Rocket Nozzle

(part of the Gridgen presentation from the United Technologies Corp. Grid Generation Workshop, 18-19 October 1993, Hartford, CT)

Gridgen is a software system for generation of 3D, multiple block, structured grids. It runs on an engineering workstation and uses an intuitive graphical interface to guide engineers through the grid generation process.

In this case study, Gridgen is used to generate a 3D, multiple block structured grid for the internal flow path of a rocket motor. Useful features of Gridgen that are shown in this example are:

• copying, rotating, and translating grid elements to speed the gridding of geometrically similar parts,
• elliptic smoothing of grids with control of interior grid point spacing and orthogonality of grid lines.

The domain to be gridded is a 180 degree sector of the axisymmetric interior of the rocket motor flow path up to the nozzle exit. The minimum flow path diameter is approximately 1/27th of the length of the flow path. A multiple block, structured grid is to be used with the number of grid points in the various sections prescribed by flow solver requirements. Very tight clustering of grid points toward the nozzle walls is desired for use in a viscous computational fluid dynamics (CFD) analysis.

The starting point for the grid is the set of curves describing the nozzle contour. These curves, shown in magenta in the adjacent figure, are imported into Gridgen using the PATRAN v2.5 neutral file format.

Connectors, Gridgen's curve grid elements, are created from the nozzle contour curves. The prescribed number of grid points are distributed along each curve using Gridgen's hyperbolic tangent distribution function. This function allows the user to prescribe a grid point clustering value anywhere along the connector's length and smoothly distribute points on the curves between prescribed values. Once the connectors are completed they are copied and rotated 180 degrees about the rocket's axis of symmetry. Circular arc connectors are added to produce the rocket's surface grids shown in the adjacent figure.

Construction of the 0 degree and 180 degree symmetry plane grids follows in a similar manner. First, connectors not on the database (such as those on block interfaces) are constructed interactively using Gridgen's curve (Catmull-Rom spline) segment. Second, grid points are assigned and distributed along each connector. Each of the seven blocks in the topology used for this grid is shown in a different color in the adjacent figure.

All surface grids are created automatically by Gridgen using transfinite interpolation (TFI). You can often improve the grid point distribution further by applying one of the elliptic partial differential equation (PDE) based smoothers available in Gridgen. While running the elliptic solver to get a smoother grid distribution, you can also choose to maintain a specified clustering at boundaries and require that grid lines are orthogonal to the boundaries. For this problem, very tight spacing is needed at the walls to resolve the high Reynolds number (thin) boundary layer. Thomas-Middlecoff background control functions are applied to ensure a smooth and well clustered grid, and Steger-Sorenson foreground control functions are applied to make a grid that holds the prescribed clustering to the walls while also making transverse grid lines orthogonal to the wall. The high quality results of this elliptic PDE surface grid refinement are shown in the figure below.

While this is a fairly simple geometry, the requirements to cluster very tightly to the rocket nozzle walls and maintain orthogonality of grid lines can cause some grid generators difficulties. As this example shows, Gridgen is able to meet these requirements with ease.