Lagrangian simulation of the unsteady near field dynamics of planar buoyant plumes

Abstract

The unsteady dynamics of planar plumes is investigated numerically with particular emphasis on the pulsating instability characterizing the source (nozzle) near field. This instability manifests itself as the periodic shedding of vortical structures from the nozzle. The Lagrangian Transport Element Method is used to provide high resolution two-dimensional simulations of the unaveraged variable density flow. Comparison with experimental results verifies that the simulations capture the plume instantaneous behavior and reproduce the pulsation frequency. The latter is controlled by a Strouhal–Richardson number correlation which implies that the instability is inviscid in nature with a frequency that is mainly dependent on the gravitational acceleration and the nozzle width, f∼g/w. The presence of a horizontal wall surrounding the nozzle exit does not affect these results. Numerical results indicate that transition from nonpulsatile to pulsatile behavior obeys a Reynolds–Richardson number correlation of the form Re∼Ri−0.627 implying a balance between buoyant and viscous forces. Arguments based on vorticity dynamics trace the origin of the instability to the mechanism of vorticity generation by buoyancy. In the nonpulsatile flow, the circulation generated by buoyancy increases monotonically with height at a rate that is approximately constant. This arrangement can be altered via perturbations that create local circulation maxima and can lead to vortex formation. Once a first vortex pair is created, a subsequent pair precipitates via a mechanism that yields circulation maxima near the nozzle exit through the interaction of the local vorticity generation by buoyancy with the strain field induced by the preceding vortex pair. This mechanism is complex enough to suggest that simple theoretical models that predict the pulsation frequency are unlikely. It does help explain, however, the relative simplicity of the functionality of the frequency and its lack of sensitivity on a variety of boundary conditions and external parameters.