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Attenuation of wall-thinning rate in deep erosion by liquid droplet impingement
Annals of Nuclear Energy 88 (2016) 151–157
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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Attenuation of wall-thinning rate in deep erosion by liquid droplet impingement Nobuyuki Fujisawa a,⇑, Takayuki Yamagata a,⇑, Keitaro Wada b a b
Visualization Research Center, Niigata University, 8050, Ikarashi 2-Nocho, Nishi-ku, Niigata 950-2181, Japan Graduate School of Science and Technology, Niigata University, 8050, Ikarashi 2-Nocho, Nishi-ku, Niigata 950-2181, Japan
a r t i c l e
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Article history: Received 16 January 2015 Received in revised form 7 September 2015 Accepted 21 October 2015 Available online 14 November 2015 Keywords: Wall thinning Liquid droplet impingement Erosion Erosion model Power plant Pipeline
a b s t r a c t This paper describes an experimental study on the wall-thinning rate in deep erosion by liquid droplet impingement (LDI) in a pipeline for application to nuclear/fossil power plant. The experiment is carried out in a spray jet apparatus, which allows the evaluation of local wall-thinning rate by the LDI erosion. The surface contour of erosion and the wall-thinning rate are measured and the observation by scanning electron microscope (SEM) is carried out in this experiment. The experimental result indicates that the wall-thinning rate is highly attenuated and the macro structure on the erosion surface grows with an increase in the erosion depth, which is due to the influence of the liquid film over the erosion surface. The erosion model for predicting the wall-thinning rate in deep erosion is proposed by introducing the attenuation factor with a function of erosion depth. The introduction of attenuation factor with liquidfilm effect shows a better correlation with the experimental data, and the accuracy of correlation is improved by a factor of 2. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Liquid droplet impingement (LDI) erosion is one of the causes of pipeline damage in nuclear/fossil power plants. The mechanism of the LDI erosion has been investigated experimentally and numerically both from the points of plant engineering and flow physics in literature. The fundamental of the LDI erosion is a single droplet impact on solid surface and the physics of the droplet impact has been studied by Field et al. (1985) using the high-speed observation of gelatin impact. The result indicates that the shock wave is generated at the instant of droplet impact on the solid wall, which propagates through the liquid medium and reflects at the free surface of the droplet and the reflected pressure wave focuses near the wall material leading to the occurrence of cavitation, while the droplet impact produces a side jet along the wall in radial direction. The side jet produces a thin film of liquid flowing over the wall with much faster velocity than that of the impact velocity of the liquid droplet. In spite of such a complex phenomenon of liquid droplet impingement on a wall, the impact pressure of the droplet roughly approximated by the impact formula, which indicates that the impact pressure is proportional to the products of the droplet density, acoustic velocity and droplet velocity (Heymann, 1969; ⇑ Corresponding authors. E-mail addresses: [email protected] (N. Fujisawa), yamagata@eng. niigata-u.ac.jp (T. Yamagata). http://dx.doi.org/10.1016/j.anucene.2015.10.024 0306-4549/Ó 2015 Elsevier Ltd. All rights reserved.
Rochester and Brunton, 1974). The result implies that the impact pressure is independent of the droplet diameter and becomes larger than the yield stress of the carbon steel, when the droplet velocity is above 100 m/s. This condition applies to the flow through the pipeline of nuclear/fossil power plant. Therefore, the main cause of LDI erosion in the power-plant pipeline is considered to be due to the high impact pressure of the liquid droplet in the high-speed steam flow. In order to estimate the lifetime of the pipeline in the power plant, the prediction of the wall-thinning rate due to the LDI erosion is becoming an important topic of interests in recent years (Ferng, 2008; Li et al., 2011; Morita and Uchiyama, 2011). For this to be done, experimental erosion models are fundamental and they are summarized in Table 1, which includes Heymann (1979), Sanchez-Caldera (1984), Itoh and Okabe (1993), Oka et al. (2007), Miyata and Isomoto (2008), Isomoto and Miyata (2008), Hattori and Takinami (2010), Ishimoto et al. (2011) and Fujisawa et al. (2012a, 2013, 2015). Using these erosion models, the wallthinning rate is evaluated from the droplet parameters, such as the droplet velocity, droplet diameter, number of droplets, and the material hardness, while the influence of the liquid-film thickness on the wall-thinning rate is found to be another important factor by the recent numerical studies of Ikohagi (2011) and Xiong et al. (2011). Later, the influence of liquid film on the wallthinning rate is experimentally studied by Fujisawa et al. (2013),
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Nomenclature c1, c2, c3 d Ed f Hr n P t Qo
constants, Eq. (1) droplet diameter maximum erosion depth attenuation factor, Eqs. (3) and (4) relative Vickers hardness with respect to aluminum power index for droplet velocity dependency pump pressure time bulk flow rate
pure
q V Vo Vd Vde Vdp Vdu x
q m
local volume flux droplet velocity velocity at nozzle exit non-dimensional erosion rate experimental erosion rate predicted erosion rate uniform erosion rate, Eq. (1) coordinate along spray centerline density of liquid kinematic viscosity of air
Table 1 Summary of previous experiments on LDI.
