Meshing Hood for Structural Analysis

JORGE LOZANO

Advanced CFD Meshing using ANSA

Challenge - 6

Meshing Hood for Structural Analysis

Objective

In this challenge a structural mesh is performed (mid surface mesh), by cleaning up an auto motive’s hood assembly, consequently meshing the complete geometry with the target size (5mm) and quality criteria respectively.

Fig. 1 Mesh quality criteria.

Theory

FEM analysis

A simulation of the car bonnet behavior in a pedestrian impact test can be performed by FEM analysis. Once the upper and the lower surfaces are reconstructed and the solid model is built, the first step is the creation of a mesh of the model. Because experimentally the pedestrian impact tests are realized by impacting a head form, this must also be simulated by a FEM model. A very important aspect of this kind of problems is the contact evolution.

Fig. 2 An example of Car bonnet [2]

As seen in the next following images Fig.3 (a and b), shows a structural FEM analysis by having the comparison between the two displacements curves, and the maximum value being a larger displacement magnitude than the first one.

Fig. 3 Structural FEA analysis.

The meshing of a geometry designates the cells or elements on which the flow is solved being a discrete representation of the geometry of the problem r project to analyze and represents a group of cells separated into boundaries zones where boundary conditions are applied into surfaces and volumes.

Importance of a good discretization

The relatively good quality mesh provides and controls in the simulation:

• Grid density
• Adjacent cell length/ volume ratios
• Skewness
• Tetrahedral vs. hexahedron
• Boundary layer mesh
• Mesh refinement through adaptation

Effect of the mesh

• Rate of convergence throughout the simulation
• Solution accuracy
• Time spent in the simulation

Effect of cell Topology in truncation error

In general, structured mesh are more aligned with flow gradient, therefore, producing less truncation errors, as depicted in Fig. 4 In contrast, tetra cells, have angle with the flow direction, it is suffice to say that the argument is not as simple as case in 2D here, like so many things in CFD where no clear cut definitions are involved.

Fig.4 Effect of truncation on HEX and TET cells.

While some application like Turbomachinery (with clear flow direction) prefer hex meshes, others depend on Tet meshes. Basically, it comes down to whom you are talking and case in hand. While unstructured meshes offer better flexibility for today’s application, then lack strict control of structure and overheads of data base. Also, the availability of resources should be factor.

Mesh quality

Mesh Quality concerns the characteristics of a mesh that permit a numerical PDE simulation to be efficiently performed, with fidelity to the underlying physics, and with the accuracy required for the problem.

Geometric quality mesh properties

• Aspect ratio

The Aspect Ratio for a simplified geometry is shown in Fig. 5 and Fig. 6 and defined for tetrahedral cells as the ratio between the maximum edge length l and the minimum cell height h as:

Fig.5 Similarity for hex and polyhedral cells.

Fig. 6 Predicted mesh quality – Aspect ratio

• Orthogonality

The concept of mesh orthogonality relates to how close the angles between adjacent element faces or adjacent element edges are to some optimal angle (for example, 90º for quadrilateral faced elements and 60º for triangular faces elements). The most relevant measure of mesh orthogonality, as defined by the CFX-Solver is illustrated in Fig. 7 it involves the angle between the vector that joins two mesh (or control volume) nodes (s) and the normal vector for each integration point surface (n) associated with that edge. Significant orthogonality and non-orthogonality are illustrated at ip1 and ip2, respectively.

Fig. 7 Concept of orthogonality in cells

• Skewness

Skew of triangular elements is calculated by finding the minimum angle between the vector from each node to the opposing mid-side, and the vector between the two adjacent mid-sides at each node of the element as shown in Fig. 8 (a). The minimum angle found is subtracted from ninety degrees and reported as the element ‘s skew. Skew in quads is calculated by finding the minimum angle between two lines joining opposite mid-sides of the element. Ninety degrees minus the minimum angle found is reported as skew of the element. Maximum of 60-70 skewed elements are accepted in most of the solver beyond this limit solver can complain about the skewness of the grid.

