Axial aspect ratio

The Reynolds number ensures turbulent flow and with it effective radial mixing. The axial aspect ratio ensures that axial dispersion is minimal. The radial aspect ratio ensures that channeling does not occur. Chan-neling refers to the situation in which the fluid close to the reactor walls travels faster than the fluid at the center of the tube. When these three dimensionless conditions are satisfied, one can usually model the reactor as a PFR. The velocity profiles are complex, however, and broad generalizations should be used with caution [28]. 

The basic message in all of the above is essentially that one may avoid axial dispersion effects if it is possible to design with the necessary axial aspect ratio, n, but there is no way in general to avoid radial dispersion effects. 

Mechanical Property Testing. Mechanical tests were performed on both unirradiated and irradiated materials at -157°C, 24°C, and 121°C. Specimens were kept dry prior to testing in an environmental chamber mounted in a tensile testing machine. Tensile test specimens of [0]4, [10]4, [45]4, and [90]4 laminates were cut from 4-ply composite panels. All specimens were straight-sided coupons. For tension and shear tests the length/width aspect ratio was 8. For the compression tests the aspect ratio was 0.25 and the unsupported length was 0.64 cm. The [0]4 laminates were used to measure the ultimate tension and compression strength, Xit the axial... 

The axial-flow compressors in aero gas turbines are heavily loaded. The aspect ratio of the blades, especially the first few stages, can be as high as 4.0, and the effect of streamline curvature is substantial. The streamline configuration is a function of the annular passage area, the camber and thickness distribution of the blade, and the flow angles at the inlet and outlet of the blades. The... 

Figure 4.5 shows the variation of A with E for flow parallel and normal to the axis, and averaged over random orientations. Except for disk-like particles, the dependence of A on aspect ratio is rather weak. In axial motion, a somewhat prolate spheroid experiences less drag than the volume-equivalent sphere A passes through a minimum of 0.9555 for E = 1.955. For motion normal to the axis of symmetry, A 2 takes a minimum of 0.9883 at = 0.702. However, the average resistance A is a minimum for a sphere. 

There is no radial velocity, and the axial velocity across the radius of the packed bed is uniform. Schwartz and Smith (1953) found that the velocity across the diameter of a packed bed is not uniform for radial aspect ratios (tube-to-particle diameter) less than about 30, due to the significant effect of the increased void space near the wall where the particles are locally ordered. This result has been verified by Hoiberg et al. (1971) for a packed bed reactor with radial aspect ratio about 50. They considered a radial velocity variation suggested by experimental observations with a sharp peak about 15% greater than the mean fluid velocity situated close to the wall. Simulations using their model showed results virtually identical to those obtained with a uniform velocity profile.3... 

Figure 4.7 represents nondimensional axial-velocity contours for two ducts, one with an aspect ratio a = 1 and the other with aspect ratio a = 0.25. The figure shows how the product /Re varies as a function of aspect ratio. For a given channel geometry, fluid properties, and flow conditions, the hydraulic diameter and the aspect ratio can be determined easily. The friction factor / follows easily, which in turn provides the mean wall shear stress. 

Previous computations (189) show that the critical value of Rat for non-Boussinesq conditions is approximately the same as that for a Boussinesq fluid in a box heated from below, at least when H2 is the carrier gas. Thus, results from the stability analysis of the classical Rayleigh-Benard problem of a two-dimensional fluid layer heated from below (see reference 190 for a review) may be used to indicate the type of behavior to be expected in a horizontal reactor with insulated side walls. As anticipated from this analysis, an increase in the reactor height from 2 to 4 cm raises the value of Rat to 4768, which is beyond the stability limit, Rat critical = 2056, for a box of aspect ratio 2 (188). The trajectories show the development of buoyancy-driven axial rolls that are symmetric about the midplane and rotating inward. For larger values of Rat (>6000), transitions to three-dimensional or time-de-... 

Where Ro is the lumen radius, I if the fiber length, u is the longitudinal convective velocity, P is pressure, X is the dimensionless axial space coordinate, R is the dimensionless radial coordinate. In writing Equation 14.24 it was assumed that flow is laminar and that entrance effects can be ignored. In addition, the axial stress terms have been neglected since the aspect ratio of the hollow fiber (Ro/L) is typically less than 0.01. The inertial terms have been neglected also, which is valid if the radial Reynolds number (ReR— puRo/fi) is much less than 1 [11], The boundary conditions for the solution ... 

A lateral percolation filter was fabricated on quartz (see Figure 8.2). The filter elements, which were located near the entry port of a channel, had 1.5 im channel width and 10 im depth. They were anisotropically etched with an aspect ratio greater than 30 1 [828], In contrast to the usual axial slit filter, in which the filter area is dictated by the channel area, the fluid flow in the lateral percolation filter... 

In this case, the potential drop across the electrode structure is related by the six dimensionless parameters ju, s, a, y as well as the aspect ratio Q and Peclet number/5 that character the convection in the axial direction. It is possible to approximately analyze this generalized theoretical nonlinear model using the set of partial differential equations with boundary conditions by ADM.22... 

Figure 1 shows the schematic of a tubular reactor, of radius a and length L, where a — a/Lis the aspect ratio. Clearly, ifa>S> 1, or a <3C 1, a physical length scale separation exists in the reactor. This length scale separation could also be interpreted in terms of time scales. For example, a 1 implies that the time scale for radial diffusion is much smaller than that of either convection and axial diffusion, and concentration gradients in the transverse direction are small compared to that in the axial direction. 

It is known that the resin behaves as an incompressible and Newtonian fluid (7), at least for a significant portion of the lamination process during which resin flow occurs. The Reynolds number of the flow is usually so small that the inertia temis in the equations of motion can be neglected. Also, because the aspect ratio, R/h (h being the thickness of the lay-up), is much greater or greater than unity in our experiments, we assume v, > > v and (dp/dr) > > (dp/dz) w here v, is the lateral velocity (in the r direction), v is the axial velocity (in the z direction) and p is dynamic pressure defined as the pressure above the ambient. Under these conditions, the resin flow satisfies... 

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