DOCUMENTATION REPORT PAGE
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1. AGENCY USE ONLY ( Leave Blank)
2. REPORT DATE
31 Jan 2003
3. REPORT TYPE AND DATES COVERED
Interim 28 March 2002 to 31 January 2003
5. FUNDING NUMBERS
4. TITLE AND SUBTITLE
Open Acoustic Resonators with Mean Flow
6. AUTHOR(S)
Grant DAAD19-00-1-0150 (P-40954-EV-DPS)
8. PERFORMING ORGANIZATION REPORT NUMBER
Michael J. Anderson, Ralph S. Budwig, E. Clark Lemmon
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
U.S. Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211
9. SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES)
KKK630 Interim 3
10. SPONSORING / MONITORING AGENCY REPORT NUMBER
U. S. Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211
11. SUPPLEMENTARY NOTES
unknown
The views, opinions and/or findings contained in this report are those of the author(s) and should not be construed as an official Department of the Army position, policy or decision, unless so designated by other documentation.
12 a. DISTRIBUTION / AVAILABILITY STATEMENT 12 b. DISTRIBUTION CODE
Approved for public release; distribution unlimited.
13. ABSTRACT (Maximum 200 words)
DOD
We report on the third year progress of a project whose goal is to enhance acoustic separation of small particles from an air stream. The effect of mean fluid flow on resonant acoustic cavity amplification has been determined. A mathematical model was developed that predicted the change in acoustic pressure amplitude caused by the presence of mean fluid flow. The mathematical model, and corresponding experiments, have shown that mean air flow velocities below 2 m/s should not change the resonant acoustic pressure amplitude by more than 10%. Secondly, development of a finite element model capable of predicting acoustic pressure in an open channel was completed. This model was used to determine that incorporation of a curved reflector into the channel geometry could significantly improve the resonant pressure amplitude. In a particular design, Inclusion of a curved reflector of a depth that was 16% of the channel width would result in a 2.5 gain in acoustic pressure amplitude.
14. SUBJECT TERMS 15. NUMBER OF PAGES
Acoustic resonators, aerosol sampling
16. PRICE CODE
n/a
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U.S. Army Research Office
REPORT DOCUMENTATION PAGE (SF298) (Continuation Sheet)
List of Papers Submitted or Published Under ARO Sponsorship Appeared in Peer Reviewed Archival Journal: Anderson, M.J., Line, K.S., Budwig, R.S., " The Effect of Large Openings on Cavity Amplification at Ultrasonic Frequencies", Journal of the Acoustical Society of America, Vol. 112, No. 6, pp. 2771-2778, 2002. Papers Presented at Meeting, Abstract Published: M.J. Anderson, K.S. Line, R.S. Budwig, "Effect of Mean Flow on An Acoustic Standing Wave in an Open Cavity", presented at the 144th Meeting of the Acoustical Society of America, Cancun Mexico, December 2002. Invited Presentation: M.J. Anderson, R.S. Budwig, K.S. Line, J.G. Frankel, "Ultrasonic Concentration of Airborne Aerosols", invited presentation at the Scientific Conference on Obscurateion and Aerosol Research, Bel Air Maryland, June 2002. Papers Presented at Meeting, and Published in Conference Proceedings: M.J. Anderson, R.S. Budwig, K.S. Line , "Use of Acoustic Radiation Pressure to Concentrate Small Particles in an Air Flow", presented at the 2002 IEEE Ultrasonics Symposium, Munich Germany, October 2002. Paper to appear in the 2002 Ultrasonics Symposium Proceedings. Scientific Personnel Supported by This Project Dr. Michael J. Anderson (PI) Dr. Ralph S. Budwig (coPI) Dr. E. Clark Lemmon (co PI) Andrew C. Cluff (Grad RA). Gabriel C. Putnam (Grad RA beginning Aug 2003) MSME awarded to Kenneth S. Line, May 2002. Report of Inventions No inventions during the reporting period.
