Transverse pitch

Two other terms need definition transverse pitch a and longitudinal pitch b. For a drawing of these dimensions see the source article. For our purposes appropriate lengths are shown in Table 3. 

Air is to be heated by passing it over a bank of 3-m-long tubes inside which steam is condensing at 100°C. Air approaches the tube bank in the normal direction at 20 C and I aim with a mean velocity of 5.2 m/s. The outer diameter of the tubes is 1.6 cm, and die lubes are arranged staggered with longitudinal and transverse pitches of = Sj = 4 cm. There are 20 row.s in the flow direction with 10 tubes in each row. Determine (a) the rate of heat transfer, (f ) and pressure drop across the tube bank, and (c) the rate of condensation of steam inside the tubes. 

The heat transfer is greater in a staggered arrangement at the same Reynolds number. However this is paid for with a larger pressure drop. With reference to Fig. 3.25a to c, the separation between the tube centres perpendicular to the flow direction is known as transverse pitch sq, tube separation in the flow direction as... 

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. 

Example 3.11 Atmospheric air (p = 0.1 MPa) is to be heated in a tube bundle heat exchanger from 10 °C to 30 °C. The exchanger consists of 4 neighbouring rows and zr rows of tubes aligned one behind the other. The outer diameter of the tubes is 25 mm, their length 1.5m, the longitudinal pitch is the same as the transverse pitch s /d = sq/d = 2. The wall temperature of the tubes is 80 °C with an initial velocity of the air of 4m/s. Calculate the required number zr of tube rows. 

The ratio of side distance to hole diameter should be not less than half the ratio of transverse pitch to hole diameter (s/dh. 5 Wj/dh). 

The best results were obtained when the transversal pitch was twice the outside diameter and the longitudinal pitch divided by the outside diameter was between 1.1 and 3.0—with this optimal geometry for Re (Reynolds Number) and Sc (Schmidt Number) each between 1 and 1000, with Re based on the external fiber diameter. In another study, Yang [71] used hydrophobic hollow fibers for the removal of oxygen or CO2 from water into nitrogen. The authors obtained the following correlations for closely and loosely packed fibers, respectively ... 

Fig. 5.5. Definition of longitudinal and transverse pitch (a) for tubes in line and (b) for staggered-tube arrangement.

Remarks Re == DmaJfi, where D is the outside diameter of tubes, G ax Mmin with is the minimum open free-flow area between tubes Xj- is the transverse pitch/tube outside diameter N is the total number of tubes in line of flow is the longitudinal pitch/tube outside diameter = 0.43 + (1.13/ ). Fluid properties for all relations are evaluated at the mean film temperature, T = 0.5 (T. + Tf,), where T. is the tube wall temperature and is the bulk temperature of fluid. See Fig. 5.5 for tube arrangement. 

Determine the friction factor and pressure drop for the low-pressure side of a coiled-tube heat exchanger where the fluid flows past 100 tubes in a staggered-tube arrangement. An air flow rate of 0.5 kg/s enters the low-pressure side of the heat exchanger at 0.121 MPa and 183 K. The outside diameter of each tube is 10 mm while the minimum flow area between each tube is 0.0125 m. The transverse pitch is 0.0003 m. 

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