ᆒ୍䛺⢒ᗘ᮲௳䜢ᣢ䛴㒔ᕷ䜻䝱䝜䝢䞊䛾ୖ✵䛻ᙧᡂ䛥䜜䜛⤌⧊ᵓ㐀䛜
䝢䞊䜽㢼㏿䛾Ⓨ⏕䛻ཬ䜌䛩ᙳ㡪
Effect of coherent structure above urban canopy with heterogeneous roughness condition on occurrence of peak velocity
Ἑྜ㻌 ⱥᚨ䠍䠅㻌 㻌 ⏣ᮧ㻌 ဴ㑻䠎䠅㻌 㻌 Hidenori KAWAI1) and Tetsuro TAMURA2)
ABSTRACT
㻌 㻌 In this study, LES results for turbulent field around building arrays are compared with wind tunnel experiments. Then, computations for cases with different heterogeneity of roughness are carried out in order to show the effect of coherent structure in each case on occurrence of peak velocity. As a result, coherent structure with low momentum region appears above building blocks, and its surrounding regions with large velocity cause peak velocity dominantly. In addition, roll-type coherent structure with scale of boundary layer thickness appears in upper heights of turbulent boundary layer, and it is suggested that air parcel with large velocity in upper heights of turbulent boundary layer contributes to occurrence of peak velocity by connecting with the regions with high velocity region above building blocks.
Key Words: LES, Peak velocity, Urban canopy, Coherent structure 䠍䠊䛿䛨䜑䛻 ㏆ᖺ㒔ᕷ䜢㏻㐣䛩䜛ྎ㢼䛻䜘䜛ᙉ㢼⿕ᐖ䛷䛿እᮦ䛾ᦆയ䛜ᩘከ䛟☜ㄆ䛥䜜䛶䛔䜛䚹䛣䜜䜙䛾⿕ᐖ䛿」㞧䛺⢒ ᗘᙧ≧䜢ᣢ䛴㒔ᕷ䜻䝱䝜䝢䞊ෆእ䛾ὶᵓ㐀䛻㉳ᅉ䛩䜛䛸⪃䛘䜙䜜䜛䚹䛣䛾䜘䛖䛺ᘓ≀䛾እᮦ䛻స⏝䛩䜛㢼ᅽຊ 䛿 CFD䠄ᩘ್ὶయຊᏛ䠅䜔㢼Ὕᐇ㦂䛻䛚䛔䛶䝢䞊䜽㢼ᅽಀᩘ䜢ホ౯䛩䜛䛣䛸䛻䜘䜚⪏㢼ᛶ⬟䛜ホ౯䛥䜜䛶䛔䜛䛜䠈 ᆒ୍䛺⢒ᗘ᮲௳䜢᭷䛩䜛ᐇ㝿䛾㒔ᕷቃ⏺ᒙ䛾୰䛷䛿䠈ᘓ≀䜈䛾᥋㏆ὶ䛾≉ᛶ䛸䛧䛶㢼㏿䛾⣔ิኚື䛾≉ᛶ䜢᫂ 䜙䛛䛻䛩䜛ᚲせ䛜䛒䜛䚹 䛣䛾䜘䛖䛺㒔ᕷ䜻䝱䝜䝢䞊ෆእ䛾ὶᵓ㐀䛻䛴䛔䛶䛿䠈ὶయຊᏛⓗ䛺どⅬ䛛䜙䝤䝻䝑䜽⩌ୖ䛾⤌⧊ᵓ㐀 1䠅䜔ᆒ ୍䛺⢒ᗘ᮲௳ୗ䛾ὶ≉ᛶ䠄䛘䜀䠈Takimoto 䜙2䠅䠅䛜☜ㄆ䛥䜜䛶䛚䜚䠈䛣䛾䜘䛖䛺⤌⧊ᵓ㐀䛿㠀ᐃᖖ䛺㢼㏿䛾ᛴ⃭ 䛺ኚ䜢䜒䛯䜙䛩䛣䛸䛜▱䜙䜜䛶䛔䜛䠄䛘䜀䠈Oikawa 䜙 3䠅䠅䚹䜎䛯䠈➹⪅䜙䛿ᮾி㒔䛾ᗈᇦᕷ⾤ᆅ䜢ᑐ㇟䛸䛧䛶㒔ᕷ ቃ⏺ᒙෆ䛾⤌⧊ᵓ㐀䛜䝢䞊䜽㢼㏿䛾Ⓨ⏕䛻ཬ䜌䛩ᙳ㡪䜢᫂䜙䛛䛻䛧䛶䛝䛯4)䚹䛧䛛䛧䛺䛜䜙䠈ᆒ୍䛺⢒ᗘ䜢᭷䛩䜛 㻌 䠍䠅㻌 ᮾிᕤᴗᏛ㻌 ⎔ቃ䞉♫⌮ᕤᏛ㝔㻌 ຓᩍ㻌 䠄䛈226-8502㻌 ᶓᕷ⥳༊㛗ὠ⏣⏫ 4259䠅 㻌2)㻌 ᮾிᕤᴗᏛ ྡᩍᤵ 䠄䛈226-8502㻌 ᶓᕷ⥳༊㛗ὠ⏣⏫ 4259䠅
