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中文摘要：
本文发展了三维离散涡模型用于模拟无粘不可压缩涡环的发展及其与气泡的相互作用，涡环被离散为平均分布在其中心线上的球形涡元，由Blot—Sarvart定律叠加每个涡元的诱导速度得到涡环的运动速度。涡环横截面上的涡量分布由二阶高斯分布来近似，而涡环随时间的演化则采用具有二阶精度的预测一校正算法。利用本文发展的三维离散涡模型，首先对圆涡环的发展进行了模拟，运动速度同理论解对比非常吻合，验证了模型的有效性。随后分别模拟了不同强度、不同核径比、不同长短轴比单个椭圆涡环的运动，成功再现了椭圆涡环的长短轴交替互换等现象，得到了不同工况下椭圆涡环随时间发展和演化的定性规律。最后本文将三维离散涡法与气泡运动方程相耦合，对涡环和气泡的相互作用进行了模拟，得到的气泡运动轨迹结果与实验结果非常一致，说明本文提出的三维涡模型可以推广到三维两相的情形。
英文摘要：
In present paper a three-dimensional discrete vortex filament method is put forward to simulate the motion and bubble entrainment of an inviscid, incompressible vortex ring. In this method the circular or elliptical vortex ring is discreted into a number of individual elements with finite spherical cores placed on the centerline of the ring and the induced velocity can be obtained by summing up the contribution of each element. The vorticity across the section of the ring is approximated by a second-order Gaussian distribution and second order predictor-corrector algorithm is adopted in the simulation of vortex ring evolution. First this model is verified by the motion of circular vortex ring through the comparison with theoretical solution. Then a parametric study of the influences of circulations, core-to-radius ratios and long-to-short axis ratios on the evolution of elliptical ring is carried out. The periodical exchange of major and minor axis is numerically reproduced and evolution rule of a single elliptical vortex ring is obtained. Finally bubble dynamic equation is introduced into the three-dimensional discrete vortex model to simulate the bubble entrainment of the vortex ring. The resemblance between calculated bubble trajectory and experiment also validate our two-phase model
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