± rÑo 5 qn k : §h ÷ö t rø v · 摩擦抵抗低減効果 24...
TRANSCRIPT
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• 2.�¨$ſƕƅEŜ0Ě,x• ,x{éŎ,x§¥őŊijŌ
2
±�,xŒ)Ģ
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V- riblet :about30μm(3M)
p�����´¿ ~10ƙp_§őŚŝøĦ (1992)→ º�-´ 2ƙ
pƍƕŷŻƕűĸyó
l Spaniwse wall-oscillationl Travellingwalll BlowingandSuction
Ā¨ÈōœŐijƜ.ő?wĿŇ|OőNŋĺ,x
p�����´¿ ~40ƙp�ÖēÈŐE�{p,xƍũżŲƌĸ�õ�Ő·ĸIJŝ
pWĹŐ�%ŧŽƒŪƗĸyóŐPAĸIJŝ
*��"���"
ƃţƗźƀŶū,x
Sĝō?wŁŝ±�|OőNŋĺĀ¨ÈŐ,x
p�����´¿ ~25%p¦įŐƓŤžƒŲ�őazpdŐij�%ŧŽƒŪƗ
p§¤ÈőħpŐ�ñĸyó(Yoshinoetal.,2007)
l Vcontrol
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4
AirbusA320
u 2Dribletssurface
Bacher&Smith(1985,1986)
@5,x
K.Koeltzsch(2002)
u Placoidscaleƚ$(.����ƛ
Rasci&Muskik(1986)
u Flightevaluationtest
SzodruchJ.,AIAAPaper91-0685(1991)
u 2Dribletssheet (3M)
Width: 152μmMaterials: plastic
u 3DribletsChoi,H.etal.,2008
5
é5,x
Yoshinoetal.,2008
ƃţƗźƀŶū,x
Į£ýŐ,xĭħ�ƜòęŐ,xÛ
x
y
z
FLOW
ƅƓŸŴƗƋƕź,x
Į�ÖēE�Èō:ÜŐ,xÛĮħij�����´¿ĭ�%ŧŽƒŪƗĸWĹijĭ,x§¥ĸ�õ�(?)
y+~15
y+~7.5
ãµ¥Ă
y z6
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• Ú{��ş�´ŁŝŇŗĉÒş�,Łŝ• ƈƒŷŶūűŰŦŽƓƗŴ
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• (�õ�)
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• (�õ�)
7
ƅƓŸŴƗƋƕź,x
�ēE�,x
x
yz
W.Jungetal,1992
x
yz
±Ş�DE�,xM.Quadrioetal,2007
x
yz
ăð¯,x
FLOW
DRrateover45%NetDRrate7%
DRrate13%NetDRrate?%
Minetal,2006
DRrateover50%NetDRrate?%
�ēE� T+
x
yz
e�,xChoietal,1994
Periodicblowingandsuction
Max.DRrate20%
8
• ŵƎŽƒ�SşƜűƁƕ�Dő�5ĽŃŝ,x
• ,xƁƐƍƗŴ• WĹĽ :Wm
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űƁƕ�DS�5,x
xz
y
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0.00
0/4π 1/4π 2/4π 3/4π 4/4π
y
9
×�űŹƗūűGġŒõ(g±ş�^)űŹƗūűg=Ľ
űƁƕ�DS�5,x
Contour:Uaty+=5(red7.0,blue2.5) Iso-surface:Q+=-0.013
FLOW
Spanwise
z
Streamwisex
t+=0
t+=150
t+=400
ãµ
xz
y
0.20
0.00
0/4π 1/4π 2/4π 3/4π 4/4π
y
10
,xŒ4¢
10
8
6
4
2
0
W0+
2 3 4 5 6 7 8 9100
2 3
T+
10
8
6
4
2
0
W0+
2 3 4 5 6 7 8 9100
2 3
T+
(Yakenoetal,2010)
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ÌŧŽƒŪƗ¿
ƠĜ,x�ŒƉƕƅ51
Ơ,x�ŒƉƕƅ51
Ơ,xőóŁŝŧŽƒŪƗ
K16�^��
Energysaving
w/controlw/ocontrol
Energy
11
�
u b+ =
