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

8.05

Q:

How is the convective heat transfer coefficient for air and flue gases determined using Grimson’s correlation?

A:

Grimson’s correlation, which is widely used for estimating hc [1], is

Coefficient B and power N are given in Table 8.5.

Example

150,000 lb=h of flue gases having an analysis (vol%) of CO2 ¼ 12, H2O ¼ 12, N2 ¼ 70, and O2 ¼ 6 flows over a tube bundle having 2 in. OD tubes at 4 in. square pitch. Tubes per row ¼ 18; length ¼ 10 ft. Determine hc if the fluid temperature is 353 F and average gas temperature is 700 F. The Appendix tables give the properties of gases.

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From Table 8.5, for ST =d ¼ SL=d ¼ 2; B ¼ 0:229 and N ¼ 0:632, so

or

hc ¼ 12:8 Btu=ft2 h F

8.06

Q:

Compare in-line versus staggered arrangements of plain tubes from the point of view of heat transfer and pressure drop considerations. In a waste heat boiler 180,000 lb=h of flue gases at 880 F are cooled to 450 F generating steam at 150 psig. The gas analysis is (vol%) CO2 ¼ 7, H2O ¼ 12, N2 ¼ 75, and O2 ¼ 6. Tube OD ¼ 2 in.; tubes=row ¼ 24; length ¼ 7.5 ft. Compare the cases when tubes are arranged in in-line and staggered fashion with transverse pitch ¼ 4 in. and longitudinal spacing varying from 1.5 to 3 in.

A:

Using Grimson’s correlation, the convective heat transfer coefficient hc was computed for the various cases. The nonluminous coefficient was neglected due to the low gas temperature. The surface area and the number of rows deep required were also computed along with gas pressure drop. The results are shown in Table 8.6.

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or

hc ¼ 12:5

Because other resistances are small, U ¼ 0:95hc ¼ 11:87 Btu=ft2 h F. Hence

21 106

A ¼ 237 11:87 ¼ 7465 ¼ 3:14 2 24 7:5 Nd =12

or the number of rows deep Nd ¼ 79.

The friction factor f , using the method discussed in Q7.27, is f ¼ 15;434 0:15ð0:044 þ 0:08 1:5Þ ¼ 0:0386

Average gas density ¼ 0:0347 lb=ft3

Gas pressure drop ¼ 9:3 10 10 60002 79 00::03860347 ¼ 2:95 in:WC The calculations for the other cases are summarized in Table 8.6.

1.The staggered arrangement of bare tubes does not have a significant impact on the heat transfer coefficient when the longitudinal spacing exceeds 2, which is typical in steam generators. Ratios lower than 1.5 are not used, owing to potential fouling concerns or low ligament efficiency.

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2.The gas pressure drop is much higher for the staggered arrangement. Hence, with bare tube boilers the in-line arrangement is preferred. However, with finned tubes, the staggered arrangement is comparable with the in-line and slightly better in a few cases. This is discussed later.

8.07a

Q:

How is the nonluminous radiation heat transfer coefficient evaluated?

A:

In engineering heat transfer equipment such as boilers, fired heaters, and process steam superheaters where gases at high temperatures transfer energy to fluid inside tubes, nonluminous heat transfer plays a significant role. During combustion of fossil fuels such as coal oil, or gas—triatomic gases—for example, water vapor, carbon dioxide, and sulfur dioxide—are formed, which contribute to radiation. The emissivity pattern of these gases has been studied by Hottel, and charts are available to predict gas emissivity if gas temperature, partial pressure of gases, and beam length are known.

Net interchange of radiation between gases and surroundings (e.g., a wall or tube bundle or a cavity) can be written as

ag is calculated similarly at To. Z is the correction factor for the water pressure, and De is the decrease in emissivity due to the presence of water vapor and carbon dioxide.

Although it is desirable to calculate heat flux by (23), it is tedious to estimate ag at temperature To. Considering the fact that To4 will be much smaller

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than Tg4, with a very small loss of accuracy we can use the following simplified equation, which lends itself to further manipulations.

The nonluminous heat transfer coefficient hN can be written as

T4 T4

hN ¼ seg g o ð26Þ

Tg To

To estimate hN , partial pressures of triatomic gases and beam length L are required. L is a characteristic dimension that depends on the shape of the enclosure. For a bundle of tubes interchanging radiation with gases, it can be shown that

L is taken approximately as 3.4–3.6 times the volume of the space divided by the surface area of the heat-receiving surface. For a cavity of dimensions a; b and c,

In the case of fire tube boilers, L ¼ di.

eg can be estimated using Figs. 8.1a–8.1d, which give ec; ew; Z, and De, respectively. For purposes of engineering estimates, radiation effects of SO2 can be taken as similar to those of CO2. Hence, partial pressures of CO2 and SO2 can be added and Fig. 8.1 used to get ec.

Example 1

Determine the beam length L if ST ¼ 5 in., SL ¼ 3.5 in., and d ¼ 2 in.

Solution.

