01 POWER ISLAND / 01 CCPP / V. Ganapathy-Industrial Boilers and HRSG-Design (2003)

Calculations based on 2.0 0.105 tubes, 29 tubes=row, 6 ft long, 0.05 in. thick serrated fins; tubes on 4.0 in. square pitch; fin height ¼ 0.75 in.; gas flow ¼ 150,000 pph; gas inlet temp ¼ 1000 F.

a Surface area At of 2 fins=in. tube ¼ 2.59 ft2=ft, and for 5 fins=in., At ¼ 6.02 ft2=ft.

2.A simple estimation of tube wall temperature can tell us that the higher

the fin density, the higher the tube wall temperature will be. For the

case of hi ¼ 100, with n ¼ 2, Ui ¼ 39.28, gas temperature ¼ 900 F, and fluid temperature of 600 F,

Heat flux qi ¼ ð900 600Þ 39:28

are comparing for the same height. The increase in wall temperature is 43 F.

3.The ratio of the gas pressure drop between the 5 and 2 fins=in. designs

(after adjusting for the effect of Ui values and differences in surface area for the same energy transfer) increases as the tube-side coefficient

reduces. It is 1.6 for hi ¼ 20 and 1.02 for hi ¼ 2000. That is, when hi is smaller, it is prudent to use a smaller fin surface.

Effect of Fouling Factors

The effects of inside and outside fouling factors ff i and ffo are shown in Tables 8.16 and 8.17. The following observations can be made.

1. With a smaller fin density, the effect of ff i is less. With 0.01 fouling and 2 fins=in., Uo ¼ 6.89 compared with 10.54 with 0.001 fouling. The ratio is 0.65. With 5 fins=in., the corresponding values are 4.01 and

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TABLE 8.16 Effect of ffi , Tube-Side Fouling Factora

a Tube-side coefficient ¼ 2000.

7.46, the ratio being 0.53. That means that with increased tube-side fouling it makes sense to use a lower fin density or smaller ratio of external to internal surface area. The same conclusion was reached with a smaller tube-side coefficient.

2. The effect of ff o is less significant, because it is not enhanced by the ratio of external to internal surface area. A review of Eq. (1) tells us that the tube-side heat transfer coefficient or fouling factor is increased by the ratio of the external to internal surface area, and hence its effect is easily magnified.

8.24

Q:

Compare the effect of tube-side fouling on bare, low, and high finned tubes.

A:

Three boiler evaporators were designed using bare tubes, 2 fins=in. and 5 fins=in., to cool 150,000 lb=h of clean flue gases from 1000 F to 520 F. The effect of fouling factors of 0.001 and 0.01 on duty, tube wall temperatures, and steam production are shown in Table 8.18. The following points may be observed [11].

1.With bare tubes, the higher tube-side fouling results in the lowest reduction in duty, from 19.65 to 18.65 MM Btu=h, with the exit gas

TABLE 8.17 Effect of ffo, Outside Fouling Factora

a Tube-side coefficient ¼ 2000.

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TABLE 8.18 Effect of Fouling Factors

temperature going up to 545 F from 520 F—see columns 1 and 2. With 2 fins=in., the exit gas temperature increases from 520 F to 604 F, with the duty reducing to 16.3 from 19.65 MM Btu=h. The steam generation is about 3200 lb=h lower. With 5 fins=in., the reduction in duty and steam generation are the greatest.

2.The heat flux increases with fin density. Therefore, with high temperature units one has to be concerned with DNB conditions; however, heat flux decreases because of fouling.

3.The tube wall temperature increases significantly with fin density. The same fouling factor results in a much higher tube wall temperature for

finned tubes than for bare tubes. The tube wall temperature increases from 530 F to 760 F with 5 fins=in., and from 437 F to 516 F for bare tubes. The effect of fouling is more pronounced in tubes of high fin density, which means that high fin density tubes have to be kept cleaner than bare tubes. Demineralized water and good water treatment are recommended in such situations.

8.25

Q:

How is the weight of solid and serrated fins determined?

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A:The weight of fins is given by the formulas

b ¼ fin thickness, in. n ¼ fin density, fins=in. h ¼ fin height, in.

do ¼ tube outer diameter, in.

Factor F corrects for material of fins and is given in Table 8.19 [9].