ᐇ㝿䛾㒔ᕷቃ⏺ᒙ䛻䛚䛔䛶䝢䞊䜽㢼㏿䛾≉ᚩ䜢୍⯡䛧䛶䛔䛟䛯䜑䛻䛿䠈⢒ᗘ䛾㧗䛥䜔㓄⨨䛾䜀䜙䛴䛝䛸䛔䛳䛯⾤ ༊䛾ᬑ㐢ⓗ䛺≉ᚩ䛸⤌⧊ᵓ㐀䠈䝢䞊䜽㢼㏿䛾Ⓨ⏕せᅉ䛾㛵ಀ䜢᫂䜙䛛䛻䛧䛶䛔䛟ᚲせ䛜䛒䜛䚹 ᮏ◊✲䛷䛿䠈⢒ᗘ᮲௳䛾ᆒ୍ᛶ䛜␗䛺䜛ᘓ≀⩌䜢ᑐ㇟䛸䛧䛯 LES 䛻䜘䜛ὶゎᯒ䜢ᐇ䛧䠈㒔ᕷ䜻䝱䝜䝢䞊䛾 ୖ✵䛻ᙧᡂ䛥䜜䜛⤌⧊ᵓ㐀䛜䝢䞊䜽㢼㏿䛾Ⓨ⏕䛻ཬ䜌䛩ᙳ㡪䜢᫂䜙䛛䛻䛩䜛䚹 䠎䠊㒔ᕷ䜻䝱䝜䝢䞊ෆእ䛾ὶሙ䛻㛵䛩䜛ゎᯒ᪉ἲ䛸䛭䛾᳨ド㻌 㻞㻚㻝㻌 ὶゎᯒ᪉ἲ㻌 ᮏ◊✲䛷䛿㒔ᕷ䜻䝱䝜䝢䞊䜢ᶍᨃ䛧䛯ᘓ≀⩌䜢ᑐ㇟䛸䛧䛯 LES 䛻䜘䜛ὶゎᯒ䜢ᐇ䛩䜛䚹ᨭ㓄᪉⛬ᘧ䛿䝣䜱䝹 䝍᧯స䜢䛧䛯㠀ᅽ⦰ᛶ䛾㐃⥆䛾ᘧ䠄ᘧ䠄䠍䠅䠅䛸 Stokes ᪉⛬ᘧ䠄ᘧ䠄2䠅䠅䛷䛒䜛䚹䝣䜱䝹䝍᧯స䛻䜘䛳䛶
Navier-Stokes ᪉⛬ᘧ䛻⏕䛨䜛 SGS䠄Sub Grid Scale䠅ᛂຊ䜢⾲⌧䛩䜛 SGS 䝰䝕䝹䛻䛴䛔䛶䛿 ⢓ᛶ㏆ఝ䠄ᘧ(4)䠅䛻ᇶ䛵䛟ᶆ
‽ Smagorinsky 䝰䝕䝹 (ᘧ(6))䜢⏝䛩䜛䚹䛺䛚䠈ቨ㠃㏆ഐ䛷䛿 ⢓ᛶ䛜㐣䛸䛺䜛䛣䛸䛛䜙䠈Van Driest 䛾ῶ⾶㛵
ᩘ䠄ᘧ(7)䠅䜢䛨䜛䚹䛺䛚䠈ᨭ㓄᪉⛬ᘧ䛾㞳ᩓ䛻䛿㠀ᵓ㐀᱁Ꮚ䛻ᇶ䛵䛟᭷㝈య✚ἲ䜢⏝䛧䠈⛣ὶ㡯䛻䛴䛔䛶䛿 2 ḟ⢭ᗘ䛾୰ᚰᕪศ䛸 TVD 䝇䜻䞊䝮䛾䝤䝺䞁䝗ᘧ䠈ᣑᩓ㡯䛿 2 ḟ⢭ᗘ䛾୰ᚰᕪศ䝇䜻䞊䝮䛻䜘䜚㞳ᩓ䛧䛶䛔䜛䚹䜎 䛯㛫㡯䛾✚ศ䛻䛿PISO 䜰䝹䝂䝸䝈䝮䛻ᇶ䛵䛟 Euler 㝜ゎἲ䜢⏝䛔䛯䚹 ቃ⏺᮲௳䛿ὶධ㠃䛻ὶධኚື㢼䛾䝕䞊䝍䝧䞊䝇䛾㏿ᗘ䝧䜽䝖䝹䜢┤᥋䛘䠈ቨ㠃䛾ቃ⏺᮲௳䛻䛿 Spalding ๎䛻 ᇶ䛵䛟ቨ㛵ᩘ䜢䛘䛶䛔䜛䚹ᅽຊ䛻㛵䛧䛶䛿ฟཱྀቃ⏺䜢ᅽຊᅛᐃ䛸䛧䠈䛭䛾䛾ቃ⏺㠃䛻䛿Neumann ᮲௳䜢䛘䛶 䛔䜛䚹 డ௨ డ௫
ൌ Ͳ
䞉䞉䞉 (1) డ௨ഥ డ௧
డ௨ഥ௨ഥೕ డ௫ೕൌ െ
ଵ ఘ డҧ డ௫
డ డ௫ೕ൫ʹߥܵҧ
൯ െ
డఛೕ డ௫ೕ㻌 㻌 㻌 㻌 㻌 䞉䞉䞉㻌 㻔㻞㻕㻌 ߬ ൌ ݑതതതതത െ ݑതపݑఫ ݑതൌ ʹߥௌீௌܵҧ㻌 㻌 㻌 㻌 㻌 䞉䞉䞉㻌 㻔㻟㻕㻌 െ߬ ൌ ݏߥௌீௌܵҧ㻌 㻌 㻌 㻌 㻌 䞉䞉䞉㻌 㻔㻠㻕㻌 㻌 㻌 㻌ܵҧ ൌଶଵ൬డ௨ഥడ௫ೕ డ௨ഥడ௫ೕ൰㻌 㻌 㻌 㻌 㻌 䞉䞉䞉㻔㻡㻕㻌 ߥௌீௌൌ ሺܥ௦߂ҧሻ ଶȁܵҧȁ䚸ȁܵҧȁ ൌ ටʹܵҧܵҧ㻌 㻌 㻌 㻌 㻌 㻌 㻌 䞉䞉䞉㻌 㻔㻢㻕㻌 㻌 㻌 㻌 㻌݂ఓൌ ͳ െ ݁ݔሺെݕାȀʹሻ㻌 ʞ㻌 㻔㻣㻕㻌 㻌 ⾲ 㻝㻌 ゎᯒ᮲௳㻌 㻌 ⾲䠎㻌 ቃ⏺᮲௳㻌 㻌 㻞㻚㻞㻌 㢼Ὕᐇ㦂䛾ᴫせ㻌 ᮏ◊✲䛷䛿ὶゎᯒᡭἲ䛾ጇᙜᛶ䜢᳨ウ䛩䜛䛯䜑䛻 Uehara 䜙 5)䛜ᐇ䛧䛯㒔ᕷ䝇䝖䝸䞊䝖䜻䝱䝙䜸䞁䠄ᅗ 1䠅䛻㛵 䛩䜛㢼Ὕᐇ㦂⤖ᯝ䛸䛾ẚ㍑䜢⾜䛳䛯䚹Uehara 䜙5)䛾ᐇ㦂䛷䛿ᩚᙧ㓄⨨䛾ᶍᆺ䝃䜲䝈䛾ᘓ≀䠄0.1m×0.1m×0.1m, ⾤༊ ᶍᆺ㡿ᇦ䛻䛚䛡䜛ᘓ≀䛾㧗䛥ܪ௩=0.1䠅⩌䛾⾤༊ᶍᆺ䜢ᐇ㦂ᑐ㇟䛸䛧䛶䛚䜚䠈❧᪉యᙧ≧䛾ᘓ≀䛾㛫㝸䛿ὶ᪉ྥ 0.1m䠈䝇䝟䞁᪉ྥ 0.05m 䛷䛒䜛䚹⾤༊ᶍᆺ䛾㢼ୖ䛻䛿༓㫽㓄⨨䛾䝷䝣䝛䝇䝤䝻䝑䜽䠄0.1m×0.1m×0.05m䠅䜢ὶ᪉ྥ Code OpenFOAM(Ver. 6.0) Algorithm PISOTime integration Euler implicit Spatial discretization
(Convection term) 2ndorder central+ 1stUpwind (TVD limiter) SGS model Smagorinsky model(Cs=0.1)
Inlet Velocity DirichletʤGiven from inflow turbulence databaseʥ Pressure Neumann Outlet Velocity Neumann
Pressure P=0
Side/Top Free-Slip
