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Liquid Particles Tracing in Three-dimensional Buoyancy-driven Flows

D. E. Melnikov1, V. M. Shevtsova2

1 ULB, Brussels, Belgium

Fluid Dynamics & Materials Processing 2005, 1(2), 189-200.


Buoyancy-driven convective flows are numerically analyzed in a cubic enclosure, containing a liquid subjected to a temperature difference between opposite lateral walls; all other walls are thermally insulated. The stationary gravity vector is perpendicular to the applied temperature gradient. The steady flow patterns are investigated within the framework of a liquid particles tracing technique. Three tracing techniques are compared: the first, based on a trilinear interpolation of the liquid velocity defined on the computational grid and an eighth order in time Runge-Kutta method; the second and the third, using a resampling the velocity field on a new approximately twice finer grid by cubic spline interpolation and then a combination of trilinear interpolation of velocity on the new grid, integrating in time with (2-nd method) a single forward time marching method; (3-rd method) a fourth order Runge-Kutta algorithm. Comparison of the results shows that for obtaining a precise tracing on a long time scale it is more important to have a good spatial velocity accuracy than precise integration in time. Unlike one vortex 2D pattern where the particles follow thin and closed circle trajectories staying in vertical cross-sections, it is shown that,the 3D flow consists of two sets of spiral-type motions identical in both halves of the cell with respect to the mid-plane. In the 3D flow even in the central vertical cross-section the particles follow spiral non-closed trajectories drifting outward the cube's walls. It demonstrates that two-dimensional approach does not provide a clear picture of 3D convection.


Cite This Article

APA Style
Melnikov, D.E., Shevtsova, V.M. (2005). Liquid particles tracing in three-dimensional buoyancy-driven flows. Fluid Dynamics & Materials Processing, 1(2), 189-200.
Vancouver Style
Melnikov DE, Shevtsova VM. Liquid particles tracing in three-dimensional buoyancy-driven flows. Fluid Dyn Mater Proc. 2005;1(2):189-200
IEEE Style
D.E. Melnikov and V.M. Shevtsova, "Liquid Particles Tracing in Three-dimensional Buoyancy-driven Flows," Fluid Dyn. Mater. Proc., vol. 1, no. 2, pp. 189-200. 2005.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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