液体中で中心を通る直線上を異なる速度で並進運動する体積不変な複数球形気泡の相互作用

概要

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Velocity potential, kinetic energy and added mass of a cluster of straightly in-line spherical and unequal constant-volume bubbles moving with different velocities in an incompressible liquid are analytically obtained in the framework of potential theory. Mutual interaction among the bubbles is taken into account in the analysis up to the order of (ai/Lij)3, where ai is the radius of bubble i(i = 1, 2, 3, ··· , N) and Lij( j ≠ i, j = 1, 2, 3, ··· , N) is the central distance of bubbles i and j. For special cases of a single and two bubbles, the velocity potential, kinetic energy and added mass in the present result are identical with those known well for the same cases. The added mass of the cluster of equal bubbles with the same inter-bubble distance and velocity largely decreases in dependence on the ratio of ai/Lij and the number of the bubbles.