Twenty-Second Symposium on Naval Hydrodynamics (1999) / Chapter Skim
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5 Cavitation and Bubbly Flows
5 Cavitation and Bubbly Flows
Pages 239-300
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From page 239... ...
and demonstrate that the very large impulsive pressures generated in bubbly cloud cavitation are caused by shock waves generated by the collapse mechanics of the bubbly cavitating mixture. Here we describe computational investigations conducted to explore these and other phenomena in greater detail as part of an attempt to find ways of ameliorating the most destructive effects associated with cloud cavitation.
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From page 240... ...
They are recorded when an ephemeral, localized and transient low void fraction structure forms in the bubbly cavitating cloud and happens to pass over the face of the transducer. While these local events are smaller and therefore produce less radiated noise, the pressure pulse magnitudes are almost as large as those produced by the global events.
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From page 241... ...
The initial radius and void fraction of the cloud are denoted by Ao and no respectively and the initial radius of the bubbles within the cloud is denoted by Ro. This parametric exploration revealed that the dynamics and acoustics depended in an important way on the "cloud interaction parameter", it, defined as ~ = aoA2/R2 (1)
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From page 242... ...
Secondly, we note that shock waves characterized by large, positive pressure pulses and zones of low void fraction may form during the cloud col lapse process. They will then propagate through the cloud and can grow to very large magnitudes due to geometric focussing.
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From page 243... ...
The initial void fraction and cavitation number are respectively 0.01 and 0.475 and other parameters are given in Colonius et al.
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From page 244... ...
tially smaller than the natural frequency of the individual bubbles in the fluid. Other non-linear effects are exhibited when the plate frequency am preaches or exceeds the bubble natural frequency.
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From page 245... ...
Five different upstream void fractions, cool of the order of 10-6 are used in the computation and the results are shown in figures 6, 7, 8 and 9. Figures 6 and 7 respectively present the axial variations of the mixture velocity and the mixture pressure coefficient in this typical calculation.
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From page 246... ...
The decrease of the pressure is fed back to the Rayleigh-Plesset equation and results in further bubble growth. In this case the velocity and void fraction of the mixture increase and the pressure coefficient of the flow decreases significantly below the upstream values and the flow flashes to vapor.
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From page 247... ...
It is not, however, clear exactly what form the foci might take in the highly non-uniform, three-dimensional bubbly environment of a cavitation cloud on a hydrofoil, for example. Experiments with hydrofoils experiencing cloud cavitation have shown that very large pressure pulses occur within the cloud and are radiated away from it during the collapse process.
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From page 248... ...
A more unexpected result was the discovery of more localized bubbly shock waves propagating within the bum bly mixture in several forms, as crescent-shaped regions and as leading edge structures. These seem to occur when the behavior of the cloud is less coherent.
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From page 249... ...
. Under these circumstances, the model would not manifest the large cloud cavitation effects which could occur in the prototype.
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From page 250... ...
and Brennen, C.E., "Observations of shock waves in cloud cavitation," J Fluid Mech., 1998, Vol.
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From page 251... ...
FEDSM97-3249. van Wijngaarden, L.,~"On the collective collapse of a large number of gas bubbles in water," Proc.
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From page 252... ...
and Plesset, M.S., "Thermal effects in the free oscillation of gas bubbles," ASME J Basic Eng., 1971, Vol.
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From page 253... ...
and Kulkarny, V.J., "The focusing of weak shock waves," J Fluid Mech., 1996, Vol.
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From page 254... ...
A small decrease in cavitation indices increases Me size of Me cavity slightly, but has a major impact on Me turbulence level and momentum deficit in Me boundary layer downstream. Introduction At early phases of sheet cavitation, when the cavitation index is just below the inception level, He cavity is typically Win and has a glossy leading edge with either a blunt front or a series of sharp thin "fingers".
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From page 255... ...
However, they mention that when the cavity is thin there can be a situation where adverse pressure gradients are too weak for a re-entrant jet. This situation is consistent with the present observations, that at early stages of cavitation, Here is no reverse flow below or downstream of the attached cavitation.
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From page 256... ...
