Tube in crossflow

Correlations for forced convection over tubes in crossflow are complicated by the effect of the tube bank arrangement. For the range of Reynolds numbers likely to be encountered in industrial boilers the following equations may be used ... 

Zukauskas, A. A., V. Makarevicius, and A. Schlanciauskas Heat Transfer in Banks of Tubes in Crossflow of Fluid, Mintis, Vilnius, Lithuania, 1968. 

For the CHF condition for two-phase crossflow on the shell side of horizontal tube bundles, few investigations have been conducted. Katto et al. (1987) reported CHF data on a uniformly heated cylinder in a crossflow of saturated liquid over a wide range of vapor-to-liquid density ratios. Recently, Dykas and Jensen (1992) and Leroux and Jensen (1992) obtained the CHF condition on individual tubes in a 5 X 27 bundle with known mass flux and quality. At qualities greater than zero, they found that the CHF data are a complex function of mass flux, local quality, pressure level, and bundle geometry. 

Nfy Number of restrictions in crossflow for window zone, pj Vertical tube pitch. 

Bertram CD, Hoogland MR, Li H, OdeU RA, and Pane AG, Plux enhancement in crossflow microfiltration using a collapsible-tube pulsation generator, J. Membr. Sci. 1993 84 279-292. 

In the following, the heat transfer and pressure drop in a tube bundle in crossflow will be investigated. The individual tubes in the bundle are either in alignment with each other or in a staggered arrangement, according to Fig. 3.25. 

Fig. 3.25 Tube bundle in crossflow, a aligned tube arrangement b staggered tube arrangement with the smallest cross section perpendicular to the initial flow direction c staggered tube arrangement with the smallest cross section in the diagonal...

The flow around and therefore the heat transfer around an individual tube within the bundle is influenced by the detachment of the boundary layer and the vortices from the previous tubes. The heat transfer on a tube in the first row is roughly the same as that on a single cylinder with a fluid in crossflow, provided the transverse pitch between the tubes is not too narrow. Further downstream the heat transfer coefficient increases because the previous tubes act as turbulence generators for those which follow. From the fourth or fifth row onwards the flow pattern hardly changes and the mean heat transfer coefficient of the tubes approach a constant end value. As a result of this the mean heat transfer coefficient over all the tubes reaches for an end value independent of the row number. It is roughly constant from about the tenth row onwards. This is illustrated in Fig. 3.26, in which the ratio F of the mean heat transfer coefficient Oim(zR) up to row zR with the end value am (zR —> oo) = amoo is plotted against the row number zR. 

In crossflow the mass velocity passes through a local maximum each time the fluid passes a row of tubes. For correlating purposes the mass velocity for crossflow is based on the area for transverse flow between the tubes in the row at or closest to the centerline of the exchanger. In a large exchanger Sc can be estimated from the equation... 

COEFFICIENTS FOR CROSSFLOW. In some exchangers such as air heaters the shell is rectangular and the number of tubes in each row is the same. Flow is directly across the tubes, and baffles are not needed. For such crossflow conditions the following equation is recommended ... 

C. M. Chu and J. M. McNaught, Tube Bundle Effects in Crossflow Condensation on Low-Finned Tubes, Proc. 10th Int. Heat Transfer Conf, Brighton, 3, pp. 293-298,1994. 

External Flow (Shell Side). Two-phase flow patterns for flow normal to tube bundles (crossflow), such as on the shell side of a shell-and-tube heat exchanger, are much more complex than those inside a plain circular tube. Consequently, prediction of flow patterns in such situations is very difficult. It is important to note that two-phase shellside flow patterns are substantially less analyzed than those for internal flows. A review of the shellside flow pattern is presented by Jensen [68]. The dominant flow patterns (see Fig. 17.51 [69]) may be assessed... 

FIGURE 10.30 Schematics of the filtration setup with collapsible-tube pulsation generator. (Adapted from J. Membr. Sci., 84, Bertram, C.D., Hoogland, M.R., Li, H., Odell, R.A., and Fane, A.G., Flux enhancement in crossflow microfiltration using a collapsible-tube pulsation generator, 279-292, Copyright 1993, with permission from Elsevier.)... 

Frequently, tubes are omitted from the baffle window areas. For this configuration, maldistribution of the fluid as it flows across the bank of tubes may occur as a result of the momentum of the fluid as it flows through the baffle window. For this reason baffle cuts less than 20% of the shell diameter should be used only with caution. Maldistribution will normally be minimized if the fluid velocity in the baffle window is equal or less than the fluid velocity in crossflow across the bundle. This frequently requires baffle cuts greater than 20% of the shell diameter. For such cases, the number of tube rows in crossflow will be less than that assumed in the methods above consequently a correction is required. In addition, the pressure drop for the first and last baffle sections assumes tubes in the baffle windows the factor 2.66 in Equation 8.19 should be reduced to 2.0 for the case of 20% baffle cuts. 

The height of liquid calculated using the correlations above is only approximate because it ignores any pressure drop effects and the fact that there are generally tubes in the flow erea calculated. However, it can be used to give a reasonable approximation. If the height of condensate calculated is appreciable, then more than one condensate connection may be desired. The flow pattern of the condenser can be changed so that vapor and condensate make only one crossflow path across the tube bundle. Other baffle types may also be used. 

In crossflow gas permeation, we have identified in Figure 7.2.1(c) a tube-side feed crossflow hollow fiber module. Unlike flat membrane systems, the radial cross-sectional area for permeation through the hollow fiber wall (inner radius r, outer radius r2) increases as the radius incretises. Develop the following expression for the molar permeation rate of species i through a hollow fiber of length Az ... 

Another typical flow arrangement in heat exchangers is known as crossflow, where the fluids flow at right angles to one another. Kays and London have determined the effectiveness-NTU relationships for several typical crossflow arrangements. In crossflow, one or both fluids may be unmixed, which means the fluid is forced to flow in a definite channel, such as a tube, or mixed where the fluid is not confined to flow within a definite channel. Figures 5.15-5.18 show the effectiveness-NTU plots for the four common flow arrangements of counterflow, parallel-flow, one-fluid mixed crossflow, and both-fluids-unmixed crossflow. 

The arbor (wicket) heater is a substantially vertical design in which the radiant tubes are inverted Us connecting the inlet and outlet terminal manifolds in parallel. An overhead crossflow convection bank is usually included. This type of design is good for heating large gas flows with low pressure drop. Typical duties are 53 to 106 GJ/h (50 to 100 10 Btu/h). 

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