2 Scientific Progress and Accomplishments Finite Element Modeling We have completed a finite element model of a shaped channel. It was hypothesized that a high pressure amplification could be achieved with a shaped channel, compared with a rectangular channel. The finite element model predicts that there is a significant gain that can be achieved using a shaped channel. Shaped channels with geometry similar to the example shown in Figure 1 were considered. The following describes the results of one finite element model computation. The nominal width of the channel was L=3.4 mm. A transducer, of width 2b=28.575 mm, excited the cavity at a velocity amplitude of 29.5 mm/sec. A curved reflector, of radius r and depth d, was placed opposite the transducer. The normalized depth of the reflector d* was defined to be d*=d/L. The effect of reflector depth on pressure amplification was assessed. Example contour plots of acoustic pressure amplitude in a shaped channel are shown in Figure 2. The pressure amplitudes shown in Figure 2 were calculated at a frequency chosen to excite a half wavelength resonance in the channel. Part 2a, 2b, and 2c show the pressure amplitude with a reflector of normalized depths d*=0, 8, and 16 percent. The contour plots in Figure show that reflector tended to concentrate the energy in front of the transducer, while bending the linear geometry of the pressure node. A plot of acoustic pressure amplitude in the channel versus the normalized reflector depth d* is shown in Figure 3. The pressure amplitude shown in Figure 3 was calculated at the location on the reflector that intersects the transducer axis, point P shown in Figure 1. This plot shows that a curved reflector of depth exceeding 4% will lead to a gain of 2.5 in acoustic pressure. This is a gain of nearly 8dB! Fortunately, it also appears that the reflectors are of machineable depth, on the order of 5-20 mil. Our calculation show that this gain can be achieved with relatively little spatial distortion of the acoustic field. Effect of Mean Fluid Flow on Acoustic Cavity Amplification One objective of our project was to determine the effect of mean fluid flow on acoustic amplification. We have nearly completed this study. Our approach to determine the effect of mean fluid flow on cavity amplification was to develop a mathematical model, and to perform corresponding experimental measurements. A perturbation method was employed to obtain a mathematical model of the effect of fluid flow on acoustic cavity. A two-dimensional geometry, shown in Figure 4, was adopted for the mathematical model. The channel was assumed to be rectangular, and of width L. A transducer of width 2b provided the ultrasonic excitation. A mean fluid flow of velocity U(z), characterized by a maximum velocity Umax, assumed was to flow from left to right. A laminar (Couette) flow profile was assumed. An example computation of acoustic pressure amplitude that would occur in the channel is shown in Figure 5. The location of the transducer is indicated with a black rectangle. Part 5a shows the pressure amplitude when mean flow is absent, i.e., Umax=0 m/s. Part 5b shows the change in pressure amplitude when the maximum mean flow velocity was Umax=100 cm/s. The value of parameters used in the computation were L=6.88mm, 2b=28.58mm, and a frequency f=49264Hz was chosen to excite a one wavelength depth resonance between the
3 walls of the channel. Furthermore, an absorption time constant =8.54 ns was used to model absorption. The value used for the absorption time constant was chosen in accordance with what we have learned to be appropriate from previous analyses and experiments [1]. From Figure 5a, it is evident in this situation that the maximum pressure amplitude was approximately 80 Pa, while from Figure 5b, the fluid flow changed the pressure amplitude by about 0.25Pa, a small amount. In general, we found the effect of mean fluid flow on acoustic amplification to be minimal, but sometimes reaches 10% of the nominal pressure amplitude. We performed a series of laboratory experiments to bracket our theoretical prediction of the effect of mean fluid flow on resonant acoustic amplification in the channel. The channel geometry in general corresponded to the geometry shown in Figure 4. A photograph of the apparatus is shown in Figure 6. A rectangular channel, machined into a polymer block, contained a square PZT transducer as shown. After the channel was assembled, a small fan was used to generate an air-flow in the channel, from right to left as shown in Figure 6. A hot-wire anemometer was used to measure the flow velocity at the centerline of the channel. Three measurement ports were machined into the upper channel wall to measure acoustic pressure on the reflector wall, on the transducer axis; and slightly upstream and downstream relative to the transducer axis. The ports were labeled as "downstream", "center", and "upstream". Measurements of the change in acoustic pressure amplitude at the upstream, center and downstream port locations are shown in Figure 7 as the maximum air flow velocity was varied from 0 to 2 m/s. These measurements are indicated with open diamonds, squares and circles on the figure. Computations of corresponding change in pressure amplitude at the same locations predicted by the mathematical model described in the previous paragraph are shown as solid lines in the same color. The experimental measurements revealed a change in acoustic pressure amplitude that was as high as 10% of the acoustic pressure amplitude with no mean fluid flow! The mathematical model predicted much smaller changes, but was correct in predicting that the acoustic pressure amplitude would increase downstream, and decrease upstream relative to the ultrasonic transducer. Subsequent calculations obtained with our mathematical model give an insight into the discrepancy between predicted and measured changes in acoustic pressure amplitude, but these indications are preliminary. Our present conclusion is that mean fluid flow does not significantly affect resonant amplification. Experimental Measurements of Particle Separation During summer 2002, some time was spent mechanically optimizing the geometry and driving circuitry for the ultrasonic particle separator described in the previous status report. This separator employed an electrostatic transducer for acoustic excitation. Some of our measurements indicated us to believe that 6-10dB increase in acoustic pressure could be obtained by ensuring that the walls of the channel were parallel. We fabricated a particle separator that allowed us to adjust the relative geometry of the reflector and transducer, and developed a new drive circuit. Unfortunately, our measurements using the electrostatic transducer technology showed that an increase in acoustic pressure beyond 155 dB was not achievable. Apparently, the machine-tolerances are adequate to maintain parallelism between transducer and refector. Because our previous measurements of separation performance used flow visualization of water particles, a quantitative measure of the separation efficiency was not possible. We have
4 now moved to the use of solid particles to determine the effectiveness of ultrasonic particle separation. An apparatus was designed that allowed the entrainment of corn-starch particles, which had ...