Connect to Part I

3.2.3. Pressure Fluctuation

Shakouchi et al. [11] [15] showed that the wall thinning rate for a single-phase water flow can be expressed by the pressure fluctuation on the pipe wall downstream of the orifice. The pressure fluctuation exerts repeated variable force on the pipe wall, and as a result the pressure fluctuation p’ on the pipe wall, which is one of the major parameters governing the FAC for a single-phase water flow, is also considered to be the governing parameter for the FAC for a two-phase air-water flow.

An example of pressure fluctuation p’ for the two-phase air-water flow with CR = 0.36 and the Std-D_p orifice with D_p = 38.8 mm is shown in Figure 13. The TR value can be approximated using the p’ value and the relation shown in Figure 9. The p’ value for the two-phase air-water flow is larger than that for the single-phase water flow because of the collision of bubbles with each other and with the wall. The maximum p’ value, , for the two-phase air-water flow is attained at the apparent void fraction α of 10% and is about 28% higher than that of the single-phase water flow.

Figure 14 shows the relation between the maximum value  and α. The value of the Std-rev orifice is much smaller than that of the Std orifice. The  value of the Std and Std-D_p orifices increase rapidly with increasing α until α = 2.5%, after which they attain a maximum value.

The relation between  and the pipe diameter D_p downstream of the orifice is shown in Figure 15. The  value is minimum at D_p = 38.8 mm regardless of α, and this minimum is approximately 10%, 9%, and 7% lower than those for α = 2.5, 5.0, and 10.0%, respectively, for the Std orifice. This means that the Std-D_p orifice can decrease the pressure fluctuation or pipe wall thinning caused by FAC downstream of the orifice.

Figure 13. Pressure fluctuation p’ of Std-D_p = 38.8 mm (CR = 0.36, Re = 5 × 10⁴).

Figure 14. Maximum pressure fluctuation p’_max of Std and Std-D_p vs. α (CR = 0.36, Re = 5 × 10⁴).

Figure 15. Maximum pressure fluctuation p’_max of Std and Std-D_p vs. D_p (CR = 0.36, Re = 5 × 10⁴).

4. Conclusions

Some of the authors [11] [15] have already reported that for a single-phase water flow one of the major parameters governing the FAC occurring on the pipe wall downstream of the orifice is pressure fluctuation p’. They have also indicated that the wall thinning rate TR can be estimated using p’, and that increasing p’ results in an increase in TR. This means that if p’ can be decreased, TR will also decrease.

In the present study, the flow-accelerated corrosion (FAC) on a pipe wall downstream of an orifice is examined phenomenologically. In particular, FAC of a two-phase, air-water bubble flow is studied and compared experimentally with that of a single-phase water flow. The main results are presented as follows:

1) For single-phase, water flow:

a) The pressure on the pipe wall downstream of the orifice fluctuates with time. For example, for CR = 0.36 and Re = 5.0× 10⁴, the dominant frequency was measured to be approximately 5 Hz, and the maximum amplitude was observed at y/D = 2.0.

b) Using a smaller pipe diameter downstream of the orifice would decrease p’ while also maintaining the functionality of the orifice. Consequently, pipe wall thinning rate due to FAC can also be decreased while maintaining the functionality of the orifice.

2) For two-phase, air-water bubble flow:

a) As stated above, for a single-phase, water flow TR can be expressed using the p’ on the pipe wall downstream of the orifice. Pressure fluctuation p’ exerts repeated variable force on the pipe wall, it can also be considered as one of the major parameters governing the FAC for a two-phase, air-water flow as for a single-phase, water flow. The pressure fluctuation on the pipe wall downstream of the orifice for a two-phase, air-water bubble flow was clarified, and the estimation of the pipe wall thinning rate TR using p’ was presented as in the case of a single-phase water flow.

b) Using a pipe with a smaller inner diameter downstream of the orifice for a two-phase, air-water bubble flow would decrease pressure fluctuation. Consequently, pipe wall thinning rate due to FAC for a two-phase, air-water bubble flow can be decreased.

Acknowledgements

The authors would like to extend their gratitude to Chubu Electric Power Co., Inc., Japan who has provided a financial support for a part of this research.

Nomenclature

A₀ cross sectional area of orifice

CR area contraction ratio of orifice

C flow rate coefficient

D, d pipe and orifice diameter, respectively

D_p pipe diameter downstream of orifice

k turbulent kinetic energy

p₁ − p₂ pressure loss at orifice

p, p’ mean and fluctuating pressure, respectively

Q volumetric flow rate

Re Reynolds number (=u_mD/ν)

TR wall thinning grate

u_m mean velocity of water flow in a pipe

u_x’, u_y’ turbulence component in x and y direction, respectively

x, y coordinate of radius and longitudinal direction, respectively

α volumetric flow rate ratio of air to mixture flow, apparent void fraction [= Q_a/(Q_a + Q_w)]

ρ density of water

Subscript

a air

w water