Heat transfer by steam condensing onto rotating cones

Abstract

A theoretical analysis is made for the condensation of steam in a laminar film on the outer surface of an axisymmetrical body. The body rotates about a vertical axis and the film is assumed to drain under the combined influence of gravitational and centrifugal accelerations. A differential equation which governs the film thickness is derived and is numerically integrated for two types of axisymmetrical body to calculate the theoretical film to surface heat transfer coefficient. The first type of body is the cone. A decrease in the apex angle on stationary cones leads to an increase in the component of gravitational acceleration along the surface and to an increase in the theoretical heat transfer coefficient. However, an increase in the apex angle of a cone rotating at high speed increases the component of the centrifugal acceleration along the surface and increases the heat transfer coefficient. A comparison is made between the heat transfer coefficient for discs and for cones. The second type of body has a concave surface described by the rotation of a circular arc and represents part of a turbine rotor at the transition from shaft to blade disc. Theoretical film thicknesses and heat transfer coefficients are presented and discussed for bodies with an arc radius- of 0.2 m and shaft diameters between 0.002 m and 0.6 m. An apparatus for making measurements of heat transfer coefficient from steam to rotating axisymmetrical bodies with diameters up to 0.6 m, is described. The heat transfer results for steam condensing on cooled rotating cones with apex angles 10 , 20 and 60 are presented and discussed. The condensate film supports various patterns of waves as it drains along the surface of the 10 , 20 and 60 cones. At high speeds, drainage on the 10 and 20 cones is assisted by the formation and detachment of drops. The pattern of waves arid the mode of drainage are shown to be dependent on the apex angle, the speed of rotation, the cone diameter and the distance from the starting point of condensation. With either mode of drainage, the experimental heat transfer coefficients are generally larger than the theoretical laminar values.