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.
Results and Discussions
Click here for the results of the 2 series of cases, completely summarized in the last two worksheet of the Excel workbook.
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.