Vorticity and Vortex Dynamics 2011 Part 1 pps

... studies. The topics of Part IV, including Chaps. 11 and 12 , are somewhat more special. As an application of vorticity and vortex dynamics to external-flow aerodynamics, Chap. 11 presents systematically ... scope of vorticity and vortex dynamics, and 1 This definition is a generalization of that given by Saffman and Baker (19 79) for inviscid flow. 2 In Chinese, the wo...

Ngày tải lên: 11/08/2014, 17:22

... inner and outer radii R 1 and R 2 and angular velocity Ω 1 and Ω 2 , respectively, the constants can be determined as A = −Ω 1 1 −µη 2 1 −η 2 ,B= Ω 1 R 2 1 (1 −µ) 1 −η 2 , (6. 21) where µ = Ω 1 /Ω 2 and ... that (5 .10 4) and (5 .10 5) can be replaced by lim T →∞ 1 T  t 0 t 0 −T ω(s, t)dt =0, (5 .11 0a) lim T →∞ 1 T  t 0 t 0 −T ω x (s, t)dt>0, (5 .11 0b)...

Ngày tải lên: 11/08/2014, 17:22

... (x 1 ,x 2 ,x 3 )-frame read (∂ i f) ·e j =    c 11 c 12 c 13 c 21 c 22 c 23 ∂ 3 f 1 ∂ 3 f 2 ∂ 3 f 3    , (A.83a) where c 11 = ∂ 1 f 1 − κ 1 f 2 − b 11 f 3 c 12 = ∂ 1 f 2 + κ 1 f 1 − b 12 f 3 c 13 = ... Lines and Surfaces 715 (A.74) can be written in a geometrically clearer form: ∂ 1 e 1 = κ 1 e 2 + b 11 e 3 ∂ 1 e 2 = −κ 1 e 1 + b 12 e...

Ngày tải lên: 11/08/2014, 18:20

... τ-frame. Then (2 .14 4) reads {D ij } =    S 11 S 12 ω r /2 S 12 r s − S 11 0 ω r /20u n,n    . (2 .14 6) We have seen in Sect. 2 .1. 2 that the first and third eigenvalues λ 1, 3 and associated ... HWD basis vectors (2 .12 1) with k = 1and = +1, not normalized u + (x)=  |k| =1 u + (k)(e 1 +ie 2 )e ik·x , |k| =1, where (e 1 , e 2 , k) form a Cartesian triad. By lettin...

Ngày tải lên: 11/08/2014, 17:22

... C 1 and C 2 .(a) α 12 =0, (b) α 12 = 1, (c) α 12 =2 C 1 C 2 C = Fig. 3 .10 . Decomposition of a knotted vortex filament can go through C 1 an integer number of times (Fig. 3.9c), so that Γ 1 = α 12 κ 2 , where ... study of Casey and Naghdi 19 91) . Then by (2 .1) , (3 .10 7), and (3 .10 9), we have ∂Ω ∂τ = 0 or ω ρ = ω 0 ρ 0 · F, (3 .13 3b) known as the Cauchy vortici...

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... Vorticity Dynamics in Boundary Layers 16 1 2.00 1. 00 2.00 3.00 4.00 5.00 6.000.00 1. 75 1. 50 1. 25 1. 00 Re 1 2 1st 3rd F 6pmU a Fig. 4 .13 . Drag coefficient of a sphere derived from (4.76) for m =1( dashed ... 18 1 0 .1 -0 .1 -0 .1 -0.2 0 .1 0 .1 0 .1 -0.2 0 .1 -0.5 0 .1 -0.8 -1. 4 -1. 5 1. 5 0 .1 0 x 0 0 .10 0.25 0.50 1. 00 2.00 4.00 y Fig. 4. 21. Early stage of...

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... ≡ π 2 q 2  U 2 = O (1) . (7.78) Having obtained dynamic relations (7.76) and (7.78), Ahlborn et al. (19 98) note that C pb and C D are related by 1 −C pb = (1 γ) (1 + C D ),γ= C D + C pb 1+ C D , (7.79) 12 Ahlborn ... al. (19 98, 2002) set A = √ 2. 360 7 Separated Vortex Flows 0.6 0.4 0.2 0 0.4 0.6 1. 50 1. 50 0.50 0.25 0.25 0.50 1. 00 1. 00 0.8 y/s z/s 1. 0 Fig. 7.20. Loca...

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... 1. 0 1. 2 1. 4 1. 6 1. 8 0.20.0 0.4 0.6 0.8 1. 0 1. 2 1. 4 1. 6 -0.02 -1. 0 -0.5 -0.5 0.0 0.0 0.5 0.5 1. 0 1. 0 1. 5 2.0 -0. 01 0.00 0. 01 0.02 0.03 0.04 0.05 0.5 1. 0 X (m) 1. 5 2.0 0.0 -0.02 -0. 01 0.00 0. 01 0.02 0.03 0.04 0.05 0.5 ... length scale of background 588 11 Vortical Aerodynamic Force and Moment n -n S V f B ∂B Fig. 11 .1. Flow domain to be analyzed and...

Ngày tải lên: 11/08/2014, 18:20

... (3 .15 7) and Sect. 4 .1. 2, although the fluid is treated as 11 .5 A DMT-Based Arbitrary-Domain Theory 625 4 4 2 2 -2 -4 0 0 6 8 10 1 214 16 4 4 2 2 -2 -4 0 0 6 8 10 1 214 16 4 4 2 2 -2 -4 0 0 6 8 10 1 214 16 (c) (b) (a) Fig. ... the vorticity advection. 11 .5 A DMT-Based Arbitrary-Domain Theory 635 1. 5 1. 5 0.5 0.5 -0.5 -0.5 -1. 5 -1 -1 1 1 0 02 x y S 1 S 2 S 3 Fig. 11 ....

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... governed Trajectory -1. 5 -1. 3 -1. 1 -0.9 0.0 0.2 0.4 0.6 0.8 1. 0 1. 2 -0.7 -0.5 -0.3 -0 .1 x y Fig. 12 .19 . Universal vortex track (solid line) for the advanced stage of two-contour vortex, computed by (12 .11 0). ... initially. Then ∇ 2 ψ 1 + 1 2 λ −2 (ψ 2 − ψ 1 )=P 1 ,r<R (12 .89a) ∇ 2 ψ 1 + 1 2 λ −2 (ψ 2 − ψ 1 )=0,r>R (12 .89b) ∇ 2 ψ 2 + 1 2 λ −2 (ψ 1 −...

Ngày tải lên: 11/08/2014, 18:20