Fractal Reconstruction of Microscopic Rough Surface for Soot Layer during Ceramic Filtration Based On Weierstrass-Mandelbrot Function

The microscopic surface of soot layer on the external surface of filtration elements is rather hard to reconstruct. In this study, an incinerator filter setup was designed to mimic the capture of soot particles in flue gas to achieve the samples to construct the rough soot-layer surface. The specific velocities around the ceramic cartridge were determined by particle image velocimetry (PIV) measurement. Resorting to a box-counting method, the fractal dimensions (FDs) were determined by Richardson Mandelbrot method with binary images of samples. Accordingly, the in situ thickness of soot layer was constructed with consideration of particle deposit and the microscopic rough surfaces were modeled by employing Weierstrass Mandelbrot (W-M) function. Additionally, a comparison between the constructed surface and real surface achieved from the image taken by atomic force microscopy (AFM) was performed. The results suggest that all roughness deviations of constructed surface from real surface of soot layer not exceed 5%.