Reaping the Whirlwind: Buoyancy Vortices as Virtual Chimneys, for Power Generation from Waste Heat

Abstract

A literature review is undertaken in the theory of concentrated buoyancy vortices and associated laboratory and field experiments. A modification of the published heat-engine theory of Renno et al. is suggested to allow an improved prediction of vortex height and consequent thermodynamic efficiency and wind-speeds, through a reconsideration of the nature of the cold reservoir of the heat engine. The theory makes two basic assumptions. The first is that the vortex will advect upwards while two criteria are met: • There is a positive Convectively Available Potential Energy (CAPE) to support convection • The lapse rate of temperature with height is lower in the vortex core than in the environment, thus providing positive buoyant vertical acceleration to stretch air parcels in the core and concentrate vorticity The second is that the vortex degrades to a turbulent plume when either of the above criteria is breached and that the plume forms the cold reservoir of the heat engine driving the vortex. The modified theory is shown to explain published results for laboratory vortices and dust-devil statistics. The modified theory is then used to scale a virtual chimney vortex, with a buoyancy vortex powered from waste-heat driving a turbine for electrical power generation. It is predicted that such a virtual chimney vortex could be used to generate electricity from waste heat with an overall conversion efficiency in the range of 2-4% without the construction of expensive towers.