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Gtheta Computations using UDF

A User Defined FLUENT script (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.

   ∑(G_cell*Ө_cell)/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. 

   Ө_floc = Vol./(Vol. flow rate)
   ∑(G_cell)/N* Ө_floc          (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.

    ∑(G_cell)/N* ∑(Ө_floc)/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)

The parameters for the K-e realizable 1_5 Width one baffle geometry for one turn are shown below:

       Π-cell:  the ratio of the length of the dissipation zone divided by the baffle spacing (approximately 6) Image Removed

       K:  Pressure drop coefficient (approximately 4)

       Image Removed
       b:  baffle width (.1 m)

       V:  Velocity (.1)

       ν:  kinematic viscosity of water (approx 1e-6 in region of interest)
      

Gtheta was also plotted using the custom function in FLUENT.  (GӨ = Const. \[ε/υ\]^1/2^ \* \[Cell Volume/Vol. flow rate\] )
\\  !aGtheta plot.png! 

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.

    Image Added

The Gθ_baffle values weighted by the area or number of cells were also examined, but these formulations do not produce sensible results.

Below is the G_theta value presented for flocculation tanks of different geometries:

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