Modelling criteria for bubble plumes—a theoretical approach

A theoretical investigation is made to derive the parameters that govern the dynamic similarity between prototype and model bubble plumes. It is shown in the study that, for a complete similarity between the prototype and the model, the buoyancy flux from the source, the size of the bubbles, and the expansion of the gas bubbles all have to be simulated. This is translated into the observation of the Froude law, the Weber law, and the expansion law in the model study. The expansion law requires that, for a reduced model, the study be conducted under partial vacuum and, for an enlarged model, the study be conducted under pressure.The physical properties of common fluids impose severe constraints on the model study. If the Weber law is to be satisfied, the smallest model permissible will only be half the prototype size. To conduct experiments under partial vacuum, the boiling of the model liquid has to be contended with. For practical reasons, a certain degree of violation of the similarity laws seems to be unavoidable. The theoretical investigation calls for systematic experiments to examine the quantitative effect of the different similarity parameters and the degree of violation of the similarity laws permissible in solving practical problems. Key words: plume, bubble, model, simulation, criteria, theoretical.