# H3D Tipgrid

## Introduction

Tipgrid is a 3D structured mesh generator tailored for turbomachinery CFD flow solvers. It employs a grid topology designed to minimize grid skewness, and it grids the volume of the tip clearance region of a rotor blade when present.  The code is applicable to axial, centrifugal, and mixed compressor and turbine configurations.

## Tipgrid Topology

Tipgrid uses the tipgrid topology, illustrated in Figure 1 on the hub surface of a compressor rotor grid.  The topology can be considered to consist of nine blocks in a 3×3 pattern, with the center block lying inside the blade.  All grid lines, however, are continuous across the block boundaries, so from a geometric point of view the entire grid can be treated as a single block (see Figure 2).  This configuration extends from the hub to the casing, including the tip clearance region between the blade tip and casing, if present (see Figure 3). The flow solver must effectively ignore the central block below the blade tip section (the interior of the blade) and apply appropriate boundary conditions to the blade surfaces.

Physical coordinates (x, y, z) obey the following convention: the positive z-axis points in the downstream axial direction; the x- and y-axes form a right-handed system with the z-axis. Cylindrical coordinates (r, Ɵ, z) use the same z-coordinate at the Cartesian system; radius (r) is the magnitude of (x, y); and Ɵ (measured in radians) increases in a left-hand sense about the z-axis.  The location of Ɵ = 0 is arbitrary.

The computational coordinates, or grid indices, obey the following convention: the first index (i) increases from inlet to outlet; the second index (j) increases in the circumferential direction (in the general positive Ɵ direction); the third index (k) increases in the spanwise direction.

The code generates a grid around a single blade in a blade row.  The blade is topologically centered in the grid.  The hub, casing, inlet and outlet surfaces are all surfaces of revolution generated by rotating profile curves in the (r, z) plane around the z-axis.  The periodic boundaries between adjacent blades in a blade row lie approximately midway between the blades in a blade passage.  Grid lines are not continuous across periodic boundaries.  Relaxing this constraint is the main feature of the tipgrid topology that allows it to yield high-quality grids.  However, it means that the flow solver must be able to interpolate flow quantities across the periodic boundaries.

## Inputs

The user interface for the Tipgrid code is primitive by modern standards.  It is, however, simple and robust and allows for easy confirmation that the inputs are correct before running the code.  All inputs consist of text files, and the entire code can be run from the command line or from scripts.

Geometric inputs consist of separate files containing the geometries of the blade and the hub, casing, inlet and exit boundaries.  When a tip clearance is being modeled, an additional file is used to define the blade tip geometry.

Various parameters that control the properties of the final grid are specified in a separate input file.  These parameters include the overall dimensions of the grid, the indices of particular locations in the grid (leading and trailing edges, blade tip, etc.), and parameters that control grid clustering and stretching.

## Outputs

Two output files are generated by the Tipgrid code: one containing the grid in cylindrical coordinates, and one in Cartesian coordinates.  The first (in cylindrical coordinates) is used as the input grid for the H3D flow solver.  The second (in Cartesian coordinates) is in Plot3D format and is useful for visualization.

## Development and Execution Environment

The Tipgrid code was originally developed on Silicon Graphics workstations in Fortran 77 under IRIX.  The code has since been converted to Fortran 90, mainly to take advantage of dynamic memory allocation.  This work was done under Linux.  The code, however, should compile and run under most Unix-like operating systems that support the Make utility for compilation.

A makefile exists for compiling individual source files and linking them into a single executable file.  This file would require minor modifications under environments other than Linux (mainly to specify the local Fortran compiler).

Execution is performed at the command line by running executable file produced by the makefile.  The code prompts for the name of the parameter input file, followed by the necessary geometry definition files.  When the grid generation is complete, the code prompts first for the name of an output file to contain cylindrical coordinates, and then the name of a file to contain Cartesian coordinates.

## Example Grids

The previous grids illustrated the Tipgrid topology and grids for an axial compressor (Rotor 37).  Figure 4 shows the hub and blade surface grids for the same case.

The following figures illustrate the grid produced for an axial turbine (Notre Dame Low Pressure Turbine).

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