Effects of slip on flow through a micro-pore and flow in a Laminar boundary layer

Abstract

This thesis comprises two problems which aim to investigate the effects of slip under two different flow conditions. The first problem is to determine the end loss for flow through a slippery circular pore in a barrier of finite thickness. To this end, an analytical model based on the fluid cylinder approximation and eigenfunction expansions is developed for the case of low Reynolds number. The hydraulic resistance comprising the end resistance and Poiseuille resistance is determined as a function of the pore thickness, slip length of the pore wall, and proximity of pores. Results are generated to reveal how slip may change the effect of the pore thickness on the end resistance. Computational Fluid Dynamics (CFD) method is also used to simulate the flow under the conditions of higher Reynolds number, a broader range of wall slip length, and more complicated pore geometry. Two-dimensional Navier slip condition on a curved surface is derived and implemented in the CFD package as User Defined Function (UDF) for calculating the flow resistance of a rounded-corner pore. Empirical formulas based on curve fitting are developed which may facilitate quick calculation of the end resistance and total resistance as a function of the controlling parameters. The second problem is to look into the hydrodynamic characteristics of incompressible viscous flow in a laminar boundary layer with slip condition. A new boundary layer equation with slip boundary condition is derived, by which it can be shown that some published results in the literature are incorrect. A non-similarity model which takes into account the variation of stream function with respect to slip length parameter is built correspondingly. An explicit marching code is used to achieve the numerical solution. The data and figures for the development of the boundary layer as a function of slip parameter are presented in this thesis to supersede the erroneous ones in the existing literature. A similarity model, which ignores the dependence of stream function on the length parameter, is also used to evaluate the hydrodynamic characteristics of the boundary layer over a flat slippery plate. The accuracy of this similarity model is found to be low, thereby verifying the validity of the non-similarity model. Also, the momentum integral method is employed to deduce a simple expression for the drag coefficient for laminar boundary layer flow over a slippery flat plate, which is of limited accuracy but is good enough for the purpose of quick and rough calculation. The results confirm that velocity slip can efficiently reduce the skin friction drag on a parallel flat plate, the effects of which can be enhanced with a large slip length. In addition, the non-similarity model is extended to the case when there is blowing or suction as well as slip on the boundary.