Thermal Science & Engineering Vol.15 No.3 (2007)ੂᵹᾲવ㆐ࠍ઻߁ࠢࠛ࠶࠻ᵹࠇߦ߅ߌࠆᄢⷙᮨ᭴ㅧႦේ 㓉⵨̐  ጤᧄ ⮍̐̑  ᴡ᧛ ᵗ̐

On the Large-Scale Structure of Turbulent Heat Transfer
in a Plane Couette Flow
Takahiro TSUKAHARA̐, Kaoru IWAMOTO̐̑ and Hiroshi KAWAMURA̐

Abstract
Direct numerical simulation of turbulent heat transfer in a plane Couette flow at Reynolds numbers of 3000 and 8600
(based on the relative wall speed and the channel width) has been performed with emphasis on a large-scale turbulence
structure (LSS). Two kinds of temperature boundary conditions are employed; one is the uniform heat flux heating(UHF) and the other is the constant temperature difference between the walls (CTD). A series of DNS has been carriedout for several larger computational box sizes than those of existing DNS’s to examine their effect upon the LSS of thethermal field and the statistical quantities such as temperature variance. The differences caused by the boundary
conditions of temperature field are discussed with respect to the LSS. For CTD, the LSS is remarkable in the outerregion and is observed to be similar to that of the velocity field. Using the present largest box size of 96h×h×12.8h, theaverage streamwise and spanwise spacing of the LSS in both velocity and thermal fields are found to be λx =32~48h andλz = 2.1~2.5h, respectively. In addition, it is concluded that the box needs to be larger than the size of the LSS in order toassess the accurate statistics such as Nusselt number.
Key Words: Turbulence, Direct numerical simulation (DNS), Plane Couette flow, Heat transfer

⸥ ภ
Cf
:
cp
:
Eij
:
h
:
ki
:
Nu
:
p
:
Pr
:
q(total) :
Rij
:
Rew
:
:
Reτ
t
:
T
:
:
Tτ

ო㕙៺ᡂଥᢙ
ቯ࿶Ყᾲࠛࡀ࡞ࠡ࡯ࠬࡍࠢ࠻࡞
࠴ࡖࡀ࡞᏷i ᣇะᵄᢙࡌࠢ࠻࡞
࠿࠶࠮࡞࠻ᢙ
࿶ജࡊ࡜ࡦ࠻࡞ᢙ
㧔ో㧕ᾲᵹ᧤
ੑὐ⋧㑐ଥᢙ
࡟ࠗࡁ࡞࠭ᢙ = (Uw h /ν)࡟ࠗࡁ࡞࠭ᢙ = (uτ δ /ν)ᤨ㑆⍍ᤨ᷷ᐲ៺ᡂ᷷ᐲ = (qw /ρ cpuτ)[J/(kg⋅K)][m3/s2]
[m]
[m-1]
[Pa]
[W/m2]

[s]
[K]
[K]

u
Uw
uτ
x
δ
∆T
θ
~
θ

:
:
:
:
:
:
:
:

λ
λi
ν
ρ
τ

:
:
:
:
:

ㅦᐲࡌࠢ࠻࡞ = (u, v, w)
ო㕙⋧ኻㅦᐲ
៺ᡂㅦᐲ = (τ w /ρ)1/2
ᐳᮡ = (x, y, z)࠴ࡖࡀ࡞ඨ᏷ = (h/2)਄ਅო㕙㑆ߩ᷷ᐲᏅ
᷷ᐲ஍Ꮕ✢ᒻߥ᷷ᐲಽᏓ㧔ጀᵹᤨߩ᷷ᐲಽᏓ㧕߆ࠄߩ஍Ꮕ
ᾲવዉ₸i ᣇะᵄ㐳
േ☼ᕈଥᢙ
ኒᐲ
ߖࠎᢿᔕജ

[m/s]
[m/s]
[m/s]
[m]
[m]
[K]
[K]
[K]
[W/(m⋅K)][m][m2/s][kg/m3][Pa]

ฃઃᣣ: 2006 ᐕ 10 ᦬ 3 ᣣ, ᜂᒰࠛ࠺ࠖ࠲࡯: ഞಷ ⾗ᓆ᧲੩ℂ⑼ᄢቇ ℂᎿቇㇱᯏ᪾Ꮏቇ⑼ (‫ޥ‬278-8510 ජ⪲⋵㊁↰Ꮢጊፒ 2641)
̑᧲੩ㄘᎿᄢቇᄢቇ㒮 Ꮏቇᐭᯏ᪾ࠪࠬ࠹ࡓᎿቇኾ᡹ (‫ޥ‬184-8588 ᧲੩ㇺዊ㊄੗Ꮢਛ↸ 2-24-16)
̐

1 -- -151

C 2007 The Heat Transfer Society of Japan○

Thermal Science & Engineering Vol.15 No.3 (2007)

ᷝሼ
( )’
( )*
( )+

()

b, t
m
rms
w

:
:
:
:
:
:
:
:

ᄌേ୯
h, Uw, ∆T ߦࠃࠆήᰴరᢙuτ , ν, Tτ ߦࠃࠆήᰴరᢙ
ࠕࡦࠨࡦࡉ࡞ᐔဋ୯
ਅო㕙߅ࠃ߮਄ო㕙ߩ୯ᷙวᐔဋߒߚ୯
ੑਸ਼ᐔဋᐔᣇᩮ
ო㕙਄ߩ୯

Hot

Const.

'T

h G

y, v
CL

u

Uw

T
Cold

G

z, w x, u

Lx(CTD : Constant Temerature Difference)



wT
wx

㧝 ✜ ⸒ࠢࠛ࠶࠻ੂᵹߪᐔⴕᐔ᧼㑆㧔࠴ࡖࡀ࡞㧕ੂᵹߩ৻ߟߢ㧘࿶ജ൨㈩㚟േߩࡐࠕ࡙࠭ࠗੂᵹߣห᭽ߦࠞࡁ

qw

⸃᣿ߩᒝജߥࠕࡊࡠ࡯࠴ߣߒߡᐢߊ૶↪ߐࠇ㧘ࠢࠛ

ฦ⒳࡟ࠗࡁ࡞࠭ᢙ߿ࡊ࡜ࡦ࠻࡞ᢙߦኻߔࠆ⹦⚦ߥ⚿ࠃࠆ⎇ⓥ଀ߪዋߥ޿㧚ࠢࠛ࠶࠻ੂᵹߢߪ㧘࠴ࡖࡀ࡞ਛᄩ߹ߢᐔဋㅦᐲ൨㈩ࠍ᦭ߒ㧘ࡐࠕ࡙࠭ࠗੂᵹߦᲧ
ߴߡੂࠇߩ㕖╬ᣇᕈ߽ᒝ޿ߎߣ߆ࠄ㧘ㅦᐲႺ⇇᧦ઙߩ㆑޿ߦࠃࠆᾲᵹേ․ᕈ߳ߩᓇ㗀ߪᒰὼߦ੍ᦼߐࠇ
ࠆ㧚ߘߒߡ㧘ࠢࠛ࠶࠻ੂᵹਛߩࠬࠞ࡜࡯㊂࡮ᾲߩャㅍਛߦⷰኤߐࠇࠆ⃻⽎㧔․ߦ㧘ᄖጀߩ᭴ㅧ߇෸߷ߔ
ᓇ㗀㧕ߦ㑐ߔࠆ⍮⷗ߪ㧘଀߃߫⋧ኻㆇേߔࠆ⊒ᾲ࡮಄ළᯏེ๟ࠅߩੂᵹᾲવ㆐ߦ߅ߌࠆࡔࠞ࠾࠭ࡓߩℂ
⸃߿ᾲᵹേ․ᕈߩ⹏ଔߦነਈߔࠆ㧚ߐࠄߦ㧘᭽‫ߥޘ‬ᾲ⊛Ⴚ⇇᧦ઙࠍઃടߒߡᓧࠆฦ⒳⛔⸘㊂ߪ㧘ࡐࠕ࡙࠭ࠗੂᵹߦ߅ߌࠆ⛔⸘㊂ߣห᭽㧘ੂᵹࡕ࠺࡞ߩ᭴▽ߦ᦭↪ߢ޽ࠆ㧚ࠢࠛ࠶࠻ੂᵹߪ㧘࠴ࡖࡀ࡞ో᏷ h ߦ෸߱ᄢⷙᮨߥ
㜞ㅦ࡮ૐㅦ㗔ၞ߇ਥᵹᣇะߦ㕖Ᏹߦ㐳޿▸࿐ߢ↢ߓ

Uw

T

T

G
Const.

Fig. 1 Configurations of the thermal fields in theplane Couette flow.

ᵹᾲャㅍߩ DNS ࠍⴕ߁ߎߣߦࠃࠅ㧘৻ቯ▸࿐ౝߩࠆߎߣ߆ࠄ߽㧘ࠢࠛ࠶࠻ੂᵹࠍኻ⽎ߣߒߚ DNS ߦu(UHF : Uniform Heat-Flux Heating/Cooling)࠶࠻ੂᵹߦߟ޿ߡ߽ㆡ↪ߐࠇߡ߈ߚ[6-9]㧚߹ߚ㧘ੂߥࠆߎߣ߇ᄙߊ[10-12]㧘ታ㛎ߦࠃࠆᬌ⸽߇࿎㔍ߢ޽

Const.

h G

z, w x, u޿㧘⋥ធᢙ୯ࠪࡒࡘ࡟࡯࡚ࠪࡦ㧔DNS㧕߇ੂᵹ⃻⽎⸃ᨆኻ⽎ߣߥࠆᵹࠇ႐ߪ㧘ࡐࠕ࡙࠭ࠗੂᵹ߇ኻ⽎ߣqw

CL

ࠇߡ߈ߚ[1-5]㧚ㄭᐕߢߪᄢဳਗ೉⸘▚ᯏߩ⊒㆐ߦ઻ᨐࠍᓧࠆߎߣ߇น⢻ߢ޽ࠆ㧚ߒ߆ߒ㧘ੂᵹᾲવ㆐ߩ

Const.

y, v࠾ࠞ࡞ߥოੂᵹߢ޽ࠅ㧘ฎߊ߆ࠄ᏷ᐢߊታ㛎߇ⴕࠊLzߪ㧘ࠢࠛ࠶࠻ੂᵹߩᄢⷙᮨ᭴ㅧࠍචಽᝒ߃ᓧࠆ⸘▚㗔ၞࠍ↪޿ߚ DNS ࠍⴕ޿㧘⊒↢ߔࠆ᭴ㅧߩࠬࠤ࡯
࡞ߦߟ޿ߡ⼏⺰ߒߚ㧚ੂᵹᾲવ㆐ࠍ઻߁ࠢࠛ࠶࠻ᵹ
ߦ㑐ߔࠆ DNS ߪ㧘Liu [13]㧘Debusschere & Rutland[14]㧘Le & Papavassiliou [15] ߇⷗ࠄࠇࠆ⒟ᐲߢ޽ࠆ㧚ߎࠇࠄߪ㧘ᧄ⺰ᢥߢᛒ߁ᾲ⊛Ⴚ⇇᧦ઙߩ৻ߟ㧔CTD㧦⺑᣿ᓟ಴㧕ߩߺߦ㑐ߔࠆ⸃ᨆߢ޽ࠅ㧘߹ߚ㧘᷷ᐲ႐ߦ߅ߌࠆᄢⷙᮨ᭴ㅧ߿࡟ࠗࡁ࡞࠭ᢙଐሽᕈߦߟ޿ߡ
ߪ᣿ࠄ߆ߦߐࠇߡ޿ߥ޿㧚ߘߎߢᧄ⺰ᢥߢߪᐔⴕᐔ᧼㑆ࠢࠛ࠶࠻ੂᵹߦ߅
޿ߡ㧘ᄢⷙᮨߥ⸘▚㗔ၞࠍ↪޿ߚ DNS ࠍታᣉߒ㧘ㅦᐲ႐࡮᷷ᐲ႐ߦⷰኤߐࠇࠆᄢⷙᮨ᭴ㅧࠍ᣿ࠄ߆ߦ
ߔࠆ߽ߩߢ޽ࠆ㧚߹ߚ㧘⇣ߥࠆ 2 ⒳ߩᾲ⊛Ⴚ⇇᧦ઙࠍ⺖ߒ㧘Ⴚ⇇᧦ઙߩ㆑޿ߦኻߔࠆᓇ㗀ࠍ⺞ߴࠆ㧚ߐࠄߦ㧘᷷ᐲ႐ߦ߅ߌࠆᄢⷙᮨ᭴ㅧߦਈ߃ࠆ⸘▚㗔ၞߩᓇ㗀߿࡟ࠗࡁ࡞࠭ᢙଐሽᕈࠍᬌ⸛ߔࠆ㧚㧞 ⸘▚ᚻᴺ

