On the stability of laminar plumes: Some numerical solutions and experiments

Abstract

An investigation of the hydrodynamic stability of a laminar plume arising from a horizontal line source of heat was carried out using the Tollmien-Schlichting theory of small disturbances. Inviscid solutions of the Orr-Sommerfeld equation were obtained for both symmetric and asymmetric disturbances and the effect of the Prandtl number on the inviscid stability was calculated for asymmetric disturbances. The base flow was found to be less stable for the asymmetric mode. In addition, the full disturbance momentum equations, coupled and uncoupled from the energy equation, were numerically integrated with the boundary conditions appropriate for asymmetric disturbances superimposed on the symmetric plume base flow. Neutral stability curves have been obtained in terms of the Grashof number. The predominance of the assumed asymmetric mode of flow oscillation was verified experimentally by perturbing a plume, in air, with a vibrating ribbon. A Mach-Zehnder interferometer was used to observe the disturbances as they were converted downstream. The experimental results demonstrate that sufficiently high frequency disturbances are stable as they are converted downstream.