Self-similarity and scale effects in physical modelling of hydraulic jump roller dynamics, air entrainment and turbulent scales

Abstract

A physical study of hydraulic jump is often undertaken using down-scaled Froude-similar models with Reynolds numbers much smaller than in prototype (e.g. spillway stilling basins). The potential viscous scale effects may affect a number of physical processes including turbulence development and air entrainment, thus challenging the extrapolation of laboratory data to the prediction of prototype conditions or justification of numerical modelling. This paper presents an experimental study of hydraulic jumps with a particular focus on the scale effects in terms of free-surface fluctuation and deformation, bubble advection and diffusion, bubble-turbulence interaction and turbulence dissipation. A broad range of free-surface, air–water flow and turbulence properties were measured systematically for Froude numbers from 3.8 to 10 and Reynolds numbers from 2.1 × 104 to 1.6 × 105. Based upon self-similarities in the longitudinal evolution of a number of characteristic flow properties, the analytical expressions of time-averaged roller surface profile, void fraction distribution and longitudinal velocity distribution were derived for given Froude number. The roller surface dynamics were found free of scale effects in terms of fluctuation amplitudes but the characteristic frequencies were scale-sensitive. While some air–water flow parameters such as bubble count rate, bubble chord time distribution and bubble grouping behaviour could only be correctly quantified at full-scale prototype conditions, the aeration level and turbulent scales might be estimated with satisfactory accuracy for engineering applications given a model Reynolds number no less than 4 × 10 to 6 × 104.