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Recirculatory flow in a cylindrical cavity

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4 indicate a large increase in pressure towards the downstream cavity wall. As the d/b ratio of the cavity was changed…
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be extended to a Reynolds number much larger than 400. . 12 Squ~re treated the fixed streamline large Reynolds number case…
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6 6 Following a suggestion by Wood he chooses ko to be the reciprocal of the rms of the velocity along Sb' i.e. ko = 2…
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7 PROBLEM FORMULATION BASIC MODEL __ --l---k7--Constant Vorticity Core ~ ___ " __ ~~:.----Boundary Layer Fig. 1. The…
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8 recirculatory flow any fluid particle must return to its initial position with the same velocity it had when it started,…
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problem of wake development far downstream. However, for the prandtl boundary layer problem this method of solution gives a…
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10 constraint is that the approximate solution for the desired property equal the exact 'solution for the desired…
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11 analysis appears to have two advantages. First equation 2b describes the forces on a fluid particle in the "natural…
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12 The linearized boundary layer equation then takes the form where (5b) At the end of the analysis, the physical x…
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K K K K u 1\ Xm Moving Wall a K K K K A Stationary Wall C Fig. 2. Typical ?oundary Layer Development
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14 The problem of determining the recircu1atory flow field is thus reduced to the simultaneous solution of the following two…
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dw J2-w { /'- - :- o < XYt'I ~ C\- d ;Xm d fL 0 .( Y' ' ad w('3~ ~ -v ( 'tJ '…
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Thus, the Green's function for equation Sa is the solution of 3~) - s ~ 3 (70) :a. 0 cSl~-S) Jl,J7? j (~3) .:; 0…
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17 (16a) co tAr (~y1 -: j j (YJ~ .v v(~/-VJSt (J-J</!s C- vsrt (16b) Formally transforming back to the s-plane, we…
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18 Briefly, Neumann's series may be obtained in the following manner . .A An initial approximation for the velocity…
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(0) Making repeated use of this result, and taking ur = 0, Neumann's method yields where and ( p) LA./" (;). (…
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20 An investigation of the solution for small x reveals that the singularity is the same as that encountered at the leading…
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21 while the author has determined that the shear stress at the wall in the -z: = -.11"1-I ?i IJ('" moving…
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22 Hence, the solutions in the physical plane for the boundary layer velocity dis- tributions are (f) (r) /,\ (~ 'f…
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the stationary wall, then the ratio ks /km can be taken to be unity. o 0 This assumption yields cp) 23 ,II ",)1/2…
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24 A comparison of the core velocity fraction K for several investigators is shown in Figure 3. The agreement between the…
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25 phenomenon that actually determines the motion of the core, as can be seen from a simple investigation of the start-up…
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ZRT 7"'"5 -- APPENDIX I The derivation for the region of validity of the Neumann series solution of…
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where d = 2/7r~ ) we have _ h L 1fI-rJ Z- -b ('f/+t:. / - - e e.... ~ lr) tA (t) _ b ("'+-J)l. -b (…
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- Restricting Ul to be an odd function this equation simplifies to Now, since a:> J/ c 1/ 2..::: f 2 r.. If') 1. d…
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