Johnson, Edward;
Marshall, Jonathan;
(2023)
The high-speed submerged hydrofoil.
Journal of Fluid Mechanics
, 954
, Article A45. 10.1017/jfm.2022.1042.
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Abstract
This paper gives, in the limit of large Froude number, a closed-form, analytical solution for steady, two-dimensional, inviscid, free-surface attached flow over a submerged planar hydrofoil for arbitrary angles of attack and depths of submergence. The doubly connected flow domain is conformally mapped to a concentric annulus in an auxiliary plane. The complex flow potential and its derivative, the complex velocity, are obtained in the auxiliary plane by considering their form at known special points in the flow, and the required conformal mapping is determined by explicit integration. The four real solution parameters are determined as the simultaneous roots of four real nonlinear algebraic equations arising from the flow normalisation. The explicit form allows accurate evaluation of various flow quantities, including the lift on the foil, and these are related to the large-Froude-number results in recent numerical solutions.
| Type: | Article |
|---|---|
| Title: | The high-speed submerged hydrofoil |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1017/jfm.2022.1042 |
| Publisher version: | http://doi.org/10.1017/jfm.2022.1042 |
| Language: | English |
| Additional information: | This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third-party material in this article are included in the Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ |
| Keywords: | Waves/free-surface flows |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10161997 |
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