MODEL- AND FULL-SCALE RANS SIMULATIONS FOR A DRIFT TANKER

The flow around a full-scale (FS) ship can be simulated by means of Reynolds-Averaged Naiver-Stokes (RANS) method, which provides a way to obtain more knowledge about scale effects on ship hydrodynamics. In this work, the viscous flow around a static drift tanker in full scale is simulated by using the RANS solver based on the open source platform OpenFOAM. The k - w SST model is employed to approximate the eddy viscosity. To reduce computational time, wall function approach is applied for the FS simulation. The flow around the ship in model scale is simulated as well, but without using any wall function, i.e., using Low-Reynolds number mode. In order to verify the computations, de- tailed studies on the computational grid including investigation of the sensitivity of computed forces to y+ (dimension- less distance of first grid point to wall) and grid dependency study are carried out. The computed forces are compared with available measured data. The scale effects are analysed and discussed by comparisons.

VISCOSITY IN SEAKEEPING

The paper addresses the issue of actuality in ship hydrodynamics: the estimation of ship’s linear and angular oscillations with respect to the state of equilibrium. The prediction of seakeeping properties raises a question about a relative importance of viscous and free-surface effects (Quérard et al. 2009), yet this question remains of more general importance in fluid mechanics, since it is related to the dynamic characteristics of objects/bodies immersed in a liquid. From a theoretical standpoint, the problem refers to flows with moving boundaries. It can also be considered in terms of fluid-structure interaction (FSI), however, not necessarily linked with the computation of the body deformation and stresses due to the flow. As the Author correctly notices, the computational solution to this problem in its full setup reveals to be extremely costly due to the 3D and unsteady nature of the fluid motion under turbulent flow conditions at nominally high Reynolds numbers (Re~109, as stated by the Author in Tab. 1) in presence of the free surface. For this reason, the full solution, or direct numerical simulation (DNS), of the governing Navier-Stokes (N-S) equations at these Re will remain unfeasible in the foreseeable future; see, e.g., Pozorski (2017) for an estimation of the DNS capability in simple wall-bounded turbulent flows. The situation gets even worse in ship hydrodynamics when a DNS of fluid flow would need to be coupled to the dynamics of the rigid body (of complex geometry, usually).

Slow Motions of A Circular Cylinder in a Liquid after a Separation Impact

The plane problem of the separation impact of a circular cylinder completely immersed in an ideal incompressible heavy liquid is considered. It is assumed that after the impact, the cylinder moves horizontally at a constant speed. An attached cavity is formed behind the body, the shape of which depends on the physical and geometric parameters of the problem. It is required to study the process of collapse of the cavity at low velocities of the cylinder, which correspond to small Froude numbers. The solution to the problem is constructed using asymptotic expansions in a small parameter, which is the dimensionless speed of the cylinder. In this case, as the characteristic speed of the problem, a value is chosen equal to the square root of the product of the radius of the cylinder and the acceleration of gravity. As a result of this choice, the indicated small parameter coincides with the Froude number, and therefore, we can assume that the asymptotics of the problem is constructed for small Froude numbers. In the leading asymptotic approximation, a mixed problem of potential theory with one-sided constraints on the surface of the body is formulated. With its help, the position of the separation points at each moment of time is determined and the time of collapse of a thin cavity is found. The results obtained can be used to solve practical problems of ship hydrodynamics, in which it is necessary to take into account the phenomenon of cavitation.

Wall-Modeled LES for Ship Hydrodynamics in Model Scale

A complete approach for wall-modeled large-eddy simulation (WMLES) is demonstrated for the simulation of the flow around a bulk carrier in the model scale. Essential components of the method are an a-priori estimate of the thickness of the turbulent boundary layer (TBL) over the hull and to use an unstructured grid with the appropriate resolution relative to this thickness. Expressions from the literature for the scaling of the computational cost, in terms of the grid size, with Reynolds number, are adapted in this application. It is shown that WMLES is possible for model scale ship hydrodynamics, with ∼108 grid cells, which is a gain of at least one order of magnitude as compared with wall-resolving LES. For the canonical case of a flat-plate TBL, the effects of wall model parameters and grid cell topology on the predictive accuracy of the method are investigated. For the flat-plate case, WMLES results are compared with results from direct numerical simulation, RANS (Reynolds-averaged Navier-Stokes), and semi-empirical formulas. For the bulk carrier flow, WMLES and RANS are compared, but further validation is needed to assess the predictive accuracy of the approach. 1. Introduction The number of applications of large-eddy simulation (LES) and other scale-resolving approaches, such as detached-eddy simulation and different forms of RANS-LES hybrids, is steadily increasing in naval hydrodynamics (Larsson et al. 2014; Fureby 2017). The importance of the hull boundary layer and the implications in terms of grid resolution requirements (and associated computational cost) for different turbulence modeling approaches is what mainly limits the application of LES in ship hydrodynamics (Liefvendahl & Fureby 2017). Wall-resolving LES (WRLES), in which the energetic flow structures in the inner part of the turbulent boundary layer (TBL) are resolved, puts excessive requirements on the grid resolution. Recently, the first model scale simulations using WRLES were reported (Nishikawa 2015; Posa & Balaras 2018). In these simulations, >109 grid points were necessary, even at low model scale Reynolds number. For full-scale simulations, WRLES is out of range of present computational resources (Liefvendahl & Fureby 2017).