A typical Computational Fluid Dynamics analysis of aerodynamic drag for a vehicle consists of three steps. First, the computational domain is discretized into a mesh that is suitable for the analysis. In this step the mesh is created and the flow and boundary conditions are defined. In the second step, the discrete problem is solved numerically, usually through the use of a solver package. Finally, the calculated results are analyzed.
In current industrial CFD analyses, commercial software packages are used in each of the above steps. From these steps, mesh generation is the most intensive and time consuming.
These three steps can be labeled as the three main elements of CFD codes: pre processor, solver and post processor.
We can describe pre processing as the input of the flow problem, the activities at pre processing stage involve the definition of the geometry of the region of interest, the grid generation and the definition of the fluid properties and boundary conditions.
The geometry of the region under study is called computational domain. The geometry can be imported from any CAD program and it is necessary to include a domain where the flow will travel.
The meshing or grid generation is the most important step in the CFD analysis, the density and quality of the mesh will determine the accuracy of the results and the CPU time. Generally the larger the number of cells the better the solution accuracy. Optimal meshes are often non uniform, the areas of interest in the domain will have a fine mesh and a large variation will be expected in further regions. There are three types of grid, the structured, unstructured and hybrid.
Regular or structured grids consists of a family of grid lines with the property that members of single family do not cross each other and cross each member of the other family only once. This is the simples grid structure
since its logically equivalent to a cartesian grid. Each point has 4 nearest neighbors in 2D and six in 3D. This neighbor connectivity simplifies programming and the matrix of the algebraic equations system has a regular structure. The disadvantage of this type of grid is that thay can only be used on simple domains. Figure 2.
Unstructured grids are used for very complex geometries, such grids could be used in any discretization scheme, but they are best adapted to the finite volume and finite element approaches. The elements or control volumes may have any shape. Grids made of trias or quads in 2D, and tetras or hexas in 3D are most often used.
This type of grid can be easily controlled and locally modified, one disadvantage is the complexity of the data sturctured compared with the structured mesh. Figure 3.
A hybrid grid features the best of both meshes, it is composed of a structured or semistructured grid for the near-wall viscous region, and an unstructured grid for the rest of the computational domain. Figure 4.
A computational grid can be defined as the discrete representation of the geometric domain on which the problem is to be solved. The generation of a computational grid for complex geometries is an issue which requires an experienced user in order to deal with the accuracy and CPU time compromise.
After creating the computational grid, boundary conditions must be defined in order to give specific characteristics to each surface, this will allow the solver to identify which face is a wall, an inlet , an outlet, etc. The fluid properties must be defined at this point, given the data of the analysis the reynolds number can be calculated, the reynolds number will determine the regime of the flow. A low reynolds number means that the viscous force is predominant leading to a laminar flow, a high reynolds number means that the inertial forces are predominant leading to a turbulent flow.
Turbulence flow is characterized by a chaotic behaviour, large eddies form leading to a random disordered flow. To simulate this type of complex flow, turbulence models were introduced. There are several turbulence models, these models have wide applicability, are accurate, simple and economical to run.
The most common turbulence models are : Spalart-Allmaras, mixing length model, K-e model, Reynold stress equation model, algebraic stress model. The difference between them is the number of partial differential equations they solve to predict the turbulence.
There is a lot of research in this field and new models are often proposed, is not clear yet which model is the best given that none is expected to behave precisely for all flows. It is common to have different results of an analysis using different models.
After seting all the flow parameters, boundary conditions and a refined mesh, the computational domain is exported to a solver. The main roll of the solver is to give a numerical solution of the behavior of the flow.
The solver perform an approximation of the unknown flow variables by means of simple functions, then discretizes by sustitution of the approximations into the governing flow equations and finally solves the algebraic equations. CFD uses steady-state formulation in which a residual error in the discretized equations is reduced iteratively to a minimum value, eventually the results are said to converge to a solution. A numerical solution is said to be stable if it does not magnify the errors that appears with the numerical solution process.