L ¼ 1:08 5 3:5 0:785 4 ¼ 7:8 in: 2

Example 2

In a fired heater firing a waste gas, CO2 in flue gases ¼ 12% and H2O ¼ 16%. The gases flow over a bank of tubes in the convective section where tubes are arranged as in Example 1 (hence L ¼ 7.8). Determine hN if tg ¼ 1650 F and to ¼ 600 F.

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FIGURE 8.1a Emissivity of carbon dioxide. (From Ref 1.)

Solution.

7:8

PcL ¼ 0:12 12 ¼ 0:078 atm ft

7:8

PwL ¼ 0:16 12 ¼ 0:104 atm ft

In Fig. 8.1a at Tg ¼ ð1650 þ 460Þ ¼ 2110 R and PcL ¼ 0:078; ec ¼ 0:065. In Fig. 8.1b, at Tg ¼ 2110 R and PwL ¼ 0:104; ew ¼ 0:05. In Fig. 8.1c, correspond-

ing to ðP þ PwÞ=2 ¼ 1:16=2 ¼ 0:58 and PwL ¼ 0:104; Z ¼ 1:1. In Fig. 8.1d,

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FIGURE 8.1b Emissivity of water vapor. (From Ref 1.)

corresponding to Pw=ðPc þ PwÞ ¼ 0:16=0:28 and ðPc þ PwÞL ¼ 0:182; De ¼ 0:002. Hence,

eg ¼ 0:065 þ ð1:1 0:05Þ 0:002 ¼ 0:118

Using Eq. (26) with the Boltzmann constant s ¼ 0:173 10 8,

hN ¼ 0:173 10 8 0:118 21104 10604 2110 1060

¼ 3:6 Btu=ft2 h F

Thus, hN can be evaluated for gases.

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FIGURE 8.1c,d (c) Correction factor for emissivity of water vapor. (d) Correction term due to presence of water vapor and carbon dioxide. (From Ref 1.)

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8.07b

Q:

Can gas emissivity be estimated using equations?

A:

Gas emissivity can be obtained as follows. hN is given by Eq. (26),

T4 T4

hN ¼ seg g o

Tg To

where

s ¼ Stefan–Boltzmann constant ¼ 0.173 10 8 Tg and To ¼ gas and tube outer wall temperature, R

eg, gas emissivity, is obtained from Hottel’s charts or from the expression

[1]

ð0:8 þ 1:6pwÞ ð1 0:38Tg=1000Þ

K ¼ p ð pc þ pwÞ ð28bÞ

ð pc þ pwÞL

Tg is in K. L is the beam length in meters, and pc and pw are the partial pressures of carbon dioxide and water vapor in atm. L, the beam length, can be estimated for a tube bundle by Eq. (27a),

L ¼ 1:08 ST SL 0:785d2 d

ST and SL are the transverse pitch and longitudinal pitch. Methods of estimating pc and pw are given in Chapter 5.

Example

In a boiler superheater with bare tubes, the average gas temperature is 1600 F and the tube metal temperature is 700 F. Tube size is 2.0 in., and transverse pitch ST ¼ longitudinal pitch SL ¼ 4.0 in. Partial pressures of water vapor and carbon dioxide are pw ¼ 0.12, pc ¼ 0.16. Determine the nonluminous heat transfer coefficient.

From Eq. (27a), the beam length L is calculated.

L ¼ 1:08 4 4 0:785 2 2 2

¼ 6:9 in: ¼ 0:176 m

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Using Eq. (28b) with Tg ¼ (1600 7 32)=1.8 þ 273 ¼ 1114 K, we obtain ð0:8 þ 1:6 0:12Þ ð1 0:38 1:114Þ

K ¼ p 0:28 0:28 0:176

¼ 0:721 From Eq. (28a),

eg ¼ 0:9 ½1 expð 0:721 0:176Þ& ¼ 0:107 Then, from Eq. (26),

hN ¼ 0:173 0:107 10 8 20604 11604 1600 700

¼ 3:33 Btu=ft2 h F

8.08a

Q:

How is heat transfer in a boiler furnace evaluated?

A:

Furnace heat transfer is a complex phenomenon, and a single formula or correlation cannot be prescribed for sizing furnaces of all types. Basically, it is an energy balance between two fluids—gas and a steam–water mixture. Heat transfer in a boiler furnace is predominantly radiation, partly due to the luminous part of the flame and partly due to nonluminous gases. A general approximate expression can be written for furnace absorption using an energy approach:

QF ¼ Apew ef sðTg4 To4Þ

¼ Wf LHV Wghe

Gas temperature (Tg) is defined in many ways; some authors define it as the exit gas temperature itself. Some put it as the mean of the theoretical flame temperature and te. However, plant experience shows that better agreement between measured and calculated values prevails when tg ¼ tc þ 300 to 400 F [1].

b characterizes flame-filling volumes. b ¼ 1.0 for nonluminous flames

¼0.75 for luminous sooty flames of liquid fuels

¼0.65 for luminous and semiluminous flames of solid fuels L ¼ beam length, m

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