量測水因球體撞擊而產生的表面變形

Abstract

本研究藉由球體撞擊流體的自由表面以產生捲氣腔(air-entraining cavity)，並量測捲氣腔頂的表面波。因為表面波的三維輪廓無法藉由接觸式方法量測，我們將使用傅立葉轉換輪廓術(Fourier transform profilometry, FTP)量測表面波的三維輪廓。FTP藉由結構光因物體輪廓起伏而形成的相位差與系統的光學幾何關係重建物體的三維輪廓。 如要在流體中產生捲氣腔，邦德數、福祿數、韋伯數與毛細數為重要的無因次參數。由於水的相關資料最豐富，本研究將先以水作為實驗流體。相關文獻指出球體撞擊水面的速度是形成不同腔體型態的主因。為了易於量測流體表面變形，我們藉由調整球體落下的高度使球體撞擊水面時產生深層密封捲氣腔。為了探討腔體的軸對稱性，我們將量測捲氣腔頂的表面波。 為了尋找最佳的量測參數設定，我們藉由程式模擬探討經FTP重建的輪廓完整度與量測參數間的關係。量測參數包含結構光的週期與傾斜角度、待測物的大小，我們將參考程式模擬的最佳參數設定設置FTP量測系統。為了確認量測誤差是否影響量測結果的可靠度，我們使用三個同尺寸的圓球製作三個不同高度的球面模型。藉由三個模型的量測結果，我們可以瞭解誤差是否與表面斜率或高度大小有關。 藉由探討三者的量測結果，結果顯示誤差是來自濾波器頻寬的大小受到限制。高度誤差的大小與表面斜率和高度無關而只與待測物的最大高度有關。結果顯示平均高度誤差與待測物的最大高度成正比，而且最大高度誤差約為平均高度誤差的3倍、最小高度誤差約為平均高度誤差的0.1倍。最大高度誤差皆出現在20%最大高度的位置。軸對稱性也只與待測物的最大高度有關而與表面斜率與高度無關，而且只有在最大高度20%到80%間的軸對稱性是可靠的。最後，我們將量測系統應用於觀測捲氣腔頂的表面波，並藉由量測結果探討表面波的高度及直徑等尺寸。

When a sphere impacts into the free surface of water, an air-entraining cavity would be created. To discuss the axis-symmetry of the cavity, we measure the surface wave created by the cavity. However, because the surface wave changes continuously, we can’t measure it by any mechanical measuring methods. Instead, we adopt Fourier transform profilometry (FTP), a kind of optical measuring method, to measure the surface wave. To measure the surface wave easily, we create deep seal impact cavity. According to the related references, there are several non-dimensional parameters which affect the phenomenon of an air-entraining cavity, including Bond number, Weber number, capillary number and Froude number. In addition, the different types of the air-entraining cavities are dependent on the different impact velocities of the spheres. In order to measure the surface wave easily, we only want to obtain a deep seal impact cavity by adjusting the non-dimensional parameters. Deep seal cavity is a type of air-entraining cavity with deeper pinch-off depth and later pinch-off time than others. Then, we measure the surface wave of a deep seal cavity by the FTP system. We use computer simulation of the FTP system parameters to find the optimum setting. In order to make sure the reliability of our FTP system, we use three spheres with the same diameter to manufacture the three models with different max heights. First, by observing the sections of the measuring result, we find out that the measuring error is from the filter. Second, we discuss the error of height and axis-symmetry of the measuring result. We find the two types of error above are only dependent on the max height of the measured object, and independent of the slope and height of the measured surface. Third, we know the maximum error of height is about 3 times the mean error of height, and it always locates at 20% of the max height. The minimum error of height is about 10% of the mean error of height. Finally, the axis-symmetry of the measuring result is believable within the range between 20% and 80% of the max height. As above mentioned, we obtain the reliability of our FTP system, and we will further use this system to measure the surface wave of an air-entraining cavity.