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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)
a. Case 1
b. Case 2a
c. Case 2b
d. Case 3
Figure 1 Plots of residuals as a function of iteration steps 
a. Case 2a
b. Case 2b
Figure 2 Contours of energy dissipation rate showing the effects of turbulence intensity and hydraulic diameters, drawn on the same scale
Figure 3 The plan where the contours were drawn, in grey
Observations:
- Case 1 converged to 10^-3 within 300 iteration steps;
- Case 2a converged to 10^-3 within 300 iteration steps, stopped converging after 500 steps and started fluctuating after 1000 steps;
- Case 2a converged to 10^-3 within 200 iteration steps, stopped converging after 1000 steps and started fluctuating after 1000 steps;
- 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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The failure of convergence was caused by ill-conditioning of the problem. In CFD simulations, numerical values are solved for from large systems of linear equations with the basic fluid variables at the mesh nodes as unknowns. In Case 1, 2a and 2b, the mesh density along the xy plane and the z direction differed by a factor of 2~5. This difference could make some numbers in the intermediate steps of iteration smaller/larger, and could be propagated through the process of matrix operations to several orders of magnitude in the 3D system of ~10^5 cells. The extremely small number thus appeared could be close to precision machine precision, and couldn't reduce to any smaller number through iteration, which led to the stagnation of residual plots observed in Figure 1. As was show in Case 3 Figure 1c, after the mesh in xy plane was coarsened to the same order as the mesh in z direction, the residual converged to 10^-9 with 1st order solver and then to 10^-6 with second order solver after enough number of steps.The fluctuation in the tails of the residual plots could either be caused by fluctuation of extremely small numbers, or the fluctuation term defined in the turbulence model. Further experiments should be designed to verify the above hypothesis.
The results were not sensitive to different inlet turbulence intensity and hydraulic radius. And this minor difference were overwhelmed around the 180 degree turning.
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Comparison of 3D simulation results with 2D
The results from Case 4 are shown in the following Figures.
a. Contour of energy dissipation rate of the 2D model
b. Contour of energy dissipation rate of the 3D model with periodic boundary condion
Figure 4 Comparison of energy dissipation maps of 2D and 3D models,drawn on the same scale
a. Contour of energy dissipation rate along the plane indicated in Figure 3
b. Contour of energy dissipation rate along the plan indicated in Figure 7
Figure 5 Contours of energy dissipation rate of the 3D model with periodic boundary conditions, drawn on its max/min scale
a. Velocity profile along the plane and line indicated in Figure 7, drawn on the max/min scale of the z velocity in the indicated line and plane
b. Velocity profile along the plane and line indicated in Figure 7, drawn on the max/min scale of the x,y,z velocity in the whole domain.
Figure 6 z velocity profile
Figure 7 The plane and line referred to in Figure 5 and Figure 6, in red
Observations:
- 3D and 2D models resulted in different predictions of the shape and size of energy dissipation region after the baffle turning; (Figure 4)
- 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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