ࠆ․ᓽ⊛ߥ᭴ㅧ㧔ᄢⷙᮨ᭴ㅧߣ๭߱㧕ࠍ߽ߟߎߣ߇
⍮ࠄࠇߡ޿ࠆ[1, 2, 4]㧚ਛᨋࠄ[3]߿ Kitoh ࠄ[5]ߪታ㛎⸃ᨆኻ⽎ߣߥࠆᵹࠇ႐ߪ㧘㕖࿶❗ᕈ࠾ࡘ࡯࠻ࡦᵹ

ߦࠃࠅ㧘Miyake ࠄ[6]߿ Lee & Kim[8]ߪ DNS ߦࠃࠅ㧘૕ߦ߅ߌࠆචಽ⊒㆐ߒߚᐔⴕᐔ᧼㑆ࠢࠛ࠶࠻ੂᵹߢ

ᄖጀߦ߅ߌࠆਥᵹᣇะߦ㕖Ᏹߦ㐳޿ᄢⷙᮨߥ❑᷵᭴޽ࠆ㧚ᵹࠇߪ㧘ਅო㕙ࠍ࿕ቯߒ㧘਄ო㕙ࠍ৻ቯㅦᐲ

ㅧߩሽ࿷ࠍᜰ៰ߒߡ޿ࠆ㧚ߒ߆ߒ㧘DNS ߢߎߩ᭴ㅧ

Uw ߢേ߆ߔߎߣߦࠃࠅ㚟േߐࠇࠆ㧚ᡰ㈩ᣇ⒟ᑼߪ㧘ࠍᝒ߃ߚ਄㧘ߐࠄߦოㄭறߩ⸃௝ᐲࠍචಽߦ⏕଻ߔએਅߩㅪ⛯ߩᑼ㧘߅ࠃ߮Navier-Stokesᣇ⒟ᑼߢਈ߃

ࠆߎߣߪ㕖Ᏹߦ࿎㔍ߢ޽ߞߚ㧚╩⠪ࠄߩࠣ࡞࡯ࡊ[9]ࠄࠇࠆ㧚

2 -- -152

C 2007 The Heat Transfer Society of Japan○

Thermal Science & Engineering Vol.15 No.3 (2007)

Table 1 Computational conditions: domain size, Li; number of grid points, Ni; spatial resolution, ∆i; and time step, ∆t.
Lx × Ly × Lz
Nx × Ny × Nz
Box size
Rew
∆x+
Reτ
∆y+
∆z+
∆t+
3000
Large
52
44.8h × h × 12.8h
1024 × 96 × 512
4.54
0.07~2.33
2.60
0.0143Small
129
24.0h × h × 6.0h
512 × 72 × 256
12.05
0.18~8.34
6.02
0.0307
Medium126
32.0h × h × 8.0h
1024 × 96 × 512
7.87
0.18~5.66
3.94
0.0295
8600
Large
126
44.8h × h × 12.8h
1024 × 96 × 512
11.03
0.18~5.67
6.31
0.0297Long
126
64.0h × h × 6.0h
2048 × 96 × 256
7.88
0.18~5.67
5.90
0.0297XL
126
96.0h × h × 12.8h
2048 × 96 × 512
11.83
0.18~5.67
6.31
0.0297

∂ui
=0
∂xi
*
∂ui*
∂p*
1 ∂ 2ui** ∂ui+uj * = − * +∂t*∂x j∂xi Rew ∂x*j 2(1)ࠍ⺖ߒߡ߅ࠅ㧘ߔߥࠊߜ㧘ਥᵹᣇะ᷷ᐲ൨㈩৻ቯ᧦
ઙߢ޽ࠆ㧚਄ਅო㕙ߢߩ᷷ᐲ႐ߩႺ⇇᧦ઙࠍએਅߦ
␜ߔ㧚ฦᣇ⒟ᑼߦ߅޿ߡ㧘i = 1~3 ߪߘࠇߙࠇ㧘ਥᵹ㧔x㧕ᣇCTD:
 UHF:ะ㧘ოု⋥㧔y㧕ᣇะ㧘ࠬࡄࡦ㧔z㧕ᣇะࠍ␜ߔ㧚ㅦㅪ⛯ߩᑼߣ Navier-Stokes ᣇ⒟ᑼߩࠞ࠶ࡊ࡝ࡦࠣߦ

(2)

θb = 0, θt = ∆Tθb = θt = 0(6)ᐲ႐ߦ㑐ߔࠆႺ⇇᧦ઙߪ㧘਄ਅო㕙਄ߢ non-slip ᧦Fractional step ᴺࠍ↪޿㧘ᤨ㑆ㅴⴕߦߟ޿ߡ☼ᕈ㗄㧔yઙߣߒ㧘ή㒢ߩᐔⴕᐔ᧼ࠍᮨᡆߔࠆߚ߼㧘x ෸߮ zᣇะ㧕ߦߪੑᰴ♖ᐲ Crank-Nicolson ᴺࠍ㧘ઁߩ㗄ߦᣇะߦߪ๟ᦼႺ⇇᧦ઙࠍ⺖ߒߡ޿ࠆ㧚ߟ޿ߡߪੑᰴ♖ᐲ Adams-Bashforth ᴺࠍㆡ↪ߒߚ㧚᷷ᐲ႐ߦ߅ߌࠆႺ⇇᧦ઙߣߒߡ㧘਄ਅო㕙㑆᷷ᐲⓨ㑆⊛㔌ᢔൻߦߪ᦭㒢Ꮕಽᴺࠍ↪޿ߚ㧚ኻᵹ㗄ߩ㔌Ꮕ৻ቯ᧦ઙ㧔constant temperature difference betweenᢔൻߦߪ㧘ࠬࡍࠢ࠻࡞ᴺߣߩᲧセߢ⦟޿৻⥌߇⏕⹺

two walls㧘CTD㧕ߣ㧘৻᭽ᾲᵹ᧤ടᾲ᧦ઙ㧔uniformߐࠇߡ޿ࠆ Consistent scheme [16]ࠍㆡ↪ߔࠆ㧚ਥᵹ

heat-flux heating/cooling㧘UHF㧕ߩ 2 ㅢࠅߩ᧦ઙਅߦ

ᣇะߣࠬࡄࡦᣇะߦ྾ᰴ♖ᐲਛᔃᏅಽࠍ㧘ოု⋥ᣇߟ޿ߡ⸃ᨆࠍⴕ߁㧔࿑ 1㧕㧚⇣ߥߞߚᾲ⊛Ⴚ⇇᧦ઙߦะߦߪੑᰴ♖ᐲਛᔃᏅಽࠍ↪޿ߚ㧚߹ߚ㧘ოု⋥ᣇ߅޿ߡߘࠇߙࠇ㧘ᰴߩࠃ߁ߦ᷷ᐲ஍Ꮕθ ࠍ↪޿ࠆ㧚ะߪਇ╬ಽഀᩰሶߣߒߡ޿ࠆ㧚~
CTD : T = Tb + θ = Tb + ∆T ⋅ y* + θdT +UHF : T + = Tw+ − θ + = m* x* − θ +dx⸘▚᧦ઙࠍ⴫ 1 ߦ␜ߔ㧚ᄢⷙᮨ᭴ㅧࠍᝒ߃ᓧࠆ⸘
▚㗔ၞࠍ⺞ߴࠆߚ߼㧘ਥᵹᣇะ㧔Lx = 24~96h㧕ߣࠬ
(3)

ࠍⴕߞߚ㧚
࡟ࠗࡁ࡞࠭ᢙࠍ Rew = 3000 ෸߮ 8600 ߣߒ㧘***ߎߎߢ㧘 θ% ( = θ − y ) ߪ᷷ᐲߩ✢ᒻ⊛ߥಽᏓ߆ࠄߩ

ᄌേಽߢ㧘ოု⋥ᣇะߩੂᵹᾲᵹ᧤ߩᓇ㗀ߦࠃࠆ߽ߩߢ޽ࠆ㧚਄ਅო㕙᷷ᐲᏅǍT ߢήᰴరൻࠍⴕ߁ߣ㧘
CTD ߩ႐ว㧘ࠛࡀ࡞ࠡ࡯ᣇ⒟ᑼߪએਅߩࠃ߁ߦ⴫ߐ
ࠇࠆ㧚

~
~*
~
∂θ *
1 ∂ 2θ ** ∂θ
+uj * =− v*
∂t *∂x j Rew Pr ∂x*j 2࡟ࠗࡁ࡞࠭ᢙଐሽᕈߦߟ޿ߡ߽ᬌ⸛ߔࠆ㧚៺ᡂ࡟ࠗࡁ࡞࠭ᢙߪ Reτ = 52 ෸߮ 126~129 ߣߥࠆ㧚ࡊ࡜ࡦ࠻࡞ᢙߪⓨ᳇ࠍᗐቯߒߡ 0.71 ߣߒߚ㧚⸘▚㗔ၞ XL ࠍ㒰ߊ⸘▚⚿ᨐߦ㑐ߒߡ㧘ᵹࠇ႐ߩੂᵹ⛔⸘㊂㧔ੂᵹᒝᐲ㧘࡟ࠗࡁ࡞࠭ᔕജߣߘߩࠛࡀ
࡞ࠡ࡯෼ᡰߥߤ㧕ߪ೨ႎ[9]ߦ␜ߒߚ㧚ઁࠣ࡞࡯ࡊߦ

(4)

ࠃࠆ DNS ߿ታ㛎୯ߣᲧセߒ㧘⸘▚ߩᅷᒰᕈࠍᬌ⸽
ߒߡ޿ࠆ㧚߹ߚ㧘ᧄ⸃ᨆߩ XL ߦ߅޿ߡ߽㧘චಽߦ

߹ߚ㧘UHF ߦ߅޿ߡ㧘ო㕙᷷ᐲTwߪਥᵹᣇะߦኻ
ߒߡ✢ᒻ⊛ߦჇടߒ㧘ਥᵹᣇะߩᐔဋ᷷ᐲ൨㈩ߪ৻
ቯ୯㧔2/um+㧕ߣߥࠆ㧚ߎࠇࠃࠅ㧘UHFߩࠛࡀ࡞ࠡ࡯
ᣇ⒟ᑼߪᰴᑼߢ⴫ߐࠇࠆ㧚+u*1 ∂ 2θ +
∂θ +
* ∂θ
−
=
u
+
2
j
u m+
∂x*j Rew Pr ∂x*j 2∂t *ࡄࡦᣇะ㧔Lx = 6~12.8h㧕ߩ㗔ၞࠨࠗ࠭ࠍᄌ߃ߡ⸃ᨆ

(5)⛔⸘⊛ቯᏱ⁁ᘒߢ޽ࠆߎߣࠍ⏕⹺ߒߡ߆ࠄ᷷ᐲ႐ߦ
߅ߌࠆฦ⒳⛔⸘୯ࠍขᓧߒߚ㧚㧟 ⚿ᨐ߅ࠃ߮⠨ኤ ᐔဋ㊂
࿑ 2 ߦ㧘᷷ᐲᦨᄢ୯θmax㧔CTD ߢߪ਄ਅო㕙᷷ᐲᧄ DNS ߦ߅ߌࠆ৻᭽ᾲᵹ᧤ߪ㧘਄ਅო㕙ߘࠇߙࠇᏅ∆T㧕ߢήᰴరൻߒߚᐔဋ᷷ᐲಽᏓࠍ␜ߔ㧚CTD ߦߦ߅޿ߡᐔဋ⊛ߦ৻᭽ߥᾲᵹ᧤㧔਄ਅߢߪ⇣ߥࠆ㧕߅޿ߡ Liu[13] ߦࠃࠆ DNS ߩ⚿ᨐࠍ␜ߔ߇㧘⦟ߊ৻

3 -- -153

C 2007 The Heat Transfer Society of Japan○

Thermal Science & Engineering Vol.15 No.3 (2007)θ /∆T, θ /θmax

1

Table 2 Skin friction coefficient and Nusselt number
defined by equations (7-9).

