Cross flows over cylinder

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. 

FIGURE 15.85 Critical heat flux in cross flow over cylinders, (a) three-dimensional jets (b) two-dimensional jets (from Lienhard and Eichorn [220], with permission from Elsevier Science). 

Cross-flow over cylinder (thin wires)... 

Hoyt and Sellin Cross-flow over cylinders (1989)... 

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 ... 

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

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. 

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 ... 

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

Turning to cross flow over bundles of tubes with surface roughness, some work has been done in the context of heat exchanger development for gas-cooled reactors and conventional shell-and-tube heat exchangers. This work is backed up by extensive studies of single cylinders, such as those with pyramid roughness elements tested in air by Achenbach [82]. Nusselt... 

The variation of the local Nu number along the circumference of a cylinder in cross flow of air (Pr= 0.7) for low and high Reynolds number is shown in Figures 3.2.10 and 3.2.11, respectively. The reason for the local variation of Nu is that the cross flow over a cylinder (and also over other bodies) exhibits complex flow characteristics. The fluid approaching the cylinder at the front stagnation point (angle y = 0) branches out and... 

As shown in Topic 3.2.4, Eq. 3.2.19 in a slightly modified form can also be used for the average Nusselt number for cross flow over a long cylinder (low diameter-to-height ratio and thus a negligible contribution of both end planes). 

Figure 3.2.14 Nu for cross-flow over a cylinder (Pr=0.7) accordingto Eq. (3.2.24d-f) (seetext). For comparison, the equation of Churchill and Bernstein (Figure 3.2.9) is also shown.

Restrictive discs and blister discs restrict the melt flow over the entire cross-section of the barrel bore. Blister discs (Fig. 12.35) are drilled cylinder discs arranged concentrically around the screw shaft with a defined gap with respect to the barrel wall. A ring is fitted to the counter shaft similar to the TME element. This blocks the entire cross-section of the... 

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. 

Equation 9.11 is usually referred to as Poiseuille s law and sometimes as the Hagen-Poiseuille law. It assumes that the fluid in the cylinder moves in layers, or laminae, with each layer gliding over the adjacent one (Fig. 9-14). Such laminar movement occurs only if the flow is slow enough to meet a criterion deduced by Osborne Reynolds in 1883. Specifically, the Reynolds number Re, which equals vd/v (Eq. 7.19), must be less than 2000 (the mean velocity of fluid movement v equals JV, d is the cylinder diameter, and v is the kinematic viscosity). Otherwise, a transition to turbulent flow occurs, and Equation 9.11 is no longer valid. Due to frictional interactions, the fluid in Poiseuille (laminar) flow is stationary at the wall of the cylinder (Fig. 9-14). The speed of solution flow increases in a parabolic fashion to a maximum value in the center of the tube, where it is twice the average speed, Jv. Thus the flows in Equation 9.11 are actually the mean flows averaged over the entire cross section of cylinders of radius r (Fig. 9-14). 

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

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

Figure 6.8 Circumferential variation of h for cross flow of air over a cylinder (from Giedt [42]).

Heat Transfer Over a Single Cylinder and Arrays of Cylinders in Low-Speed Cross Flow. 

Cross flow boiling. In this case, a flow is imposed over the surface. A typical example would be a cylinder with a liquid flow across it in a direction normal to the cylinder axis. At low cross flow velocities, the situation approaches that for pool boiling. 

The couple on the sphere vanishes unless it is restrained from rotating. If the sphere is also neutrally buoyant then F = 0, and only the last term in Eq. (147a) survives. By noting that the local rate of mechanical energy dissipation in the unperturbed flow is 2/iSjj Sjj, this ultimately leads to a simple proof of Einstein s law of suspension viscosity (Ela) for flow through cylinders (B17), provided that the spheres are randomly distributed over the duct cross section. 

A previous paper [ ] presented much of the experimental data which are analyzed in this report and the reader is referred to this work for a detailed description of the experimental equipment and procedures. Briefly, the experimental apparatus consisted of a cylinder containing liquid nitrogen in a cross-flow of air with the air velocity, humidity, and temperature as controlled variables over the following range air velocity 5 to 60 mph, air temperature 40° to 120°F, and specific humidity 16 to 325 gr/lb. 

Convection from a cylinder in cross flow has been widely investigated. The results for many liquids over a wide size range can be summarised as ... 

Figure 3.2.9 Average Nu number for the cross-flow of a gas (Pr= 0.7) over a cylinder according to Eq. (3.2.18). For comparison, two other equations proposed by Churchill and Bernstein (for Rex Pr>0.2,dotted-dashed line,Cengel,2002) and by Collis and Williams (for 0.02 < Re < 44, dotted line,...

A laboratory study of convective heat transfer to a cylinder in cross-flow was conducted in a small wind tunnel. The sensor was located at the forward stagnation line and tests were performed over a range of air speeds. For each test were the Reynolds NgJ and Nusselt numbers were calculated based on fluid, flow, and geometrical properties. 

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