Axisymmetric parameterized hex mesh for corrugated pipes

Corrugated pipes are used in industry purposes to allow a certain bending, while still having structural stiffness and withstanding i.e pressure forces. The hose of a vacuum cleaner is perhaps the most widely known example.

Recently I was introduced to the problem of determining the pressure loss in such a pipe. The Moody diagram and Darcy-Weisbach equation can be employed to determine this, at least for «normal» pipes. The Moody diagram and Colebrook equation are well suited for smooth pipes – but how well do they perform for pipes with roughness in the magnitude of several centimeters?

In October [2010] I started the work on creating a parameterized mesh script for these corrugated pipes, using the internal meshing capabilities of OpenFOAM. But getting to know the characteristics of corrugations, the problem became making the mesh in a general fashion – as corrugations can be produced in several ways:

Semi-circle wise
Sinusoidal
Semi-circle extremas connected with vertical lines
Semi-circle tapered (sloped straight sections)

And after numerous pencil sketches, and a horrendous amount of hours programming and troubleshooting, I came up with a design capable of producing most of the cases above. And with a minimum of parameters:

Corrugation pitch (axial distance between «amplitudes», or period)
Corrugation depth
Corrugation slope

And that’s all. All points and distances can be determined from these three parameters, using a rather intricate and non-linear geometric formula, plotted like this:

The geometry is designed to take advantage of the wedge capabilities of OpenFOAM, that is a 5 degree axial slice, or 1:72 of original geometry. Still, it is possible to export this geometry to a Fluent mesh, and create a complete 3D version of it. Though, that would introduce 72 times more cells… for a one meter pipe with fine mesh, probably several million cells.

And the resulting meshes turns out like this:
87 degrees slope

75 degrees slope

65 degrees slope