• Warpage

This is the amount by which an element (or in the case of solid elements, an element face) deviates from being planar. Since three points define a plane, this check only applies to quads. The quad is divided into two triangles along its diagonal, and the angle between the triangles normal is measured as shown in Fig.8 (b). The maximum angle found between the planes is the warpage of the element. Warpage in three-dimensional elements is performed in the same fashion on all faces of the element. Warpage of up to five degrees is generally acceptable.

Fig.8 Skewness and warping.

• Jacobian

This measures the deviation of an element from its ideal or \"perfect\" shape, such as a triangle ‘s deviation from equilateral. The Jacobian value ranges from -1.0 to 1.0, where 1.0 represents a perfectly shaped element. As the element becomes more distorted, the Jacobian value approaches zero. A Jacobian value of less than zero represents a concave element, which most analysis codes do not allow. So, it is a good practice to keep the Jacobian of the grid greater than zero.

• Tetrahedral Volume

Since the tetrahedral is the most elementary of volumes, we start with that. Calculates the volumes of a tetrahedron and a parallelepiped which encompasses it with 6 volumes, given four vertices in right hand side order (see Fig. 9):

Fig. 9 Tetrahedral Volume, and its equations.

Choice of Grid

The choice of whether to use a structured or an unstructured mesh is problem specific which is discussed in detail before. Some advantages of structured meshes that hold generally over most applications are simplicity, availability of code, and suitability for multigrid and finite difference methods. On the other hand, unstructured meshes conform to the domain more easily and allow element sizes to vary more dramatically. Structured meshes are currently more popular, but unstructured are catching up. Here some guidelines are listed based on three parameters for choosing between structured and unstructured grid:

1. Complex geometry: Unstructured grid generation is usually much faster than structured one. However, if the geometry is only slightly modified from a previously existing geometry with a structured grid, then structured grid generation can occur very rapidly. For a problem structured grid can take say a man weeks to one-man month. On the other hand, unstructured grid will take a man hour to a few days.
2. Accuracy: For simpler problem such as airfoil (single element) or an isolated wing, structured grids are generally more accurate per unknown than unstructured. However, for more complex flows, the adaptively facilitated by an unstructured grid may allow more accurate solutions.
3. Convergence: Structured grid calculations usually take less time than an unstructured grid calculation because, to date, the existing algorithms are more efficient.

Checking Quality

To achieve accurate and reliable results, it is important to fulfill the following requirements in terms of quality:

• Make sure that a particle coming from the inlet area and following a path to the front stagnation point of the car would have to pass through minimum 100 cells. If this region is under resolved, the pressure coefficient will go far beyond 1 and spoil the overall solution.
• Check that the largest cells within the flow domain are smaller than those attached to the bounding box (for pure tetrahedral meshes)
• Check that Quality of cells is below 0.9 for the whole domain. It is recommended to have a quality of below 0.85 for prism elements on the car surface. Use T-Grid’s Mesh Repair functionalities to fix local quality problems.

Next we can see some of the used and important tools to use while meshing a shell or surface, although there are more, depending on the application and type of mesh.

Deducing Results

CFD solver developers believe mesh quality affects convergence much more than accuracy. Therefore, the solution error due to poor or incomplete convergence cannot be ignored. One researcher was able to show a complete lack of correlation between mesh quality and solution accuracy. It would be valuable to reproduce this result for other solvers and flow conditions. Use as many grid points as possible (Dannenhoffer, McDaniel). In many cases, resolution trumps quality. However, the practical matter of minimizing compute time by using the minimum number of points (what Thornburg called an optimum mesh) means that quality still will be important. A priori metrics are valuable to users as an effective confidence check prior to running the solver. It is important that these metrics account for cell geometry but also the solver’s numerical algorithm. The implication is that metrics are solver dependent. A further implication is that Dannehoffer’s grid validity checks be implemented. There are numerous quality metrics that can be computed, but they are often computed inconsistently from program to program. Development of a common vocabulary for metrics would aid portability. Interpreting metrics can be difficult because their actual numerical values are non-intuitive and stymie development of domain expertise. A metric vocabulary should account for desired range of result numerical values and the meaning of “bad” and “good.

