Abstract
This work proposed a method to reconstruct the 3D bubble shape in a transparent medium utilizing the three orthographic digital images. The bubble was divided into several ellipse slices. The azimuth angle and projection parameters were extracted from the top view image, while the formulas for dimensionless semi-axes were derived according to the geometric projection relationship. The elliptical axes of each layer were calculated by substituting the projection width into the formulas. All layers of slices were stacked to form the 3D bubble shape. Reconstruction accuracy was evaluated with spheres, ellipsoids, and inverted teardrops. The results show that the position contributes greatly to the reconstruction accuracy of the bubbles with serious horizontal deformation. The method in Bian et al. (2013) is sensitive to both horizontal and vertical deformations. The vertical deformation has little influence on the method in Fujiwara et al. (2004), whereas the horizontal deformation greatly impacts its accuracy. The method in this paper is negligibly affected by vertical deformation, but it does better in reconstructing single bubbles with large horizontal deformation. The azimuth angle affects the accuracy of the methods in Bian et al. (2013) and Fujiwara et al. (2004) more than the method in this paper.
Highlights
Studying the hydrodynamics of a single bubble growth and detachment in motionless fluids always attracts researchers [1,2]
Some studies focused on the dependence of the single bubble shape on their dynamics such as velocity discontinuity, as well as on the contact angle, viscosity, and surface tension [4,5]
The 3D bubble shape reconstruction is vital for the further analysis of hydrodynamic interactions among a single bubble and surrounding liquid
Summary
Studying the hydrodynamics of a single bubble growth and detachment in motionless fluids always attracts researchers [1,2]. Noninvasive measurement techniques such as electrical tomography [14], interference technology [15], laser tomography [16], and optical imaging [17] have widely been utilized since they have no effect on fluid structure Among these techniques, the optical imaging technology can completely and conveniently capture the transient changes of a single bubble with high speed cameras and has gradually become the common prevailing method for reconstructing the 3D shape of a single bubble in a sparse bubbly flow. Based on the orthographic images of a single bubble and the method in Fujiwara et al [21], this paper proposes an improved method, which deals with the unsatisfied results that seriously deformed bubble always leads to incredible reconstruction errors. The verifying tests show that, compared with the methods in Bian et al [20] and Fujiwara et al [21], the proposed method has higher accuracy when reconstructing bubbles with larger horizontal and vertical deformations, which leads to its extensive applicability
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