Some problems in fluid mechanics with special reference to turbomachinery

Abstract

This thesis includes some investigations on continuum flows through turbomachines and some slip flow problems. Rarefied gas flow through a nozzle is studied with the aim that this may lead to a greater understanding of rarefied gas flows through turbomachines. Rayleigh problem with modified initial conditions has been studied. An initial value method has been applied to study the two-point boundary value problem. This thesis consists of four chapters. A brief survey of the problem solved and the author's contributions are given at the beginning of each chapter. Chapter I contains a general introduction to the subject. Chapter II is devoted to the study of non-free vortex flows through turbomachines. In Part I the inverse problem for an axial flow fan containing a rotor only is studied by lifting line theory. The expressions for the induced velocity components are obtained in closed form using the Biot–Savart rule. The isolated airfoil method has been used for design purposes for fans with small hub. In the second part, the same problem as in Part I is studied for fans with large hub where the cascade method has been used for design purposes. In the third part, flow through a stage of an axial flow compressor is investigated by the method of radial equilibrium. All these methods have been illustrated with some numerical examples. This chapter is based on the following papers:

Three-Dimensional Non-Free Vortex Flow in Axial Fans (in collaboration with Dr. G. Nath). Accepted for publication in Acta Technica. Design of Axial Flow Fans by Cascade Method. Communicated to Acta Technica. Non-Free Vortex Flow through a Stage of an Axial Flow Compressor. To be communicated.

In Chapter III the decay of viscous spiral trailing vortices downstream of the rotor of an axial flow fan is studied. The governing Navier–Stokes equations have been linearized and solved. This chapter is based on the following paper: Decay of Viscous Trailing Vortices (in collaboration with Dr. G. Nath). Rev. Roum. Sci. Techn. Mec. Appl., Vol. 16, No. 2, p. 409–418, 1971. In Part I of Chapter IV the effect of slip on three-dimensional free-vortex flow and heat transfer through a nozzle with a variable-property, axisymmetric laminar compressible boundary layer has been investigated for a slightly rarefied gas. The boundary layer equations are numerically solved using appropriate boundary conditions which take into account the effect of slip. In the second part the effect of suction or injection on Rayleigh problem using modified initial conditions for velocity slip and temperature jump has been studied. In the third part the solution of the compressible laminar boundary layer equations on a permeable and impermeable flat plate with uniform free stream velocity and constant surface temperature is obtained by reducing this two-point boundary value problem to an initial value problem. These problems also have been illustrated with numerical examples.