# The Deal with Electronics Cooling CFD - Meshing

### John Parry

Posted Jun 16, 2009

When we started in electronics cooling, electronics products were built out of objects that were almost entirely Cartesian, so a Cartesian mesh made perfect sense – and still does in many cases.

One of the inherent issues in CFD is mesh associated error. One source of error arises from the mesh being too coarse to capture the gradients of temperature, pressure, velocity etc. When I started in CFD I was using a Perkin-Elmer 3220 – mini-computer that had 2Mb of RAM (0.002Gb Wow!) shared with a number of other users. Grid coarseness could be a major source of error. The problem hasn’t entirely gone away, but it’s now much less of an issue. Today a 2M+ cell case run on a desktop PC is commonplace.

A second source of error arises from the approximations used to ‘discretize’ the equations onto the mesh. An example of discretization is treating the gradient of temperature between two cells as a linear piecewise function, better known as a straight line calculated as the temperature difference divided by the distance between them. Simple enough.

The finite volume method on which CFD is based works by conserving physical quantities such as mass and heat over each grid cell. To do that it has to work out the amounts of these conserved quantities that flow through the faces of the cells. So far, so good.

If the temperature gradient is at right angles to the cell face (termed orthogonal in CFD parlance) then the heat flux through the cell face only depends on this one gradient (as shown on the left below). Otherwise the flux will depend on temperature gradients in the other directions (as shown on the right).

Cell Shape and Its Effect on “Grid Quality”

This non-orthogonality is where things start to get messy since it’s harder to work out these secondary contributions to the flux through the face, and the more distorted the mesh the worse this gets.

Cartesian meshes are free from this second form of error and have the additional benefit of being almost instantaneous to create. Their use in CFD is experiencing something of a renaissance through the efforts of NASA AMES, Cambridge University and others. If you’re interested in meshing, take a look at this free web presentation or download this white paper

Over the years we’ve moved away from a pure Cartesian mesh for electronics cooling, providing the ability to embed a local fine mesh around an object. This makes it easier to resolve the gradients in the flow that are key to predicting heat transfer, plus the mesh region moves with the object if it is repositioned.

Cartesian meshes can also be extended to deal with non-Cartesian geometry by using an Octree approach, in which cells are successively subdivided to refine the mesh nearer to the surface. Again it can be highly automated to produce a mesh that is free from mesh quality issues, and can also be made ‘adaptable’ or self-refining to capture gradients in the flow. This really comes into its own for shock capture in high-speed flows.

There are other things to say about electronics cooling CFD – turbulence for example, but I’m going to leave it at that for the moment and talk about when liquid cooling might become mainstream for high-end consumer electronics.