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This section will start off with some general considerations for grid construction followed by design criteria that have specifically been derived for the current grids. The basic principles behind grid generation are more restrictive than would be expected considering the unlimited possibilities to vary aspects of a numerical mesh. From a topological point of view it can be concluded that grids constructed according to similar design choices resemble each other on a fundamental level, even though they might look quite differently. A good example of this is the modeling of the contact patch for a tyre in the symmetry plane with a structured hexahedral grid; in essence only either a ‘wedge’ with highly skewed cells near the contact line, or a (vertical) ‘plint’ - a curtain between the wheel and ground - that avoids the actual occurrence of the sharp angled wedge can be used (see figure 2.13).

The fundamental choices, which shape a grid, have to be made carefully, because it is very difficult or even impossible to alter the consequences of each choice at a later stage. This decision process can be considered to follow a cascade, where each option restricts the possibilities at the next level. In descending order these choices concern:

• The type of grid: structured (hexahedral cells in 3D), unstructured (tetrahedral cells in 3D) or hybrid (a combination of these and / or prisms in 3D).

• The conformity of the grid: using non-conformal zones or only one-to-one interfaces.

• The grid block topology: including non-regular nodes, which have less or more con- nectors than required for a regular hexahedral mesh, grid wrapping around bound- aries and grid line ending on boundaries and at the domain extremities.

• The connector dimensions: the number of cells per connector; for a fully structured grid the total number of cells in the grid are determined at this level.

• The cell distribution: allowing for local refinements and to limit skewness, grid line discontinuities and / or abrupt cell volume changes.

Aspects that make a good grid include regular cells, little skewness of the cells, aspect ratio near to unity, grid line continuity, grid line alignment with the flow, local refinement wherever required and gradual cell volume changes. Satisfying these conditions will result in a mesh that resolves the gradients of the flow quantities in the best way and these requirements have to be kept in mind therefore, while making the previous choices. Any

Research description

grid irregularities can dampen the flow physics and must thus be used in areas away from the critical regions.

A grid design strategy has been derived based on the previously mentioned considera- tions. It has been decided to use high quality structured hexahedral grids, as it is deemed essential in studying aerodynamic interaction effects that flow quantities, such as vortic- ity, are conserved as much as possible and not dampened by grid features. If required, non-conformal zones will be used instead of unstructured tetrahedral ‘glue’ zones, because the cell quality of the latter is much harder to control with the grid generation program that has been used. The use of irregular nodes is unavoidable because of the complex geometrical shapes of the models. Furthermore irregular nodes will be used to limit the influence of high density boundary layer blocks on the far field number of cells and to simplify the block topology towards the outer domain extents. Boundary layer wrapping around the geometry and grid line ending on the geometry and on the ground will also be used for these reasons. The irregular nodes will be located outside the boundary layer blocks, whenever possible.

All boundary layers on the models and on the ground will be created with an initial cell spacing that results in y+_-values16 _{of the order 1. This ensures that the boundary}

layers are fully resolved towards the walls, instead of using the ‘law of the wall’ near the surface [97] to approximate the boundary layer development. The minimum skewness angle will not exceed 50◦ _{and the block topology as well as the cell distribution will be}

used to achieve this. The total number of cells for an isolated wheel or wing grid will be kept to around 4 million cells and 5 million for the combined configuration to ensure workable computational times and case sizes that allow postprocessing with the available programs. Finally, for efficiency it has been decided to create one separate mesh module for the wheel and one for the wing, which form simple blocks that can easily be combined and repositioned relative to each other. The wing ride height can be altered by moving the wing mesh module in the vertical direction, whereas the overlap and gap are changed by moving the wheel mesh module in respectively the spanwise and streamwise direction. The complete mesh can then be constructed by filling the rest of the domain with cells. Next these two mesh modules will be discussed in more detail.

16_{The quantityy}+ _{is a geometry and flow field dependent parameter that is used as coordinate perpen-}

Research description