㧗䝬䝑䝝ᩘቨ஘ὶ䛻䛚䛡䜛ᦶ᧿᢬ᢠ䛾పῶ 䛻㛵䛩䜛ᇶ♏ⓗ◊✲

(1)

㧗

㧗䝬䝑䝝ᩘቨ஘ὶ䛻䛚䛡䜛ᦶ᧿᢬ᢠ䛾పῶ 䛻㛵䛩䜛ᇶ♏ⓗ◊✲

៞᠕⩏ሿ኱Ꮫ⌮ᕤᏛ㒊ᶵᲔᕤᏛ⛉

῝₲ ᗣ஧

2010-11-26 JAXA APGබເᆺ◊✲ሗ࿌఍

ὶయ䛾ᦶ᧿᢬ᢠ 2/22

• ᦶ᧿᢬ᢠ

• ᦶ᧿᢬ᢠಀᩘ

w

dU W P dy

(1 / 2) 2

4 w f

f

C U

f C W

U

y

U(y)

^⢓ᗘ

W w

(2)

ᒙ 3/22

ᒙὶ䛸஘ὶ

←ᒙὶ

஘ὶ→

(Homsy et al., Multimedia Fluid Mechanics)

ᒙὶ䛸஘ὶ䛾ᦶ᧿᢬ᢠ 4/22

•

஘ὶ䛾ᦶ᧿᢬ᢠ䛿ྠ䛨䝺䜲䝜䝹䝈ᩘ䛾ᒙὶ䛾ᦶ᧿᢬ᢠ䜘䜚᱁ẁ䛻኱䛝䛔䟿

(White, 2008)

(3)

⩼ 5/22

⩼䛻ᑐ䛩䜛ᦶ᧿᢬ᢠపῶ䛾⪃䛘᪉

• 䜎䛪䚸ୖὶ䛷䛿䛷䛝䜛䛰䛡 ᒙὶ䜢ಖ䛴ດຊ䜢䛩䜛

– ⮬↛ᒙὶ⩼

– ୍ᵝ྾㎸䜏

• ஘ὶ䛻㑄⛣䛧䛶䛧䜎䛳䛯䜙

஘ὶ䛾ᦶ᧿᢬ᢠ䜢ῶ䜙䛩 ດຊ䜢䛩䜛

– ஘ὶᦶ᧿᢬ᢠపῶไᚚ

(NASA Report, 1979)

஘ὶᦶ᧿᢬ᢠ䛾ཎᅉ 6/22

• ↓ᩘ䛾⦪ 䛻䜘䜛㐠ື㔞஺᥮䛾άⓎ໬䛜ཎᅉ

(Fukagata et al., 2006)

(4)

7/22

⦪

⦪ 䛾᫬✵㛫䝇䜿䞊䝹

(Kasagi, Suzuki, and Fukagata, Annu. Rev. Fluid Mech. 41 , 2009)

8/22

஘

஘ὶᦶ᧿᢬ᢠ䛾ᩘᏛⓗศゎ䠖 FIK ᜏ➼ᘧ

(Fukagata Iwamoto and Kasagi Phys Fluids 14 2002) ^8/22 (Fukagata, Iwamoto, and Kasagi, Phys. Fluids 14 , 2002)

• 䝏䝱䝛䝹ὶ 2 ^* ^*

R U ^b G Re _b ^b *

Q

Nondimensionalized

,

1

0 12 24 (1 )( )

f Re

b

C ³ y u v dy c c

• ෇⟶ὶ

Nondimensionalized by 2U _b ^* and G ^{(or R} ^* )

laminar drag , turbulent contribution (=weighted integral of RSS)

2 U ^* R ^*

1

0 16 16 2

f Re r z

b

C ³ r u u c c rdr ^Re ^b

2 U _b R Q ^*

• ✵㛫Ⓨ㐩ቃ⏺ᒙ

4(1 ) 1

4 (1 )( )

C G d ³ y u v dy c c Nondimensionalized

0 1

2 4 (1 )( )

Re 2 (1 )

C f y u v dy

uu uv

y d y

G

§ w w ·

¨ ¸

³

³ ^Re ^b ^2U ^f

* G _99% ^*

*

by U _f ^* and G *

0 ( y ) y

x y

¨ w w ¸

© ¹

³ ^b _Q

G d : nondimensionalized

displacement thickness

Contribution of spatial development

(5)

஘ 9/22

஘ὶ䛾䜰䜽䝔䜱䝤ไᚚ䛻䜘䜛ᦶ᧿᢬ᢠపῶ

•

⌮ㄽ䠋ᩘ್䝅䝭䝳䝺䞊䝅䝵䞁

–

䝣䜱䞊䝗䝞䝑䜽ไᚚ

•

ὶ䜜ሙ䛾඲᝟ሗ䜢⏝䛔䛯᭱㐺ไᚚ 䛷䛿෌ᒙὶ໬䜒(Bewley et al., 2001)