UHF

0.8
0.6

CTD

0.4

Present
Rew=3000
Rew=8600 (S)Rew=8600 (M)Rew=8600 (Large)
Rew=8600 (Long)
Rew=8600 (XL)

Kawamura et al. (2000)
Rew=12800
Liu (CTD, 2003)
Rew=3000

0.2
0
0

0.2

0.4

0.6

y/h

0.8

20

15

3000
3000[13]Large
6h×h×5h
Small
Medium
Large
Long
XL
6h×h×h3.2h×h×1.6h

12000[14]12800[17]1Cf(×103)
9.59
9.9
7.15
6.86
6.90
6.90
6.90
6.69
6.42

UHF
Nub
Nut
8.87 11.28
17.25 19.76
16.38 18.82
16.52 18.99
16.44 18.90
16.57 19.04
22.10 24.88

CTD
Nu
6.19
6.5
13.46
12.69
12.85
12.85
12.85
17.2 .
17.83

ಽ߆ࠆ㧚৻ᣇ㧘CTD ߢߪㅦᐲಽᏓߦ↱᧪ߔࠆ㕖ኻ
⒓ᕈߪ⷗ࠄࠇߥ޿㧚ߎߎߢ㧘ౝጀߩ( )+ߢࠬࠤ࡯࡝ࡦࠣࠍⴕ߁ߣ㧔࿑ 3

Komminaho et al. (1996)
Rew=3000Liu (CTD, 2003)
Rew=3000ෳᾖ㧕㧘⸘▚㗔ၞ߇ዊߐ޿႐ว㧔Small㧕㧘࠴ࡖࡀ࡞ਛ
ᔃઃㄭߢߪ㧘
ઁߩࠤ࡯ࠬߦᲧߴૐ޿᷷ᐲಽᏓࠍ␜ߔ㧚Ყセߩߚ߼ታ㛎[2, 4]߅ࠃ߮ࠬࡍࠢ࠻࡞ᴺߦࠃࠆ

u+=(1/0.42)lny++5.5

DNS[8]ߩ⚿ᨐ߽␜ߔ㧚ߎߩ௑ะߪ㧘࿑ 3 ߦ޽ࠊߖߡ
θ+=(1/0.42)lny++2.5

u+, θ+

Box size

8600

Fig. 2 Mean temperature profile normalized withmaximum value.
El Telbany et al. (Exp., 1982)
Rew=38000
Tillmark (Exp., 1995)
Rew= 4960
Rew=13600

Rew␜ߔᐔဋㅦᐲಽᏓߦߟ޿ߡ߽ⷰኤߐࠇࠆ㧚ߎࠇߪ㧘

10

Small ߦ߅ߌࠆ uτ ߿ Tτ ߇ᄢ߈ߊߥߞߡ޿ࠆߚ߼ߢ޽
u+=y+ࠆ㧚߹ߚ㧘ㅦᐲ႐ߣ CTD ߢߪ㧘y+ > 40 ߆ࠄ࠴ࡖࡀ
࡞ਛᄩ߹ߢኻᢙೣߦว߁㗔ၞ߇⷗ࠄࠇ㧘ᐔဋಽᏓߩ

5࡟ࠗࡁ࡞࠭ᢙଐሽᕈߪዊߐ޿㧚ߎࠇߪ㧘࠴ࡖࡀ࡞ਛ
+ᄩ߹ߢᐔဋㅦᐲ㧔᷷ᐲ㧕൨㈩߇޽ࠆߚ߼ߣ⠨߃ࠄࠇ+θ =Pr·y

0

0

UHF
0

100

ࠆ㧚ห⒟ᐲߩ៺ᡂ࡟ࠗࡁ࡞࠭ᢙߦ߅ߌࠆࡐࠕ࡙࠭ࠗ

Present
Rew=3000
Rew=8600 (S)Rew=8600 (M)Rew=8600 (Large)
Rew=8600 (Long)
Rew=8600 (XL)
Kawamura et al. (2000)
Rew=12800

CTD

101

y+

ੂᵹߢߪ㧘ኻᢙ㗔ၞߪ⴫ࠇߕ㧘ㅦᐲᰳ៊ೣߩߺ߇ᄖ
ጀߢ㗼⪺ߣߥࠆ[18]㧚৻ᣇ㧘ᐔဋ᷷ᐲಽᏓ߇ࡐࠕ࠭
࡙ࠗဳߣߥࠆ UHF ߢߪ㧘ᄖጀߦ߅ߌࠆ㗼⪺ߥ࡟ࠗࡁ࡞࠭ᢙଐሽᕈ߇⷗ࠄࠇࠆ㧚102ࠢࠛ࠶࠻ᵹࠇߢߪ㧘࠴ࡖࡀ࡞ਛᄩߦ߅޿ߡ߽ᐔဋ

Fig. 3 Mean velocity and temperature profiles (in thebottom half channel) scaled with the wall
units.

ㅦᐲ൨㈩ࠍ߽ߟߚ߼㧘ੂࠇߩ↢ᚑ߇ⴕࠊࠇ㧘↢ߓߚੂࠇߩࠛࡀ࡞ࠡ࡯߇ੂᵹ᜛ᢔߦࠃࠅ㧘ࡐࠕ࡙࠭ࠗੂ
ᵹߦᲧߴᄙߊߩㆇേ㊂߇࠴ࡖࡀ࡞ోၞߦャㅍߐࠇࠆ㧚⥌ߒߡ޿ࠆ㧚ਔႺ⇇᧦ઙߣ߽㧘⸘▚㗔ၞߩ㆑޿ߦࠃ

หᤨߦᾲャㅍ߽ᵴ⊒ߦߥࠅ㧘ࠢࠛ࠶࠻ੂᵹߣࡐࠕ࠭

ࠆᓇ㗀ߪ߈ࠊ߼ߡዊߐߊ㧘࡟ࠗࡁ࡞࠭ᢙଐሽᕈߩߺ

࡙ࠗੂᵹࠍห⒟ᐲߩ៺ᡂ࡟ࠗࡁ࡞࠭ᢙߢᲧߴߚߣ߈㧘ⷰኤߐࠇࠆ㧚UHF ߦ߅޿ߡ㧘᷷ᐲಽᏓ߇਄ო஥ߣਅ

ࠢࠛ࠶࠻ੂᵹߩ࠿࠶࠮࡞࠻ᢙ߇ࡐࠕ࡙࠭ࠗੂᵹߦᲧ

ო஥ߢኻ⒓ߣߥߞߡ޿ߥ޿ߎߣ߇⷗ฃߌࠄࠇࠆ㧚ߎߴ㜞ߊߥࠆߎߣ߇⠨߃ࠄࠇࠆ㧚⴫ 2 ߦ㧘ฦ࡟ࠗࡁ࡞

ࠇߪㅦᐲಽᏓߩ㕖ኻ⒓ᕈ㧔ub = 0㧘ut = Uw㧕ߦ↱᧪ߒ㧘࠭ᢙ࡮ടᾲ᧦ઙߦ߅޿ߡᰴᑼ߆ࠄᓧࠄࠇࠆ៺ᡂଥᢙ

ო㕙߆ࠄᵹ౉ߔࠆᾲᵹ᧤߇਄ਅߢ⇣ߥࠆ㧔qb < qt 㧕ߣ࠿࠶࠮࡞࠻ᢙࠍ␜ߔ㧚ߚ߼ߢ޽ࠆ㧔Kawamura ࠄ[17]ෳᾖ㧕㧚ߎߩ㕖ኻ⒓ᕈ

Cf =ߪࡐࠕ࡙࠭ࠗੂᵹߦ߅ߌࠆ UHF ߢߪⷰኤߐࠇߥ޿

=2

1 ρu 2 u + 2m2 m
h qw 2 Reτ Pr
Nu =
=
θm+
λ θm

[12]㧚ࠢࠛ࠶࠻ੂᵹߢߪ㧘㚟േ㕙ߢ޽ࠆ਄ო஥ߢᵹ
ㅦ߇ㅦ޿ߚ߼㧘ᾲવ㆐₸߇㜞ߊߥࠅ㧘ਅო஥ߦኻߒ᷷ᐲθ ߇⧯ᐓ㜞ߊߥࠆ㧚ߘߩߚ߼㧘UHF ߦ߅ߌࠆ᷷
ᐲߩࡇ࡯ࠢ૏⟎ߪ߿߿਄ო஥ߦ⒖േߒߡ޿ࠆߎߣ߇

τw

(7)

(8)

ߎߎߢ㧔qw /θm㧕ߪᐔဋᾲવ㆐₸ࠍ␜ߔ㧚UHFߦ߅޿

4 -- -154

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Thermal Science & Engineering Vol.15 No.3 (2007)ߡߪ㧘਄ਅო㕙ߢᐔဋᾲᵹ᧤㧔qb < qt㧕߇⇣ߥࠆߚ߼㧘h qb 2 Reτ Pr Nub = λ θ = θ T

m
m
τ ,b

 Nu = h qt = 2 Reτ Pr t λ θmθm Tτ ,t(a) streamwise velocity fluctuation.
1.00

y/h

0.75
0.50
0.25

(9)

0.00
0

1

2

z/h

3

z/h

3

z/h

3

4

(b) temperature fluctuation for CTD.
1.00
0.75

y/h

ߣߔࠆߣ㧘࠴ࡖࡀ࡞਄ਅߢ࠿࠶࠮࡞࠻ᢙߦᏅ߇⷗ࠄ
ࠇࠆ㧔Nub < Nut㧕㧚ห᭽ߩቯ⟵ߦࠃࠆࡐࠕ࡙࠭ࠗੂ

0.50
0.25
0.00
0

ᵹߢߩ࠿࠶࠮࡞࠻ᢙߪ㧘Reτ = 110ߢNu = 7.57㧔CTD㧕߅ࠃ߮11.6㧔UHF㧕ߢ޽ࠅ[18]㧘ߎࠇߦᲧߴߡࠢࠛ࠶

1

2

4

(c) temperature fluctuation for UHF.
1.00࠻ੂᵹߦ߅ߌࠆNuߪᄢ߈޿୯ߢ޽ࠆߎߣ߇ಽ߆ࠆ㧚
y/h

0.75

߹ߚ㧘⴫2ߦߪDNSߢઁߩ⎇ⓥࠣ࡞࡯ࡊ[13, 14, 17]

0.50
0.25

߇ᓧߚCfߣNuࠍᲧセߣߒߡ␜ߔ㧚ᧄ⎇ⓥߢߪ㧘ߎࠇ

0.00
0ࠄㆊ෰ߦⴕࠊࠇߚDNSࠃࠅ߽ᄢ߈޿⸘▚㗔ၞࠍ↪

1

2

4

Fig. 4 Instantaneous velocity and temperature field inan (x, y) plane for Rew = 8600 (Large); red,
positive fluctuation (u’+, θ’+ > 1.5); blue,
negative (u’+, θ’+ <−1.5). The v and w velocities
are superimposed as vectors. A large-scale
structure that fills the entire gap between theplates can be seen in (a) and (b).