0.1m䠈䝇䝟䞁᪉ྥ 0.1m 䛾㛫㝸䛷㓄⨨䛧䠈ὶධẼὶ䜢సᡂ䛧䛶䛔䜛䚹ὶධẼὶ䛾䝥䝻䝣䜯䜲䝹䛻䛴䛔䛶䛿ୖὶഃ䛾⢒
ᗘ䝤䝻䝑䜽⩌ᚋ➃䛷 ᐃ䛥䜜䛶䛚䜚䠈⾤༊ᶍᆺ䛾䜻䝱䝜䝢䞊ෆእ䛾㢼㏿䛻䛴䛔䛶䛿LDA䠄Laser Doppler Anemometer䠅
ィ 䛻䜘䜚ὶ≉ᛶ䛜᫂䜙䛛䛻䛥䜜䛶䛔䜛䚹 㻌 ᅗ 㻝㻌 ᳨ド䛷⏝䛔䜛㢼Ὕᐇ㦂䛾䝰䝕䝹䛾ᴫせ䠄㼁㼑㼔㼍㼞㼍 䜙㻞㻕䠅㻌 㻌 㻞㻚㻟 㢼Ὕᐇ㦂䛸䛾᳨ド⤖ᯝ㻌 LES 䛷䛿䠈⾤༊䝰䝕䝹䜢㢼Ὕᐇ㦂䛾⾤༊ᶍᆺ䛸ྠ䛨ᘓ≀䝃䜲䝈䛸㓄⨨㛫㝸䛷ὶ᪉ྥ䛻 15 ิ䠈䝇䝟䞁᪉ྥ䛻 18 ิ㓄⨨䛧䛯ゎᯒ䜢ᐇ䛧䛯䚹ゎᯒ㡿ᇦ䛾䝃䜲䝈䛿ὶ᪉ྥ4.9䡉䠈䝇䝟䞁᪉ྥ 3m䠈㧗䛥᪉ྥ 1.6m 䛷䛒䜛䚹ᮏ◊✲䛷 䛿㔝⃝䜙6)䛾‽࿘ᮇቃ⏺᮲௳䛾䝗䝷䜲䝞㡿ᇦ䛾ゎᯒ䛻䜘䜚⢒㠃ୖ䛾ὶቃ⏺ᒙ䜢⌧䛧䠈䛭䛣䛷సᡂ䛥䜜䛯Ẽὶ䜢䝇 䝖䝸䞊䝖䜻䝱䝙䜸䞁䝰䝕䝹䛾㢼ୖഃ䛛䜙ὶධቃ⏺᮲௳䛸䛧䛶᥋⥆䛧䛶䛔䜛䚹䠄᥋⥆⨨䛻䛴䛔䛶䛿ᅗ 1 䜢ཧ↷䠅䚹ゎᯒ 㡿ᇦ䛿䝔䝖䝷᱁Ꮚ䜢䝧䞊䝇䛸䛧䛯㠀ᵓ㐀᱁Ꮚ䛷ศ䛥䜜䛶䛚䜚䠈ቨ㠃ቃ⏺䛻䛿3 ᒙ䛾ቃ⏺ᒙ䝺䜲䝲䝯䝑䝅䝳䜢ᤄධ䛧䛶 䛔䜛䠄ᅗ 2䠅䚹✵㛫ゎീᗘ䛿ቃ⏺ᒙ䝺䜲䝲䛾ཌ䛥䛜᭱ᑠ䛷⣙ 0.0025m䠄ܪ௩/40䠅,䝔䝖䝷せ⣲䛜᭱ᑠ䛷⣙ 0.005m 䠄ܪ௩/20)䛷䛒䜛(⾲ 3)䚹 㻌 ᅗ 㻞㻌 ゎᯒ㡿ᇦ䛸᱁Ꮚศ㻌 ⾲ 㻟㻌 ィ⟬᮲௳㻌 㻌 ḟ䛻䠈ᅗ3 䛻ὶධ⨨䛸㒔ᕷ䜻䝱䝜䝢䞊ෆ䠄ᅗ 1 䛻♧䛩ᆅⅬ X䠅䛻䛚䛡䜛㢼㏿ศᕸ䛾ẚ㍑䜢♧䛩䚹ᅗ 3(a)䛻♧䛩䜘 䛖䛻LES 䛾ᖹᆒ㢼㏿䛿ᆅ⾲䛾㏆ഐ䛻䛚䛔䛶ᐇ㦂䛾᪉䛜䜔䜔㢼㏿䛜ప䛟䛺䛳䛶䛔䜛䛜䠈ቃ⏺ᒙཌ δ 䛿䛚䜘䛭 7.0ܪ௩ 䛷䛒䜚䠈ݖ ܪΤ ௩=6 ௨ୗ䛾ᖹᆒ㢼㏿䛾ศᕸ䛿᪥ᮏᘓ⠏Ꮫ䛾ᘓ⠏≀Ⲵ㔜ᣦ㔪 7)䛻♧䛥䜜䛯ᆅ⾲㠃⢒ᗘ༊ศⅢ䛻ᑐ ⾤༊ᶍᆺ䠄XӍ12m䛻㓄⨨䠅 1䝤䝻䝑䜽䠖0.1m㽢0.1m㽢0.1m ࣈࣟࢵࢡࡢ㓄⨨㛫㝸㸸ὶ㏿᪉ྥ0.1m㸪ࢫࣃࣥ᪉ྥ0.05mࡢᩚᙧ㓄⨨ ὶ㏿᪉ྥ䠖15ิ䠈䝇䝟䞁᪉ྥ䠖6ิ /(6࡛ࡢὶධኚື㢼᥋⥆⨨ ᩿㠃ᅗ ᆅⅬ;㸸/'$ィ ⨨ 㻸㻱㻿䛷䛾ゎᯒ⠊ᅖ Inflow ⢒ᗘ䝤䝻䝑䜽䠄2m䠘X䠘12m䛻㓄⨨䠅 1䝤䝻䝑䜽䠖0.1m㽢0.1m㽢0.05m ࣈࣟࢵࢡࡢ㓄⨨㛫㝸㸸ὶ㏿᪉ྥ0.1m㸪ࢫ ࣃࣥ᪉ྥ0.1mࡢ༓㫽㓄⨨ 0m 2m 11.8m 12m 13m 㢼Ὕᐇ㦂࡛ࡢ᥋㏆ὶィ ⨨ 䝖䝸䝑䝢䞁䜾䝣䜵䞁䝇 ܺሾ݉ሿ ᆅⅬ;㸸/'$ィ ⨨ ࠙Ỉᖹ㠃ࠚ Vol. 3: 4.9 x 3.0 x 1.6[m] Vol. 2: 3.15ʹ2ʹ1[m]
0.
6m
0.6m
ᣑᅗ ᣑᅗ Vol. 1: 2.55 ʹ1ʹ0.5[m]2.55m
1.75m
0.5m
0.5m
Domain size
(x,y,z)=(4.9m x 3.0m x 1.6m)
Time increment
1.0x10
-3[s]
Mesh size
Tetra mesh(Vol.1)ʁ0.005mʤܪ
௩/20ʥ
Tetra mesh(Vol.2)ʁ0.01mʤܪ
௩/10ʥ
Tetra mesh(Vol.3)ʁ0.02mʤܪ
௩/5ʥ
ᛂ䛧䛶䛔䜛䚹ὶᙉᗘ䛻䛴䛔䛶䛿Uehara 䜙䛾ᐇ㦂䛻䛚䛔䛶ᆅ⾲㏆䛷ߪ௨Ȁݑכ=2 䛾ὶᙉᗘ䛜♧䛥䜜䛶䛚䜚䠈LES 䛾 ὶධ᮲௳䛸䜋䜌୍⮴䛧䛶䛔䜛䚹ᅗ3(c)䛻䝇䝖䝸䞊䝖䜻䝱䝙䜸䞁୰ኸ㒊䛻⨨䛩䜛ᆅⅬ X 䛻䛚䛡䜛㢼Ὕᐇ㦂䛸 LES 䛾ᖹ ᆒ㢼㏿䛾ẚ㍑⤖ᯝ䜢♧䛩䚹㒔ᕷ䜻䝱䝙䜸䞁ෆ䠄ݖ ܪΤ ௩<1䠅䛷䛿㢼㏿䛾ศᕸ䛜 LES 䛻䛚䛔䛶䜔䜔㐣䛷䛒䜛䛜䠈ஏ఼ ; Ͷ͕͜Ζᘓ≀䜘䜚ୖ㒊䛾ᖹᆒ㢼㏿䛜䜋䜌୍⮴䛧䛶䛔䜛䚹 㻌 ᅗ3㻌 ὶධ⨨䛸㒔ᕷ䜻䝱䝜䝢䞊ෆ䠄ᆅⅬ X䠅䛻䛚䛡䜛㢼㏿ศᕸ䛾ẚ㍑ 㻌 䠏䠊㒔ᕷ䜻䝱䝜䝢䞊ෆእ䛾ὶሙ䛾≉ᛶ㻌 㻟㻚㻝 ゎᯒᴫせ㻌 ᮏ❶䛷䛿⢒ᗘ䛜ᆒ୍䛺㒔ᕷ䛻䛚䛡䜛䝢䞊䜽㢼㏿䛾≉ᛶ䜢᫂䜙䛛䛻䛩䜛䛯䜑䛻䠈⢒ᗘせ⣲䛾㧗䛥䛾䜀䜙䛴䛝䛜␗