•

⌧ᐇⓗ䛺䝉䞁䝃᝟ሗ䜢⏝䛔䛯ไᚚ䛷䛿

12%᢬ᢠపῶ(Fukagata & Kasagi, 2004) –

䝥䝺䝕䝍䞊䝭䞁䝗ไᚚ

•

䝉䞁䝃䜢⏝䛔䛪䚸኱䛝䛺᢬ᢠపῶຠᯝ

(Min et al., 2006; Mamori et al., 2010)䠈

෌ᒙὶ໬䜒(Nakanishi et al., 2010)

•

㢼Ὕᐇ㦂

–

䝣䜱䞊䝗䝞䝑䜽ไᚚ

(ྜྷ㔝䜙, ᶵㄽ, 2006䠗 Yoshino et al., 2008)

ᚑ᮶䛾ᦶ᧿᢬ᢠపῶ䛾䜰䜽䝔䜱䝤ไᚚ䛻㛵䛩䜛◊✲䛿㠀ᅽ⦰ὶ䜜䛜ᑐ㇟ → 㧗䝬䝑䝝ᩘ䛷䛾ຠᯝ䛿ᮍ▱

ቨ஘ὶ䛾䝣䜱䞊䝗䝞䝑䜽ไᚚ䝅䝇䝔䝮

(ྜྷ㔝䜙, ᶵㄽ, 2006) - ⣙6%᢬ᢠపῶ

10/22

䝣䜱䞊䝗䝞䝑䜽ไᚚ䛾౛䠖C䡄oi et al. (1994)䛾Vไᚚ

෇⟶ὶ䛾ሙྜ䠄

Fukagata & Kasagi, 2003

䠅

(6)

11/22

䝥

䝥䝺䝕䝍䞊䝭䞁䝗ไᚚ䛾౛䠖Min et al. (2006)䛾㐍⾜Ἴไᚚ

(Mamori, 2009)

12/22

• ቨ ቨ஘ὶ䛻䛚䛡䜛ᦶ᧿᢬ᢠ䛾ཎᅉ䠙ቨ㠃㏆ഐ䛾䝺䜲䝜䝹䝈䛫䜣᩿ᛂຊ

– FIKᜏ➼ᘧ(Fukagata et al., 2002) Æ

䛣䜜䜢ᐃ㔞ⓗ䛻ㄝ᫂

–

ᅽ⦰ᛶFIKᜏ➼ᘧ(Gomez et al., 2009)

Æ

䝬䝑䝝ᩘM = 2䛾䝏䝱䝛䝹 ὶ䛷䜒䚸ቨ㠃㏆ഐ䛾䝺䜲䝜䝹䝈䛫䜣᩿ᛂຊ䛜ᦶ᧿᢬ᢠ䛾୺ᅉ

Æ ᇶᮏⓗ䛻䛿䚸㠀ᅽ⦰ቨ஘ὶ䛻ᑐ䛧䛶ᥦ᱌䛥䜜䛯ᦶ᧿᢬ᢠప ῶᡭἲ䛜 M = 2 䛾ቨ஘ὶ䛻䜒㐺⏝䛷䛝䛭䛖䞉䞉䞉

• ၥ㢟Ⅼ

–

ᐇ㝿M=2䛾ቨ஘ὶ䛻ไᚚ䜢ຍ䛘䛯ሙྜ䛻ఱ䛜㉳䛣䜛䛛୙᫂

–

እ㒊ὶ䠄䠙✵㛫Ⓨ㐩ቃ⏺ᒙ䠅䠈䛥䜙䛻㏫ᅽຊ໙㓄ୗ䛷䛾ไᚚຠᯝ䛿㠀 ᅽ⦰䛾ሙྜ䛷䜒୙᫂

–

㠀ᅽ⦰ቨ஘ὶ䛸䛾㐪䛔䜢฼⏝䛧䛶䚸㧗䝬䝑䝝ᩘቨ஘ὶ䛻䜘䜚㐺䛧䛯ไ ᚚ๎䜢ᥦ᱌䛷䛝䛺䛔䛛䠛

㧗䝬䝑䝝ᩘቨ஘ὶ䛾ไᚚ

(7)

13/22

◊

◊✲┠ⓗ

• 㧗䝬䝑䝝ᩘ䠄M=2⛬ᗘ䠅䛾✵㛫Ⓨ㐩஘ὶቃ⏺ᒙ䛻ᑐ䛩䜛䜰䜽䝔䜱䝤ᦶ᧿᢬ᢠపῶไᚚ䛾ᇶ┙ᢏ⾡䜢☜❧

• ⎔ቃ䞉䜶䝛䝹䜼䞊㈨※䛻ඃ䛧䛔㟼⢔㉸㡢㏿ᶵ䛾ᐇ⌧

䛻ᐤ୚

(JAXA HP

䜘䜚

)

