Correlations for CHF (Critical Heat Flux) and Allowable Steam Quality

Correlations for CHF (Critical Heat Flux) and Allowable Steam Quality

One may obtain the heat flux given the steam quality, mass flow inside tubes, steam pres- sure, and tube inner diameter or conversely obtain the allowable steam quality given a heat flux. There are several correlations for CHF, and the Kastner correlation [4] is one of them. It gives the allowable quality at any mass flow and heat flux and steam pressure.

For 0.49 < P < 2.94 MPa [5] x c = 25.6(1000q) −0.125 m (−0.33) (1000d i ) −0.07 e 0.1715P (2.22)

For 2.94 < P < 9.8 MPa x c = 46(1000q) −0.125 m (−0.33) (1000d i ) −0.07 e −0.0255P (2.23)

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For 9.8 < P < 19.6 MPa x c = 76.6(1000q) −0.125 m (−0.33) (1000d i ) −0.07 e −0.0795P (2.24)

(Steam pressure P in MPa, d i in m, q in kW/m 2 , m in kg/m 2 s)

Example 2.12

Steam is generated at 50 bara in a boiler using 40 mm tubes. Heat flux is 300 kW/m 2 . Mass velocity of steam water mixture inside tubes is 750 kg/m 2 s. Determine the maxi- mum allowable quality or CR to avoid DNB conditions.

x c = 46(1000q) −0.125 m (−0.33) (1000d i ) −0.07 e −0.0255P

P = 50 bara = 5 MPa, m = 750 kg/m 2 s, d i = .040 m, q = 300 kW/m 2 . x c = 46 × (300,000) −0.125 750 −0.33 40 −0.07 e −0.0255×5 = 0.73 or 73% allowable quality or a CR of

1.37 minimum. CR in practice will be much higher than this, and hence, this heat flux is acceptable.

Macbeth correlation gives the CHF, given the other variables, and takes the following form:

(2.25) where

q c = 0.5025 h fg d i −0.1 (G i ) 0.51 (1 − x)

q c = CHF, kW/m 2 x is the steam quality, fraction d i is the tube ID, m

G i is the mass velocity, kg/m 2 s

Example 2.13

If G = 816.7 kg/m 2 s, x = 0.2, d i = 0.0381 m, and P = 6.9 MPa (h fg = 361.1 kcal/kg), then q c = 0.5025 × 361.1 × (0.0381) (−0.1) × 816.7 0.51 × 0.8 = 6150 kW/m 2

This being a theoretical correlation does not account for tube-side fouling, and the actual value of CHF could be 20%–30% of this.

Groeneveld’s lookup tables are also used to check for CHF. Table 2.5 shows an extract from 1996 tables.

TABLE 2.5

Groeneveld’s Lookup Tables for CHF in kW/m2 for 8 mm Tubes

Pressure, kPa

G, kg/m 2 s

Source: IAEA April 2001 report, Thermo-hydraulic relationships for advanced water cooled reactors, IAEA-TECDOC-1203.

Note: P in kPa, G in kg/m 2 s, CHF in kW/m 2 . Use a correction factor of 0.79 for tube ID > 16 mm. This table is based on a tube ID of 8 mm.

For diameter above 16 mm, use a correction factor of 0.79.

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

Example 2.14

At 50 barg and with 1000 kg/m 2 s mass velocity and 40 mm tube ID and quality = 0.2, the CHF = 4957 × 0.79 = 3916 kW/m 2

Though there are several correlations for CHF, many have been developed in labora- tories under controlled conditions. They may show different CHF values for the same steam parameters and tube geometry. Hence, charts such as Figure 2.15 developed by boiler firms have more practical value as the results are backed by operation of steam generators [6].

40 1.100,000(0.32) 2.150,000(0.47) 3.200,000(0.63) 4.250,000(0.79) Btu/ft 2 h (MW/m 2 )

Pressure, MPa

Qu –20

Steam quality vs. critical heat flux

–30 (a)

The number on each curve indicates heat flux as Btu/ft 1400 2 h of internal Tube surface.

ss velo 600

Quality, % steam by weight

FIGURE 2.15

(a) Allowable steam quality as a function of heat flux Btu/ft 2 h (MW/m 2 ) and steam pressure. (b) Allowable qual- ity for nucleate boiling at 2700 psia. (From Babcock and Wilcox, Steam: Its Generation and Use, 38th edn., B&W, Barlerton, OH, 1992.)

Steam Generator Furnace Design