【技術書典17】OpenFOAM（自宅で極める流体解析）2次元円柱まわりの流れ

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2. 1 OpenFOAM — ࣗ୐ͰۃΊΔྲྀମղੳ — ʦஶʧӉ஦ʹೖͬͨΧϚΩϦ ٕज़ॻయ 17ʢ2024 ೥ౙʣ৽ץ 2024 ೥ 11 ݄ 2 ೔ɹ ver 1.0
3. 2 ˙໔੹ ຊॻ͸৘ใͷఏڙͷΈΛ໨తͱ͍ͯ͠·͢ɻ ຊॻͷ಺༰Λ࣮ߦɾద༻ɾӡ༻ͨ͜͠ͱͰԿ͕ى͖Α͏ͱ΋ɺͦΕ͸࣮ߦɾద༻ɾӡ༻ͨ͠ਓ ࣗ਎ͷ੹೚Ͱ͋Γɺஶऀ΍ؔ܎ऀ͸͍͔ͳΔ੹೚΋ෛ͍·ͤΜɻ ˙঎ඪ ຊॻʹొ৔͢ΔγεςϜ໊΍੡඼໊͸ɺؔ܎֤ࣾͷ঎ඪ·ͨ͸ొ࿥঎ඪͰ͢ɻ ·ͨຊॻͰ͸ɺ™ɺ®ɺ© ͳͲͷϚʔΫ͸লུ͍ͯ͠·͢ɻ
4. 3 ͸͡Ίʹ ຊॻΛखʹऔ͍͖ͬͯͨͩɺ͋Γ͕ͱ͏͍͟͝·͢ɻ ຊॻʹ͍ͭͯ ຊॻͰ͸ɺΦʔϓϯιʔειϑτ΢ΣΞ OpenFOAM Λ׆༻ͯ͠ɺྲྀମղੳͷجຊ ΛֶͿ͜ͱ͕Ͱ͖·͢ɻஶऀ͕ϒϩάͰެ։ͨ͠಺༰Λߍਖ਼͠ɺ͞Βʹৄ͘͠·ͱΊ ͨ΋ͷͰ͢ɻ *1ɻલճͷٕज़ॻయ 16 ʹग़యͨ͠ʮOpenFOAMʢࣗ୐Ͱ࢝ΊΔྲྀମղ ੳʣ ʯ [6] Ͱ͸ɺ ԁ؅಺ͷ૚ྲྀྲྀΕΛऔΓѻ͍ɺ ྲྀମղੳͷجૅతͳ಺༰Λ OpenFOAM ֶ͕΂Δߏ੒ʹ͠·ͨ͠ɻຊॻ͸ͦͷଓฤͱͯ͠ɺதڃऀ޲͚ͷ಺༰ʹ͠·ͨ͠ɻ۩ ମతʹ͸ɺ2 ࣍ݩͷԁப·ΘΓͷྲྀΕͱ͍͏ݱ৅ΛऔΓ্͛ɺ࣮ݧ஋΍ཧ࿦ʹجͮ͘ ଎౓෼෍΍ѹྗ෼෍ͱ OpenFOAM Λ༻͍ͨܭࢉ݁ՌͱΛൺֱ͠ͳ͕Βɺͦͷϓϩ ηεΛஸೡʹղઆ͍ͯ͠·͢ɻ ຊॻ͸ҎԼͷΑ͏ͳߏ੒ʹͳ͍ͬͯ·͢ɻ • ୈ 1 ষͰ͸ɺ2 ࣍ݩԁப·ΘΓͷྲྀΕʹؔ͢Δجຊతͳཧ࿦ʹ͍ͭͯղઆ͠ɺ ղੳΛਐΊΔ্ͰඞཁͱͳΔલఏ஌ࣝΛ੔ཧ͠·͢ɻ • ୈ 2 ষͰ͸ɺOpenFOAM ͷ blockMesh πʔϧΛ࢖༻͠ɺ2 ࣍ݩԁபͷϞσ ϧ࡞੒͔Βղੳͷ࣮ߦ·ͰͷखॱΛֶͼ·͢ɻୈ 1 ষͰղઆͨ͠ཧ࿦Λ࣮ࡍͷ खॱΛ௨ͯ֬͠ೝ͠ɺཧղΛਂΊ·͢ɻ • ୈ 3 ষͰ͸ɺඇѹॖੑྲྀΕʹ͓͚Δྗֶత૬ࣅੑʹ͍ͭͯऔΓ্͛ɺྲྀମղੳ Λ௨ͯͦ͡ͷݪཧΛ࠶ݱ͠·͢ɻ͜͜Ͱɺແ࣍ݩ਺Ͱ͋ΔϨΠϊϧζ਺͕ྲྀΕ ͷڍಈʹͲͷΑ͏ʹӨڹΛ༩͑Δ͔ʹ͍ͭͯཧղ͢Δ͜ͱ͕Ͱ͖·͢ɻ • ୈ 4 ষͰ͸ɺOpenFOAM ͷࣗಈԽΛՄೳʹ͢Δ Python ϥΠϒϥϦͰ͋Δ PyFoam ͷجຊతͳ࢖͍ํʹ͍ͭͯ঺հ͠·͢ɻ • ୈ 5 ষͰ͸ PyFoam Λ࢖ͬͯԁப·ΘΓͷྲྀΕʹର͢ΔύϥϝʔλελσΟ ͷࣗಈԽΛߦ͍·͢ɻ 2 ࣍ݩԁப·ΘΓͷྲྀΕ͸ɺҰݟ୯७ͳྲྀΕͰ͋ΔΑ͏Ͱ͍ͯɺԁப·ΘΓͷണ཭ ݱ৅ͷ࠶ݱ΍Ͳͷ৚݅Ͱ΋࠶ݱͰ͖ΔཚྲྀϞσϧཱ͕֬͞Ε͍ͯͳ͍͜ͱ͔Βɺݱ ࡏͰ΋ྲྀମղੳख๏ͷݚڀ͕ଓ͚ΒΕ͍ͯ·͢ɻಛʹϨΠϊϧζ਺ͱ߅ྗ܎਺ɺӔͷ ৼಈप೾਺ͷؔ܎ʹ͍ͭͯ͸ɺ࣮ݧͱྲྀମղੳͷ྆ํͰ੝Μʹݚڀ͞Ε͍ͯ·͢ɻಛ *1 Ӊ஦ʹೖͬͨΧϚΩϦɿhttps://takun-physics.net/ – i –
5. 4 ͸͡Ίʹ ʹɺ೉қ౓͕ߴ͍ͷ͸ɺϨΠϊϧζ਺͕ 105 Λ௒͑ΔΑ͏ͳྖҬͰɺ͜͜Ͱ͸Ӕͷണ ཭ݱ৅Λਖ਼֬ʹ࠶ݱ͠ͳ͚Ε͹ͳΒͳ͍ͨΊɺΑΓߴ౓ͳղੳ͕ٻΊΒΕ·͢ɻҰํ ͰɺϨΠϊϧζ਺͕ 1000 ҎԼͰ͋Ε͹ɺཚྲྀϞσϧΛ࢖Θͳͯ͘΋ྲྀମղੳͷଥ౰ ੑΛࣔ͢͜ͱ͕ՄೳͰ͋Γɺຊষͷର৅ͱ͍ͯ͠·͢ɻ ͜ͷΑ͏ʹɺԁப·ΘΓͷྲྀΕ͸ྲྀମྗֶͷجૅ͕٧·͓ͬͯΓɺཧղΛਂΊΔͨ Ίͷઈ޷ͷ୊ࡐͰ͢ɻຊষͰ͸ɺ࣮ݧσʔλ΍ཧ࿦ղΛʮઌੜʯͱͯ͠ɺྲྀମղੳ݁ Ռͷଥ౰ੑΛݕূ͢Δํ๏Λղઆ͍͖ͯ͠·͢ɻօ͞Μ͕ࣗΒߦͬͨղੳ݁Ռʹࣗ৴ Λ࣋ͯΔΑ͏ʹͳΔ͜ͱ͕ɺຊষͷ໨ඪͰ͢ɻ ·ͨɺPyFoam Λ࢖ͬͨࣗಈԽͷεςοϓΛৄ͘͠঺հ͓ͯ͠Γɺ͜ΕʹΑΓ OpenFOAM ͷԠ༻ྗ͕ٻΊΒΕɺதڃऀ޲͚ͷ಺༰ͱͳ͍ͬͯ·͢ɻPyFoam Λ ׆༻͢Δ͜ͱͰɺ൓෮తͳ࡞ۀΛޮ཰Խ͠ɺղੳ݁Ռͷଥ౰ੑݕূΛΑΓਂ͘ߦ͏͜ ͱ͕Ͱ͖ΔΑ͏ʹͳΓ·͢ɻதڃऀϨϕϧͷ௅ઓͱͯ͠ɺͥͻຊॻΛ௨ͯ͠஌ࣝΛ޿ ͍͍͛ͯͬͯͩ͘͞ɻ ຊॻͷର৅ಡऀ ຊॻͰ͸࣍ͷΑ͏ͳਓΛର৅ͱ͍ͯ͠·͢ɻ • OpenFOAM ʹ͍ͭͯڵຯ͕͋Δਓ • ࣗ୐ͰγϛϡϨʔγϣϯ͢Δ͜ͱʹϫΫϫΫ͍ͯ͠Δਓ • 2 ࣍ݩԁப·ΘΓͷྲྀΕΛ୊ࡐʹྲྀମղੳͷଥ౰ੑݕূΛߦ͍͍ͨਓ લఏͱ͢Δ஌ࣝ ຊॻΛಡΉʹ͋ͨΓɺ࣍ͷΑ͏ͳ஌͕ࣝඞཁͱͳΓ·͢ɻ • ྲྀମྗֶͷجૅ஌ࣝ • Linux ʹ͍ͭͯͷجૅ஌ࣝ • Python ʹ͍ͭͯͷجૅ஌ࣝ • OpenFOAM Λ࣮ߦͰ͖Δ؀ڥΛ༻ҙͰ͖Δ ࢖༻͢Διϑτ΢ΣΞͷόʔδϣϯ ຊॻͰ࢖༻͢Διϑτ΢ΣΞ͸ҎԼͱͳΓ·͢ɻ • OpenFOAM v2406 (WSL2) • ParaView 5.12 • Python 3.10.12 • gnuplot 5.4 WSL2 ͷ Ubuntu-22.04 ʹ OpenCFD ͕ϦϦʔε͢Δόʔδϣϯ (ESI ൛) ͷ OpenFOAM v2406 ΛΠϯετʔϧ͍ͯ͠Δ͜ͱΛ૝ఆ͍ͯ͠·͢ɻParaView Λ Windows ΋͘͠͸ Mac ʹΠϯετʔϧ͓ͯ͠࢖͍͍ͩ͘͞ɻUbuntu-22.04 ʹ͸ – ii –
6. 5 ͸͡Ίʹ Python3.10 ͕طʹೖ͍ͬͯ·͕͢ɺຊॻͰ࢖༻͢ΔϥΠϒϥϦͳͲ͸ผ్Πϯε τʔϧ͢Δඞཁ͕͋Γ·͢ɻ ෇࿥ C ʹඞཁͳιϑτ΢ΣΞͷΠϯετʔϧํ๏Λهࡌ͍ͯ͠·͢ͷͰɺࣗ͝਎ Ͱ؀ڥΛ༻ҙ͍ͯͩ͘͠͞ɻ ԋश༻ͷϞσϧ ຊॻͰ࢖༻ͨ͠ԋश༻ͷϞσϧ͸ Github ΑΓࢀর͍ͩ͘͞ɻ Githubɿhttps://github.com/kamakiri1225/OpenFOAM_contents17 ͓໰͍߹Θͤઌ ຊॻʹؔ͢Δ࣭໰΍͓໰͍߹Θͤ͸ X ΋͘͠͸ϒϩάͷ͓໰͍߹ΘͤϑΥʔϜΑ Γ͓ئ͍͍ͨ͠·͢ɻ • Xɿhttps://x.com/t_kun_kamakiri • ϒϩά͓໰͍߹Θͤɿhttps://takun-physics.net/page-908/ – iii –