14/22

◊✲ィ⏬䠄2010䠉2012ᖺᗘ䠅

2010ᖺᗘ

䐟ᅽ⦰ᛶ䝏䝱䝛䝹ὶDNS 䝁䞊䝗䛾㛤Ⓨ䛚䜘䜃᳨ド䐠㠀ᅽ⦰✵㛫Ⓨ㐩஘ὶቃ⏺ᒙไᚚ䛾

DNS

2011

ᖺᗘ

䐟ᅽ⦰ᛶ✵㛫Ⓨ㐩஘ὶቃ⏺ᒙDNS 䝁䞊䝗䛾㛤Ⓨ䛚䜘䜃᳨ド

䐠㠀ᅽ⦰ቨ஘ὶ䛾ᦶ᧿᢬ᢠపῶ䛾䛯䜑䛻㛤Ⓨ䛥䜜䛯ไᚚ๎䜢㐺⏝䛧䛯

M = 2䛾✵㛫Ⓨ㐩஘ὶቃ⏺ᒙ䛾DNS䛚䜘䜃ไᚚຠᯝ䛻䛚䛡䜛┦㐪

Ⅼ䛾ᢳฟ

2012

ᖺᗘ

㧗䝬䝑䝝ᩘቨ஘ὶ䛻㐺䛧䛯ไᚚ๎䛾㛤Ⓨ䛚䜘䜃DNS䜢⏝䛔䛯ไᚚຠ

ᯝ䛾ホ౯

㧗䝬䝑䝝ᩘቨ஘ὶ䛻䛚䛡䜛ᦶ᧿᢬ᢠపῶ䛾䛯䜑䛾ᇶ┙ᢏ⾡

䛾☜❧䜈

(8)

㠀

㠀ᅽ⦰✵㛫Ⓨ㐩஘ὶቃ⏺ᒙ䛻䛚䛡䜛୍ᵝ྿ฟ䛧䠋྾㎸䜏ไᚚ䛾DNS

Kametani & Fukagata (EFMC-8, Bad Reichenhall, Germany, September 2010)䜘䜚

16/22

Physical decomposition of skin friction drag 1

FIK identity for spatially developing boundary layer.

II. Reynolds Shear Stress, c

^T

I. Boundary Layer

Thickness, c

^G

III. Mean Convection, c

^C

IV. Spatial Development, c

^D

f : Spatial average value in z direction G d : Displacement thickness

: Non-dimenstionalized by

99% BL thickness G & Streamwise velocity U _∞

FIK identity (Fukagata et al., 2002)

(9)

17/22

Direct Numerical Simulation

` Governing Equations

` Continuity equation & Navier-Stokes equation

` DNS Code : Based on Fukagata & Kasagi(JCP, 2002), Fukagata et al. (Phys. Fluids, 2006)

` Creating boundary layer: Rescaling; using Lagrange interpolation (linear), Lund et al. (1996)

B.C on wall

B.C. on roof u , v , p : Neumann & w : Dirichlet ( w = 0) u = w = 0, v = V ctr & p : Neumann

for Both parts…

Inlet : Rescaled velocity (Lund et al.

1996) & NSCBC (Miyauchi et al., 1994)

Outlet : Convective outlet & NSCBC

18/22

Ctrl. input [%]

0 S 2 S 3 S 4 S 5 S 6 S 7 S 8 S 9 S

x/ G 0

Uniform blowing Uniform suction

Amp.

0.01 U -0.01 U

0.005 U

0.001 U -0.005 U

-0.001 U

Parameters Standing zone

Uniform Blowing

Uniform Suction

Uniform blowing & Uniform suction

(10)

19/22

Flow visualization

20/22

Statistics at Re _T _,nc =430

> ^ln

²

² ^Re ² ^ln ² ^Re @

¹

31 .

0 u

_T

c

f

Shoenherr (1932)

Increase Increase

RSS VSS

Red: 1% UB Orange: 0.5%UB Yellow: 0.1%UB

Blue: 1% US

Light blue: 0.5%US

Green: 0.1%US

(11)

21/22

Decomposition of C _f

C

T

C ^C < 0

C ^C > 0

Uniform blowing

Uniform suction

Reduction factor

Enhancement factor

Friction coeff. x 1000 Mean convection

22/22

Summary

DNS with uniform blowing (UB) or suction (US) was performed aiming at skin-friction drag reduction.

Effect of UB & US on skin friction drag

Mechanism of drag reduction or enhancement by using FIK identity.

– Spatial development term, c ^D , and Reynolds shear stress term, c ^T are dominant for skin friction drag. Mean convection term, c ^C , reduces skin friction drag.

• UB: Mean convection term works as larger drag reduction factor.

• US: Mean convection term changes into drag enhancement factor.

Control Type Skin friction drag Viscous shear stress Reynolds Shear Stress Uniform Blowing

Uniform Suction

㧗䝬䝑䝝ᩘቨ஘ὶ䛻䛚䛡䜛ᦶ᧿᢬ᢠ䛾పῶ 䛻㛵䛩䜛ᇶ♏ⓗ◊✲

㧗