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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2021 Volume 61, Number 11, Pages 1873–1893 (Mi zvmmf11319)

This article is cited in 7 papers

Mathematical physics

Analytical solution for the cavitating flow over a wedge. II

V. I. Vlasovab, S. L. Skorokhodova

a Federal Research Center "Computer Science and Control", Russian Academy of Sciences, 119333, Moscow, Russia
b Lomonosov Moscow State University, Moscow Center for Fundamental and Applied Mathematics, 119991, Moscow, Russia

Abstract: This work continues previous studies of the authors and provides an analytical solution to the plane problem of symmetric cavitating flow of an ideal fluid over a wedge for Tulin's cavity closure model with a double-spiral vortex. The solution is expressed in terms of the Lauricella hypergeometric function. A numerical implementation of the solution is described in detail, and an asymptotic analysis of the solution is given. The spiral structure of vortices closing the cavity is studied, and the vortex size is estimated. An asymptotic representation of the wake width as $x\to\infty$ is found. Additionally, the asymptotics of the drag coefficient $\mathbf{C}_x$ and the relative sizes of the cavity as the cavitation number $Q$ tends to zero are established.

Key words: plane theory of ideal fluid jets, cavitating flow over a wedge, Tulin's double-spiral vortex closure model, explicit analytical solution, Lauricella hypergeometric function, numerical implementation, asymptotic analysis of flow.

UDC: 517.95

Received: 11.03.2021
Revised: 18.04.2021
Accepted: 19.05.2021

DOI: 10.31857/S0044466921110156


 English version:
Computational Mathematics and Mathematical Physics, 2021, 61:11, 1834–1854

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© Steklov Math. Inst. of RAS, 2025