Predicting the Hydrodynamics of Heaving Twin Cylinders in a Free Surface Using an Unsteady-RANS Method

Predicting the Hydrodynamics of Heaving Twin Cylinders in a Free Surface Using an Unsteady-RANS Method

The successful estimation of a ship’s motions in regular waves depends on the accurate calculation of its hydrodynamic properties and exciting forces. Estimation of the hydrodynamic coefficients and the excitation force/moment of a ship’s sections is the most time-consuming aspect of the strip theory approach. The vast majority of the available techniques rely on assumptions from potential flow theory, including free surface effects. However, many previous studies, such as Schmitke (1978), have shown that viscous effects are likely to be the most significant, particularly for lateral plane motions and for some ship sections. In addition, Beck and Reed (2001) state that vertical plane motions in catamarans undergo significant viscous damping. An appropriate numerical model therefore has to be applied to solve the viscous formulation of the seakeeping problem.

Continued technological advances offer ever-increasing computational power. This can be utilised for viscous flow simulations to solve Reynolds Averaged Navier-Stokes (RANS) equations in the time domain. This is the most recent area of research on seakeeping problems, as discussed in detail in the 26th International Towing Tank Conference (ITTC, 2011).

The key objective of this work is therefore to perform a fully non-linear unsteady RANS simulation to predict the hydrodynamic coefficients of a two-dimensional twin section heaving at a free surface, covering a range of oscillation frequencies. The analyses are performed using CD-Adapco’s commercial Computational Fluid Dynamics (CFD) software package STAR-CCM+, version 7.02.011. The outputs are then compared with the potential flow results of Lee et al. (1971) and the experimental results of Wang and Wahab (1971).

The study presented in this paper forms part of a larger body of work aiming to develop an improved strip theory which uses the hydrodynamic coefficients of each section of a catamaran, obtained using the unsteady RANS method, to predict its responses to regular incident waves. The resulting model should be robust, reliable and provide more accurate results, whilst minimising the required computational time, and hence the cost. Figure 1 illustrates an overview of the stages of this model to predict ship motion characteristics.


Figure 1. Overview of the proposed strip theory model, using a CFD-based URANS method.

As illustrated in Figure 1, a fully non-linear URANS solver is employed to obtain the excitation force/moment time history of different ship sections. In this stage, both viscous and rotational effects in the flow and generated free surface wave are taken into account. Fourier analysis is then applied to the hydrodynamic force/moment time histories to determine the sectional hydrodynamic coefficients of the ship. The proposed method has been applied to a circular cylinder harmonically heaving about a calm free surface.

The added mass and fluid damping coefficients of the section in question have been obtained at fifteen frequencies of oscillation. The results have been found to be in reasonably good agreement with the experimental results. At high frequencies, the added mass coefficients are underestimated in the CFD method. These discrepancies may be attributed to the highly non-linear feature of the flow at high frequencies. The current CFD simulation can be developed in order to capture this phenomenon more precisely.

For more information about the project contact Prof. Atilla Incecik ( or Prof. Osman Turan ( at the Department of Naval Architecture, Ocean and Marine Engineering at the University of Strathclyde.
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