7. 6 ໨࣍ ͸͡Ίʹ i ୈ 1 ষ ԁப·ΘΓͷྲྀΕͷ֓ཁ 1 1.1 ϨΠϊϧζ਺ʹΑΔྲྀΕͷύλʔϯ . . . . . . . . . . . . . . . . . . 1 1.2 ෺ମʹಇ͘ྗͱετϩʔϋϧ਺ . . . . . . . . . . . . . . . . . . . . 3 ߅ྗͱ༲ྗ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 ߅ྗ܎਺ͱ༲ྗ܎਺ . . . . . . . . . . . . . . . . . . . . . . . . . 5 ετϩʔϋϧ਺ . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 ཧ૝ྲྀମͱ࣮ࡍͷྲྀମ . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 ྗֶత૬ࣅੑ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5 ·ͱΊ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 ୈ 2 ষ ԁப·ΘΓͷྲྀମղੳ 11 2.1 ղੳͷ໨త . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 OpenFOAM ͰͷγϛϡϨʔγϣϯ . . . . . . . . . . . . . . . . . . 11 ղੳϑϩʔ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 ιϧόͷબ୒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 ࢧ഑ํఔࣜ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 ࡞ۀϑΥϧμͷ࡞੒ . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4 νϡʔτϦΞϧͷίϐʔ . . . . . . . . . . . . . . . . . . . . . . . . 16 2.5 ϝογϡ࡞੒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 blockMeshDict Λฤू . . . . . . . . . . . . . . . . . . . . . . . 18 mirrorMesh Λฤू . . . . . . . . . . . . . . . . . . . . . . . . . 24 extrudeMesh Λฤू . . . . . . . . . . . . . . . . . . . . . . . . 31 ϝογϡ඼࣭ͷ֬ೝ . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.6 ղੳઃఆ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 ઃఆϑΝΠϧߏ੒ . . . . . . . . . . . . . . . . . . . . . . . . . . 35 ෺ੑ஋ͷઃఆ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 ཚྲྀϞσϧͷઃఆ . . . . . . . . . . . . . . . . . . . . . . . . . . 36 ڥք৚݅ͷઃఆ . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 ཭ࢄԽεΩʔϜ . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 – iv –
8. 7 ໨࣍ ܭࢉͷ੍ޚ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 ฒྻ෼ׂ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.7 ܭࢉ࣮ߦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 ݁ՌͷՄࢹԽ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.8 ܭࢉ݁Ռͷଥ౰ੑͷݕূ . . . . . . . . . . . . . . . . . . . . . . . . 67 ߅ྗ܎਺ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2.9 ετϩʔϋϧ਺ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 2.10 ѹྗ܎਺ͷ෼෍ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 2.11 ղੳʹ͓͍ͯ஫ҙͨ͠఺ . . . . . . . . . . . . . . . . . . . . . . . . 72 2.12 ·ͱΊ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 ୈ 3 ষ ྲྀମղੳʹΑΔྗֶత૬ࣅੑͷݕূ 74 3.1 ϨΠϊϧζ਺ҧ͍ʹΑΔղੳ . . . . . . . . . . . . . . . . . . . . . 74 3.2 ϞσϧͷมߋՕॴ . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 ྲྀ଎ͷมߋ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 ௚ܘͷେ͖͞ͷมߋ . . . . . . . . . . . . . . . . . . . . . . . . . 76 ߅ྗ܎਺ͷઃఆมߋ . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.3 ܭࢉ݁Ռ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.4 ·ͱΊ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 ୈ 4 ষ PyFoam ͷجૅ 80 4.1 PyFoam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.2 Python ͷ࣮ߦ؀ڥͱىಈ . . . . . . . . . . . . . . . . . . . . . . . 