Concentric annular pressure flow

Axial Pressure Flow between Concentric Cylinders Solve the problem of flow in the horizontal concentric annular space formed by two long cylinders of length L and radii Rt and Ra, caused by an entrance pressure Pp, which is higher than the exit (atmospheric) pressure. Consider the limit as (Rp — R,) / (Rp + Rt) approaches zero. 

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,... 

MSFC Report ER11 -05-WI4d-001, dated 28 October 2005, Heat Transfer and Pressure Drop in Concentric Annular Flows of Binary Inert Gas Mixtures, R. Reid, J. Martin, D. Yocum, E. Stewart... 

Fig. 13. A hoUow-fibet reverse osmosis membrane element. Courtesy of DuPont Permasep. In this twin design, the feedwater is fed under pressure into a central distributor tube where half the water is forced out tadiaUy through the first, ie, left-hand, fiber bundle and thus desalted. The remaining portion of the feedwater flows through the interconnector to an annular feed tube of the second, ie, right-hand, fiber bundle. As in the first bundle, the pressurized feedwater is forced out tadiaUy and desalted. The product water flows through the hoUow fibers, coUects at each end of the element, and exits there. The concentrated brine from both bundles flows through the concentric tube in the center of the second bundle and exits the element on the right.

The tube-in-tube or multitube-in-tube heat exchangers are useful in small Linde lique-fiers or in the final Joule-Thomson stage of any liquefier. The performance of Linde-type exchangers is easy to calculate, and their realization is simple. In the examples shown in Fig. 5.12 (a)-(c), the tubes are concentric and the outer wall contributes appreciably to the pressure drop in the outer stream without contributing to the heat transfer. Usually, the smaller inner tube is used for the high-pressure stream and the low-pressure stream flows through the outer annular space. The tubes in Fig. 5.12 (d) and (e) are solder bonded while that in (f) is flattened and twisted before insertion into an outer tube. 

Pressure oscillations in the first arrangement depended on the equivalence ratio of the flow in the annulus and decreased with velocities in the pilot stream greater than that in the main flow due to decrease in size of the recirculation zone behind the annular ring and its deflection towards the wall. Increase in swirl number of the second arrangement caused the lean flammability limit to decrease, and the pressure oscillations to increase at smaller values of equivalence ratio. Unpremixedness associated with large fuel concentrations at the centre of the duct increased the pressure oscillations. Pressure oscillations caused the position of flame attachment to move downstream in both flows with a decrease in amplitude of oscillations. 

Levy et al. (L5) have studied the effect of eccentricity on the bum-out flux in upward vertical annular flow. Eccentricity does not affect the burn-out flux until the annular separation is about 20% or less of its concentric value. Bum-out fluxes for great eccentricities are increased about 30%, which is ascribed to poor fluid mixing pressure-drop at the same conditions is reduced. The small effect of moderate eccentricity in downward annular flow of steam-water mixtures was also reported earlier by Stein et al. (Sll) in their study of pressure-drop and critical flow. 

Helical Flow between Concentric Cylinders Consider the helical flow in an annular space created by a constant pressure drop (Pp — P ) and the rotation of the inner cylinder with an angular velocity il(s ). 

Helical Annular Flow Consider the helical annular flow between concentric cylinders with an axial pressure gradient and rotating outer cylinder as shown in the accompanying figure. Specify the equations of continuity and motion (z and 6 components) and show that, if a Newtonian fluid is used, the equations can be solved independently, whereas if tj = t](y), where y is the magnitude of y, the equations are coupled. 

The orifice-type flow measurement has been modified, and new, special-purpose devices have been introduced to meet particular process requirements. One such unique design is the annular orifice used to measure the hot and dirty gases in the steel industry. Here, the process flow passes through an annular opening between the pipe and a disk-shaped, concentrically located plate the pressure difference is detected between the upstream and downstream faces of that disk. (Refer to Table 3.81 for recommendations on selecting the right orifice plate design for various applications.)... 

A solar collector consists of a horizontal copper tube of outer diameter 5 cm enclosed in a concentric thin glass tube of 9 cm diameter. Water is heated as it flows through the tube, and the annular space between the copper and glass lube is filled with air at 1 atm pressure. During a clear day, the temperatures of the tube surface and the glass cover are measured to be bO C and 32°C, respectively. Determine the rale of heat loss from the collector by natural convection per meter length of the tube. Answer 17.4 W... 

The dynamic adsorption capacity of the annular bed was calculated by integrating the concentration vs. time curves up to a point close to the dynamic equilibrium time. Typical results of the dynamic adsorption capacity as a function of the SO2 inlet partial pressure, the feed flow rate and the feed concentration are shown in Figures 3 to 5. The effect of temperature on the dynamic adsorption capacity is shown in Figure 6 where the higher temperature data were taken from reference (5). 

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