We assumed a free stream turbulence level of 1% (in reality it is significantly lower - about 0.1%) and a unifonn inflow to the test section.
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From page 257... ...
Fur~ennore, even when si is only slightly below the inception level, He flow behind die attached cavitation consists of a series of either large scale bubble-containing eddies or Winner horse-shoe like vortices with vaporous cores. These eddies are considerably higher than any boundary layer structure that exists in He absence or upstream of He cavitation.
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From page 258... ...
d.~ 1-150o 1~2ooo 1-2500 Figure 6: A sample Distal eous vorticity 0.12 distribution upstream and along the stable part of Me a.' attached cavitation ~ L = 0.254 m )
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From page 259... ...
The "large" vapor cavities simply shrink as Me vapor condenses and the horizontal velocity around them remains positive. This observation is not consistent with the typical re-entrant flow model for the closure region of attached cavitation (see the introduction)
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From page 260... ...
. v around the cavity closure is negative except for a narrow region very close to the wall.
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From page 261... ...
However, unlike typical shear flows, in the closure region of attached cavitation He high vorticity is generated by collapse of He vapor cavities.
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From page 263... ...
~4.41. The dimension of stresses is m2/s2 Summary and Conclusions PIV is used to resolve the flow structure at the closure region and downstream of attached cavitation.
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From page 264... ...
, "Flow In The Closure Region Of closed Partial Attached Cavitation", Third International Symposium on Cavitation, Grenoble, France, April, pp.
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From page 265... ...
AUTHORS' REPLY The flow is not periodic; i.e., the breakup process appears to be random, as long as the closure region of the cavitation is located on the straight part of the nozzle throat. In this region He horizontal pressure gradients in the closure region are small (xlL=0.2 - 0.4, see Figure 3 in the text)
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From page 266... ...
For moderately large attack angles, a region of flow separation exists near the hydrofoil's leading edge. An attached cavity forms within the separation bubble when the cavitation number is reduced.
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From page 267... ...
the cavitation number, a, and the cavity length, Lc, to give a relatively constant Strouhal number: St=f LclU~~0.3 Re-entrant flow can occur in the cavity closure. The existence' momentum, and direction of the reentrant flow will profoundly effect the cavity flow and the formation of cloud cavitation.
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From page 268... ...
average flow velocity in the center of the empty test section. The free and dissolved air content of the BDWT can be qualitatively controlled through deaeration and by allowing free gas bubbles to reach the free surfaces in the two tanks.
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From page 269... ...
O 0.5 1 1.5 2 2.5 3 3.5 44.5 Ls (cm) Figure 3: Plot of the separation bubble thickness, he, versus separation bubble length, Ls, for varying attack angles.
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From page 270... ...
The cavity thickness, he, is plotted against cavity length, Lc, in Figure 8. Cavities forming at higher attack angles are shorter than the length of the original separation bubble.
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From page 271... ...
However, recirculation can be seen for the high attack angle cases. At higher attack angles, the cavity does not fill the original non-cavitating separation bubble.
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From page 272... ...
(b) Figure 10: Cinematic PIV images in me dosum anion of cavities on me 1wo-dim=~onsl bail (~0°1 (~)
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From page 273... ...
Previous experimental observations of high sweepangle "delta" wings suggest that an attached leading edge vortex has foxed on the swept hydrofoil (see, for example, Thwaites [26~. In this case, there is flow within the separation bubble with a strong component parallel to the direction of the swept leading-edge, and the re-entrant flow at the closure of the separation bubble may be entrained into the vortex.
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From page 274... ...
Figure 14 presents a plot of the separation bubble thickness versus the bubble length for ~ = 2° and 5° for the three spanwise planes. The range hS / LS = 0.13 + 0.03 determined for the twodimensional leading edge separation bubble is also shown.
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From page 275... ...
These portions of the cavity are closed. Once the re-entrant liquid impinges ore the cavity interface, bubbly clouds are shed from We now open cavity.
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From page 276... ...
The cavity at the mid plane can be either open or closed, depending on the specif~c condition. The cavity at the right plane was almost always open, but it was possible at low attack angles to have a closed cavity that nearly spans the test section.