䛺䜛2 䜿䞊䝇 CaseA, CaseB 䛾ゎᯒ䜢ᐇ䛩䜛䚹CaseA 䛿ᘓ≀䛾㧗䛥䛜ݖ Τ ܪ௩=1 䛷ᆒ୍䛺㧗䛥䜢ᣢ䛴ᶍᆺ䝃䜲䝈䛾
ᘓ≀⩌䠄ᩚᙧ㓄⨨䠅䛷䛒䜚䠈CaseB 䛿ݖ Τ ܪ௩=0.5, 1.5 䛾 2 ✀㢮䛾㧗䛥䛾䝤䝻䝑䜽䛜ΰᅾ䛧䛯䜿䞊䝇䠄ᅗ 4䠈CaseB ᖹ㠃
ᅗ䜢ཧ↷䠅䛷䛒䜛䚹ܪ௩䛿ᘓ≀䛾ᖹᆒ㧗䛥䜢♧䛧䠈2 䜿䞊䝇䛸䜒䛻 0.1m 䛷䛒䜚䠈⢒ᗘᐦᗘ䛿ྠ୍䛷䛒䜛䚹䜎䛯䠈ṇ᪉ᙧ
䜢ᗏ㠃䛻ᣢ䛴ᘓ≀䛾㛫㝸䛿ὶ᪉ྥ䠈䝇䝟䞁᪉ྥ䛸䜒䛻0.1m 䛷䛒䜛䚹ὶධ᮲௳䛸ቃ⏺᮲௳䛿 2.1 ⠇䠈⾲ 1 䛸ྠ୍䛾
䜒䛾䜢㐺⏝䛩䜛䚹䜎䛯䠈ྛ䜿䞊䝇䛻䛚䛔䛶⢒ᗘ᮲௳䛾㐪䛔䛜㢼㏿䛾㖄┤䝥䝻䝣䜯䜲䝹䛻ཬ䜌䛩ᙳ㡪䜢☜ㄆ䛩䜛䛯䜑 䛻䠈CaseA 䛷䛿 Point1䡚4 䛾 4 ᆅⅬ䛷䠈CaseB 䛷䛿㏆㞄䛾⢒ᗘ㧗䛥䛻ྜ䜟䛫䛶䠈Point1a䡚Point4a, Point1b䡚Point4b
䛾 8 ᆅⅬ䛻䛚䛔䛶㢼㏿䛾㖄┤䝥䝻䝣䜯䜲䝹䜢☜ㄆ䛧䛯䚹䛺䛚䠈ゎᯒ㛫䛿ᶍᆺ䝇䜿䞊䝹䛷 20 ⛊䛷䛒䜚䠈್᭱䠈ᖹ ᆒ್䛾⟬ฟ䛻䛚䛔䛶䛿8䡚20 ⛊䛾್䜢⏝䛔䛯䚹 㻌 ਦ ᑐ㇟䜿䞊䝇䠄CaseA䠈CaseB䠅䛸ィ⟬᮲௳ 㻌 㻌 0 5 10 15 20 0 1 Exp. LES
ݖܪΤ
0 5 10 15 20 0 1 2 3ߪ
௨Ȁݑ
כLES
Exp: ߪ௨Ȁݑכ=2 ܷ ܷΤ 0.01 0.1 1 10 -0.5 0 0.5 1 1.5 EXPɿ LES ܷ ܷΤ ݖܪΤ
D ὶධ᮲௳ࡢ ᖹᆒ㢼㏿ศᕸ E ὶධ᮲௳ࡢ ὶᙉᗘ F 㒔ᕷ࢟ࣕࣀࣆ࣮ෆ㸦ᅗ㸯 ࡢᆅⅬ;㸧࠾ࡅࡿ㢼㏿ศᕸ 4.4m 0m 0.5m 3.4m InflowPoint1a Point1b Point2aPoint2b
Point3a Point3b Point4b Point4a Case B ⢒ᗘせ⣲䠖㻜㻚㻝㼙㽢㻜㻚㻝㼙㽢㻜㻚㻜㻡㼙 ⢒ᗘせ⣲䠖㻜㻚㻝㼙㽢㻜㻚㻝㼙㽢㻜㻚㻝㻡㼙 CaseA CaseB Domain size[m] (x,y,z)=(4.4m x 1.9m x 0.75m) Time increment[s] 1.0x10-3[s] Average height(ܪ௩)[m] 0.1 0.1 Maximum Height(ܪ௫)[m] 0.1 0.15 Minimum spatial resolution(Tetra mesh)[m] (ܪ0.005௩/20) 0.005 (ܪ௩/20) Inflow
Point1 Point2 Point3 Point4
Case A ⢒ᗘせ⣲䠖㻜㻚㻝㼙㽢㻜㻚㻝㼙㽢㻜㻚㻝㼙 㻜㻚㻝㼙 㻜㻚㻝㼙 ⢒ᗘせ⣲䠖 㻜㻚㻝㼙㽢㻜㻚㻝㼙㽢㻜㻚㻜 㻡㼙 ⢒ᗘせ⣲䠖 㻜㻚㻝㼙㽢㻜㻚㻝㼙㽢㻜㻚㻝㻡 㼙 ʴCaseB ฑਦʵ 㻜㻚㻝㼙
㻟㻚㻞 ⢒㠃ቃ⏺ᒙෆ䛷䛾㢼㏿䛾ศᕸ≉ᛶ㻌
ᅗ5 䛻 CaseA,B 䛾ὶ㏿䛾᩿㠃ศᕸ䜢♧䛩䚹ᘓ≀䛾㧗䛥䛜ᆒ୍䛺 CaseA 䛷䛿 skimming flow 䛾䜘䛖䛺ὶ䜜ሙ䛸䛺
䛳䛶䛚䜚䠈㒔ᕷ䜻䝱䝜䝢䞊ෆእ䛾ΰྜ䛜ᑡ䛺䛟䠈㞳䛫䜣᩿ᒙ䛾ᦂື䛜ᑠ䛥䛔ὶ䜜ሙ䛸䛺䛳䛶䛔䜛䚹୍᪉䛷⢒ᗘ䛜
ᆒ୍䛻䛺䛳䛶䛔䜛CaseB 䛷䛿䠈㒔ᕷ䜻䝱䝜䝢䞊ෆ䛷䛾䜜䜒䛝䛟䠈㧗䛔ᘓ≀䛛䜙Ⓨ⏕䛩䜛㞳䛫䜣᩿ᒙ䛾ᣲື䜒ୖ
ୗ䛻䛝䛟ᦂື䛧䛶䛔䜛䚹
ḟ䛻䠈ྛ䜿䞊䝇䛷䛾ᖹᆒ㢼㏿䛸ὶᙉᗘ䛾㖄┤䝥䝻䝣䜯䜲䝹䜢ᅗ 6 䛻♧䛩䚹㖄┤䝥䝻䝣䜯䜲䝹䛾䝃䞁䝥䝸䞁䜾⨨
䛿ὶධ┤ᚋ䛾 inlet(ὶධ㠃䛛䜙 0.1m ᆅⅬ)䛸ᖹᆒ㢼㏿䛜ᘓ≀⩌๓➃䛾ᙳ㡪䜢ཷ䛡䛶䛔䛺䛔 Point3䠄CaseA䠅䠈
Point3a(CaseB)䛷䠈䛭䜜䛮䜜䛾⨨䛿ᅗ 4 ୰䛻♧䛧䛶䛔䜛䚹Point3㸦CaseA㸧㸪Point3a (CaseB)ࡢྛⅬ࡛ࡣ㸪ὶධ┤ᚋ
