International Journal of Fluid Machinery and Systems
Online ISSN : 1882-9554
ISSN-L : 1882-9554
Original papers
Stochastic Impact Model: Poisson Processes and Copulas to Model Cavitation Erosion Impacts
Gabriel TaillonKazuyoshi Miyagawa
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2019 Volume 12 Issue 4 Pages 418-428


A statistical model that represents impacts caused by cavitation bubble collapse on material surfaces is developed, as one step in the development of a novel cavitation erosion model. This model uses stochastic processes, for example the non-homogeneous Poisson process (NHPP), to represent impact events as points randomly distributed in time and space. Then, marks which represent the impact properties are computed using empirical distributions. This model is based on experimental data and empirical observations using a high-speed pressure sensor in a vibratory cavitation apparatus based on the ASTM G32 standard. A total of 41581 impacts were measured over 100 realizations of 4ms long recording. The rate of the non-homogeneous Poisson is shown to be a sinusoidal function, but the process is over-dispersed. The spatial distribution of points is independent from the temporal portion, so modeled independently as a Poisson cluster process. Two marks were measured for each impact event: the impact duration and amplitude. These mark’s joint marginals are modeled as gamma distributions, determined by a Kolmogorov-Smirnov (KS) test. The marks are shown to be dependent, prompting the use of copulas to model their joint distribution. The best-fitting copu-la is a highly asymmetric Tawn copula, in the class of so-called extreme value copulas. Almost no impacts were ob-served with a combination of a high amplitude (>12MPa) and low duration (<5µs). An extension of the KS test to two dimensions demonstrated that the copula is a better fit compared with a joint distribution of independent marginals. The combination of the spatio-temporal processes, with the mark’s distributions combine to produce the stochastic impact model for cavitation erosion in the vibratory apparatus.

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© 2019 Turbomachinery Society of Japan, Korean Fluid Machinery Association, Chinese Society of Engineering Thermophysics, IAHR
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