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

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, C_D are discussed. First, the orifice model does not predict bidirectional flows at zero-to-moderate Δp. Also, when Δp exceeds the critical value, Δp_FL, which defines the onset of unidirectional or “flooding” flow, there is a significant dependence of C_D on the relative buoyancy of the upper and lower fluids (i.e., C_D 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.