పࣞࣀࣝࢬᩘᇦᚋ᪉ࢫࢸࢵࣉὶࢀࡢᏳᐃゎᯒࢆ⏝࠸ࡓไᚚ
ᒣ⏣ಇ㍜ࠊᮏ㜿ᘺ┾ࠊඖ♸ᫀᘅࠊ▼ᕝோ㸦ᮾ⌮㸧 Control of backward facing step flow by stability analysis in low Reynolds number S. Yamada
*, S. Honami
*, M. Motosuke
*, and H. Ishikawa
**
Tokyo University of Science
ABSTRACT
The objective of this study is to control the reattachment process of the separating and reattaching flow by the synthetic jet over a backward facing step in a low Reynolds number range. To determine the exciting frequency of the synthetic jet, this paper presents the stability analysis of the separating shear layer downstream of the step. The Reynolds number based on the step height ranges from 133 to 3670. The results show effectiveness of the synthetic jet for flow control. The reattachment length on the lower wall decreases due to the vortices which are generated by the synthetic jet with the exciting frequency.
Key Words: backward facing stepࠊseparating shear layerࠊinstability analysisࠊflow control
1. ᗎㄽ
㏆ᖺࠊᑠᆺὶయᶵᲔࡢ㛤Ⓨࡀὀ┠ࡉࢀࠊపࣞࣀࣝࢬ
ᩘᇦ࠾ࡅࡿࡣࡃ㞳╔⌧㇟ࡣࠊὶయᶵᲔࡢ㥑ືຠ
⋡ᙳ㡪ࡍࡿࡇࡽࠊࡣࡃ㞳╔ὶࢀࡢไᚚࡀᚲ せ⪃࠼ࡽࢀࡿ(1)ࠋᮏ◊✲࡛ࡣࠊపࣞࣀࣝࢬᩘᇦᚋ᪉ ࢫࢸࢵࣉὶࢀ࠾ࡅࡿ╔㊥㞳ࡢࣞࣀࣝࢬᩘ౫Ꮡ ᛶཬࡧ࿘ᮇⓗ࡞ὶࢀࡢᵓ㐀╔┠ࡋࠊࡣࡃ㞳ࡏࢇ᩿ᒙ
࠾ࡅࡿᏳᐃᛶゎᯒࢆ⾜ࡗࡓࠋࡇࡢᏳᐃᛶゎᯒᇶ࡙࠸࡚ࠊ ࢩࣥࢭࢸࢵࢡࢪ࢙ࢵࢺ( ௨ୗSJ )ࡢࡌࡻ࠺࿘Ἴᩘࢆ
Ỵᐃࡋࠊࡣࡃ㞳ࡏࢇ᩿ᒙࡢບ㉳ࡼࡿ╔㊥㞳ࡢไ ᚚཬࡧࡑࡢὶືᶵᵓࢆゎᯒࡍࡿࡇࢆ┠ⓗࡍࡿࠋ
