An investigation of numerical analysis for modeling free-surface elevation from flow over a shallowly submerged 2D naca0012 hydrofoil

Abstract

The bulbous bow is a common feature for large displacement vessels. The purpose of the bulbous bow is to reduce the bow wave, hereby making use of wave cancellation theory. The main drawback of these type of bows is that the drag reduction effect is only present for a limited range of sailing speeds. If the transit velocity is altered, the effect of the bulbous bow can even result in an increase of wave making drag. Due to this sensitivity to the sailing speed it is important to be able to predict the location of the waves generated by the protruding bulb. Computational fluid dynamics is gaining interest in commercial marine industries. The size and transit velocity at which the previously mentioned vessels that employ the protruding bulb operate, results in the common use of Reynolds averaged Navier Stokes (RANS) models. To investigate the accuracy of these RANS models, a 2D model is presented in this thesis. The bulbous bow is modeled as a shallowly submerged 2D naca0012 hydrofoil. The justification for this simplification is that the geometry and flow over a bulbous bow is too complex for the duration of this project. A submerged 2D hydrofoil can still capture the important flow dynamics for free-surface waves. In this thesis we focused on evaluating the accuracy of RANS models for simulating the wave dynamics that arise when a shallowly submerged 2D naca0012 hydrofoil moves through water. The main objective is to find which geometrical and fluid dynamic properties have an effect on the free surface wave profile. Apart from questioning if these properties have an influence on the wave profile, we also want to know how the wave profile changes by altering these properties.
The interFoam package from OpenFoam was used for simulating the flow. InterFoam adopts the volume of fluid (VOF) approach proposed by Weller (Weller, 2008) for simulating multiphase flows. Turbulence modeling was done using the k-ωSST two equationmodel from Menter et al. (Menter, 1992). In 1983 Duncan and his colleagues published a paper on the free surface wave dynamics generated by a towed naca0012 hydrofoil (Duncan, 1983). The results from their experiments are used as a benchmark for the present study. From a single phase test we found that the experiments from Duncan where performed in the regime where transition of the boundary layer from laminar to turbulent is present. The presence of this transition is expected to be one of the reasons for the disagreement in literature on wave elevation, wavelength zero point crossings and lift and drag coefficients. It is shown that the relatively small gap between the basin floor and the hydrofoil of 0.86 chord lengths has a significant impact on the wave profile and the flow at the hydrofoil. Reynolds independence is found to be at Re ¸ 2•10⁵ for a towed hydrofoil submerged at h/c = 0.955 with the basin floor located 10 chord lengths below the hydrofoil. Below this value a reduction in Reynolds number results in an decrease of the wave amplitude and an increase in the wavelength. The assumption to neglect the resistance from the hydrofoil wake made by Duncan is shown to be false. The dominating dimensionless parameters for these types of flows are: Froude based on submergence Frh, Froude based on basin to foil height Fr_D and the Reynolds number based on the chord length and the bottom fluid parameters Rec . Note that in this thesis the angle of attack (α) has been kept constant at 5° which does
effect the flow but this has not been investigated during this research. A attempt is made to simulation breaking waves in the present model. The Breaker type in the present study differs from the one found by Duncan et al. (Duncan, 1983). Even if the same breaker type was found the elevation and wavelength differ a lot. It is therefore concluded that The present model is not suited for predicting
breaking waves.