Modelling of thermal plumes under mixed convection with application to indoor air

Abstract

The temperature and velocity profiles of thermal plumes have been widely investigated under different conditions using a variety of methods. However, the situation where a turbulent asymmetric thermal plume evolves in a uniform upward flow of air in the region of mixed convection, where the far field velocity has a magnitude comparable to the velocities generated by the plume, as can occur in a ventilated room, does not seem to have attracted much attention. For such case, it would be expected that the relative motion of the fluid would affect the rate of growth of the plumes. In addition, the entrained fluid has a net vertical momentum that adds up to that driving the plume. This work revolves around the study of such situations. In the progress an analytical analysis using a first order solution of the governing equation about the far stream velocity is carried out. The equations derived are then compared with experimental data available in literature - wherever this has been possible - as well as to simulations obtained using computational fluid dynamics. It is shown that in both cases the agreement is good. The model is subsequently used to provide insight on how plumes in confined and ventilated environments might evolve. Furthering on the analytical analysis, the closed form solution in terms of power series for both laminar and turbulent plumes in natural convection is presented. The technique presented here is expected to lead the way for more complete solutions in the case when mixed convection prevails.