A comparative study of two methods for estimating aluminum agglomerate sizes: Cohen's pocket model and density-based clustering

Abstract

The effectiveness of two calculation methods—Cohen's pocket model and the cluster analysis method (specifically Density-Based Spatial Clustering of Applications with Noise, DBSCAN)—was compared in predicting aluminum agglomeration on the burning surfaces of solid propellants. The comparison focused on the effects of ammonium perchlorate (AP) particle size, AP size gradation, and the relative proportions of coarse and fine AP. Experimental investigations were also conducted on four hydroxyl-terminated polyether (HTPE) propellant samples and compared with the two methods. The results show that with larger AP particle sizes and higher coarse AP content, both methods predict an increase in average aluminum volume—whether in a pocket (according to Cohen's pocket model) or in localized aluminum-rich regions (as identified by DBSCAN)—which is consistent with experimental results on agglomerate diameter variations. Additionally, DBSCAN more accurately predicts the number mean (D_1,0) and number-volume mean (D_3,0) agglomerate diameters, while the pocket model provides results that are closer to the volume-moment mean diameters (D_4,3). For monomodal AP size distributions, the average aluminum volume calculated by DBSCAN correlates with the cubic power of AP size, which aligns with the results from the pocket model. However, for bimodal distributions, DBSCAN results deviate from the pocket model due to particle gradation effects. Using the Voronoi diagram, it was found that the spatial volumes partitioned by AP particles approximate a log-normal distribution. This finding explains the log-normal-like agglomerate size distributions predicted by DBSCAN and suggests that the pocket volumes should also follow a log-normal distribution when AP particles are graded and randomly distributed.