An efficient and accurate approach for zero-frequency added mass for maneuvering simulations in deep and shallow water. (September 2022) - el Moctar, Ould; Lantermann, Udo; Chillcce, Guillermo
Abstract: An overall increase in ship sizes in conjunction with a general decrease in ship powering has increased the relevance of reliably predicting a ship's maneuvering performance. These predictions rely often on mathematical models based on modified Taylor series expansion, where nonlinear multivariate algebraic polynomials that require hydrodynamic coefficients are determined from physical or numerical planar motion mechanism (PMM) tests. The added mass coefficients are needed for a fast and accurate simulation. For maneuvering simulations, these added mass coefficients should be obtained for zero frequency. Despite the advance of high-performance computing, numerical PMM tests based on solving the unsteady Reynolds-averaged Navier–Stokes equations is time-consuming and often not suitable for practical design-related investigations. Furthermore, hydrodynamic coefficients obtained from PMM tests are frequency-dependent. An alternative to numerical PMM tests consists of steady numerical tests. This kind of analysis requires much less computing time and effort for the users. However, the acceleration-dependent hydrodynamic forces and moments cannot be derived from these steady computations. Here we introduced a fast and accurate procedure to obtain water depth-dependent zero-frequency added mass and added moment of inertia. Using Euler Equations, we impulsively accelerated the ship hull over only one time step. We validated our method against an analytical solution for an ellipsoid. We performed systematic computations of added mass and added moment of inertia for two benchmark containerships, a benchmark tanker, and a cruise ship, thereby demonstrating the effects of water depth on added mass for different hull shapes. Highlights: A new numerical method to compute added masses and added moment of inertia for zero frequency. The method is fast and reliable in deep and shallow water conditions. The method is validated against the analytical solution of a fully submerged ellipsoid. Added masses in deep and shallow water were computed for four different ships.