Reτ3
− 1− y +
Reτ
⎛ ⎝ ⎜
⎞ ⎠ ⎟ 0
Reτ∫ − ′ u + ′ v +( )dy +
Ú{����ŎƓŤžƒŲz1
(Ref.Yakenoetal.,2014)
�
− ′ u ′ v = ′ u 2 ′ v 2 ⋅R ′ u ′ v
�
′ u 2 ′ u ′ v ′ u ′ w ′ u ′ v ′ v 2 ′ v ′ w ′ u ′ w ′ v ′ w ′ w 2
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
�ƓŤžƒŲz1ŷƕųƒ
±Ş�DāpŒŞrpħĽ�DāpŒŞrpu’Ŏv’ŒËĔ��
ËĔ�� =1őÿij à ãµ¥Ă
�
R ′ u ′ v
±őŚŝĊ)g±őŚŝĊ)
12
K16�^��
�
C f =2τw (= ρuτ
2)ρUb
2
⎛ ⎝ ⎜
⎞ ⎠ ⎟ =
6Ub2 Reτ
+ 6 1− y +
Reτ
⎛ ⎝ ⎜
⎞ ⎠ ⎟ − ′ u ′ v +( )dy +
0
Reτ∫(Ref.Fukagataetal.,2002)
ûď±ď�^��
• ŵƎŽƒ±PŒƓŤžƒŲz1
• ƓŤžƒŲz1œ�ËU5ŎŅŞ�VŒŞ~)ő)õōĹŝ
ƓŤžƒŲz1Œ)k
0.8
0.6
0.4
0.2
0.0
-u"v"
12 3 4 5 6 7
102 3 4 5 6 7
100y+
w/o controlW0
+ = 5.0, T+ = 16.0
W0+ = 5.0, T+ = 50.0
W0+ = 5.0, T+ = 250
(Yakenoetal.,2014)14
µ¥ĂŎƓŤžƒŲz1
u”
v”
Q4
Q2Q1
Q3
Ejection
Sweep
Interaction
Interaction
±Ş�Dāpuĸ�ijĠM
Q2Q4
Q3
Q1u”<0
u”>0
15
レイノルズ応力四象限のUb 増加への寄与
�T = 75 が最適な制御周期, レイノルズ応力Q2 イベントが最も低減✓長い制御周期では, レイノルズ応力Q4 イベントが増加→ 摩擦が増加する
�
u b+ =
Reτ3
− 1− y +
Reτ
⎛ ⎝ ⎜
⎞ ⎠ ⎟ 0
Reτ∫ − ′ u + ′ v +( )dy +
SĝķśŒħĽyŒčŖ�ĹÔ)ď
16
ãµ¥ĂŒ条件付き抽出
Greyiso-surfaceQ=-0.02
Blue/Rediso-surface-u”v”=0.2
�Q=∂ui/∂xj ∂uj/∂xi <-0.02�Qの最小となる点✓回転方向ωx >0✓平均する渦構造周りの検査体積
0 11780
471 ���Ĺ�(ĿŇãµ¥ĂŎƓŤžƒŲz1Q2ŎQ4
17
ƓŤžƒŲz1Œ�ËU7
40
30
20
10
0
y +
-40 -20 0 20 40z+
40
30
20
10
0
y +
-40 -20 0 20 40z+
40
30
20
10
0
y +
-40 -20 0 20 40z+
40
30
20
10
0
y +
-40 -20 0 20 40z+
T = 50+
40
30
20
10
0
y +
-40 -20 0 20 40z+
40
30
20
10
0
y +
-40 -20 0 20 40z+
40
30
20
10
0
y +
-40 -20 0 20 40z+
40
30
20
10
0
y +
-40 -20 0 20 40z+
T = 250+
40
30
20
10
0 -5 0w +
0/8 π
40
30
20
10
0 50 w +
4/8 π
40
30
20
10
0 50 w +
8/8 π
40
30
20
10
0 -5 0w +
12/8 π
Q2event Q4event
18
Optimal Long
ãµ¥ĂŎűƁƕ�D#Ĺ
21
¡ 乱流エネルギー方程式
Redistribution
Production
z
x
Highspeedstreaku”<0
Lowspeedstreaku”<0
y
x
Incliningofvortex
tiltingofvortex
RedistributionàMaintenanceofavortex
means(Yakenoetal.,2014)
縦渦構造の傾き
22
z
x%�#�
z
x
,�#�
Iso-surfaceQ=-0.02
greycontour<-2p”∂u”/dx>
0 4/8π 8/8π 12/8π φ [rad]
(Yakenoetal.,2014)
Q4Œ�´ŎR2
0 4/8π 8/8π 12/8π φ [rad]
0 4/8π 8/8π 12/8π φ [rad]
0 4/8π 8/8π 12/8π φ [rad]
0 4/8π 8/8π 12/8π φ [rad]
0 4/8π 8/8π 12/8π φ [rad]
0 4/8π 8/8π 12/8π φ [rad]
0 4/8π 8/8π 12/8π φ [rad]
��#���+!
