(11-5) Abstract : An ultrasonic air pump utilizing acoustic streaming is discussed and its efficient simulation method using finite element analysis (

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1 (11-5) Abstract : An ultrasonic air pump utilizing acoustic streaming is discussed and its efficient simulation method using finite element analysis (FEA) is suggested in this report. The pump induces air streaming in a thin air layer between a bending transducer and a reflector by exciting an intense sound field. The absolute sound pressure and streaming velocity in the air layer are calculated through following three steps: 1. linear acoustic analysis, 2. calculation of acoustics streaming driving force and radiation pressure, and 3. static incompressible flow analysis. The calculation results are compared with experimental results for the sound pressure and flow velocity. As a result, the sound pressure is calculated in the derivation of the error of 8.5%, and the measurement and analysis results for the streaming distribution are in good agreement. keywords : acoustic streaming, air pump, bending vibration, driving force, FEA, radiation pressure 1 [1, 2, 3, 4] W. L. Nyborg [5, 6] O. V. Rudenko, S. I. Soluyan [7] [4, 8] [9, 10, 11, 12, 13, 14] (FEA) Nyborg 2 Nyborg[5] p ρ u p p 0 = p 1 + p 2 +, p p 0 = p 2 (1) ρ ρ 0 = ρ 1 + ρ 2 +, ρ ρ 0 = ρ 2 (2) u = u 1 + u 2 +, u = u 2 (3) p 0, ρ 0 0 ( p 0 = Pa ρ 0 = 1.3 kg/m 3 ) U = u 2 + ρ 1 u 1 /ρ 0 U t + (U )U η ρ 0 2 U = p 2 ρ 0 + F (4) η 1

2 Fig. 1: Block diagram for the analysis. F Fig. 2: Basic structure of the device. F = (u 1 )u 1 u 1 div u 1 (5) p 2 [5] Nyborg[15] p 2 p 2 = e p e k = p 1 2 4ρ 0 c 2 ρ 0 u (6) F e f f U/ t = 0 (7, 8) (U )U η ρ 0 2 U = F e f f (7) F e f f = (u 1 )u 1 u 1 div u 1 e p ρ 0 + e k ρ 0 (8) 3 Fig. 3: Bending vibration mode on the transducer at the resonant frequency of 26.2 khz. F e f f F e f f 4 Fig. 2 PZT ( 10 mm 30 mm 0.4 mm) 20 mm 30 mm 1 mm 4 Fig mm x y z p 1 u 1 0 Fig. 3 (x u 1 ) 1 2

Table 1: Material properties used in calculations. Air Sound speed [m/s] 340 Density [kg/m 3 ] 1.29 Viscosity coefficient [ 10 6 Pa sec] 1.62 PZT Young s modulus [GPa] 74.

3 Table 1: Material properties used in calculations. Air Sound speed [m/s] 340 Density [kg/m 3 ] 1.29 Viscosity coefficient [ 10 6 Pa sec] 1.62 PZT Young s modulus [GPa] 74.7 Density [kg/m 3 ] 7700 Poisson rate Electromechanical coupling factor Relative permittivity 1450 Q-farctor 200 Aluminum Young s modulus [GPa] 70.3 Density [kg/m 3 ] 2698 Poisson rate Q-farctor 200 Table 2: Specifications of Computer, FEA, and the resources spent for the calculations. CPU AMD Phenom 9550 Quad-Core Processor 2.20 GHz Memory 8.0 Gbyte Operation System CentOS Linux 5.4 Nodes 25,662 Elements 23,142 Shared-Memory Parallel 2 process Memory used MByte Calculation time for sound sec Calculation time for fluid sec Fig. 4: FEA model. ANSYS11.0 ANSYS Inc.) Table 1, 2 1 mm 0.5 mm ANSYS 1 mm PZT (x ) 3 [16] (y ) 1 (n x, n y ) = (3, 1) (3,1) f = 26.2 khz F e f f 1 2 mm 0.5 m/s 5 ( ) Fig.4 32x38x15 mm [17] Fig.5 3

Lock in Amp Ref. Sig. Amp. Function Generator Fig.

