Publication detail

A (non-)hydrostatic free-surface numerical model for two-layer flows

BOHÁČEK, J. KHARICHA, A. LUDWIG, A. WU, M. KARIMI-SIBAKI, E. PAAR, A. BRANDER, M. ELIZONDO, L. TRICKL, T.

Original Title

Type

journal article in Web of Science

Language

English

Original Abstract

A semi-implicit (non-) hydrostatic free-surface numerical model for two layer flows is derived from the Navier-Stokes equations by applying kinematic boundary conditions at moving interfaces and by decomposing the pressure into the hydrostatic and the hydrodynamic part. When the latter is ignored, the algorithm conveniently transforms into a solver for a hydrostatic flow. In addition, when the vertical grid spacing is larger than the layer depths, the algorithm naturally degenerates into a solver for the shallow water equations. In this paper, the presented numerical model is developed for the horizontal centrifugal casting, a metallurgical process, in which a liquid metal is poured into a horizontally rotating cylindrical mold. The centrifugal force pushes the liquid metal toward the mold wall resulting in a formation of a sleeve with a uniform thickness. The mold gradually extracts the sensible and the latent heat from the sleeve, which eventually becomes solid. Often a second layer of another material is introduced during the solidification of the first layer. The proposed free-surface model is therefore coupled with the heat advection-diffusion equation with a stiff latent heat source term representing the solidification. The numerical results show a good agreement with measurements of temperatures performed in the plant. A validation of the proposed model is also provided with the help of using other numerical techniques such as the approximate Riemann solver for the two layer shallow water equations and the volume of fluid method. (C) 2017 Elsevier Inc. All rights reserved.

Keywords

numerical modeling; free-surface model; centrifugal casting; solidification; advection-diffusion equation; shallow water equations

Authors

BOHÁČEK, J.; KHARICHA, A.; LUDWIG, A.; WU, M.; KARIMI-SIBAKI, E. PAAR, A.; BRANDER, M.; ELIZONDO, L.; TRICKL, T.

Released

15. 2. 2018

Publisher

ELSEVIER SCIENCE INC

Location

NEW YORK

ISBN

0096-3003

Periodical

APPLIED MATHEMATICS AND COMPUTATION

Year of study

319

Number

State

United States of America

Pages from

301

Pages to

317

Pages count

URL

https://www.scopus.com/record/display.uri?eid=2-s2.0-85017559816&doi=10.1016%2fj.amc.2017.03.030&origin=inward&txGid=5f01d72ceef57f34bdca57e0282570c3

BibTex

@article{BUT164742,
  author="BOHÁČEK, J. and KHARICHA, A. and LUDWIG, A. and WU, M. and KARIMI-SIBAKI, E. PAAR, A. and BRANDER, M. and ELIZONDO, L. and TRICKL, T.",
  title="A (non-)hydrostatic free-surface numerical model for two-layer flows",
  journal="APPLIED MATHEMATICS AND COMPUTATION",
  year="2018",
  volume="319",
  number="1",
  pages="301--317",
  doi="10.1016/j.amc.2017.03.030",
  issn="0096-3003",
  url="https://www.scopus.com/record/display.uri?eid=2-s2.0-85017559816&doi=10.1016%2fj.amc.2017.03.030&origin=inward&txGid=5f01d72ceef57f34bdca57e0282570c3"
}