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From page 277... ...
This is seen in Figure 20, which is a plot of the cavity thickness versus cavity length for attack angles of 2° and 5° compared with the data from Figure 14. The length of the closed cavity is approximately 1.5 - 2 times the length of the original non-cavitating separation bubble.
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From page 278... ...
Figures 24 and 25 present the cavity appearance on these hydrofoils for attack angles of 2° and 5°, respectively. At the low attack angle, a clear cavity can be seen on the 15° swept hydrofoil near the upstream leading edge.
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From page 279... ...
For moderately large attack angles, a region of flow separation exists near the hydrofoil's leading edge. With a reduction in cavitation number, an attached cavity forms within the separation bubble.
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From page 280... ...
Laberteaux, K.L, Ceccio, S.L., 1998' "Flow in the Closure Region of Closed Partial Attached Cavitation," Proc. of the Third International Symposium on Cavitation, April 1998, Grenoble, France, pp.
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From page 281... ...
25. Tassin-Leger, Ceccio, S.L., Bernal, L.P., 1998, "Examination of the Flow Near the Leading Edge of Attached Cavitation: Part 2- Incipient Breakdown of Two-Dimensional Cavities," accepted for J
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From page 282... ...
Motion is considered for two adjacent gas bubbles beneath a free surface and a gas bubble near an inclined wall in the gravity field. The present numerical method is characterized in the calculations of the normal vector and tangential velocity vector at a node, the calculation of the solid angles and the influence coefficients, and the boundary triangulation, etc.
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From page 283... ...
The evolution of a gas bubble with buoyancy near an inclined wall was investigated in Section 5. The interaction of two adjacent gas bubbles with buoyancy and a free surface was simulated and analysed in Section 6.
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From page 284... ...
and (4) form a complete set of equations for the motion of the two gas bubbles and free surface.
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From page 285... ...
The tangential velocity vector at a node is calculated by averaging the tangential velocity vectors on the surrounding elements in the same way as that for the normal vector at a node. Solver for linear algebraic equations The linear algebraic equations discretized from the boundary integral equation (3)
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From page 286... ...
The bubble remains roughly spherical for the expansion phase except that the nght-lower part of its surface is flattened against We wall at We end of the expansion phase. When the bubble collapses, the flat part of the bubble surface is attracted by the rigid wall, and the rest of the surface migrates upwards due to buoyancy.
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From page 287... ...
The adjacent bubble surfaces press against each other and are flattened at the later stage of expansion phase (sequence 3~. Around the middle stage of the collapse phase, the lower-left part of the right bubble surface and the corresponding part of the left bubble surface are flattened (sequence 5~.
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From page 288... ...
7. Summary and conclusions The nonlinear evolution of 3D gas bubbles has been investigated numerically based on a timeintegration boundary integral method.
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From page 289... ...
Y 1996 Nonlinear interaction between gas bubble and free surface.
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From page 290... ...
1. Geomeny and coordinate system used to model the interaction among two gas bubbles and a free surface.
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From page 291... ...
:. Evolution of a gas bubble beneath a free surface for ~ = 100 ~ ~ = 0.
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From page 294... ...
8. The evolution of a gas bubble under a wall at an angle of 4~° to Me horizontal charactensed by ~ = 100, ~ = 0.S, and fly, = I.0.
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From page 295... ...
9. Evolution of two gas bubbles beneath a bee surface for ~ = loo, ~ = 0.5, and Of = 1.0.
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From page 296... ...
10. Evolution of two gas bubbles beneath a free surface for ~ = 100, ~ = 0.5, and yf = 1.0.
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From page 297... ...
11. Evolution of two gas bubbles beneath a free surface for ~ = 100, ~ = 0.5, and Of = 1.0.
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From page 298... ...
2. For a gas bubble, the bubble surface is continuously smooth until a water jet is formed.
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From page 299... ...
1998. The numerical analysis of the evolution of a gas bubble near an inclined wall.
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From page 300... ...
1995, 1997~. In He present work, He smooth jets were simulated nearly until the jet impacts upon He opposite bubble surface.
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