Batch Sedimentation: A Two-phase Flow Validation Example
Batch sedimentation consisting of solid particles settling out in a column of liquid is an example of a two-phase flow that can be well simulated using the drift-flux model in FLOW-3D. In the example shown here the column is 0.5m high and is filled with water. At the beginning of the flow a packed bed of solid glass spheres of diameter 0.008m (8mm) extends from a height of 0.32m above the bottom of the column to 0.42m. The initial volume fraction of the packed spheres is 0.6, their density is 2.6kg/m3.
The experiment motivating this application was performed by M.J. Lopez and G.B. Wallis, Thayer School of Eng., Dartmouth College, Hanover, N.Y., 1998. There authors reported the heights of the top and bottom boundaries of the solid particles as a function of time (see blue solid lines in plot). To simulate this experiment the one-fluid, variable density model in FLOW-3D was used with a drag coefficient dfcd=0.5 corresponding to spheres and a particle radius dfrad=0.004m. The column was subdivided into 50 grid cells of 0.01m size. Computational results (red lines with dot in the plot) are seen to compare favorably with the experimental data (blue lines).
In both the experiment and computation there is some leeway in identifying the top and bottom phase boundaries. For the computation we used 5% solid fraction for the bottom surface for the first 0.6s. After that time, as particles accumulated at the bottom of the column, we used the point of 50% of the close packing limit. For the top surface we used the point of the maximum density for the first 1.0s. After that time, when the spheres begin to pack up at the bottom, the top interface was more diffuse and was defined as the point of the highest spheres in the column. This choice was made because the reported experimental data near the end of the test indicates the top interface of the spheres does not agree with the top interface of the compacted spheres at the bottom of the cylinder. Since the top of the packed spheres is nearly at the initial thickness of the spheres, the experimental top interface must be the height of the highest few remaining spheres visible above the packed pile at the bottom. A review of the experimental data confirms this change in recording method. Even with this choice there is some oscillation in the computed data for the top surface during the first 1.0s. This variation arises primarily because of the change in defining exactly what observational choice was made in the experiments.
In the figure above, two-dimensional plots of the density distribution are shown at equally spaced intervals from t=0 to t=2s in the following figure.The maximum density depicted is the initial density of the region with the packed spherical particles 1960kg/m3.