Elliptical channel flow

Hydrodynamic Dispersion, Figure 2 Effect of aspect ratio on solute dis-persivity in pressure-driven flow systems for a fixed channel depth. ( ) rectangular channels ( ) single-etched isotropic channels (x) elliptical channels ( ) optimum double-etched isotropic channels (a) optimum double-etched rectangular channels ( ) optimum channels with bowing (- - ) parallel plate limit... 

To calculate the flow rate Q for the elliptic channel, we need to evaluate a 2D integral in an elliptically shaped integration region. This is accomplished by coordinate transformation. Let p, 4>) be the polar coordinates of the unit disk, that is, the radial and azimuthal coordinates, which obey 0 < p < 1 and 0 < (p < 2n, respectively. The physical coordinates (y, z) and the velocity field u can then be expressed as functions of p, [Pg.33]

The start-up of methane-fueled, catalytic, channel-flow microreactors has been investigated numerically with a transient code that included full elliptic flow description, detailed hetero-Zhomogeneous chemistry, and all relevant heat transfer mechanisms in the reactor. Of particular interest were operating conditions pertinent to microturbine-based microreactor systems. Parametric studies have been carried out to identify the effect of various operations parameters, such a pressure, equivalence ratio, solid material properties and radiation properties on the transient process leading to ignition and finally to steady state operation. The following are the key conclusions of this smdy. 

Carrousel An unconventional aerobic treatment system for sewage and industrial effluents, providing efficient oxygenation, mixing, and quiescent flow in an elliptical aeration channel fitted with baffles. Developed in The Netherlands by DHV Raagevend Ingenieursbureau B.V., and licensed in the United Kingdom by Esmil. 

As Fig. 12.1 indicates, the manifold cross section may be bead shaped and not circular. Thus, pressure flow in an elliptical cross-section channel may be more appropriate for the solution of the manifold flow. Such a problem, for Newtonian incompressible fluids, has been solved analytically. (J. G. Knudsen and D. L. Katz, Fluid Dynamics and Heat Transfer, McGraw-Hill, New York, 1958). See also, Table 12.4 and Fig. 12.51. 

Before closing this chapter, we feel that it is useful to list in tabular form some isothermal pressure-flow relationships commonly used in die flow simulations. Tables 12.1 and 12.2 deal with flow relationships for the parallel-plate and circular tube channels using Newtonian (N), Power Law (P), and Ellis (E) model fluids. Table 12.3 covers concentric annular channels using Newtonian and Power Law model fluids. Table 12.4 contains volumetric flow rate-pressure drop (die characteristic) relationships only, which are arrived at by numerical solutions, for Newtonian fluid flow in eccentric annular, elliptical, equilateral, isosceles triangular, semicircular, and circular sector and conical channels. In addition, Q versus AP relationships for rectangular and square channels for Newtonian model fluids are given. Finally, Fig. 12.51 presents shape factors for Newtonian fluids flowing in various common shape channels. The shape factor Mq is based on parallel-plate pressure flow, namely,... 

A Ml-elliptic, two-dimensional CFD code [1-4] has been used to simulate the flow domain in a plane ehannel eonfiguration having length L, height 2b and wall thiekness 6. The full ehannel-flow reactor height was modeled in the fundamental studies of lean propane/air combustion on platinum, while in all other cases only half of the channel domain was modeled due to symmetry. 

A full-elliptic, 2-D steady laminarl CFD code [4-6] was employed to simulate the flow domain in a plane channel configuration having a total length L— 0 mm, channel heights of either 7h = 0.3 or 1 mm, and wall thickness of = 0.1 mm (Fig. 7.1). The first 1 mm was catalyticaUy inert and the remaining La — 9 mm was coated with platinum. Due to symmetry, only half of the flow domain was solved. The flow solver was coupled to a 2-D heat conduction solver for the solid substrate (wall thermal conductivity k ). External heat losses were applied to the outer channel surface as heat flux h(J — T ) using an effective heat transfer coeflicient h, with Ty, the outer surface temperature and set to 298 K. Propane and methane fuels... 

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