The bubbles and the flow field at a late time for two simulations of bubbles injected into a turbulent flow in a vertical channel. In the left frame, the surface tension is sufficiently high so the bubbles remain nearly spherical, but in the right frame the bubbles are much more deformable. The isocontour lines of the vertical velocity are also plotted in a plane through the center of the domain.
The path of bubbles. The wall-normal coordinate vs time for the spherical bubble case (left) and the deformable bubble case (right) after the flow has reached an approximate steady state.
The average wall shear stress (a) and the total flow rate (b) vs time for both cases, after the flow has reached an approximate steady state.
The average void fraction profile across the channel at steady state for nearly spherical bubbles and deformable bubbles. The thick solid line is the hydrostatic model presented in Ref. 6.
The average aspect ratio of spherical bubbles and deformable bubbles. The definition of aspect ratio is as in Ref. 4.
The average liquid velocity profile vs the wall-normal coordinate for the spherical bubble case (top) and the deformable bubble case (bottom). The velocity profile for flow without bubbles is also included in both frames. The average velocity of the bubbles is also shown.
(a) The rms velocity fluctuations in the streamwise direction. (b) The wall-normal direction. (c) The average Reynolds stress profile vs the wall-normal coordinate. (d) The streamwise vorticity squared profile vs the wall-normal coordinate.
The bubbles and isocontours of the vertical velocity at a late time for (left) and (right). (b) The average distance of the centroid of the bubbles from the walls vs time, for four Eortvos numbers.
Parameters list for the spherical bubble case and the deformable bubble case.
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