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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on March 2, 2009
The Quarterly Journal of Mechanics and Applied Mathematics 2009 62(2):167-200; doi:10.1093/qjmam/hbp003
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© The author 2009. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Circular map for supercavitating flow in a multiply connected domain

Y. A. Antipov{dagger}

( Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA )

V. V. Silvestrov{ddagger}

( Department of Mathematics, Gubkin Russian State University of Oil and Gas, Moscow 119991, Russia )

{dagger} Corresponding author. <antipov{at}math.lsu.edu>

{ddagger} <v_silvestrov{at}mail.ru>

Received 21 July 2008. Revise 18 January 2009. Accepted 21 January 2009.


  Abstract

A nonlinear free boundary-value problem of supercavitating flow past n + 1 hydrofoils is analyzed. To describe the cavities’ closure mechanism, the Tulin–Terent'ev single-spiral-vortex model is employed. The flow domain is considered as the image of an (n + 1)-connected circular domain. The conformal map is constructed in terms of the solutions to two Riemann–Hilbert problems of the theory of symmetric automorphic functions. One of the problems is homogeneous and its coefficients are continuous functions while the second problem is inhomogeneous and has discontinuous coefficients. The exact solutions to the problems are found by using quasiautomorphic and quasimultiplicative analogs of the Cauchy kernel. The case of a single plate is considered in detail and the numerical results are reported.


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Y. A. Antipov and A. Y. Zemlyanova
Single- and double-spiral-vortex models for a supercavitating non-symmetric wedge in a jet
Proc R Soc A, December 8, 2009; 465(2112): 3817 - 3837.
[Abstract] [Full Text] [PDF]


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