摘要

本研究主要針對翼型擴散器泵，在隨時間正弦變化之動態壓力作動下，探討翼型擴散器幾何形狀與操作參數對泵效能的影響。本研究分為數值模擬與實驗量測兩部分。
數值模擬的壓力振幅固定為 200 Pa，外部半角範圍為9°至45°，內部半角範圍為0°至45°，頻率為1 Hz至2000 Hz。模擬結果顯示，對於所有翼型擴散器泵而言，淨流率皆為擴散器方向。頻率在小於20 Hz時，頻率對淨流率之影響很小，但當頻率大於20 Hz時，淨流率隨頻率增加而大幅下降。
實驗量測分為穩態量測與動態量測兩部分，壓頭振幅為40 mm至60 mm，外部半角範圍為9°至45°，內部半角範圍為3°至27°，頻率為0.24 Hz至0.68 Hz。在穩態量測下，淨流率皆為擴散器方向，但在動態量測時，頻率與壓頭振幅越大則往擴散器方向的淨流率越小，在頻率為0.68 Hz且壓頭振幅為60 mm時，淨流率甚至轉為噴嘴方向。
在數值模擬與實驗量測下，加入導翼後會增加摩擦損耗，導致淨流率皆大幅下降，但實驗量測之降幅較數值模擬之預測為小。對翼型擴散器而言，數值模擬與實驗量測皆有相同之結論，即外部半角越大淨流率亦越大，而內部半角為外部半角的三分之一時，泵效能最佳。在頻率為0.24 Hz且壓頭振幅為40 mm時，外部半角為45°內部半角為15°，可得最大淨流率0.121 μl/s。

Abstract

In this study, the performance of vaned microdiffuser pumps under sinusoidal pressure actuation is explored. Both numerical simulation and experiments are investigated for comparison.
In numerical simulation, the outer half-angle θ varies from 9° to 45°, the inner half-angle φ varies from 0° to 45°, and the excitation frequency f varies from 1 Hz to 2000 Hz. The pressure amplitude P0 is fixed at 200 Pa. The numerical results show that net flow rate is in the diffuser direction for all vaned diffuser micropumps. Best flow rectification is achieved atθ = 45° andφ = 15°. For f < 20 Hz, net flow rate is independent of the excitation frequency, but net flow rate decreases greatly with increasing excitation frequency for f > 20 Hz.
The experiments are conducted under both steady and transient conditions. Four parameters, the outer half-angle (θ = 9° to 45°), the inner half-angle (φ = 3° to 27°), the excitation frequency (f = 0.24 Hz to 0.68 Hz), and the amplitude of pressure head (h0 = 40 mm to 60 mm), are considered. Under steady state, the experimental results show that net flow rate is in the diffuser direction for all vaned diffuser micropumps. Nevertheless, the transient experiments reveal that net flow rate decreases as the frequency and pressure amplitude increase, and even turns to the nozzle direction at f = 0.64 Hz and h0 = 60 mm. Similar to the numerical simulation, the experiment results suggest that when vanes equally divide the diffuser into three sub-diffuser, i.e. θ = 3φ, the pumping effect is optimized. As the outer half-angle increases, net flow rate is augmented. Atθ = 45° andφ = 15°, Qmax = 0.121 μl/s is attainable. Adding vanes in diffuser micropump diminishes net flow rate significantly due to the strong friction influences in microscale.

[1] N.-T. Nguyen, X. Huang, and T. K. Chuan, "MEMS-micropumps:a review," Fluids Engineering, vol. 124, pp. 384-392, 2002.
[2] O. G. Feil, "Vane systems for very-wide-angle subsonic diffusers," Journal of Basic Engineering, vol. 86, pp. 759-764, 1964.
[3] I. E. Idelchik, Handbook of hydraulic resistance. Washington, DC: U.S. Atmoic Commission and National Science Foundation, 1966.
[4] A. M. Wo, "Comparison between the use of vanes and boundary layer section to improve the performance of a wide-angle diffuser," Journal of Chinese Society of Mechanical Engineers, vol. 17, pp. 1-12, 1996.
[5] H. Andersson, W. ven der Wijngaart, P. Nilsson, P. Enoksson, and G. Stemme, "A valve-less diffuser micropump for microfluidic analytical systems," Sensors and Actuators, vol. B 72, pp. 259-265, 2001.
[6] J.-H. Tsai and L. Lin, "A thermal-bubble-actuated micronozzle-diffuser pump," Journal of Microelectromechanical Systems, vol. 11, pp. 665-671, 2002.
[7] W. Y. Lee, M. Wong, and Y. Zohar, "Microchannels in series connected via a contraction/expansion section," Journal of Fluid Mechanics, vol. 459, pp. 187-206, 2002.
[8] C. J. Kang and Y.-S. Kim, "A disposable polydimethylsiloxane-based diffuser micropump actuated by piezoelectric-disc," Journal of Microelectronic Engineering, vol. 71, pp. 119-124, 2004.
[9] M. Gad-el-Hak, "Fluid mechanics of microdevices-the Freeman scholar lecture," Journal of Fluids Engineering, vol. 121, pp. 5-33, 1999.
[10] P. A. Thompson and S. M. Troian, "A general boundary condition for liquid flow at solid surfaces," Nature, vol. 389, pp. 360-2, 1997.
[11] J. D. Anderson, Computational Fluid Dynamics: McGraw-Hill, 1995.
[12] J. R. Taylor, An Introduction to Error Analysis, 2nd ed. Sausalito, CA: University Science Books, 1997.
[13] C. Loudon and A. Tordesillas, "The use of the dimensionless Womersley number to characterize the unsteady nature of internal flow," Journal of Theoretical Biology, vol. 191, pp. 63-78, 1998.
[14] R. L. Norton, Design of Machinery, 1st ed. New York: McGraw-Hill, pp. 295-323, 1992.