Aerospace computational techniques

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Meshing Methods

A significant phase of the finite element method for numerical computation is mesh generation. Meshing is defined as substituting of solid geometry model with a set of distinct points, lines, panels, elements. The approach to cut whole flow domain in to small elements is called meshing technique. Particular portions of the domain require small elements in order that the computation is more precise. The meshing methods include structured, unstructured, hybrid, adaptive etc.

Structured Meshing

It is defined as in which the elements are laid in a regular grid acknowledged as block. Structured meshing requires more elements and saves constant factor in runtime. It makes use of hexahedral elements in 3D and quadrilateral elements in 2D in a computationally rectangular selection. In addition to it, it develops elliptic equations in order to optimize the outline of the mesh intended for orthogonality and uniformity. The mesh can be formed to body fitted by means of stretching and twisting of the block.

Multi block unstructured mesh generation used for solution domains with complex geometries which involves a complex solution domain partitioned into simpler sub-domains. Hereafter, mesh is produced in apiece sub-domain and matching routine which bear a resemblance to the sub-domains and correspond with the individual mesh at the boundaries of the sub-domains.

Unstructured Meshing

It is defined as arrangement of elements with no discernible pattern acknowledged as unstructured meshing. It uses random assembly of elements in order to pile up the domain and utilize triangles in 2D and tetrahedral in 3D.

Unstructured meshing offer more flexibility as compared to the structured mesh and hence is very useful in finite element and finite volume methods. It permits automatic adaptive refinement based on the pressure gradient or regions interested. However, it has several disadvantages which include limitation to largely isotropic due to the triangle and tetrahedral elements ability of twisting and stretching.

Unstructured mesh techniques depend upon the features of the Delaunay triangulation and voronoi diagram. Delaunay triangulation is defined as set of triangles of the points in plane such that no point is within the circumcircle of a triangle. The triangulation is distinctive on stipulation that no four points are on the same circle and no three points are on the same line. In addition to it, a related definition holds for higher dimensions, with tetrahedral replacing triangles in 3D.

Hybrid Meshing

Utilization of structured mesh in the local area whereas unstructured mesh in the bulk of the domain known as hybrid meshing (quasi structured). It consists of triangles and quadrilateral elements in 2D and hexahedral, tetrahedral, prismatic and pyramidal elements in 3D. Hybrid meshing has the aptitude to manipulate the shape and the division of the mesh which yields immense mesh.

  • Hexahedral elements are immense where the field flow gradients are high and a greater extent of control but consumes time to get produced
  • Tetrahedral elements are utilized to fill up the remaining volume.
  • Pyramid elements are utilized to alteration from hexahedral to tetrahedral elements.
  • Prismatic meshes are produced by defining the surface mesh and marching off the surface to generate the 3D elements. Prismatic elements defined as triangles extruded into section are utilized for
    determining nearby wall gradients, however unable to gather in the lateral directions because of underlying triangular structure.

Adaptive Meshing

In adaptive mesh, the algorithm begins with a structured base coarse grid. The individual grid cells are filtered by means of enhanced mesh is overlayed on the coarse. Subsequent to refinement, particularized mesh pieces which are on a specific stage of refinement are conceded to an integrator which develops cells within time.

Enhanced meshes and sub-mesh are recursively advanced in anticipation of maximum stage of refinement is achieved. However, the concentration of refinement at certain points in a cell is higher than needed; the high determination mesh will be replaced with a coarser grid. Adaptive meshing is categorized into three types which follow as:-

r-refinement: - Characterized as alteration of mesh determination without changing the number of nodes exhibit in a mesh. Moving the mesh points into the areas of movement increases the mesh determination which yields in greater scattering of points in areas. However, the nodes movement can be controlled by deforming the mesh.

h-refinement: - Defined as alteration of mesh determination by varying the mesh connectivity. Although, it would not result in change in number of overall mesh cells. The simplest strategy for this type of refinement subdivides cells, while more complex procedures may insert or remove nodes (or cells) to change the overall mesh topology.

p-refinement: - It attains increased mesh determination by means of increasing the order of accuracy of the polynomial in each element (or cell).

