Three-dimensional calculations of parallel blade-vortex interaction have been performed using the present numerical procedure

Ꮕಽᩰሶࡏ࡞࠷ࡑࡦᴺߦࠃࠆBVIߩᢙ୯⸃ᨆ

↰᧛ ᣿♿㧘⬵ේ ㆏ਭ㧘 ጟ ᱞ㧘㕍ጊ ೰ผ㧘᪞ ᔘᮨ

␹ᚭᄢቇᄢቇ㒮⥄ὼ⑼ቇ⎇ⓥ⑼

,#:#㧘✚วᛛⴚ⎇ⓥᧄㇱ

Numerical Simulation of Blade-Vortex Interactions Using the FDLBM

by

Akinori Tamura, Michihisa Tsutahara, Takeshi Kataoka, Takashi Aoyama and Choongmo Yang ABSTRACT

Parallel blade-vortex interactions have been calculated using the finite difference lattice Boltzmann method of the compressible Euler model. The perturbed discrete Boltzmann equation based on a prescribed vortex method has been proposed in order to prevent a vortex from diffusing by numerical dissipation. The discretization of the governing equation is based on a second order accurate explicit Runge- Kutta time integration and a fifth order accurate upwind scheme which includes additional terms to capture shock waves clearly. Transonic flow around an airfoil without vortexes has been simulated to validate the perturbed discrete Boltzmann equation system. A surface pressure distribution and pressure contour lines around the airfoil have been compared with other numerical data, and good agreements have been obtained. As a simple model of parallel blade-vortex interaction, two-dimensional blade-vortex interaction has been calculated using the proposed numerical method. An instantaneous pressure coefficient, a time history of a lift coefficient and patterns of acoustic waves have been compared with other numerical results, and agreed with them very well. Mechanism of noise generation has been also captured from numerical results. Three-dimensional calculations of parallel blade-vortex interaction have been performed using the present numerical procedure. Time variations of surface pressure distributions have been compared with Euler calculation and experimental data, and good agreements have been obtained.