Procedure

To begin with the meshing procedure first is necessary to open the .stp file which contains the CAD geometry, with all the geometry errors, and unchecked coons or surfaces, we proceed to refine the mesh length in the edges and return to the TOPO window which defines as seen in Fig.10 the types of conns and crossed surfaces.

Fig.10 Topo module CAD geometry Hood representation.

The next step is to delete all unchecked errors bye using the check manager- geometry check all needle faces, coons, and other errors may appear.

As seen in the previous images there are two main parts which have a thickness and are mainly symmetrical except for three surfaces one of them very noticeable at the front.

By using the offset tool and by selecting only one of the parts a surface will be created with the same dimensions in between the thickness of it, .0375 from the selected surface. The same will be done for the other part, with the same distance due to having the same thickness material, at the end both the original parts will be deleted, having on the last two surfaces.

Geometry errors in the check manager -geometry tab will appear and must be fixed, and have both surfaces connected.

A new tool: RM dbl, is used which we can obtain a geometry symmetry between a part and by default symmetry plane. By having 0.05 as nodes tolerance and 90-100% similarity factor, we see in the geometry the real symmetry parts, which we can delete one face and leave the other one to clean the geometry and obtain a better-quality geometry and very similar mesh parameters.

Once we have deleted one of the symmetry sides, we continue to select in the Mesh window, Mesh generation- Best and perform a 5mm length mesh and the next command Release in the element tab will be very important because it will separate the CAD geometry from the generated mesh, which will be mirrored (only the symmetrical parts), and will have the same mesh quality.

Fig.11 (a)Mesh quality errors showing elements size and warping, (b) Mesh window used tools (Release, Best, Move).

By seeing Fig.11 a and b we see some errors obtained in the first half meshed and some tools that were used to recreate or modify a better mesh quality, besides using the FIX option used in the check manager tab which is helpful but it might disrupt the geometry taking care more in the mesh elements besides the position as seen in Fig. 12.

Fig. 12 Check manager – mesh errors.

In Fig. 13 the left image shows the 322 errors obtained by the mesh quality parameters that were considered to be off limit in the mesh performed, by using the tools mentioned and by recognizing each of the quality errors let’s say warping or skewness we must performed the necessary actions to obtain the results within the parameters required for each one of them, having at the right a final good mesh, with in the mesh quality parameters.

Fig. 13 Mesh quality errors before and after fixing them.

When re-running again the check manager mesh quality we obtain a mesh quality sharp edges error obtained in the connection of both parts meshed, as in Fig. 14.

Fig. 14 Mesh error when re-run surface mesh checks

By moving each element of the error check separating them further we must obtain a better-quality mesh, which the angle in between the connecting element was being very close and by doing this it increases the angle and modifies the error.

In Fig. 15 both sides of the assembly mesh are finished showing both PIDs given and having only mesh surfaces releasing the original geometry and deleting it, also by using the compress tool we clean the complete ANSA file to keep only the important data and save it.

Fig. 15 Proper quality mesh check for the assembly showing both PIDs given.

In Fig. 16 and 17 all checked properly marks are obtain, not showing any inconsistency within any of the meshed parts, having a total of 68196 surface elements ready to perform an FEA analysis.

Fig. 16 Proper quality mesh check for the top part.

Fig. 17 Proper quality mesh check for the bottom part.

Fig. 18 Shows a good presented Hood assembly mesh ready to analyze and be tested for different tests, vibration, stress analysis, fatigue, crash, depending in the company necessities.

Fig. 18 Completed surface mesh, and PID, ready for an FEA analysis.

References:

1. “Mesh Generation in CFD”, by: Ideen Sarehaghighji, Ph.D., CFD Open Series Patch 1.86.5, ANNAPOLIS, MD.
2. Application of Reverse Engineering Technique in Target Setting Process for Improving the Vehicle Safety Performance. By: Massimo Martorelli, et al., Research Gate.