Thickness and velocity of wavy liquid films on rotating conical surfaces

Abstract

The thickness and velocity of the thin liquid films flowing up a rotating cone surface are among the key parameters determining mass transfer characteristics and overall performance of gas–liquid contacting devices such as spinning cone distillation columns and centrifugal film evaporators. Laminar model predictions for these devices are inapplicable under the turbulent flow conditions of commercial-scale equipment. In this work, dimensionless empirical models for the average thickness and radial velocity of wavy films have been developed based on thickness measurements on a laboratory-scale cone. The experimental method registered the intensity of induced fluorescence of a flowing film illuminated by an ultraviolet light source. The film is modelled as a wavy layer on top of a laminar sub-layer attached to the disk surface. The thickness of the film is an additive modification of the Nusselt model thickness δ += δ N ++ δ wave +=0.91 η −2/3+1.95 η −3, where η is a normalised radial distance. The thickness of the wavy layer δ wave + has been correlated with 95% confidence limits of ±12%. In the dimensional form, the proposed models express the film thickness and radial velocity as functions of cone geometrical and operating parameters. The validity of the models is consistent with independent velocity measurements on a rotating cone and film thickness measurements on rotating disks. The normalised film thickness is shown to be essentially preserved for spinning cone columns of varying size scaled at constant relative capacity.