80 4.3 OpenFOAM ͷϑΝΠϧͷॻ͖׵͑ . . . . . . . . . . . . . . . . . . 81 4.4 νϡʔτϦΞϧͷίϐʔ . . . . . . . . . . . . . . . . . . . . . . . . 85 PyFoam ϥΠϒϥϦΛ࢖͏ํ๏ . . . . . . . . . . . . . . . . . . . 85 Python ͷඪ४ϥΠϒϥϦΛ࢖͏ํ๏ . . . . . . . . . . . . . . . . . 86 4.5 ܭࢉ࣮ߦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 PyFoam Λ࢖͏ํ๏ . . . . . . . . . . . . . . . . . . . . . . . . . 88 Allrun εΫϦϓτͱ Python ͷඪ४ϥΠϒϥϦΛซ༻͢Δํ๏ . . . . 91 όοΫάϥ΢ϯυ࣮ߦ . . . . . . . . . . . . . . . . . . . . . . . . 93 PyFoam ʹΑΔܭࢉ࣮ߦʢόοΫάϥ΢ϯυʣ . . . . . . . . . . . . 93 Allrun ࣮ߦʢόοΫάϥ΢ϯυʣ . . . . . . . . . . . . . . . . . . 95 4.6 ·ͱΊ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 ୈ 5 ষ PyFoam Λ༻͍ͨύϥϝʔλελσΟͷ࣮ફ 98 – v –
9. 8 ໨࣍ 5.1 ύϥϝʔλελσΟͷྲྀΕ . . . . . . . . . . . . . . . . . . . . . . . 98 5.2 ϓϩάϥϜͷ֓ཁ . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 5.3 ϨΠϊϧζ਺ҧ͍ʹΑΔ߅ྗ܎਺ . . . . . . . . . . . . . . . . . . . 106 5.4 ·ͱΊ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 ෇࿥ A gnuplot ʹΑΔάϥϑॲཧ 112 A.1 Re = 200 Ͱͷԁபͷ߅ྗ܎਺ . . . . . . . . . . . . . . . . . . . . . 112 ෇࿥ B OpenFOAM ͷ Tips 116 B.1 ϝογϡ඼࣭ͷ֬ೝ . . . . . . . . . . . . . . . . . . . . . . . . . . 116 B.2 ࿈ଓࣜͷޡࠩ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 B.3 y+ ͷ֬ೝ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 B.4 ྲྀྔͷ੔߹ੑ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 ෇࿥ C ιϑτͷΠϯετʔϧ 122 C.1 OpenFOAM ͷΠϯετʔϧ . . . . . . . . . . . . . . . . . . . . . 122 C.2 ParaView ͷΠϯετʔϧ . . . . . . . . . . . . . . . . . . . . . . . 124 C.3 Python ͷϥΠϒϥϦͷΠϯετʔϧ . . . . . . . . . . . . . . . . . 124 C.4 gnuplot ͷΠϯετʔϧ . . . . . . . . . . . . . . . . . . . . . . . . 126 ࢀߟจݙ 128 ͋ͱ͕͖ 130 – vi –
10. 9 ୈ 1 ষ ԁப·ΘΓͷྲྀΕͷ֓ཁ ͜ͷষͰ͸ɺԁப·ΘΓͷྲྀΕʹؔ͢Δجຊతͳ֓೦ʹ͍ͭͯ঺հ͠·͢ɻ ԁப·ΘΓͷྲྀΕ͸ཧ࿦తʹ΋޿͘ཧղ͞Ε͓ͯΓɺϨΠϊϧζ਺ʹΑͬͯྲྀ Εͷύλʔϯ͕มΘΔڵຯਂ͍ݱ৅͕஌ΒΕ͍ͯ·͢ɻ͜ΕΒͷ஌ࣝ͸ɺ࣍ষ Ҏ߱Ͱղઆ͢Δྲྀମղੳͷલఏ஌ࣝͰ͢ɻ 1.1 ϨΠϊϧζ਺ʹΑΔྲྀΕͷύλʔϯ ԁப·ΘΓͷྲྀΕ͸ϨΠϊϧζ਺ Re ͸ɺ୅ද௕͞ dʢԁப௚ܘʣ ɺ୅ද଎౓ UʢҰ ༷ྲྀ଎ʣ ɺಈ೪ੑ܎਺ ν ʹΑͬͯɺਤ 1.1 ͷΑ͏ʹྲྀΕͷ༷૬͕େ͖͘มΘΓ·͢ɻ ࣜ 1.1: ϨΠϊϧζ਺ Re = Ud ν ҎԼͷΑ͏ʹɺԁபपΓͷྲྀΕͷ༷૬͸ϨΠϊϧζ਺ʹΑͬͯ 4 ͭͷΧςΰϦʔʹ ෼ྨ͞Ε·͢ɻ – 1 –
11. 1 0 ୈ 1 ষ ԁப·ΘΓͷྲྀΕͷ֓ཁ 1.1 ϨΠϊϧζ਺ʹΑΔྲྀΕͷύλʔϯ Re < 1 (1) 1 < Re < 40 (2) 40 < Re < 500 (3) 1000 < Re (4) ˛ ਤ 1.1: ԁப·ΘΓͷྲྀΕ (1) ϨΠϊϧζ਺͕ 1 ఔ౓·ͨ͸ͦΕҎԼͷ৔߹͸ɺྲྀΕ͸্Լରশͷఆৗ૚ྲྀͰ ͋Γɺԁபഎޙʹ͸Ӕ͸ൃੜ͠ͳ͍ɻ (2) ϨΠϊϧζ਺͕໿ 40 ఔ౓ͷ৔߹͸ɺྲྀΕ͸্Լରশͷఆৗ૚ྲྀͰ͋Δ͕ɺԁ பഎޙʹ্Լରশͷ૒ࢠͷӔ͕ൃੜ͢Δɻ (3) ϨΠϊϧζ਺͕ 50ʙ500 ఔ౓ͷ৔߹͸ɺྲྀΕͷ্Լͷରশੑ่͕Εͯԁபഎޙ ͷӔ͸্Լʹ์ग़͠ɺޙྲྀʹपظతʹ্Լʹަޓʹ์ग़͞ΕΔΧϧϚϯӔྻΛ ܗ੒͢Δɻ (4) ϨΠϊϧζ਺͕ 1000 ఔ౓Ҏ্ʹͳΔͱɺޙྲྀʹ์ग़͞ΕΔӔ͸ཚΕɺ༷ʑͳ େ͖͞ͷӔΛؚΉΑ͏ʹͳΓɺཚྲྀͷ༷૬Λఄͯ͘͠Δɻ ྲྀମղੳͷ؍఺͔Β΋৮Ε͓͖ͯ·͢ɻ (1) ͱ (2) ͸૚ྲྀͷఆৗղੳͱͯ͠ྲྀମղੳΛߦ͏͜ͱ͕Ͱ͖·͢ɻ΋ͪΖΜඇఆ ৗղੳΛߦ͍ɺे෼͕࣌ؒܦաͨ݁͠ՌΛऩଋղͱͯ͠ٻΊͯ΋ྑ͍Ͱ͕͢ɺ͋·Γ ޮ཰తͰ͸͋Γ·ͤΜɻ (3) ͷΧϧϚϯӔྻ͸૚ྲྀͰ͋Γ·͕͢ɺӔ͕पظతʹ์ग़͞ΕΔඇఆৗੑ͕͋Δ ͨΊɺྲྀΕ͸ඇఆৗ૚ྲྀղੳͰߦ͏ඞཁ͕͋Γ·͢ɻඇఆৗͷݱ৅Λແཧʹఆৗղੳ Ͱߦ͏ͱɺऩଋղΛಘΒΕͳ͔ͬͨΓɺܭࢉ͕ൃࢄ͠΍͔ͬͨ͢Γ͠·͢ɻ (4) Ͱ͸ཚྲྀͷऔΓѻ͍͕ॏཁʹͳΓ·͢ɻେখ͞·͟·ͳӔ͕ݟΒΕΔͨΊɺ ϝογϡαΠζ͚ͩͰখ͞ͳӔΛ࠶ݱ͠Α͏ͱ͢Δͱɺ๲େͳϝογϡ਺ʹͳͬͯ͠ ·͍·͢ɻͦ͜ͰɺϝογϡαΠζΛখ͘͢͞Δ͜ͱͳ͘Ӕͷݱ৅Λ਺ཧతʹѻ͏ཚ – 2 –
