薄液膜内非定常温度差マランゴニ対流の高抑制制御へ向けた次元縮約モデルの開発

抄録

The purpose of this study is to construct a reduced-order model (ROM) for real-time control to suppress three-dimensional unsteady thermocapillary convection in a thin liquid layer, a simple physical model for single-crystal manufacturing. To manufacture single crystals with high quality and at low cost, it is essential to suppress unsteady thermocapillary convection. If a full order model based on fluid governing equations is used for control to obtain high performance, they involve high computational costs and require significant time. To address this issue, we developed a Galerkin-ROM (G-ROM), constructed using Proper Orthogonal Decomposition (POD). As a results, the velocity fields reconstructed with POD largely matched the original data, but discrepancies were observed in the velocity fields reproduced by the G-ROM. To improve accuracy, closure models with pseudo-viscosity and higher-order mode corrections were introduced. However, as these improvements failed to resolve the issue, combined with insights from our previous research, we concluded that POD bases are unsuitable for constructing ROMs targeting HTW.