Direct Numerical Simulation of Bubbly Flows and Application to Cavitation Mitigation

[+] Author and Article Information
Tianshi Lu

Computational Science Center, Brookhaven National Laboratory, Upton, NY 11973tlu@bnl.gov

Roman Samulyak

Computational Science Center, Brookhaven National Laboratory, Upton, NY 11973

James Glimm

Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600

J. Fluids Eng 129(5), 595-604 (Oct 25, 2006) (10 pages) doi:10.1115/1.2720477 History: Received September 28, 2005; Revised October 25, 2006

The direct numerical simulation (DNS) method has been used to the study of the linear and shock wave propagation in bubbly fluids and the estimation of the efficiency of the cavitation mitigation in the container of the Spallation Neutron Source liquid mercury target. The DNS method for bubbly flows is based on the front tracking technique developed for free surface flows. Our front tracking hydrodynamic simulation code FronTier is capable of tracking and resolving topological changes of a large number of interfaces in two- and three-dimensional spaces. Both the bubbles and the fluid are compressible. In the application to the cavitation mitigation by bubble injection in the SNS, the collapse pressure of cavitation bubbles was calculated by solving the Keller equation with the liquid pressure obtained from the DNS of the bubbly flows. Simulations of the propagation of linear and shock waves in bubbly fluids have been performed, and a good agreement with theoretical predictions and experiments has been achieved. The validated DNS method for bubbly flows has been applied to the cavitation mitigation estimation in the SNS. The pressure wave propagation in the pure and the bubbly mercury has been simulated, and the collapse pressure of cavitation bubbles has been calculated. The efficiency of the cavitation mitigation by bubble injection has been estimated. The DNS method for bubbly flows has been validated through comparison of simulations with theory and experiments. The use of layers of nondissolvable gas bubbles as a pressure mitigation technique to reduce the cavitation erosion has been confirmed.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Schematic of the numerical experiments on the propagation of linear and shock waves in bubbly fluids

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Figure 2

Comparison of the dispersion relation between the simulation and the theory. R=0.06mm, β=0.02%. (a) The phase velocity; (b) the attenuation coefficient. In both figures, the crosses are the simulation data and the solid line is the theoretical prediction from Eq. 6 with δ=0.7. The horizontal line in (a) is the sound speed in pure water.

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Figure 3

The pressure profile in bubbly water 23μs after the incidence of the sound wave with a wavelength of 1cm in pure water. The default resolution used in the simulations was 100grids∕mm, under which the bubble radius R=0.06mm corresponds to 6 grids. The solid line is the default resolution of 100grids∕mm, the dashed-dotted line is 50grids∕mm, the dashed line is 200grids∕mm.

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Figure 4

The shock profiles in glycerol filled with SF6 bubbles. The parameters in the simulations were from the experiments (2). Pa=1.11bar, Pb=1.80bar, ρf=1.22g∕cm3, Ra=1.15mm, γ=1.09, and β=0.25%. The top figure is from the simulation, the bottom one is from the experiment. The curves in the experimental figure is the original fitting with artificial turbulent viscosity (2).

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Figure 5

The pressure distribution right after a pulse of proton beams in the mercury target of the Spallation Neutron Source (courtesy of SNS experimental facilities, Oak Ridge National Lab)

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Figure 6

The pressure profile at the center of the entrance window. (a) The pure mercury. (b) The mercury injected with noncondensable gas bubbles of radius 1.0mm and volume fraction 2.5%.

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Figure 7

Bubble size evolution with different ϕ0. R0=1.0μm, pg0=0.01bar, P=100bar, T=20μs.

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Figure 8

The first collapse pressure Pc versus ϕ0 under the sinusoidal pressure waves with different amplitude P and period T. The solid line and the dashed line correspond to the pure mercury, the dotted line and the dashed-dotted line correspond to the mercury filled with air bubbles of radii 1.0mm and volume fraction of 2.5%.




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