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KENZOU 2008 8 9 5 1 2 3 4 2 5 6 2 6.1......................................... 2 6.2......................................... 2 6.3......................................... 4 7 5 8 6 8.1................................................. 6 8.2......................................... 7 8.2.1........................................ 8 8.2.2........................................ 9........................................ 11.................................... 11 ============================ 1

6 Blasius 6.1 1 d ρvdv = ρvv n ds pnds + ρkdv (6.1 dt V S V n 2 3 2 dg 2 S V dg = (pn + ρvv n ds (6.2 n v n 6.2 x, y n = (dy/ds, dx/ds 3 ψ nds = (dy, dx v n ds = dψ 6.2 dg x = pdy ρudψ dg y = pdx ρvdψ } (6.3 6.2 x, y 6.3 i dg x idg y = ip(dx idy ρ(u ivdψ (6.4 f = φ + iψ, f = φ iψ ψ = 1 (f f 2i dψ = 1 2i ( d f dψ = 1 ( d f 2i d d ( = u iv, = d f d d = u + iv f d = u2 + v 2 = q 2 (6.5 1 dp dt = F, p, F 2 2 ds ds 3 4 5.1 2

p 0 p = p 0 1 2 ρq2 = p 0 1 2 ρ d f d d(g x ig y = ipd + i 2 ρ = ipd + i 2 ρ ( = ip 0 d + i 2 ρ ( ( d f d d 2 i ( F (X, Y 6.2 F dg X = F x = dg x, Y = F y = X iy = = i 2 ρ (6.6 ( d 2 ρ f d d 2 (6.7 d(g x ig y = ip 0 ( 2 (... d + i ( 2 2 ρ d = [ ] = 0 dg y (6.8 6.9 4 (6.9 F ig.34 p n B ds -22 5.3.2 P x = 0, P y = ρuγ (6.10 4 5.3.2 R 6.2 6.8 v r U cos θ, v θ U sin θ + Γ 2πR u = u r cos θ u θ sin θ, v = u r sin θ + u θ cos θ X = Y = dg x = dg y = 2π 0 2π p cos θrdθ p sin θrdθ 2π 0 2π ρuu r Rdθ ρvv r Rdθ (6.11 0 0 Z b 4 f( D f( = 0 a f 3

U(= vr 2 + vθ 2 p p + 1 2 ρu 2 = p + 1 2 ρv2 p + 1 ( 2 ρ U 2 2U Γ 2πR sin θ... p = p + Γ ρu sin θ (6.12 2πR 6.11 X = 0, Y = ρuγ -23 22 1 f f = U (a + a2 2 + iγ c 2π log (a = U a2 2 + iγ c 2π 1 6.9 X iy = i 2 ρ = i 2 ρ ( {U (1 2 2a2 2 2 = i { 2 ρ U = iρ iuγ 2 π 2πi = iρuγ... X = 0, Y = ρuγ = ρuγ + a4 4 (a a2 2 + iuγ π + iγ c 2π ( 1 a2 3 } 2 } Γ2 4π 2 2 m = { 0 m 1 2πi m = 1 6.3 5 ds dm = r dg = (ydg dg y, dg x xdg, xdg y ydg x = (0, 0, xdg y ydg x (6.13 6 { dm = Im{(x + iy(dg x idg y } = Im ip 0 d i ( 2 } 2 ρ { = Re p 0 d 1 ( { 2 ( } 2 ρ = p 0 2 d( ρ 2 } 2 Re (6.14 M p 0 M = dm = 2 d( ρ { ( 2 } 2 Re = ρ { ( 2 } 2 Re (6.15 5 L = r p 6 Re(d = xdx + ydy = 1 2 d( 4

