles placed above the electrode holes are kept free by the air flowing through the holes. Particles that come to rest away from the electrode holes tend to stick, unless knocked free by another particle.

0 -1.25

0

1.25

2.5

Time (ms)

(c) Figure 14: Hot wire anemometry velocity traces. The supply voltage is a square pulse. (a) 50 V drive voltage, 1 ms period, 500 µs pulse width. (b) 50 V drive voltage, 2 ms period, 500 µs pulse width. (c) 70 V drive voltage, 2 ms period, 500 µs pulse width.

displaced by the membrane should be approximately the same in all cases shown in the figure. However, increase voltage may result in significantly different membrane release modes. In all cases, the peak fluctuating velocities are very low, less than 0.1 m/s. Figure 14a shows the response for a 1 ms period with 500 µs positive pulse width. The time duration of the jet is about 150 µs, significantly longer than the 50 µs membrane release time. The velocity trace shows inflow (lower velocity) during the collapse of the membrane corresponding to the positive transition of the drive voltage, and inflow during the release


of the membrane corresponding to the negative transition. It should be noted that the lack of directional sensitivity of the hot wire is not found here. This is attributed to two effects: only 15% of the wire is in the jet, and the velocity magnitude is very small, much less than the speed of natural convection currents in the laboratory. Figure 14b is identical to 14a, maintaining a 500 µs pulse width, but doubling the period to 2 ms. The flow velocity is reduced significantly compared to the square wave test in figure 14a. Figure 14c is the same as 14b, only the voltage has been increased by 2 , doubling the forcing on the membrane. In this case the flow velocity is comparable to the figure 14a case. These results suggest that the output velocity is very sensitive to the mean membrane position that is proportional to the mean square drive voltage (1250, 650 and 1250 V2 for cases a, b and c respectively).

Some care must be taken in interpreting these measurements. Typical of MEMS, the devices are manufactured in bulk. On each wafer are four quadrants of 280 actuators. The current spectrum measurement technique is performed simultaneously on all devices in a quadrant, while the other tests are performed on individual devices. As the yield of the MEMS devices is not 100% (for these devices, the yield is about 80%), any test performed on an entire quadrant should be regarded as some type of average. It is clear that certain features of the propulsion system are operating as intended. For instance the maximum membrane deflection is 3 µm, as intended. However, it is not clear if the difference between ‘average’ responses is due to limited number of individual measurements or if a few units are affecting the average. More independent membranes and nozzles need to be examined.

.

ACKNOWLEDGEMENTS CONCLUSION

An analytic model that couples the structure and acoustic features of an electrostatically actuated synthetic jet was developed. It demonstrates interesting coupled behavior where there are multiple ‘resonances,’ that do not coincide with the resonances of the separate structural or fluid systems. The controlling parameter is the ratio of pressure force on the membrane to its inertia. The trust produced by the resonator increases as the pressure coupling parameter is reduced. It is also shown that increase membrane stiffness results in higher thrust. A series of measurement techniques have been developed or used at microscales to characterize the structural and fluidic properties of a synthetic jet micro propulsion device. These include a current measurement method that takes advantage of the nonlinear properties of the system, a direct surface measurement using optical interferometry, flow visualization using small particles, and hot wire anemometry. From the structural membrane testing, two conclusions can be made. First, the membrane structural (first) resonance occurs at 56 kHz. Secondly, the maximum operating frequency for full deflection is between 15 and 20 kHz. There are significant differences between mechanical and aerodynamic resonant frequency. From the aerodynamic testing, a resonant frequency of 80 kHz is observed.

This research was supported by DARPA under contract number N00019-98-K-0111. REFERENCES 1

SMITH, B. L. AND GLEZER , A. 1997 Vectoring and smallscale motions effected in free shear flows using synthetic jet actuators. AIAA paper 97-0213. 2 COE, D.J., ALLEN, M.G., SMITH, B.L., AND GLEZER , A. 1995 Addressable Micromachined Jet Arrays. Proceedings of Transducers.. 3 COE, D.J., ALLEN, M.G., T RAUTMAN, M., AND GLEZER , A. 1994 Micromachined Jets for Manipulation of Macro Flows. Proceedings of Solid State and Sensor Workshop 4 PARVIZ, B.A., B ERNAL, L.P., AND NAJAFI, K. 1999 A Micromachined Helmholtz Resonator for Generation of Microjet Flows. Proceedings of Transducers 5 PARVIZ, B. A., CHOU, T. -K., ZHANG,C., NAJAFI, K., MULLER , M. O., BERNAL , L. P., AND W ASHABAUGH, P., 2000 A wafer-integrated array of micromachined electrostatically-driven ultrasonic resonators for microfluidic applications. Submitted to MEMS 2000 conference, January 23-27, 2000, Miyazaki, Japan. 6 MULLER, M. O., BERNAL , L. P., MORAN, R.P., W ASHABAUGH, P., AMIR PARVIZ, B., AND NAJAFI, K., 2000 Micromachined acoustic resonators for microjet propulsion. AIAA paper 200000547. 7 MIHORA, D.J., REDMON, P.J., 1980 Electrostatically formed antennas, Journal of Spacecraft, vol. 17(5), pp.465-473. 8 KOLMANOVSKY, I. V., MILLER , R. H., W ASHABAUGH, P.D. AND GILBERT, E.G. 1998 Nonlinear Control of Electrostatically Shaped Membrane with State and Control Constraints. 1998 American Control Conference, Philadelphia, PA USA. June 24-26, 1998.
