Gtheta Computations using UDF
UDF was created to extract the post processing result from individual cell of the model.
There are four methods used in the calculation of the Gtheta values.
The first method is to extract the individual G and theta values from the cell and sum up all the cells to obtain the total Gtheta. The total Gtheta is then divided by the total cells to get the average Gtheta.
∑(Gcell*Өcell)/N (1)
The second method was to extract individual G value and take the average of the G value. The theta is calculated by volume divided by inlet flow rate.
Өfloc = Vol./(Vol. flow rate)
∑(Gcell)/N* Өfloc (2)
The third method is multiple the sum of the G-value and the sum of the theta value and divide by the number of cells.
∑(Gcell)/N* ∑(Өfloc)/N (3)
The fourth method is to determine Π-value of the energy dissapation region and pressure drop of the flow:
sqrt(Π-cell*K*b*V/(2ν)) (4)
Π-cell: the ratio of the length of the dissipation zone divided by the baffle spacing
K: Pressure drop coefficient
b: baffle width
V: Velocity
ν: kinematic viscosity
Method |
Gtheta Value for k-e realizable 1_5 W one baffle |
|---|---|
Ave of Cell's Product (1) |
.6698 |
Ave G* Floc residence time (2) |
45 |
Ave G*Ave N (3) |
.617 |
Gtheta was also plotted using the custom function in FLUENT.
GӨ = Const. [ε/υ]1/2 * [Cell Volume/Vol. flow rate] (4)
With Const.=1, the Gtheta values range from 0 to 430 with the highest values at the boundary and in the separation regime. The plot ranges from 0 to .1 for contrast.
Conclusion
The Gtheta that compares best to mechanically mixed floculators is the Gtheta calculated from method 2, where the G value is averaged, and this averaged value is multiplied by the residence time of a particle. As suggested in discussions with Monroe, this simplistic definition fails to incorporate the weighted flow average.
The values for the other methods represent this weighted flow average, however they are much smaller. This reflects how most of the cells are in extremely low flow stagnant conditions. This is not physically the case and represents how the converged solution represents the time-averaged value. The fluctuations which would decrease resonance time and increase shear in all regions are not present in the flow in FLUENT.