Combined Buoyancy and Pressure-Driven Flow Through a Shallow, Horizontal, Circular Vent

Abstract

Combined buoyancy and pressure-driven (i.e., forced) flow through a horizontal vent is considered where the vent-connected spaces are filled with fluids of different density in an unstable configuration (density of the top is larger than that of the bottom). With zero-to-moderate cross-vent pressure difference, Δp, the instability leads to bidirectional exchange flow between the two spaces, e.g., as in the emptying from the bottom of a liquid-filled can with a single vent opening. For relatively large Δp, the flow through the vent is unidirectional, from the high to the low-pressure space, e.g., as is the case when the can has a large enough second vent at the top. Problems of a commonly used unidirectional orifice vent flow model, with Bernoulli’s equation and a constant flow coefficient, CD are discussed. First, the orifice model does not predict bidirectional flows at zero-to-moderate Δp. Also, when Δp exceeds the critical value, ΔpFL, which defines the onset of unidirectional or “flooding” flow, there is a significant dependence of CD on the relative buoyancy of the upper and lower fluids (i.e., CD is not constant). Analysis of relevant boundary value problems and of available experimental data leads to a mathematical vent flow model, which removes the problems of the orifice flow model. The result is a general algorithm to calculate flow through shallow, horizontal, circular vents under high-Grashof-number conditions.