2.3. Image processing method

All the image-based 2D measurements have been performed along thex -z plane shown in Figure 1(a). Note, unless specially mentioned, all imaging data have been acquired during the steady-state of the fluidization at least 5 min after the start of supplying the gas flow. The lower frame rate data (100 fps) have been used for extracting the expanded bed height temporal evolution matching the acquisition frequency of pressure signals. The detailed image processing algorithms have been reported in Gao et al .7 Briefly, the processing steps include, (1) identifying the region of interest and global thresholding using Otsu mehod28, (2) filtering out sticky particles clusters on the wall due to electrostatic forces using morphological and size filters, and (3) estimating the bed height as the maximum height that particle pixel fraction at which height reduces to 5%. The times series are used later for the calculation of the mean and standard deviation of bed height, as well as the bed height spectrum. At least 100 seconds of bed height data has been acquired for statistically robust results. Figure 2 provides a sample convergence test of velocity statistics for the bed height data on mean bed height and standard deviation of bed height as a function of sample time length, denoted as <H b>t and \(\sigma_{H_{b,t}}\). As it shows, both the mean and the standard deviation value fluctuate intensely for ~10 second and approaches to a constant value as the sample time length increases.
The higher frame rate particle image series at 800 fps have been recorded to acquire the particle velocity and wood particle orientation statistics. The processing steps involve three phases: (a) segmentation of particle types and background, (b) generate particle images containing only one component, (c) perform PIV or PIV on the corresponding image series. During phase (a), owing to the complexity of the backlit images due to illumination and binary particle spatial distribution, segmentation based on global or adaptive local thresholding methods has been proved inadequate for accurately identifying different particle types. Consequently, a machine learning-based pixel-wise classification has been applied, following Arganda-Carreras et al.29 The resulting probability maps of classified pixels are then segmented by Otsu’s method. Figure 3 provides a sample image series showing the results of the steps during wood particle extraction. As shown in Figure 3(b), the segmentation results based on the machine learning approach successfully classify all pixels into three categories, namely wood particles (red), LDPE particles (green), and background (purple). Afterward, the wood particle masks are generated (Figure 3c,d), and the geometric parameters including, particle center, width/length, aspect ratio, and orientation are measured (Figure 3e). Due to the inherent limitation in 2D imaging, the 3D orientation of the particle relative to the bed central axis is not readily measured. To eliminate the limitation, only particles aligning almost parallel to the imaging plane (x-z plane, see Figure 1) are sampled as statistics. This is implemented by filtering out all particles having lengths less than 90% of the length. The detected wood particles videos are provided as supplemental information. Based on the particle location, wood particles are tracked undergoes particle tracking velocimetry (PTV) to provide Lagrangian particle tracks of the wood pellets, using an algorithm developed previously by Ouellette et al.30. Only tracks with lengths larger than 5 frames have been used. Next, the wood pellets are masked out in the original image. The Eulerian velocity fields of the LDPE particles were then computed using a particle image velocimetry (PIV) open software PIVlab31, with a final interrogation windows size of 64 × 64 pixels with 50% overlap. Figure 4 shows the sample images illustrating the PIV analysis. Figure 4a shows a raw image with LDPE particles with the inserts showing the particle image of the 64 × 64 pixels interrogation window. The LDPE particles mask (Figure 4b) generated using the abovementioned machine-learning algorithm was used for determining the LDPE particle pixel percentage within the interrogation window. Only interrogation windows with LDPE particle pixel percentages larger than 10% are used for providing velocity values of the LDPE particles as shown in Figure 4c.