ABSTRACT

The OpenFOAM package is used to study unsteady two-dimensional cross-flow over an infinite rigid cylinder as a prelude to studies on ship hydrodynamics. The Reynolds number ranges from 1e2 to 1e6. The kω Shear Stress Transport turbulence model is used and the normalized maximum thickness of the wall-adjacent layer, (equation), is less than one for all the cases. The time-step is chosen such that the maximum Courant–Friedrichs–Lewy (CFL) number is less than one and the oscillating drag and lift are sampled at a high rate. For a fixed domain size, when the Reynolds number decreases, the time, normalized by the flow-through-time, taken to reach the first mode of nearly steady-state oscillations increases. At the inlet, two sets of values for the turbulence kinetic energy, k, turbulence specific dissipation rate, ω, and turbulence kinetic eddy viscosity, νt are used for air and water. The coefficients of drag and lift, CD and CL, respectively are of primary interest. The time-averaged coefficient of drag, (equation), the rms value of (equation), CDrms, and the rms value of the coefficient of lift, CLrms, are computed. It is shown that the values of these statistical quantities are the same in air and water only under certain conditions that are not always satisfied in the literature.

INTRODUCTION

Workshops on ship hydrodynamics are held at regular intervals (Larsson et al, 2014; Hino et al., 2015) to compare the resistance of benchmark ships and other fine details of the flow, especially at the air-water interface, computed by research groups around the world. Many of the results are obtained using Computational Fluid Dynamics (CFD) packages and compared with experimental and other numerical results. There is a large spread in the values of the resistance, computed using finite volume cells varying in number from one million to tens of millions, and an increase in the number of cells is not always accompanied by a decrease in the error when compared across packages. All the details of the analysis are seldom reported and, therefore, the results cannot be reproduced. The local Reynolds number of interest ranges from zero at the bow of the ship to 1e9 for full-scale ships. The Unsteady Reynolds-Averaged-Navier-Stokes (URANS) equations are usually solved and other methods such as Large Eddy Simulation (LES) are seldom used at ship or even model-scale. The differences in the results are partly due to the user-defined domain and the mesh and partly due to the CFD package used. In this paper, two-dimensional (2D) cross-flow over a deeply submerged cylinder in air and water is studied using OpenFOAM, a CFD package, to learn lessons and apply them to ship hydrodynamics. The emphasis is on average and root-mean-square values of the drag and lift and not on the fine details of the flow itself which cannot be obtained by solving the URANS equations.

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