Critical flow model

Leung, J. C. and Epstein, M., A Generalized Critical Flow Model for Nonideal Gases, AIChEJ, 34 (9), 1568-1572, September 1988. 

Caraher, D. L., and T. L. DeYoung, 1975, Interim Report on the Evaluation of Critical Flow Models, Aerojet Nuclear Company, San Diego, CA. (3)... 

Kim Y, O Neal D.L., 1995. A comparison of critical flow models for estimating two-phase flow of HCFC22 and HFC134a through short tube orifices. International Journal of Refrigeration, 18(7) 447—455. 

G is a multiplier which is zero at locations where slip condition does not apply and is a sufficiently large number at the nodes where slip may occur. It is important to note that, when the shear stress at a wall exceeds the threshold of slip and the fluid slides over the solid surface, this may reduce the shearing to below the critical value resulting in a renewed stick. Therefore imposition of wall slip introduces a form of non-linearity into the flow model which should be handled via an iterative loop. The slip coefficient (i.e. /I in the Navier s slip condition given as Equation (3.59) is defined as... 

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. 

Instead of using just energy conservation, Moody (1975) derived a revised model that takes into account all the conservation laws. He found that critical flow rate is given by a determinantal equation that gives G as a function of p, X, and S. 

Henry and Fauske (1971) developed a model for critical flow in nozzles and short tubes, which allows for nonequilibrium effects and considers a two-phase mixture upstream of the break by using an empirical correlation to relate actual dXIdp to the value (flXJdp) under equilibrium conditions. For a dispersed flow, they assumed that... 

The annular flow model is useful for diabatic flow beyond critical heat flux (CHF). Hewitt and Govan (1990) introduced a model for the CHF state that is... 

Richter, H. J., 1983, Separated Two-Phase Flow Model, Application to Critical Two-Phase Flow, Int. J. Multiphase Flow 9(5) 511-530. (5)... 

On the basis of different assumptions about the nature of the fluid and solid flow within each phase and between phases as well as about the extent of mixing within each phase, it is possible to develop many different mathematical models of the two phase type. Pyle (119), Rowe (120), and Grace (121) have critically reviewed models of these types. Treatment of these models is clearly beyond the scope of this text. In many cases insufficient data exist to provide critical tests of model validity. This situation is especially true of large scale reactors that are the systems of greatest interest from industry s point of view. The student should understand, however, that there is an ongoing effort to develop mathematical models of fluidized bed reactors that will be useful for design purposes. Our current... 

Resin flow models are capable of determining the flow of resin through a porous medium (prepreg and bleeder), accounting for both vertical and horizontal flow. Flow models treat a number of variables, including fiber compaction, resin viscosity, resin pressure, number and orientation of plies, ply drop-off effects, and part size and shape. An important flow model output is the resin hydrostatic pressure, which is critical for determining void formation and growth. 

Two-phase flow models allow the calculation of both the two-phase mass flow rate per unit area (G) and also the critical pressure for choking. DIERS recommend the homogeneous equilibrium model (HEM, see 9.4.1) for this calculation. 

L.L. Raja, R J. Kee, O. Deutschmann, J. Wamatz, and LD. Schmidt. A Critical Evaluation of Navier-Stokes, Boundary-Layer, and Plug-Flow Models of the Flow and Chemistry in a Catalytic-Combustion Monolith. Catalysis Today, 59 47-60,2000. 

Table IX. Critical SD Values for the Parallel-Flow Model...

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