The pre-processing is quite complex since it deals with mesh configurations. For a race car, which is a machine that has many complex shape devices, the mesh properties should be very well configured. This article continues the overview of pre-processing, but now approaching the detail of the race car mesh configuration.

PID splitting

The surfaces of the CAD model is split in groups due to the different boundary conditions of these ones. For instance, there are the tires and the rims and the fact that their rotations are not the boundary condition that will be applied to the wall surfaces. This is one of the reasons that CAD models should have their surfaces grouped in different parts. This is called PID splitting.

Usually it is introduced groups of forces to locally track and monitor them. For instance, the front wing, the rear wing and the underfloor are separated areas. Typically, during the development of the project, the modifications are performed in all the surfaces of the car. In some situations, as the one which is being tested the different geometries of the front wing, it is useful to have a local contribution of the modification together with its global contribution. This procedure is applied for the front wing, the rear wing and the diffuser. Then if it is being evaluated different angles for the diffuser, it is mandatory to know the local effects of the diffuser and also on the other devices. The reason is due to that there is no better solution to control the geometry modification in terms of awareness of what is happening in all parts of the car.

CAD to mesh basic rules

Although the CAD is a high fidelity model of the real car, there are some parts of the surfaces which can not be meshed properly. For this reason, there are some good practices in the meshing process for race car applications.

Mesh generation good practices

The meshing should be very well succeed in all parts of the model, for this reason it should be given special attention in the following parts.

  • Patches;
  • Degraded rounds;
  • Cusps;
  • Invalid normal;
  • Sharp angles;
  • Sharp edges and convex angles.

These are just some examples, the important point here is that each of them requires a proper simplification.

Patches

The patches are usually very small and in great amount. When the mesh is generated without careful, those patches result in very small distances between the elements that either requires a huge computation or crash. A common problem with patches is seen in regions of small curvatures (Figure 3). The good practice is to have an unique macro surface, because this reduces the amount of elements. Actually, when the surface mesh is being generated over an edge, this represents a constraint that increase the amount of elements. Usually, edges are avoided in the design phase, but in specific cases which the watertight model preserve those edges, the only solution is to delete the edges and join the surfaces.

Degraded rounds

In some parts of the surface there are regions that exhibit a very small curvature. When the mesh is generated, the probability is to obtain the element shape as the one seen at Figure 4, the NOK (not ok) one. This results in more computational effort on that region, which in the most of the cases is not important. Hence, it is useful to avoid those edges to help the solver to provide an OK mesh (Figure 4).

Cusps

In race cars there are many parts of the body work that there are transitions between two different shapes (Figure 5). Some of these generate cusps. Usually, these have sharp angles of at least 30° and leads to low quality elements. A solution for this is the same as the patches, transform the region in macro surfaces.

Invalid normal

This is a problem that occurs in regions which there is a perpendicular encounter between two shapes, the result is a sharp edge. Usually, the good practice in the mechanical design is to avoid 90° edges, because the stress concentration is very high. Hence, fillets or chamfers are applied, which is the case in Figure 6.

Sharp angles

An angle is considered sharp when it is lower than 35°. Some components exhibits sharp angles as the one seen in Figure 7. It is possible to observe that the junction between the components results in a very sharp edge. When these are generated, the distance between the elements will be very small, which tends to crash the mesh. This occurs when the angle is between 35° and 80°, thus during the mesh generation the prisms are shrinked. To avoid this, it is usual to add some surface at the edge, which results in the aspect seen in Figure 7. In this case it is defined that prisms are put inside the angle. In cases which the angle is lower than 35° a fillet or a chamfer is the best way to by-pass this situation.

Sharp edges and convex angles

This case is basically the opposite of the previous one (Figure 7). In these cases, it is said that there is a convex angle. If this one is greater than 145°, a chamfer is recommended to improve the mesh quality (Figure 8).

The symmetry plane

The simulation domain is cut in half and the symmetry plane is introduced. In terms of mesh, the surfaces of the car and the boundary layers have prisms introduced between them. Actually, the symmetry plane is not a physical plane, it is just a numerical plane. Hence, the prisms are not growing into the symmetry plane. However, since the strategy adopted is bottom to top, the prisms are extruded. If the prisms go towards the symmetry plane and the extrusion is performed, the prisms will be floating into the symmetry plane and their sides will be projected onto adjacent surfaces.

When a prism is growing, there is two matching areas, the gray and light green prisms and the symmetry plane , which is seen in green color (Figure 9). The algorithm builds prisms as seen in the left picture of Figure 9, the prisms have a triangular surface. Actually, the surface is originally a triangle, but if the prism is touching the symmetry plane, the algorithm performs a local re-mesh. In this region (right picture of Figure 9), the surface mesh is not extruded from the symmetry plane, it comes from a extruded rectangular prism. This is important, because it creates the ideal 90° angle between the surface from which the prisms grow and the symmetry plane. When this prism (gray) is going close to this surface, which does not grow a prism, the side wall is projected into this surface in order to have the original surface mesh locally erased, then the prism (gray) is attached to the retangular one, as seen in the right side of Figure 9. If this surface is moved, the lateral side of the prism is bi-quandrangulated or locally misfacing. The result is that the frontal part and the sides of the prism are saw and the triangle surface is meshed again. This is the procedure adopted on the symmetry plane. Hence, the car has many prisms, while the symmetry plane has not. Actually, the prisms are attached to the symmetry plane. Otherwise, there will be floating quadrangular not attached prisms. The boundary layer mesh is not able to solve floating quadrangular prisms, just floating triangular ones. To avoid this situation near to the symmetry plane, where there are narrow edges, it is introduced a small step (Figure 9, right side) making the prism attaching nicely to this small plane. This is a complex adjustment.

