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- Case 1: 1st order solver with convergence criteria of 10^-3 ;
- Case 2: 1st order solver with convergence criteria of 10^-6, and to investigate the effect of inlet turbulence intensity and hydraulic radius:
- turbulence intensity: 10%, hydraulic radius: 0.004;
- turbulence intensity: 1%, hydraulic radius: 0.04;
- Case 3: Coarsened mesh in x, y and z directions, 1st order solver with convergence criteria of of 10^-9 and 2nd order solver with convergence criteria of of (solution obtained from the 1st order solver was used as an initial guess for the 2nd order solver).
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Results are shown in Figure 1 and Figure 2 below. Figure 3 indicates the plane where the contour in Figure 2 were drawn, in grey.
(Click on the image for larger view)
Observations:
- Case Case 1 converged to 10^-3 within 300 iteration steps;
- Case Case 2a converged to 10^-3 within 300 iteration steps, stopped converging after 500 steps and started fluctuating after 1000 steps;
- Case Case 2a converged to 10^-3 within 200 iteration steps, stopped converging after 1000 steps and started fluctuating after 1000 steps;
- Case Case 3 converged to 10^-9 with 1st order solver and then to 10^-6 with second order solver within altogether 8000 iteration steps.
- There was no observable significance difference in the results between different turbulence intensity and hydraulic diameters at the inlet, except for less turbulent flow had lower minimum energy dissipation rate at the entrance region.
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Comparison of 3D simulation results with 2D
Observations:
- 3D 3D and 2D models resulted in different predictions of the shape and size of energy dissipation region after the baffle turning; (Figure 4)
- 3D 3D model predicted a higher maximum energy dissipation rate and a smaller energy dissipation zone; (Figure 4)
- Energy dissipation rate was uniform along the z direction, as expected;(Figure 5)
- There were still non-zero components of velocity in z direction, though insignificant, and not uniform along the z direction.
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Furthermore, the importance of z components could put the validity of 2D model as an approximation in question: in Case 4, even small components in z direction could make significant difference in results from 2D model, let alone in the real flow.
However, the above hypothesis must be further investigated, ruling out all other possible causes of differences. Particularly, the effect of the length of the period must be investigated by vary the width of the flocculator. Ideally, periodic repetition with infinitely small period length is equivalent to "uniform".
Conclusions
To To build a well-conditioned model that converges to accurate numerical solution, the mesh density in all 3 dimensions must be in the same order of magnitude, and refined enough to resolve the region where fluid flows vary violently; "uniform" in z direction is not equivalent to no components in z direction, thus 3D model with periodic boundary condition may not be equivalent to 2D model, which also put more doubts in the validity of 2D models.