...
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.
...
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 put the validity of 2D models in doubts.
Future Simulation Experiments
Possible future simulation experiments and research topics are:
- To create refined mesh with proper boundary conditions, and run simulations on SGI server, check grid convergence;
- To investigate the fluctuating tail of residual plots;
- Design numerical experiments to observe the fluctuation of extremely small numbers;
- Use difference turbulence models and compare the shape of the tails;
- Simulation with periodic boundary conditions with various period length
- Use backstep experimental data to validate 3D models with periodic boundary conditions