Experimental investigation of a line plume in a filling box

A series of experiments were conducted to quantify the dynamics of a filling box driven by a line plume that spans the full width of the enclosure. Three configurations were tested namely symmetric (centrally located plume), wall-bounded (plume attached to an end wall), and asymmetric. The front movement for the symmetric and wall-bounded configurations was well described by the standard filling box model. The front movement results indicate that the typical value of the entrainment coefficient α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left( \alpha \right) $$\end{document} for an unconfined plume (α=0.16\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \alpha = 0.16 $$\end{document}) could be used to accurately predict the front movement for both the centrally located plume and the wall-attached plume. This is in contrast to other studies that suggest that wall-bounded plumes have a significantly lower entrainment coefficient. The standard filling box model broke down for the asymmetric configuration. As the plume was closer to one wall than the other, the plume outflows that spread out and reflected off the end walls returned to the plume at different times. This created a pressure imbalance across the plume that caused the plume to bend sharply toward the nearest wall. Analysis of the plume outflow as a constant flux gravity current showed that the outflow velocity scaled on the cube root of the plume buoyancy flux per unit width f\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ f $$\end{document}, a result confirmed by further experiments. This result was used to quantify the time at which the plume bends and the standard filling box model breaks down.