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SPECIAL SECTION ON CFD METHODS

# Implementation of a Level Set Interface Tracking Method in the FIDAP and CFX-4 Codes

[+] Author and Article Information
Sergey V. Shepel

Thermal-Hydraulics Laboratory, Paul Scherrer Institut, CH-5232, Villigen PSI, Switzerlandsergey.shepel@psi.ch

Brian L. Smith

Thermal-Hydraulics Laboratory, Paul Scherrer Institut, CH-5232, Villigen PSI, Switzerlandbrian.smith@psi.ch

Samuel Paolucci

Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USApaolucci.1@nd.edu

J. Fluids Eng 127(4), 674-686 (Apr 21, 2005) (13 pages) doi:10.1115/1.1949636 History: Received October 14, 2004; Revised April 12, 2005; Accepted April 21, 2005

## Abstract

We present a streamline-upwind–Petrov-Galerkin (SUPG) finite element level set method that may be implemented into commercial computational fluid dynamics (CFD) software, both finite element (FE) and finite volume (FV) based, to solve problems involving incompressible, two-phase flows with moving interfaces. The method can be used on both structured and unstructured grids. Two formulations are given. The first considers the coupled motion of the two phases and is implemented within the framework of the commercial CFD code CFX-4 . The second can be applied for those gas-liquid flows for which effects of the gaseous phase on the motion of the liquid phase are negligible; consequently, the gaseous phase is removed from consideration. This level set formulation is implemented in the commercial CFD code FIDAP . The resulting level set formulations are tested and validated on sample problems involving two-phase flows with density ratios of the order of $103$ and viscosity ratios as high as $1.6×105$.

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## Figures

Figure 1

Construction of the FE mesh by overlaying the FV grid. Schematic of grids, nodes, and elements. The dashed lines show the edges of the finite elements.

Figure 2

Schematic of the computational domain of the level set fluid-void formulation. The domain Ω is divided into three regions: the fluid region Ωf, the buffer zone Ωb, and the empty region Ωe. The surface γbf separates Ωb from Ωf, and γbe separates Ωb from Ωe. The surface γbc is that part of the boundary of Ωb located on the container walls.

Figure 3

Element bands built around the zero level set (shown in bold). The shaded region is the “zero-element band.” The blank and shaded elements are those located in the fluid region Ωf. Numbered elements are those located in the buffer zone Ωb. Numbers inside elements indicate the element band number.

Figure 4

First column: steady-state solutions of the reinitialization problem defined by Eq. 8 for (a) the unit circle and (b) the unit square, on the 4×4 domain. The bold line shows the zero level set; the contours of constant ϕ are spaced Δx=0.25 apart from each other. Second column: errors resulting from the convergence study. The mesh is unstructured.

Figure 5

Schematic diagram of the broken-dam problem.

Figure 6

Fluid configurations for the broken-dam problem at different times obtained by the two level set formulations and the PCSS VOF method. The latter solution was obtained using a regular grid. The container dimensions are nondimensionalized with the value of the initial height of the water column hc. The average mesh size is h*=0.02.

Figure 7

Effect of the viscosity of the fictitious fluid inside the buffer zone on the level set fluid-void solution

Figure 8

Effect of the buffer zone thickness Nb on the level set fluid-void solution. The error Ẽ1i is calculated in terms of the solution obtained with Reb=1 and Nb=12.

Figure 9

Variation of the mass of water as a function of time in the level set solution of the broken-dam problem for two mesh resolutions

Figure 10

Comparison of the predicted water front positions with the experimental data for the broken-dam problem.

Figure 11

Collapsing cylinder of water: left column shows pictures obtained experimentally by Munz and Maschek (33); right column shows the numerical predictions obtained using the FE-FV level set fluid-fluid formulation (CFX-4 ) for the free and no-slip boundary conditions. Rows correspond to characteristic times t0,t1,t2, and t3.

Figure 12

Variation of mass of water as a function of time in the solution for the collapsing water cylinder obtained using the level set fluid-fluid method; the mesh size is 4.44 mm.

Figure 13

Bubble rise velocity as a function of time: (a) level set solution and (b) standard CFX-4 model

Figure 14

Bubble mass as a function of time in the problem of a rising bubble: (a) level set solution and (b) standard CFX-4

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