Author(s): Carsten Thorenz; Annika Grefenstein

Linked Author(s): Carsten Thorenz

Keywords: Hydraulic structure; Air-water-mixture; Physical model; CFD; OpenFOAM; VOF

Abstract: Air-water mixtures are a very typical phenomenon near hydraulic structures. Physical scale models are well established to study some of these phenomena, but due to scale effects it is not feasible to study all effects in physical models. For the numerical simulation of the flow field around hydraulic structures the volume-of-fluid method (VoF) is often used. Unfortunately, VoF is only applicable for situations where a well defined air-water interface exists. If mixing occurs, VoF is not able to predict the behavior of the mixture correctly. Here, a simplistic enhancement to the VoF is presented which helps to simulate air-water mixtures with small amounts of dispersed air in the water. It is assumed that the global momentum transport is modelled sufficiently with the VoF, even for fluid mixtures. The effect of the mixture on the flow behavior is taken into account by the reduced density and shows up as buoyancy effects. The presented idea is focused on the transport of the air-water distribution in the model on sub-grid-scale. In a traditional VoF scheme, the transport is described by a pure advection equation. Here, a physically based relative flux of air against water is added. The air bubble rise velocity (“terminal velocity”) for bubbles in resting water is well known. The terminal velocity is interpreted as a relative velocity against the moving fluid within a small control volume. The transport equation for the air-water mixture is expanded by an additional flux term to account for the relative velocity of the bubbles and impact of turbulence. Turbulent diffusion is estimated from the turbulent viscosity by the turbulent Schmidt number. Summarizing, this is an enhancement to the VOF method which adds a physical approach to the sub-grid-scale movement of air bubbles in water. The results of the numerical model are validated against probe measurements from a physical model of a weir. For the physical model a flume of 20 m length; 0.6 m width and 1.2 m height was used. The scale of the model is 1:20 and a longitudinal section of the real weir was investigated. The original goal of the model was a study on the energy dissipation behind the weir. The air content in the entrainment and transport zone behind the weir was measured with conductivity probes at several locations. The results of these measurements are compared to the numerical modeling results and the sensitivity of the physical model measurements to different postprocessing strategies is shown.

DOI: https://doi.org/10.3850/IAHR-39WC252171192022308

Year: 2022