平板翼の後流に形成される定在波とコヒーレント構造
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1 35 Ω Ω r 'w' r 'w' The Standing Wae Formed in the Wake of a Flat Plate Blade and the Coherent Structure Souichi SASAKI and Yoshio KODAMA, Dept. of Mechanical Sstems Engineering, Nagasaki Uniersit Receied 9 September, ; in reised from 9 June, 3 When the wake characteristics of a flat plate blade supported b the were measured in a wind tunnel eperiment in a uniform flow, the cell such an element of the coherent structure of the wake to the span direction will be maintained at a certain sie. In this stud, authors analed the generating mechanism and the stead characteristics of the coherent structure in the wake. According to the flow field isualied b a 3-dimensional numerical soler with the streamline and the normalied helicit, it was clarified that the streamwise ortices were generated in the wake. Then the orticities Ω formed regularl ten cells rotating alternatel to the span direction. On the limiting stremline inside of the boundar laer on the blade surface, the same distribution as the orticities Ω in the wake occurred at the trailing edge, howeer, the regularit distribution did not eist at the leading edge or the almost inside region of the boundar laer. Moreoer, when the orte motion to the span direction was estimated b each production terms of the orticit transport equation, the production of the orticit Ω b the Renolds share stress r 'w' was the largest among the production terms b turbulent flow, and it distributed structurall to the span direction. When it was summaried as if the motion of the Renolds share stress r 'w' formed a standing wae, authors pointed out that the condition which satisfied motion b the standing wae eisted in the coherent structure at the far wake. KEY WORDS Blade, Wake, Standing Wae, Coherent Structure, Vorticit, Renolds Stress
2 36 r 'w'
3 37 U ; Uniform Flow L S b RANS q F G H F t éu q = ë w p / ù b û, F é u + pù u = uw ë u û, G G + éu + = w ë H + p, H û = éwu w = w + ë w, p é u ù éu + ù éu + wù + u + w F = -n,g = -n, H = -n w + u w + w ë û ë û ë û U C m t n º + Re r Blade b / ; Half width of the half depth β β = µ t RANS MUSCAL Re L S ù ; Span-wise Correlation Length Cell ù û Baldwin-Loma B-L /C = /C = C = /C = η min C f Re /C C f. - - im=6 jm=3 km=5 Upstream Plate Re = 4 Re = 5 Re = 6 Re = 7 Leading edge, /C= Trailing edge, /C= /C Dh min Down stream
4 38 η min = C f Re C f B-L B-L Blasius Schoenherr C f b Blade Cal. (without B-L model) Cal. (with B-L model) Blasius Eq. (laminar flow) Schoenherr Eq. (turburent flow) Re C D/C=. b/c=4. D + = b/c= - D/C = b/c= C /C /C /C U Dirichlet Neumann Non-slip Chord Thickness Span Number of point Scale of grid C D/C b/c Blade side Wake side /C /C /C.., 3.,
5 39 C mm D mm b mm m/s C Re mm AD rms æ ö u ç u w + + W = W + W è ø æ u u w ö + ç + + è ø æ ö + ç - è ø w W = -, W æ Ñ = ç è + ( ) - w + nñ W ö ø ( w w ) - u u + W u w u = -, W = - Ω Ω -, w = /C Blade / b/ l» W l /» L S /C -
