Spheres cross-flow

More recently, Henry and Epstein (H3) reported data on psychrometric ratios for cylinders in cross-flow and spheres. Their experimental results, which covered the Lewis number range of 3.7 to 7.2, were identical for spheres and cylinders. Furthermore, their results could best be represented by an equation similar to that of Bedingfield and Drew (Bl) as follows ... 

In addition, stagnation point (it is a point at which the net magnitude of velocity is zero, such as at the midpoint of a cylinder or a sphere in cross flow) devices, such as the dough roll mill, cross slot flow, and opposing jet devices can be used in which an area of intense extensional flow is created without the need to sustain a continuous filament. The latter technique is illustrated in Figure 3-27. Clark (1997) obtained extensional viscosity data on syrups and food gums dispersions using creation of... 

The average drag coefficients C j, for cross-flow over a smooth single circu lar cylinder and a sphere aie given in Fig, 7-17. The curves exhibit different behaviors in different ranges of Reynolds numbers ... 

Average drag coefficient for cross-flow over a smooth circular cylinder and a smooth sphere. From //. ScMichtift. Boyndary Layer Theory 7c. Copyright Q i979 The McGrow-Hill Companies. 

Once the drag coefficient is available, the drag force acting on a body in cross-flow can be determined from Fq. 7-1 where A is the frontal area (A = LD for a cylinder of length L and A for a sphere). It should be kept... 

The average Nusselt numbers for cross flow over a cylinder and sphere are... 

Sparrow, E.M. Abraham, J.P. Tong, J.C.K. Archival correlations for average heat transfer coefficients for non-circular and circular cylinders and for spheres in cross flow. Int. J. Heat Mass Transfer 47 (2004) 5285-5296... 

In the past ten to fifteen years or so, the applications sphere of cross-flow filtration has been extended to include microfiltration (MF) which primarily deals with the filtration of colloidal or particulate suspensions with size ranging from 0.02 to about 10 microns. Microfiltration applications are rapidly developing and range from sterile water production to clarification of beverages and fermentation products and concentration of cell mass, yeast, E-coli and other media in biotechnology related applications. 

This parameter is the ratio of number of particles, captured by the sphere per unit time, to number of partides per unit time that would pass through cross-sectional area equal to the sphere s projection, far from the sphere. Since Dbr flp and Pcd D, Espt, that is, the efficiency of capture decreases with increase of particle s size. When the collector is a grid, the deposition on it can be modeled by deposition on cylinders in a cross flow. In work [61] the expression for effidency of particle s capture by a cylinder has been obtained ... 

Based on the slip-line field theory [e.g., see Hill (1950)], Adachi and Yoshioka (1973) also extended the analysis of Ansley and Smith (1967) for spheres to include the creeping cross-flow over cylinders and obtained the following approximation expression for X ... 

As part of preliminary studies, the separation model in Eq.(3) was applied for the classification of sand/split and gravel, Table 3. In Fig. 3, the measured values for the three separation experiments with the cut size dr = 2,1 4.6 and 6.7 mm are shown. Despite reduction by particle shape impact, the quasi-statlonary settling velocity of spheres v,t at this cut-point is higher than the averaged channel air flow rate u being characteristically for the predominant cross-flow separation principle. 

Forced convection Sphere cross-flow Laminar Turbulent Like plate with L — d ... 

We will start by considering an uncharged molecule A surrounded by a statistically symmetrical distribution of B molecules (Figure 9.6). The flow, J, of B molecules in the direction towards A can be considered to be the flow of B molecules which cross a sphere centred on A, with radius r. 

Here, p is the density of the fluid, V is the relative velocity between the fluid and the solid body, and A is the cross sectional area of the body normal to the velocity vector V, e.g., nd1/4 for a sphere. Note that the definition of the drag coefficient from Eq. (11-1) is analogous to that of the friction factor for flow in a conduit, i.e.,... 

If the reverse of Reaction 1 is slow compared to 2 ( the colli sional stabilization step) then overall cluster growth will not depend strongly upon the total helium pressure. This is found to be the case using RRK estimates for k n and hard sphere collision cross sections for ksn for all clusters larger than the tetramer. The absence of a dependence on the total pressure implies that the product of [M] and residence time should govern cluster growth. Therefore, a lower pressure can be compensated for by increasing the residence time (slower flow velocities). 

In contrast to single-phase flow in a pipe of constant cross section, flow around a sphere or other bluff object exhibits several different flow regimes at different values of the Reynolds number. 

Achenbach based Re on flow conditions in the smallest cross section between sphere and tube. With this definition, wall effects increase Re, . 

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