㧝㧚✜⸒

BVIߦࠃࠅ⊒↢ߔࠆⓨജ㛍㖸㧔BVI㛍㖸㧕ߪ㧘․ߦ⌕㒽

ᤨߦ⊒↢ߒࡋ࡝ࡐ࡯࠻๟ㄝߩⅣႺ߳ߩᓇ㗀߇ᄢ߈޿ߚ߼㧘 ߘߩૐᷫ߇ᒝߊᦸ߹ࠇߡ޿ࠆ㧚BVIߪ৻⥸⊛ߦ㕖ቯᏱ㧟ᰴ

ర⊛ߥ⃻⽎ߢ޽ࠆ߇ޔ޽ࠆ㘧ⴕ᧦ઙਅߢߪࡉ࡟࡯࠼ߣ⠢┵

᷵ߩ੤Ꮕⷺȁ߇0ߣߥࠅ㧘੕޿߇ᐔⴕߦㄭ޿⁁ᘒߢᐓᷤߔ ࠆߚ߼⃻⽎߇㧞ᰴర⊛ߦߥࠆ㧚ߎߩ⃻⽎ߪParallel BVIߣ

๭߫ࠇ㧘৻⥸⊛ߥBVIߦᲧߴߡ⸃ᨆߪኈᤃߢ޽ࠆ㧚ᧄ⎇ⓥ

ߢߪ㧘ߎߩParallel BVIߣߘࠇߦࠃࠅ↢ߓࠆⓨജ㛍㖸ࠍ⎇

ⓥኻ⽎ߣߒߚ㧚

ߔߢߦParallel BVIߦߟ޿ߡታ㛎߽ߒߊߪᢙ୯⸘▚ߦၮ

ߠ޿ߚᄙߊߩ⎇ⓥ^(1)-(4)߇ⴕࠊࠇߡ޿ࠆ㧚BVI㛍㖸ૐᷫߩߚ

߼ߦߪ㧘ߘߩ⊒↢ࡔࠞ࠾࠭ࡓࠍ᣿ࠄ߆ߦߔࠆߎߣ߇᦭ലߢ

޽ࠆߣᕁࠊࠇࠆ߇㧘⊒↢ࡔࠞ࠾࠭ࡓߦߟ޿ߡ⹦ߒߊ⠨ኤߒ ߚ߽ߩߪ⷗ᒰߚࠄߥ޿㧚

৻ᣇߢ㧘Tsutaharaࠄߪᣂߒ޿⸘▚ᚻᴺߢ޽ࠆᏅಽᩰሶࡏ

࡞࠷ࡑࡦᴺ㧔FDLBM㧕ࠍ↪޿ࠇ߫㧘ᓥ᧪ߩࠦࡦࡄࠢ࠻ࠬࠠ

࡯ࡓࠍ↪޿ߚ㜞♖ᐲߥ⸘▚ᴺߦᲧߴߡዋߥ޿⸘▚ᩰሶᢙߢ 㖸ᵄߩ⋥ធ⸘▚߇น⢻ߢ޽ࠆߎߣࠍ␜ߒߚ⁽⁵⁾㧚

એ਄ߩ⢛᥊߆ࠄ㧘ᧄ⎇ⓥߢߪFDLBMࠍ↪޿ߡParallel BVI㛍㖸ߩ⋥ធ⸘▚ࠍⴕ޿㧘ߘߩ⊒↢ࡔࠞ࠾࠭ࡓߦߟ޿ߡ

⠨ኤߔࠆߎߣࠍ⋡⊛ߣߒߚ㧚

㧞㧚⸘▚ᣇᴺ

㧞㧚㧝㧚Ꮕಽᩰሶࡏ࡞࠷ࡑࡦᴺ㧔FDLBM㧕

FDLBM ߩၮ␆ᣇ⒟ᑼߪ㔌ᢔࡏ࡞࠷ࡑࡦᣇ⒟ᑼ㧔㔌ᢔ

BGKᣇ⒟ᑼ㧕ߢ޽ࠆ㧚੹࿁ߩ⸘▚ߢߪ⒖േߔࠆ⠢ࠍขࠅᛒ ߁ߚ߼㧘⒖േᩰሶߦኻᔕߒߚࡕ࠺࡞⁽⁶⁾ࠍ↪޿ࠆ㧚⬵ේࠄߦ ࠃࠅឭ᩺ߐࠇߚㅊട㗄ࠍ฽ࠎߛ㔌ᢔࡏ࡞࠷ࡑࡦᣇ⒟ᑼ^(5),(7) ߪᤨ㑆㧘ⓨ㑆ࠍߘࠇߙࠇt㧘x_Dߘߒߡ☸ሶߩㅦᐲಽᏓ㑐ᢙ ࠍf_iߣ⴫ߔߣ㧘

i i^eq

eq i i i i i

i f f

x f c f

A x V f t c

f

w w

w w w

w

I

I D

D D D D

1 (1)

ߎߎߢᷝ߃ሼD ߪᐳᮡߩᣇะࠍ⴫ߒߡ޿ࠆ㧚A߅ࠃ߮I

ߪᱜߩቯᢙߢ޽ࠅ㧘Iߪන৻✭๺ᤨ㑆ߣ๭߫ࠇࠆ㧚ࡌࠢ࠻

࡞V_Dߪᩰሶߩ⒖േㅦᐲࡌࠢ࠻࡞ߢ޽ࠆ⁽⁶⁾㧚c_iD߅ࠃ߮ f_i^eq

ߪ i ⇟⋡☸ሶߩㅦᐲࡌࠢ࠻࡞߅ࠃ߮ዪᚲᐔⴧಽᏓ㑐ᢙࠍ⴫

ߒߡ߅ࠅ㧘ᓟ⠪ߪၮ␆ᣇ⒟ᑼ♽߇ㆡಾߥᵹ૕ߩᡰ㈩ᣇ⒟ᑼ ࠍ࿁ᓳߔࠆࠃ߁ߦ☸ሶࡕ࠺࡞ߦࠃߞߡ᳿ቯߐࠇࠆ㧚੹࿁ߪ

☸ሶࡕ࠺࡞ߣߒߡ Kataokaࠄߦࠃࠆ࿶❗ᕈࠝࠗ࡜࡯ࡕ࠺࡞

(8)㧔㧞ᰴర㧥ㅦᐲ㧘㧟ᰴర㧝㧡ㅦᐲࡕ࠺࡞㧕ࠍ↪޿ߚ㧚ᧄ ࡕ࠺࡞ߦ߅޿ߡዪᚲᐔⴧಽᏓ㑐ᢙߪએਅߩࠃ߁ߦ⴫ߐࠇࠆ㧚

¸¹

¨ ·

©

§ ^{D D} _{D D E E}

U i i i

i i i eq

i u c u c

D c c

c B u A

f ₂ 1₄ (2)

ߎߎߢ cߪၮḰ☸ሶㅦᐲߢ޽ࠆ㧚U^㧘uDߪኒᐲ߅ࠃ߮ᵹ ㅦࠍ⴫ߒߡ޿ࠆ㧚A_i㧘B_i߅ࠃ߮D_iߪᵹㅦ㧘ౝㇱࠛࡀ࡞ࠡ

࡯eߦࠃࠅ᳿ቯߐࠇࠆଥᢙߢ޽ࠆ㧚ኒᐲ㧘ᵹㅦ㧘ౝㇱࠛࡀ

࡞ࠡ࡯ߪㅦᐲಽᏓ㑐ᢙߣ☸ሶㅦᐲߩࡕ࡯ࡔࡦ࠻๺ߦࠃࠅએ ਅߩࠃ߁ߦቯ⟵ߐࠇࠆ㧚

¦i

fi

U

¦i i ic f

u_{D D}

U

1 (3)