2. ᐇ㦂⨨ཬࡧ᪉ἲ
ᅗ1ᐇ㦂ὶ㊰ࡢᴫ␎ࢆ♧ࡍࠋ㢼Ὕࡣὶ㊰ධཱྀࣈࣟ
࣡ࢆタ⨨ࡋࡓྤฟࡋᘧ࡛ࠊ10150mm ࡢ▴ᙧ᩿㠃(
ࢫ࣌ࢡࢺẚ15)ࢆ᭷ࡋࠊࢫࢸࢵࣉ㧗ࡉHࡣ4mmࠊᣑ
ẚࡣ1.67ࡋࡓࠋSJࡣ10150150mmࡢ࢟ࣕࣅࢸ
ࢆ᭷ࡋࠊ࢜ࣜࣇࢫ㒊ࡢ㛗ࡉࡣ10mmࠊࢪ࢙ࢵࢺᏍᚄ
dࡣ1mmࠊࢪ࢙ࢵࢺᏍ㛫㝸10dࡢከᏍࢪ࢙ࢵࢺࡋࡓࠋ
㥑ື※ࡣࢫࣆ࣮࢝ࢆ⏝࠸ࠊࢫࢸࢵࣉࡢᑐቨഃ࡛ࠊࢫࢸ
ࢵࣉ➃ୖὶ40mm ࡢ⨨タ⨨ࡋࡓࠋ
௦⾲㏿ᗘࢆࢫࢸࢵࣉୖὶ㒊ࡢ᩿㠃ᖹᆒὶ㏿Umࠊ௦⾲
㛗ࡉࢆHࡍࡿࣞࣀࣝࢬᩘ ReHࡣ133ࡽ3670ࠊ ࡑ࠸࡚ࠊSJࡢVR (ࢪ࢙ࢵࢺࡢ᭱྿ࡁฟࡋ㏿ᗘUm
ࡢ㏿ᗘẚ )ࡣ3ࡋࡓࠋ ᐃࡣࠊቨ㠃㏆ഐࡢὶ㏿ὶ
ࢀ᪉ྥࢆ᳨▱ྍ⬟࡞Micro Flow Sensor (௨ୗMFS)ࢆ
⏝࠸ࡓࠋMFS ࡣࢫࢸࢵࣉቨഃࡢࢫࣃࣥ୰ኸタ⨨ࡋࠊ X/H = 1ࡽX/H = 28.5ࡲ࡛ィ ࡋࡓࠋMFSࡢࢧࣥࣉ
ࣜࣥࢢ࿘Ἴᩘࡣ1kHzࠊࢧࣥࣉࣜࣥࢢ㛫ࡣ10s࡛࠶ࡿࠋ
╔Ⅼࡣࠊィ 㛫ᑐࡍࡿ㡰ὶ㛫ࡢྜ࡛࠶ࡿ㡰 ὶ⋡JPࡀୗὶྥࡗ࡚ቑຍࡍࡿࡢ50%ࡢ⨨ᐃ
⩏ࡍࡿࠋࡲࡓࠊXY᩿㠃ࡢὶࢀࡢྍどࢆᐇࡋࡓࠋࢺ
࣮ࣞࢧࡋ࡚ࣝࢥ࣮࣑ࣝࢫࢺࠊග※ࡣYAG࣮ࣞࢨࠊ
ᙳࡣࣁࢫࣆ࣮ࢻ࣓࢝ࣛࢆ⏝࠸ࡓࠋ
ࡣࡃ㞳ࡏࢇ᩿ᒙࡀᏳᐃ࡞ࡿ࿘Ἴᩘᖏࢆゎᯒࡍࡿ
ࡓࡵࠊᏳᐃᛶゎᯒࢆ⾜ࡗࡓࠋᏳᐃᛶゎᯒࡣࠊḟඖ
᧠᪉⛬ᘧࡋࡓOrr-Sommerfeld᪉⛬ᘧࡢᅛ᭷್ゎ
ࡽࠊࡣࡃ㞳ࡏࢇ᩿ᒙࡀᏳᐃ࡞ࡿ↓ḟඖἼᩘ㛫ᡂ 㛗⋡ࢆィ⟬ࡋࡓࠋࡇࡢ↓ḟඖἼᩘ㛫ᡂ㛗⋡ࡽ
Gasterኚࢆ⏝࠸࡚✵㛫ᡂ㛗⋡ࢆ⟬ฟࡋࡓࠋ
ࡲࡓࠊOrr̺Sommerfeld ᪉⛬ᘧࡢᅛ᭷್ゎࢆ⟬ฟࡍ
ࡿࡓࡵࠊPIVィ ࡼࡾᚓࡽࢀࡓ╔Ⅼୖὶᇦ࠾
ࡅࡿᖹᆒ㏿ᗘศᕸࢆ⏝ࡋࡓࠋ
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Lower wall Upper wall
All dimensions in mm
ᅗ㸯 ᐇ㦂⨨
ࠕቃ⏺ᒙ㑄⛣ࡢゎ᫂ไᚚࠖ◊✲ㅮ₇ㄽᩥ㞟㸦➨ ᅇ࣭➨ ᅇ㸧 3
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3.
⤖ᯝ࠾ࡼࡧ㆟ㄽ
ᅗ2ᑐቨഃࢫࢸࢵࣉഃ࠾ࡅࡿReHࡣࡃ㞳ཬࡧ
╔㊥㞳Xij/H ࢆ♧ࡍࠋῧᏐ iࡣLࡀࢫࢸࢵࣉቨഃࠊ Uࡀᑐቨഃࢆ♧ࡍࠋࡲࡓࠊῧᏐjࡣࠊR࡛╔ⅬࠊS ࡀࡣࡃ㞳Ⅼࢆ♧ࡍࠋReH = 133ࡼࡾࢫࢸࢵࣉഃࡢ╔
㊥㞳XLRࡣቑຍࡋࠊReH = 670ࡽῶᑡࡍࡿࠋ
ᅗ3XLRࡀቑຍࡍࡿ㡿ᇦ࡛ReH = 552࠾ࡅࡿFFT ゎᯒࡢࣃ࣮࣡ࢫ࣌ࢡࢺࣝᐦᗘ(PSD)ศᕸࢆ♧ࡍࠋ╔
Ⅼ㏆(X/H 㸻 20)ࡽ༟㉺࿘Ἴᩘ36Hz(༳A)ࢆ୰ᚰ
㧗࠸PSD್ࡀศᕸࡍࡿࠋࡲࡓࠊ36Hzࡼࡾࡸࡸప࠸ࣆ࣮
