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).