Effect of Outside Fouling Factor

The effect of outside fouling factor is not significant. The decrease in duty is marginal with gas-side fouling (Table E.13).

TABLE E.13

Effect of Gas-Side Fouling

Case 3 Case 4

Gas temp. in, °C

600 Gas out, °C

345 Duty, MM kcal/h (MW)

7.51 (8.73) 7.37 (8.56) Gas pressure drop, mm wc

11 11 12.5 12.5 Steam flow, kg/h

13,500 Fins—n × h × b

95 × 95 Tubes/row

28 28 28 28 Number of rows deep

10 10 6 6 Length, m

0.002 U o , kcal/m 2 h °C

Gas-side fouling, m 2 h °C/kcal

34.39 32.36 22.1 21.23 Ratio A t /A i

109,930 Tube wall temp., °C

Heat flux inside tubes, kcal/m 2 h 73,390

438 Appendix E: Calculations with Finned Tubes

For the evaporator used in the earlier example, the effect of gas-side fouling was studied for two fin geometries, namely, 78 and 216 fins/m. It is seen that the effect is marginal only, about 2%–3% loss in duty. Hence, tube-side fouling is more serious compared to gas-side fouling.

Optimizing Finned Surface Design Example E.8

An evaporator has to be designed for the following parameters. Turbine exhaust gas flow = 100,000 kg/h at 600°C in and 315°C out. Duty = 7.65 MM kcal/h. Steam pressure

is 40 kg/cm 2 g. Tube size 51 × 43 mm and 95 mm square pitch. Steam flow = 14,000 kg/h at 40 kg/cm 2 a, and 120°C feed water. How does one arrive at the optimum design?

Solution

Though this problem is often encountered by the boiler supplier, plant engineers should know that several design options are possible with finned tubes. Here is a way to review options for a finned evaporator bundle (one could extend this concept to superheaters and economizers also). It gives the effect of fin geometry and gas velocity on gas pressure drop for the same duty at one glance. Curves are shown for just two fin geometries, but one can work out for different tube sizes and fin geometries and plot the gas pressure drop on one scale and surface area on the other. Now for a desired gas pressure drop, one can select various tube or fin geometry as described later.

It is seen that as fin density increases, the surface area required for the same duty is more. The gas pressure drop is higher for the smaller fin density for the same duty. One can see that the variation in surface area can be 50% for the same duty and gas pressure drop. Hence, while evaluating bids for HRSGs, one should not get carried away by surface areas but understand why there is so much difference. The smaller fins have a higher U as discussed earlier and hence lesser surface area requirements. However, as more rows are required with smaller fins, the gas pressure drop goes up. The results are shown in Figure E.5 as well as in Table E.14.

Let us, say, limit the gas pressure drop to 30 mm wc. As we move from 30 mm wc on the right-hand scale to the left, the line intersects the pressure drop curve. For the

78 fins/m design, the gas velocity to meet this pressure drop is about 19 m/s, while for the 216 fins/m design, it is about 21.5 m/s. Then go up to intersect the corresponding

Surf. area, m 2 Gas press drop, mm wc

45 216 ﬁns/m 1700

40 78 ﬁns/m 1500

35 78 ﬁns/m 30 216 ﬁns/m 1300

12 17 22 27 Gas velocity, m/s

FIGURE E.5

Chart relates gas velocity, pressure drop, and surface area.

Appendix E: Calculations with Finned Tubes 439

TABLE E.14

Evaporator Design with Different Gas Velocities and Fin Geometry Tubes/row

20 20 20 20 20 20 20 20 Number of

13 15 16 7 8 9 8 14 rows deep

Length 6.22 4.67 3.73 7.71 5.78 4.62 5.5 5.0 m Fins/m

78 Fin height

19 19 19 19 19 19 19 19 mm Fin thick

1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 mm Serration

4 4 4 4 4 4 4 4 mm Surf. area

1,155 m 2 U o

34.3 40.4 45.7 20.9 24.5 27.5 25.1 38.9 kcal/m 2 h °C Gas press. drop

18 35 57 13 26 45 28 28 mm wc Gas velocity

15 20 25 15 20 25 21 19 m/s Weight

lines for surface areas. It is seen that for 78 fins/m design, the surface area is about

1200 m 2 , while for the 216 fins/m design, it is about 1800 m 2 . Table E.14 shows the actual

results from a computer program. The last two columns show the desired design for both the fin geometries.

Developing such charts helps one to understand the effect of fin geometry and also how an optimum design can be arrived at. Based on tubes deep and length and fin geometry, one can estimate the material and labor cost and arrive at an optimum design. Say for 28 mm wc gas pressure and same duty, we have two options; one with 78 fins/m, but it has 14 rows deep, while the 216 fins/m option has 8 rows deep, and though the surface area is more, the labor cost could be less. One can also study the effect of using 38 mm tubes and so on as discussed earlier. Plant engineers need to be aware that a wide difference can exist in tube or fin geometry or surface area for the same performance with finned tube exchangers, and hence, this study explains the reason.

Effect of Outside Fouling Factor