¦

i

i i

ic u

f

e ²

2 2

2 1 2 1

D

D K

U

ߎߎߢK_iߪ☸ሶߩ⥄↱ᐲࠍ଻ߟߚ߼ߩቯᢙߢ޽ࠆ㧚࠴ࡖ࠶

ࡊࡑࡦ࡮ࠛࡦࠬࠦࠣዷ㐿ߦࠃࠅ㧘એ਄ߩ㔌ᢔࡏ࡞࠷ࡑࡦᣇ

⒟ᑼ♽߇࿶❗ᕈࠝࠗ࡜࡯ᣇ⒟ᑼࠍḩ⿷ߔࠆߎߣ߇⏕⹺ߐࠇ ߡ޿ࠆ㧚

㧞㧚㧞㧚Prescribed-vortex approachߩዉ౉

BVI ߩᢙ୯⸘▚ߦ߅޿ߡᦨ߽໧㗴ߣߥࠆߩߪᢙ୯᜛ᢔߦ ࠃࠅ᷵߇ᢔㅺߔࠆߎߣߢ޽ࠆ㧚Srinivasanࠄߪࠝࠗ࡜࡯ᣇ⒟

ᑼߩ⸃ࠍ᷵ߦࠃࠆᚑಽߣߘߩઁߩᚑಽߦಽഀߒߡ㧘᷵ߩᢙ ୯᜛ᢔࠍᛥ߃ࠆPrescribed-vortex method⁽¹⁾ࠍឭ᩺ߒߚ㧚ᧄ⎇

ⓥߢߪ᷵ߩᢙ୯᜛ᢔᛥ೙ߩߚ߼㧘ߎߩᚻᴺࠍ FDLBM ߦዉ

౉ߔࠆ㧚㔌ᢔࡏ࡞࠷ࡑࡦᣇ⒟ᑼߩ⸃ f_i㧘ኒᐲU^㧘ᵹㅦuD ߅ࠃ߮ౝㇱࠛࡀ࡞ࠡ࡯eࠍ᷵ᚑಽ㧔ᷝ߃ሼ V㧕ߣߘߩઁߩ ᚑಽ㧔ᷝ߃ሼP㧕ߦએਅߩࠃ߁ߦಽഀߔࠆ㧚

i P i V

i f f

f _{, ,}

P

V U

U

U

D D D uV, uP,

u (4)

P

V e

e

e

ߎߎߢ᷵ᚑಽߪ᷵ࡕ࠺࡞ߦࠃࠅ⸃ᨆ⊛ߦਈ߃ࠄࠇࠆ㧚ߎࠇ ࠄࠍ㔌ᢔࡏ࡞࠷ࡑࡦᣇ⒟ᑼ♽(1)-(3)ߦઍ౉ߔࠆ㧚(3)ᑼࠃࠅ ኒᐲ㧘ᵹㅦ㧘ౝㇱࠛࡀ࡞ࠡ࡯ߩ៨േᚑಽߦኻߔࠆᣇ⒟ᑼ߇ એਅߩࠃ߁ߦᓧࠄࠇࠆ㧚

¦i i P

P f _,

U

V P

V P i

i i P P V P

c u f

u U U

U U

U

D D

D

¦ ^{, ,}

,

1 (5)

, , ²

2 , 2

2 ,

2 1

2 2

1

D D

D K U D

U U

P V V

V V V i

i i i P P V P

u u e

e u f c

e

°¿

°¾

½

°¯

°®

­

¸¸

¹

·

¨¨

©

§

¦

߹ߚ㧘᷵ᚑಽ߇㔌ᢔࡏ࡞࠷ࡑࡦᣇ⒟ᑼ♽(1)-(3)ߩ⸃ߢ޽ࠆ ߎߣߦᵈᗧߔࠆߣ㧘 (1)ᑼࠃࠅㅦᐲಽᏓ㑐ᢙߩ៨േᚑಽ f_P,i

ߦኻߔࠆએਅߩᣇ⒟ᑼ߇ᓧࠄࠇࠆ㧚

Pi P^eqi

eq i P i P i i P i

i

P f f

x f c f

A x V f t c

f

, , ,

, ,

, 1

w

w

w w w

w

I

I D

D D D D

(6)

