Theoretical Study of Supercavitation Bubble Formation Based on Gillespie’s Algorithm

Abstract

Understanding the creation and development of a supercavitation bubble is essential for the design of supercavitational underwater vehicles and applications. The pressure field of the supercavitation bubble is one of the most significant factors in these processes, and it should be taken into account in the analysis. The underwater vessel is surrounded by a supercavitation bubble which is, in fact, an inhomogeneous fluid containing cavities (also described as microbubbles). The distribution of the cavities in the supercavitation volume dictates the pressure field and thus determines the stresses and forces that act on the vessel and affect its motion and stability. In this research, we suggest a new approach to studying the bubbles’ formation and learning about the cavities’ distribution in the low-pressure volume that envelops the underwater vehicle. We used Logvinovich’s principle to describe a two-dimensional ring of fluid that is created at the front edge of the supercavitation body and moves downstream along the vessel. To describe the distribution of the cavities we used Gillespie’s algorithm, which is usually used to describe biological and chemical systems. The algorithm succeeded in describing the random movement of the cavities in the cross-section under various conditions and also in describing their distribution and effects on the macroscopic system. A few factors of the physical characteristics of the fluid and the flow conditions were examined (the initial bubble supply, and the rate coefficients of creation and collapse). The results led to the conclusion that with an examination of those factors and using Gillespie’s algorithm, predictions of the distribution and thus the development of supercavitation could be achieved. The main finding of the analysis was that asymmetric development of the bubbles took place, in spite of the symmetry of the physical problem, as observed in high-resolution experiments.