ࡢᆅⅬ inlet ࡢ㖄┤ࣉࣟࣇࣝẚ㍑ࡍࡿ㸪ゎᯒ㡿ᇦෆࡢࣈࣟࢵࢡࡼࡾݖ ܪΤ ௩ ൏ ʹ㸦CaseA㸧㸪ݖ ܪΤ ௩ ൏ ͵(CaseB)ࡢ㡿ᇦ࠾࠸࡚㏿ᗘḞᦆࡀⓎ⏕ࡋ࡚࠸ࡿࡇࡀ☜ㄆ࡛ࡁࡿࠋ䛺䛚䠈ୗὶഃ䛾 Point3,Point3a 䛾ୖ᪉ 䠄ݖ ܪΤ ௩>4䠅䛷䛿ὶධ㠃(inlet)䛸ẚ㍑䛧䛶 0.1䡚0.2m/s ⛬ᗘ䛾ቑ㏿䛜䜏䜙䜜䠈㛢ሰ⋡䜔྿㉮㐣⛬䛷䛾ቃ⏺ᒙ䛾Ⓨ㐩 䛾ᙳ㡪䛜⪃䛘䜙䜜䜛䛜䠈ᮏ◊✲䛷䛿ゎᯒ㡿ᇦෆ䛾䝤䝻䝑䜽䛻䜘䛳䛶⏕ᡂ䛥䜜䜛ὶᵓ㐀䜢ᑐ㇟䛸䛧䛶䝢䞊䜽㢼㏿䛾≉ ᛶ䜔Ⓨ⏕せᅉ䜢㆟ㄽ䛩䜛䛣䛸䛻║䜢⨨䛟䛣䛸䛸䛧䠈ὶධኚື㢼䛜䜒䛴ቃ⏺ᒙཌ䛥௨ୗ䛾ὶᵓ㐀䛻䛴䛔䛶㆟ㄽ䛩 䜛䚹
ḟ䛻䠈CaseA, CaseB 䛾⢒ᗘ᮲௳䛾㐪䛔䛜㢼㏿䛾㖄┤䝥䝻䝣䜯䜲䝹䛻ཬ䜌䛩ᙳ㡪䛻╔┠䛩䜛䛸䠈CaseB 䛾ᖹᆒ㢼
㏿䛾㖄┤䝥䝻䝣䜯䜲䝹䛿 CaseA 䛻ẚ䜉䛶㏿ᗘḞᦆ䛜ⴭ䛧䛟䠈㏿ᗘḞᦆ䛾ᙳ㡪䛜ཬ䜆㡿ᇦ䛿 CaseA 䛾䛚䜘䛭 1.5 ಸ 䛷䛒䜛䚹ὶᙉᗘ䠄ᅗ 6(b)䠅䛻䛴䛔䛶䜒 CaseA 䛷䛿ݖ ܪΤ ௩=1 ┤ୖ䛻ὶᙉᗘ䛜᭱䛻䛺䜛䛾䛻ᑐ䛧䠈CaseB 䛷䛿 ݖ ܪΤ ௩=2 ㏆䛷ὶᙉᗘ䛜᭱䛸䛺䜛䚹 ᅗ5㻌 ྛ䜿䞊䝇䛾᩿㠃㢼㏿ศᕸ ᅗ6 ྛ䜿䞊䝇䛾ᖹᆒ㢼㏿䛸ὶᙉᗘ䛾㖄┤䝥䝻䝣䜯䜲䝹 㻟㻚㻟㻌 ᘓ≀⩌䛾ୖ㒊䛻Ⓨ⏕䛩䜛⤌⧊ᵓ㐀䛾ศ㢮㻌 ⢒㠃ቃ⏺ᒙෆ䛷䛾⤌⧊ᵓ㐀䛾ศ㢮䛻ᙜ䛯䜚䠈ᖹᆒ㢼㏿䛸┦ఝ๎䛸䛾㛵ಀ䜢♧䛩䛯䜑䛻ᅗ 7(i)䛻➼౯◁⢏ᚄ݇௦䛸 ᦶ᧿㏿ᗘ䛻䜘䜚↓ḟඖ䛧䛯 CaseA,B 䛾ᖹᆒ㢼㏿䛾㖄┤䝥䝻䝣䜯䜲䝹䛸⢒㠃䜢௬ᐃ䛧䛯➼౯◁⢏ᚄ݇௦䛻ᇶ䛵䛟 ᑐᩘ๎䠄ᘧ(8)䠅䜢♧䛩䚹➼౯◁⢏ᚄ݇௦䛿㔝⃝䜙8)䛜♧䛧䛯᪉ἲ䠄ᘧ(9)䠅䛻ᚑ䛳䛶⟬ฟ䛩䜛䚹 0 1.8 1.0 U Magnitude [m/s] Case A Case B Point3 Point3a Point3b 0 1 2 3 4 5 6 7 -0.5 0.5 1.5 CaseB_point3a CaseB_point3b CaseA_point3 CaseA_inlet 0 1 2 3 4 5 6 7 0 0.2 0.4 CaseB_point3a CaseB_point3b CaseA_point3 CaseA_inlet ݖȀܪ ௩
ݖȀܪ
௩ ܷ௩ሾ݉Ȁݏሿ ߪ௨ ݉Ȁݏ (a)ฑۋ෫ଐ (b)ཛྷླྀکౕ ௨ഓ
ൌ ͷǤͷ݈݃
௭ ೞ ͺǤͷ
㻌 㻌 䞉䞉䞉(8)㻌 㻌 ೞ ൌ ͳͲ
ఴǤఱషಳ ఱǤళఱ㻌 䠈
ܤ ൌ ͷǤͷ݈݃
ଵ ఒ㻌 㻌 䞉䞉䞉
(9)
䛺䛚䠈ᮏ◊✲䛷䛿 ൌ ܪ௩, ߣ ൌ ߣ(㢼ୖ䛛䜙ぢ䛯䝤䝻䝑䜽䛾❧㠃✚䛻ᇶ䛵䛟⢒ᗘᐦᗘ䠅䛸䛧䠈ᦶ᧿㏿ᗘ䛿ᘓ≀⩌ ୖ 㒊 䛾 䝺 䜲 䝜 䝹 䝈 ᛂ ຊ 䠄 ᅗ 7(ii) 䛻 ♧ 䛩 ᆅ Ⅼ 䛷 ✵ 㛫 ᖹ ᆒ 䛥 䜜 䛯 ್ 䠅 䛾 ᭱ ್ 䜘 䜚 ồ 䜑 䠈 CaseA 䛷 䛿 ݑఛൌ ͲǤͲͻ͵(ݖ ܪΤ ௩=1.07)䠈CaseB 䛷䛿ݑఛൌ ͲǤͳ͵(ݖ ܪΤ ௩=1.61)䛷䛒䜛䚹ᘧ(9)䛿⢒㠃䛜௬ᐃ䛷䛝䠈⢒ᗘ䛜ẚ㍑ⓗᑠ䛥 䛔᮲௳䜢௬ᐃ䛧䛯ᘧ䛷䛒䜛䛜䠈CaseA䠈CaseB 䛔䛪䜜䛾䜿䞊䝇䛻䛚䛔䛶䜒䠈୍ᐃ䛾㧗䛥௨ୖ䛾ୖ✵䛻䛚䛔䛶⢒㠃 䜢௬ᐃ䛧䛯ᑐᩘ๎䛻ᑐᛂ䛧䛯┤⥺䛾ศᕸ䜢♧䛧䛶䛔䜛䚹䛣䛾⤖ᯝ䛿䠈䛭䛾㡿ᇦ䛿䛒䜛୍ᐃ䛾㧗䛥䠄CaseA䠖ݖ ݇Τ ʹ䠈௦ CaseB䠖ݖ ݇Τ ͵䠅䛛䜙ቃ⏺ᒙୖ➃㏆䜎䛷ᑐᩘ๎䛜ᡂ❧䛩䜛ᒙ䛜Ꮡᅾ䛩䜛䛣䛸䜢♧၀䛧䛶䛔䜛䛜䠈ᑐᩘ๎䛜ᡂ❧䛩௦ 䜛ෆᒙ䛸䛭䛾ୖ㒊䛷ᑐᩘ๎䛛䜙እ䜜䜛እᒙ䛾༊ศ䛜᫂☜䛷䛿䛺䛔䚹䝺䜲䝜䝹䝈ᛂຊ䛜᭱䛸䛺䜛⨨䜔ᖹᆒ㢼㏿䛾 ✵㛫ⓗ䛺䜀䜙䛴䛝䛛䜙᥎ 䛧䛶䜒䠈CaseA, CaseB 䛾ቃ⏺ᒙཌ䛻ẚ䜉䛶⢒ᗘᗏᒙ䛾ཌ䛥䛜༑ศ䛻䛝䛟䠈⢒ᗘᐦᗘ䛜 䛝䛔䛣䛸䛻㉳ᅉ䛩䜛䛸⪃䛘䜙䜜䜛䚹≉䛻 CaseB 䛷䛿㏿ᗘḞᦆ䛾㡿ᇦ䛜 CaseA 䜘䜚䛝䛔䛣䛸䛛䜙䠈䛣䛾ഴྥ䛜㢧ⴭ 䛷䛒䜛䚹䛺䛚䠈ᅗ7(i)䛾 CaseA,CaseB 䛾㢼㏿ศᕸ䛿ݖ ݇Τ 䛷♧䛥䜜䛯ᑐᩘ๎䛾ศᕸ䛸ẚ䜉䛶䛪䜜䛜⏕䛨䛶䛔䜛䛜䠈䛣䜜௦ 䛿݇௦䜢⢒ᗘᐦᗘ䛾䜘䛖䛺ᙧ≧䛻ᇶ䛵䛟䝟䝷䝯䞊䝍䛾䜏䛷ホ౯䛧䛶䛔䜛䛣䛸䛜せᅉ䛸⪃䛘䜙䜜䜛䚹ḟ䛻CaseA, CaseB 䛾ᘓ≀⩌䛾ୖ㒊䛻Ⓨ⏕䛩䜛⤌⧊ᵓ㐀䛸䛧䛶䠈ᅗ 7(iii)䡚(vi)䛻Ỉᖹ᩿㠃䛻䛚䛡䜛㢼㏿䛾ኚື್
