How to Define Filters in FLOW-3D
Metallic or ceramic filters are commonly used in foundry applications to trap inclusions and control turbulence in the metal flow. To accurately predict the die filling pattern and die fill time it is important to model the effect of the filter correctly.
FLOW-3D’s "Reynolds number dependent" porous media model provides an efficient way of simulating filters.
The filter geometry can be constructed using FLOW-3D's geometry features or by importing a STL file. The constructed filter geometry should correctly represent the overall shape of the filter. This geometry is then made into a filter by specifying the component type as "porous."
The filter characteristics are then defined by specifying porous properties: porosity, drag coefficient 'a' and drag coefficient 'b'. The procedure to calculate the drag coefficients depends on the amount of information available on the filter.
A. If only porosity and particle size are known:
Specify the porosity value as a fraction (percentage porosity/100) and the drag coefficients 'a' and 'b'. The following equations show how to calculate the drag coefficients:
Where, d is the particle size and β is a roughness factor in the range of 1.8 to 4.0 (smooth to rough). The particle size is the diameter of the grain or the fiber that makes up the filter.
B. If the complete filter data is known:
If the manufacturer's data on porosity, Darcian and non-Darcian permeability coefficients is known then again, porosity input in FLOW-3D should be specified as fraction porosity (percentage porosity/100). But the drag coefficients 'a' and 'b' should be calculated as follows:
Where, Vf is porosity, k1 is Darcian permeability coefficient (m2) and k2 is non- Darcian
permeability coefficient (m). For example for a filter with porosity value of 43%, value of k1 equal
to 1.789x10-08 m2 and value of k2 equal to 1.197x10-03 m inputs in FLOW-3D will be as follows:
|Porosity (Vf)||= 0.43|
|Drag Coeff. ‘a’||= 3.18 x10+07 (1/ m2)|
|Drag Coeff. ‘b'||= 630.23 (1/m)|