ߎߎߢ f_P^eq_,iߪએਅߩᑼߢቯ⟵ߐࠇࠆዪᚲᐔⴧಽᏓ㑐ᢙߩ៨

േᚑಽߢ޽ࠆ㧚

P P P

eq i

P V P V P V eq i eq

i P

e u f

e e u u f

f

, ,

, ,

, , , ,

D D D

U U U

(7)

એ਄ߩ៨േ㔌ᢔࡏ࡞࠷ࡑࡦᣇ⒟ᑼ♽(5)-(7)ࠍ↪޿ߡ BVI ߩ ᢙ୯⸘▚ࠍⴕ߁㧚

㧞㧚㧟㧚⸘▚ࠬࠠ࡯ࡓ

Tsutahara ࠄ⁽⁵⁾ߪ㧟ᰴ♖ᐲ㘑਄Ꮕಽᴺࠍ↪޿ߡ㖸ᵄߩ⋥ធ

⸘▚ࠍⴕߞߚ߇㧘ⴣ᠄ᵄ߇↢ߓࠆ໧㗴ߦ߅޿ߡߪⴣ᠄ᵄߩ ೨ᓟߢᢙ୯ᝄേ߇↢ߓࠆ㧚ߘߎߢⓨ㑆Ꮕಽࠬࠠ࡯ࡓߣߒߡ 㧡ᰴ♖ᐲ㘑਄Ꮕಽࠬࠠ࡯ࡓߦⴣ᠄ᵄ೨ᓟߢߩᢙ୯ᝄേࠍᛥ

೙ߔࠆ᜛ᢔ㗄ࠍㅊടߒߚࠬࠠ࡯ࡓࠍ↪޿ߚ㧚(6)ᑼߩ⒖ᵹ㗄 ࠍc[wg w[㧘ᩰሶ⇟ภࠍjߣߔࠆߣ↪޿ߚࠬࠠ࡯ࡓߪᰴߩ ࠃ߁ߦ⴫ߐࠇࠆ㧚

2 0

60

3 30 20 60 15 2

1 1

2 1 1

2 3

' !

'

w w

[ [

[ [

N [

[ [

g c g c g

g g g g g c g

c g

j j j

j j j j j j j

2 0

60

2 15 60 20 30 3

1 1

3 2 1 1

2

'

'

w w

[ [

[ [

N [

[ [

g c g c g

g g g g g c g

c g

j j j

j j j j j j

j

(8)

ߎߎߢNߪᢙ୯᜛ᢔߩᄢ߈ߐࠍ᳿ቯߔࠆଥᢙߢ޽ࠅ㧘࿶ജ

pࠍ↪޿ߡᰴߩࠃ߁ߦਈ߃ࠄࠇࠆ㧚

1 1

1 1

2 2

j j j

j j j

p p p

p p W p

N (9)