�&�)-
Q4イベント
縦渦構造の傾き角度はy~15 付近の
平均速度勾配の傾きに一致する
(Yakenoetal.,2014)
23
摩擦抵抗低減効果
24
�Q2イベントの低減は渦の下部 y ~ 10 での渦回転と反対方向の平均速度剪断が最大となる位相で起こる
✓長い周期でのQ4の増加は渦の存在する y ~ 15 付近の平均速度剪断により渦構造が傾けられ,渦内部の圧力ひずみ相関が増加し,生成が増加するために起こる
✓摩擦抵抗低減効果は,ストークス層の解析解から得られる によって以下のように見積もられると考えられる
Q2の低減 Q4の増加
(Yakenoetal.,2014)
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• 2.�¨$ſƕƅEŜ0Ě,x• ,x{éŎ,x§¥őŊijŌ
26
�¨$ſƕƅEŜ0Ě,x
27
x
y
z
Reattachmentoccurs
Controlposition
Iso-surfacesofII(thesecondinvariantof∂Ui/∂xj)coloredwithvelocity
ŅŘŅŘ0Ě,xōœ�şŁŝŒķơ
• K1��Œ�´ĸÉÈ• �®Ơą5ďş��Łŝ
• ±āşR2Łŝ• ŞşR2Łŝ
28
z
x
Attached
z
x
Separated
z
x
Reattached
āp)kŒU7à0ĚĠMŒ�´
SchematicdiagramisfromAono,Sekimoto,Sato,Yakeno,NonomuraandFujii,2015
±�,xŸƀŤűƅƐŲƊŢūŵƏŧƗŴ
• Characteristics• :ÜŐůűŷƌ• §¤Èő5ķŐij• ±ďŒR´ĸŐij• ħěKĸyó(<ė)
• Consistof• îijàâ��şĐfêō�Šň¥Ă
• �±ěKş��ŁŝŎƅƐŲƊ¾}ĸ�śŞŝ
• ěĚ¾}ōÂŀŇĘŤŨƕŒÒ5ĸÖ«±ŎŐŝ
• Computation &Experiment• Moreal,2007,Corke etal.,2009,ChoandShyy,2010,Wangetal.,2013,Aono etal.,2015
30
0.0 0.1 0.2-0.1-0.2
0.7
0.0
x
z
Dc/DcMax.
