Shocks in Quasi-One-Dimensional Bubbly Cavitating Nozzle Flows

A continuum bubbly mixture model coupled to the Rayleigh-Plesset equation for the bubble dynamics is employed to study one-dimensional steady bubbly cavitating flows through a converging-diverging nozzle. A distribution of nuclei sizes is specified upstream of the nozzle, and the upstream cavitation number and nozzle contraction are chosen so that cavitation occurs in the flow. The computational results show very strong interactions between cavitating bubbles and the flow. The bubble size distribution may have significant effects on the flow; it is shown that it reduces the level of fluctuations and therefore reduces the “cavitation loss” compared to a monodisperse distribution. Another interesting interaction effect is that flashing instability occurs as the flow reaches a critical state downstream of the nozzle. A stability analysis is proposed to predict the critical flow variables. Excellent agreement is obtained between the analytical and numerical results for flows of both equal bubble size and multiple bubble sizes. [S0098-2202(00)00702-1]

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Near-frozen quasi-one-dimensional flow I. The reservoir problem

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences ◽

10.1098/rsta.1967.0048 ◽

1967 ◽

Vol 262 (1125) ◽

pp. 203-224 ◽

Cited By ~ 2

Keyword(s):

Relaxation Time ◽

Entropy Production ◽

Asymptotic Expansions ◽

Flow Time ◽

Stagnation Zone ◽

Rate Parameter ◽

One Dimensional ◽

Frozen Solution ◽

Nozzle Flows ◽

Relaxing Gas

Non-equilibrium quasi-one-dimensional nozzle flows are considered in the limit when the relaxation time is large compared with some characteristic flow time. Non-uniformities which arise in the reservoir region, for convergent-divergent nozzles, are treated by the method of matched asymptotic expansions (see, for example, Van Dyke 1964). It is shown that even away from this stagnation zone the solution does not proceed simply in integral powers of the rate parameter. The correct solution is deduced for a vibrationally relaxing gas. It is noted, however, that this near-frozen solution does not necessarily remain valid at downstream infinity where the overall entropy production may become important. Solutions valid in this region are presented in part II of this paper.

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Near-frozen quasi-one-dimensional flow II. De-excitation shocks

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences ◽

10.1098/rsta.1967.0049 ◽

1967 ◽

Vol 262 (1125) ◽

pp. 225-250 ◽

Cited By ~ 3

Keyword(s):

Power Law ◽

Infinite Sequence ◽

Relaxation Frequency ◽

One Dimensional ◽

Dimensional Flow ◽

Nozzle Flows ◽

Non Equilibrium

The possible existence of compression regions, analogous to condensation shocks, in expanding non-equilibrium nozzle flows is noted. For power-law nozzle shapes the structure and position of these ‘de-excitation shocks’ are derived when the relaxation frequency decays algebraically with temperature. The asymptotic limiting solutions downstream of the de-excitation shocks are also discussed. For certain nozzle shapes it appears that this limiting solution is an infinite sequence of such shocks separated in part by regions of near-frozen flow.

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Semianalytical solution of unsteady quasi-one-dimensional cavitating nozzle flows

Journal of Engineering Mathematics ◽

10.1007/s10665-013-9645-6 ◽

2013 ◽

Vol 86 (1) ◽

pp. 49-70 ◽

Cited By ~ 2

Author(s):

Can F. Delale ◽

Şenay Pasinlioğlu ◽

Zafer Başkaya ◽

Günter H. Schnerr

Keyword(s):

One Dimensional ◽

Nozzle Flows

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