Level-Set Computations of Free Surface Rotational Flows

[+] Author and Article Information
Giuseppina Colicchio1

School of Civil Engineering and the Environment, University of Southampton, Southampton, UKg.colicchio@insean.it

Maurizio Landrini

 INSEAN, The Italian Ship Model Basin

John R. Chaplin

School of Civil Engineering and the Environment, University of Southampton, Southampton, UKj.r.chaplin@soton.ac.uk


Present address: INSEAN, The Italian Ship Model Basin.

J. Fluids Eng 127(6), 1111-1121 (Jul 08, 2005) (11 pages) doi:10.1115/1.2062707 History: Received November 03, 2004; Revised July 08, 2005

A numerical method is developed for modeling the violent motion and fragmentation of an interface between two fluids. The flow field is described through the solution of the Navier-Stokes equations for both fluids (in this case water and air), and the interface is captured by a Level-Set function. Particular attention is given to modeling the interface, where most of the numerical approximations are made. Novel features are that the reintialization procedure has been redefined in cells crossed by the interface; the density has been smoothed across the interface using an exponential function to obtain an equally stiff variation of the density and of its inverse; and we have used an essentially non-oscillatory scheme with a limiter whose coefficients depend on the distance function at the interface. The results of the refined scheme have been compared with those of the basic scheme and with other numerical solvers, with favorable results. Besides the case of the vertical surface-piercing plate (for which new laboratory measurements were carried out) the numerical method is applied to problems involving a dam-break and wall-impact, the interaction of a vortex with a free surface, and the deformation of a cylindrical bubble. Promising agreement with other sources of data is found in every case.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Flow around a surface piercing plate accelerated horizontally from rest. The interface between air and water is strongly deformed by the movement of the plate with velocity U(t). At the lower tip of the plate a region of high vorticity becomes detached (shown as a shadowed area), and interacts with the surface.

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Figure 2

The narrow region surrounding the interface in which a distance function is defined

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Figure 3

Contour levels of the distance function at a time when the surface approaches the bottom edge of the plate

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Figure 4

Smoothing of the density and of its inverse across the interface

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Figure 8

Comparison of the interface location with (solid line) and without using (dashed line) the variable-coefficient limiter function. The SPH solution (dots) is used as a reference. τ=5.64.

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Figure 9

Effects of different reinitialization procedures. Solid line: present reinitialization, dashed line from Russo and Smereka (21). The two methods differ in the small cavity created at the right wall. The SPH has been used as a reference solution.

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Figure 10

Parasitic currents for different numerical solvers. Above, the classic solver (Brackbill (23)); below, the present solver. Δx=R∕33, t=Δt=R∕(2σκ∕ρ), δst=δρ∕2=0.4Δx.

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Figure 11

2D air bubble in water. The top figures are extracted from the experiments presented by Walter and Davidson (25). The lower figures are the numerical results. t=0.0125s, 0.0625s, 0.1125s.

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Figure 12

See Fig. 1; t=0.1625s, 0.2125s, 0.2625s

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Figure 13

Right vortex of a vortex pair rising towards a free surface. On the left the results from Ohring and Lugt (26) and on the right the present results. The continuous contours represent the clockwise rotating vorticity and the dashed contours the counterclockwise rotation.

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Figure 14

Break up of the water above the vortex and formation of a region of high counterclockwise vorticity

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Figure 15

Experimental arrangements

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Figure 16

Velocity of the plate in the experiments

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Figure 17

Numerical and experimental results for the flat plate moving with the velocity of Fig. 1. The shaded background represents the experiments, the water is darker grey and the free surface is almost black. The numerical results are superimposition on the experimental data. The vorticity field is highlighted in the numerical part with some contour lines; t=0.28s, t=0.34s, t=0.45s, t=0.52s.

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Figure 18

Numerical and experimental results after the breaking; t=0.64s, t=0.74s, t=0.80s, t=0.83s

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Figure 5

Definition sketch for the dam-break problem. The shaded area represents the initial configuration of the water.

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Figure 6

Free surface evolution after the dam-break. The dashed line represents the BEM, the solid line the Level-Set, and the dotted double line the SPH.

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Figure 7

Effects of different numerical schemes for smoothing at the interface in the dam break problem. Dashed line: exponential smoothing, solid line: trigonometric smoothing.

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Figure 19

Relative changes in total mass for a discretization N×N

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Figure 20

Relative changes in total energy for a discretization N×N

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Figure 21

Verification of the level set solutions after one revolution of the Zalesak circle




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