12. 1 1 ୈ 1 ষ ԁப·ΘΓͷྲྀΕͷ֓ཁ 1.2 ෺ମʹಇ͘ྗͱετϩʔϋϧ਺ ྲྀϞσϧ͕ඞཁʹͳΓ·͕͢ɺద੾ʹྲྀΕΛ༧ଌͰ͖ΔཚྲྀϞσϧͷݚڀ͸ࠓ΋ߦΘ Ε͍ͯ·͢ɻ Ҏ্Λද 1.1 ʹ·ͱΊ·͢ɻ ˝ ද 1.1: ྲྀΕͷղੳͷछྨ ϨΠϊϧζ਺ ఆৗ or ඇఆৗ ཚྲྀϞσϧ Re < 1 ఆৗղੳ ૚ྲྀ 1 < Re < 40 ఆৗղੳ ૚ྲྀ 50 < Re < 500 ඇఆৗղੳ ૚ྲྀ 1000 < Re ඇఆৗղੳ ཚྲྀ ୈ 2 ষͰ͸ɺΧϧϚϯӔྻͷྲྀମղੳͷઃఆํ๏Λղઆ͠·͢ɻ·ͨɺୈ 5 ষͰ ͸ɺPython ࢖ͬͨύϥϝʔλελσΟͷதͰϨΠϊϧζ਺ΛมԽ͠ɺਤ 1.1 ͷΑ͏ ͳྲྀΕ͕ग़ݱ͢Δ͜ͱΛ֬ೝ͠·͢ɻ 1.2 ෺ମʹಇ͘ྗͱετϩʔϋϧ਺ ߅ྗ܎਺ͱετϩʔϋϧ਺ʹ͍ͭͯجຊతͳ͜ͱΛ֬ೝ͠ɺ࣍ষͷྲྀମղੳͱͷൺ ֱͷࡍͷલఏ஌ࣝΛ͓͓͖͑ͯ͞·͢ɻ ߅ྗͱ༲ྗ Ұ༷ͳྲྀΕʹஔ͔Εͨ෺ମʹ͸ɺਤ 1.2 ʹྲྀମ͔ΒྗΛड͚·͢ɻྲྀΕʹରͯ͠ฏ ߦͳํ޲ͷྗΛ߅ྗ D ͱ͍͍ɺਨ௚ํ޲ͷྗΛ༲ྗ L ͱ͍͍·͢ɻ – 3 –
13. 1 9 ୈ 2 ষ ԁப·ΘΓͷྲྀମղੳ ͜ͷষͰ͸ɺԁப·ΘΓͷྲྀΕΛղੳ͢ΔͨΊͷ OpenFOAM ͷઃఆํ๏ Λৄ͘͠ղઆ͠·͢ɻີ౓มԽΛ൐Θͳ͍ඇѹॖྲྀΕΛԾఆ͓ͯ͠Γɺܭࢉෛ ՙ͕௿͍͜ͱ͔Β࣮ݧͱͷൺֱ͕༰қͳ୊ࡐͰ͢ɻલষͰࣔͨ͠Α͏ʹɺϨΠ ϊϧζ਺͸ྲྀΕͷಛੑΛେ͖͘ࠨӈ͠·͢ɻຊষͰ͸ɺಛఆͷϨΠϊϧζ਺Λ ઃఆ͠ɺΧϧϚϯӔྻͷܗ੒Λ؍࡯͠·͢ɻղੳઃఆͷखॱΛཧղ͠ɺ࣮ݧͰ ಘΒΕͨ߅ྗ܎਺΍ετϩʔϋϧ਺ͱ OpenFOAM ͷ݁ՌΛൺֱ͢Δ͜ͱͰɺ ܭࢉ݁Ռͷଥ౰ੑΛݕূ͠·͢ɻ 2.1 ղੳͷ໨త ຊॻͰ͸ɺԁப·ΘΓͷྲྀΕΛ OpenFOAM Ͱղੳ͠·͢ɻ·ͨɺಘΒΕͨ߅ྗ ܎਺ͱετϩʔϋϧ਺͕࣮ݧ஋ͱҰக͍ͯ͠Δ͜ͱΛ֬ೝ͠·͢ɻ ԁப·ΘΓͷྲྀΕʹ͍ͭͯͷϙΠϯτ͸ҎԼͱͳΓ·͢ɻ • ྲྀΕͷ༷ࢠ͸ϨΠϊϧζ਺ʹΑͬͯมΘΔ • ϨΠϊϧζ਺ʹΑͬͯ߅ྗ܎਺͕มԽ͠ɺ࣮ݧͰ͔֬ΊΒΕ͍ͯΔ • ཚྲྀঢ়ଶͰ͸ɺ߅ྗ܎਺͸ Cd = 1.0 ∼ 1.2 • ཚྲྀঢ়ଶͰ͸ɺετϩʔϋϧ਺͸ St = 0.2 • ѹྗ܎਺͸ཧ૝ྲྀମͱ࣮ࡍͷྲྀମͰ͸ҟͳΔ • ྗֶత૬ࣅੑʹΑΓɺྲྀΕͷಛ௃͸ओʹϨΠϊϧζ਺Ͱܾ·Δ 2.2 OpenFOAM ͰͷγϛϡϨʔγϣϯ OpenFOAM Λ༻͍ͯਤ 2.1 ͷΑ͏ͳ 2 ࣍ݩͷԁப·ΘΓͷྲྀΕͷγϛϡϨʔγϣ ϯΛߦ͍·͢ɻ – 11 –
14. 2 0 ୈ 2 ষ ԁப·ΘΓͷྲྀମղੳ 2.2 OpenFOAM ͰͷγϛϡϨʔγϣϯ 0.15m/s d = 20 mm ˛ ਤ 2.1: ԁப·ΘΓͷྲྀΕͷγϛϡϨʔγϣϯ݁Ռ z ࣠ํ޲ʹແݶʹ௕͍ԁப͕͋Γɺz ࣠ํ޲ʹ͸Ұ༷Ͱ͋ΔͨΊɺx-y ฏ໘Λ੾Γ औͬͨ 2 ࣍ݩϞσϧͰ͢ɻ ղੳϑϩʔ ·ͣ͸ղੳΛ࣮ߦ͢Δ·ͰͷશମͷྲྀΕΛԡ͓͖͑ͯ͞·͠ΐ͏ɻ • ιϧόͷબ୒ • ࡞ۀϑΥϧμͷ࡞੒ • νϡʔτϦΞϧΛίϐʔ • ϝογϡੜ੒ (blockMesh) • ղੳઃఆ (OpenFOAM ͷઃఆϑΝΠϧ) • ܭࢉ࣮ߦ (OpenFOAM) • ղੳ݁ՌͷՄࢹԽ (ParaViewɺPython) ௨ৗɺղੳϑϩʔͷதʹ͸ղੳ༻ͷϞσϧ࡞੒ͷ޻ఔ͕͋Γ·͕͢ɺࠓճ͸ blockMesh ͰϝογϡΛอ࣋ͨ͠ܗঢ়Λ࡞੒͠·͢ͷͰ 3D-CAD Λ༻͍ͨϞσϧ࡞ ੒ͷ޻ఔ͸ෆཁͰ͢ɻblockMesh ͸ OpenFOAM ͷඪ४ϢʔςΟϦςΟʹؚ·Εͯ ͍ΔϓϩάϥϜͰɺOpenFOAM ΛΠϯετʔϧࡁͰ͋Ε͹৽ͨʹΠϯετʔϧͷख ଓ͖͸ෆཁͰ͢ɻ – 12 –
15. 2 1 ୈ 2 ষ ԁப·ΘΓͷྲྀମղੳ 2.2 OpenFOAM ͰͷγϛϡϨʔγϣϯ プリ処理 モデル作成 メッシュ作成 解析設定 計算実行 結果処理 blockMesh ソルバ ポスト処理 OpenFOAM ParaView Python ˛ ਤ 2.2: ղੳϑϩʔ ιϧόͷબ୒ OpenFOAM ͸ղ͖͍ͨ໰୊ʹదͨ͠ιϧόΛબ୒͢Δඞཁ͕͋Γ·͢ɻ୯૬ྲྀͰ Թ౓มԽͱີ౓มԽ͕ແࢹͰ͖ΔඇѹॖྲྀΕͱԾఆͯ͠ղੳΛߦ͏ͨΊɺͦΕʹద͠ ͨιϧόͷબ୒͕ඞཁͰ͢ɻԁப·ΘΓͷྲྀΕ͸ϨΠϊϧζ਺ʹΑͬͯྲྀΕͷঢ়ଶ͕ มΘΓ·͢ɻϨΠϊϧζ਺͕ Re = 40 ∼ 50 ҎԼ৔߹͸ɺఆৗྲྀΕͱͯ͠ѻ͍ɺͦΕ Ҏ্͸ඇఆৗྲྀΕͱͯ͠ѻ͍·͢ɻ ͜ͷΑ͏ͳ৚݅ʹదͨ͠ OpenFOAM ͷ୅දతͳιϧόͱͯ͠͸ද 2.1 ͷ΋ͷ͕ ڍ͛ΒΕ·͢ɻ ˝ ද 2.1: ඇѹॖྲྀΕͷ୅දతͳιϧό ιϧό໊ ҙຯ icoFoam ඇఆৗ૚ྲྀղੳιϧό pimpleFoam ඇఆৗཚྲྀղੳιϧό ʢPISO+SIMPLE ͷ PIMPLE ΞϧΰϦζϜʣ pisoFoam ඇఆৗཚྲྀղੳιϧόʢPISO ๏ʣ simpleFoam ఆৗཚྲྀղੳιϧόʢSIMPLE ๏ʣ ඇఆৗղੳΛߦ͏ͨΊ PIMPLE ๏ (PISO+SIMPLE) ΞϧΰϦζϜʹै͏ඇৗཚ ྲྀղੳͷιϧόͷ pimpleFoam Λ࢖͍·͢ɻ – 13 –
16. 2 6 ୈ 2 ষ ԁப·ΘΓͷྲྀମղੳ 2.5 ϝογϡ࡞੒ 2.5 ϝογϡ࡞੒ OpenFOAM ͷϝογϡ࡞੒ϢʔςΟϦςΟͰ͋Δ blockMesh Λ࢖ͬͯԁப· ΘΓͷϝογϡΛ 6 ໘ମͰ࡞੒͠·͢ɻ ࠷ऴతʹ͸ਤ 2.4 ͷΑ͏ʹͳΓ·͢ɻ 10d 10d 50d d = 20 mm ˛ ਤ 2.4: blocMesh ʹΑΔϝογϡ࡞੒ʢ׬੒ʣ ௚ܘ d ͸ 20 mmɺx × y ํ޲ʹ 40d × 50d ͷ֎෦ྖҬͱ͠·͢ɻԁபճΓ͸Ӕ͕ ൃੜ͢ΔͨΊࡉ͔͍ϝογϡʹ͠ɺԁபഎޙ͸ཚΕ͕ܹ͍ͨ͠Ίे෼޿͘ղੳྖҬΛ ͱ͍ͬͯ·͢ɻ ϝογϡ࡞੒͸ܗঢ়ͷରশੑΛར༻ͯ͠ɺ3 ஈ֊Ͱ࡞੒͍ͯ͠·͢ɻ - 1. blockMesh Ͱ 1/4 ϞσϧΛ࡞੒- 2. mirrorMesh ͰϛϥʔϝογϡΛ࡞ ੒- 3. extrudeMesh Ͱ֎෦ྖҬΛԡ͠ग़͢ গʑखؒͷ͔͔Δํ๏Λऔ͍ͬͯ·͕͢ɺ ͋ͱͰϝογϡ෼ׂ਺Λมߋͨ͠Γɺ ֎෦ ྖҬΛҾ͖Ԇ͹ͨ͠Γ͢Δͷʹָͳํ๏Λͱ͍ͬͯ·͢ɻ΋ͪΖΜ blockMesh ͷ ΈͰಉ༷ͷ͜ͱ͸ߦ͏͜ͱ͕Ͱ͖·͕͢ɺOpenFOAM ͷ͍Ζ͍ΖͳϢʔςΟϦςΟ Λମݧͯ͠ΈΔͷ΋ຊষͷ໨తͷͻͱͭͰ͢ɻ blockMeshDict Λฤू Ͱ͸ɺ blockMesh Ͱ 1/4 ϞσϧΛ࡞੒͠·͠ΐ͏ɻ – 18 –
