Analytical Solution for the Cavitating Flow over a Wedge. II

• Published in: Computational mathematics and mathematical physics Vol. 61; no. 11; pp. 1834 - 1854
• Main Authors: Vlasov, V. I., Skorokhodov, S. L.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-11-2021; Springer Nature B.V
• Subjects: Asymptotic properties; Cavitation number; Computational Mathematics and Numerical Analysis; Drag coefficients; Exact solutions; Fluid flow; Hypergeometric functions; Ideal fluids; Mathematical Physics; Mathematics; Mathematics and Statistics; plane theory of ideal fluid jets; cavitating flow over a wedge; asymptotic analysis of flow; Tulin’s double-spiral vortex closure model; Lauricella hypergeometric function; numerical implementation; explicit analytical solution
• ISSN: 0965-5425; 1555-6662
• DOI: 10.1134/S0965542521110154

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
is found. Additionally, the asymptotics of the drag coefficient
and the relative sizes of the cavity as the cavitation number
tends to zero are established.