Heymann (1979) Itoh and Okabe (1993) Isomoto and Miyata (2008), Miyata and Isomoto (2008) Hattori and Takinami (2010) Fujisawa et al. (2012a) Fujisawa et al. (2013) Fujisawa et al. (2015)
Power index n
Test method
Droplet velocity V (m/s)
Droplet diameter (lm)
Test material
5.8 (maximum rate point) 6–8 (terminal stage)
Rotating disk Rotating disk Spray
810–2000 195–269 immersion drop sampling method 20–200 immersion drop sampling method 60–120
A1100-0, A6061-T6, Ni270, SUS316 12 Cr steel, cobalt base alloy, titanium alloy A5083, SS400, SUS410 J1, SUS304 SK3 S15C, STPA24, SUS304
Spray
93–400 (rotating speed) 400,480 (rotating speed) 40,300 (impact force) 80–184 (nozzle pressure) 130–160 (PIV)
60–120 shadowgraph
A1050
Spray Spray
140–175 (PIV) 140–180 (PIV)
30 shadowgraph 30 shadowgraph
A1070 A1070, A5056, C3604, SS400, S20C, SUS304
6 (<100 m/s) 2 (>150 m/s) 6.0–7.4 (maximum rate stage) 7 (maximum rate point) 6.6 (terminal stage) 7 (terminal stage)
Water jet
leads to a leak of the steam flow to the outside, as was the case of Onagawa power plant in 2007. In the case of deep erosion, the wall-thinning rate may be influenced by the erosion depth, while the details of such a deep erosion have not been studied in literature. In the present study, the deep LDI erosion is experimentally studied using a high-speed spray jet for characterizing the influence of erosion depth on the wall-thinning rate. An attention is placed on the deep LDI erosion model including the influence of erosion depth.
Fig. 1. LDI erosion in bent pipe downstream of orifice.
who carried out an experiment using the spray jet. They found that the wall-thinning rate is strongly attenuated by increasing the liquid-film thickness over the specimen surface. On the other hand, the wall-thinning rate has been formulated by a power law of droplet velocity with a constant power index n = 7, while it is scattering in a range from 3 to 8, as seen in Table 1. It should be mentioned that the power index n = 5 is derived from the dimensional analysis by Sanchez-Caldera (1984). Such large scattering of the power index can be explained by the influence of experimental conditions, erosion stage, material hardness, droplet diameter, liquid-film thickness and so on, while the reason of the scattering is still not clear due to the limitation of experimental study in literature (Fujisawa et al., 2012b). The LDI erosion often occurs in a steam pipeline of the nuclear/ fossil power plant, where the steam flow is highly accelerated downstream of the orifice and it impinges on the bent pipe downstream, as illustrated in Fig. 1. Once the erosion on the pipe wall is highly accelerated, the LDI erosion may cause deep erosion. This
2. Experiment Fig. 2 shows a schematic illustration of the experimental apparatus, which consists of a straight nozzle and a pure aluminum test specimen (Al070), which is a circular plate of 40 mm in diameter with a thickness of 8 mm. The nozzle exit diameter is 0.8 mm and it generates a straight liquid column at the nozzle exit (MCP08, Ikeuchi Co.), while the liquid column changes to a spray jet immediate downstream due to the instability of the liquid-air interface associated with the entrainment of the surrounding air. The erosion experiment was carried out by impinging the jet on the test specimen from the top in the present study. Note that the erosion rate in vertical impingement agrees with that in horizontal impingement, which suggests negligibly small influence of the gravity on the erosion rate. The spray image taken by a digital camera with strobe-flush is shown in Fig. 3, which is an instantaneous spray image covering the spray jet of a distance 500 mm downstream of the nozzle exit. It is seen that the flow of liquid column is limited near the nozzle and the flow spreads almost linearly from the nozzle downstream. The detail observation of the spray jet indicates that the transition of the liquid column to the spray
