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- 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.
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Summary of completed tests
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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 simulations2 series of cases, completely summarized in an the last two worksheet of the 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.
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Convergenc level
As shown in the workbook, the contour of energy dissipation rate changed little judging from eyeball examination between different convergence levels, but the calculated performance parameters still showed some variability as the convergence level changes. However, they stablized from e-5 to e-6.
Boundary conditions
A larger varibility was shown in the parameters when compared between symmetry and wall boundary conditions, while little differences were observed in the energy dissipation contours with bare eyes. However, the variability are still within an acceptable ranging in terms of a varieity of other uncertainties in the practice of design and operation.
Convergence rate
The iteration steps needed for each cases at the three different convergence levels:
The above table suggests the case with wall boundary condition converges a lot faster
More comments
Also note that in all these cases the solutions were obtained by directly iterating towards e-6 with second order scheme, instead of the normal practice: iterating with first order to obtain an good initial guess and then with second order for more accurate values.
Conclusions
- e-6 is a residual level where the solutions are stablized.
- Using wall boundary condition to replace the symmetry boundary condition is justifiable.
- Wall boundary condition makes iteration converge a lot faster.
- A residual of e-6 could be obtained by directly iterate toward e-6 with second order scheme.