低 Pr 流体液柱内の3次元マランゴニ対流の数値シミュレーション

抄録

Recent developments of the numerical simulations of three dimensional Marangoni convection were reviewed. Based on the authors recent results of numerical simulations conducted by using a finite difference method, general feature of oscillatory Marangoni convection in half-zone liquid bridges of low Prandtl number fluids ( Pr= 0 , 0.01, 0.02) with a cylindrical liquid surface was discussed over a wide range of aspect ratio (As=0.6 to 2.2) . The simulation results indicated that under smaller temperature differences the flow in the liquid bridge was axisymmetric , but the flow became steady 3-D at and beyond the first critical Reynolds number Rec1. This steady 3-D flow became unstable against time-de­ pendent 3-D disturbances beyond a second critical condition, Re, 2. The numerical simulations revealed the critical conditions and flow structures in detail for Pr=0 fluid and rough sketches for fluids of Pr=0.01 and 0.02. These non-linear simulations gave reasonable values of Rec1 in good agreements with those of linear stability analyses and also Re,2 close to the available numerical results. A stability map for low Pr fluids ( Pr=0, 0.01 and 0.02) indicates the effect of aspect ratio on the critical Reynolds numbers.