The process of submicron particle movement in laminar boundary layers is present in many practical applications such as the particles depositing on the turbine blade and mist droplets depositing on the surface of aircrafts. Although great progress has been made on this issue during the last decades, many underlying mechanisms still remain unclear. Here, we developed a theoretical model to understand how submicron particles will behave when they enter a supersonic laminar boundary layer above an adiabatic plate along with the main stream. In this model, we used the Lagrangian method to track the particles and calculate their trajectories, and the Eulerian method was used to calculate the flow field. Because of the large velocity and temperature gradient near the wall and the small size of the particle in this question, four forces (e.g., drag force, Saffman lift force, thermophoretic force and Brownian force) acting on the particle are considered. The effects of entering position, Mach number, the size and density of particles are investigated. We discovered that there are three particle movement patterns when they enter the supersonic boundary layer, and that the drag force and Saffman lift force play dominating roles on which pattern will happen in this process. Moreover, the results also reveal that the particle tends to move towards the wall as the diameter and the density of the particle and the Mach number of main flow increases. Finally, we suggested a dimensionless number to describe the three patterns of particle motion. This research provides a better understanding of the particle movement process in the supersonic laminar boundary layer, which can be a useful guidance for the industrial processes involving this phenomenon.
Approximate Solutions of Three Dimensional Laminar Boundary Layers : A Boundary Layer and Its Separation Produced by a Circular Cylinder Mounted to a Flat Plate
