# LEADING EDGE Résumé de rapport

Project ID:
G3RD-CT-2002-00818

Financé au titre de:
FP5-GROWTH

Pays:
Sweden

## Enhanced volume grid methods (D2-2)

Grid generation is a significant part of a CFD application, and much of the time is spent on grid generation. Moreover, the quality and the density of the grid are important parameters regarding the reliability of the final CFD results.

- A system for grid generation can be evaluated from its ability to:

- Model the shape of a complex geometry

- Make grids elements of good quality

- Ease of grid modification and grid refinement

- Make grids that perform well in the CFD solver

A grid can roughly be divided into two types, structured and unstructured. In a structured grid, every point has the same number of neighbouring points while in an unstructured grid the number of neighbours will vary.

Finite element methods generally use unstructured grids. These methods take no particular advantage in using structured grids. An unstructured grid can model very complex geometrical shapes and it is easy to use local grid refinement to achieve a denser grid. The storage of the grid, however, is not very effective compared to a structured grid.

A structured grid is able to take advantage of factored and directional solvers. They are normally used in computations utilizing finite differences. In general structured grids are less computation intensive than the unstructured ones. It is not necessary to store the topology of the grid points since this is obvious from the structure. On the other hand, complex geometries cannot always be represented using one mapping from a rectangular computational domain. The resulting grid could be very skewed.

When the geometry gets too complex for a single structured grid, a multiblock approach may be used. The physical region is broken up into pieces or blocks that have a simple mapping from a rectangular grid. Several regular blocks are fitted together with some degree of continuity. Often adjacent blocks are required to have identical grid nodes at the common boundary, and the grid spacing should vary gradually over a block boundary. Orthogonality of the grid towards the boundary can also be desired. Block structured grids provide additional flexibility regarding representation of a complex geometry while maintaining simple storage of grid points for most points. The block creation is often a manual process while the grid generation once the blocks are defined, is easier to automate.

Common for all types of grids is that high density of the grid points gives more accuracy, but the computations using this grid will take longer. Moreover, large variations in the grid density can lead to inaccurate results or instability. Non- orthogonality or skew elements in the physical grid increase the truncation error. Especially, at boundaries, skewed elements should be avoided.

Propellers have a complex geometrical shape. In leading edge, we are considering propellers of three different types, a conventional propeller, a highly skewed propeller, and an end plate propeller. All propellers are four bladed. Already the conventional propeller has a complex shape and the two others even more so. There is also a strong twisting of the blade central plane.

In Leading Edge, a number of partners are making grids for one or more of the benchmark propellers.

A general conclusion from all grid generations in the project is that a multi grid approach seems to meet the requirements of representing a complex propeller geometry and at the same time maintain a good grid quality.

- A system for grid generation can be evaluated from its ability to:

- Model the shape of a complex geometry

- Make grids elements of good quality

- Ease of grid modification and grid refinement

- Make grids that perform well in the CFD solver

A grid can roughly be divided into two types, structured and unstructured. In a structured grid, every point has the same number of neighbouring points while in an unstructured grid the number of neighbours will vary.

Finite element methods generally use unstructured grids. These methods take no particular advantage in using structured grids. An unstructured grid can model very complex geometrical shapes and it is easy to use local grid refinement to achieve a denser grid. The storage of the grid, however, is not very effective compared to a structured grid.

A structured grid is able to take advantage of factored and directional solvers. They are normally used in computations utilizing finite differences. In general structured grids are less computation intensive than the unstructured ones. It is not necessary to store the topology of the grid points since this is obvious from the structure. On the other hand, complex geometries cannot always be represented using one mapping from a rectangular computational domain. The resulting grid could be very skewed.

When the geometry gets too complex for a single structured grid, a multiblock approach may be used. The physical region is broken up into pieces or blocks that have a simple mapping from a rectangular grid. Several regular blocks are fitted together with some degree of continuity. Often adjacent blocks are required to have identical grid nodes at the common boundary, and the grid spacing should vary gradually over a block boundary. Orthogonality of the grid towards the boundary can also be desired. Block structured grids provide additional flexibility regarding representation of a complex geometry while maintaining simple storage of grid points for most points. The block creation is often a manual process while the grid generation once the blocks are defined, is easier to automate.

Common for all types of grids is that high density of the grid points gives more accuracy, but the computations using this grid will take longer. Moreover, large variations in the grid density can lead to inaccurate results or instability. Non- orthogonality or skew elements in the physical grid increase the truncation error. Especially, at boundaries, skewed elements should be avoided.

Propellers have a complex geometrical shape. In leading edge, we are considering propellers of three different types, a conventional propeller, a highly skewed propeller, and an end plate propeller. All propellers are four bladed. Already the conventional propeller has a complex shape and the two others even more so. There is also a strong twisting of the blade central plane.

In Leading Edge, a number of partners are making grids for one or more of the benchmark propellers.

A general conclusion from all grid generations in the project is that a multi grid approach seems to meet the requirements of representing a complex propeller geometry and at the same time maintain a good grid quality.