W ߪછᗧߩࡄ࡜ࡔ࡯࠲ߢ޽ࠅᧄ⸘▚ߢߪ 2.0 ߣߒߚ㧚ᤨ㑆

ㅴⴕߦߪ Tsutaharaࠄ⁽⁵⁾ߣห᭽ߦ㧞ᰴ♖ᐲ࡞ࡦࠥ࡮ࠢ࠶࠲ᴺ

ࠍ↪޿ߚ㧚

㧟㧚NACA0012⠢๟ࠅߩᵹࠇ

ឭ᩺ߒߚ៨േ㔌ᢔࡏ࡞࠷ࡑࡦᣇ⒟ᑼ♽(5)-(7)ߩᅷᒰᕈࠍ

⏕⹺ߔࠆߚ߼㧘㕒ᱛᵹ૕ਛࠍ৻ቯㅦᐲߢ⒖േߔࠆ⠢๟ࠅᵹ ࠇߩᢙ୯⸘▚ࠍⴕ߁㧚⠢ᒻ⁁ߪNACA0012ߣߒߚ㧚⸘▚ᩰ

ሶߣߒߡOဳᩰሶࠍ↪޿㧘ᩰሶᢙߪඨᓘᣇะߦ101ὐ㧘๟

Fig. 1 Comparison of surface pressure distributions

(a) Present calculation

(b) Euler calculation, Pulliam⁽¹⁰⁾ Fig. 2 Comparison of pressure contour lines

ᣇะߦ301ὐߣߒߚ㧚⸘▚㗔ၞߪඨᓘᣇะߦ⠢ߩࠦ࡯࠼㐳 ߩ10୚ߣߒߡ㧘⸘▚㗔ၞߩᄖㇱߦ෻኿ࠍ㒐ߋߚ߼ߩࠬࡐࡦ

ࠫ㗔ၞࠍ⸳ߌߚ㧚(5)ᑼߦ߅ߌࠆᣢ⍮ᚑಽ㧔᷵ᚑಽ㧕ߦߪ㕒 ᱛᵹ૕ߦ߅ߌࠆ୯ࠍਈ߃ߚ㧚ㄫ߃ⷺD₀ 0^{q㧘⠢ߩࡑ࠶ࡂ}

ᢙM 0.8ߣߒߚ⸘▚ߣD₀ 1.25^{q㧘M 0.8ߣߒߚ⸘}

▚ߩ㧞ㅢࠅߩ⸘▚ࠍⴕ޿㧘ߘࠇߙࠇࠝࠗ࡜࡯⸘▚^(9),(10)ߣߩ Ყセࠍⴕߞߚ㧚Figure 1ߪD₀ 0qߢߩ⠢⴫㕙ߦ߅ߌࠆ࿶

ജಽᏓߢ޽ࠅ㧘Fig. 2ߪD₀ 1.25qߣߒߚߣ߈ߩ⠢๟ࠅߩ

࿶ജಽᏓࠍ␜ߒߡ޿ࠆ㧚៨േ㔌ᢔࡏ࡞࠷ࡑࡦᣇ⒟ᑼ♽ߦࠃ

ࠆ⚿ᨐߪ޿ߕࠇ߽ࠝࠗ࡜࡯⸘▚^(9),(10)ߦ⦟ߊ৻⥌ߒ㧘ᧄ⸘▚

ࡕ࠺࡞߇ᅷᒰߢ޽ࠆߎߣ߇␜ߐࠇߚ㧚 㧠㧚㧞ᰴరBVI⸘▚⚿ᨐ

Parallel BVI߇ቢోߦ㧞ᰴర⊛ߢ޽ࠆߣߺߥߖ߫㧘໧㗴ߪ

Fig. 3 ߦ␜ߔࠃ߁ߥ㧞ᰴర BVI ߣߥࠆ㧚⠢ᢿ㕙ߩᒻ⁁ߪ

NACA0012ߢ޽ࠅ㧘᷵ߪScully᷵ࡕ࠺࡞ߦࠃࠅਈ߃ࠆ㧚ฦ

ࡄ ࡜ ࡔ࡯ ࠲ߪઁ ߩ ⸘▚^(1)-(3)ߣ ห ᭽ߦ ⸳ቯߔ ࠆ 㧔M=0.8㧘 a=0.05㧘ī=-0.2㧘YV=-0.26㧕㧚ߪߓ߼ߦ᷵ߩή޿⁁ᘒߢߩቯ Ᏹ⸃ࠍ᳞߼㧘ߘߩᓟߦ਄ᵹ஥ߦ᷵ࠍዉ౉ߔࠆ㧚⸘▚ᩰሶᢙ ߪࠦࡦࡄࠢ࠻ࠬࠠ࡯ࡓࠍ↪޿ߚ BVI 㛍㖸ߩ⋥ធ⸘▚⁽²⁾ߩ⚂

ඨಽ㧔301˜201㧕ߣߒߚ㧚

Fig. 3 Parameters of two-dimensional BVI

Fig. 4 Lift variation during parallel BVI

Fig. 5 Instantaneous surface pressure distribution (XV=1.0)