17. 3 9 ୈ 2 ষ ԁப·ΘΓͷྲྀମղੳ 2.5 ϝογϡ࡞੒ } Xmax { type patch; nFaces 120; startFace 83480; } ) ڥք໘ͷ໊લ͸ਤ 2.13 ͷΑ͏ʹͳ͍ͬͯ·͢ɻ Xmin Ymin Ymax Xmax hole empty ˛ ਤ 2.13: createPatch ࣮ߦޙͷڥք໘ͷ໊લ extrudeMesh Λฤू ࠨଆ͔Βྲྀೖ৚݅Λ༩͑ɺԁபͷഎޙʢӈଆʣʹӔ͕Ͱ͖ΔͷͰ͕͢ɺղੳྖ Ҭ͕খ͍͞৔߹ɺٯྲྀ͕ൃੜͨ͠Γਫ਼౓͕ѱ͍ղੳ΍৔߹ʹΑͬͯ͸ܭࢉΤϥʔ ʹͳΔ͜ͱ΋͋Γ·͢ɻ΋͏Ұ౓͸͡Ί͔ΒϝογϡઃఆΛ͢Δͷ͸໘౗Ͱ͕͢ɺ extrudeMesh Λ࢖͑͹ಛఆͷ໘ͩԡ͠ग़͢͜ͱ͕Ͱ͖·͢ɻ extrudeMeshDict Λద౰ͳνϡʔτϦΞϧ͔Βίϐʔ͠·͢ɻ ˝ extrudeMesh – 31 –
18. 4 1 ୈ 2 ষ ԁப·ΘΓͷྲྀମղੳ 2.5 ϝογϡ࡞੒ 押し出 し方向 層数、厚み ˛ ਤ 2.14: extrudeMesh ࣮ߦޙͷϝογϡ Ҏ্Ͱ blockMesh ͷΈͰ 6 ໘ମϝογϡΛ࡞੒͕Ͱ͖·ͨ͠ɻ ϝογϡ඼࣭ͷ֬ೝ ϝογϡ࡞੒ޙʹ͸ඞͣ checkMesh Λ࣮ߦͯ͠ɺϝογϡ඼࣭ͱηϧ਺ͳͲΛ֬ ೝ͓͖ͯ͠·͢ɻ $ checkMesh Check mesh... Time = 0 Mesh stats points: 61760 ˡઅ఺ͷ਺ internal points: 0 faces: 122080 ˡ໘ͷ਺ internal faces: 60320 ˡ಺෦ͷ໘ͷ਺ cells: 30400 ˡηϧ਺ faces per cell: 6 boundary patches: 6 point zones: 0 face zones: 0 cell zones: 0 ...(লུ)... – 33 –
19. 7 4 ୈ 2 ষ ԁப·ΘΓͷྲྀମղੳ 2.7 ܭࢉ࣮ߦ (9) (10) ˛ ਤ 2.30: ઢͷଠ͞ͱϨϯμϦϯάͷઃఆ (9) Line Width Λ 4 ʹมߋ (10) Render Lines As Tubes ʹνΣοΫΛೖΕΔ ͜ΕʹΑΓɺઢ͕͸͖ͬΓ͠·ͨ͠ɻྲྀઢΛදࣔͨ͠ࡍʹɺ post.foam ͷද͕ࣔ ফ͍͑ͯΔͱࢥ͍·͢ɻ࠶౓දࣔͯ͠ྲྀઢͱ߹Θͤͯ֬ೝ͠·͠ΐ͏ɻ (12) (13) ˛ ਤ 2.31: post.foam ͷಁ໌౓ͷઃఆ – 66 –
20. 7 5 ୈ 2 ষ ԁப·ΘΓͷྲྀମղੳ 2.8 ܭࢉ݁Ռͷଥ౰ੑͷݕূ (11) post.foam Λදࣔ (12) Opacity Λ 0.5 ʹͯ͠ಁ໌౓Λௐ੔ Ҏ্Ͱྲྀ଎ίϯλͱྲྀઢΛ߹ΘͤͯՄࢹԽ͢Δ͜ͱ͕Ͱ͖·ͨ͠ɻ 2.8 ܭࢉ݁Ռͷଥ౰ੑͷݕূ ྲྀମղੳͷଥ౰ੑΛݕূ͢ΔͨΊʹɺ߅ྗ܎਺ Cd ɺετϩʔϋϧ਺ St ɺ͓Αͼѹ ྗ܎਺ͷ෼෍ Cp Λ࣮ݧ஋΍ཧ࿦ͱͷൺֱΛߦ͍·͢ɻϨΠϊϧζ਺ Re = 200 ʹ͓ ͍ͯɺ߅ྗ܎਺͸ Cd = 1.5ɺετϩʔϋϧ਺͸ St = 0.2 Ͱ͋Δ͜ͱ͕஌ΒΕ͍ͯ· ͢ɻ͜ΕΒͷ஋ͱɺࠓճͷྲྀମղੳ݁Ռ͕ۙࣅ͍ͯ͠Δ৔߹ɺղੳͷଥ౰ੑ͕֬ೝ͞ ΕΔ͜ͱʹͳΓ·͢ɻ Python ʹΑΔάϥϑԽͷίʔυͷղઆ͸ɺຊষͰѻ͍·ͤΜ͕ɺgithub ͷ Jupyter ϊʔτϒοΫΛެ։͍ͯ͠·͢ͷͰɺ͝ࢀߟ͍ͩ͘͞ɻ ߅ྗ܎਺ ߅ྗ܎਺͸Ϧετ 2.27 ͷΑ͏ʹ postProcessing/forces/0/coefficient.dat ʹग़ྗ ͞Ε͍ͯ·͢ɻ ˝ Ϧετ 2.27: postProcessing/forces/0/coefficient.dat # Force and moment coefficients # dragDir : (1.000000e+00 0.000000e+00 0.000000e+00) # sideDir : (0.000000e+00 0.000000e+00 -1.000000e+00) # liftDir : (0.000000e+00 1.000000e+00 0.000000e+00) # rollAxis : (1.000000e+00 0.000000e+00 0.000000e+00) # pitchAxis : (0.000000e+00 0.000000e+00 -1.000000e+00) # yawAxis : (0.000000e+00 1.000000e+00 0.000000e+00) # magUInf : 1.500000e-01 # lRef : 2.000000e-02 # Aref : 2.000000e-04 # CofR : (0.000000e+00 0.000000e+00 0.000000e+00) # # Time Cd ... Cl ... 0.00011999 1.716351e+03 ... 4.095318e-03 ... 0.000263965 1.781495e+01 ... -6.134204e-03 ... 0.000436705 9.864620e+00 ... 4.928078e-03 ... ... ʢ লུ ʣ ... – 67 –