޿ߡ޿ࠆ㧚ߎߎߢ㧘⸘▚㗔ၞߦኻߔࠆଐሽᕈߦᵈ⋡ߔࠆߣ㧘㗔ၞߩዊߐ޿႐วߦ߅޿ߡCfߣNu߇ᄢ߈ߊߥࠆ௑ะ߇⷗ฃߌࠄࠇࠆ㧚ߎߩࠃ߁ߦ㧘Rew = 8600ߩ႐วࠍ଀ߦขࠆߣ㧘⸘▚㗔ၞߩᓇ㗀߇ήⷞ಴᧪ࠆ
ߚ߼ߦߪ㧘Mediumએ਄ߩ⸘▚㗔ၞ߇ᔅⷐߢ޽ࠆߎߣ
߇ࠊ߆ࠆ㧚Smallߢᓧߚ୯ߪ㧘ઁߩ႐วߩ୯ࠃࠅ߽⚂4%ᄢ߈ߊ⷗Ⓧ߽ࠄࠇߡ޿ࠆ㧚ᰴ▵ߦ␜ߔࠃ߁ߦ㧘 ᄢⷙᮨ᭴ㅧ

Smallએਅߩ⸘▚㗔ၞߢߪ㧘ਥᵹᣇะߦᄢⷙᮨ᭴ㅧ

ᾲ⊛Ⴚ⇇᧦ઙߦኻߔࠆ᭴ㅧߩ㆑޿ࠍⷰኤߔࠆߚ

㧔߽ߒߊߪ❑᷵ኻ㧕߇৻ᵄ㐳ಽ߽ᝒ߃ࠄࠇߡ޿ߥ޿㧚߼㧘Rew = 8600㧔Large㧕ߦ߅޿ߡ㧘หᤨೞߩห㧔z, y㧕ߟ߹ࠅ㧘ߎߩ႐วߦ㧘᭴ㅧߩᒻᚑ߿ㆇേ㊂࡮ᾲャㅍᢿ㕙ౝߢนⷞൻߒߚ⍍ᤨߩㅦᐲ႐߅ࠃ߮ฦ᷷ᐲ႐ࠍ

ߦߟ޿ߡߩ๟ᦼႺ⇇᧦ઙߩᓇ㗀߇㗼⪺ߦߥࠆߣ⸒߃

࿑ 4 ߦ␜ߔ㧚ਥᵹߪ⚕㕙ု⋥ᣇะߢ޽ࠆ㧚ߎߎߢߩࠆ㧚นⷞൻߪ⸘▚㗔ၞో૕ߢߪߥߊ㧘ౖဳ⊛ߥ᭴ㅧ߇⏕(a) streamwise velocity fluctuation.
1.00

y/h

0.75
0.50
0.25
0.00

0

1

2

3

4

5

x/h

6

x/h

6

x/h

6

7

8

9

10

7

8

9

10

7

8

9

10

(b) temperature fluctuation for CTD.
1.00

y/h

0.75
0.50
0.25
0.00

0

1

2

3

4

5

(c) temperature fluctuation for UHF.
1.00

y/h

0.75
0.50
0.25
0.00

0

1

2

3

4

5

Fig. 5 Instantaneous velocity and temperature field in an (x, y) plane for Rew=8600 (Large); red, positive fluctuation(u’ +, θ’ + >1.5); blue, negative (u’ +, θ’ + <−1.5). The u’ and v’ velocity fluctuations are superimposed as
vectors. Mean flow direction is from left to right. A large-scale structure of fluid with low streamwise velocity
which is moved from the lower wall towards the upper one can be seen inside the white dashed box.
5 -- -155

C 2007 The Heat Transfer Society of Japan○

Thermal Science & Engineering Vol.15 No.3 (2007)⹺ߐࠇߚછᗧߩ㗔ၞߢ޽ࠆ㧚࿑ౝߩࡌࠢ࠻࡞ߪᢿ㕙ᱜߩᄌേ㧔u’ > 0㧘θ’ > 0㧕߇↢ߓߡ߅ࠅ㧘ᄢⷙᮨߥㆇ

ߦᐔⴕߥㅦᐲᚑಽ㧔v, w㧕ࠍ⴫ߒ㧘ࠦࡦ࠲࡯ߪ u’߹േ㊂࡮ᾲャㅍ߇ⴕࠊࠇߡ޿ࠆ㧚৻ᣇ㧘UHF ߢߪ㧘࠴ߚߪθ’ߢ޽ࠆ㧚ㅦᐲ႐㧔࿑ 4(a)㧕ߣ CTD㧔࿑ 4(b)㧕

ࡖࡀ࡞ਛᄩߢᄌേ߇ᒙߊߥࠅ㧘਄ო஥ߢ CTD ߣㅒߢߪ㧘࠴ࡖࡀ࡞ో᏷ߦ෸߱㜞ㅦ࡮ૐㅦ㧔㜞᷷࡮ૐ᷷㧕╓ภߩ᷷ᐲᄌേ߇⏕⹺ߢ߈ࠆ㧚ߎࠇߪ㧘UHF ߦ߅ߌ㗔ၞߩ⊒↢߇⏕⹺ߢ߈ࠆ㧚⍍ᤨ႐ߢߩᄢⷙᮨߥ❑᷵ࠆᐔဋ᷷ᐲ൨㈩߇਄ო஥㧔dθ /dy < 0㧕ߣਅო஥㧔dθ /dyኻߩ⏕⹺ߪ࿎㔍ߢ޽ࠆ߇㧘ߎࠇࠄᱜ⽶ߦᄌേߒߚ㗔> 0㧕ߢ⇣ߥࠆߚ߼ߢ޽ࠆ㧚ߟ߹ࠅ㧘࠴ࡖࡀ࡞ਛᔃࠍ

ၞౝߢᄢⷙᮨߥ็߈ਅߍ㧔v’ < 0㧕߿็߈਄ߍ㧔v’ > 0㧕߹ߚߋᄢⷙᮨߥ็߈਄ߍ࡮ਅߍ߇↢ߓߚ႐วߦ㧘߇⊒↢ߒߡ޿ࠆ௑ะ߇⷗ฃߌࠄࠇࠆ㧚ოㄭߊߢߪ㧘UHF ߢߪ࠴ࡖࡀ࡞ਛᔃઃㄭߢ᷷ᐲᄌേߩᱜ⽶߇ㅒ

ejection࡮sweep ߦࠃߞߡ㧘ዊߐ޿ⓨ㑆ࠬࠤ࡯࡞ߢᱜ

ォߔࠆ㧚⽶ߩᄌേ߇↢ߓߡ޿ࠆ㧚UHF㧔࿑ 4(c)㧕ߢߪ㧘ਅოߎߎߢ㧘⛔⸘⊛ߥ᭴ㅧߩⓨ㑆ࠬࠤ࡯࡞߿ᒻ⁁ࠍ⍮ㄭறߩ᷷ᐲᄌേߪ CTD ߿ㅦᐲ႐ߣㄭߊ㧘Ⴚ⇇᧦ઙࠆߚ߼㧘2 ᰴరੑὐㅦᐲ⋧㑐߅ࠃ᷷߮ᐲ⋧㑐ࠍ㧔z, y㧕ߦࠃࠆ㆑޿ߪዊߐ޿㧚ߒ߆ߒ㧘࠴ࡖࡀ࡞ਛᄩㇱߢߪ㧘ᐔ㕙ߦߟ޿ߡ࿑ 6 ߦ㧘
㧔x, y㧕ᐔ㕙ߦߟ޿ߡߪ࿑ 7 ߦ᷷ᐲᄌേ߇ዊߐߊ㧘ᄢⷙᮨߥ㜞᷷࡮ૐ᷷㗔ၞߪ⏕⹺␜ߔ㧚ၮḰὐ㜞ߐ y’ߪ㧘mid-height㧔y’ = h/4㧕ߣߒ㧘ߢ߈ߥ޿㧚ߎࠇߪ㧘UHF ߦ߅޿ߡᐔဋ⊛ߥ᷷ᐲ൨㈩࠴ࡖࡀ࡞਄ਅ㑆ߢߩ⋧㑐ࠍ⹏ଔߔࠆ㧚ੑὐ⋧㑐 Rij߇࠴ࡖࡀ࡞ਛᄩㇱߢ㔖ߦߥࠆߚ߼ߢ޽ࠆ㧚ߪᰴᑼߦࠃࠅᓧߡ޿ࠆ㧚ห᭽ߦ㧘
㧔x, y㧕ᢿ㕙ౝߢนⷞൻߒߚ⍍ᤨ႐㧔⸘▚
u i′ ( x , y ′, z ) ⋅ u ′j ( x , y , z + ∆z )
 Rij (∆z , y , y ′) =u i′rms ( y ′) ⋅ u ′j rms ( y ) R (∆x , y , y ′) = u i′ ( x , y ′, z ) ⋅ u ′j ( x + ∆x , y , z ) ij
u i′rms ( y ′) ⋅ u ′j rms ( y )㗔ၞߩ৻ㇱ㧕ࠍ࿑ 5 ߦ␜ߔ㧚ਥᵹᣇะߪฝะ߈ߢ޽
ࠆ㧚࿑ 5(a, b)ߩ⊕⎕✢ߩᨒౝߦᵈ⋡ߔࠆߣ㧘ㅦᐲ႐ߣ᷷ᐲ႐㧔CTD㧕ߦ߅޿ߡ㧘ᄢⷙᮨߥ็߈਄ߍߦࠃ
ࠅᄢⷙᮨߥૐㅦ㧔ૐ᷷㧕㗔ၞ߇⊒↢ߒߡ޿ࠆߎߣ߇

(10)⏕⹺ߢ߈ࠆ㧚ߎߩนⷞൻ߆ࠄߪ㧘ߘߩਥᵹᣇะߩ㐳ㅦᐲ႐ߦ߅޿ߡ࿑ 6(a)ߩ Ruu ߩಽᏓ߇਄ო㕙߹ߢ⋧ߐ߿᭴ㅧߪ㧘ㅦᐲ႐ߣ᷷ᐲ႐㧔CTD㧕ߢห৻ߢ޽ࠆ

㑐߇㜞ߊ㧘࠴ࡖࡀ࡞ో᏷㧔y ᣇะ㧕ߦ߅ࠃ߱ᄢⷙᮨ

ߎߣ߇⷗ฃߌࠄࠇࠆ㧚߹ߚ㧘ߎߩ⊕ᨒౝߢዪᚲ⊛ߥ᭴ㅧ߇⏕⹺ߢ߈ࠆ㧚ߐࠄߦ㧘ࠬࡄࡦᣇะߦ∆z ≈ ±h ߩ็߈ਅߍ߿㧘ߘࠇߦ઻߁㜞ㅦ㧔㜞᷷㧕㗔ၞ߇⷗ࠄࠇ

૏⟎ߢ⽶ߩ⋧㑐߇㧘∆z ≈ ±2.3h ߢᱜߩ⋧㑐߇⴫ࠇ㧘Ḱࠆ߇㧘ߎࠇࠄߪოㄭறߩࠬ࠻࡝࡯ࠢ᭴ㅧߣᓸ⚦ߥ❑๟ᦼ⊛ߥ᭴ㅧ߇⷗ฃߌࠄࠇࠆ㧚࿑ 6(b)ߩ Ruv ߦᵈ⋡᷵ߦࠃࠆ߽ߩߢ޽ࠆ㧚࿑ࠃࠅ㧘ߘߩਥᵹᣇะ㐳ߐߪߔࠆߣ㧘ၮḰὐઃㄭߢ⽶୯㧔−0.4 ⒟ᐲ㧕㧘਄ო஥߹

1~2h㧘☼ᕈ㐳ߐߢ 250~500 ⒟ᐲߦࠬࠤ࡯࡝ࡦࠣߢ߈

ߢ⽶ߩ㗔ၞ߇ᐢ߇ߞߡ޿ࠆ㧚߹ߚ㧘∆z ≈ ±h ߢ⋧㑐߇ࠆ㧚࿑ਛએᄖߩ㗔ၞߢߪ㧘ᄢⷙᮨߥ็߈ਅߍ߇⿠߈

ᱜߩ㗔ၞ߇⃻ࠇ㧘ߎࠇߪ㧘❑᷵ኻߦࠃߞߡᄢⷙᮨߥ

ߡ޿ࠆᚲ߽ห᭽ߦሽ࿷ߒ㧘߶߷หߓⓨ㑆ࠬࠤ࡯࡞ߢ

ਥᵹᣇะㅦᐲᄌേ߇↢ߓߡ޿ࠆߎߣߣ⍦⋫ߒߥ޿㧚

1.00

-0.04

0.00

-6

-4

-0.16

-0.04
0.24
0.36

0.12

-0.04

0.48
0.6

-0.04

0

2

z/h

4

6

0.00

(b)

1.00
0.2

0.08

0.25

-0.08

-6

-4

-2

0

0 08

z/h

-0.08

2

4

6

-4

-2

0

-0.02
0.06

-0.02

z/h

2

4

6

0.04

-6

-4

-2

z/h

2

4

6

z/h

2

4

6

-0.1
-0.04-0.16
-0.22
-0.28
-0.34
-0.04

0

1.00
0.75

0.50

0.2
-0.08

0.25
-6

-4

-2

y/h

y/h

-6

-0.38
-0.26

0.50

0.00

(d)

