| Summary: | 碩士 === 國立臺灣大學 === 機械工程學研究所 === 107 === 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.
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