7 4 5.3.2 U Γ ρuγ 7 Kutta-Joukowski 2 1 2 x 2 / 1 1/ 8 = U + c 1 + c 2 2 + c 3 3 + (7.1 / = U U c n f = U + c 0 + c 1 log c 2 c 3 2 (7.2 c 0 f = = = c 1 2πi dφ + i U + dψ = Γ( + iq( (7.3 c 1 + c 2 2 + c 3 3 + c 1 = Q 2π + i Γ (7.4 2π 7.3 Q Γ 7.1 1 2 3 2 3 9 2 7.1 1 X, Y 7.1 ( 2 = U 2 + 2Uc 1 + (c 2 1 + 2Uc 2 1 2 + (7.5 1 6.9 X iy = i ( 2 2 ρ = i { 2 ρ U 2 + 2Uc 1 1 + (c 2 1 + 2Uc 2 2 + = i 2 ρ 2Uc 1 = iρ 2 2Uc 12πi = 2πρUc 1 = ρu( Q( + iγ( (7.6 7 8 [ ] 9 P90 5

X = ρuq(, Y = ρuγ( (7.7 7.7 2 4 5.3.2 [ ] Γ U L = ρuγ L 10 7.7 1 Q > 0 Q < 0 Q = 0 X = 0 2 6.15 M = ρ { ( 2 } 2 Re = ρ2 { } Re U 2 + 2Uc 1 + (c2 1 + 2Uc 2 + = ρ { (c 2 } 2 Re 1 + 2Uc 2 = ρ 2 Re { (c 2 1 + 2Uc 2 2πi } = πρre(ic 2 1 + 2iUc 2 (7.8 c 1 7.4 c 2 c 2 = Re(c 2 + iim(c 2 7.8 M = ρqγ 2π + 2πρUIm(c 2 (7.9 2 8 8.1 2 = x + iy ζ ζ = ξ + iη 2 ζ = g(ζ (8.1 g( 8.1 g( ζ g( 11 f( 8.1 w(ζ f( = f(g(ζ w(ζ (8.2 w(ζ ζ g ζ 10 11 6

8.2 = g(ζ = ζ + a2 ζ, a > 0 (8.3 - ζ ζ = Re iθ = x + iy = Re iθ + a2 R e iθ = (R + a2 cos θ + i (R a2 R R... x = (R + a2 cos θ y = (R a2 R R sin θ (8.4 sin θ (8.5 F ig.35 y ζ η 2a 2a x a a ξ ζ R = const 8.3 R = a a x = 2a cos θ, y = 0 x x = 2a 2a 4a R > a 8.5 θ x 2 ( 1 + a 2 R 2 + y 2 ( 1 a 2 R 2 = 1 (8.6 x R + a 2 /R 2 R a 2 /R 2 ± 2a, 0 R < a, ζ a x = 2a 2a ζ θ = const 8.5 2 ±2a, 0 x 2 cos 2 θ y2 sin 2 θ = 4a2 (8.7 x U x 4a f( = U (8.8 8.3 ζ ζ f = U (ζ + a2 ζ 5.3.1 (8.9 7

8.2.1 x α U x a F ig.36 y y, ζ η ζ η θ x 4a 4a a α x U α 2a cos α xξ U 2a cos α α ξ x U f( = U ( + a2 = e iα f( = U (e iα + a2 eiα ζ = + a2 a ζ 4a 8.11 (8.10 (8.11 = 1 2 (ζ + ζ 2 4a 2 12 ζ w( ( ζ + ζ w(ζ = f(ζ = U 2 4a 2 e iα 2a 2 + 2 ζ + ζ 2 4a 2 eiα = U(ζ cos α i ζ 2 4a 2 sin α (8.12 dw/dζ = (dw/(/dζ = 0 dw/ = 0 dw = U ζ ζ 8.12 ( (e iα a2 e iα = 0 s = ±ae iα (8.13 2 ζ s = + a2 = ±a(eiα + e iα = ±2 cos α (8.14 w(ζ = Uζ cos α i 1 4a2 ζ 2 ξ α U sin α Ue iα ζ (8.15 12 ζ 8

