Performance parameters analysis in 2D - sensitivity analysis: convergence level and boundary condition at the water-air interface
Objective
The preliminary simulation experiments suggested that the results are sensitive to the residual levels the solutions converged to and the boundary conditions defined at the water-air interface. A more detailed sensitivity analysis is discussed in this section to exam the accuracy and validity of the results obtained in the simulation experiments section, with respect to the above two conditions.
Methods and Procedures
An h/b ratio=5 was chosen for both the cases with symmetry(frictionless) and wall(no slip)boundary condition defined at the water-air interface. The solution data were saved for both simulations cases at the residual levels of e-4, e-5 and e-6 were saved and the respondant performance parameters were calculated. (Refer to Method and Procedures sections of either simulation experiments section or preliminary simulation experiments section for the creation of geometries and meshes, and the report summaries about all FLUENT settings).
The choices of h/b=5 and residual levels are decided based on the following:
- The optimal h/b were shown to be 3~5.
- Symmetry boundary condition cases had difficulty in converging to e-5, and e-4 in some cases.
- The results change little from e-5 to e-6.
Summary of completed tests
The series of geometries and meshes were created using the journal file, by varying the flocculator height. The boundary conditions and all the other FLUENT settings can be found in the report summaries: symmetry top boundary condition and wall top boundary condition
Results and Discussions
Click here for the results of the preliminary simulations, completely summarized in an Excel workbook. Only parts of the graphical results are given below.
Shown below are contours of energy dissipation rate for h/b of 5 and 10, with symmetry boundary condition at the water air interface and one case with no slip(i.e. wall) boundary conditions.
As shown in the Excel workbook of graphical and quantitative results, the energy dissipation pattern is very sensitive to convergence level. One order of magnitude difference in residual results in completely different shapes of energy dissipation region at the top of flocculator. It is also noted that using symmetric boundary condition at the water-air interface at top of the flocculator makes it more difficult to converge to lower residual levels. The original purpose of using symmetric boundary condition is to mimic the frictionless condition at the water-air interface, but the energy dissipation contour of h/b=20 may also suggest whether using wall or symmetry boundary condition at water-air interface may not make a significant difference, and both cases could produce similar results at a better convergence level, which is consistent with our physical intuitions.
Conclusions
- Energy dissipation rate contour and quantitative analysis show dependence of performance parameters as a function of h/b ratio, which suggest it worth further investigation.
- Results are very sensitive to convergence levels.
- Symmetric boundary condition makes it difficult to converge.
- Symmetric boundary condition and wall boundary condition may have similar results at good convergence levels (residual below e-6). We can use wall boundary condition to replace symmetry boundary condition to ensure accuracy of the results.
SHOULD DIRECTLY ITERATE TO E-6