Annular channels

Parallel-Leaf Cartridge. A parallel-leaf cartridge consists of several flat plates, each having membrane sealed to both sides (Fig. 13). The plates have raised (2—3 mm) rails along the sides in such a way that, when they are stacked, the feed can flow between them. They are clamped between two stainless-steel plates with a central tie rod. Permeate from each leaf drains into an annular channel surrounding the tie rod (33). 

The transport salt is usually eutectic NaCl-KCl but NaCl-CaC12 can also be used. As liquid plutonium metal builds up on the cathode it drips off into an annular channel surrounding the anode cup where it coalesces into a pool of metal and is recovered after the cell is cooled. The entire chemical process is performed in a molten salt bath. 

Figure 2.42 shows boiling curves obtained in an annular channel with length 24 mm and different gap size (Bond numbers). The heat flux q is plotted versus the wall excess temperature AT = 7w — 7s (the natural convection data are not shown). The horizontal arrows indicate the critical heat flux. In these experiments we did not observe any signs of hysteresis. The wall excess temperature was reduced as the Bond number (gap size) decreased. One can see that the bubbles grew in the narrow channel, and the liquid layer between the wall and the base of the bubble was enlarged. It facilitates evaporation and increases latent heat transfer. 

H2. It may be noted that the HI and H2 boundary conditions for the symmetrically heated passages with no sharp corners (e.g., circular, flat, and concentric annular channels) are identical they are simply designated as H. 

Wurtz, J., 1978, An Experimental and Theoretical Investigation of Annular Steam-Water Flow in Tubes and Annular Channels, Riso Natl. Lab., Oslo, Norway. (5)... 

The general expression for the average mass-transfer rate over length L in annular channels is given by Eq. (5a) in Table VII... 

Equation (31) has also been used to correlate results obtained in annular channels with insufficient hydrodynamic entrance length (B2, B3). Some of the data fit Eq. (31) with a slightly smaller coefficient. A similar expression, including terms for the hydrodynamic entrance length, was used by Pickett and Ong (P3a). 

Fig. 2.23 Computational solution to a CVD reactor, stagnation-flow problem. The white arrows illustrate the streamlines, and the color (grayscale) illustrates the temperature field. Flow enters both through a porous showerhead assembly and through an annular channel adjacent to the outer wall. The exhaust exits downward through the annular channel. The process is running at a reduced pressure of 10,000 Pa (approximately one-tenth of atmospheric pressure). The fluid properties are those for air.

Fig. 4.18 Pressure-driven flow in a long annular channel.

Fig. 4.19 Forced flow through an annular channel, with a moving rod in the center.

Assuming a long shaft and negligible end effects at the inlet and outlet regions and negligible circumferential pressure drop, develop a system of equations to describe the flow in the annular channel. 

Fig. 4.23 Flow in the annular channel between a rotating, translating rod in a fixed housing.

Consider the fully developed steady flow of an incompressible fluid through an annular channel, which has an inner radius of r, and an outer radius of r0 (Fig. 4.27). The objective is to derive a general relationship for the friction factor as a function of flow parameters (i.e., Reynolds number) and channel geometry (i.e., hydraulic diameter Dh and the ratio f A friction factor /, which is a nondimensional measure of the wall... 

Beginning with the definition of a hydraulic diameter (Dh = 4Ac/P), show that the hydraulic diameter of the annular channel may be written as... 

A new flame-based process is being considered to oxidize a film on a wafer. As illustrated in Fig. 17.22, a combustible mixture flows downward from a showerhead manifold onto the wafer and the exhaust products are drawn out through an annular channel. A control system is presumed to hold the wafer temperature at a fixed temperature. The objective of the process is to deliver an atomic-oxygen number density of approximately 1015 cm-3 at the wafer surface while the wafer temperature is held at approximately Tw = 320°C. Assume the following nominal process conditions showerhead-to-... 

Fig. E6.6b The synthesis of the free rotating flight pump from building block 2. (a) an annular channel is created between the rotating shaft and hollow cylinder (b) the channel is twisted and extended into a helical spiraling channel (c) the channel is formed by a spiral that rotates between a stationary shaft and stationary barrel, with a feed port and exit port machined into the barrel.

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,... 

However, this design has an inherent disadvantage, namely the annular channel at the cone base is compulsorily narrow. With cone base diameters of Dc 0.5 m, a possible clogging can take place, especially if the nozzle is used for waste water treatment. 

Apparatus construction companies specializing in these reactors have developed a detailed and comprehensive know-how as regards flow control of the heat transfer medium [28, 29], This concerns the uniform supply and removal of the heat transfer medium, which generally takes place vial external annular channels, as well as the flow control within the reactor. Some recent publications illustrate the major differences in the behavior of different tube sections that can arise due to an inadequate design and layout of the heat transfer medium circuit [30-32]. 

It would be necessary to decouple the radio frequency to prevent it interfering with the function of the potentiometric recorder (or signal processing amplifier). The resistance capacity decoupling shown in their circuit appears hardly sufficient to achieve this in a satisfactory manner and consequently, the circuit shown in figure 11 may be only schematic. The column was connected directly to the sensor and the eluent passed through the annular channel between the central electrode and the sensor wall. 

Figure 5 Approximation of a central subchannel in (a) a square array by (b) an annular channel.

In confined space, the heat transfer enhancement is caused by evaporation a thin liquid film in near comer area (see Fig. 12) and dry spot formation on the channel wall. The dry spot formation in this area can explain low dependence of heat transfer coefficient on wall superheat [21]. For this case heat flux in vicinity of liquid-solid-vapor contact line has higher level due to evaporation in ultra thin film area [20]. In that way high level of heat transfer in vicinity of contact line is responsible for the heat transfer enhancement during boiling in mini-channels. The possibility of dry spot formation on the wall for water boiling in narrow annular channel was observed in [35] also. At wall superheat over 4.5 K the drying-out of liquid is responsible for decrease of heat transfer when the size of dry area becomes very large. 

Data have been presented allowing identification of different flow patterns in a narrow annular channel with a gap less than capillary constant. For large superficial velocities the flow with Taylor bubbles and cell flow regime with liquid plugs are typical. 

Kozelupenko, Yu. D., Smirnov, G.F., Koba, A. L., (1985), Heat transfer crisis in subcooled liquid in narrow annular channels at low velocities of motion, Promushlennaya Teploenergetica, 1, 1, pp 30-32. 

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