The wing mesh

Wings are devices with important details and these are important in the moment of mesh generation. Usually, leading and trailing edge concentrates all the attention, but the upper and lower portion of the wings are also important.

The trailing edge

In many wing applications, these are very thin into the CAD model. In the real model this is not true due to the industrial and design limitations. The same requirement is adopted by the CFD model. The minimum thickness of the trailing edge region ranges between 1 and 2 mm (Figure 10). Typically in the trailing edge areas, where there are strong curvatures, it is applied small resolution elements, because high resolution mesh can worse the numerical solution.

Actually, this also depends of the methodology applied for the prism layer growth. For instance, the aspect ratio method implies, that if the total height of the prism cells depends on the surface mesh resolution, an over refinement of this region can result in a very thin boundary layer, which is the opposite case of the real (physical) situation, that increases. In general, 2 elements are required to ensure the prisms layers to bypass the trailing edge preserving a good skewness (Figure 11).

The leading edge

If the trailing edge can have some errors in terms of CAD and it must be ensured a reasonable height to make it similar to real, the leading edge (Figure 12, red highlighted region) is a region of the front wing where there is a strong acceleration of the fluid. Hence, there is the stagnation point and then the fluid is accelerating over the curvature. Therefore, it is important to measure the gradients of this acceleration. In the leading edge there are high resolution elements, thus more elements.

Hence, breaking that into a flatter surface and going into a higher resolution to not raise the amount of elements. The minimum target of the number of elements into the leading edge is, for a 90° round shape, at least 4 elements (Figure 13). This is a rule which is strictly applied, because it is accepted to waste repeatable elements in order to have very nice curvature caption. If there is more constraints in terms of cells, it is important to guarantee at least 4 cells at the leading edge.

Surface gradients

Referring to the surface gradients, at the flat area of the wing profile the solution is more quiet, while at the bottom there is the fluid circulation that motivates the pressure distribution requested to create downforce. Hence, to accomplish this acceleration it is required a lower resolution relative to the upper surface to capture the surface gradients. This is an adjustment of the surface mesh according to the surface gradients expected on the solution.

Tire-ground mesh

Figure 14 illustrates the details of the tire plinth mesh. Since this is an area of high sensitivity, there are four elements inside the plinth length, which is 0.5 mm. Hence, there is an average of 0.125 mm discretization. This is a very helpful also in terms of volume mesh extrusion. As the strategy is bottom-to-top, the volume mesh is inherent to small areas, the surface resolution is 0.5 mm, it is quite sure that also the volume mesh will adapt to sizes like this one, which happens in case that accuracy is important. The reason of this careful approach is that tire deformation generates vortices that have a great influence on the aerodynamic performance of the underwing close to the wheel side.

Meshing results

Figure 15 illustrates examples of surface meshes. All the rules discussed above basically stated that as high the curvature is, as high is the resolution required, thus smaller elements. In addition, edges also require a small resolution. Hence, these are areas (Figure 15) where it is required more accuracy to solve better how the flow is having vortices. Suspensions also require a fine mesh in their arms, because these have a streamlined shape.

Volume mesh

Figure 15 illustrates what is happening with the surface mesh, this is based on the algorithm used. The algorithm of the volume mesh (Figure 16) starts with a triangular mesh, then it creates the boundary layer mesh and the hexa mesh. Meshing hexahedrons and prisms in a conformal way (read more) require the generation of the tetrahedron elements. This kind of elements are not good, because considering that the finite volume method (FVM) and the balance of fluxes for each element, if a good accuracy is obtained, this means that the element has a good quality and more faces. As much faces a single element has, more accurate the balance of fluxes will be, thus the tetrahedron elements (four faces) are not good for accuracy.

Polyhedrons, instead, are nice for accuracy. Hence, the algorithm begins with a triangular mesh, generate the boundary layer and the hexa meshes, that result in tetrahedron elements and then apply another algorithm, the Agglomeration one. The agglomeration puts tetrahedron elements and creates polyhedron ones. The results on the surface and on the volume is the one seen at Figure 17. As can be seen, it has a very high mesh quality and low number of elements, thus improving accuracy.

ANSA procedure

The algorithm procedure is pure triangles (ANSA), then it goes to the volume mesh. The car has the boundary layer mesh, which is created extruding the triangles from the surface mesh. After that, the algorithm creates the outside hexa mesh. Matching hexahedrons and prisms are complex tasks. These are performed by an intermediate step that creates tetrahedrons. Hence, there is first the triangle base prims, which is the tetrahedron after their extrusions and reach the prisms. For instance, in ANSA, the volume is generated until reach that surface. The last step is the agglomeration. In this process, the set of triangles has for each node the triangle round, which instead of creating six faces, these create a polyhedron. Hence, the interface between the prism and the hexahedron becomes a polyhedron. Previously, the interface between the prisms and hexahedrons were tetrahedrons.

References

  • This article was based on the lecture notes written by the author during the Industrial Aerodynamics course taken at Dallara Academy.