21. 7 6 ୈ 2 ষ ԁப·ΘΓͷྲྀମղੳ 2.9 ετϩʔϋϧ਺ Ϧετ 2.27 ͷ Cd ͕߅ྗ܎਺ͳͷͰɺ͜ΕΛάϥϑʹͨ͠΋ͷ͕ਤ 2.32 Ͱ͢ɻ 0 5 10 15 20 25 Time (s) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Force Coefficient Drag Force Coefficient over Time Drag Force Coefficient ˛ ਤ 2.32: ߅ྗ܎਺ͷ݁Ռ ԁபޙํʹӔ͕์ग़͞Ε͔ͯΒ͸ɺ߅ྗ܎਺͕ৼಈ͓ͯ͠Γɺ15 s Ҏ্ͰฏۉΛͱ Δͱɺ ߅ྗ܎਺͸ Cd = 1.38 Ͱͨ͠ɻ͜ͷ஋͸ɺ ઌߦݚڀͰͷϨΠϊϧζ਺ Re = 200 ʹ͓͚Δ߅ྗ܎਺ Cd = 1.5 ʹۙ͘ɺܭࢉ݁Ռ͸֓Ͷྑ͍ҰகΛ͍ࣔͯ͠·͢ɻ 2.9 ετϩʔϋϧ਺ ετϩʔϋϧ਺͸ɺԁபޙํʹੜ੒͞ΕΔӔͷपظʹΑͬͯɺਤ 2.33 ͷΑ͏ʹɺྲྀ Εʹਨ௚ͳํ޲ͷྗʢ༲ྗʣ͕ৼಈ͢Δ༷ࢠΛද͠·͢ɻ͜ͷৼಈͷपظ f ͸ɺӔͷ ੜ੒पظͱҰக͍ͯ͠Δͱߟ͑ΒΕ·͢ɻ – 68 –
22. 7 7 ୈ 2 ষ ԁப·ΘΓͷྲྀମղੳ 2.9 ετϩʔϋϧ਺ 0 5 10 15 20 25 Time (s) 1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00 Lift Force Coeff Lift Force Coefficient over Time Lift Force Coefficient ˛ ਤ 2.33: ༲ྗ܎਺ͷ݁Ռ ͦ͜Ͱɺ༲ྗͷ࣌ܥྻσʔλʹରͯ͠ϑʔϦΤม׵Λߦ͍ɺಛ௃తͳप೾਺Λࢉग़ ͠·͢ɻ͜ͷप೾਺ΛӔੜ੒ͷपظͱͯ͠༻͍ɺετϩʔϋϧ਺ΛٻΊ·͢ਤ 2.34ɻ – 69 –
23. 7 8 ୈ 2 ষ ԁப·ΘΓͷྲྀମղੳ 2.10 ѹྗ܎਺ͷ෼෍ 0 1 2 3 4 5 Frequency (Hz) 0.0 0.1 0.2 0.3 0.4 0.5 Amplitude FFT of Cl FFT Amplitude Peaks ˛ ਤ 2.34: ༲ྗ܎਺ͷप೾਺ ਤ 2.33 ͷ༲ྗ܎਺Λ΋ͱʹɺ15 s Ҏ্ͰϑʔϦΤม׵ͨ݁͠Ռ͕ɺਤ 2.34 Ͱ͢ɻ ࠷େৼ෯Λ࣋ͭप೾਺͸ f = 1.48Hz Ͱ͢ɻҰ༷ྲྀ଎͸ U = 0.15 m/sɺ୅ද௕͞ d = 0.02 m ͳͷͰɺετϩʔϋϧ਺͸ɺSt = fd U = 1.47×0.02 0.15 = 0.2 ͱͳΓ·͢ɻ ͜ͷ஋͸ɺઌߦݚڀͰͷϨΠϊϧζ਺ Re = 200 ʹ͓͚Δετϩʔϋϧ਺ St = 0.2 ͱܭࢉ݁Ռ͸ྑ͍ҰகΛ͍ࣔͯ͠·͢ɻ 2.10 ѹྗ܎਺ͷ෼෍ ߅ྗ܎਺͸Ϧετ 2.28 ͷΑ͏ʹ postProcessing/patchProbes/0/cp ʹग़ྗ͞Ε ͍ͯ·͢ɻ ˝ Ϧετ 2.28: postProcessing/patchProbes/0/cp # Probe 0 (-0.01 0 0.005) at patch hole with a ... ʢ লུ ʣ ... ... ʢ লུ ʣ ... – 70 –
24. 7 9 ୈ 2 ষ ԁப·ΘΓͷྲྀମղੳ 2.10 ѹྗ܎਺ͷ෼෍ # Time 0 1 ... ʢ লུ ʣ ... 0.5 1.12171 1.03761 ... ʢ লུ ʣ ... 1 1.09921 1.02045 ... ʢ লུ ʣ ... ... ʢ লུ ʣ ... 29 1.11018 1.0566 ... ʢ লུ ʣ ... 29.5 1.10108 0.989234 ... ʢ লུ ʣ ... 30 1.10598 0.99292 ... ʢ লུ ʣ ... ਤ 2.35 ͸ɺྲྀମղੳͰಘΒΕͨ 3.5 ඵͱ 30 ඵͰͷԁप্Ͱͷѹྗ܎਺ͱϙςϯ γϟϧྲྀΕʹ͓͚Δѹྗ܎਺ Cp = 1−4 sin2 θ ͱͷൺֱΛ͍ࣔͯ͠·͢ɻϙςϯγϟ ϧྲྀΕʹ͓͍ͯ͸ɺԁபલޙͰѹྗ܎਺͕ରশͰ͋Δͷʹର͠ɺྲྀମղੳͷѹྗ܎਺ ͸ɺ30 ∼ 40 Ҏ্ͷ֯౓Ͱ͸ෛͷ஋Λऔ͓ͬͯΓɺԁபͷલޙͰѹྗ͕ରশͰ͸ͳ͍ ͜ͱ͕Θ͔Γ·͢ɻ͜ͷ͜ͱ͕ɺϙςϯγϟϧྲྀΕͰ͸߅ྗ͕ൃੜ͠ͳ͍ҰํͰɺ࣮ ࡍͷྲྀΕͰ͸߅ྗ͕ੜ͡ΔݪҼͱཧղͰ͖·͢ɻ 0 10 20 30 40 50 60 70 80 90 100110120130140150160170180 deg 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.5 1.0 Cp (Pressure Coefficient) Probe Data at Time 3.5s and 30s OpenFOAM Time 3.5s OpenFOAM Time 30s 1 4sin2 ( ) ˛ ਤ 2.35: ԁप্ͷѹྗ܎਺ͷ෼෍ ਤ 2.36 ͸ɺ3.5 ඵͱ 30 ඵͷѹྗ෼෍Λ͍ࣔͯ͠·͢ɻ࣮ࡍͷྲྀΕͰ͸ɺྲྀମͷ೪ ੑ͕ӨڹΛٴ΅͠ɺޙྲྀʹ͓͍ͯྲྀମͷണ཭΍Ӕͷܗ੒͕ݟΒΕ·͢ɻ͜ͷͨΊɺԁ பͷલޙͰѹྗ͕ࠩੜ͡ɺ߅ྗ͕ൃੜ͠·͢ɻ͔͜͜Βɺ೪ੑޮՌ͕ྲྀΕ৔ͷඇରশ – 71 –
25. 8 0 ୈ 2 ষ ԁப·ΘΓͷྲྀମղੳ 2.11 ղੳʹ͓͍ͯ஫ҙͨ͠఺ ੑΛҾ͖ى͜͠ɺ߅ྗ͕ੜ͡ΔཁҼͰ͋Δ͜ͱ͕ཧղͰ͖·͢ɻ ˛ ਤ 2.36: 3 ඵͱ 30 ඵͷԁப·ΘΓͷѹྗ෼෍ 2.11 ղੳʹ͓͍ͯ஫ҙͨ͠఺ ຊষͷղੳʹ͓͍ͯ஫ҙ͢΂͖఺ͱͯ͠ɺܭࢉ࣌ؒࠁΈ ∆t ʹ͍ͭͯه͓͖ͯ͠ ·͢ɻ ༲ྗͷ࣌ࠁྺΛݟΔͱɺ1 ඵؒʹ໿ 1.5 ճৼಈ͓ͯ͠Γɺ͜ͷৼಈͷ೾Λे෼ͱΒ ͑Δ͜ͱ͕Ͱ͖Δ͚ͩͷ࣌ؒࠁΈΛઃఆ͢Δඞཁ͕͋Γ·͢ɻ࠷௿Ͱ΋ 1 ͭࢁʢ൒प ظ෼ʣʹରͯ͠͸ɺ4 ఺ඞཁͩͱͯ͠΋ɺ࠷௿Ͱ΋ ∆t = 1 2×1.5 × 1 4 = 0.08 ҎԼͰͳ ͚Ε͹ͳΓ·ͤΜɻࠓճ͸ controlDict ͷ adjustTimeStep yes; ʹΑΓɺΫʔ ϥϯ਺ࢦఆͰ࣌ؒࠁΈΛࣗಈͰઃఆ͢ΔΑ͏ʹ͍ͯ͠·͢ɻΫʔϥϯ਺͸ܭࢉͷ҆ఆ ԽʹؔΘΔ΋ͷͰɺݱ৅ʹରͯ͠े෼ͳ࣌ؒࠁΈ͔ͱ͸ผͰߟ͑Δඞཁ͕͋Γ·͢ɻ maxCo 0.9; Ͱ࠷େΫʔϥϯ਺͸ 0.9 ͱ͍ͯ͠·͢ɻ Ϧετ 2.29 ͷΑ͏ʹ log.pimpleFoam ʹ࣌ؒࠁΈ͕ग़ྗ͞Ε͍ͯ·͢ɻ ˝ Ϧετ 2.29: log.pimpleFoam ... ʢ লུ ʣ ... Courant Number mean: 0.031598 max: 0.892659 deltaT = 0.000178571 Time = 0.3 PIMPLE: iteration 1 ... ʢ লུ ʣ ... – 72 –