The weight of the tubes has to be added to the fin weight to give the total

where

dm ¼ mean diameter of tube, in. tm ¼ average wall thickness, in.

Example

Determine the weight of solid carbon steel fins on a 2 in. OD tube if the fin density is 5 fins=in., height ¼ 0.75 in., and thickness ¼ 0.05 in. Average tube wall thickness is 0.120 in.

TABLE 8.19 Table of F Factors

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Solution. F from Table 8.19 ¼ 1. Using Eq. (67a), we have

Wf ¼ 10:68 1 0:05 5 ð2 þ 0:75Þ

ð0:75 þ 0:03Þ ¼ 5:725 lb=ft

The tube weight has to be added to this. The tube weight is given by

Wt ¼ 10:68 1:94 0:12 ¼ 2:49 lb=ft

Hence the total weight of the finned tube ¼ 2.49 þ 5.725 ¼ 8.215 lb=ft.

8.26

Q:

What is the effect of fin thickness and conductivity on boiler performance and tube and fin tip temperatures?

A:

Table 8.20 gives the performance of a boiler evaporator using different fins.

In-line arrangement, 4 in. square pitch.

It can be seen that

1.Due to the slightly larger surface area and higher heat transfer coefficient, more duty is transferred with higher fin thickness.

TABLE 8.20 Fin Configuration and Performance

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2.The overall heat transfer coefficient is increased owing to higher fin effectiveness for the same fin conductivity and greater fin thickness.

3.Lower fin conductivity reduces the fin effectiveness and the overall heat transfer coefficient U, and hence less duty is transferred.

4.Though fin tip temperature is reduced with greater fin thickness, owing to improved effectiveness the tube wall temperature increases. This is due to the additional resistance imposed by the larger surface area.

8.27a

Q:

Is surface area an important criterion for evaluating different boiler designs?

A:

The answer is yes if the person evaluating the designs is knowledgeable in heat transfer–related aspects and no if the person simply compares different designs looking only for surface area information. We have seen this in the case of fire tube boilers (Q8.11), where, due to variations in tube size and gas velocity, different designs with over 40–50% difference in surface areas were obtained for the same duty. In the case of water tube boilers also, due to variations in tube size, pitch, and gas velocity, one can have different surface areas for the same duty; hence one has to be careful in evaluating boilers based only on surface areas.

In the case of finned tube boilers, in addition to tube size, pitch, and arrangement (staggered or in-line), one has to review the fin configuration—the height, thickness, and fin density. The higher the fin density or ratio of external to internal surface area, the lower the overall heat transfer coefficient will be even though the surface area can be 100–200% greater. It is also possible to transfer more duty with less surface area by proper selection of fin geometry.

Example

A superheater is to be designed for the conditions shown in Table 8.21. Study the different designs possible with varying fin configurations.

Solution. Using the methods discussed above, various designs were arrived at, with the results shown in Table 8.22 [10]. Several interesting observations can be made. In cases 1 and 2, the same energy of 19.8 MM Btu=h is transferred; however, the surface area of case 2 is much higher because of the high fin density, which decreases U, the overall heat transfer coefficient. Also, the tube wall and fin tip temperatures are higher because of the large ratio of external to internal surface area.

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TABLE 8.21 Data for HRSG Superheater

Gas flow ¼ 240,000 lb=h

Gas inlet temperature ¼ 1300 F

Gas analysis (vol%)

CO2 ¼ 7

H2O ¼ 12

N2 ¼ 75

O2 ¼ 6

Comparing cases 3 and 4, we see that case 3 transfers more energy with less surface area because of better fin selection. Thus it is not a good idea to select or evaluate designs based on surface area alone, because this can be misleading. In addition, excessive fin surface can lead to higher tube wall and fin tip temperatures, forcing one to use better materials and increasing the cost. Some purchasing managers believe incorrectly that if they can get more surface area for the same price, they are getting a good deal. Nothing could be further from the truth.

8.27b

Q:

When extended surfaces are used, the choice of fin density is generally arrived at based on optimization studies as illustrated below. Varying the fin density affects

TABLE 8.22 Effect of Fin Geometry on Superheater Performance

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the gas pressure drop, surface area, and weight of the boiler, not to mention the tube wall and fin tip temperatures. An incineration plant evaporator is to be designed to cool 550,000 lb=h of clean flues gases from 1000 F to about 460 F. Steam pressure is 250 psig sat. Feedwater enters the evaporator at 230 F. Flue gas analysis (vol%) is CO2 ¼ 7, H2O ¼ 12, N2 ¼ 75 O2 ¼ 6. Fouling factors are 0.001 ft2 h F=Btu on both the gas and steam sides. Study the effect of fin configuration on the design.