0.75

(e)

0.06

-0.14 -0.02

-0.02

0.25

0.56
0.32 0.44

1.00

0.00

-0.02
-0.2

0.75

-0.08

y/h

y/h

-0.08

0.50

0.00

-0.02

1.00

0.75

(c)

-0.08

0.50
0.25

-0.04

0.12
0 24

-2

y/h

y/h

-0.16

0.50

0.75

-0.04

-0.04

0.25

(a)

1.00

-0.04

0.12

0.75

0.08

0.56
0.68

0

0.50
0.04
-0.1
-0.04
-0.34
-0.16
-0.28

0.25

z/h

2

4

6

(f)

0.00

-6

-4

-2

0

Fig. 6 Contours of the two-dimensional two-point correlation coefficient as a function of spanwise and wall-normal
separation, Rij (∆z, y, y’) defined by equation (10), for Rew = 8600 (XL): (a) Ruu , (b)Ruv , (c, e) Rθθ , (d, f) Rθv ; (c, d) for
CTD, (e, f) for UHF. The location of the fixed correlation point is y’/h = 0.244 (y’ + = 61). The solid contours denotepositive correlation, and dashed contours negative. The contour increment is 0.04 (a, c, e) and 0.02 (b, d, f).
6 -- -156

C 2007 The Heat Transfer Society of Japan○

Thermal Science & Engineering Vol.15 No.3 (2007)

1.00
0.02

y/h

0.75

0.02

0.32
0.560.44

0.25

(a)

0.00

0.14
0.26

-40

-45

-35

-30

-25

-20

-15

-5

-10

0.8
0.62

0

0.02

0.2

0.38

0.50

0.02
0.26

0.08
0.14

15

10

x/h 5

20

25

30

35

40

45

20

25

30

35

40

45

1.00

y/h

0.75

0.16

0.50

(b)

0.00

-0.04

0.4
0.1

0.25

0.04

-40

-45

-35

-30

-25

-20

-15

-5

-10

0.52
0.220.94
0.34
0.66
0.28
0.46
0.22
0 28

0

0.1

0.04

10

x/h 5

1.00

y/h

0.50

-45

0.2

0.02

-40

0.02

0.92
0.38
0.56
0.32
0.14 0.44
0.26

-35

-30

-25

-20

-15

0.02

0.08

0.02
0.02

0.25
0.00

0.02

-0.06

0.75

(c)

15

B

-5

-10

0

0.02

x/h 5

10

15

20

25

30

35

40

45

A
A
Fig. 7 Contours of the two-dimensional two-point correlation coefficient as a function of streamwise andwall-normal separation, Rii (∆x, y, y’) defined by equation (10), for Rew = 8600 (XL): (a) Ruu , (b, c) Rθθ ; (b)for CTD, (c) for UHF. The location of the fixed correlation point is y’/h = 0.244 (y’+ = 61). The solid
contours denote positive correlation, and dashed contours negative. The contour increment is 0.04.
᷷ᐲ႐㧔CTD㧕ߦ߅޿ߡ߽ห᭽ߦ⺑᣿ߢ߈ࠆᄢⷙᮨ

߮࡟ࠗࡁ࡞࠭ᢙࠍᄌ߃㧘ߘࠇߦኻߔࠆᄢⷙᮨ᭴ㅧߩ

ߥ᭴ㅧࠍ߽ߟߎߣ߇㧘Rθθ ߣ Rθv ߩಽᏓ߆ࠄ⏕⹺ߢ߈ଐሽᕈߦߟ޿ߡᬌ⸛ߔࠆ㧚࿑ 8 ߦ㧘ოㄭற߹ߚߪ࠴

ࠆ㧔࿑ 6(c, d)ෳᾖ㧕
㧚UHF ߦ߅޿ߡߪ㧘೨ㅀߒߚࠃ

ࡖࡀ࡞ਛᄩߦ߅ߌࠆࠬࡄࡦᣇะੑὐ⋧㑐ଥᢙ㧘Ruu߁ߦ࠴ࡖࡀ࡞ਛᄩㇱࠍႺߦ᷷ᐲᄌേߩᱜ⽶߇ㅒߦߥ(∆z)߅ࠃ߮ Rθθ (∆z)ߩಽᏓࠍ␜ߔ㧚ࠆߚ߼㧘࿑ 6(e)ߩࠃ߁ߦ਄ო஥ߢߩ⋧㑐 Rθθ ߇ߥߊRij ( ∆ z ) =ߥࠆ㧔߽ߒߊߪ㧘ዊߐ޿ߥ߇ࠄ߽ㅒ╓ภߩ⋧㑐߇⏕⹺ߐࠇࠆ㧕㧚࿑ 6(f)ߦ␜ߔ⋧㑐ଥᢙ Rθv ߩಽᏓߪ㧘਄ui′ ( x, y,z ) ⋅ u′j ( x, y,z + ∆ z )ui′rms ( y ) ⋅ u′j rms ( y )(11)ო஥ߣਅო஥ߢ⋧㑐ߩᱜ⽶߇ㅒォߒߡ޿ࠆ㧚ߟ߹ࠅ㧘࿑ 8(a)ߩოㄭறߢߪ㧘޿ߕࠇߩࠤ࡯ࠬߢ߽∆z+ ≈ 50ᄖጀߢ↢ߓߚ็߈਄ߍߪ࠴ࡖࡀ࡞ో᏷㧔y ᣇะ㧕ߦߦ⋧㑐ଥᢙߩᭂዊ୯߇޽ࠅ㧘Ḱ⒎ᐨ᭴ㅧߣߒߡࠃߊ

߅ࠃ߮㧘ਅო஥ߢ⽶ߩ᷷ᐲᄌേ㧘਄ო஥ߢᱜߩ᷷ᐲ

⍮ࠄࠇࠆࠬ࠻࡝࡯ࠢ᭴ㅧߩሽ࿷ࠍ␜ໂߒߡ޿ࠆ㧚ᒝᄌേࠍ↢ߓߐߖߡ޿ࠆ㧚็߈ਅߍߩ႐วߪ㧘ਅო஥

޿⽶ߩ⋧㑐ࠍ␜ߔ㑆㓒߇࡟ࠗࡁ࡞࠭ᢙߦࠃߞߡ⇣ߥߢᱜ㧘਄ო஥ߢ⽶ߩ᷷ᐲᄌേ߇↢ߓࠆ㧚ߞߡ޿ࠆ㧚߹ߕ㧘Rew = 8600 ߦ߅޿ߡߪ㧘ࠬࡄࡦᣇ࿑ 7 ߩਥᵹᣇะߦ߅ߌࠆ 2 ᰴరੑὐ⋧㑐 Rij(∆x, y,ะߦ∆z+ = 250~300 ߢ⽶ߩࡇ࡯ࠢ୯ࠍ␜ߔ߇㧘ߎࠇߪy’)߆ࠄߪ㧘ᄢⷙᮨߥㅦᐲ࡮᷷ᐲᄌേߩ᭴ㅧߪ਄ო஥

∆z = 1~1.2h ߦ⋧ᒰߒ㧘ᓟߦ␜ߔ࠴ࡖࡀ࡞ਛᄩߢ㗼⪺ਅᵹߦિ߮㧘y ゲߦኻߒߡ௑޿ߚ᭴ㅧߢ޽ࠆߎߣ߇

ߥᄢⷙᮨ᭴ㅧߩ㑆㓒ߣࠃߊ৻⥌ߔࠆ㧚ห᭽ߩ௑ะ߇

ಽ߆ࠆ㧚ㅦᐲ႐߅ࠃ᷷߮ᐲ႐ߣ߽ߦ∆x ≈ ±15~20h 㔌

Rew = 3000 ߩ႐วߢ߽⷗ࠄࠇࠆ߇㧘ࠬ࠻࡝࡯ࠢ᭴ㅧ

ࠇߚᚲߦ⽶ߩ⋧㑐㧔Ruu < 0㧘Rθθ < 0㧕߇⴫ࠇߡ޿ࠆ㧚㧔∆z+ = 50 ߢ⽶ߩ⋧㑐㧕ߣᄢⷙᮨ᭴ㅧ㧔∆z = 1~1.2h⋧㑐ߩၮḰὐ߆ࠄ㔌ࠇߡ߽㧔∆x >40h㧘⍫ශ A ઃㄭ㧕㧘ߢ⽶ߩ⋧㑐㧕㑆ߩⓨ㑆ࠬࠤ࡯࡞ߩᏅ߇ዊߐ޿ߚ߼㧘⋧㑐ଥᢙ߇᦭ᗧߥ୯ࠍ߽ߟߎߣ߆ࠄ㧘ਥᵹᣇะߦ߽

ਔ⠪ߩੑὐ⋧㑐ߦ෸߷ߔᓇ㗀ࠍ඙೎ߔࠆߎߣߪ㔍ߒḰ๟ᦼ⊛ߦᄢⷙᮨ᭴ㅧ߇↢ߓߡ޿ࠆߎߣ߇ಽ߆ࠆ㧚޿㧚ࠃߞߡ㧘࿑ 8(a)ߩ㑆㓒∆z+߇㐿޿ߚߣ߈ߩ࡟ࠗࡁ

UHF ߩ⋧㑐ଥᢙ Rθθ ߩಽᏓߦᵈ⋡ߔࠆߣ㧘ၮḰὐߩ࡞࠭ᢙߦࠃࠆᏅ⇣ߪ㧘࠴ࡖࡀ࡞᏷ h ߢࠬࠤ࡯࡝ࡦࠣ

਄ო஥߿߿ਅᵹ㧔࿑ਛߦ␜ߔ㗔ၞ B㧕ߦ߅޿ߡ㧘Rθθߔࠆߎߣߢዊߐߊߥࠆ㧚ᄖጀߩ᭴ㅧ߇ოㄭறߦ߹ߢ

߇㗼⪺ߦ⽶ߣߥࠆ৻ᣇ㧘ਅო஥ߦߟ޿ߡߪ㧘CTD ߣᓇ㗀ߔࠆ௑ะߪ㧘☼ᕈ㐳ߐߣᄖጀࠬࠤ࡯࡞㑆ߦᄢ߈ห᭽ߦ∆x ≈ ±15~20h ߢ⋧㑐߇⽶ߣߥࠆ㧚ߎߩߚ߼㧘ߊᏅ߇޽ࠆ႐ว㧔㜞࡟ࠗࡁ࡞࠭ᢙ㧕ߦ㧘଀߃߫ࡐࠕ࿑ 7(c)ߦ⷗ࠆࠃ߁ߦ㧘ၮḰὐ߿߿ਅᵹߢ CTD ߣߪㅒ࡙࠭ࠗੂᵹߦ߅޿ߡ߽⷗ฃߌࠄࠇࠆ㧔Abe ࠄ[11]ߩ

ะ߈㧔ฝਅะ߈㧕ߩ⽶ߩ㗔ၞ߇⴫ࠇߡ޿ࠆ㧚࿑ 10 ෳᾖ㧕㧚ߒ߆ߒ㧘Ყセ⊛࡟ࠗࡁ࡞࠭ᢙ߇ૐ޿႐

਄⸥ߩ 2 ᰴరੑὐ⋧㑐ߪ㧘ᧄ⸘▚ߢᦨᄢߩ⸘▚㗔ၞߦ߅޿ߡᓧߚ⚿ᨐߢ޽ࠆ㧚ߎߎߢ㧘⸘▚㗔ၞ߅ࠃวߢ߽㧘ᄖጀߩᓇ㗀߇ოㄭறߦ㗼⪺ߦ⃻ࠇࠆ௑ะߪ㧘ࠢࠛ࠶࠻ੂᵹߩ․ᓽߢ޽ࠆ㧚

7 -- -157

C 2007 The Heat Transfer Society of Japan○

Thermal Science & Engineering Vol.15 No.3 (2007)(a) at the near-wall region.

