Flow Across the Tube Banks

The following equation may be used to predict pressure drop for fluids flowing across banks of tubes  

Equation 8.16 applies only when the shellside Reynolds number (DqG/p) is greater than 300. 

Equation 8.16 is a simplified equation which is based upon equipment with a certain amount of fouling present on the shell side. Consequently, it may predict values of pressure drop higher than actually present for certain applications. A more rigorous method for calculating pressure drop across banks of tubes is presented here. The pressure drop for fluids flowing across the tube banks may be determined by calculating the following components  

0 for inlet nozzle with impingement plate K = 1.25 for outlet nozzle 

Frictional pressure drop for tube bundles may be calculated as below  

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The combustion gases flow across the tube banks in the convection section and the correlations for cross-flow in tube banks can be used to estimate the heat transfer coefficient. The gas side coefficient will be low, and where extended surfaces are used an allowance must be made for the fin efficiency. Procedures are given in the tube vendors literature, and in handbooks, see Section 12.14, and Bergman (1978b). 

Saturated steam at 100 lb/in2 abs is to be used to heat carbon dioxide in a cross-flow heat exchanger consisting of four hundred 1-in-OD brass tubes in a square in-line array. The distance between tube centers is j in, in both the normal- and parallel-flow directions. The carbon dioxide flows across the tube bank, while the steam is condensed on the inside of the tubes. A flow rate of I lb ,/s of CO at 15 lb/in2 abs and 70°F is to be heated to 200°F. Estimate the length of the tubes to accomplish this heating. Assume that the steam-side heat-transfer coefficient is 1000 Btu/h ft2 °F, and neglect the thermal resistance of the tube wall. 

For pressure drop inside tubes, d is 0.046 and F is the fluid-flow path length. Across tubes banks, a is 0.75 and F is the product of the number of tube rows and the number of fluid passes across the tube bank. The physical property term is again tabulated after being normalised so that the lowest value is approximately unity. 

Preheater vibration. Air preheaters or any type of waste-heat recovery device designed for horizontal flow across vertical tubes, may be subject to vibration produced by the velocity of gas across the tube banks. The velocity produces a vortex-shedding wave pattern that could correspond to the natural harmonic frequency of the tube bank. If the natural harmonic frequency is reached, excessive vibration of the tubes will occur. Redesign of the internal baffle system by inserting dummy baffles can stop the vibration. 

A simpler method due to Kem (1950, pp. 147-152) nominally considers only the drop across the tube banks, but actually takes account of the added pressure drop through baffle windows by employing a higher than normal friction factor to evaluate pressure drop across the tube banks. Example 8.8 employs this procedure. According to Taborek (HEDH, 1983, 3.3.2), the Kern predictions usually are high, and therefore considered safe, by a factor as high as 2, except in laminar flow where the results are uncertain. In the case worked out by Ganapathy (1982, pp. 292-302), however, the Bell and Kem results are essentially the same. 

A tube bank uses an in-line arrangement with S = Sp = 1.9 cm and 6.33-mm-diameter tubes. Six rows of tubes are employed with a stack 50 tubes high. The surface temperature of the tubes is constant at 90 C, and atmospheric air at 20°C is forced across them at an inlet velocity of 4.5 m/s before the flow enters the tube bank. Calculate the total heat transfer per unit length for the tube bank. Estimate the pressure drop for this arrangement. 

Select the appropriate heat-transfer coefficient equation. Heat-transfer coefficients for fluids flowing across ideal-tube banks may be calculated using the equation... 

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. 

VISCOUS FLUIDS If mechanical cleaning is not required, higher heat transfer rates may be obtained by placing the viscous fluid on the shell side. Due to the flow pattern across the tube bank, turbulent flow may be maintained on the shell side at mass velocities which would yield laminar flow on the tube side. 

Air cooled heat exchangers have rectangular bundles containing several rows of tubes, horizontally aligned and vertically offset. Air flows vertically upward across the tube bank. The flow can be induced by fans above the bundle or forced by fans below the bundle. The heat transfer is countercurrent, because the hot fluid enters at the top of the bundle and flows downward through successive passes. The cost of an air cooler depends on the length of the tubes and the number of the tube rows. 

In this equation, N is the nnmber of major restrictions in the tube bank (i.e., the nnmber of times the flow reaches its maximnm velocity in flowing throngh the tube bank). In the 30° and 90° arrangements, N is equal to the number of tube rows crossed in the bank for the 45° and 60° layonts, N is one less than the number of rows crossed. The term Ap is the frictional pressure drop across the tube bank. 

The heat-transfer phenomena for forced convection over exterior surfaces are closely related to the nature of the flow. The heat transfer in flow over tube bundles depends largely on the flow pattern and the degree of turbulence, which in turn are functions of the velocity of the fluid and the size and arrangement of the tubes. The equations available for the calculation of heat transfer coefficients in flow over tube banks are based entirely on experimental data because the flow Is too complex to be treated analytically. Experiments have shown that, in flow over staggered tube banks, the transition from laminar to turbulent flow Is more gradual than in flow through a pipe, whereas for in-line tube bundles the transition phenomena resemble those observed in pipe flow. In either case the transition from laminar to turbulent flow begins at a Reynolds number based on the velocity in the minimum flow area of about 100, and the flow becomes fully turbulent at a Reynolds number of about 3,000. The equation below can be used to predict heat transfer for flow across ideal tube banks. 

Air preheaters, or any type of waste-heat recovery devices that are designed for horizontal flow of fuel gas across vertical tubes, are subject to vibration produced by the velocity of the gas across the tube banks. 

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 ... 

Air at 1 atm and 10°C flows across a bank of tubes 15 rows high and 5 rows deep at a velocity of 7 m/s measured at a point in the flow before the air enters the tube bank. The surfaces of the tubes are maintained at 65°C. The diameter of the tubes is 1 in [2.54 cm] they are arranged in an in-line manner so that the spacing in both the normal and parallel directions to the flow is 1.5 in [3.81 cm]. Calculate the total heat transfer per unit length for the tube bank and the exit air temperature. 

Bundles with tubes omitted from baffle windows. 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 percent of the shell diameter should only be used with caution. Maldistribution will normally be minimized if the fluid velocity in the baffle window is equal to or... 

Calcnlate the heat-transfer coefficient and frictional pressure loss for the following case Water at an average temperatnre of 20°C (68°F) is flowing at the rate of 50 kg/s (110 Ib j/s) across a tube bank composed of 274 tnbes, each 25.4 mm (1.00 in.) in diameter and 1 m long in a 30° layout with a 1.25 pitch ratio, as shown in Fignre 6.21. 

FIGURE 6,21 Flow across the 30°, 1.25 pitch ratio tube bank in Example 6.10. 

A tube bank (12 rows high, 6 rows deep) is arranged in a staggered manner (tube centers form an equilateral triangle of 0.045-m sides), and air (1 atm, 20°C) flows across the bank at 10 m/sec approach velocity. Tubes have a diameter of 0.026 m and length of 4 m. Determine the heat transfer rate if the tubes are at 100°C. 

This convective heat transfer coefficient is used with Ai, the area of the surface inside the tubes, to determine the thermal resistance between the cold fluid and the TVS tube walls in Equation (9.10). The heat transfer resistance across the tube is simply a function of the mean cross-sectional area Am across the tube wall, the thickness of the wall 0.05 cm (0.020 in.) and its thermal conductivity k, as shown in Equation (9.10). The convective heat transfer ho of the warmer LAD fluid outside the tube is calculated using the Churchill and Bernstein relation of fluid flow aroimd a bank of tubes from Incropera and DeWitt (1996). 

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