M.Sc Thesis


M.Sc StudentBaruch Gaiduk
SubjectRarefied Gas Dynamic Interactions in the Motion of a
Particle near a Wall
DepartmentDepartment of Aerospace Engineering
Supervisor Full Professors Frankel Itzchak
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


Abstract

The aim of the present study is to analytically and numerically investigate the effect of hydrodynamic interactions for a particle moving near a planar wall in a highly rarefied gas (free molecular flow). In this case, the Knudsen number (Kn) which is the ratio between the local molecular mean free path and the characteristic dimensions of the problem is very large (Kn>>1). The study focuses on the motion of spherical particle near an infinite planar wall. Unless Kn<<1 the continuum assumption and the Navier-Stokes equations based on it fail. The molecular structure of the gas needs to be considered and its motion is governed by the Boltzmann equation. The general problem is time-dependent and nonlinear even though the collision integral becomes negligible in the present limit of large Kn numbers. To calculate the effects of the adjacent wall on the forces and torques acting on the moving particle, the method of Gopinath and Koch (1997) has been applied. Assuming that typical solid velocities are much smaller than the mean thermal speed of the gas molecules, the Mach number is much smaller than one. Under this assumption, the problem is linearized and becomes quasi-steady. The problem is then reduced to the calculation of the fluxes of gas molecules incident and reflected from solid surfaces for prescribed velocities and geometrical configurations of the solids. Purely diffuse reflection is assumed and thus molecules reflected from each body have an appropriate Maxwell distribution of velocities. Once the distributions of molecular densities on the on the solid surfaces have been obtained the resultant hydrodynamic forces and torques are readily calculated by appropriate surface integrations. Gopinath and Koch (1997,1999) applied this method to the calculation of hydrodynamic interactions between parallel cylinders and spheres moving along their line of centers. The calculation of the distribution of molecular densities requires the solution of the pair of coupled integral equations. The linearity of these equations allows us to represent the general problem of the motion of a sphere moving near a plane as superposition of four basic cases: Translational motion of the sphere parallel or perpendicular to the plane and rotation of the sphere around an axis parallel or perpendicular to the plane. For each of these cases the integral equations have been solved by an iterative numerical scheme.