Cylinders cross-flow

Figure 1 shows the geometry. Strictly speaking, equation 2 applies only to single cylinders in slow cross flow, for point particles with negligible deposition and with the thickness of boundary layer much less than the radius of the cylinder. 

After regeneration, the catalyst enters the first reactor at the top. It passes through the reactor by gravity and is then transferred from the bottom of each reactor to the top of the next by a gas-lift. To minimize the pressure drop across the bed, a cross-flow technology was adopted The catalyst flows downwards from the top of the reactor between two concentric cylinders made up of grids, this allowing the radial passage of the gas phase. 

Effect of flow direction on the temperature field around a heated cylinder. (From Krause, J.R., "An Interferometric Study of Mixed Convection from a Horizontal Cylinder to a Cross Flow of Air , M.E.Sc. Thesis, The University of Western Ontario. London. Ontario. Canada. 1985. By... 

Because cross flow over a horizontal cylinder is being considered, the results given in Table 9.1 indicate that ... 

While the engineer may frequently be interested in the heat-transfer characteristics of flow systems inside tubes or over flat plates, equal importance must be placed on the heat transfer which may be achieved by a cylinder in cross flow, as shown in Fig. 6-7. As would be expected, the boundary-layer development on the cylinder determines the heat-transfer characteristics. As long as the boundary layer remains laminar and well behaved, it is possible to compute the heat transfer by a method similar to the boundary-layer analysis of Chap. 5. It is necessary, however, to include the pressure gradient in the analysis because this influences the boundary-layer velocity profile to an appreciable extent. In fact, it is this pressure gradient which causes a separated-flow region to develop on the back side of the cylinder when the free-stream velocity is sufficiently large. 

Fig. 6-8 Velocity distributions indicating flow separation on a cylinder in cross flow.

Fand [21] has shown that the heat-transfer coefficients from liquids to cylinders in cross flow may be better represented by the relation... 

Choice of Equation for Cross Flow Over Cylinders... 

The choice of equation to use for cross flow over cylinders is subject to some conjecture. Clearly, Eq. (6-17) is easiest to use from a computational standpoint, and Eq. (6-21) is the most comprehensive. The more comprehensive relations are preferable for computer setups because of the wide range of fluids and Reynolds numbers covered. For example, Eq. (6-21) has been successful in correlating data for fluids ranging from air to liquid sodium. Equation (6-17) could not be used for liquid metals. If one were making calculations for air either relation would be satisfactory. 

Assume that one-half the heat transfer from a cylinder in cross flow occurs on the front half of the cylinder. On this assumption, compare the heat transfer from a cylinder in cross flow with the heat transfer from a flat plate having a length equal to the distance from the stagnation point on the cylinder. Discuss this comparison. 

A 3.0-cm-diameter cylinder is subjected to a cross flow of carbon dioxide at 200°C and a pressure of 1 atm. The cylinder is maintained at a constant temperature of 50°C and the carbon dioxide velocity is 40 m/s. Calculate the heat transfer to the cylinder per meter of length. 

External Flows For a single cylinder in cross flow, Churchill and Bernstein recommend [ /. Heat Transfer, 99, 300 (1977)]... 

No. 69004 (1969) Convective heat transfer during forced cross flow of fluids over a circular cylinder, including convection effects. 

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... 

Cross-flow over a cylinder exhibits complex flow patterns, as shown in Fig. 7-16, The fluid approaching the cylinder branches out and encircles the cylinder, forming a boundary layer that wraps around the cylinder. The fluid particles on Ihe inidplane strike Ihe cylinder at Ihe stagnation point, bringing the fluid to a complete stop and ihus raising the pressure at that point. The pressure decreases in the flow direction while the fluid velocity increases. 

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 discussions above on the local heat transfer coefficients arc insightful however, they are of limited value in heal transfer calculations since the calculation of heat transfer requires the average heat transfer coefficient over the entire. surface. Of the several such relations available in the literature for the average Nusselt number for cross flow over a cylinder, we present the one proposed by Churchill and Bernstein ... 

Variation of the local heal transfer coefficient along the circumference of a circular cylinder in cross flow of air (from Giedl, 1949). 

Empirical correlations for the average Nusselt number for forced convection over circular and noncircular cylinders in cross flow (from Zukauskas, 1972 and Jakob, 1949)... 

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

S. W, Churchill and M. Bernstein. A Correlating Equation for Forced Convection from Gases and I.iquids to a Circular Cylinder in Cross Flow." Journal of Heat Transfer 99 (1977), pp. 300 -306. 

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