Critical Heat Flux q c

Critical Heat Flux q c

With flue gas boilers in general, the heat transfer coefficients as well the heat flux outside the tubes are low, typically less than 30,000 kcal/m 2 h (35 kW/m 2 ), and hence, DNB is not an issue. In the case of reformed gas, the heat transfer coefficient and the heat flux will be much higher, about five to eight times more, and hence, the allowable heat flux has to be checked.

Waste Heat Boilers 243

There are a few widely used correlations for CHF in pool boiling. These are mainly for clean tubes and clean water. In practice, oxides and deposits on tubes will limit the allow- able heat flux to about 15%–20% of that calculated. Many boiler suppliers use their own margins and correction factors for CHF based on experience.

Kutateladze recommends the following correlation for q c :

Zuber’s correlation is also widely used:

(H fg is the latent heat, kcal/kg, q c in kcal/m 2 s, g = 9.81 m/s 2 ,ρ f ,ρ g the density of saturated

water and steam in kg/m 3 ).

Motsinki’s correlation takes the following form:

30937  P s   1 P s q  c = P c    − (4.15)

(here, q c is in kcal/m 2 h).

Example 4.12

Determine the CHF for the boiler discussed in Example 4.7.

Solution

Using Zuber’s correlation, at 10.5 kg/cm 2 g, σ = 0.04077 N/m, ρ f = 881.8 kg/m 3 ,

ρ g = 5.78 kg/m 3 ,H fg = 476.6 kcal/kg for steam from Appendix F.

Then, q c = 0.13 × 5.78 × 476.6 × 3600[.0477 × 9.81 × (881.8 − 5.78)/5.78 2 ] 0.25 × (881.8/887.6) 0.5 = 2,405,000 kcal/m 2 h = 893,600 Btu/ft 2 h (the 3600 factor converts the kcal/m 2 s to kcal/ m 2 h). Using Motsinki’s correlation, q c = 30,836 × 226(11.5/226) 0.35 × (1 − 11.5/226) 0.9 = 2,344,560 kcal/m 2 h = 871,000 Btu/ft 2 h. As mentioned earlier, these values are based on research

and laboratory tests. In actual practice, a value of about 15%–20% of this is used based on field experience.

A correction factor is applied to CHF in pool boiling as discussed later in case of tube bundles.

Example 4.13

A fire tube boiler operates at 10.5 kg/cm 2 g with the following data. Tube OD = 50.8 mm, 600 number, 6.1 m long. Shell inner diameter = 2133 mm. Surface area of tubes based on tube OD = 583 m 2 . Compute a factor ψ = DbL/A (Db = bundle diameter, m; L = length, m; A = surface area on OD basis, m 2 ) = 2.133 × 6.1/583 = 0.022. (ψ corrects for bundle effect.)

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

Correction factor F is obtained from the following equation: = log F . 0 8452 0 994 + . log y = . 0 8452 0 994 1 6575 − . × . =− . 0 802 or F = 01 . 557

Hence, the corrected heat flux = 0.157 × 2,405,000 = 377,585 kcal/m 2 h (138,800 Btu/ft 2 h) (439 kW/m 2 ). It may be noted that the actual heat flux was lower than 20,000 kcal/m 2 h,

significantly lower than the allowable limit. In case of reformed gas boilers, however,

the actual heat flux may be in the range of 200,000–300,000 kcal/m 2 h, and one may

check the actual and allowable heat fluxes more carefully and ensure that the actual heat flux is much lower than the allowable CHF by a reasonable margin, say, 20%. One can lower the actual heat flux by using a lower gas velocity, which reduces U o and hence q o . One may also use a larger-diameter tube that lowers U o and hence the heat flux. However, this may add to the boiler weight and length as shown.