Types of Element that can be utilized in adaptive meshing pursue as: -

2-D Structural Solids: - 2-D 6-Node Triangular Solid, Axisymmetric Harmonic Solid, 2-D 4-Node Isoperimetric Solid

3-D Structural Solids:- 3-D 8-Node Isoperimetric Solid, 3-D Anisotropic Solid,
3-D 8-Node Solid with Rotational DOF

3-D Structural Shells:- Plastic Quadrilateral Shell, Elastic Quadrilateral Shell,
8-Node Isoparametric Shell

2-D Thermal Solids:- 2-D 6-Node Triangular Solid, Axisymmetric Harmonic Solid
2-D 4-Node Isoparametric Solid

3-D Thermal Shells :- Plastic Quadrilateral Shell

Overset Meshing

In overset meshing, composite geometry is partitioned in overlapping structured grids geometrically. Boundary information is replaced between the grids through interpolation of the flow variables and also holes points are not utilized. Every block has fringe points which are situated in the internal of the adjacent block and will necessitate information from the containing block. In order to associate an overset simulation requires three steps which pursue as: -

  • Grid generation: - Simple and Structured
  • Hole Cutting
  • Determination of interpolation weights

Volume Unstructured Meshing

The generation of the mesh is based on three major steps which include the following:-

  • Generation of the triangular surface mesh by the advancing layer method
  • Production of thin tetrahedral cells within the boundary layer by the advancing layer method
  • Making of inviscid tetrahedral outside the boundary layer by means of advancing-front method.

It is capable of producing anisotropic stretched meshes for the intention of enhanced efficiency of the mesh clustering. Volume meshing suitable in producing tetrahedral meshes of inviscid and viscous flows around composite geometries. In addition to it, revelation of surface and volume mesh and mesh interactive surface mesh edge transaction.

Meshing Options

The meshing options in ansys mesh module includes: -

  • Automatic (Patch Conforming/Sweeping)
  • Tetrahedrons (Patch Independent)
  • Tetrahedrons (Patch Conforming)
  • CFX-Mesh

Automated Sweeping Mesh

It is defined as sweepable bodies which are detected automatically and meshed with hex-mesh. Advantages include sizing and mapping controls and opt for faces in order to alter and hold the fort over the automated sweeping. Furthermore, sweep paths for all regions in a multi body are found automatically and mapping is done automatically. Distinct inflation is carried via associated swept bodies.

Tetrahedrons (Patch Independent)

A meshing method in which faces and their boundaries are dependent on a load, named selection and boundary condition. It is useful when a consistently mesh is required and virtual topology is utilized with it, although the boundaries of the virtual cells may be scoped on the virtual cells. Distinctive array of faces and their boundary edges includes of all entities with the named selections, boundary conditions and contacts; surface bodies with contrary thickness will be formed and confined protected by the mesher. In addition to it, the boundaries at confined topology will not traverse.

Patch independent mesh method for tetrahedron is based on the following spatial subdivision algorithm: This algorithm ensures refinement of the mesh where required, however maintains larger elements where possible allowing for faster computation.

Once the root tetrahedron which encloses the entire geometry has been initialized, the patch independent mesher subdivides the root tetrahedron until all the elements size requirements are met. The patch independent mesh method includes the pursuing setting:-

  • Element midsides Nodes
  • Defined by - Maximum element size and approximate number of elements
  • Maximum element size- The size of initial subdivision

Applications

  • Solid Bodies (patch Independent tetra, Multi zone)
  • Surface bodies (Uniform Quad/tri, Uniform Quad)

Tetrahedrons (Patch Conforming)

It is a meshing technique in which all faces and their boundaries surrounded by a small tolerance are consequence for a specified part. Mesh origin defeaturing is utilized to conquer complexity with small features and geometries. Virtual topology can be utilized to raise limitations on the patches. Patch conforming tetra mesh method is a Delaunay tetra mesher with an advancing -front intersection techniques utilized in mesh refinement. The patch conforming tetra mesh method provides support for 3D inflation, built in pyramid layer for conformal quad-tet transition and built-in growth and smoothness control based on specified growth factor. Patch conforming mesh has following advantages:-

  • Allows for conformal mesh between bodies wit tetrahedral mesh method and sweep mesh method applied
  • Provides a high quality mesh that is suitable for both CFX and FLUENT.
  • More tightly integrated onto meshing process

Applications

  • Solid Bodies (patch conforming tetra, general sweeping, thin Sweeping, Hex Dominant)
  • Surface Bodies ( Quad Dominant) (All triangles)

CFX Mesh

It produces high quality mesh for use in computation fluid dynamics simulations. The requirement for CFD analysis is for meshes that resolve boundary layer and satisfy more stringent element shape criteria than meshes in mechanical analysis. CFX-Mesh creates linear tetrahedron, hexahedron and wedge (prism) element shapes. THE CFX mesh method operates at the part level. Because of this if one body of multibody part is selected all the bodies of the multibody part are automatically selected. This creates a limitation, in that you cannot have conformal mesh between bodies meshed with the CFX-Mesh method and any other mesh method.

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