Numerical studies of rotating laminar boundary-layer flows

Abstract

This thesis presents numerical studies on certain problems in steady and unsteady laminar boundary?layer flows involving rotation of either the fluid or the body. It consists of four chapters: the first is introductory, and the remaining three present the author's investigations.

Chapter I – Introduction Chapter I provides an introduction to boundary?layer theory with special reference to rotating boundary?layer flows. Various analytical and numerical methods used to solve boundary?layer problems are also discussed briefly.

Chapter II – Steady Laminar Compressible Flow over a Rotating Sphere This chapter investigates steady, laminar, non?similar, compressible subsonic flow about a rotating sphere, whose axis of rotation is taken to be parallel to the direction of the undisturbed free stream.

The governing equations are transformed into a suitable nondimensional form. Solutions are obtained at different meridional locations, starting at the pole. Parameters studied include:

rotation rate mass transfer (suction and injection) wall temperature

In several cases, computation is continued to the point where the longitudinal skin friction becomes zero, to analyse flow behaviour near separation. The usual numerical difficulties near this point are overcome using quasilinearization combined with a finite?difference scheme, with very small step sizes as the zero?skin?friction point is approached.

Chapter III – Unsteady Compressible MHD Boundary Layers at a Rotating Stagnation Point This chapter examines unsteady, compressible, magnetohydrodynamic (MHD) boundary?layer flows at the stagnation point of a rotating sphere with massive blowing, in the presence of a magnetic field. Two classes of flows are considered: 1. Semi?similar flows

Free?stream velocity and angular velocity of the sphere are taken as arbitrary functions of time. Solutions are obtained for:

accelerating and oscillating free?stream flows accelerated rotation of the body

2. Self?similar flows

Free?stream velocity components and angular velocity are assumed to vary inversely as linear functions of time.

In both cases:

Transformed equations are solved by quasilinearization + finite?difference schemes. A non?uniform mesh with decreasing step size across the boundary layer is used. A realistic gas model is adopted.

The effects of unsteadiness, large mass injection, magnetic field strength, and wall temperature on velocity and thermal boundary layers are analysed in detail.

Chapter IV – Steady Incompressible Swirling Flow in a Conical Hydrocyclone This chapter studies steady incompressible swirling flow of water in a conical hydrocyclone, taking into account the variation of:

viscosity Prandtl number

with temperature, using empirical relations. The non?similar boundary?layer equations are transformed and solved using:

a further transformation mapping the infinite domain to a finite one an implicit finite?difference scheme

The results demonstrate that temperature dependence of viscosity and Prandtl number has a pronounced effect on the boundary?layer development.