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cross-correlation algorithm combined with the sub-pixel analysis (Kiuchi et al., 2005). The interrogation window size was set to 31 31 pixels and was set to satisfy 50% overlap condition. The measurement of droplet diameter was made by the shadowgraph technique combined with the image processing (Fujisawa et al., 2012a). The shadowgraph is an inline imaging technique illuminated by the Nd:Yag pulse laser with an optics for laser and the images are captured by a CCD camera with a spatial resolution of 1008 1018 pixels. The target area of measurement is set to 10 mm 10 mm. Then, the droplet diameter was found to be 25 ± 5 lm in the volume average diameter at x = 270 mm and 480 mm downstream of the nozzle, which is a slightly smaller diameter in comparison with the former spray nozzle used in the uniform erosion (Fujisawa et al., 2013). The details of the measurement technique for the droplet diameter have been described by Fujisawa et al. (2012a).
Fig. 2. Experimental apparatus for LDI erosion.
jet is completed within a distance of 200 mm from the nozzle and the flow is considered as spray jet further downstream. Therefore, the LDI experiments have been carried out in the standoff distances x = 270 mm and 480 mm from the nozzle, where the fully developed spray structure is observed. This condition can be applied to the real pipeline, such as the Onagawa power plant (NUCIA, 2007). The LDI experiments on the test specimen were carried out by changing the nozzle pressure from 16 to 28 MPa. The wall-thinning rate of the test specimen was evaluated by measuring the maximum erosion depth Ed, which is measured near the center of the specimen by using the scanning optical microscope with an accuracy of 0.01 mm. Note that the scanning optical microscope allows the measurement of the maximum erosion depth as well as the whole contour of erosion surface in the area of observation. It should be mentioned that the maximum erosion depth is the major concern, so that the local depth on the groove slope is not studied here. The non-dimensional erosion rates Vd (=DEd/qDt) were evaluated from the present measurement, where DEd is the variation of maximum erosion depth, q is the local volume flux and t is an elapsed time. The local volume flux q was measured by a sampling probe with an inner diameter of 1.18 mm (Fujisawa et al., 2012a). The droplet velocity was measured by the particle image velocimetry (PIV) without adding any tracer particles (Fujisawa et al., 2012a). Note that the pattern of droplet images are considered as the tracers in the measurement. The standard PIV system is used for the measurement. It consists of a CCD camera (spatial resolution of 1008 1018 with 8 bits), the Nd:Yag double pulse laser of 50 mJ and the pulse controller. The target area of measurement is 10 mm 10 mm. The droplet velocity was obtained by time-averaging 1000 instantaneous velocity fields measured from the PIV images taken in every 1/5 s time interval. It should be mentioned that the PIV analysis was carried out using the
3. Results and discussions 3.1. Droplet velocity and local volume flux The experiments on LDI erosion are carried out for various nozzle pressures P = 16–28 MPa to evaluate the wall-thinning rate in the deep LDI erosion. The experimental conditions of total flow rate Q0 and nozzle exit velocity V0 for various nozzle pressures P are shown in Table 2. Note that the total flow rate Q0 was evaluated from the bulk volume measurement of water in a storage tank in a unit time, while the nozzle exit velocity V0 was evaluated from Q0 using the continuity equation, which agrees closely with that from the nozzle pressure measurement by the Bernoulli equation. The local droplet velocity V/V0 and local volume flux q/Q0 in the spray centerline are measured by particle image velocimetry (PIV) and sampling probe, respectively, and they are summarized in Table 2 for both standoff distances of x = 270 mm and 480 mm. Generally speaking, the droplet velocity V/V0 and the local volume flux q/Q0 decrease downstream in a fixed nozzle pressure, though they increase with increasing the nozzle pressure. Note that the droplet velocity in this experiment agrees with those of the prototype power plant. 3.2. Depth distribution on erosion surface Fig. 4 shows an example of the cross-sectional surface contour of LDI erosion at x = 270 mm, which is measured by a scanning optical microscope. The measurement is done in the nozzle pressure 16 MPa. The observation of erosion surface in the initial stage is featured by the smaller erosion depth than the spray size, which is the condition of the previous studies summarized in Table 1. With the progress of erosion, the depth of erosion increases and the maximum erosion depth becomes comparable to the spray size. This is the case of the deep erosion and is the case of this
Fig. 3. Spray image.
