Flow over banks of tubes

The frictional loss for a fluid flowing parallel to the axes of the tubes may be calculated in the normal manner by considering the hydraulic mean diameter of the system, although this applies strictly to turbulent flow only. 

For flow at right angles to the axes of the tubes, the cross-sectional area is continually changing, and the problem may be treated as one involving a series of sudden enlargements and sudden contractions. Thus the friction loss would be expected to be directly proportional to the number of banks of pipes j in the direction of flow and to the kinetic energy of the fluid. The pressure drop — AP/ may be written as  

---

Heat transfer to the tubes on the furnace walls is predominantly by radiation. In modern designs this radiant section is surmounted by a smaller section in which the combustion gases flow over banks of tubes and transfer heat by convection. Extended surface tubes, with fins or pins, are used in the convection section to improve the heat transfer from the combustion gases. Plain tubes known as shock tubes are used in the bottom rows of the convection section to act as a heat shield from the hot gases in the radiant section. Heat transfer in the shield section will be by both radiation and convection. The tube sizes used will normally be between 75 and 150 mm diameter. The tube size and number of passes used depend on the application and the process-fluid flow rate. Typical tube velocities will be from 1 to 2 m/s for heaters, with lower rates used for reactors. Carbon steel is used for low temperature duties stainless steel and special alloy steels, for elevated temperatures. For high temperatures, a material that resists creep must be used. 

W = lb cooling water/hr flowing over length of tube L = length of each pipe in bank, ft Do = O.D. of pipe, ft... 

Mass-Transfer Coefficient Denoted by kc, kx, Kx, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theory, the surface renewal theory and the penetration theory, all of which pertain to idealized cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flow through banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

Problem. In this example, we consider the flow around a body. Air, at atmospheric pressure, flows at 20 m s 1 across a bank of heat exchanger tubes. A l/10th-scale model is built. At what velocity must air flow over the model bank of tubes to achieve dynamic similarity ... 

Pressure drop for flow of gases over a bank of tubes may be calculated with... 

Horizontal In-Shell Condensers The mean condensing coefficient for the outside of a bank of horizontal tubes is calculated from Eq. (5-93) for a single tube, corrected for the number of tubes in a vertical row. For undisturbed laminar flow over all the tubes, Eq. (5-97) is, for realistic condenser sizes, overly conservative because of rippling, splashing, and turbulent flow (Process Heat Transfer, McGraw-Hill, New York, 1950). Kern proposed an exponent of -Ve on the basis of experience, while Freon-11 data of Short and Brown General Discussion on Heat Transfer, Institute of Mechanical Engineers, London, 1951) indicate independence of the number of tube rows. It seems reasonable to use no correction for inviscid liquids and Kern s correction for viscous condensates. For a cylindrical tube bundle, where N varies, it is customary to take N equal to two-thirds of the maximum or centerline value. 

Heat-transfer coefficient for cross flow over an ideal tube bank Fouling coefficient on outside of tube Heat-transfer coefficient in a plate heat exchanger Shell-side heat-transfer coefficient Heat transfer coefficient to vessel wall or coil Heat transfer factor defined by equation 12.14 Heat-transfer factor defined by equation 12.15 Friction factor... 

The nature of flow around a tube in the first rmv resembles flow over a single tube discussed in Section 7-3, especially when the tubes are not too close to each other. Therefore, each tube in a tube bank that consists of a single transverse row can be treated as a single tube in cross-flow. The nature of flow around a tube in the second and subsequent rows is very different, however, because of wakes formed and the turbulence caused by the tubes upstream. The level of turbulence, and thus (he heat transfer coefficient, increases with row number because of the combined effects of upstream rows. But there is no significant change in turbulence level after the first few rows, and thus the heat transfer coefficient remains constant. 

Shah, A. K. and Webb, D. R., Condensation of Single and Mixed Vapors from a Non-Condensing Gas in Flow Over a Horizontal Tube Bank, The Institution of Chemical Engineers Symposium Series No. 75, Condensers Theory and Practice, 356-371 (1983). 

