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The conservation of Momentum equation can be simplified to Reynolds Averaged Navier Stokes Equation (for x,y directions) in Fig. 3 by estimating velocity and pressure in terms of mean value (u) and fluctuation (u') and averaging all terms as shown below:
With the conservation of mass equation, and conservation of momentum equations in each the x and y direction, there are four three governing equations. However with the introduction of the velocity fluctuation variable (u'), there are six five variables (u,v,w,u',v',w'p). Thus, the problem becomes unresolvable unless additional equations are formulated to relate the variables. This is the Turbulence Modeling Resolution Problem.
The k-eps models overcome this problem by
We have turbulence flow in our flocculation tank. Since we have unresolvable term in turbulence flow, different turbulence models or "estimation" were created to resolve turbulence flow with different characteristic. To decide on the turbulence model to use, a flow over backstep was compared with the literature experimental data. Figure 1 shows the flow of Re = 48000 over the channel. In the middle of the channel, the flow separate due to the small step size of height h. The flow reattaches at about 7 times the step height further downstream. This flow properties is similar to the 180 degree bend in the flocculation tank where we have flow separation and reattachment downstream (Figure 2).
Figure 1: Flow over backstep in a open channel (Re = 48000, Reattachment length = 7h)
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