发表机构
Mathematics Institute, University of Warwick; Vanellus Technologies Ltd.（华威大学数学研究所; 凡努斯科技有限公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究利用加权残差模型设计LQR反馈控制，结合直接数值模拟，成功稳定三维下落液膜，并揭示了执行器数量与位置对控制性能的关键影响。
AI 中文摘要
我们考虑了利用同种流体通过基底进行吹气和吸气的三维下落液膜的控制问题。基于对应二维问题的近期研究成果，我们采用一个降维的加权残差模型来描述液膜高度和下游通量，并以此作为控制器设计的基础。线性稳定性分析用于估计稳定液膜所需的执行器数量，而线性二次型调节器（LQR）框架则用于为线性化系统构建反馈控制。由此得到的增益矩阵与三维纳维-斯托克斯方程的直接数值模拟（DNS）观测相结合，使得从降维模型导出的控制能够直接应用于完整流动。通过系统的数值测试，我们证明了这些控制能够在物理相关的雷诺数和域配置范围内成功稳定平坦液膜解。我们进一步表明，执行器的数量和位置对控制性能起着关键作用，其中展向不稳定性需要在横向方向上增加额外的执行器覆盖。尽管从二维扩展到三维显著增加了控制器构建的成本，但这一成本完全在增益矩阵计算的离线阶段产生，使得整体框架在计算上具有可行性。我们的结果表明，从三维加权残差模型导出的LQR反馈控制在应用于完全解析的DNS时仍保持预测价值，扩展了先前的二维控制方法，并有助于弥合理论控制设计与实验相关下落液膜流动之间的差距。
英文摘要
We consider the problem of controlling a three-dimensional falling liquid film using same-fluid blowing and suction through the substrate. Building upon recent results for the corresponding two-dimensional problem, we employ a reduced-dimensional weighted-residual model for the film height and downstream flux as the basis for controller design. Linear stability analysis is used to estimate the number of actuators required to stabilise the film, while a linear-quadratic regulator (LQR) framework is used to construct feedback controls for the linearised system. The resulting gain matrix is then combined with observations from direct numerical simulation (DNS) of the three-dimensional Navier-Stokes equations, allowing controls derived from the reduced-dimensional model to be applied directly to the full flow. Through systematic numerical tests, we demonstrate that these controls successfully stabilise the flat-film solution across a physically relevant range of Reynolds numbers and domain configurations. We further show that both the number and placement of actuators play a crucial role in control performance, with spanwise instabilities requiring additional actuator coverage in the cross-stream direction. Although the extension from two to three dimensions substantially increases the cost of controller construction, this cost is incurred entirely offline during the computation of the gain matrix, making the overall framework computationally tractable. Our results demonstrate that LQR feedback controls derived from a three-dimensional weighted-residual model retain predictive value when applied to fully resolved DNS, extending previous two-dimensional control methodologies and helping bridge the gap between theoretical control design and experimentally relevant falling-film flows.
Comments28 pages, 11 figures