ࢡࡀ21Hzࡽ27Hz㏆ศᕸࡋࠊࡑࡢ࠺ࡕ24Hz(༳ B)ࡀ᭱ࡶ㧗࠸ࠋୗὶྥ࠸24Hzࠊ36HzࡢPSD್ࡢ
ࣆ࣮ࢡࡣ㧗ࡃ࡞ࡿࠋXLRࡀቑຍࡍࡿὶࢀ࡛ࡣࠊ࿘ᮇⓗ࡞
ὶࢀࡢᵓ㐀ࡀXLRୗὶᇦ࡛⌧ࢀࡿࠋ
ᅗ 4 Ᏻᐃᛶゎᯒࡼࡿ↓ḟඖἼᩘDrᑐࡍࡿ✵㛫 ᡂ㛗⋡Diࢆ♧ࡍࠋྛReH࠾ࡅࡿDrࡢᴟ್ࡣ࠾ࡼࡑ 3.2࡞ࡿࠋࡇࡢDrࢆ࿘Ἴᩘ⟬ࡋࠊᏳᐃᛶゎᯒࡢ⤖
ᯝࡼࡾSJࡢ࿘ἼᩘFSJࢆ10ࠊ36ࠊ70ࠊ150Hzࡋࡓࠋ ᅗ5ཬࡧ6ࠊSJࡼࡿὶࢀࡢྍどJPࢆ♧ࡍࠋ ᅗ5(b)࡛ࡣࠊࡣࡃ㞳ࡏࢇ᩿ᒙࡢᶓ ࡣࠊᅗ5(a)ࡢᶓ ࡼ
ࡾࡶୖὶࡽᙧᡂࡉࢀࠊᶓ ࡣX/H = 6㏆࡛ࢫࢸࢵࣉ
ഃࡢቨ╔ࡍࡿࠋᅗ6(a)ࢆぢ࡚ࡶࠊFSJ = 36Hzࡢࠊ
XLRࡣῶᑡࡋࠊSJ ࡢຠᯝࡀ☜ㄆ࡛ࡁࡿࠋ୍᪉ࠊᅗ6(b)
࡛ࡣࠊ࡚ࡢ࿘Ἴᩘ࡛JP ࡢഴྥࡣ FSJ = 0Hzࡢࡣ
ࡁࡃ␗࡞ࡾࠊ╔㊥㞳ࡶⴭࡋࡃῶᑡࡍࡿࠋࡲࡓࠊSJ
ࡼࡿJPࡣࢫࢸࢵࣉ㏆ࡽ㧗ࡃࠊୗὶྥ࠺ᚑࡗ
࡚ῶᑡࡽቑຍ㌿ࡌࡿࠋ
ᅗ7ࡣࠊFSJ = 0 HzࡢࡢXLR࡛↓ḟඖࡋࡓྛࡌࡻ
࠺࿘Ἴᩘࡢ╔㊥㞳ࢆ♧ࡍࠋ╔㊥㞳ࡢῶᑡຠ
ᯝⓗ࡞ࡌࡻ࠺࿘Ἴᩘࡣ㸪ReHࡢቑຍక 36ࠊ70ࠊ 150Hzቑຍࡋ࡚࠸ࡿࠋᚑࡗ࡚ࠊReHࡢቑຍక࠸ࠊSJ
ࡼࡿไᚚ᭷ຠ࡞࿘Ἴᩘᇦࡣᣑࡍࡿࠋ
4. ⤖ㄽ
పࣞࣀࣝࢬᩘᇦᚋ᪉ࢫࢸࢵࣉὶࢀࡢไᚚᑐࡋࠊᏳ ᐃᛶゎᯒࡽỴᐃࡋࡓࡌࡻ࠺࿘Ἴᩘࡣࠊ╔㊥㞳ࡢ ไᚚ᭷ຠ࡛࠶ࡿࡇࡀุ᫂ࡋࡓࠋ
ཧ⪃ᩥ⊩
(1) M. G. el. Hak, (2000)”Flow Control : Passive, Active, and Reactive Flow Management”, Cambridge University Press, London, United Kingdom
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(a) ReH = 300㸪FSJ =0Hz (b) ReH = 300㸪FSJ = 36Hz ᅗ ὶࢀࡢྍど
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䢲䣊䣼 䢳䢲䣊䣼 䢵䢸䣊䣼䢹䢲䣊䣼 䢳䢷䢲䣊䣼
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䢲䣊䣼 䢳䢲䣊䣼䢵䢸䣊䣼 䢹䢲䣊䣼 䢳䢷䢲䣊䣼
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ᅗ 6-ࡼࡿ㡰ὶ⋡
Ᏹᐂ⯟✵◊✲㛤Ⓨᶵᵓ≉ู㈨ᩱ䚷JAXA–SP–09–014 4
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