0Ě,xŒÊ��!öÙ
~~
FreeFiltered
Humpheightin x
33.026.0-2.0-4.0 4.02.00.0
Constant
Constant
~ ~
-12.0
~ ~
40.0
l U�œ ρinf,uinf ,h(ſƕƅħĽ)ō¸¨$7
l ±%QÅ�� :ƄƐŰťűQÅg (δin =0.25)l ±(QÅ�� :2nd orderfiltering
l ,x�Ô1œſƕƅĞ� (xact =0.0) 31
Suzenmodel
4,00016,000
0.2
ƅƐŲƊŢūŵƏŧƗŴ�Ô1Œùü±Ş
• ƆƗűE¯� (fbase )œħĺƜƀƗűŹª (BR/fh )œcĽĺ÷^ (1%)<<2Dvortexscale
33
w:-0.15to0.15
Continuousmode BR=0.01 BR=0.10
4000-1 4000-3 4000-2
fh =∞ fh =0.05 fh =0.05
� weuseBR=0.012DŷűŹöÙ
öÙÞ¢ ,xŐĿ
Reh =4,000 Reh =16,000
0.0 0.02.0 2.0
4.04.0
Q=1.0Contouru:-1.0– 1.0
Q=0.1Contouru:-1.0– 1.0
v±őœ�¨$ŒƔƗƒµĸÇÂƜŅŒēő�¨$ŒƑƄ¥ĂĸÂŀƜļŞő�ijűƁƕ�DāpU5œR2ĿŌijĺ
2D-Roll3D-Ribs
34
(Yakenoetal.,2015)
�ēmLŒßöď
10.08.06.04.02.00.0x
0.030
0.020
0.010
0.000
-0.010C f
Reh = 4000, xact = 0.0 w/o control fh = 0.025 fh = 0.05 fh = 0.10 fh = 0.20 fh = 0.50 fh = 1.00 fh = 5.00
-0.05
0.25u
0.0 2.0 4.0 6.0 8.0 10.0-4.0 -2.0-6.0
0.0 2.0 4.0 6.0 8.0 10.0-4.0 -2.0-6.0
fh=0.2(optimal)
w/ocontrol
±Ş�DāpŒ�ēmL)k
fh =0.2ŒPAō�Ř�ĺ�ÍŁŝĆ>ŒÎôŎ�ì
36
(Yakenoetal.,2015)
0ĚĠMđĽ xsep.
Uncontrolled
h
sep
Uncontrolled
h
sep
4
4
(a) (b)0.050.100.20
0.501.005.00
0Ě�ä
0ĚĠM
'�Í�ä
Re = 4,000 Re = 16,000
�Ř�ĺ�ÍŁŝE¯� fh =0.2œƓŤžƒŲ�ő�YĿŐijƘ
(Yakenoetal.,2015)
37
E¯��Y{őŊijŌ
38
Low-frequency(fh =0.05)
High-frequency(fh =1.0)
�ijE¯�ōœƜWĹŐƔƗƒµĸ�ŊÂŀŝ
ħijE¯�ōœƜƔƗƒµŒ*ĸōĹŝ
Optimal(fh =0.2)
(Yakenoetal.,2015)
(a) (b)
1.0
0.965
0π
0.4π
0.8π
1.2π
1.6π
0.0 2.0 4.0 6.0 8.0
0.0 2.0 4.0 6.0 8.0
0.0 2.0 4.0 6.0 8.0
0.0 2.0 4.0 6.0 8.0
0.0 2.0 4.0 6.0 8.0
0.0 2.0 4.0 6.0 8.0
0.0 2.0 4.0 6.0 8.0
0.0 2.0 4.0 6.0 8.0
0.0 2.0 4.0 6.0 8.0
0.0 2.0 4.0 6.0 8.0
0π
0.4π
0.8π
1.2π
1.6π
fh = 1.0fh = 0.1
�ËU5ŒK1)kLow frequency High frequency
39
(Yakenoetal.,2015)
ëÄŃŠ�gŒát\^{
40
• N�±• Hyperbolic-tangent
• ÖēRl¿
(HoandHuerre,1984)
fh =0.5 fh =1.0
=0.032
ħE¯�őŚŝ,xŒPAőËs
�¨$ƔƗƒµŒűŬƗƒõ¡
1ƀƗűŹ =1
1.0
0.9650.0 2.0 4.0 6.0 8.0
4321High frequency
41
1.0
0.965
1.6π
0.0 2.0 4.0 6.0 8.0
Low frequency
µŒÊu
µŒÊuĸ¬ŕʼnŌijŝ
ſƕƅħĽŒµĸ�śŞŝ�ēűŬƗƒœĶŚŅ
fh = 0.25
(�IøĿŇŬƗűŒ�ō)�Ř4¢ŒħijE¯�
fh =0.2Ŏÿij!