6 33 r 'w' æ ö ç - è ø ' w' = ( Q ' w' ) w r 'w' æ p ö æ p ö ' w' = T sinç + w t sinç + w t ç l è ø è l ø Τ r 'w' λ λ λ = λ = b/ æ p öì æ p ö æ p öü ' w' = T sinç + w t ísinç + w t + sinç - w t ý ç l l l è øî è ø è øþ æ p ö æ p ö = T sinç + w t sinç cos( w t ) ç l l è ø è ø λ ¹ - u/u a b u/u D /C= /C /C r uõõ.. blade D/C=. Re= 5 Trailing edge D/C=. Re= 5 Trailing edge a b.. /C /C blade /C D/C =. Re = 5 /C =. Ep. Cal. r u' '
7 r r r r 33 r u' ' r u' ' b Ω Ω = a ba A U -H n +H n A D/C=. b/c=4. Re= 5 a H n = W V W V W V a - b B a D/C=. b/c=4. Re= 5 U b A +H n H n = U -Ω + Ω Ω = B D/C=. b/c=4. Re= 5
8 33 ( = u + + w ) Ω Ω Ω b/c = D L s = d ( / Re ) δ D /C= - /C < a f b u / Ω d u / e Ω c Ω f u / Ω u / Ω a Ω c Ω f u / /C. D/C=. b/c=4. /C=. Re= /C - D/C=. - b/c= /C=. Re= /C - D/C=. - b/c= /C=. Re= /C /C /C a Ω b u / c Ω d u / e Ω f u /
9 333 a e a b c r ' ' d r w'w' r ' ' e r 'w' - r 'w' a b/cb b/cc b/c r 'w' /C. D/C=. b/c=4. /C=. Re= 5. /C D/C= /C D/C=. b/c= b/c=4. /C=. - Re= /C=. Re= /C /C /C a u ' ' b uw ' ' c ( ) ' ' d ( ww ' ') e ( ) w ' ' /C.. D/C=. b/c=. /C=. -5 Re= blade /C 3.. D/C=. b/c=3. /C=. Re= 5 blade /C 3.. D/C=. b/c=4. /C=. Re= 5 blade /C /C /C a b/c =. b b/c = 3. c b/c = 4. r 'w'
10 334 r 'w' r 'w' λ / N r 'w' λ / b/c b/c= b /D Schlichting b / /D b/c D/C 3.. D/C=. Re= /D N 6 λ / b / Ep. Cal. (λ /)/D µ a a ( b ) / λ / /D b λ / b λ = λ Ω Ω r 'w' λ / λ = λ
11 335 Y. Maruta, S.Kotake : Separated Flow Noise of a Flat Plate at Large Attack Angles, Journal of Sound and Vibration 89(3) (983) B 6-59(995-) B (99-) B 63-64(997-) B 64-6(998-6) H. Haashi, S. Sasaki, Y. Kodama and T. Fukano : Stud of 3-dimensional Coherent Structure of Wake Vortices and Aeroacoustic Source, 6th. AIAA/CEAS Aeroacoustics Conference, AIAA () CD-ROM. No.8- (-7) 7-8. LES B 6-569(994-) 6. (998-8) 46. M.GASTER : Vorte shedding from circular clinder at low Renolds numbers, J. Fluid Mech. ol.46 part4 (97) Yoshiaki Kodama : Computation of Ship s Resistance Using an NS Soler with Global Conseration Flat Plate and Series 6(C B =.6) Hull, Journal of The Societ of Naal Architects of Japan Vol.7 (99) B.S. Baldwin and H. Loma : Thin laer Approimation and Algebraic Model for Separated Turbulent Flows, AIAA 6th Aerospace Sciences Meeting at Huntsille, Alabama (Jan. 978) pp.-8. Hermann Schlichting : Boundar-Laer Theor Sith Edition McGRAW-HILL BOOK COM- PANY (968) pp.6, pp.693. A.A. Townsend : The Structure of Turbulent Shear Flow nd. Edition, Cambridge Uniersit Press (976) 38. (983) B 66-65(-) L. R. Kubendran, H. M. McMahon and J. E. Hubbartt : Turbulent Flow Around a Wing/ Fuselage-Tpe Junction, AIAA JOURNAL Vol.4 No.9 (986) W. A. Eckerle, L. S. Langston : Horseshoe Vorte Formation Around a Clinder, Transactions of the ASME Vol.9 (987) B (-4)97. EFD/CFD (-7) 5-8. A.A. B 5-468( 6-8)
平板翼後流の三次元コヒーレント構造
NAOSITE: Nagasaki Uniersit's Ac Title 後流渦の特性に基づく多翼ファンの空力騒音および比騒音の予測 Athor(s) 佐々木 壮一 Citation (7-9-) Isse Date 7-9- URL http://hdl.handle.net/69/946 Right This docment is donloaded http://naosite.lb.nagasaki-.ac.jp
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