26. 8 2 ୈ 3 ষ ྲྀମղੳʹΑΔྗֶత૬ࣅੑͷ ݕূ ͜ͷষͰ͸ɺྗֶత૬ࣅੑʹ͍ͭͯɺOpenFOAM Λ༻͍ͨྲྀମղੳͰ֬ೝ Λߦ͍·͢ɻୈ 1 ষͰղઆͨ͠Α͏ʹɺφϏΤ-ετʔΫεํఔࣜΛແ࣍ݩԽ ͢Δ͜ͱͰɺ͢΂ͯͷ෺ཧྔ͕ϨΠϊϧζ਺ʹू໿͞ΕɺྲྀΕ͕ϨΠϊϧζ਺ ͷΈʹґଘ͢Δ͜ͱ͕ࣔ͞Ε·͢ɻ͜͜Ͱ͸ɺ࣮ࡍʹྲྀମղੳΛ௨ͯ͜͡ͷཧ ࿦Λݕূ͠ɺڭՊॻͰֶͿ಺༰Λ͞Βʹਂ͘ཧղ͢Δମݧ͕Ͱ͖ΔΑ͏ʹ͠· ͢ɻཧ࿦తͳཧղΛ࣮ࡍͷղੳ݁ՌͱরΒ͠߹ΘͤΔ͜ͱͰɺྗֶత૬ࣅੑͷ ֓೦͕۩ମతʹͲͷΑ͏ʹద༻͞ΕΔ͔Λମײ͍ͯͩ͘͠͞ɻ 3.1 ϨΠϊϧζ਺ҧ͍ʹΑΔղੳ ϨΠϊϧζ਺Λ߹Θͤͨ 4 ͭͷղੳέʔεͰൺֱ͠·͢*1ɻ ˝ ද 3.1: ྲྀΕͷղੳͷछྨ ղੳέʔε ԁப௚ܘ d ྲྀ଎ U ϨΠϊϧζ਺ Re έʔε 1 2 mm 0.15 m/s 20 έʔε 2 0.2 mm 1.5 m/s 20 έʔε 3 20 mm 0.15 m/s 200 έʔε 4 2 mm 1.5 m/s 200 • ղੳ৚݅ ◦ ιϧόɿpimpleFoam ◦ ཚྲྀϞσϧɿlaminarʢཚྲྀϞσϧແ͠ʣ *1 ղੳ༻ͷϞσϧ͸ɺgithub ͷ 003_mechanicalSimilarity ʹެ։͍ͯ͠·͢ɻ – 74 –
27. 8 6 ୈ 3 ষ ྲྀମղੳʹΑΔྗֶత૬ࣅੑͷݕূ 3.3 ܭࢉ݁Ռ ケース1 ケース2 ケース3 ケース4 Re = 20 Re = 20 Re = 200 Re = 200 ˛ ਤ 3.1: ղੳέʔεҧ͍݁Ռ ·ͨɺ߅ྗ܎਺ͱετϩʔϋϧ਺ͷ݁ՌΛද 3.2 ʹࣔ͠·͢ɻϨΠϊϧζ਺ Re = 20 Ͱ͸ɺपظతͳӔੜ੒͕ى͜ΔղੳέʔεͰ͸ͳ͍ͨΊɺετϩʔϋϧ਺͸ ۭനʹ͍ͯ͠·͢ɻ ˝ ද 3.2: ߅ྗ܎਺ͱετϩʔϋϧ਺ͷ݁Ռ ղੳέʔε ߅ྗ܎਺ Cd ετϩʔϋϧ਺ St έʔε 1 2.18 - έʔε 1 2.18 - έʔε 1 1.38 0.20 έʔε 1 1.38 0.19 ྲྀ଎΍௚ܘ͕ҟͳͬͨͱͯ͠΋ɺϨΠϊϧζ਺͕ಉ͡Ͱ͋Ε͹ɺྲྀΕͷ༷ࢠ΍߅ྗ ܎਺ɺετϩʔϋϧ਺ͳͲͷ஋΋ಉ͡ʹͳΓ·͢ɻ͜Ε͸ɺ΋ͱͷ෺ཧݱ৅͕ྗֶత ૬ࣅੑʹج͍͍ͮͯΔͨΊͰ͢ɻྗֶత૬ࣅੑʹΑΓɺແ࣍ݩ਺Ͱ͋ΔϨΠϊϧζ਺ ͕Ұக͢ΔݶΓɺϞσϧͱ࣮෺ͷྲྀΕͷύλʔϯ΍ಛੑ͸ಉ͡ʹͳΔ͜ͱ͕อূ͞Ε ·͢ɻͦͷͨΊɺ࣮෺ʹ͓͍ͯ΋ɺϨΠϊϧζ਺Λج४ʹͯ͠ൺֱ͢Δ͜ͱͰɺ͞· ͟·ͳεέʔϧͰͷྲྀΕͷੑ࣭Λ༧ଌ͢Δ͜ͱ͕Ͱ͖·͢ɻ ͨͩ͠ɺ೤ྲྀମղੳͷΑ͏ʹුྗ΍ॏྗͷӨڹ͕͋Δ৔߹͸ɺϨΠϊϧζ਺͚ͩͰ ͸ෆे෼Ͱ͢ɻྫ͑͹ɺϑϧʔυ਺͸ɺॏྗͷӨڹΛड͚ΔྲྀΕ΍ࣗ༝ද໘͕ଘࡏ͢ ΔྲྀΕͷղੳʹ͓͍ͯॏཁͳࢦඪͰ͢ɻϑϧʔυ਺͕Ұக͢Δ͜ͱͰɺॏྗ΍ුྗͷ ӨڹΛड͚ΔྲྀΕͷ༷૬͕Ұக͠ɺྗֶత૬ࣅੑ͕੒ཱ͠·͢ɻ͜ΕʹՃ͑ͯɺ೤ྲྀ – 78 –
28. 1 0 6 ୈ 5 ষ PyFoam Λ༻͍ͨύϥϝʔλε λσΟͷ࣮ફ ͜ͷষͰ͸ɺୈ 4 ষͰֶΜͩ஌ࣝΛ͞ΒʹਂΊɺ࣮ફతʹ׆༻͍͖ͯ͠· ͢ɻϨΠϊϧζ਺ͷҧ͍ʹΑΔԁப·ΘΓͷ߅ྗ܎਺ͷมԽΛɺ࣮ࡍʹྲྀମղ ੳͰ֬ೝ͠·͢ɻϨΠϊϧζ਺Λม͑Δ࡞ۀ͸ɺPyFoam Λ࢖͑͹ޮ཰తʹ ࣮ߦՄೳͰ͢ɻ 5.1 ύϥϝʔλελσΟͷྲྀΕ ͜ͷষͰͷύϥϝʔλελσΟ͸ɺಈ೪ੑ܎਺Λύϥϝʔλͱͯ͠ɺϨΠϊϧζ਺ Λม͑ͨͱ͖ͷ߅ྗ܎਺ͱͷؔ܎ΛݟΔ͜ͱΛ໨తͱ͠·͢ɻ ҎԼͷϑΥϧμΛ࡞੒͠ϑΥϧμҠಈ͓͖ͯ͠·͢ɻ ˝ ղੳϑΥϧμ $ mkdir 005_cylinder2DParaSutdy ˡϑΥϧμͷ࡞੒ $ cd 005_cylinder2DParaSutdy ˡϑΥϧμͷҠಈ ύϥϝʔλελσΟͷϑϩʔ͸ਤ 5.1 ʹࣔ͢௨ΓͰ͢ɻϓϩάϥϜͷ࣮ߦ͸ Jupyter lab Λ࢖͍·͢ɻ ҎԼ͕खॱͰ͢ɻ 1. results ϑΥϧμΛ࡞੒ 2. original ͷϑΥϧμͷΫϩʔϯΛ࡞੒ 3. ಈ೪ੑ܎਺Λมߋ 4. Allrun εΫϦϓτ࣮ߦ 5. ࣍ͷܭࢉऴྃ·Ͱ଴ػ ͜ΕΒͷϓϩάϥϜ͸όοΫάϥ΢ϯυͰ࣮ߦ͞Ε͍ͯΔͨΊɺJupyter Lab ͷ – 98 –
29. 1 0 7 ୈ 5 ষ PyFoam Λ༻͍ͨύϥϝʔλελσΟͷ࣮ફ 5.1 ύϥϝʔλελσΟͷྲྀΕ ૢ࡞͕ՄೳͰ͢ɻ ޻෉ͱͯ͠͸ɺoriginal ϑΥϧμΛҰࣜίϐʔ͢Δͱɺϝογϡ৘ใΛؚΉ con- stant/polyMesh ϑΥϧμ΋ίϐʔ͞Ε·͢ɻϝογϡ৘ใ͸ൺֱతʹ༰ྔ͕େ͖͍ ͨΊɺ΋͠ original ϑΥϧμͱಉ͡ϝογϡ৘ใͰΑ͍৔߹ɺϑΥϧμશମΛίϐʔ ͢ΔͷͰ͸ͳ͘ɺγϯϘϦοΫϦϯΫͱͯ͠ࢀর͢Δ͜ͱͰ༰ྔΛ࡟ݮͰ͖·͢ɻί ϐʔઌͷϝογϡ৘ใ͸ৗʹ original ϑΥϧμͷϝογϡ৘ใΛࢀর͢Δ͜ͱʹͳΓ ·͢ɻ ·ͨɺAllrun ʹΑΔ࣮ߦ͸ɺܭࢉ͕׬ྃ͢Δ·Ͱ࣍ͷεΫϦϓτ͕଴ػ͢Δ࢓༷ͱ ͳ͍ͬͯ·͢ɻ .ipynb 計算終了まで待機 Re5 Re10 計算終了まで待機 計算終了まで待機 Allrun Re2 0 system constant polyMesh 操作可能 バックグラウンドで実行 ・・・ Allrun original 0 system constant polyMesh クローン results ˛ ਤ 5.1: ύϥϝʔλελσΟͷྲྀΕ ԁப·ΘΓͷྲྀΕʹ͓͍ͯ͸ɺϨΠϊϧζ਺ Re = 40 ۙลͰఆৗ͔Βඇఆৗʹͳ Δ͜ͱ͕Θ͔͍ͬͯΔͨΊɺද 5.1 ʹࣔ͢Α͏ʹ Re = 40 ҎԼͰ͸ɺఆৗղੳιϧ ό simpleFoam Λ࢖͍ɺͦΕΑΓେ͖͍ϨΠϊϧζ਺ Re Ͱ͸ɺඇఆৗղੳιϧό pimpleFoam ʹ੾Γସ͑ΔΑ͏ʹ͍ͯ͠·͢*1ɻ • ղੳ৚݅ ◦ ιϧόɿද 5.1 ◦ ཚྲྀϞσϧɿlaminarʢཚྲྀϞσϧແ͠ʣ *1 ϨΠϊϧζ਺͕খ͍͞ྖҬͰ͸ pimpleFoam ͕҆ఆʹܭࢉ͢ΔϝογϡΛ࡞੒͢Δͷ͕೉͔ͬ͠ ͨͨΊͰ͢ɻରྲྀ߲ͷεΩʔϜ΍ཚྲྀϞσϧΛ޻෉͢Δͱ҆ఆʹܭࢉͰ͖ΔՄೳੑ͸͋Γ·͕͢ɺ ޿ൣғͷϨΠϊϧζ਺ҬͰ౷Ұͤͨ͞ϞσϧΛͰ͖Δ͚ͩ࢖༻͔ͨͬͨ͠ࢥ͍͕͋Γɺࠓճ͸ఆৗ ͱඇఆৗͰιϧόΛ࢖͍෼͚Δ͜ͱʹ͠·ͨ͠ɻ – 99 –
