A fractal method to calculate the permeability for compressible gas flow through a porous restrictor in aerostatic bearings

In this study, a fractal method was applied to calculate the permeability for compressible gas flow through a porous restrictor in aerostatic bearings. A mathematical permeability model without any empirical parameters was established according to the fractal theory, gas conservation equations and Darcy's Law. The box-counting method was applied to determine the pore area fractal dimension and tortuosity fractal dimension. The effects of the scanning magnification and image size on the calculation results of the fractal dimension were also investigated. The porosity characteristics of the scanning images have obvious self-similarity, and the diameters of the maximum pore and minimum pore satisfy the fundamental condition of fractal analysis. Magnification ranges of 50-100× and 1-2k× were appropriate for calculating the permeability of ceramic and graphite porous restrictors, respectively. Image pixels of 512×512 were sufficient to ensure the accuracy of permeability calculation. In addition, an experimental platform was constructed to measure the permeability of ceramic and graphite porous restrictors. The differences between the calculation results and the experimental data for both ceramic and graphite porous restrictors were less than 10%, which demonstrated that the permeability for compressible gas flow through a porous restrictor in aerostatic bearings can be accurately predicted by the fractal calculation method.