䠄▐㛫್䜢ྛᆅⅬ䛾ᖹᆒ್䛷ᕪ䛧ᘬ䛔䛯್䠅䛾ศᕸ䜢♧䛩䚹ᅗ 7(iii)䛿 CaseA 䛾ᘓ≀䛾ୖ㒊䛻䛷䛝䜛⤌⧊ᵓ㐀䛾≉ ᚩ䜢♧䛧䛶䛚䜚䠈ὶ㏿䛾ኚື್䛜ᑠ䛥䛔ప㏿ὶయሢ䛜ฟ⌧䛧䛶䛔䜛䚹Coceal 䜙1)䛻䜘䜛䛸❧᪉య䛜༓㫽㓄⨨䛻୪䜆⢒ ᗘ䝤䝻䝑䜽⩌ୖ䛾ゎᯒ䛛䜙ݑ ൏ ͲǤͺܷ䛸䛺䜛ప㏿ὶయሢ䛜ݖ ͳǤͷܪ௨ୖ䛻㡿ᇦ䛻ฟ⌧䛩䜛䛣䛸䜢♧䛧䛶䛚䜚䠈䛭䛾㛫㝸 䛿2H ⛬ᗘ䛸䛺䜛䛣䛸䛸䜒䜋䜌ᑐᛂ䛧䛶䛔䜛䚹䜎䛯䠈ᮏゎᯒ䛷䛿䛒䜎䜚᫂░䛷䛿䛺䛔䛜䠈ᦂື䛧䛺䛜䜙ὶ᪉ྥ䛻ᘏ䜃䛶 䛔䜛ప㏿ὶయሢ䛾ഃ➃䠄ݑǯ䛾➢ྕ䛜ኚ䜟䜛㡿ᇦ䠅䛻䛚䛔䛶㖄┤᪉ྥ䜢㍈䛸䛧䛯 䛾Ꮡᅾ䛜♧၀䛥䜜䠈᪤ ᩥ⊩䛷♧ 䛥䜜䛶䛔䜛ప㏿ὶయሢ䜢ྲྀ䜚ᅖ䜐䜘䛖䛻Ⓨ⏕䛩䜛䝦䜰䝢䞁≧䛾 䠄ᅗ 7(iii),Ⅼ⥺䛾䠅䛸䜒ᑐᛂ䛩䜛䚹ྠᵝ䛾ᵓ㐀䛿㧗 䛥䛜␗䛺䜛䜒䛾䛾䠈CaseB 䛻䛚䛔䛶䜒☜ㄆ䛷䛝䜛䠄ᅗ 7(iv)䠅䚹 䛥䜙䛻䠈䝤䝻䝑䜽ୖ㒊䛾⤌⧊ᵓ㐀䛸䛧䛶䡖ൗܪ௩ ൌ Ͷ䛾Ỉᖹ㠃ศᕸ䛻╔┠䛩䜛䛸䠈CaseA, CaseB 䛸䜒䛻ቃ⏺ᒙཌ䝇䜿 䞊䝹䛾䜸䞊䝎䞊䛾㛫㝸䜢ᣢ䛱䠈ὶ᪉ྥ䛻㛗䛔ᵓ㐀䜢ᣢ䛴⤌⧊ᵓ㐀䛜☜ㄆ䛷䛝䜛䠄ᅗ 7(v),(vi)䠅䚹䛥䜙䛻ྛ䜿䞊䝇䛾 ὶ᪉ྥ᩿㠃䠄ᅗ 8䠈⨨䛿ᅗ 7 䛾 PlaneX 䛾⨨䠅䜢☜ㄆ䛩䜛䛸䠈ඛ䛻♧䛧䛯䝤䝻䝑䜽⩌ୖ䛾⤌⧊ᵓ㐀䛾ୖ㒊䛻䜘䜚 䛝䛺ᚠ⎔䜢ᣢ䛳䛯ቃ⏺ᒙཌ䛸ྠ➼䛾䝇䜿䞊䝹䜢ᣢ䛳䛯䝻䞊䝹≧䛾ᵓ㐀䛜☜ㄆ䛷䛝䜛䚹ᅗ 6 䛻䛚䛔䛶ゎᯒ㡿ᇦෆ䛾 䝤䝻䝑䜽䛻䜘䛳䛶㢼㏿䛾㖄┤䝥䝻䝣䜯䜲䝹䛻㏿ᗘḞᦆ䛜䜏䜙䜜䜛䛣䛸䜢⪃៖䛩䜛䛸䠈䛣䛾ᵓ㐀䛿䠈ゎᯒ㡿ᇦෆ䛾䝤䝻䝑䜽
䛻䜘䛳䛶⏕ᡂ䛥䜜䛯䜒䛾䛸᥎ 䛥䜜䜛䚹CaseA, CaseB 䛸䜒䛻 u’䛾➢ྕ䛜ኚ䜟䜛䛒䛯䜚䛾㡿ᇦ䛷ᙉ䛔ୖ᪼䛸ୗ㝆䛜㉳䛣
䛳䛶䛔䜛䠄ᅗ8䠅䚹 䠐䠊㒔ᕷ䜻䝱䝜䝢䞊ෆእ䛻䛚䛡䜛䝢䞊䜽㢼㏿䛾Ⓨ⏕㐣⛬䛾ศᯒ㻌 㻠㻚㻝㻌 䝢䞊䜽㢼㏿Ⓨ⏕䛾≉ᛶ㻌 㒔ᕷ䜻䝱䝜䝢䞊ෆእ䛻䛚䛡䜛䝢䞊䜽㢼㏿䛾≉ᛶ䜢ᢕᥱ䛩䜛䛯䜑䠈ᅗ 9(a)䛻㢼㏿䛾ኚື್䛾್᭱ݑԢ௫䛾㖄┤䝥 䝻䝣䜯䜲䝹䜢♧䛩䚹ᅗ 6(b)䛷♧䛧䛯ὶᙉᗘ䛾ศᕸ䛸ྠᵝ䛻 CaseA 䛷䛿ݑԢ௫䛾᭱䛿ᘓ≀䛾┤ୖݖ ܪΤ ௩=1䡚1.5 䛾㡿ᇦ䛻ศᕸ䛧䠈ᘓ≀⩌ୖ㒊䛻Ⓨ⏕䛩䜛㞳䛫䜣᩿ᒙ䛾⨨䛸䛚䛚䜐䛽ᑐᛂ䛩䜛䚹୍᪉䛷 CaseB 䛷䛿㞳䛫䜣᩿ ᒙ䛾ୖୗ䛾ᦂື䛜 CaseA 䛻ẚ䜉䛶䛝䛔䛣䛸䛛䜙䠈ݑԢ௫䛾್䛿 CaseA 䛻ẚ䜉䛶䛝䛟䠈ݑԢ௫䛜᭱䛸䛺䜛 ݖ ܪΤ ௩=2 䜢୰ᚰ䛻ݖ ܪΤ ௩=1.5䡚2.5 ㏆䛷ݑԢ௫䛾್䛜䛝䛟䛺䛳䛶䛔䜛䚹䜎䛯䠈㒔ᕷ䜻䝱䝜䝢䞊ෆ䛾ݑԢ௫䛾ศᕸ䛻 ╔┠䛩䜛䛸䠈CaseA 䛷䛿ᚠ⎔ὶ䛾䜘䛖䛺ὶ䜜ሙ䛾≉ᛶ䛛䜙䜻䝱䝜䝢䞊ෆ䛾୰ኸ䜘䜚ྑഃ䛻䛝䛺㢼㏿䛜ฟ⌧䛧䛶䛔䜛 䛜䠈CaseB 䛷䛿㧗䛥ݖ ܪΤ ௩=0.5 䛾ᘓ≀䛾ୖ✵䛛䜙䜒㧗䛔䝢䞊䜽㢼㏿䛜Ⓨ⏕䛧䛶䛚䜚䠈䛭䛾ᚋὶഃ䛾㡿ᇦ䛾ݑԢ௫䜒㧗 䛟䛺䛳䛶䛔䜛䠄ᅗ9(c)䠅䚹
ਦ ϔϫρέ܊෨Ͷܙ͠ΗΖૌ৭ߑଆʤ෫ଐรಊݑԢਭฑஇɾһͺ෫ଐรಊݑԢ ݒԢ ͶخͰ͚ୱҒϗέφϩɾ3ODQH< ͺਦ ԘஇҒʥ ਦ ෫ଐรಊͶؖͤΖकླྀ๏இ ʤ෫ଐรಊݑԢ [ >P@Ͷ͕͜ΖஇɽஇҒͺ ਦ Y YL 3ODQH; Νࢂলɽһͺ෫ଐรಊݒԢZԢͶخͰ͚ୱҒϗέφϩʥ -5 0 5 10 15 20 0.1 1 10 log-law CaseB_pt3a CaseA_pt3 (iii) (iv) L ᖹᆒ㢼㏿ᑐᩘ๎ࡢ㛵ಀ ܷݑ ఛ Τ ݖȀ݇௦ (v),(vi) ⢒ᗘせ⣲䠖㻜㻚㻝㼙㽢㻜㻚㻝㼙㽢㻜㻚㻜㻡㼙 ʴCaseA ฑਦʵ ʹ ʹ ʹ ʹʹ ʹ ʹ ʹʹ ʹ ʹ ʹʹ ʹ ʹ ʹ point3 ⢒ᗘせ⣲䠖㻜㻚㻝㼙㽢㻜㻚㻝㼙㽢㻜㻚㻜㻡㼙 ⢒ᗘせ⣲䠖㻜㻚㻝㼙㽢㻜㻚㻝㼙㽢㻜㻚㻝㻡㼙 ʴCaseB ฑਦʵ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ ʹ point3a LL &DVH$&DVH%࠾ࡅࡿᦶ᧿㏿ᗘ⟬ฟࡢࡓࡵࡢ 䝺䜲䝜䝹䝈ᛂຊ䛾ࢧࣥࣉࣜࣥࢢ⨨ 㽢䠖㖄┤䝥䝻䝣䜯䜲䝹䛾䝃䞁䝥䝸䞁䜾⨨ 0 5 10 15