30. 1 0 8 ୈ 5 ষ PyFoam Λ༻͍ͨύϥϝʔλελσΟͷ࣮ફ 5.2 ϓϩάϥϜͷ֓ཁ ◦ ಈ೪ੑ܎਺ɿද 5.1 ◦ ཭ࢄԽεΩʔϜɿ2 ࣍ਫ਼౓෩্ࠩ෼ • ڥք৚݅ ◦ inletɿྲྀ଎نఆ (0.15, 0, 0) ◦ outletɿࣗવྲྀग़ ◦ wallsɿ׈Γ৚݅ ◦ emptyɿ2 ࣍ݩ৚݅ ˝ ද 5.1: ղੳέʔε ղੳέʔε ಈ೪ੑ܎਺ ν ϨΠϊϧζ਺ Re ιϧό Re2 1.5 × 10−3 2 simpleFoam Re5 6.0 × 10−4 5 ˢ Re20 3.0 × 10−4 10 ˢ Re40 7.5 × 10−5 40 ˢ Re100 3.0 × 10−5 100 pimpleFoam Re200 1.5 × 10−5 200 ˢ Re500 6.0 × 10−6 500 ˢ Re1000 3.0 × 10−6 1000 ˢ Re2000 1.5 × 10−6 2000 ˢ Re5000 6.0 × 10−7 5000 ˢ Re10000 3.0 × 10−7 10000 ˢ ຊདྷͰ͋Ε͹ϨΠϊϧζ਺ Re = 1000 Ҏ্Ͱ͸ཚྲྀͷ༷૬͕ݦஶʹදΕͯ͘Δ ͨΊɺϝογϡαΠζ΍ཚྲྀϞσϧͷݕ౼Λे෼Λߦ͏ඞཁ͕͋Γ·͕͢ɺຊॻͷ ಺༰Λେ͖͘ҳ୤͢ΔͨΊɺࠓճ͸ཚྲྀϞσϧΛ࢖༻͠ͳ͍ൣғͷϨΠϊϧζ਺Ҭ Re = 2 ∼ 2000 ͱɺղੳϞσϧతʹ͸ద༻֎ Re = 5000, 10000 Ͱͷύϥϝʔλελ σΟΛߦ͍·ͨ͠*2ɻ 5.2 ϓϩάϥϜͷ֓ཁ ҎԼɺϓϩάϥϜͷશମΛࣔ͠·͢ɻ *2 ࣮͸ࠓճͷϞσϧͰ͸ Re = 5000 Ҏ্Ͱ͸ɺԁபޙํͷཚΕ͕ܹ͘͠ɺ extrudeMesh Ͱϝο γϡΛԆ௕ͨ͠෦෼ͰྲྀΕ͕ෆ҆ఆʹͳ͍ͬͯΔɻ – 100 –
31. 1 1 4 ୈ 5 ষ PyFoam Λ༻͍ͨύϥϝʔλελσΟͷ࣮ફ 5.3 ϨΠϊϧζ਺ҧ͍ʹΑΔ߅ྗ܎਺ simpleFoam pimpleFoam 40 1000 乱流モデル？ Re Re = 2 Re = 20 Re = 200 Re = 1000 ˛ ਤ 5.4: ϨΠϊϧζ਺ʹΑΔྲྀΕͷ༷ࢠ 5.3 ϨΠϊϧζ਺ҧ͍ʹΑΔ߅ྗ܎਺ ϨΠϊϧζ਺ҧ͍ʹΑΔύϥϝʔλελσΟΛऴ͑ͨͨΊɺϨΠϊϧζ਺ Re ͱ߅ ྗ܎਺ Cd ͷؔ܎Λ֬ೝ͠·͢ɻԁப·ΘΓͷ߅ྗ܎਺ͷۙࣅࣜʹ͍ͭͯ͸ɺ͞·͟ ·ͳఏҊ͕ͳ͞Ε͍ͯ·͢ [24]ɻ ࣜ 5.1 ͸ɺRe = 105 ∼ 106 ͷυϥοάΫϥΠγεݱ৅͸࠶ݱͰ͖ͳ͍΋ͷͷɺϨ Πϊϧζ਺ͷ޿͍ൣғͰྑۙ͘ࣅ͍ͯ͠·͢ɻ ࣜ 5.1: Sucker & Brauwer ͷۙࣅࣜ Cd = 1.18 + 6.8 R0 e .89 + 1.96 √ Re − 0.0004Re 1 + 3.63 × R2 e ࣜ 5.1 ͱ Cd = 1.2 ͷઢΛࣔ͠ͳ͕ΒɺOpeFOAM Ͱͷ݁ՌΛϓϩοτ͢Δϓϩά ϥϜ͕Ϧετ 5.2 Ͱ͢ɻ ˝ Ϧετ 5.2: ߅ྗ܎਺ͱϨΠϊϧζ਺ͷؔ܎Λϓϩοτ͢ΔϓϩάϥϜ import os import pandas as pd import numpy as np import matplotlib.pyplot as plt – 106 –
32. 1 1 8 ୈ 5 ষ PyFoam Λ༻͍ͨύϥϝʔλελσΟͷ࣮ફ 5.4 ·ͱΊ 100 101 102 103 104 105 106 Reynolds Number (Re) 10 1 100 101 102 Drag Coefficient (Cd) Cd Mean vs Re with Sucker & Brauer Comparison Cd Mean (Re <= 40, simpleFoam) Cd Mean (Re > 40, pimpleFoam) Sucker & Brauer Cd = 1.2 ˛ ਤ 5.5: OpenFOAM ʹΑΔϨΠϊϧζ਺ͱ߅ྗ܎਺ͷؔ܎ ͨͩ͠ɺϨΠϊϧζ਺͕ Re = 1000 Λ௒͑ΔྖҬʹ͓͍ͯ͸ɺࣜ 5.1 ͱͷࠩҟ͕େ ͖͘ͳΔ܏޲͕ݟΒΕ·͢ɻ 5.4 ·ͱΊ ຊষͰ͸ɺPyFoam Λ༻͍ͨ OpenFOAM ʹΑΔύϥϝʔλελσΟͷ࣮ફྫͱ ͯ͠ɺ2 ࣍ݩԁப·ΘΓͷ߅ྗ܎਺ͱϨΠϊϧζ਺ͷؔ܎ੑʹ͍ͭͯղੳΛߦ͍·͠ ͨɻୈ 4 ষͰֶΜͩجૅతͳૢ࡞ΛԠ༻͠ɺϨΠϊϧζ਺ΛมԽͤͨ͞ෳ਺έʔεͷ ޮ཰తͳղੳ͕ՄೳͰ͋Δ͜ͱΛΈ·ͨ͠ɻ ղੳ݁Ռ͸ɺϨΠϊϧζ਺ͷ޿ൣғͰࣜ 5.1 ͷཧ࿦ࣜͱྑ޷ʹҰக͓ͯ͠Γɺຊղ ੳϞσϧͷଥ౰ੑΛ֬ೝͰ͖·ͨ͠ɻಛʹɺϨΠϊϧζ਺͕ Re = 40 ҎԼͷఆৗྲྀ ΕྖҬͱɺͦΕҎ্ͷඇఆৗྖҬͰιϧόΛ੾Γସ͑Δ͜ͱͰɺ਺஋తͳ҆ఆੑͱܭ ࢉਫ਼౓Λཱ͍྆ͤͯ͞·͢ɻ ҰํͰɺϨΠϊϧζ਺ Re = 1000 Ҏ্ͷྖҬͰ͸ࣜ 5.1 ͱͷࠩҟ͕େ͖͘ͳΓɺ ΑΓߴਫ਼౓ͳཚྲྀϞσϧ΍ϝογϡղ૾౓ͷݟ௚͕͠ඞཁͱͳΔՄೳੑ͕ࣔࠦ͞Ε – 110 –
33. 1 3 8 ͋ͱ͕͖ ຊॻΛ͝ߪೖ͍͖ͨͩ͋Γ͕ͱ͏͍͟͝·͢ɻຊॻͰ͸ɺԁப·ΘΓྲྀΕΛର৅ʹ ྲྀମղੳʹ͍ͭͯղઆΛߦ͍·ͨ͠ɻࠓճ͸ OpenFOAM ͷଟ༷ͳػೳͷҰ෦ͷΈ Λ͝঺հͰ͖·͕ͨ͠ɺ͞Βʹৄࡉͳઆ໌͕ඞཁͳ఺΋͋Δ͔ͱࢥ͍·͢ɻ ݫີղΛٻΊΔͷ͕ࠔ೉ͳղੳର৅Ͱ͸ɺγϛϡϨʔγϣϯΛ௨ͯ͡ݱ৅Λཧղ͢ Δ͜ͱ͕ඇৗʹॏཁͩͱஶऀ͸ߟ͍͑ͯ·͢ɻͦͷͨΊɺຊॻͰ͸ཧ࿦ͱ࣮ݧͰͷݚ ڀ͕੝Μͳԁப·ΘΓͷྲྀΕΛ୊ࡐʹબͼ·ͨ͠ɻγϛϡϨʔγϣϯͷଥ౰ੑΛ֬ೝ ͢ΔͨΊʹ͸ɺ࣮ݧσʔλ΍ط஌ͷݫີղͱͷൺֱΛߦ͍ɺ݁Ռͷ৴པੑΛݕূ͢Δ ඞཁ͕͋Γ·͢ɻຊॻΛ͖͔͚ͬʹࣗ͝਎ͰγϛϡϨʔγϣϯ͍ͨ͠಺༰ʹ౰ͯ͸Ί ͍͚ͯͨͩΕ͹ͱࢥ͍·͢ɻ Ӊ஦ʹೖͬͨΧϚΩϦ • Xɿhttps://x.com/t_kun_kamakiri • ϒϩά URLɿhttps://takun-physics.net/: – 130 –
34. 1 3 9 OpenFOAM ࣗ୐ͰۃΊΔྲྀମղੳ 2024 ೥ 11 ݄ 2 ೔ɹ ver 1.0 ʢٕज़ॻయ 17ʣ ஶɹऀ Ӊ஦ʹೖͬͨΧϚΩϦ ൃߦऀ ΧϚΩϦ ࿈བྷઌ https://takun-physics.net/ https://x.com/t_kun_kamakiri ҹ࡮ॴ Ӊ஦ʹೖͬͨΧϚΩϦ © 2024 Ӊ஦ʹೖͬͨΧϚΩϦ (powered by Re:VIEW Starter)