8.2.2 x α U x 4a Γ x α = e iα F ig.37 η y y θ, α x = re i(θ+α = e iα = e iα U = Ue iα x Γ 4a α U ξ f( = U (Ue iα, (8.16 ζ α = ζ + a2 ζ 4a ζ a w(ζ = f(ζ = U (e iα ζ + a2 e iα ζ = e iα ζ = ζe iα (8.17 2 w(ζ = f(ζ = U (e iα ζ + a2 e iα iγ ζ 2π log ζe iα = U (e iα ζ + a2 e iα iγ log ζ (8.18 ζ 2π log (Γ/2πα Γ 8.18 dw/dζ = 0 dw dζ = U (e iα a2 e iα ζ 2 ζ 2 + iγeiα 2πU a2 e i2α = 0 + iγ 2πζ (8.19... ζ s = eiα 4πU (iγ ± 16π 2 a 2 U 2 Γ 2 (8.20 9

4 5.3.2 x s s = 1 4πU (iγ ± 16π 2 U 2 a 2 Γ 2 s = s e iα 8.20 3 3 5.3.2 = ( 1 = U(e iα a 2 e iα /ζ 2 iγ/2πζ dζ dζ 1 a 2 /ζ 2 (8.21 ζ = a = 2a 13 Kutta 14 ζ = a 8.21 Γ 15 [ U (e iα a2 e iα ζ 2 iγ ] = 0 2πζ ζ=a 8.21 lim ζ a... Γ = 4πUa sin α (8.22 U(e iα a 2 e iα /ζ 2 iγ/2πζ (ζ 2 a 2 cos α i(ζ a 2 sin α = u iv = lim ζ a 1 a 2 /ζ 2 = U lim ζ a ζ 2 a { 2 = U lim cos α i ζ a } ζ a ζ + a sin α = U cos α x 8.20 8.22 ζ s = eiα 4πU (iγ ± 16π 2 a 2 U 2 Γ 2 = eiα 4πU ( i4πua sin α ± 4πUa 1 sin 2 α = ae iα (i sin α cos α = ae 2iα, a ζ = a x = 2a Fig.37 F ig.37 ζ Γ < 4πaU Γ = 4πaU Γ > 4πaU 13 ζ = ±a ζ = a P148 14 P146 15 10

7 L = ρu( Γ = 4πρU 2 a sin α (8.23 x 7.9 2 M = ρqγ 2π + 2πρUIm(c 2 a/, a/ ζ 1 x U Ue iα Q = 0 M = ρqγ 2π + 2πρUIm(c 2e iα = 2πρUIm(c 2 e iα (8.24 M c 2 = ζ + a2 ζ ζ = 1 2 ( + 2 4a 2 = 1 2 { 1 + ( 1 (2a/ 2 1/2 } a 2 / + O(1/ = [ 1 + O(1/ 2 ] 1 ζ = 1 [ ( ] 1 1 1 + O 2 = 1 [ ( ] 1 1 + O 2 = 1 + O(1/3 8.21 = U(e iα a 2 e iα /ζ 2 iγ/2πζ 1 a 2 /ζ 2 = U(e iα a 2 e iα (1/ + O(1/ 2 2 iγ/2π(1/ + O(1/ 2 1 a ( 2 1 = Ue iα iγ 1 2π 2iUa2 sin α 1 2 + O(1/3 = Ue iα + c 1 + c 2 2 + O(1/3 + O(1/3 2 c 2 = i2ua 2 sin α (8.25 8.24 M = 2πρUIm(c 2 e iα = 2πρUIm(i2Ua 2 e iα sin α = 4πρUa 2 sin α cos α = La cos α (L (8.26 D O D d L O Ld cos α 8.26 M = La cos α = Ld cos α d = a (8.27 D α 1/4 L = L (1/2ρU 2 l, D = D (1/2ρU 2 l, M = M (1/2ρU 2 l (8.28 11

F ig.38 L 4a A D d O B U α l l = 4a L = 2π sin α, D = 0, M(O = π/2 sin α cos α (8.29 ( 5 12

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