Many types of commercial heat exchangers are constructed with multiple rows of tubes, where the fluid flows at right angles to the bank of tubes. An example is a gas heater in which a hot fluid inside the tubes heats a gas passing over the outside of the tubes. Another example is a cold liquid stream inside the tubes being heated by a hot fluid on the outside. 

In many process situations, flow is over a bank of tubes rather than a single tube. There are two basic possible configurations (in-line and staggered see Figure 6-4). Geometry is an important consideration in particular, the Sp and S ... 

It is shown in Section 9.9.5 that, with the existence of various bypass and leakage streams in practical heat exchangers, the flow patterns of the shell-side fluid, as shown in Figure 9.79, are complex in the extreme and far removed from the idealised cross-flow situation discussed in Section 9.4.4. One simple way of using the equations for cross-flow presented in Section 9.4.4, however, is to multiply the shell-side coefficient obtained from these equations by the factor 0.6 in order to obtain at least an estimate of the shell-side coefficient in a practical situation. The pioneering work of Kern(28) and DoNOHUE(lll who used correlations based on the total stream flow and empirical methods to allow for the performance of real exchangers compared with that for cross-flow over ideal tube banks, went much further and. 

Using Tinker s approach, BELL(12, i22) has described a semi-analytical method, based on work at the University of Delaware, which allows for the effects of major bypass and leakage streams, and which is suitable for use with calculators. In this procedure, the heat transfer coefficient and the pressure drop are obtained from correlations for flow over ideal tube banks, applying correction factors to allow for the effects of leakage, bypassing and flow... 

Pierson, O.L. Trans. Am. Soc. Mech. Eng. 59 (1937) 563. Experimental investigation of influence of tube arrangement on convection heat transfer and flow resistance in cross flow of gases over tube banks. 

The complex flow pattern on the shell-side, and the great number of variables involved, make it difficult to predict the shell-side coefficient and pressure drop with complete assurance. In methods used for the design of exchangers prior to about 1960 no attempt was made to account for the leakage and bypass streams. Correlations were based on the total stream flow, and empirical methods were used to account for the performance of real exchangers compared with that for cross flow over ideal tube banks. Typical of these bulk-flow methods are those of Kern (1950) and Donohue (1955). Reliable predictions can only be achieved by comprehensive analysis of the contribution to heat transfer and pressure drop made by the individual streams shown in Figure 12.26. Tinker (1951, 1958) published the first detailed stream-analysis method for predicting shell-side heat-transfer coefficients and pressure drop, and the methods subsequently developed... 

In Bell s method the heat-transfer coefficient and pressure drop are estimated from correlations for flow over ideal tube-banks, and the effects of leakage, bypassing and flow in the window zone are allowed for by applying correction factors. 

Cross-flow over tube banks is commonly encountered in practice in heal transfer equipment such as the condensers and evaporators of power plants, refrigerators, and air conditioners. In such equipment, one fluid moves through the tubes while the other moves over the tubes in a perpendicular direction. 

Flow through tlie tubes can be analyzed by considering flow through a single tube, and multiplying the results by the number of tubes. This is not Ihe case for pw over the tubes, however, since the tubes affect the flow pattern and turBuletice level downstream, and thus heat transfer to or from them, as shown in Fig. 7-25. Therefore, when analyzing heat transfer from a tube bank in cross flow, we must consider alj the tubes in the bundle al once. 

Another quantity of interest associated with tube hanks is the pressure drop AP, which is the irreversible pressure loss between the inlet and the exit of the lube bank. It is a measure of the resistance the tubes offer to flow over them, and is expressed as... 

In an industrial facility, air is to be preheated before entering a furnace by geo-u thermal water at 120°C flowing through the tubes of a tube bank located in a S duct. Air enters the duct at 20°C and 1 atm v/ith a mean velocity of 4.5 m/s, H and flows over the tubes in normal direction. The outer diameter of the tubes is 1.5 cm, and the lubes are arranged in-line with longitudinal and transverse pilches of Sr = Sf = 5 cm. There are 6 rows in the flow direction with 10 tubes i in each row, as shown in Fig. 7-28. Determine the rate of heat transfer per unit 3 length of the tubes, and the pressure drop across the tube bank. 

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. 

---