Numerical procedure for free-surface detection using a Volume-of-Fluid model

During the design of a stepped spillway it is fundamental to predict the maximum water depth to define wall height. Many experimental and numerical studies have been made on this subject, however the combination of both, in order to enhance aspects related to free-surface characteristics and their numerical prediction, are still uncovered. While experimentally the free-surface position is defined as the line where air-concentration reaches 90%, numerically the free-surface is defined by the equilibrium of volume between the water and air. In this work, the free-surface, captured with a modified version of three-dimensional Volume-of-Fluid model for the combined air-water flow, is compared to the flow depths measured with three ultrasonic sensors in a stepped spillway. This comparison is used to reach an equilibrium between the theoretical definition of the numerical and experimental free-surface position and to propose a numerical procedure to predict the free-surface using the three-dimensional modified Volume-of-Fluid. The numerical model uses the Shear-stress transport k-ω model to calculate the turbulent characteristics of the flow in a uniform and orthogonal mesh. Fit coefficients between experimental and numerical free-surfaces are calculated along with this procedure to obtain the best relation. In non-aerated regions of the flow, free surface should be represented by α=0.7 while for the aerated region, α=0.1 should be used instead, both with errors of 2%.