(iii) CaseA: z= 1.5Have(1.5Hmax) (iv) CaseB: z=2Have (1.33Hmax)
(v) CaseA: z=4Have (4Hmax) (vi) CaseB: z=4Have(2.66Hmax)
ݑԢሾ݉Ȁݏሿ -0.5 0.5 0 ݑԢሾ݉Ȁݏሿ -0.5 0.5 0 10 20 30 ݔ ܪΤ ௩ ݔ ܪΤ ௩ 10 20 30 ݔ ܪΤ ௩ 10 20 30 ݔ ܪΤ ௩ 10 20 30 Point3
Point3 Point3a Point3b
Point3a Point3b Plane X Plane X Plane Y Plane Y Plane Y Plane Y 0 5 10 15 ܪ ௩ Τ ܪ ௩ Τ 7 5 0 ݖ ܪ௩ Τ 7 5 0 ݖ ܪ௩ Τ ݑԢሾ݉Ȁݏሿ -0.5 0 0.5 ݑԢሾ݉Ȁݏሿ -0.5 0 0.5
(a) CaseA (b)CaseB
˟Plane(ii) ˟Plane(iv)
˟Plane(iii) ˟Plane(v)
ᅗ9㻌 ྛ䜿䞊䝇䛻䛚䛡䜛ኚື್䛾್᭱ݑԢ௫䛾ศᕸ 㻠㻚㻞㻌 㒔ᕷ䜻䝱䝜䝢䞊ෆእ䛾䝢䞊䜽㢼㏿䛾Ⓨ⏕㐣⛬㻌
ᅗ10 䛻䛿ݑԢ䛾⣔ิኚ䛸⤌⧊ᵓ㐀䛾㛵ಀ䛸䛧䛶䠈CaseB 䛾ྛ ᐃⅬ䠄point2a, point3a, point4a, ⨨䛿ᅗ 4 䜢
ཧ↷䠅䛾ݑᇱǡ Ԣ䛾⣔ิኚ䛸ྛ ᐃⅬ䛻⨨䛔䛶ݑԢ䛜ᴟ䛸䛺䜛้䠄t=13,16,18.4[s]䠅䛾Ỉᖹ㠃ศᕸ䠄㧗䛥䛿 ݖ ܪΤ ௩ ൌ ʹǤͲ䠅䜢♧䛩䚹ྛ้䛾Ỉᖹ㠃ศᕸ䛻䛿3.3 ⠇䛷♧䛧䛯䜘䛖䛻ὶ᪉ྥ䛻ఙ䜃䛯ప㏿ὶయሢ䛾ᵓ㐀䛜䛒䜚䠈 䛭䜜䛻㝶䛧䛶㢼㏿䛾㧗䛔㡿ᇦ䜒ὶ᪉ྥ䛻ఙ䜃䛶䛔䜛䚹ᅗ 10(b)䛾 Point3a 䛾䜘䛖䛻䠈ݑԢ䛜ᴟ䛸䛺䜛้䛻䛿 ᐃⅬ䛿䛣䛖䛧䛯㧗㢼㏿䛾㡿ᇦ䛻Ꮡᅾ䛧䠈t=16[s]䛾䜘䛖䛻㧗㢼㏿䛾㡿ᇦ䛜ὶ᪉ྥ䛻⣽㛗䛔ሙྜ䛿㢼㏿䛾㧗䛔้ 䛜ẚ㍑ⓗ㛗䛟⥅⥆䛩䜛䛣䛸䛜☜ㄆ䛷䛝䜛䚹 䜎䛯䠈㒔ᕷ䜻䝱䝜䝢䞊ෆ䛷䛾ݑԢ௫䛾Ⓨ⏕㐣⛬䜢♧䛩䛯䜑䛻䠈ᅗ11(a), (b)䛻 CaseB 䛻䛚䛡䜛ྛ้䛾㢼㏿䛾ኚື ್ݑԢ䛸 8[s]䛛䜙ྛ้䜎䛷䛾㢼㏿䛾ኚື್䛾್᭱ݑԢ௫䜢♧䛩䚹≉䛻ᮏ◊✲䛷䛿ୖ✵䛾ὶᵓ㐀䛜ᘓ≀⩌㏆ഐ 㻌 ᅗ10 CaseB 䛾ྛ ᐃⅬ䛻䛚䛡䜛ݑԢ䛾⣔ิኚ䛸⤌⧊ᵓ㐀䛾㛵ಀ ݑԢ௫ሾ݉Ȁݏሿ 0.8 0 ݑԢ௫ሾ݉Ȁݏሿ 0.8 0 E &DVH$ࡢኚື್ࡢ್᭱ݑԢ௫ 㹼V F &DVH%ࡢኚື್ࡢ್᭱ݑԢ௫ 㹼V CaseA Point3 CaseB Point3b Point3a 0 1 2 3 4 5 6 7 0 0.5 1 CaseB_point3a CaseB_point3b CaseA_point3 D ኚື್ࡢ್᭱ݑԢ௫ 㸦⨨ࡣ E F ୰ᅗ♧㸧 ݑԢ௫ሾ݉Ȁݏሿ ݖȀܪ ௩ 15 25 35 15 25 15 25 35 16s -0.6 -0.3 0 0.3 0.6 12 14 16 18 20 -0.6 -0.3 0 0.3 0.6 12 14 16 18 20 -0.6 -0.3 0 0.3 0.6 12 14 16 18 20 18.4s 2a 3a 4a 2a 3a 4a 13s 2a 3a 4a (b)Point3a (ݖ ܪΤ ୟ୴ୣൌ ʹǤͲ) (a)Point2a (ݖ ܪΤ ୟ୴ୣൌ ʹǤͲ) (c)Point4a (ݖ ܪΤ ୟ୴ୣൌ ʹǤͲ) ݑԢ ݓԢ ݑ ᇱǡݓ ᇱሾ݉ Ȁݏ ሿ ݑ ᇱ ǡݓ ᇱ ሾ݉ Ȁݏ ሿ ݑ ᇱǡݓ ᇱሾ݉ Ȁݏ ሿ ݑԢ ݓԢ ݑԢ ݓԢ
Time[s] Time[s] Time[s]