A:

The calculation procedure for finned tubes is detailed in Q8.19a–Q8.19c. Only the results from using a computer program will be discussed here. Using serrated fins of density 2, 4, and 6 fins=in., 0.75 in. high, 0.05 in. thick with 30 tubes=row, 4 in. square pitch configuration, the lengths were varied to obtain different gas mass velocities. The number of rows deep was adjusted to obtain an exit gas temperature of about 460 F or a duty of about 82 MM Btu=h. Figure 8.8 shows the results from the study.

As the gas mass velocity increases we see that the gas pressure drop increases, whereas the surface area decreases for both 2 and 6 fins=in. designs, which should be obvious. The surface area required for the 6 fins=in. design is much larger than with 2 fins=in. As discussed in Q8.27a, the heat transfer coefficient with higher fin density or large external fin surface area is lower. The weight of the tube bundle is also higher with higher fin density.

FIGURE 8.8 Effect of fin geometry on HRSG surface area and gas pressure drop.

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Table 8.23 summarizes the designs for the 2 and 6 fins=in. cases for the same duty and gas pressure drop of 4 in.WC. It is seen that the surface area is much larger with the 6 fins=in. design. The tube wall temperature is also higher due to the higher heat flux, and the weight is slightly more. However, the fabrication cost may be less due to the smaller number of rows deep. Depending on the design, the drum length could also be smaller due to this. One may evaluate these factors and select the optimum design.

Note on Surface Areas

As discussed earlier, surface areas from different designs should be interpreted carefully. One should not select a design based on surface area considerations. With higher fin density, the heat transfer coefficient will be lower and vice versa. Simply looking at a spreadsheet that shows surface areas of tubes of different suppliers and deciding that the design with more surface area is better is technically incorrect. As can be seen below, the higher surface area option has higher tube wall temperature and heat flux inside the tubes. If one wants to compare alternative designs, one should look at UA, the product of overall heat transfer coefficient U and surface area A and not the surface area alone. The equation for energy transfer is Q ¼ UADT: Q and DT being the same, UA should be constant for the various options. Unless one knows how to calculate the heat transfer coefficients, comparison of surface areas alone should not be attempted, because it can be misleading. Factors such as tube size, spacing, geometry, and fin configuration affect U. The discussion also applies to fire tube boilers, where tube sizes and gas velocities can impact surface areas.

TABLE 8.23 Design of a Boiler with 2 and 6 Fins=in.

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8.28

Q:

How are tubular air heaters designed?

A:

Let Wg, and Wa be the gas and air quantities. Normally, flue gas flows inside the tubes while air flows across the tubes in crossflow fashion, as shown in Fig. 8.9. Carbon steel tubes of 112 –3.0 in. OD are generally used. Thickness ranges from 0.06 to 0.09 in. because high pressures are not involved. The tubes are arranged in in-line fashion and are connected to the tube sheets at the ends. More than one block may be used in series; in this case, air flows across the tube bundles with a few turns. Hence, while calculating log-mean temperature difference, we must consider correction factors FT .

Flue gas velocity is in the range of 40–70 fps, and air-side mass velocities range from 4000 to 8000 lb=ft2 h. Nw and Nd, the numbers of tubes wide and deep, can be decided on the basis of duct dimensions leading to the air heater. In the case of a separate heater, we have the choice of Nw or Nd. In a boiler, for example, duct dimensions at the economizer section fix dimensions of the air heater also, because the air heater is located below the economizer.

To size the air heater, first determine the total number of tubes Nt [1]:

ST =d and SL=d range from 1.25 to 2.0. For the gas-side heat transfer coefficient hi, Eq. (12) is used:

Values of C are evaluated at average flue gas temperature.

The air-side heat transfer coefficient ho is given by Eq. (19) (variation in ho between staggered and in-line arrangements is small in the range of Reynolds number and pitches one comes across),

The value ho is calculated at air film temperature.

Because the temperature drops across the gas and air films are nearly the same, unlike in an evaporator or superheater, film temperature is approximated as

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