低雷諾數等速近牆之固體球其流體力邊界效應之即時量測

In-Situ Measurement of Wall Effect on The Hydrodynamic Force for a Solid Sphere in Constant Approach at Low Reynolds Number

李峻華(Jung-Hua Lee)

指導教授 ： 楊馥菱

國立臺灣大學/工學院/機械工程學研究所/碩士(2012年)

https://doi.org/10.6342/NTU.2012.02397

摘要

中文摘要
本論文以系統性實驗探討沉浸球體在軸對稱的環境中靠近一下游牆面時的所受到的流體力。以精密的伺服馬達使球體以等速度運動，藉由改變球體的速度與流體黏滯係數使得顆粒雷諾數的範圍在0.5至6.8之間。並企圖利用整合傳統應變規與壓力感測器的結果達到同步即時量測球體表面的總動態力與動態壓力分量。分別於停滯點起0°, 45°以及90°的位置量測壓力。除移動球體上的流體力外，我們並嘗試非侵入性地量測因球體靠近而產生的近牆間隙流體膜的強度。
對於總力與壓力分量，量測所得的數據皆以遠牆的結果無因次化以觀察牆面對流體力的影響。無因次化的擬穩態阻力即為牆面修正係數，並與一些低雷諾數下的理論預測定性地吻合。在實驗的雷諾數範圍中，總流體力的牆面修正係數與理論預測有相同的趨勢：牆面修正係數隨著間隙的的減小而單調遞增。在停滯點以及與球體運動方向夾θ=45º的壓力也觀察到此隨漸小間隙的近牆增強效應。但在停滯點的壓力的增強效應似乎隨雷諾數增加，且此增加的趨勢遠大於牆面修正。在θ=45°的壓力增加則較為溫和，且只有在極小的間隙才比較明顯。對比之下，在θ=90°的壓力則一直維持在一相對極小的數值，且無法觀測到任何與間隙相關的改變。同時，隨著球體運動的增加－也就是雷諾數的增加－被擠壓的流體膜會有較強烈的運動並反應在應變規讀數上。

關鍵字:流體力即時量測，史托克阻力，邊壁放大效應，荷重元，壓力感測器，應變規

關鍵字

流體力即時量測 ； 史托克阻力 ； 邊壁放大效應 ； 荷重元 ； 壓力感測器 ； 應變規

並列摘要

Abstract
This thesis investigates the hydrodynamic forces of an immersed sphere in axis-symmetric approach to a downstream wall via systematic experiments. Sphere motion at constant velocity was generated by precision servo motor to cover a range of particle Reynolds number, 0.5 to 6.8, by changing sphere velocity and liquid viscosity. We attempted synchronized in-situ measurements of the resulting total dynamic force and its dynamic pressure components by integrating conventional load cells and pressure transducers. Pressure measurements were conducted at 0º, 45º, and 90º from the front stagnation point. In addition to the fluid force on the moving sphere, we also attempted a non-intrusive measurement to monitor the strength of the interstitial film motion near wall induced by the approaching sphere.
For both the total force and the pressure components, the data obtained far away from the wall were employed to scale the near-wall data to determine the wall influences. The measured factor for quasi-steady total drag is known as the wall correction factor was found to agree qualitatively with a few model predictions at low Reynolds. For all the examined Re, the wall correction factors for total hydrodynamic force falls on the same trend that increases monotonically with diminished interstitial gap. Such near-wall amplification with dropping gap is also observed for the pressure at front stagnation point and at θ=45º from the approach line. However, the front stagnation point shows an amplification that seems to grow with Re and at a trend much higher than the wall correction factor. The pressure at θ=45º shows much milder rise and only takes place at very small gaps; contrastingly, the pressure at θ=90º remains a comparably small value without any detectable dependence on interstitial gap. At the same time, the squeezed film motion seems to increase with the sphere motion and hence Re, as expected.

Keywords: in-situ measurement of total hydrodynamic force, Stokes drag, wall amplification function, load cell, pressure transducer, strain gauge,

並列關鍵字

in-situ measurement of total hydrodynamic force ； Stokes drag ； wall amplication function ； load cell ； pressure tranducer ； strain gauge

參考文獻

Stoks G.G. “On the theories of the internal friction of fluids in motion,” Trans. Camb. Phil. Soc, 1845

Odar F. and Hamilton S.W., “Forces on a sphere accelerating in a viscous fluid,” J. Fluid Mech. 18, 302-314, 1964

Odar F. and Hamilton S.W., “Verification of the proposed equation for calculation of the forces on a sphere accelerating in a viscous fluid,” J. Fluid Mech. 18, 591-592, 1964

Brenner H., “The slow motion of sphere through a viscous fluid towards a plane surface,” 1961

Cox R.G. and Brenner H., “The slow motion of a sphere through a viscous fluid towards a plane surface-II small gap widths, including inertial effects”, May 12,1967.