UCL Discovery
UCL home » Library Services » Electronic resources » UCL Discovery

Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

Doak, A; Vanden-Broeck, J-M; (2021) Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge. Journal of Engineering Mathematics , 126 (1) 10.1007/s10665-020-10086-z. Green open access

[thumbnail of depo200.pdf]
Preview
Text
depo200.pdf - Published version

Download (1MB) | Preview

Abstract

This paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

Type: Article
Title: Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s10665-020-10086-z
Publisher version: http://dx.doi.org/10.1007/s10665-020-10086-z
Language: English
Additional information: Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Keywords: Free surface flows, Gravity–capillary flows, Numerical methods
UCL classification: UCL
UCL > Provost and Vice Provost Offices
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.ucl.ac.uk/id/eprint/10125832
Downloads since deposit
20Downloads
Download activity - last month
Download activity - last 12 months
Downloads by country - last 12 months

Archive Staff Only

View Item View Item