Critical flow pattern

Figure 3.61 Critical flow patterns in a short pipe. (From Zaloudek, 1963. Reprinted with permission of U.S. Department of Energy, Washington, DC, subject to the disclaimer of liability for inaccuracy and lack of usefulness printed in cited reference.)...

Figure 10.7 shows the critical flow patterns obtained with the three models. It is shown that BLM is a convection cell sitting above the mush/melt interface and MLM consists of two separated cells, one in the mushy layer and one in the fluid layer. The critical flow patterns for the three models are similar except that the critical wavelength differs from one another. 

Because mass flow bins have stable flow patterns that mimic the shape of the bin, permeabihty values can be used to calculate critical, steady-state discharge rates from mass flow hoppers. Permeabihty values can also be used to calculate the time required for fine powders to settle in bins and silos. In general, permeabihty is affected by particle size and shape, ie, permeabihty decreases as particle size decreases and the better the fit between individual particles, the lower the permeabihty moisture content, ie, as moisture content increases, many materials tend to agglomerate which increases permeabihty and temperature, ie, because the permeabihty factor, K, is inversely proportional to the viscosity of the air or gas in the void spaces, heating causes the gas to become more viscous, making the sohd less permeable. 

To be consistent with a mass flow pattern in the bin above it, a feeder must be designed to maintain uniform flow across the entire cross-sectional area of the hopper outlet. In addition, the loads appHed to a feeder by the bulk soHd must be minimised. Accuracy and control over discharge rate ate critical as well. Knowledge of the bulk soHd s flow properties is essential. 

Approximate prediction of flow pattern may be quickly done using flow pattern maps, an example of which is shown in Fig. 6-2.5 (Baker, Oil Gas]., 53[12], 185-190, 192-195 [1954]). The Baker chart remains widely used however, for critical calculations the mechanistic model methods referenced previously are generally preferred for their greater accuracy, especially for large pipe diameters and fluids with ysical properties different from air/water at atmospheric pressure. In the chart. 

Clearly, the flow pattern established in a mixing vessel depends critically upon the vessel/impeller configuration and on the physical properties of the liquid (particularly viscosity). In selecting the appropriate combination of equipment, it must be ensured that the resulting flow pattern is suitable for the required application. 

Qu W, Mudawar I (2002) Prediction and measurement of incipient boiling heat flux in micro-channel heat sinks. Int J Heat Mass Transfer 45 3933-3945 Qu W, Mudawar I (2004) Measurement and correlation of critical heat flux in two-phase micro-channel heat sinks. Int J Heat Mass Transfer 47 2045-2059 Quiben JM, Thome JR (2007a) Flow pattern based two-phase pressure drop model for horizontal tubes. Part I. Diabatic and adiabatic experimental study. Int. J. Heat and Fluid Flow. 28(5) 1049-1059... 

In the following sections, the flow patterns, void fraction and slip ratio, and local phase, velocity, and shear distributions in various flow patterns, along with measuring instruments and available flow models, will be discussed. They will be followed by the pressure drop of two-phase flow in tubes, in rod bundles, and in flow restrictions. The final section deals with the critical flow and unsteady two-phase flow that are essential in reactor loss-of-coolant accident analyses. 

The phenomenon of critical flow is well known for the case of single-phase compressible flow through nozzles or orifices. When the differential pressure over the restriction is increased beyond a certain critical value, the mass flow rate ceases to increase. At that point it has reached its maximum possible value, called the critical flow rate, and the flow is characterized by the attainment of the critical state of the fluid at the throat of the restriction. This state is readily calculable for an isen-tropic expansion from gas dynamics. Since a two-phase gas-liquid mixture is a compressible fluid, a similar phenomenon may be expected to occur for such flows. In fact, two-phase critical flows have been observed, but they are more complicated than single-phase flows because of the liquid flashing as the pressure decreases along the flow path. The phase change may cause the flow pattern transition, and departure from phase equilibrium can be anticipated when the expansion is rapid. Interest in critical two-phase flow arises from the importance of predicting dis-... 

The effect of local enthalpy at CHF is due primarily to the wall voidage, which impairs the critical flux, and secondarily to the bulk voidage, which affects the flow pattern. The coupled effects of local subcooling and flow velocity in a subcooled bubbly flow were first reported by Griff el and Bonilla (1965), neglecting the pressure effect ... 

Bergles, A. E., R. F. Lopina, and M. P. Fiori, 1967b, Critical Heat Flux and Flow Pattern Observations for Low Pressure Water Flowing in Tubes, Trans. ASME, J. Heal Transfer 59 69-74. (6)... 

Tippets, F. E., 1962, Critical Heat Fluxes and Flow Patterns in High Pressure Boiling Water Flows, ASME Paper 62-WA-162, Winter Annual Meeting, ASME, New York. (5)... 

The two goals of this chapter were to provide a critical review of the current state of the art in the field of two-phase flow with heat transfer and to provide procedures which can be used for the design of tubular fluid-fluid systems. Both heat transfer without phase change and with phase change were discussed in detail. In each case the analysis was based on an understanding of the flow patterns and the hydrodynamics of the system. 

General Considerations 1 Location of people relative to the unit 2 Location of critical systems 3 Dominant wind direction 4 Climate and weather extremes earthquake, flooding, windstorms 5 Site topography 6 External hazards or threats (fire/explosion/toxic release from nearby process or facility aircraft subsidence sabotage) 7 Traffic flow patterns and clearances from process vessels and lines 8 Security and reliability of all critical feeds and utilities 9 Command center and alternate command center locations 10 Evacuation routes, emergency exits, safe rally spots... 

When the shear rate reaches a critical value, secondary flows occur. In the concentric cylinder, a stable secondary flow is set up with a rotational axis perpendicular to both the shear gradient direction and the vorticity axis, i.e. a rotation occurs around a streamline. Thus a series of rolling toroidal flow patterns occur in the annulus of the Couette. This of course enhances the energy dissipation and we see an increase in the stress over what we might expect. The critical value of the angular velocity of the moving cylinder, Qc, gives the Taylor number ... 

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