Direct numerical simulations of multifluid flows in a vertical channel undergoing topology changes

Multifluid flows in a vertical channel are examined by direct numerical simulations, for situations where the topology of the interface separating the different fluids changes. Several bubbles are initially placed in a turbulent channel flow at a sufficiently high void fraction so that the bubbles collide and the liquid film between them becomes very thin. This film is ruptured at a predetermined thickness and the bubbles are allowed to coalesce. For the cases with high surface tension the bubbles continue to coalesce, eventually forming one large bubble. At low surface tension, on the other hand, the large bubbles break up again, sometimes undergoing repeated coalescence and breakup. The evolution of various integral quantities, such as the average flow rate, wall shear, and interface area, are monitored and compared for different governing parameters. Averages of the flow field and the phase distribution over planes parallel to the walls are also examined, and the microstructure, at statistically steady state, is examined using low-order probability functions.

Figure 1

The effect of the resolution on the coalescence of several bubbles into a large one. The initial bubble distribution is shown in panel (a), and the results as computed at time 40 on $128\times 64\times 64$, $192\times 96\times 96$, and $256\times 128\times 128$ grids are shown in panels (b)–(d), respectively.

Figure 2

The effect of the resolution on the average wall shear (top) and the surface area projected onto a plane perpendicular to the flow direction (bottom).

Figure 3

The effect of the critical coalescence distance on the coalescence of several bubbles. The initial bubble distribution is shown in panel (a), and the results at time 40 for the critical distance of 0.006, 0.003, and 0.0015 are shown in panels (b)–(d), respectively.

Figure 4

The effect of the critical coalescence distance on the average wall shear (top) and the surface area projected onto a plane perpendicular to the flow direction (bottom). Results for five different coalescence criteria are shown.

Figure 5

The fluid interface at five times for four cases with different surface tension. The rows represent different cases, and columns show different times of 2.0, 20.0, 40.0, 70.0, and 100.0.

Figure 6

The bubbles and the vortical structures at a late time for all four cases. The isosurfaces of vortices represent ${\lambda }_2=-5.0$. (a) case 1; (b) case 2; (c) case 3; (d) case 4.

Figure 7

The void fraction (left) and the average liquid velocity (right) versus the wall-normal coordinate for all four cases. (a) case 1; (b) case 2; (c) case 3; (d) case 4.

Figure 8

Various averaged quantities for the different cases versus time. (a) The volumetric flow of the heavy fluid; (b) the volumetric flow of the light fluid; (c) the average wall shear stress; (d) the total interface area; (e) normalized projections of the surface area in the $y\text{−}z$ plane; (f) normalized projections of the surface area in the $x\text{−}z$ plane.

Figure 9

The Sauter mean diameter (top) and the equivalent number of bubbles (bottom) versus time for all four cases.

Figure 10

The various averaged quantities versus the wall-normal coordinate, for all four cases after the flow has reached an approximate steady state. (a) The average velocity of the heavy fluid; (b) the void fraction of the light fluid; (c) the Reynolds stresses; (d) the area concentration.

Figure 11

Correlation functions for case 4 in three planes parallel to the walls after the flow has reached an approximately steady state. (a) Streamwise two-point correlation function; (b) spanwise two-point correlation function; (c) streamwise linear path correlation function; (d) spanwise linear path correlation function.

Figure 12

Integral scales for the distribution of the light fluid versus the wall-normal coordinate for cases 3 and 4. ${\ell }_1^S$ in the streamwise direction on the left and ${\ell }_2^S$ in the spanwise direction on the right.

Figure 13

Two-point correlation functions for the velocity fluctuations for case 4. (a) Correlation of streamwise velocities in streamwise direction; (b) correlation of streamwise velocities in spanwise direction; (c) correlation of spanwise velocities in streamwise direction; (d) correlation of spanwise velocities in spanwise direction.

Figure 14

Integral scale for the streamwise velocity fluctuations. Streamwise direction on the left and spanwise direction on the right.