0.8

at the channel center
Present
Rew=3000
Rew=8600 (S)Rew=8600 (M)Rew=8600 (Large)
Rew=8600 (Long)
Rew=8600 (XL)
Kawamura et al. (2000)
Rew=12800

0.4

Ruu

0

0.3

Rθθ (∆x), Ruu (∆x)

at y+=5 ~ 6Rθθ (∆z), Ruu (∆z)

0.6

Rθθ (CTD)

0Rθθ (UHF)

0
0

200

+

∆z

400

at the channel centerRθθ (∆z), Ruu (∆z)

0.4

Ruu

0

Rθθ (UHF)

0

600

10

20

∆x/h

30

40

Fig. 9 Streamwise two-point correlation coefficient of
streamwise velocity fluctuation or temperaturefluctuation at the channel center.

Present
Rew=3000
Rew=8600 (S)Rew=8600 (M)Rew=8600 (Large)
Rew=8600 (Long)
Rew=8600 (XL)
Kawamura et al. (2000)
Rew=12800

᭽ߢ޽ࠆ㧚⇣ߥࠆᾲ⊛Ⴚ⇇᧦ઙߦࠃࠆ㆑޿ߪ㧘࿑ 9 ߢ␜ߒߚਥᵹᣇะੑὐ⋧㑐ଥᢙߩಽᏓߢ㗼⪺ߦ⷗ࠄࠇࠆ㧚ㅦ
ᐲ႐ߣ CTD ߦ߅޿ߡ⸘▚㗔ၞ߳ߩଐሽᕈ߇⴫ࠇߡ
޿ࠆ৻ᣇߢ㧘UHF ߢߪ⸘▚㗔ၞߦࠃࠆ᦭ᗧߥᏅߪ⷗

Rθθ (CTD)

0Rθθ (CTD)00(b) at the channel center.

0.8

Ruu

0

Present
Rew=3000
Rew=8600 (S)Rew=8600 (M)Rew=8600 (Large)
Rew=8600 (Long)
Rew=8600 (XL)
Kawamura et al. (2000)
Rew=12800

ࠄࠇߥ޿㧚߹ߕ㧘ㅦᐲ႐ߣ CTD ߦ߅ߌࠆ⋧㑐ଥᢙಽᏓߦᵈ⋡ߔࠆ㧚Small ߦ߅޿ߡߪ⋧㑐߇㔖ߦ⪭ߜߕ㧘⸘▚㗔ၞ߇ᄢⷙᮨ᭴ㅧࠍᝒ߃ࠄࠇߡ޿ߥ޿㧚㗔Rθθ (UHF)0㧔Medium ߿ Large㧕㧘ၞࠍ Lx ≥ 32h ߹ߢ᜛ᄢߔࠆߎߣߢ
ਥᵹᣇะߦ᦭㒢㐳ߩ᭴ㅧ߇ 1 ᵄ㐳ಽߛߌᝒ߃ࠄࠇߡ

0

2

∆z/h

4

6

޿ࠆ㧚ߐࠄߥࠆ㗔ၞ᜛ᄢߢᢙᵄ㐳ಽߩᄢⷙᮨ᭴ㅧࠍ
ᝒ߃㧘⋧㑐ߪ㔖ߦẋㄭߒߡ޿ࠆ㧚UHF ߢᓧࠆ⋧㑐

Fig. 8 Spanwise two-point correlation coefficient of
streamwise velocity fluctuation or temperaturefluctuation.

Rθθ (∆x)ߪ㧘Small ߩ႐วߢ߽⋧㑐߇㔖ߦẋㄭߒߡ޿ࠆ㧚UHF ߩ⸘▚㗔ၞ XL ߦᵈ⋡ߔࠆߣ㧘⚂ 24h ߩ㑆㓒ߢ㧘ᒙ޿⋧㑐ߩᄌേ߇⷗ࠄࠇࠆ㧚৻ᣇ㧘ㅦᐲ႐෸࿑ 8(b)ߩ࠴ࡖࡀ࡞ਛᄩߦ߅޿ߡ h ߢࠬࠤ࡯࡝ࡦࠣ

߮ CTD ߢߪ㧘ࠃࠅ㐳޿㑆㓒ߢᒝ޿⋧㑐ߩᄌേ߇⴫

ߔࠆߣ㧘⋧㑐ߩᦨዊ୯㧔ᒝ޿⽶ߩ⋧㑐㧕߇∆z ≈ 1.2hࠇߡ޿ࠆ㧚߹ߚ㧘࡟ࠗࡁ࡞࠭ᢙଐሽᕈ߇ㅦᐲ႐ߣ

ߦ⴫ࠇ㧘ᄢⷙᮨ᭴ㅧߩ㑆㓒ࠍ␜ߒߡ޿ࠆ㧚ߎߩࠬࡄ

CTD ߦ⷗ࠄࠇ㧘Rew = 3000 ߢߪ⋧㑐߇⽶ߦ⪭ߜࠆߎࡦᣇะ㑆㓒ߦ߅ߌࠆ࡟ࠗࡁ࡞࠭ᢙଐሽᕈߪᒙߊ㧘ⓨߣߪߥߊᓢ‫ߦޘ‬ዊߐߊߥࠅ㧘᦭㒢㐳ߩᄢⷙᮨ᭴ㅧߩ

㑆⊛ᵄ㐳λߢ␜ߖ߫㧘λz ≈ 2.4h ⒟ᐲߢ޽ࠆ㧚Kawamuraᓇ㗀߇ⷰኤߐࠇߥ޿㧚ߎࠇߪ㧘࡟ࠗࡁ࡞࠭ᢙ߇ૐ޿

ࠄ[17]ߩ DNS ߢߪ᭴ㅧࠍᝒ߃ࠆߦߪ⸘▚㗔ၞ߇ዊߐ㧘ოߩ☼ᕈ߇࠴ࡖࡀ࡞ਛᄩㇱ߹ߢ߅
ߚ߼㧔Reτ = 52㧕޿ߚ߼㧘ࠬࡄࡦᣇะ㑆㓒߇⸘▚㗔ၞࠨࠗ࠭ߦ࿕ቯߐ

ࠃ߮㧘ᄢⷙᮨ᭴ㅧࠃࠅ߽☼ᕈ㐳ߐࠬࠤ࡯࡞ߩ᭴ㅧ߇

ࠇߡ޿ࠆߣ⠨߃ࠄࠇࠆ㧚߹ߚ㧘ᧄ⸘▚ߢ߽ Lz < 8h ߩ

ᡰ㈩⊛ߦߥࠆߚ߼ߣ⠨߃ࠄࠇࠆ㧚Rew = 8600 ߦ߅޿႐วߦ㧘λz ≈ 2.1h ⒟ᐲߦࠬࡄࡦᣇะ㑆㓒߇❗߼ࠄࠇߡ߽㧘࠴ࡖࡀ࡞ਛᄩㇱߢᄢⷙᮨ㗔ၞ߇ߥߊߥࠆ UHFߡ޿ࠆ㧚࠴ࡖࡀ࡞ਛᄩߦ߅ߌࠆ UHF ߢߩ⋧㑐߇㧘ߢߪ㧘CTD ߩࠃ߁ߥ࡟ࠗࡁ࡞࠭ᢙଐሽᕈߪ⷗ฃߌࠄ

ㅦᐲ႐߿ CTD ߦᲧߴߡዊߐ޿ߎߣ߇ಽ߆ࠆ߇㧘਄ࠇߥ޿㧚⸥ߩ㐳ᵄ㐳ᚑಽ㧔λz ≈ 2.4h㧕߇ᡰ㈩⊛ߢ޽ࠆߎߣߪห

8 -- -158ࠬࡄࡦᣇะߦ߅ߌࠆⓨ㑆⊛ߥㅦᐲᄌേ߅ࠃ᷷߮
C 2007 The Heat Transfer Society of Japan○

Thermal Science & Engineering Vol.15 No.3 (2007)

at y+~53.2

1.2

kz Euu

2.4

0.8
0.4
0

1.0
0.8

0.8
0

CTD

kz Eθθ

0.2
0

Rew=8600
Lx=32h (M)Lx=45h (Large)
Lx=64h (Long)
Lx=96h (XL)+

0.8kz Eθθ

0.6

2.4
1.6

0.6
0.4

at y ~5

Rew=8600
Lx=32h (M)Lx=45h (Large)
Lx=64h (Long)
Lx=96h (XL)

1.6

Rew=8600
Lx=32h (M)Lx=45h (Large)
Lx=64h (Long)
Lx=96h (XL)

at y+~5at the channel centerkx Euu /u'rms2, kx Eθθ /θ'rms2

1.6

at the channel center
Rew=8600
Lx=32h (M)Lx=45h (Large)
Lx=64h (Long)
Lx=96h (XL)

CTD

0.3
0.2

at the channel center
Rew=8600
Lx=32h (M)Lx=45h (Large)
Lx=64h (Long)
Lx=96h (XL)

UHF

0
10-1

101

λz /h

0.1
0 -1
10

100

0
10-1

101
103

λx /h 102

λx+ 104ࡄࡦᣇะ㑆㓒߇ 2.0~2.5h ߣ޿߁⚿ᨐ߇಴ߡ޿ࠆ㧚ᧄ

0.1

100

0.2

ߎࠇߪ Tillmark [4]ߩታ㛎ߣ⦟ߊ৻⥌ߒ㧘᷵᭴ㅧߩࠬ

0.4
0.2

Rew=8600(XL)

Fig. 11 Pre-multiplied energy spectra normalized by
the RMS values as a function of streamwise
wavelength at the channel center.

0

UHF

0.3

kx Euu /u'rms2
kx Eθθ /θ'rms2 (CTD)
kx Eθθ /θ'rms2 (UHF)

102

0.8

Rew=8600
Lx=32h (M)Lx=45h (Large)
Lx=64h (Long)
Lx=96h (XL)

0.4⸘▚ߢߪ㧘⸘▚㗔ၞߩ᜛ᄢߦࠃߞߡ MEW ߣߘߩࠛ
100

101

λz /h

ࡀ࡞ࠡ࡯฽᦭㊂ߦᄌൻ߇⷗ࠄࠇߡ޿ࠆ㧚ઁߩࠤ࡯ࠬ
㧔Large એ਄ߩ⸘▚㗔ၞ㧕ߦᲧߴ㧘ਥᵹᣇะߦ 1 ᵄ

Fig. 10 Pre-multiplied energy spectra kz+Eii+(kz) as afunction of spanwise wavelength λz.

㐳ಽᝒ߃ߚ Medium ߦ߅ߌࠆ MEW ߩࠛࡀ࡞ࠡ࡯߇

ᐲᄌേߩࠛࡀ࡞ࠡ࡯ࠬࡍࠢ࠻࡞ࠍ␜ߔ㧚ߎߎߢ㧘1ߴ⸘▚㗔ၞ߇ਥᵹᣇะߦ㐳ߊߡ߽㧘ࠬࡄࡦᣇะߦ⁜ᰴరࠛࡀ࡞ࠡ࡯ࠬࡍࠢ࠻࡞ߪ㧘ᰴᑼߩࠃ߁ߦቯ⟵ߐ޿ߚ߼ࠛࡀ࡞ࠡ࡯߇ዊߐߊߥߞߡ޿ࠆ㧚Large ߆ࠄࠇࠆ㧚

XL ߳ߩ᜛ᄢ㧔ਥᵹᣇะ⸘▚㗔ၞࠍ 2 ୚㧕ߦࠃࠅ㧘u’ߦ߅ߌࠆ MEW ߇λz =2.1h ߣ 2.5h ߢห⒟ᐲߣߥߞߡ

 E ( k )dk = E ( k )dk = u ′∫0 uu x x ∫0 uu z z ∞ Eθθ ( k x )dk x = ∞ Eθθ (k z )dk z = θ rms
′2
∫0
 ∫0
∞

∞

ዊߐ޿ߎߣ߇ಽ߆ࠆ㧚߹ߚ㧘Long ߢߪ㧘Large ߦᲧ2rms㧚ߎࠇࠄߩߎߣ
޿ࠆ㧔᷷ᐲ႐θ’ߢߩ MEW ߪλz=2.1h㧕(12)ࠃࠅ㧘⸘▚㗔ၞ᜛ᄢߦ઻޿ᄢⷙᮨ᭴ㅧ߇ⓨ㑆⊛ߦំࠄߋࠃ߁ߦߥࠅ㧘߹ߚ㧘ࠛࡀ࡞ࠡ࡯฽᦭㊂߇Ⴧ߃ࠆࠬࡍࠢ࠻࡞ᒝᐲߪන૏ᵄᢙ޽ߚࠅߩࠛࡀ࡞ࠡ࡯฽᦭

