The transition of a line plume to round plume

Buoyant turbulent plumes are often categorized by their geometry and described as either round plumes, issuing from a point source, or line/planar plumes, issuing from an elongated source. As line plumes rise above their source they get thicker (normal to the source axis) and, far from the source, they will no longer be planar but more resemble a round plume. However, the vast majority of experimental measurements of line plumes focus on the near source region, where they are still planar and the flow is two-dimensional. Further, these experiments constrain the ends of the plume with barriers to prevent entrainment through the ends of the plume and maintain a two-dimensional flow. Herein, results are presented from a series of experiments that were conducted to measure the transition of an unconstrained line plume into a round plume. A model is presented that allows the calculation of the entrainment into a plume of arbitrary cross sectional shape in terms of the hydraulic radius of the plume defined as the cross-sectional area divided by the perimeter over which entrainment is occurring. This formulation, along with a smooth transition function that changes both the geometry and entrainment coefficient, is used to make predictions of the front position over time for a line plume in a filling box. The model was run for different values of the nozzle width to box height ratio. Results of the model were compared to the experimental front position measurements and show that an unconstrained line plume will transition to a round plume at a height equal to approximately three times the source width. This is consistent with the idea that the line plume will transition when its thickness is similar in magnitude to its nozzle width.