Modes of Adiabatic and Diabatic Fluid Flow in an Annulus With an Inner Rotating Cylinder

Abstract

Abstract The present report is the first phase of an investigation of those variables which control the rate of heat transfer in the air gap of a rotating electrical machine. This phase of the problem reduces to obtaining a basic understanding of the fluid-flow and heat-flow processes in an annulus, formed by two concentric cylinders, with the inner cylinder rotating and with the outer cylinder stationary. The primary independent variables and effects are, first, the axial velocity of the air through the air gap, which is combined with other variables to form the customary Reynolds number; second, the speed of rotation, which is combined with other variables to form a new dimensionless group, called the Taylor number, in honor of G. I. Taylor, who laid the theoretical and experimental foundations for this problem; third, the temperature gradients at the walls; fourth, the surface roughness in the air gap; and finally, the “entrance effects” introduced by the development of the boundary-layer flow in the air gap. The present report gives the experimental results obtained for two smooth and long annuli, thereby eliminating from consideration, at present, the last two effects given above. It is shown that four distinct modes of flow exist for adiabatic and diabatic flow of air in these annuli. The demarcation lines of these flow regions were investigated in detail for adiabatic flow with hot-wire anemometers and also by means of visual and photographic methods. The results showed that four modes of flow exist over regions of Reynolds number and Taylor number for both adiabatic and diabatic flow. These modes are: 1 purely laminar flow; 2 laminar flow plus Taylor vortexes; 3 purely turbulent flow; 4 turbulent flow plus vortexes. The results obtained here for adiabatic flow were found to agree well with the work of Cornish for the boundary line between the regions of laminar flow and laminar-plus-vortexes flow, but they did not agree with similar results by Fage. Preliminary results are also presented here for diabatic flow in the annulus in the form of heat-transfer coefficients. These results are shown in the form of a three-dimensional surface in which the Nusselt number is represented as a function of the Reynolds number and Taylor number.