# Fluid Dynamics Model

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ABSTRACT A Computational Fluid Dynamics (CFD) model to simulate the water and air flow around competition kayak hulls was developed, with the principal aim of allowing accurate drag force predictions. The models used the Volume of Fluid (VoF) method to determine the location of the free surface, and the k-ω Shear-Stress Transport (SST) model to account for turbulent effects. The open-source CFD software package OpenFOAM was used for this purpose, namely its solver application interFoam. The model was first tested on the Wigley hull, a typical validation case for models of flow around marine vessels. Effects of mesh refinement and alteration were studied, and results for total drag force and hull wave profiles were obtained from the model for…show more content…
For an object immersed in a certain fluid, there are two components of drag: pressure drag (or form drag), which is a result of the pressure distribution along the surface of the object, and friction drag, caused by the shear forces acting on it [1]. Marine vessels move through an interface between two fluids, typically water and air. When a vessel moves, its movement will cause a deformation in the shape of that interface, creating a pattern of surface waves, and the hull of the vessel needs to exert a force to sustain this pattern. The drag force (or resistance force) on a ship hull can then be considered to be the sum of three components: the pressure drag and friction drag typical of any external flow, and a wave-making drag component [2]. The dimensional analysis of the drag force should then include the total drag force Dt , the length of the hull L , its velocity U , the wetted surface area S , the liquid medium’s density ρ and kinematic viscosity υ , and the gravitational acceleration g , on which the surface wave pattern heavily depends. These parameters can be expressed in terms of three non-dimensional quantities, the total drag coefficient Ct , the Reynolds number Re and the Froude number Fr : Ct = D_t/(0.5ρSU^2 )…show more content…
So, if the fluid being tracked is water, the value of α will be equal to 1 in cells completely filled with water and equal to zero in cells that do not contain any water, taking intermediate values for cells intersecting the free surface [3]. Fluid properties such as density and viscosity are calculated as a weighted average of the different fluids’ properties according to the volume fraction. So, for a case with only two fluids, 1 and 2, where α is the volume fraction of 1, the density ρ and kinematic viscosity υ will be given by [4]: α = αρ1 + (1-α)ρ2 (2.5) υ = αυ1 + (1-α)ρ2 (2.6) The value of α for each point in the domain can typically be calculated from previous values of α and the velocity field. There are many methods that can be used to calculate the volume fraction of a fluid for a given time instant. The method used in OpenFOAM interFoam solver decomposes the velocity vector field U in the same way as density and viscosity are decomposed, and creates an auxiliary vector Ur field that is used in the calculation of the field [5]: U = αU1 + (1-α)U2 (2.7) Ur = U1 – U2 (2.8) 2.3 Turbulence