Abstract
The paper is devoted to the simulation of maritime two-phase flows of air and water. Emphasis is put on an extension of the classical Volume-of-Fluid (VoF) method by a diffusive contribution derived from a Cahn-Hilliard (CH) model and its benefits for simulating immiscible, incompressible two-phase flows. Such flows are predominantly simulated with implicit VoF schemes, which mostly employ heuristic downwind-biased approximations for the concentration transport to mimic a sharp interface. This strategy introduces a severe time step restriction and requires pseudo time-stepping of steady flows. Our overall goal is a sound description of the free-surface region that alleviates artificial time-step restrictions, supports an efficient and robust upwind-based approximation framework, and inherently includes surface tension effects when needed. The Cahn-Hilliard Navier-Stokes (CH-NS) system is verified for an analytical Couette-flow example and the bubble formation under the influence of surface tension forces. 2D validation examples are concerned with laminar standing waves reaching from gravity to capillary scale as well as a submerged hydrofoil flow. The final application refers to the 3D flow around an experimentally investigated container vessel at fixed floatation for Re = 1.4 × 107 and Fn = 0.26. Results are compared with data obtained from VoF approaches, supplemented by analytical solutions and measurements. The study indicates the superior efficiency, resharpening capability, and wider predictive realm of the CH-based extension for free-surface flows with a confined spatial range of interface Courant numbers.
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Acknowledgements
The current work is a part of the research projects “Drag Optimisation of Ship Shapes” funded by the German Research Foundation (DFG, Grant No. RU 1575/3-1) as well as “Dynamic Adaptation of Modular Shape Optimization Processes” funded by the German Federal Ministry for Economic Affairs and Energy (BMWi, Grant No. 03SX453B). This support is gratefully acknowledged by the authors. Selected computations were performed with resources provided by the North-German Supercomputing Alliance (HLRN). In addition, we would like to mention the Matlab Symbolic Toolbox (The MathWorks, 2019), which was a great help when calculating the analytical solutions.
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Kühl, N., Hinze, M. & Rung, T. Cahn-Hilliard Navier-Stokes simulations for marine free-surface flows. Exp. Comput. Multiph. Flow 4, 274–290 (2022). https://doi.org/10.1007/s42757-020-0101-3
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DOI: https://doi.org/10.1007/s42757-020-0101-3