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A semi-implicit method for the analysis of two-dimensional fluid flow with moving free surfaces

  • Thermal Engineering · Fluid Engineering · Energy and Power Engineering
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Abstract

Flow with moving free surfaces is analyzed with an the Eulerian coordinate system. This study proposes a semi-implicit filling algorithm using VOF in which the PLIC (Piecewise Linear Interface Calculation)-type interface reconstruction method and the donor-acceptor-type front advancing scheme are adopted. Also, a new scheme using extrapolation of the stream function is proposed to find the velocity of the node that newly enters the computational domain. The effect of wall boundary conditions on the flow field and temperature field is examined by numerically solving a two-dimensional casting process.

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Abbreviations

A j :

Area of thej-th face

c p :

Specific heat

C(u) :

Convection matrix

D e (k) :

Divergence of element

f :

Volume fraction of element

F :

Force matrix

h :

Heat transfer coefficient

H :

Pressure gradient matrix

h e :

Pressure gradient matrix of element

h e T :

Divergence operator of element

K :

Diffusion matrix

k :

Thermal conductivity

M :

Mass matrix

m e :

Mass matrix of element

p :

Pressure

T :

Temperature

u,u i :

Velocity vector and its component

V i :

Volume of the i-th element

μ:

Viscosity

ϱ:

Density

σ ij :

Viscous stress tensor

Φ:

Stream function

T :

Transpose

n :

Time step

(k):

Iteration number

e :

Element

i :

Cell number

inlet :

Inlet

j :

Face number

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Authors and Affiliations

  1. School of Mechanical and Aerospace Engineering, Seoul National University, San 56-1, Shinlim-dong, Kwanak-ku, 151-742, Seoul, Korea

    Jong Sun Park, Joon Sik Lee & Woo Il Lee

  2. MEMS Lab., Samsung Advanced Institute of Technology, 440-600, Suwon, Korea

    Min Soo Kim

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  1. Jong Sun Park
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  2. Min Soo Kim
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Correspondence to Woo Il Lee.

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Park, J.S., Kim, M.S., Lee, J.S. et al. A semi-implicit method for the analysis of two-dimensional fluid flow with moving free surfaces. KSME International Journal 16, 720–731 (2002). https://doi.org/10.1007/BF03184822

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  • DOI: https://doi.org/10.1007/BF03184822

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