13s 16s 18.4s 13s 16s 18.4s 13s 16s 18.4s G ݑԢࡢỈᖹ᩿㠃ࡢኚ㸦㧗ࡉݖ ݖ ܪΤ ୟ୴ୣൌ ʹǤͲሻ ݕܪ ௩ Τ ݔ ܪΤ ௩ 15 5 10 35 ݔ ܪΤ ௩ ݔ ܪΤ ௩ 0.6 -0.6 ݑԢሾ݉Ȁݏሿ
ᅗ11㻌 䝢䞊䜽㢼㏿䛾Ⓨ⏕㐣⛬䠄CaseB䠅 䛾䝢䞊䜽㢼㏿䛻ཬ䜌䛩ᙳ㡪䛻╔┠䛩䜛䚹⢒㠃ቃ⏺ᒙ䛾ୖ㒊䛷䛿3.3 ⠇䛾ᅗ 7(iv),(v)䛸ᅗ 8 䛷♧䛧䛯⢒㠃ቃ⏺ᒙ䛾ୖ 㒊䛻Ⓨ⏕䛩䜛䝻䞊䝹≧䛾ᵓ㐀䛻క䛖ὶᵓ㐀䛜Ꮡᅾ䛧䛶䛚䜚䠈ᘓ≀⩌䛾ୖ㒊䛻ᙧᡂ䛥䜜䜛ప㏿ὶయሢ䛾ୖ㒊䛷 ὶ᪉ྥ䛻⛣ὶ䛧䛶䛔䜛䠄ᅗ 11(a)䠈ձ䠅䚹䛣䛾ᵓ㐀䛿 t=12.3[s]㏆䛷ప㏿ὶయሢ䛾㛫䛻ᙧᡂ䛥䜜䜛㧗㢼㏿䛾㡿ᇦ䛸୍ య䛸䛺䜚䠈ᘓ≀䛾๓➃㏆䛻ᴟ䛺ݑԢ䛜ฟ⌧䛩䜛䠄ᅗ 11(a)䠈ղ䠅䚹䛥䜙䛻 t=12.7[s]㏆䛷䛿䛣䛾ᵓ㐀䛿䛝䛺ݑԢ䜢ಖ䛳 䛯䜎䜎䠈ᘓ≀䛾ᚋ᪉䛻ఙ䜃䠈t=13[s]䜎䛷⛣ὶ䜢⥆䛡䜛䠄ᅗ 11(a)䠈ճ䠅䚹䛭䛾⤖ᯝ䠈ᅗ 11(b)䛾Ⅼ⥺㡿ᇦෆ䛻䛚䛔䛶㧗 㢼㏿䛸䛺䜛ݑԢ䛾ὶయሢ䛜⛣ὶ䛩䜛䛣䛸䛻䜘䛳䛶䠈㧗㢼㏿䛸䛺䛳䛶䛔䜛ݑԢ௫䛾㡿ᇦ䛜㖄┤᪉ྥ䛻ᗈ䛜䜛䛸䛸䜒䛻䠈㧗㢼 ㏿䛺㡿ᇦ䛾ݑԢ௫䛜䜘䜚䛝䛺್䛻᭦᪂䛥䜜䜛ᵝᏊ䛜☜ㄆ䛷䛝䜛䠄ᅗ 11(b)䠈մ䠅䚹௨ୖ䛾⤖ᯝ䛿䠈ୖ✵䛾䝻䞊䝹≧䛾 ᵓ㐀䛻క䛖ὶᵓ㐀䛜䝢䞊䜽㢼㏿䛾Ⓨ⏕䛻ᐤ䛩䜛䛣䛸䜢♧၀䛧䛶䛔䜛䚹≉䛻䠈⢒ᗘ䛜ᆒ୍䛸䛺䛳䛶䛔䜛 CaseB 䛷 䛿䠈㒔ᕷ䜻䝱䝜䝢䞊ෆ䛷䛾ᚠ⎔ὶ䛜ᨭ㓄ⓗ䛺ὶ䜜ሙ䛸䛺䜛CaseA 䛸␗䛺䜚䠈㒔ᕷ䜻䝱䝜䝢䞊ෆእ䛾㖄┤᪉ྥ䛾㢼㏿ኚ ື䛜䛝䛟䛺䜛䛣䛸䛛䜙䠈ప㏿ὶయሢ䛸ୖ✵䛾䝻䞊䝹≧䛾ᵓ㐀䛜୍య䛸䛺䛳䛯ᵓ㐀䠄ᅗ 11(a)䛾䐠䜔䐡䠅䜢ᙧᡂ䛧䜔䛩 䛟䠈䛭䛾⤖ᯝ䛸䛧䛶CaseA 䜘䜚ᗈ⠊ᅖ䛻ᙉ䛔䝢䞊䜽㢼㏿䛜ᙧᡂ䛥䜜䜛䛸⪃䛘䜙䜜䜛䚹 䠑䠊䜎䛸䜑㻌 ᮏ◊✲䛷䛿䠈㒔ᕷ䜻䝱䝜䝢䞊䜢⌧䛧䛯㒔ᕷ䝰䝕䝹䛻䛴䛔䛶䠈㢼Ὕᐇ㦂䛾⤖ᯝ䛸䛾ẚ㍑䛻䜘䜛᳨ド䜢⾜䛔ὶゎ ᯒᡭἲ䛾⢭ᗘ䜢☜ㄆ䛧䛯䚹䛥䜙䛻䠈⢒ᗘ䛾ᆒ୍ᛶ䛜␗䛺䜛ィ⟬䝰䝕䝹䛻䜘䛳䛶䠈ᘓ≀⩌ୖ㒊䛻Ⓨ⏕䛩䜛⤌⧊ᵓ㐀 䛾ศ㢮䜢⾜䛳䛯䛖䛘䛷䠈⤌⧊ᵓ㐀䛜䝢䞊䜽㢼㏿䛾ศᕸ≉ᛶ䛸Ⓨ⏕㐣⛬䛻ཬ䜌䛩ᙳ㡪䜢♧䛧䛯䚹䛭䛾⤖ᯝ䠈⢒ᗘ䝤䝻䝑 䜽⩌䛾┤ୖ䛻䛿᪤ ᩥ⊩䛸ྠᵝ䛻ᘓ≀⩌䛾䝇䜿䞊䝹䛸ᑐᛂ䛧䛯ప㏿ὶయሢ䛻క䛖⤌⧊ᵓ㐀䛜☜ㄆ䛥䜜䠈䛣䛾⤌⧊ᵓ 㐀䛻㝶䛧䛶㢼㏿䛾ኚື್䛜䛝䛟䛺䜛䛣䛸䛜♧䛥䜜䠈⢒㠃ቃ⏺ᒙ䛾ୖ㒊䛷䛿ቃ⏺ᒙཌ䝇䜿䞊䝹䛾䝻䞊䝹≧䛾ᵓ㐀 䛜☜ㄆ䛥䜜䛯䚹䛥䜙䛻䠈⢒ᗘ䛜ᆒ୍䛷䛒䜚䠈㒔ᕷ䜻䝱䝜䝢䞊ෆእ䛾㖄┤᪉ྥ䛾㢼㏿ኚື䛜䛝䛔ゎᯒ䜿䞊䝇䛻䛚䛔 䛶䝢䞊䜽㢼㏿䛾Ⓨ⏕㐣⛬䜢ศᯒ䛧䛯⤖ᯝ䠈⢒㠃ቃ⏺ᒙ䛾ୖ㒊䛻䛒䜛䝻䞊䝹≧䛾ᵓ㐀䛸ᘓ≀⩌┤ୖ䛾㧗㢼㏿䛾㡿ᇦ 䛜୍య䛻䛺䜛䛣䛸䛻䜘䛳䛶䠈㏿ᗘ䛾䛝䛺ὶయሢ䜢ᙧᡂ䛧䠈ᙉ䛔䝢䞊䜽㢼㏿䜢ᙧᡂ䛩䜛䛣䛸䛜♧၀䛥䜜䛯䚹㻌 ᚋ㸪ྎ㢼➼ࡢᙉ㢼࠾࠸࡚㒔ᕷ࢟ࣕࣀࣆ࣮ෆ࡛ࡢᙉ㢼⿕ᐖࢆ᥎ᐃࡋ࡚࠸ࡃ࠺࠼࡛ࡣ㸪Ẽ㇟ᨐࢆྵࢇࡔ ὶධẼὶࢆ⏝࠸ࡓゎᯒࡼࡾẼ㇟ሙ≉᭷ࡢὶᵓ㐀ࡸᨐࡀ㒔ᕷ࢟ࣕࣀࣆ࣮ෆእࡢࣆ࣮ࢡ㢼㏿ཬࡰࡍᙳ㡪 t=8-11[s] t=8-12[s] t=8-13[s] ݑԢ௫ሾ݉Ȁݏሿ 0.8 0 (b)䝢䞊䜽㢼㏿ݑԢ௫ (t=8[s]䛛䜙ྛ้䜎䛷䛾ኚື䛾್᭱) (a)㢼㏿䛾ኚື್ݑԢ (CaseB) t=11[s] t=13[s] ݑᇱሾ݉Ȁݏሿ t=12.3[s] t=12.7[s] t=13[s] t=8-12.3[s] t=8-12.7[s] t=8-12.3[s] ᶅۯཛྷླྀߑଆ մ್ࡢ᭦᪂ ᶆ ᶇ
ࢆ᫂ࡽࡋ࡚࠸ࡃᚲせࡀ࠶ࡿࠋࡲࡓ㸪ᘓ≀⩌࿘ࡾࡢὶࢀሙࡢ㠀ᐃᖖⓗ࡞ኚࡀᘓ≀⾲㠃ࡢ㢼ᅽຊཬࡰࡍ ຠᯝࡢ᳨ウࡶᚋࡢㄢ㢟ࡍࡿࠋ㻌 ㅰ㎡㻌 ᮏ◊✲䛿チ䝁䜴䝅䞁ྩ䛾ಟኈㄽᩥ䛾୍⎔䛸䛧䛶ᐇ䛥䜜䛯䜒䛾䛷䛒䜛䚹ᮏ◊✲䛾ᡂᯝ䛿䠈⌮Ꮫ◊✲ᡤ䛾䛂ி䛃 䝁䞁䝢䝳䞊䝍௧ඖᖺᗘ 㻴㻼㻯㻵㻌 䝅䝇䝔䝮⏝◊✲ㄢ㢟䠄ㄢ㢟␒ྕ㻦㼔㼜㻝㻥㻜㻝㻡㻢䠅䜢⏝䛧䛶ᚓ䜙䜜䛯䜒䛾䛷䛒䜛䚹䛣䛣䛻 グ䛧䛶ㅰព䜢⾲䛩䜛䚹㻌 ཧ⪃ᩥ⊩㻌
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