Void distribution

Two-phase flows are classified by the void (bubble) distributions. Basic modes of void distribution are bubbles suspended in the liquid stream liquid droplets suspended in the vapor stream and liquid and vapor existing intermittently. The typical combinations of these modes as they develop in flow channels are called flow patterns. The various flow patterns exert different effects on the hydrodynamic conditions near the heated wall thus they produce different frictional pressure drops and different modes of heat transfer and boiling crises. Significant progress has been made in determining flow-pattern transition and modeling. 

Figure 3.24 Measured void distribution in low and high void flows. (From Gill et al., 1963. Reprinted with permission.)...

A general expression for average void fraction in an adiabatic two-phase flow or in saturated boiling was suggested by Zuber and Findlay (1965). Defining the local superficial velocities, VSG(= Qc/A) and VSL (= QJA), as volumetric flux densities, they assumed the velocity and void distributions to be... 

Void distribution measurement. The local void fraction is an important parameter in the reduction and analysis of hydraulic test data in two-phase flow. In addition to photographic visualization and fiber optic video probes for observation (Donaldson and Pulfrey, 1979), the following other methods are currently available, each with its own unique set of attributes and drawbacks (Delhaye et al., 1973 Delhaye, 1986 Andreychek et al., 1989). 

Farrest, C. F., W. T. Hancox, and W. B. Nicoll, 1971, Axial Void Distributions, in Forced Convection Boiling A Survey of Prediction Techniques and Their Efficiency, Int. J. Heat Mass Transfer 14 1 377-1394. (3)... 

Fond et al. [84] developed a numerical procedure to simulate a random distribution of voids in a definite volume. These simulations are limited with respect to a minimum distance between the pores equal to their radius. The detailed mathematical procedure to realize this simulation and to calculate the stress distribution by superposition of mechanical fields is described in [173] for rubber toughened systems and in [84] for macroporous epoxies. A typical result for the simulation of a three-dimensional void distribution is shown in Fig. 40, where a cube is subjected to uniaxial tension. The presence of voids induces stress concentrations which interact and it becomes possible to calculate the appearance of plasticity based on a von Mises stress criterion. 

Finally, it is reasonable to discuss the relationships between fractions [Eqs. (32) and (33)]. Assuming that the neck arrangement is random and taking into account that the fractions of necks and voids with r < rp are defined by 1 — I (rp) and 1 - F(rp) [cf. Eqs. (32) and (33)], we have the following obvious constraint for the neck and void distributions ... 

Fig. 4 Typical void distributions in vessels with a single impeller. (From Ref. l) (View this art in color at www.dekker.com.)...

In a pioneering investigation, Serizawa [127, 128] measured the lateral void distribution as well as the turbulent axial liquid velocity fluctuations for bubbly air/water up-flows in a vertical pipe of diameter 60 (mm) inner diameter. They used electrical resistivity probes to measure the local void fraction, the bubble impaction rate, the bubble velocity and its spectrum. Turbulence quantities, such as the liquid phase mean velocity, and the axial turbulent fluctuations were measured using a hotfilm anemometer. A supplementary... 

Anglart H, Andersson S, Podowski MZ, Kurul N (1993) An Analysis of Multidimensional Void Distribution in Two-Phase Flows. Proc 6th Int Topical Meeting on Nuclear Reactor Thermal Hydraulics NURETH-6, Grenoble, October 5-8, 1 139-153... 

The results obtained from the 2D simulations with a uniform void distribution are given in Pig 11.6 and Pig 11.7. 

The use of a full 2D pseudo-homogeneous axi-S3Tnmetric model has the advantage, compared to the conventional 2D pseudo-homogeneous dispersion model, that it enables an evaluation of the influence of a non-uniform void distribution in the reactor. 

Void distribution is not uniform (15. 17). In the radial direction of the cedsle relatively few are located at the conductor side and at the outside surface, and the distribution curve peaks between the midpoint and the outer surface (18). This distribution is associated with the effect of steam used to cure XLPE. 

Thermal treatment was shown to diminish void number and size (18). This would necessitate an increase in density and such an increase was reported by Nitta and al (6 ). Electric stress and dielectric heating among other factors could result in a rearrangement of void distribution, shape, size and number, and is a possible cause of some slowly occurring changes during service. 

Li, C.J. and Wang, W.Z. (2004) Quantitative characterization of lamellar microstructure of plasma-sprayed ceramic coatings through visualization of void distribution. Mater. Sci. Eng., A, 386, 10-19. 

Forest Fire has been successfully applied to many explosives and shock-sensitive propellants. The results are sensitive to the Pop plot, and small experimental errors at low pressures can be magnified in the rate sufficiently to cause large errors in the calculated time histories of a building shock wave. For example, the PBX-9404 that Kennedy used for some of his experiments was slightly different from the type described in this chapter. Unfortunately different batches of the same explosive can have different void distributions even at the same density and hence have different Pop plots. 

The gas lift system is designed for argon supply in the lead-bismuth coolant under the core, for the creation of a required gas void distribution in the core and lateral blanket, as well as for the organization of the primary coolant circulation. 

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