Distribution of Radiation to Tube Banks

Distribution of Radiation to Tube Banks

When boiler screen section or superheater is located at the furnace exit, direct radiation from the furnace is absorbed by these heating surfaces and increases the heat flux inside the tubes and hence the tube wall temperature. This radiation is generally absorbed completely within the first four to five rows of tubes depending on the tube spacing. Figure 2.11 shows the distribution of external radiation to different rows depending on tube spacing. Direct radiation adds to the energy absorbed by the tubes and increases the metal tem- perature and may cause overheating and thermal expansion problems. Hence, one should

be careful while locating superheaters at the furnace exit. When a screen section is used at the furnace exit, the tubes will not be overheated as these tubes operate at slightly above saturation temperature of steam, while a superheater operates at much higher temperature.

The following formula predicts the radiation to the tubes:

 where a = fraction of energy absorbed by row 1. The second row absorbs (1 − a)a, the third

row, [1 − {a + (1 − a)a}a], and so on.

62 Steam Generators and Waste Heat Boilers: For Process and Plant Engineers

Tube diameter is d N

1.2 2 in. on 4 in. centers 1 3 in. on 3.75 in. centers

factor 0.6 ew

Angle from vertical

FIGURE 2.10

(a) View factor estimation. (b) View factors for 2 in OD tube on 4 in and 3 in OD tube on 3.75 in. spacing around tube periphery.

Steam Generator Furnace Design

h = 0.25, 0.5, 1.0 in. 1.0 in.

0.5 in tip—sat temp.)

(F

Heat flux inside tubes 2h

h = Membrane height

(c)

Heat flux

FIGURE 2.10 (Continued)

(c) Relating fin tip temperature to heat flux.

TABLE 2.1

View Factors for Typical Configurations of Membranes

Angle from Horizontal θ

View Factor—Case 1

View Factor—Case 2

Quarter point on fin 0.83 0.57 Midpoint of fin

Note: Case 1:2 in. OD tubes on 4 in. spacing. Case 2:3 in. OD tube on 3.75 in. spacing.

Example 2.5

A superheater with 50 mm OD tubes at 200 mm spacing is exposed to direct furnace radiation. Estimate the energy absorbed by the first four rows. Assume Qr the direct radiation is 1 MW. (The radiation to the superheater may be estimated based on the heat flux and opening area of the exit plane as discussed earlier.)

Solution

d = 50 mm, S T = 200 mm. a = 3.14 × 50/2/200 −50/200[sin −1 (50/200) + {(200/50) 2 − 1} 0.5 − 200/50] = 0.3925 − 0.25(0.2526 + 15 0.5 – 4) = 0.361. Hence, first row absorbs 0.361 MW. (See Figure 2.11, which

gives the total energy absorbed from external radiation for a certain number of rows. For two rows, the total absorbed is 0.6 MW as seen from the figure.)

The second row absorbs (1 − 0.361) × 0.361 = 0.2306 MW (total of two rows absorb nearly 0.6 MW). The third row receives [1 − (0.361 + 0.2306)] × 0.361 = 0.147 MW. The fourth row = [1 − (0.361 + .2306 + 0.147)] × 0.361 = 0.094 MW and so on. Typically, a minimum of four rows will absorb the external radiation completely. If

the tube spacing were smaller, then a large amount of radiation is absorbed within the first few rows resulting in high heat flux to these tubes; hence, it is better to use a wider

64 Steam Generators and Waste Heat Boilers: For Process and Plant Engineers

2 No. of rows de

Distribution of external radiation to tubes.

spacing when the external radiation is large so that the radiation is spread over more rows, and heat flux is not intense in the first two or three rows. Screen tubes in boilers and heaters perform this function. Good boiler designs shield the superheater from fur- nace radiation by using more than six to eight rows of screen tubes. This is discussed in Chapter 3 on steam generators.