Twenty-Fourth Symposium on Naval Hydrodynamics (2003) / Chapter Skim
Currently Skimming:
An Evaluation of Verification Procedure for CFD Applications
An Evaluation of Verification Procedure for CFD Applications
Pages 568-587
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 568... ...
A procedure to estimate the uncertainty when the number of grids available is greater than the minimum required for Richardson extrapolation is also tested. The results indicate that the main sources of the scatter observed in the data for ship flows are the insufficient geometrical similarity of the grids and the use of numerical interpolation to obtain flow quantities at locations that do not coincide with grid nodes.
|
From page 569... ...
In general, the flow quantities of interest in a complex turbulent flow are not directly available from the flow field. Numerical techniques for integration and interpolation are usually required to compute resistance coefficients or flow quantities at physical locations which do not coincide with grid nodes.
|
From page 570... ...
= 0 when ng is equal to the number of grids required by the number of terms retained in the Taylor series expansion. Therefore, the least squares root approach demands at least one more grid than the minimum required to obtain the unknowns 00, pj and ocj.
|
From page 571... ...
can be restricted to a 3 x 3 system, while for the one term expansion a further reduction to 2 x 2 is appropriate. The application of the least squares root approach to the power series expansion with fixed exponents leads to a system of two, three or four linear equations, depending on the number of terms retained in the series.
|
From page 572... ...
For the one term expansion with fixed exponent, the In the present study, we have in all the six examples a number of grids which is significantly larger than the minimum number required to apply any of the procedures described above. Therefore, the procedures may be applied to different sets of grids leading to different values for the error estimation.
|
From page 573... ...
In each case, we generated 24 grids with an equal number of nodes in each direction with a coarsest grid of 11 x 11 grid nodes and a finest grid of 241 x 241 grid nodes. These 24 grids have 81 common grid nodes in the interior of the domain.
|
From page 574... ...
in the 2-D incompressible potential flow. Least squares root approach with one term and an unknown exponent.
|
From page 575... ...
· In the equally-spaced Cartesian grids, the error estimation with the one term expansion and a fixed exponent, tl, does not perform well for the three largest Reynolds numbers. In these three cases, the observed order of accuracy is greater or equal than 3 and the assumed exponent is 2.
|
From page 576... ...
The three power series expansions with fixed exponents do not include the first order term. However, in this test case, it is possible to obtain an observed order of accuracy below the theoretical value of 2.
|
From page 577... ...
for Rn = 100 and the extrapolated cell size zero values with the band of uncertainty as a function of the typical cell size of the coarsest grid used in the least squares root approach for the p, tl andtll approaches. 3.4 Flow around the Wigley Hull We proceed with a numerical verification for a 3-D flow, viz.
|
From page 578... ...
For the turbulent flow, the finest grid has the same number of grid nodes in the streamwise and girthwise directions, but it has 121 grid nodes in the normal direction, which implies 33 in the coarsest grid to preserve geometrical similarity. The four sets of grids were generated with the same technique.
|
From page 579... ...
The three resistance coefficients, CF, CP and Car, are plotted as a function of the typical cell size for sets A and B in figure 7. The variation of the integral parameters with the typical cell size does not exhibit scatter.
|
From page 580... ...
Rn = 7.4 x 106. Set A Set B CF CP ct CF | CP | Ct Pmin 0.15 0.11 0.15 0.16 Pmax 0.79 0.49 1.38 2.41 _ Table 3: Minimum and maximum orders of accuracy estimated from different grid triplets for the resistance coefficients of the turbulent flow around the Wigley hull.
|
From page 581... ...
Least squares root approach. Turbulent flow around the Wigley hull.
|
From page 582... ...
For both Reynolds numbers, the flow quantities that coincide with grid nodes exhibit scatter in its variation with the typical cell size. This result confirms that one of the sources of scatter is the imperfect geometrical similarity of the grids, which is almost unavoidable in turbulent flows around complex geometries.
|
From page 583... ...
The comparison between the four different schemes tested is equivalent to the one obtained in the flow around the Wigley hull. Table 5 presents the estimated orders of accuracy at model scale Reynolds number obtained from different grid triplets at these five locations using the data of the Thirds interpolation scheme.
|
From page 584... ...
In these cases, which include scatter, the solution with the minimum number of grids required by the power series expansion adopted was disregarded. The estimate of Up for the fixed exponents expansion with more than one term leads to much larger values than the p method.
|
From page 585... ...
Understandably, the least squares root approach can cope better with the scatter. The use of power series expansions with fixed exponents and terms of order larger than two leads to a large variation in the error estimation from different sets of grids.
|
From page 586... ...
- PARNASSOS: An Efficient Method for Ship Stern Flow Calculation - Third Osaka Colloquium on Advanced CFD Applications to Ship Flow and Hull Form Design, Osaka, Japan, 1998.
|
From page 587... ...
We have done the similar work using CFD tools together with gradient-based optimization techniques to minimize wave drag. We have found that the hull form optimized for a single design speed may yield less desirable hull form for other speeds.
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.