Figure 4㧘5ߪ឴ജߩᤨ㑆ᄌേ߅ࠃ߮᷵ߩxᐳᮡ૏⟎Xv

߇1.0ߢߩ⠢⴫㕙਄ߦ߅ߌࠆ࿶ജಽᏓߢ޽ࠆ㧚ߎࠇࠄߩ⚿

ᨐ߆ࠄ㧘ឭ᩺ߒߚ⸘▚ࡕ࠺࡞ ߦࠃࠅᓧࠄࠇߚBVI⸘▚⚿

ᨐ߇ઁߩBVI⸘▚⚿ᨐߦ⦟ߊ৻⥌ߔࠆߎߣ߇ಽ߆ࠅ㧘ᧄ ࡕ࠺࡞ߩᅷᒰᕈ߇⏕⹺಴᧪ߚ㧚 ߹ߚ㧘ᩰሶᢙ߇ࠦࡦࡄࠢ

࠻ࠬࠠ࡯ࡓߦࠃࠆ⸘▚ߩ⚂ඨಽߢ޽ࠆߦ߽߆߆ࠊࠄߕⴣ᠄

ᵄ߇ࠪࡖ࡯ࡊߦ⸃௝ߐࠇߡ޿ࠆߎߣ߇᣿ࠄ߆ߦߥߞߚ㧚

(a)Xv=-0.5

(b)Xv=0.0

(c)Xv=0.5

Fig. 6 Instantaneous surface pressure distribution

Figure 6ߪ᷵ߩxᐳᮡ૏⟎߇ߘࠇߙࠇ-0.5㧘0.0, 0.5ߩߣ ߈ߩ⠢⴫㕙਄ߢߩ࿶ജಽᏓߢ޽ࠆ㧚ߎࠇࠄߩ⚿ᨐ߆ࠄ߽ⴣ

᠄ᵄ߇ࠪࡖ࡯ࡊߦ⸃௝ߢ߈ߡ޿ࠆߎߣ߇⏕⹺಴᧪ߚ㧚 Figure 7 ߪ ᄌ േ ࿶ ജ ಽ Ꮣ ࠍ ⴫ ߒ ߡ ߅ ࠅ 㧘 ߎ ߩ ࿑ ߆ ࠄ

Parallel BVIߦࠃࠅ↢ߓߚ㖸ᵄߩᵄᒻ߇⏕⹺಴᧪ࠆ㧚ߪߓ߼

ߦ⠢਄㕙ߦᱜ㧘ਅ㕙ߦ⽶ߩ࿶ജࡄ࡞ࠬ߇↢ߓ㧘ߘߩᓟ㧘਄

ਅߢ╓ภߩ౉ࠇᦧࠊߞߚࡄ࡞ࠬ߇⊒↢ߔࠆ㧚

ߎࠇࠄߩ㖸ᵄߩ⊒↢ࡔࠞ࠾࠭ࡓࠍ⺞ߴࠆߚ߼㧘Fig. 8 ߦ

⠢ઃㄭߩᄌേ࿶ജಽᏓࠍߘࠇߙࠇ␜ߒߚ㧚⽶ߩ᷵ᐲ㧔෻ᤨ

⸘࿁ࠅߩ᷵ᐲࠍᱜߣቯ⟵ߔࠆ㧕ࠍᜬߟ᷵߇ㄭߠߊߦߟࠇ 㧔Fig. 8a㧕㧘࡝࡯࠺ࠖࡦࠣࠛ࠶ࠫ਄㕙ߢ࿶ജ߇਄᣹ߒਅ㕙 ߢᷫዋߔࠆ㧚ߎࠇࠄߩ࿶ജᄌേߪ㧘᷵ߦ⺃ዉߐࠇߚᤨ⸘๟

ࠅߩᵹࠇ߇⠢਄㕙ߢⴣ⓭ߔࠆߚ߼ߦ↢ߓࠆߣᕁࠊࠇࠆ㧚᷵

߇࡝࡯࠺ࠖࡦࠣࠛ࠶ࠫࠍㅢㆊߒߚᓟ㧘ߎࠇࠄߩ࿶ജᄌേߪ 㖸ᵄߣߒߡ᡼಴ߐࠇࠆ㧔Fig. 8b ߅ࠃ߮ c㧕㧚᷵߇ⴣ᠄ᵄࠍ ㅢㆊߒߚ⋥ᓟ㧘᷵ߦࠃࠆᵹࠇ߇ⴣ᠄ᵄᓟᣇߩ⠢ਅ㕙ߦⴣ⓭ ߒ㧘࿶ജ߇ᄢ߈ߊ਄᣹ߔࠆ㧔Fig. 8c㧕㧚ߘߩᓟ㧘⠢ਅ㕙߆ ࠄ࿶❗ᵄ߇㖸ᵄߣߒߡ᡼಴ߐࠇࠆ㧔Fig. 8d㧕㧚߹ߚ㧘⠢਄

㕙 ߆ ࠄ ᡼ ಴ ߐ ࠇ ࠆ ⽶ ߩ ࿶ ജ ࡄ ࡞ ࠬ 㧔Fig. 7 ߩ ⽶ ߩ 2nd

pulse㧕ߩ㖸Ḯߦߟ޿ߡ⠨ኤߔࠆߚ߼㧘Fig. 9 ߦዪᚲࡑ࠶ࡂ

ᢙಽᏓࠍ␜ߒߚ㧚Fig. 9aߪ᷵ߦࠃࠆᓇ㗀߇߶ߣࠎߤή޿⁁

ᘒߢߩಽᏓࠍ⴫ߒߡ޿ࠆ㧚᷵߇⠢ਅ㕙ߩ⿥㖸ㅦ㗔ၞ߳೔㆐

ߒߚߣ߈㧔Fig. 9b㧕㧘⠢਄㕙ߩⴣ᠄ᵄᓟᣇߢࡑ࠶ࡂᢙߩჇ ടߒߚ㗔ၞ߇᷹ⷰߐࠇࠆ㧚ߎߩᕆỗߥㅦᐲჇടߪ㧘ೋ߼ߦ

⠢ਅ㕙ߢ⊒↢ߒߚ⽶ߩ࿶ജࡄ࡞ࠬ߇⠢ߩᓟᣇࠍㅢㆊߒߡⴣ

᠄ᵄߦ೔㆐ߔࠆߎߣߢ↢ߓࠆߣᕁࠊࠇ㧘ߎࠇ߇⠢਄㕙߆ࠄ

⊒↢ߔࠆ⽶ߩ࿶ജࡄ࡞ࠬߩ㖸Ḯߢ޽ࠆߣ⠨߃ࠄࠇࠆ㧚

Fig. 7 Patterns of parallel BVI noises (XV=3.0)

