Two-phase air-water flows in hydraulic jumps at low Froude number

Abstract

A hydraulic jump is a region of rapidly-varied flow that is extremely turbulent. While the one-dimensional continuity and momentum principles have been successfully applied to express the relationships between upstream and downstream conditions, the three-dimensional equations cannot be resolved without some complicated turbulence closure, often involving two phases, i.e. air and water. Based upon a new dataset, the current investigation has the double objective of presenting a novel experimental investigation of the air-water flow characteristics in hydraulic jumps with a small Froude number (Fr₁ = 2.1) and discussing the potential scale effects involving several Reynolds numbers (0.078 × 10⁵ < Re < 3.05 × 10⁵). Four unique features are the low inflow Froude number Fr₁ = 2.1, the wide range of Reynolds numbers tested systematically, the broad amount of air-water flow properties investigated, and the relatively high Reynolds number (Re = 3.05 × 10⁵) achieved in the largest experiment. More than two dozen of parameters were tested systematically under Froude similar conditions. All the data demonstrated that the selection of relevant (air-water) flow property(ies) used to assess similarity and scale effects is most essential. Further the concept of similarity and scale effects must be linked to specific flow conditions. At low Froude number (Fr₁ = 2.1), the present results showed that many hydraulic jump properties could not be extrapolated from laboratory study to full scale hydraulic structures without substantial scale effects. These findings have profound implications for engineering design applications, often operating with Reynolds numbers in excess of 10⁵.