Submersibles used for exploration, maintenance and naval warfare have to be both manoeuvrable and easy to control. Simulation of the trajectory for these vessels requires the accurate determination of the hydrodynamic forces and moments which are determined by model-testing, empirical methods or a combination of both. CFD can play a role here by permitting an easier and more accurate determination of these loads. In this paper we focus on the accurate prediction of the manoeuvring forces of free swimming streamlined submersibles (submarines) using CFD. We compare simulations of a standardised well-known submarine shape (DARPA SUBOFF) for two configurations, one bare hull (AFF-1) and one fully-appended hull (AFF-8), under different inflow angles. The viscous-flow solvers used are the finite volume solver ReFRESCO developed by MARIN, and the finite element commercial solver AcuSolve. Verification studies are performed and the numerical results are validated with the experimental data available in the literature. The influence of different turbulence models is investigated and results obtained with a RANS (Reynolds-Averaged-Navier-Stokes) approach are compared with the theoretically more realistic DDES (Delayed-Detached-Eddy-Simulation) results. The influence of the appendages on the forces and flow fields is also investigated and analysed. As a last example, results of a forced pitch motion including dynamic effects are presented.
This article discusses numerical errors in unsteady flow simulations, which may include round-off, statistical, iterative, and time and space discretization errors. The estimation of iterative and discretization errors and the influence of the initial condition on unsteady flows that become periodic are discussed. In this latter case, the goal is to determine the simulation time required to reduce the influence of the initial condition to negligible levels. Two one-dimensional, unsteady manufactured solutions are used to illustrate the interference between the different types of numerical errors. One solution is periodic and the other includes a transient region before it reaches a steady-state. The results show that for a selected grid and time-step, statistical convergence of the periodic solution may be achieved at significant lower error levels than those of iterative and discretization errors. However, statistical convergence deteriorates when iterative convergence criteria become less demanding, grids are refined, and Courant number increased.For statistically converged solutions of the periodic flow and for the transient solution, iterative convergence criteria required to obtain a negligible influence of the iterative error when compared to the discretization error are more strict than typical values found in the open literature. More demanding criteria are required when the grid is refined and/or the Courant number is increased. When the numerical error is dominated by the iterative error, it is pointless to refine the grid and/or reduce the time-step. For solutions with a numerical error dominated by the discretization error, three different techniques are applied to illustrate how the discretization uncertainty can be estimated, using grid/time refinement studies: three data points at a fixed Courant number; five data points involving three time steps for the same grid and three grids for the same time-step; five data points including at least two grids and two time steps. The latter two techniques distinguish between space and time convergence, whereas the first one combines the effect of the two discretization errors.
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