(a)X_V=-0.4

(b)XV=0.2

(c)XV=0.7

(d)XV=1.2

Fig. 8 Parallel BVI noise generation

(a)XV=-5.0

(b)XV=0.2

Fig. 9 Local Mach number distributions

㧡㧚㧟ᰴర⸘▚⚿ᨐ

㧞ᰴర BVIߪParallel BVIߩ⦟޿ㄭૃߢ޽ࠆ߇㧘ታ㓙ߩ

Parallel BVIߢߪ⠢┵╬ߩᓇ㗀߇޽ࠆߚ߼ߦ⃻⽎ߪ㧟ᰴర⊛

ߦߥࠆ㧚ߘߩߚ߼㧘ࠃࠅ⹦ߒߊ⃻⽎ࠍℂ⸃ߔࠆߚ߼ߦߪ㧟

ᰴ ర ⸘ ▚ ߇ ᔅ ⷐ ߦ ߥ ࠆ 㧚 ߘ ߎ ߢ ᧄ ⸘ ▚ ࡕ ࠺ ࡞ ࠍ ↪ ޿ ߡ

Parallel BVI ߩ㧟ᰴర⸘▚ࠍⴕߞߚ㧚߹ߚ㧘Caradonnaࠄߦ

ࠃࠆታ㛎୯⁽¹¹⁾߅ࠃ߮ Aoyamaࠄߦࠃࠆࠝࠗ࡜࡯⸘▚ߩ⚿ᨐ

(12)ߣᲧセࠍⴕߞߚ㧚

㧟ᰴర⸘▚ߩ᭎ⷐ࿑ࠍFig. 10ߦ␜ߔ㧚ฦࡄ࡜ࡔ࡯࠲ߪታ 㛎⁽¹¹⁾߅ ࠃ ߮ ࠝ ࠗ ࡜ ࡯ ⸘ ▚⁽¹²⁾ߣ ห ߓ ୯ 㧔 ⠢ ┵ ࡑ ࠶ ࡂ ᢙ Mtip=0.715㧘೨ㅴᲧȝ=0.198㧘᷵ߩု⋥૏⟎ZV=0.25㧕ࠍ↪޿

ߚ㧚ࡠ࡯࠲ߪ㧞ߟߩࡉ࡟࡯࠼߆ࠄᚑࠆ߇㧘੹࿁ߩ⸘▚ߢߪ ࡉ࡟࡯࠼ߩㄫⷺ߇ 0qߢ޽ࠅ⠢┵᷵ߩᓇ㗀߇߶ߣࠎߤߥ޿

ߚ߼㧘⸘▚ߪ㧝ᨎߩࡉ࡟࡯࠼ࠍኻ⽎ߣߒߚ㧚⸘▚ᩰሶߦߪ O-Hဳᩰሶࠍ↪޿㧘ᩰሶᢙߪ129˜22˜45ߢ޽ࠆ㧚 ࠕࠫࡑࠬⷺȌ㧩180q㧘183.5q㧘187q㧘190.5q㧘194q ߩߣ߈ߩ⠢㕙਄ߩ࿶ജಽᏓࠍFig. 11ߦ␜ߔ㧚ߥ߅᷹ⷰᢿ㕙 ߩඨᓘᣇะ૏⟎ߪࡠ࡯࠲ඨᓘߩ87.6㧑ߩ૏⟎ߢ޽ࠆ㧚࿑߆ ࠄᧄ⸘▚ࡕ࠺࡞ߦࠃࠆ⚿ᨐ߇ታ㛎୯⁽¹¹⁾߅ࠃ߮ࠝࠗ࡜࡯⸘▚