4 ASE light source PD Mesurement object Circulator Single mode fiber Transducer Lock in Amp Ref. Sig. Amp. Function Generator Fig. 5: Measurement setup for sound pressure. Fig. 7: Sound pressure distribution. Fig. 6: Measurement setupt for PIV < x < 15 mm 15 < y < 15 mm 1 mm 6.2 (PIV) Fig.6 LED 1/ fps 10 µs 13.7 < x < 20.1 mm, 9.6 < y < (1.16 ) PIV ( mm) 2 Fig.7 ( ) x ( ) ( ) Pa Pa (3,1) Pa(8.7%) 68.5 Pa(8.6%) 100 Pa 7.2 Fig.8 F( ) Fgradp 2 /ρ 0 F e f f x x ( ) F e f f ( ) 0 4 F 4

5 Fig. 8: Driving force distribution. Fig. 9: Flow velocity distribution when the gradient of the reflector is 0 degree. 0 4 x = 5 mm 7.3 Fig PIV 0 PIV 0 4 Fig. 10: Flow velocity distribution when the gradient of the reflector is 4 degrees. 5

6 8 5.8% [16], (1974) [17] H. Takei, T. Hasegawa, K. Nakamura, and S. Ueha: Jpn. J. Appl. Phys. 46 (2007) [1] H. Takei, D. Koyama, K. Nakamura, and S. Ueha: Jpn. J. Appl. Phys. 47 (2008) [2] H. Takei, D. Koyama, K. Nakamura, and S. Ueha: Denshi Joho Tsushin Gakkai Ronbunshi A 91 (2008) 1152 [in Japanese]. [3] D. Koyama, Y. Wada, K. Nakamura, M. Nishikawa, T. Nakagawa and H. Kihara: IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 57 (2010) 253. [4] Y. Wada, D. Koyama, K. Nakamura: Jpn. J. Appl. Phys HE15 (2010). [5] Wesley L. Nyborg : J. Acoust. Soc. Am., 25 (1953) pp [6] Wesley L. Nyborg : J. Acoust. Soc. Am., 30 (1958) pp [7] O. V. Rudenko and S. I. Soluyan THEO- RETICAL FOUNDATIONS OF NONLINEAR ACOUSTICS (Consultants Bureau, New York, 1977) [8] L. P. Cheng and S. Y. Zhang : Appl. Phys. Lett. 90, (2007). [9] M. Kawahashi and M. Arakawa: JSME Int. J. 39B (1996) pp [10] T. Yano: J. Acoust. Soc. Am. 106 (1999) L7-L12. [11] A. Alexeev and C. Gutfinger: Phys. Fluids 15 (2003) pp [12] M. K. Aktas and B. Farouk: J. Acoust. Soc. Am. 116 (2004) pp [13] J. P. Boris, A. M. Landsberg, E. S. Oran, and J. H. Gardner, LCPFCT A flux-corrected transport algorithm for solving generalized continuity equations, Report No. NRL/MR/ , (1993). [14] : 24 (2005) pp [15] Wesley L. Nyborg : J. Acoust. Soc. Am., 42 (1967) pp

75 unit: mm Fig. Structure of model three-phase stacked transformer cores (a) Alternate-lap joint (b) Step-lap joint 3 4)

75 unit: mm Fig. Structure of model three-phase stacked transformer cores (a) Alternate-lap joint (b) Step-lap joint 3 4) 3 * 35 (3), 7 Analysis of Local Magnetic Properties and Acoustic Noise in Three-Phase Stacked Transformer Core Model Masayoshi Ishida Kenichi Sadahiro Seiji Okabe 3.7 T 5 Hz..4 3 Synopsis: Methods of local