Porous Resistance Specification Example

Consider a block of honeycomb material, much like a bunch of drinking straws glued together. This porous medium is situated in a section of the duct that is oriented at 45 degrees to the x-axis of the Laboratory Coordinate System as shown below.

Measurements of the honeycomb material in a wind tunnel (air is the working fluid) have shown that it results in a pressure drop of 70 Pa per meter of the material when the velocity is 1 m/s. In addition, for the range of velocities of interest, the pressure drop varies linearly with velocity.

Since the porous resistance is a linear function of flow velocity, only the viscous resistance tensor

needs to be specified. In the principal coordinates, the primary coefficient will be 70. To restrict the flow in the directions perpendicular to the primary direction, a resistance coefficient that is 2-3 orders of magnitude larger than primary coefficient should be chosen, for example 10000. Choosing a larger resistance will not affect the flow but might adversely affect the convergence characteristics. Therefore the viscous resistance tensor in principal coordinates will be chosen to be:

There are a number of ways this tensor can be specified in STAR-CCM+, including:

using the principal tensor profile method. The XX, YY and ZZ components are 70, 10000 and 10000 respectively. The XX Axis is the vector (1, 1, 0) relative to the Laboratory Coordinate System, representing a vector tilted at 45 degrees to the Laboratory x-axis. The YY Axis is then (-1, 1, 0), also relative to the Laboratory Coordinate System.

using the composite symmetric tensor method. This is simplified by creating a local Cartesian Coordinate System with (1, 1, 0) as the X Axis Direction corresponding to x' and (-1, 1, 0) as the Y Axis Direction corresponding to y'. Using this coordinate system, the tensor components are all zero except for the XX, YY and ZZ components, which are 70, 10000 and 10000 respectively.