Gas stirring is an important process used in secondary metallurgy. It allows to homogenize the temperature and the chemical composition of the liquid steel and to remove inclusions which can be detrimental for the end-product quality. In this process, argon gas is injected from two nozzles at the bottom of the vessel and rises by buoyancy through the liquid steel thereby causing stirring, i.e., a mixing of the bath. The gas flow rates and the positions of the nozzles are two important control parameters in practice. A continuous optimization approach is pursued to find optimal values for these control variables. The effect of the gas appears as a volume force in the single-phase incompressible Navier–Stokes equations. Turbulence is modeled with the Smagorinsky Large Eddy Simulation (LES) model. An objective functional based on the vorticity is used to describe the mixing in the liquid bath. Optimized configurations are compared with a default one whose design is based on a setup from industrial practice.

中文翻译：

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用单相 Navier-Stokes 方程建模的浮力驱动钢水搅拌的优化控制

气体搅拌是二次冶金的重要工艺。它可以使钢水的温度和化学成分均匀，并去除可能对最终产品质量有害的夹杂物。在这个过程中，氩气从容器底部的两个喷嘴喷入，通过钢水的浮力上升，从而引起搅拌，即熔池的混合。气体流速和喷嘴的位置是实践中的两个重要控制参数。追求连续优化方法来寻找这些控制变量的最佳值。在单相不可压缩 Navier-Stokes 方程中，气体的作用表现为体积力。湍流使用 Smagorinsky 大涡模拟 (LES) 模型进行建模。基于涡度的目标函数用于描述液体浴中的混合。优化配置与默认配置进行比较，默认配置的设计基于工业实践的设置。