############################################################## 水中に沈めた鉄塊からの自然対流冷却 ############################################################## * シミュレーション名 :: heatConduction__box_in_water_XYZ3D ========================================================= シミュレーション体系 ========================================================= * 基本方程式は、 **熱輸送方程式( Heat Equation )** と **Navier-Stokes方程式** + 流体は、 **非圧縮** , **Boussinesq近似** + 熱輸送は、 熱伝導、熱対流、輻射を取り扱う． * シミュレーション対象は直方体 ( 50 [cm] x 50 [cm] x 50 [cm] )の箱のなかに、直方体の鉄塊が ( 20 [cm] x 20 [cm] x 20 [cm] ) が安置してあり、周囲を水が満たしている． * 初期温度、 20 [℃] の水が鉄塊に触れて、自然対流し、鉄塊が冷却される． * 流体は、すべり境界条件とする． --------------------------------------------------------- 物性条件 --------------------------------------------------------- .. csv-table:: **Materials Settings** :header: "Target", "Parameters", "Value", "Unit", "Description" :widths: 20, 20, 15, 10, 35 :width: 800px "空気", "Heat Conductivity", "0.0257", "W/m.K", "熱伝導度" "", "Heat Capacity", "1.005e+3", "J/kg.K", "比熱" "", "Density", "1.166e+0", "kg/m3", "密度" "", "Heat Expansion Coefficient", "3.665e-3", "1e-6", "体積膨張率(1K毎に(0.29e-3)分の体積増加(線形近似))" "", "Reference Temperature", "293.15", "K", "参照温度 (体積膨張率の測定温度：Boussinesq近似)" "", "viscosity", "1.512e-5", "Pa.s", "粘度" "水", "Heat Conductivity", "0.602", "W/mK", "熱伝導度" "", "Heat Capacity", "4.18e3", "J/kg K", "比熱" "", "Density", "9.97e3", "J/kg K", "密度" "", "Reference Temperature", "293.15", "K", "参照温度" "", "Heat Expansion Coefficient", "0.29e-3", "1/K", "体積膨張率 (体積膨張率の測定温度：Boussinesq近似)" "", "viscosity", "1.18e-3", "Pa s", "粘度" "SS400", "Heat Conductivity", "51.6", "W/m.K", "熱伝導度" "", "Heat Capacity", "473.0","J/kg.K", "比熱" "", "Density", "7.85e+3", "kg/m3", "密度" "定数", "gravity", "0,0,-1,9.8", "m/s2", "重力加速度" "", "Stefan Boltzmann", "5.68e-8", "W/m2K4", "Stefan-Boltzmann係数" ========================================================= メッシュ ========================================================= * メッシュ生成スクリプト ( mesh.py ) .. literalinclude:: ../../code/heat/heatConduction__box_in_water_XYZ3D/mesh.py :caption: mesh.py ( heatConduction__box_in_water_XYZ3D ) :language: python * geometry.conf .. literalinclude:: ../../code/heat/heatConduction__box_in_water_XYZ3D/geometry.conf :caption: geometry.conf ( heatConduction__box_in_water_XYZ3D ) * boundary.json .. literalinclude:: ../../code/heat/heatConduction__box_in_water_XYZ3D/boundary.json :caption: boundary.json ( heatConduction__box_in_water_XYZ3D ) * phys.conf .. literalinclude:: ../../code/heat/heatConduction__box_in_water_XYZ3D/phys.conf :caption: phys.conf ( heatConduction__box_in_water_XYZ3D ) * mesh.conf .. literalinclude:: ../../code/heat/heatConduction__box_in_water_XYZ3D/mesh.conf :caption: mesh.conf ( heatConduction__box_in_water_XYZ3D ) * 生成したメッシュを次に示す． .. image:: ../../image/heat/heatConduction__box_in_water_XYZ3D/mesh.png :width: 800px :align: center ========================================================= Boussinesq近似の確認 ========================================================= --------------------------------------------------------- シミュレーション設定 --------------------------------------------------------- * 流体境界を (i) 鉄塊境界, (ii) 容器境界 の２つに分ける． * (i) 鉄塊境界に温度のDirichlet境界条件 T= 600 [K] = 330 [℃] を課す． * 流体としては、 "Normal-Tangential velocity = True" を指定し、滑り壁条件 ( :math:`v_\perp=0` ) を課した． * Boussinesq近似の挙動を確認する． .. literalinclude:: ../../code/heat/heatConduction__box_in_water_XYZ3D/boussinesq.sif :caption: boussinesq.sif ( heatConduction__box_in_water_XYZ3D ) --------------------------------------------------------- 確認結果 --------------------------------------------------------- * 自然対流が生じている． .. image:: ../../image/heat/heatConduction__box_in_water_XYZ3D/boussinesq_anime.gif :width: 800px :align: center ========================================================= 水中の鉄塊における自然対流冷却 ========================================================= --------------------------------------------------------- シミュレーション設定 --------------------------------------------------------- * Dirichlet条件の場合、空気の動きは見えても、鉄塊内部の冷却の様子はわからない． * 解析対象を鉄塊部分の熱伝導も含めて解く． * 空気→水へ変更する． .. literalinclude:: ../../code/heat/heatConduction__box_in_water_XYZ3D/heat.sif :caption: heat.sif ( heatConduction__box_in_water_XYZ3D ) --------------------------------------------------------- シミュレーション結果 --------------------------------------------------------- * 結果は以下の通り．