ߣ⸒߃ࠆ㧚ߟ߹ࠅ㧘ᄢⷙᮨ᭴ㅧ߇ᜬߟ⌀ߩࠛࡀ࡞ࠡ

㊂ߣ⸃㉼ߢ߈ࠆ߇㧘ࠬࡍࠢ࠻࡞ᒝᐲߦᵄᢙࠍ߆ߌߚ

࡯฽᦭㊂ࠍᓧࠆߦߪ㧘๟ᦼႺ⇇ߩᓇ㗀߇චಽߦήⷞ

㊂ࠍ pre-multiplied ࠬࡍࠢ࠻࡞ߣ๭ࠎߢ޿ࠆ㧚ߎࠇߦߢ߈ࠆ߹ߢߦ⸘▚㗔ၞࠍ᜛ᄢߔࠆᔅⷐ߇޽ࠆ㧚ߐࠄࠃࠆߣ㧘ᮮゲࠍᵄᢙ߹ߚߪᵄ㐳λi = 2π/ki ߩኻᢙߦኻ

ߦ㧘ოㄭறߩࠬࡍࠢ࠻࡞ߦ߽ዪᚲ⊛ߥ㐳ᵄ㐳ၞߢߩߒߡࡊࡠ࠶࠻ߒߚߣ߈ߦࠛࡀ࡞ࠡ࡯฽᦭㊂ࠍ␜ߔᜰࡇ࡯ࠢ߇⷗ࠄࠇ㧘࠴ࡖࡀ࡞ਛᔃߢߩ MEW ߩ㐳ᵄ㐳ᮡߣߥࠆߎߣ߇⍮ࠄࠇߡ޿ࠆ[19, 20]㧚ߎߩߣ߈⃻ࠇߣ৻⥌ߔࠆ㧚ߟ߹ࠅ㧘ᄖጀߢᡰ㈩⊛ߥᄢⷙᮨ᭴ㅧߩ

ࠆࡇ࡯ࠢߩᵄ㐳㧔most energetic wavelength㧘MEW㧕

ૐᵄᢙᚑಽ߇㧘ოㄭறߩㅦᐲ࡮᷷ᐲᄌേࠛࡀ࡞ࠡ࡯

߇㧘႐ߦ⃻ࠇࠆⓨ㑆⊛ߥ᭴ㅧߩᐔဋ㑆㓒ߦ⦟ߊ৻⥌ߦ߽ነਈߒߡ޿ࠆ㧚ߔࠆߎߣ߇⍮ࠄࠇߡ޿ࠆ㧚࿑ 10 ߦᮮゲࠍࠬࡄࡦᣇะ
+ਥᵹᣇะߦߟ޿ߡ߽㧘ᮮゲࠍਥᵹᣇะᵄᢙλx ߦኻߩᵄ㐳λz ߣߒߡࡊࡠ࠶࠻ߒߡ޿ࠆ㧚ოㄭற㧔y =5㧕ߒߡ pre-multiplied ࠬࡍࠢ࠻࡞ࠍ࿑ 11 ߦ␜ߔ㧚࿑ߪ㧘ߦ߅޿ߡ㧘MEW ߪㅦᐲ႐࡮᷷ᐲ႐ߣ߽ߦλz ≈ 0.4hㅦᐲ႐ߣ᷷ᐲ႐ߩߘࠇߙࠇߦ߅ߌࠆ࠴ࡖࡀ࡞ਛᄩߢ

ઃㄭߦ⃻ࠇߡ޿ࠆ㧚ߎࠇߪო㕙㊂ߢλz+ ≈ 100 ߦ⋧ᒰߩࠬࡍࠢ࠻࡞ಽᏓߢ޽ࠆ㧚ߎߎߢ㧘ߘࠇߙࠇߩ୯ࠍ

ߒ㧘ო㕙ㄭறߩḰ⒎ᐨ⊛ߥࠬ࠻࡝࡯ࠢ᭴ㅧߩ㑆㓒ߣ

RMS ୯ߢᱜⷙൻߒߡ␜ߔ㧚ߎࠇߪ㧘ᄌേࠛࡀ࡞ࠡ࡯

⦟ߊ৻⥌ߒߡ޿ࠆ㧚ㅦᐲ႐ߣ᷷ᐲ႐ߩ޿ߕࠇ߽㧘⍴ਛߦභ߼ࠆฦᵄᢙࠛࡀ࡞ࠡ࡯ࠍోࠛࡀ࡞ࠡ࡯ߦኻߔ

ᵄ㐳㗔ၞߦ߅޿ߡ⸘▚㗔ၞߦࠃࠆ᦭ᗧߥᓇ㗀ߪ⷗ฃࠆഀวߣߒߡᲧセߔࠆߎߣߢ㧘ᄌേᒝᐲߩ⇣ߥࠆ‛ߌࠄࠇߥ޿㧔ᓸዊߥᏅ⇣ߪ㧘⸘▚ᩰሶ᏷ߩ㆑޿ߦࠃ

ℂ㊂ߦߟ޿ߡ⋧੕Ყセߔࠆߚ߼ߢ޽ࠆ㧚࿑ 11 ߢߪ㧘ࠆ߽ߩ㧕㧚࠴ࡖࡀ࡞ਛᄩߢߩ MEW ߪλz =2.1~2.5h ߢ㧘⍴ᵄ㐳ߣ㐳ᵄ㐳ߢ 2 ߟߩࡇ࡯ࠢ߇⷗ฃߌࠄࠇࠆ߇㧘9 -- -159

C 2007 The Heat Transfer Society of Japan○

Thermal Science & Engineering Vol.15 No.3 (2007)

θ'rms+

3
2

CTD

Present
Rew=3000
Rew=8600 (S)Rew=8600 (Large)
Rew=8600 (XL)ౝጀߩࠬࠤ࡯࡝ࡦࠣߦࠃࠅ㧘ࡐࠕ࡙࠭ࠗੂᵹߣ߽ࠃ

Kawamura et al. (2000)
Rew=12800
Liu (CTD, 2003)
Rew=3000ߊ৻⥌ߔࠆ㧚৻ᣇ㧘CTD ߢߪ਄ਅ㕖ኻ⒓ᕈߪ⷗ฃߌ
ࠄࠇߥ޿㧚Liu [13]ߩ DNS ߦࠃࠆ⚿ᨐߪᧄ⸘▚ߣ௑ะߪ⦟ߊว߁߇㧘ᐞಽ㜞޿୯ߣߥߞߡ޿ࠆ㧚UHF

Komminaho ࠄ[8]ߩ DNS ߆ࠄᓧߚ⍮⷗ߦࠃࠇ߫㧘⸘

CTD▚㗔ၞ߇㕖Ᏹߦ⍴޿႐วߦੂᵹᒝᐲߩࡇ࡯ࠢ୯ߪᭂ

10┵ߦ㜞޿୯ߣߥࠆ㧚ߎߩߎߣ߆ࠄ㧘Liu ߩ⚿ᨐߣቢోߦ৻⥌ߒߥ޿ߩߪ㧘ᓐߩ⸘▚㗔ၞ㧔⴫ 2 ෳᾖ㧕߇UHF
100 + 101 0
y

0.2

0.4

y/h

0.6

0.8

᭴ㅧࠍචಽߦᝒ߃ࠆ߶ߤߩᄢ߈ߐߢߪߥ޿ߚ߼ߣ⠨1߃ࠄࠇࠆ㧚⸘▚㗔ၞ߳ߩଐሽᕈߟ޿ߡ㧘Small ߢᓧߚ୯߇ઁߩࠤ࡯ࠬߦᲧߴߡᄖጀోၞߢ⚂ 5%ዊߐ޿㧚

Fig. 12 Temperature variance.

ߎࠇߪ㧘Small ߩ⸘▚㗔ၞߢߪࠛࡀ࡞ࠡ࡯ࠍᜬߟ㐳⍴ᵄ㐳ၞߩ MEW ߪ࠹ࠗ࡜࡯ࡑࠗࠢࡠࠬࠤ࡯࡞╬ߢᵄ㐳ᚑಽ㧔࿑ 11 ෳᾖ㧕߇ᝒ߃ࠄࠇߡ޿ߥ޿ߚ߼ߣ⠨ࠬࠤ࡯࡝ࡦࠣߐࠇࠆ᭴ㅧߢ޽ࠅ㧘㐳ᵄ㐳ၞߩλx =߃ࠄࠇࠆ㧚ਔᾲ⊛Ⴚ⇇᧦ઙߩოㄭறߦ߅ߌࠆࡇ࡯ࠢ

24~48h ߇ᄢⷙᮨ᭴ㅧߩࠬࠤ࡯࡞ߦ⋧ᒰߔࠆ㧚ߎߩ㐳୯ߦᵈ⋡ߔࠆߣ㧘UHF ߦ߅޿ߡ㗼⪺ߥ࡟ࠗࡁ࡞࠭ᢙ

ᵄ㐳ၞߦ߅ߌࠆ MEW ߦᵈ⋡ߔࠆߣ㧘ㅦᐲ႐㧔λx =ଐሽᕈ߇⷗ฃߌࠄࠇࠆ㧚ߒ߆ߒ㧘࠴ࡖࡀ࡞ਛᄩㇱߢ

32h㧕࡮CTD㧔48h㧕࡮UHF㧔24h㧕ߢߘࠇߙࠇࠛࡀ࡞

ߪ UHF ߦ߅ߌࠆ࡟ࠗࡁ࡞࠭ᢙଐሽᕈߪዊߐ޿㧚৻ࠡ࡯฽᦭₸ߩᄢ߈޿ᵄᢙ߇⇣ߥࠆὐ߇⥝๧ᷓ޿㧚ㅦᣇ㧘CTD ߪ࠴ࡖࡀ࡞ਛᄩ߹ߢ㧘ო㕙㊂ߦࠃࠆࠬࠤ࡯

ᐲ႐ߣ CTD ߦᲧߴ㧘UHF ߦ߅޿ߡߪ㐳ᵄ㐳ၞߩ㕙࡝ࡦࠣ߇⦟ߊᚑࠅ┙ߟ㧚ߎࠇࠄߪ᷷ᐲࡃ࡝ࠕࡦࠬߦ

Ⓧ߇ዊߐߊ㧘㐳ᵄ㐳ߩභ߼ࠆࠛࡀ࡞ࠡ࡯߇ᒙ޿ߎߣ

߅ߌࠆࠛࡀ࡞ࠡ࡯෼ᡰ㧔ャㅍᣇ⒟ᑼ㧕߆ࠄ⺑᣿ߢ߈߇ಽ߆ࠆ㧚ߎࠇߪ㧘࿑ 9 ߇␜ߔ௑ะߣ߽⦟ߊ৻⥌ߒ

ࠆ㧚

ߡ޿ࠆ㧚
࿑ 7 ߩ 2 ᰴరੑὐ⋧㑐ߢ␜ߒߚࠃ߁ߦ
㧔UHF

ߎߎߢ㧘᷷ᐲࡃ࡝ࠕࡦࠬߩࠛࡀ࡞ࠡ࡯෼ᡰࠍ࿑ 13ߦߟ޿ߡߪਅო㕙஥ߩಽᏓ㧕㧘ਥᵹᣇะߩᄢⷙᮨ᭴ㅧ

ߦ␜ߔ㧚෼ᡰߩᱷᏅߪචಽߦዊߐߊ㧘Rew = 8600 ߩߩ㑆㓒ߦߎߩ᭽ߥᏅߪ⷗ฃߌࠄࠇߕ㧘ㅦᐲ႐ߣ᷷ᐲ

ฦ⸘▚㗔ၞߦ߅ߌࠆ⚿ᨐߪ޿ߕࠇ߽⦟ߊ৻⥌ߒߡ޿႐ߦ߅޿ߡߘߩਥᵹᣇะ㑆㓒ߪ߶߷ห৻ߢ޽ࠆ㧚ߟࠆ㧔Medium㧘Large㧘Long ߩ⚿ᨐߪ㕖ឝタ㧕㧚ߎߩ߹ࠅ㧘‛ℂⓨ㑆㧔ታ㓙ߩㅦᐲ႐߿᷷ᐲ႐㧕ߢ⴫ࠇࠆಽᏓߦ߅ߌࠆᾲ⊛Ⴚ⇇᧦ઙߢߩ㆑޿ߪ㧘࠴ࡖࡀ࡞ਛ

