Cahn-Hilliard Navier-Stokes simulations for marine free-surface flows
Cahn-Hilliard Navier-Stokes simulations for marine free-surface flows
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DOI：
10.1007/s42757-020-0101-3
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发表时间：
2020-02
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通讯作者：
Niklas Kühl;M. Hinze;T. Rung
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作者：
Niklas Kühl;M. Hinze;T. Rung
本文致力于海洋气水两相流的模拟。重点放在扩展的经典的流体体积（VoF）方法的Cahn-Hilliard（CH）模型和它的好处，模拟不混溶，不可压缩的两相流的扩散贡献。这种流动主要是用隐式VoF方案来模拟的，该方案主要采用启发式顺风偏置近似来模拟尖锐的界面。该策略引入了严格的时间步长限制，并需要稳定流的伪时间步长。我们的总体目标是一个健全的描述的自由表面区域，简化人工时间步长的限制，支持一个有效的和强大的基于逆风的近似框架，并固有地包括表面张力的影响时，需要的。Cahn-Hilliard Navier-Stokes（CH-NS）系统被验证为一个分析的Couette流的例子和气泡的形成下的表面张力的影响。二维验证的例子涉及层流驻波达到从重力到毛细尺度，以及淹没水翼流。最后应用于Re = 1.4 × 107、Fn = 0.26的固定浮力下的集装箱船三维绕流实验研究。结果进行了比较，从VoF的方法得到的数据，辅以分析解决方案和测量。研究表明，优越的上级效率，再锐化能力，和更广泛的预测领域的CH为基础的扩展自由表面流动与有限的空间范围内的接口柯朗数。
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 forRe= 1.4 × 107andFn= 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.