ߦࠃࠆ⚿ᨐ⁽¹²⁾ߣ⦟ߊ৻⥌ߔࠆߎߣ߇ಽ߆ࠆ㧚ߎߩߎߣ߆ࠄ ᧄ⸘▚ࡕ࠺࡞߇㧟ᰴర⸘▚ߦ߅޿ߡ߽ᅷᒰߢ޽ࠆߎߣ߇⸽

᣿ߐࠇߚ߇㧘੹࿁ߩ⸘▚ߢߪ⸘▚ᩰሶߩਇ⿷ߩߚ߼ߦ㖸ᵄ ࠍ᝝߃ࠆߎߣߪ಴᧪ߥ߆ߞߚ㧚ߒ߆ߒߥ߇ࠄ㧘㧞ᰴర⸘▚

ߦ߅޿ߡ㧘ࠦࡦࡄࠢ࠻ࠬࠠ࡯ࡓߦࠃࠆ⋥ធ⸘▚ߩඨಽߩᩰ

ሶߢߪߞ߈ࠅߣ㖸ᵄ߇⸃௝ߐࠇߡ޿ࠆߎߣ߆ࠄ㧘㧟ᰴర

(a) Top view

(b) Side View

Fig. 10 Schematic representations of 3D parallel BVI

⸘▚ߦ߅޿ߡ߽ᧄᚻᴺࠍ↪޿ࠇ߫㧘ᓥ᧪ߩᚻᴺߦᲧߴߡዋ ߥ޿⸘▚ࠦࠬ࠻ߢBVI㛍㖸ߩ⋥ធ⸘▚߇น⢻ߢ޽ࠆߣ⠨߃ ࠄࠇࠆ㧚

㧢㧚⚿⸒

BVI 㛍㖸ߩ⋥ធ⸘▚ߩߚ߼ߦᏅಽᩰሶࡏ࡞࠷ࡑࡦᴺߦ

Prescribed Vortex Methodࠍ⚵ߺㄟࠎߛ⸘▚ᚻᴺࠍឭ᩺ߒߚ㧚

ᧄ⸘▚ᚻᴺߦࠃࠅ㧘Parallel BVI㛍㖸ߩ㧞ᰴర⋥ធ⸘▚ࠍⴕ

޿㧘BVI 㛍㖸߇᷵ߣ⠢ߩ࡝࡯࠺ࠖࡦࠣࠛ࠶ࠫߣߩᐓᷤ߅ࠃ

߮᷵ߣⴣ᠄ᵄ㧘⠢ਅ㕙ߩᐓᷤߦࠃࠅ⊒↢ߔࠆߎߣࠍ᣿ࠄ߆ ߦߒߚ㧚߹ߚ㧘Parallel BVIߩ㧟ᰴర⸘▚ࠍⴕ޿㧘⠢⴫㕙ߢ ߩ࿶ജಽᏓ߇ታ㛎୯߅ࠃ߮ࠝࠗ࡜࡯⸘▚ߦࠃࠆ⚿ᨐߣ৻⥌

ߔࠆߎߣࠍ⏕⹺ߒ㧘ᧄ⸘▚ᚻᴺ߇㧟ᰴర⸘▚ߦ߅޿ߡ߽ᅷ ᒰߢ޽ࠆߎߣࠍ␜ߒߚ㧚

ෳ⠨ᢥ₂

1) Srinivasan, G. R., McCroskey, W. J., and Baeder, J. D.,

"Aerodynamics of Two-Dimensional Blade-Vortex Interaction," AIAA Journal, Vol. 24, No. 10, 1986, pp. 1569- 1576.

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40, No. 3, 2002, pp. 474-480.

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Interaction," AIAA Journal, Vol. 26, No. 11, 1988, pp. 1346- 1353.

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"New Model and Scheme for Compressible Fluids of the Finite Difference Lattice Boltzmann Method and Direct Simulations of Aerodynamic Sound," Computers and Fluids, (to be published).

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2006-2489, 2006.

7) Tsutahara, M., Kurita, M. and Iwagami, T., "A Study of New Finite Difference Lattice Boltzmann Model," Journal of the Japan Society of Mechanical Engineers, Series B, Vol.

68, No. 665 (2002), pp15-21.

8) Kataoka, T., and Tsutahara, M., "Lattice Boltzmann Method for the Compressible Euler Equations," Phys. Rev. E, Vol.

69, 2004, 056702.

9) Jameson, A., Schmidt, W., and Turkel, E., "Numerical Solutions of the Euler Equations by Finite Volume Method Using the Runge-Kutta Timestepping Schemes," AIAA Paper No. 81-1259, 1981.

10) Pulliam, T. H., "Artificial Dissipation Models for the Euler Equations," AIAA Journal, Vol. 24, No.12, 1986, pp. 1931- 1940.

11) Caradonna, F. X., et al., "A Review of Methods for the Prediction of BVI Noise," AHS Technical Specialists' Meeting for Rotorcraft Acoustics and Aerodynamics, Williamsburg, VA, Oct. 1997.

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"Fundamental Analysis of Passive and Active Techniques for BVI Noise Reduction by Euler/FW-H Method," The American Helicopter Society 57th Annual National Forum, Washington DC, May 2001.

(a)Ȍ=180q

(b)Ȍ=183.5q

(c)Ȍ=187q

(d)Ȍ=190.5q

(e)Ȍ=194q

Fig. 11 Surface pressure distributions during parallel BVI