時間変化する境界をもつ粘性流体の運動に対するSPHを用いた基礎研究

使用 SPH 对时变边界粘性流体运动进行基础研究

• 批准号: 03J52081
• 负责人: 永弘 進一郎
• 金额: $ 1.09万
• 依托单位: Tohoku University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for JSPS Fellows
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-03J52081/
• 关键词: 自由境界; SPH; 石の水切り; 粘性流体; 衝突

流体表面と物体の衝突過程に対する最近の研究として、L.Boquetらの石の水切りの実験[Nature, vol.427,29(2004)]に着目した。彼らはアルミニウムの円盤に回転を与えて水面に対して衝突させ、円盤の入射角度θと水面に対する傾き角度φを変えた時の反発の起こる条件を調べた。その結果、傾き角度φ=20°の時に反発が起こる為に必要な速度v_<min>が最小になる事を見いだした。これを再現する事、また傾き角度φについて最小値が生じるその物理的理由を明らかにする事を目的として、3次元の流体シミュレーションとモデル解析の双方から研究を行った。シミュレーションを行う場合の困難の一つは、大変形を起こす流体表面の境界条件の扱いである。ナビエ・ストークス方程式をラグランジュ描像で数値的に解くSPH(Smoothed Particle Hydrodynamics)法を用いた。SPH法は、流体を流体粒子の集まりとして記述する為、変形する表面を扱う際に格子生成などの煩雑な手続きをさける事が出来る点がかかる問題に対して有利な特徴である。表面張力を無視し、粘性の殆ど効かない領域で行ったSPHシミュレーションが、L.Boquetらによる実験を定性的に再現することを確認した。この結果から「石の水切り」のようなレイノルズ数が10^5のオーダーに達する衝突過程においては、物体が流体に運動量を与える事によって受ける反作用力が最も重要であると予想できる。これを考慮し流体表面の変形を無視した単純な微分方程式モデルを提案し、円盤の衝突に対して適用した。微分方程式を近似的に扱い、v_<min>とθ,φの関係について実験と定性的に一致する解析的な表式を得ることができた。

The process of fluid surface abrupt change has been studied recently. L.Boquet, water-cut and water-cut materials [Nature, vol.427,29 (2004)] are focused on. In the other direction, the impact angle of the water surface, the angle of incidence, the angle of incidence, the angle The result of the test, the angle of the cycle φ = 20 °, the starting speed of the cycle is the necessary speed, and the minimum speed is the minimum speed. The reason for the physics is to understand the reason for the purpose of the matter, and the three-dimensional fluid is used to analyze the behavior of both sides. The boundary condition of the fluid surface is the boundary condition of the fluid surface. Use the SPH (Smoothed Particle Hydrodynamics) method to solve the equation. The SPH method, the fluid particle analysis method and the fluid particle analysis method. The surface force is independent and viscous. In the field, the SPH is sensitive, the L.Boquet is sensitive, and the confirmation is correct. The results show that the number of water cutters in stone is 10. 5%, and that of the object is the most important factor that is affected by the reaction force. The shape of the fluid surface is independent of the differential equation, the proposal and the application of the differential equation. The approximate equation of differential equation, the approximate equation of differential equation, the equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the approximate equation of differential equation, the equation of differential equation

项目成果

Shin-ichiro Nagahiro, Yoshinori Hayakawa: "Numerical simulation for collisions of a rigid disk on fluid surface"AIP conference proceedings. (to be published). (2004)

Shin-ichiro Nagahiro、Yoshinori Hayakawa：“流体表面上刚性盘碰撞的数值模拟”AIP 会议记录。

Theoretical and numerical approach to the "magic angle" of stone-skipping

跳石“魔角”的理论和数值方法

• 发表时间: 2005
• 期刊: Physical Review Letters (In Press)
• 作者: Shin-ichiro Nagahiro;Yoshinori Hayakawa
• 通讯作者: Yoshinori Hayakawa