(Yakenoetal.,2015)
41
0Ě,xŕŎŗƞ
• �śŞŝ�¨$ƔƗƒµ (�ËU5~)) œE¯�őŚʼnŌÆŐŝ#D
• ħE¯�Œ,xĥ5ōœƜ�¨$ƔƗƒŒµ*ĸÂ~ƜŅŒ¯đœ�5E¯�ő�YŁŝ
• �E¯�Œ,xĥ5ōœƜ�¨$ƔƗƒµĸ�ŊÂ~ƜŅŒ¯đœſƕƅħĽō^ŕŝƝ
• (�IªþĿŇ�ō)�Ř4¢ÈŐE¯�œƓŤžƒŲ�őŚśŐij
• ijłŞŒƓŤžƒŲ� ( Reh = 4,000 or 16,00)ōŘ fh = 0.20ĸŚij
• ſƕƅħĽűŬƗƒŒµĸ�ŊÂ~Łŝ�ēűŬƗƒœƜ (�IªþĿŇ�ō)�Ř4¢ÈŐE¯�ŎBŀ
• ſƕƅħĽşÊuŎŁŝµűŬƗƒœ fh = 0.25ŎŐŝ 42
(Yakenoetal.,2015)
0.0
0.25v”
0.0 2.0 4.0 6.0 8.0 10.0-4.0 -2.0
0.0 2.0 4.0 6.0 8.0 10.0-4.0 -2.0
rms
±U5~)
43
űƁƕ�DāpU5Œrms)k
fh=0.2(optimal)
w/ocontrol
8.06.04.02.00.0x
0.4
0.3
0.2
0.1
0.0
peak
val
ue o
f v'
rms
w/o control fh = 0.2 fh = 0.1 fh = 0.05 fh = 0.025
8.06.04.02.00.0x
0.4
0.3
0.2
0.1
0.0
peak
val
ue o
f v'
rms
w/o control fh = 0.2 fh = 0.5 fh = 1.0 fh = 5.0
(Yakenoetal.,2015)
0.0
0.25v”
0.0 2.0 4.0 6.0 8.0 10.0-4.0 -2.0
0.0 2.0 4.0 6.0 8.0 10.0-4.0 -2.0
rms
±U5~)
űƁƕ�DāpU5Œrms)k
fh=0.2(optimal)
w/ocontrol
8.06.04.02.00.0x
0.4
0.3
0.2
0.1
0.0
peak
val
ue o
f v'
rms
w/o control fh = 0.2 fh = 0.1 fh = 0.05 fh = 0.025
8.06.04.02.00.0x
0.4
0.3
0.2
0.1
0.0
peak
val
ue o
f v'
rms
w/o control fh = 0.2 fh = 0.5 fh = 1.0 fh = 5.0
44
(Yakenoetal.,2015)
(b)(a) 0.4
0.3
0.2
0.1
0.0
peak
value
of v' rm
s
8.06.04.02.00.0x
Uncontrolled fh = 0.40 fh = 0.20 fh = 0.10 fh = 0.05
8.06.04.02.00.0x
0.4
0.3
0.2
0.1
0.0
peak
value
of v' rm
s
Uncontrolled fh = 1.0 fh = 0.50 fh = 0.20 fh = 0.10 fh = 0.05
Reh =4,000 Reh =16,000
±U5~)
• ħƓŤžƒŲ�ōœƜE¯�őŚŜIJŕŜU7ĿŐij
• �ijE¯�(ſƕƅħĽűŬƗƒµşÂ~)ōœv±ŒƔƗƒµŒIJŝ�ÿōR2
• ±U5~)ŒƂƗū!œƜ0Ě,xŒ4¢ŎËĔĿŌijŝ45
(Yakenoetal.,2015)
0Ě,xŕŎŗ2
• �¨$ƑƄ¥Ă (±U5~)) ŒR2œ,x{éŎËĔĿŌijŝ
• ±U5~)Œ! fh =0.20ō�ŘWĹĺŐŝ
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46
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