Gtheta Computations using UDF
Methodology
A User Defined FLUENT script (UDF) was created to extract the G_theta value from the flocculator. The UDF loops through all of the individual cells of the converged solution, and extracts the energy dissipation^1/2 times the cell area. The sum of this quantity for all cells divided by flow and square of viscoisty results in the G_theta value of the entire flocculator as shown in equation 1.
Gθ_baffle=1/Q*vis^(-1/2)*∑(ε^(1/2)*cell_area) Eq. 1
The above formulation has been determined (with Monroe's help) by weighting the value of Gθ by volume.
The Gθ_baffle values weighted by the area or number of cells were also examined, but these formulations do not produce sensible results.
Gθ Computation
Below is the Gθ values for flocculation tanks of different geometries:
Case Geometry (h-height,b-width,N-baffles) |
Gθ_Flocculator |
|---|---|
b=.1, h=1, N=1, Clearance height=.15 |
430 |
b=.1, h=.3, N=5, sym bc |
1330 |
b=.1, h=.2, N=5 |
1060 |
Normalizing the Gθ parameter
The Gθ value increases with increasing flocculation tank volume. Thus, when comparing different designs, each case should be normalized by the volume (or area for 2D geometries). This results in the following normalized values.
Case Geometry (h-height,b-width,N-baffles) |
Gθ_Flocculator/m^2 |
|
|---|---|---|
b=.1, h=1, N=1, Clearance height=.15 |
4,300 |
|
b=.1, h=.3, N=5, sym bc |
8,870 |
|
b=.1, h=.2, N=5 |
10,600 |
|
Comparison to Flocculation Tanks
Literature rates flocculators based on the Gθ value, as well as the G, epsilon value, and θ-value. For flocculators without recirculating solids, the recommended Gθ is 20,000-150,000 (Schulz, C. R. and D. A. Okun (1984). Surface Water Treatment for Communities in Developing Countries, John Wiley & Sons). This would correspond to 2-15 m^2 of flocculator area based on the weighted Gθ-values calculated. This seems to be the area of flocculators currently used in practice in Honduras. Thus, the calculated Gθ-values seems sensible.
Another check of the accuracy of the results can be seen by comparing the dissipation rate of the flocculation tanks to values recommended by Schulz and Okun of .4-10 mW/kg. The energy dissipation plotted in this region for the fh=3 case results in the plot shown below:
Figure 1: Energy Dissipation Rate in the range of .4-10 mW/kg for fh/w=3, Re=10,000
The regions in white are outside of this region, indicating that energy dissipation values above and below this recommended region exist in the flocculator.