Divergent flow

Fig. 23. Oscillatory convergent-divergent flow (depth of the cell = 14 mm, contraction width e = 0.9 to 1.8 mm)...

However, this expression assumes that the total resistance to flow is due to the shear deformation of the fluid, as in a uniform pipe. In reality the resistance is a result of both shear and stretching (extensional) deformation as the fluid moves through the nonuniform converging-diverging flow cross section within the pores. The stretching resistance is the product of the extension (stretch) rate and the extensional viscosity. The extension rate in porous media is of the same order as the shear rate, and the extensional viscosity for a Newtonian fluid is three times the shear viscosity. Thus, in practice a value of 150-180 instead of 72 is in closer agreement with observations at low Reynolds numbers, i.e.,... 

In Fig. 18, flow path lines are shown in a perspective view of the 3D WS. By displaying the path lines in a perspective view, the 3D structure of the field, and of the path lines, becomes more apparent. To create a better view of the flow field, some particles were removed. For Fig. 18, the particles were released in the bottom plane of the geometry, and the flow paths are calculated from the release point. From the path line plot, we see that the diverging flow around the particle-wall contact points is part of a larger undulating flow through the pores in the near-wall bed structure. Another flow feature is the wake flow behind the middle particle in the bottom near-wall layer. It can also be seen that the fluid is transported radially toward the wall in this wake flow. 

The pressures developed in the deton reaction zone in condensed expls are of the order of 103 to 10 atm. Material at such pressures cannot in general be contained, so that the flow behind the front has a component radially outward. Gases, which develop much lower deton pressures (of the order of 10 atm), can be confined in a tube, and for them the one- dimensional approximation is good. The diverging flow is expected and is found experimentally to result in lower pressures and densities within the steady wave, and consequently in lower detonation velocities. 

In Section V,A (Ref 66, p 157) theories are discussed which assume diverging flow in the steady-state zone, whiie in Section V,B those that assume parallel flow within the steady zone... 

Eyring et al (Refs 9 22a) postulated that the curved shock front is made up of spherical segmen ts and that behind each segment is the radially divergent flow which occurs behind a spherical deton wave initiated at a point inside an explosive (Taylor, Ref... 

Accdg to these assumptions, the reduction of deton vel with diam is due not to diverging flow but to the circumstance that... 

Fig. 13.18 Predicted velocity field showing fountain flow around the melt front region for non-Newtonian fiber suspension flow at about half the outer radius of the disk. The reference frame is moving with the average velocity of melt front, and the length of arrow is proportional to the magnitude of the velocity. The center corresponds to z/b = 0 and wall is z/b = 1, where z is the direction along the thickness and b is half-gap thickness. [Reprinted by permission from D. H. Chung and T. H. Kwon, Numerical Studies of Fiber Suspensions in an Axisymmetric Radial Diverging Flow The Effects of Modeling and Numerical Assumptions, J. Non-Newt. Fluid Mech., 107, 67-96 (2002).]...

D. H. Chung and T. H. Kwon, Numerical Studies of Fiber Suspensions in an Axisymmetric Radial Diverging Flow the Effects of Modeling and Numerical Assumptions, J. Non-Newt. Fluid Meek, 107, 67-96 (2002). 

Fig. 8a. Sharp-edged orifice meter. The pressure loss in the converging-diverging flow can be related to the mass flow rate through the pipe.

If the reactor has a converging or diverging flow pattern, a more general expression for E is needed. In tensor notation, the expression is... 

The computational snapshot approach was used to simulate flow generated in these three impeller configurations (for more details, see Deshpande and Ranade, 2001). The predicted velocity vectors in the r-z plane located midway between the two baffles for parallel, merging and diverging flow configurations are shown in... 

FIGURE 10.21 Schematic of stable flow patterns observed with dual Rushton turbines (from Rutherford et o/ 1996). (a) Parallel flow, (b) merging flow, (c) diverging flow. 

FIGURE 10.24 Comparison of experimental ((a) Rutherford et a/., 1996) and predicted ((b) Deshpande and Ranade, 2001) results for dual Rushton turbines (diverging flow regime). 

An analysis of the consequences of divergent flow provided further insight into detonations in cylindrical charges. However, the radius of curvature, a difficult quantity to measure, is needed for application of the theory [27]. A rotating mirror camera was used to take head-on photographs of detonations and confirmed that curved fronts occur [25]. 

Among the consequences of this general circulation are convergent and divergent flows in the surface wind leading to systematic vertical motions, es-... 

The most efficient orientation fields are exten-sional. Using convergent and divergent flow one may control orientation of anisometric particles. Most of the work in this area has been done with fiber-filled materials but the effects are equally important for flow of neat semicrystafline polymer melts or liquid crystal polymers [Goettler and Shen, 1983 Goettler, 1984]. There is less information on the flow-induced orientation of platelets. In extensional flow, these particles are less susceptible to orientation. Two-stage orientation mechanism was observed in converging flow [Utracki, 1988]. 

The convergent-divergent flow should be generated in the radial not axial direction. 

Constitutive equation Continuous mixers Continuum mechanies Convergence Convergent flow Convergent-divergent flow (e-d) COPO (Aliphatic Polyketone)... 

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