ᄢⷙᮨ᭴ㅧߩⓨ㑆⊛ࠬࠤ࡯࡞ߪหߓߢ߽㧘ᦨ߽ᡰ㈩ᔃߦ߅޿ߡ㧘CTD ߩ↢ᚑ㗄ߪ޽ࠆ৻ቯ୯ࠍ଻ߟߎߣ

⊛ߥࠛࡀ࡞ࠡ࡯ᵄᢙߪㅦᐲ႐ߣ᷷ᐲ႐ߢᔅߕߒ߽৻

ߦኻߒ㧘UHF ߩ↢ᚑ㗄ߩ୯ߪ㔖ߦߥࠆߎߣߢ޽ࠆ㧚⥌ߒߡ޿ߥ޿㧚kθ+ߩ↢ᚑ㗄ߪ㧘+Pθ++ + ∂θ
′′= −v θ
Pr∂y + ੂᵹ⛔⸘㊂೨▵ߢ㧘᷷ᐲ႐ߦ߅ߌࠆᄢⷙᮨ᭴ㅧߩⓨ㑆⊛ࠬࠤ(࡯࡞߿ⓨ㑆⊛ᄌേߩࠛࡀ࡞ࠡ࡯ࠬࡍࠢ࠻࡞ߦᵈ⋡ߒ+= −v′+ θ ′+ qtotal+ v ′ + θ ′+ߡ߈ߚ㧚ᧄ▵ߢߪฦ⒳ੂᵹ⛔⸘㊂ࠍ㧘⸘▚㗔ၞߣᄢⷙᮨ᭴ㅧߦࠃࠆᓇ㗀ߦᵈ⋡ߒߥ߇ࠄ␜ߒߡ޿ߊ㧚․ߦ㧘Rew = 8600 ߦ߅޿ߡ᦭㒢㐳ߩ᭴ㅧࠍᝒ߃ᓧߥ߆

)

(13)

ߢ޽ࠅ㧘− v ′ + θ ′ + ߇q+totalߩඨ୯ߦߥࠆ㜞ߐymaxߢ㧘Pθ+ߪᦨᄢ୯ࠍߣࠆ㧚CTDߩߣ߈㧘ᑼ(13)ߩq+total = 1ߢ޽

ߞߚ Small ߩ⚿ᨐߣઁࠤ࡯ࠬߩ⚿ᨐߩ㑆ߦ⷗ࠄࠇࠆ

ࠆߩߢ࡟ࠗࡁ࡞࠭ᢙߦଐࠄߕ㧘࿑13(a)ߩࠃ߁ߦ

Ꮕ㧘߅ࠃ߮࡟ࠗࡁ࡞࠭ᢙଐሽᕈߦߟ޿ߡᬌ⸛ߒߡ޿

Pθ+max = Pr/4ࠍߣࠆ㧚ߐࠄߦ㧘CTDߢߪ޿ߕࠇߩ㗄߽㧘ߊ㧚ო㕙㊂ߢࠃߊࠬࠤ࡯࡝ࡦࠣߐࠇࠆ㧚৻ᣇ㧘UHFߦ߅᷷ᐲᄌേߩ RMS ୯ࠍ࿑ 12 ߦ␜ߔ㧚ਔᾲ⊛Ⴚ⇇᧦ߌࠆࡇ࡯ࠢ୯ߪ㧘ઙ౒ߦ㧘ᐔဋ᷷ᐲ൨㈩߇ᄢ߈޿ოㄭறߢࡇ࡯ࠢ୯ࠍ
+
θ max

P

␜ߔ㧚UHF ߦ߅޿ߡᐔဋ᷷ᐲಽᏓߩ਄ਅ㕖ኻ⒓ᕈߦ
⿠࿃ߒߡ㧘᷷ᐲࡃ࡝ࠕࡦࠬ╬ߩ⛔⸘㊂ߦ߽⧯ᐓߩ਄

+

ymax
Pr 
≈
1 −

4 
Reτ 

2

(14)

ਅ㕖ኻ⒓ᕈ߇⃻ࠇߡ޿ࠆ㧚਄ო஥ߩࡇ࡯ࠢ߇ਅოߦ

ߣߥࠆ㧚y+maxߪ࡟ࠗࡁ࡞࠭ᢙߦଐࠄߕ߶߷৻ቯ୯ࠍ

Ყߴૐߊߥߞߡ޿ࠆߎߣ߇ಽ߆ࠆ߇㧘ࡇ࡯ࠢ૏⟎ߪߣࠆߩߢ㧘࿑13(b)ߩࠃ߁ߦReτ ߇ᷫዋߔࠆߦߟࠇߡ

10 ---160

C 2007 The Heat Transfer Society of Japan○

Thermal Science & Engineering Vol.15 No.3 (2007)

Production

0.1

Gain

Residualᮨ᭴ㅧߦߟ޿ߡߩ⍮⷗ࠍ㓸߼ߚ㧚ฦ⒳⛔⸘㊂ࠍ᳞߼㧘

PresentReτ=3000Reτ=8600 (Small)Reτ=8600 (XL)ߘࠇࠄߦኻߔࠆ᭴ㅧߩᓇ㗀ߦߟ޿ߡ߽⼏⺰ߒߚ㧚ࠢࠛ࠶࠻ੂᵹߦ߅޿ߡߪ㧘࠴ࡖࡀ࡞᏷ࠬࠤ࡯࡞ߩ
❑᷵ኻߦࠃߞߡ㧘CTD ߢߪㅦᐲ႐ߦૃߚᄢⷙᮨߥ㜞᷷࡮ૐ᷷㗔ၞ߇⊒↢ߔࠆ㧚ઁᣇ UHF ߢߪ㧘ౝጀߦ

0

Loss

߅޿ߡߪૐᵄᢙᚑಽߩᓇ㗀߇㗼⪺ߢߪ޽ࠆ߇㧘࠴ࡖࡀ࡞ਛᄩߢߩ᭴ㅧߪ߶ߣࠎߤሽ࿷ߒߥ޿㧚ᄢⷙᮨ᭴

Dissipation-0.1

Turbulent diffusion(a) CTDㅧߪ㧘ㅦᐲ႐࡮᷷ᐲ႐ߣ߽ߦ㧘ਥᵹᣇะߦ 32~48h㧘

Molecular diffusion0ࠬࡄࡦᣇะߦ 2.1~2.5h ߩࠬࠤ࡯࡞ࠍ߽ߟ㧚ߎߩ᦭㒢y+ 10050㐳ߩ᭴ㅧࠍᝒ߃ࠆߎߣߦࠃࠅ㧘៺ᡂଥᢙߪ⚂ 4%ߩ㧘ᾲવ㆐₸ߢߪ⚂ 5%ߩᏅ⇣߇↢ߓߡ޿ࠆ㧚ฦ⒳ੂᵹ

Production

0.1

Gain

Residual⛔⸘㊂ࠍචಽ♖ᐲ⦟ߊᓧࠆ਄ߢ㧘චಽߥ⸘▚㗔ၞߦ

PresentReτ=3000Reτ=8600 (Small)Reτ=8600 (XL)ࠃࠆᄢⷙᮨ᭴ㅧߩᛠីߪ㊀ⷐߢ޽ࠆߎߣ߇␜ߐࠇߚ㧚⻢ㄉᧄ⎇ⓥߩ৻ㇱߪ⑳ቇ࡮ቇⴚࡈࡠࡦ࠹ࠖࠕផㅴ੐ᬺ

0

Loss

‫⑼▚⸘ࠆࠃߦ࠴࡯ࡠࡊࠕࠢ࠶ࠖ࠹ࠬ࡝ࡎޟ‬ቇߩᣂዷ㐿‫ࠆࠃߦޠ‬ᡰេࠍ㧘╙৻⪺⠪ߪᣣᧄቇⴚᝄ⥝ળ․೎

Dissipation-0.1

Turbulent diffusion(b) UHF⎇ⓥຬᅑബ⾌(18-81)ߩេഥࠍฃߌߚ㧚ᧄ⸘▚ߪ਻Ꮊ

Molecular diffusion

050ᄢቇᖱႎၮ⋚࠮ࡦ࠲࡯෸߮᧲ർᄢቇᖱႎࠪ࠽ࠫ࡯࠮

y+ 100ࡦ࠲࡯ᄢⷙᮨ⑼ቇ⸘▚ࠪࠬ࠹ࡓࠍ೑↪ߒߡⴕߞߚ㧚߹ߚ㧘ᧄ⸘▚ߩ৻ㇱߪ㧘᧲੩ℂ⑼ᄢቇᄢቇ㒮࡮⠀ᩮ

Fig. 13 Budget of temperature variance.

዁๋ำߩදജߩ߽ߣߦⴕࠊࠇߚ㧚⸥ߒߡ⻢ᗧࠍ⴫ߔ㧚↢ᚑ㗄߽ዊߐߊߥࠆߎߣ߇ಽ߆ࠆ㧚ੂᵹ᜛ᢔ㗄ߣಽሶ᜛ᢔ㗄ߩ࡟ࠗࡁ࡞࠭ᢙଐሽᕈߪ㧘ਔႺ⇇᧦ઙߣ߽ዊߐ޿߇㧘Rew = 3000ߦ߅޿ߡߪੂᵹ᜛ᢔ㗄ߦࠃࠆࡃ࠶ࡈࠔ࡯ጀ߆ࠄ࠴ࡖࡀ࡞ਛᄩㇱ߳ߩࠛࡀ࡞ࠡ࡯ャㅍ߇㗼⪺ߦߥࠆ㧚․ߦ㧘UHFߢߪ࠴ࡖࡀ࡞ਛᄩߢੂᵹ
᜛ᢔ㗄ߣᢔㅺ߇㊒ࠅวߞߡ޿ࠆ㧔࿑13(b)㧕㧚Rew =8600㧔CTD㧕ߦ߅޿ߡߪ࠴ࡖࡀ࡞ਛᄩㇱߢ↢ᚑߣᢔㅺ߇╬ߒߊዪᚲᐔⴕ⁁ᘒࠍ଻ߞߡ޿ࠆ㧔࿑13(a)㧕㧚
⸘▚㗔ၞߩᓇ㗀ߦߟ޿ߡߪ㧘Smallߦ߅ߌࠆ↢ᚑ㗄߇
XLߢߩ୯ࠃࠅࠊߕ߆ߦዊߐߊߥߞߡ޿ࠆ߇㧘ઁߩ㗄ߦߟ޿ߡ߽߶ߣࠎߤ᦭ᗧߥᏅߪ⷗ࠄࠇߥ޿㧚㧠 ⚿ ⸒ᦨᄢߢ 96h×h×12.8h ߩ⸘▚㗔ၞࠍ↪޿ߡ㧘ੂᵹᾲવ㆐ࠍ઻߁ᐔ㕙ࠢࠛ࠶࠻ᵹࠇߦ߅ߌࠆ⋥ធᢙ୯ࠪࡒ
ࡘ࡟࡯࡚ࠪࡦࠍⴕߞߚ㧚࡟ࠗࡁ࡞࠭ᢙߪ Rew = 3000
ߣ 8600 ߦ⸳ቯߒ㧘៺ᡂ࡟ࠗࡁ࡞࠭ᢙߢߘࠇߙࠇ Reτ
= 52 ߣ 126~129 ߦ⋧ᒰߔࠆ㧚ᵹࠇᣇะߩ⸘▚㗔ၞࠍᲑ㓏⊛ߦᄌ߃ࠆߎߣߢ㧘⇣ߥࠆᾲ⊛Ⴚ⇇᧦ઙߦ߅ߌ
ࠆ᷷ᐲ႐ࠍ฽߼ߚੂᵹ᭴ㅧ㧘․ߦᄖጀߦ߅ߌࠆᄢⷙ

ෳ⠨ᢥ₂
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