Abstract
In the paper, we solve the problem of designing a hydrofoil in the supercavitation regime simulated by the Wu model. The distributions of velocities along the wetted part of the hydrofoil and the cavitation number are assumed to be given. We derive formulas that allow one to express the lift and drag forces in terms of integral functionals of the initial data. Thus, the formulas generalize the Kutta-Zhukovskii theorem on the lift force of a profile in continuous flow for the case of supercavitational flow. The shape of the hydrofoil is reconstructed by the methods of inverse boundary value problems. It has been rigorously proven that for lifting profiles, the lift-to-drag ratio increases monotonically with increasing cavitation numbers.
REFERENCES
D. V. Maklakov and S. E. Gazizova, “Inverse nonlinear problem of designing supercavitating hydrofoils,” Lobachevskii J. Math. 40, 1371–1382 (2019). https://doi.org/10.1134/s1995080219090154
T. Ya.-T. Wu, “A wake model for free-streamline flow theory. Part 1. Fully and partially developed wake flows past an oblique flat plate,” J. Fluid Mech. 13, 161–181 (1962). https://doi.org/10.1017/s0022112062000609
T. Ya.-T. Wu and D. P. Wang, “A wake model for free-streamline flow theory. Part 2. Cavity flows past obstacles of arbitrary profile,” J. Fluid Mech. 18, 65–93 (1964). https://doi.org/10.1017/s0022112064000052
M. I. Gurevich, Theory of Jets of Ideal Liquid, 2nd ed. (Nauka, Moscow, 1979).
A. G. Terentiev, I. N. Kirschner, and J. S. Uhlman, The Hydrodynamics of Cavitating Flows (Backbone, 2011).
D. V. Maklakov, “Analog of the Kutta–Joukowskii theorem for the Helmholtz–Kirchhoff flow past a profile,” Dokl. Phys. 56, 573–576 (2011). https://doi.org/10.1134/s1028335811090096
D. V. Maklakov, “On the lift and drag of cavitating profiles and the maximum lift and drag,” J. Fluid Mech. 687, 360–375 (2011). https://doi.org/10.1017/jfm.2011.358
Funding
The study was supported by the Russian Science Foundation, project no. 23-11-00066.
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Maklakov, D.V., Gazizova, S.E. Application of the Wu Model for Solving the Inverse Problem of Designing Supercavitating Hydrofoils. Russ Math. 67, 77–83 (2023). https://doi.org/10.3103/S1066369X23070071
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DOI: https://doi.org/10.3103/S1066369X23070071