Gtheta computation

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.

   ∑(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)

       K:  Pressure drop coefficient (approximately 4)

      
       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] )
 

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.