Random walk dispersion model for missile contrail particles in cross-airspace environments

Missiles provide long-range precision strike capabilities and have become a cornerstone of modern warfare. The contrail clouds formed by missile during their active flight phase present significant challenges to high-altitude environmental observation and target detection and tracking. Existing studies primarily focus on specific airspace regions, leaving critical gaps in understanding the effects of long dispersion times, wide altitude ranges, and variable atmospheric conditions on missile contrail clouds. To address these gaps, this article develops a numerical method based on the Lagrangian random walk model, which incorporates various velocity variation terms, including particle velocity caused by the difference of wind field, by the thermal motion of local gas molecules and by random collisions between contrail cloud particles to capture the influence of environmental wind fields, atmospheric conditions, and particle concentrations on the motion of contrail cloud particles. A general coordinate system aligned with the missile's flight trajectory is employed to represent particle distribution characteristics. The proposed method is in good agreement with the conducted experiments as well as with the available numerical simulations. The results demonstrate that the proposed model effectively simulates the dispersion state of contrail clouds, accurately reflecting the impact of large-scale wind field variations and altitude changes with high computational efficiency. Additionally, simulation results indicate that the increased distance between gas molecules in rarefied environments facilitates enhanced particle dispersion, while larger particles exhibit a faster dispersion rate due to their greater mass.