有限体積法による高粘性ニュートン流体の容器充填の数値計算

Abstract

ニュートン流体である高粘性液体を鉛直下方に流入させて，上面に開口部を有する 2 次元矩形容器内に充填する数値計算を行った．周囲の低粘性気体を同時に計算するため，密度と粘性の異なる 2 つの非圧縮性流体に対する相平均モデルを利用し，これをコロケート格子有限体積法で離散化した．特に，計算セル境界における粘性係数，密度および流速の平均化手法に考察を加え，ダムブレイク問題を通じてその有効性を確認した．提案された計算手法を用いて，高さ H の矩形容器に幅 d の上部流入口から高粘性液体を充填する問題を計算した結果，高粘性液体のレイノルズ数 Re と H/d の条件により発生する，steady filling, spreading, splashing, buckling という異なるフローパターンが既往研究と同様に再現されることを示した．

Computations of the two dimensional rectangular container filling are conducted by injecting the highly viscous Newtonian fluids, vertically downward through an aperture on the top boundary. In order to simultaneously calculate the low-viscosity gas surrounding the highly viscous liquid, phase-averaged governing equations are used for two immiscible incompressible fluids with different densities and viscosities. The governing equations are discretized with the finite volume method in the collocated grid system. In particular, the estimation methods of viscosity, density and velocities on computational cell boundaries in the discretized governing equations are investigated and their effectiveness was confirmed through the application to the dam-break flows. As a result of the computations of the container filling with the highly viscous liquid, it was confirmed that the proposed method enables us to reasonably predict flow patterns of the highly viscous liquid, such as steady filling, spreading, splashing and buckling, which arise in the specific relationships between Reynolds number and the ratio H/d, where H is the height of the container and d is the inlet width, as reported in the preceding studies.