Free streamline detachment with surface tension: A conformal mapping-based numerical solution

Semenov, Yuriy, Ni, Baoyu and Blyth, M. G. (2025) Free streamline detachment with surface tension: A conformal mapping-based numerical solution. Theoretical and Computational Fluid Dynamics. ISSN 0935-4964 (In Press)

Full text not available from this repository. (Request a copy)

Abstract

The problem of the detachment of a free-streamline from a smoothly shaped body is considered taking into account the effect of surface tension. The fluid is assumed to be inviscid and incompressible, and the flow is assumed to be irrotational and stationary in the body-fixed frame but corresponds to a progressive capillary waves in the freestream frame. We employ the Brillouin-Villat criterion to determine the position of the free-streamline detachment. Using the integral hodograph method, we derive expressions for the complex velocity and the derivative of the complex potential, both defined in an auxiliary parameter plane. A system of singular integral equations, formulated in terms of the velocity magnitude along the free surface and the slope of the body, is derived by applying the dynamic and kinematic boundary conditions. The numerical method is highly efficient, as it only requires the evaluation of these two nonsingular functions. Numerical results demonstrate the effect of surface tension on the free-streamline detachment, the drag force and the free surface shape for a wide range of Weber numbers. It is shown that the surface tension generates capillary waves due to the distortion of the magnitude of the inflow velocity at the detachment point.

Item Type:	Article
Additional Information:	The work of YAS and BN was supported by the National Natural Science Foundation of China (Nos.W2541018, 52521009, 52192693, 52192690, 52371270, 52350410468, and W2433140), to which the authors are most grateful. This work was supported by EPSRC grant EP/V521929/1.
Uncontrolled Keywords:	brillouin-villat criterion for free-streamline detachment,capillary water waves,conformal mapping,fully nonlinear computations
Faculty \ School:	Faculty of Science > School of Engineering, Mathematics and Physics
UEA Research Groups:	Faculty of Science > Research Groups > Fluids & Structures
Depositing User:	LivePure Connector
Date Deposited:	29 Oct 2025 12:31
Last Modified:	29 Oct 2025 12:31
URI:	https://ueaeprints.uea.ac.uk/id/eprint/100830
DOI:	issn:0935-4964

Actions (login required)

View Item