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Table 2 Summary of experimental conditions. Nozzle pressure P (MPa)
Bulk flow rate Q0 (mm3/s)
Nozzle exit velocity V0 (m/s)
16 20 24 28
1.03 105 1.10 105 1.22 105 1.29 105
179 200 219 237
Local volume flux q and velocity V at x = 270 mm
Local volume flux q and velocity V at x = 480 mm
q (mm/s)
V (m/s)
q (mm/s)
V (m/s)
3.50 103 3.78 103 4.08 103 4.38 103
159 174 189 207
2.10 103 2.14 103 2.27 103 2.36 103
146 158 170 178
Fig. 4. Cross-sectional contours of LDI erosion (P = 16 MPa, x = 270 mm).
study. The time variation of the erosion distribution indicates that the growth rate of erosion is larger in the groove center than in the surrounding, so that the erosion distribution becomes sharper near the groove center with increasing the elapsed time. Therefore, the growth of the groove may lead to a pin-hole type erosion with an increase in the elapsed time, which results in the leak of steam flow in the pipeline as observed in Onagawa power plant (NUCIA, 2007). It should be mentioned that the erosion surface distribution is fluctuating with time due to the randomness of the erosion damage by LDI. Fig. 5 shows the angle of erosion groove h plotted against the depth of maximum erosion Ed near the center of the groove. It should be mentioned that all the experimental results of nozzle pressures P = 16–28 MPa and standoff distances (x = 270 mm, 480 mm) are plotted in this figure. Note that the groove angle is obtained from the volume loss of the material and the maximum erosion depth assuming the cone-shape erosion contour. The groove angle corresponds to the average gradient of the grove surface with respect to the non-eroded surface. The results indicate that the groove angle increases gradually with an increase in the maximum erosion depth, which is almost independent of the nozzle pressure and only weakly dependent on the standoff distance. Fig. 6 shows the SEM observation on the surface of shallow erosion at Ed = 1 mm (a) and that of deep erosion at Ed = 4 mm (b) in the nozzle pressure P = 16 MPa and the standoff distance x = 270 mm. The surface images are taken by the SEM with a magnification factor 20. The image of shallow erosion shows that the macro structure with a scale of 200–300 lm exists on the erosion surface, which is similar to that observed on the uniform erosion surface (Fujisawa et al., 2013). The size of the macro structure on the erosion surface decreases near the edge of the erosion, where the direct impingement of liquid droplets is weakened and the side jet effect is expected. On the other hand, a large-scale structure of several hundreds of lm appears near the center of the groove in deep erosion (b), while the scale of the structure decreases on the side wall of the groove and a small structure appears near the edge of the erosion surface. The occurrence of large-scale structure near the deep-groove center may be due to the influence of the thick liquid film on the groove surface. It should be mentioned that the SEM observation with a magnification factor 200, which was not shown here, showed similar scale of micro structure on
Fig. 5. Variation of groove angle.
the erosion surface independent of the erosion depth, as was the case of uniform erosion (Fujisawa et al., 2013). This result suggests that the macro structure of the erosion surface is modified in the deep LDI erosion, while the micro structure does not change with the erosion depth. 3.3. Depth variation of wall-thinning rates Fig. 7 shows the variation of maximum erosion depth Ed with the local volume flux qt of the spray jet in the nozzle pressure ranging from P = 16 to 28 MPa and the standoff distance of x = 270 mm. The close-up view of small qt is shown in Fig. 7(a) and the whole field is described in Fig. 7(b). A linear growth rate of uniform erosion of the test specimen of 2.5 mm diameter is evaluated from the following Eq. (1) by Fujisawa et al. (2013) and the results are shown by the straight lines in Fig. 7(a) for comparative purposes.
V du ¼ c1 H3:3 V 7 f1 þ c2 ðh=dÞg r
c3
ð1Þ
where Vdu is the wall-thinning rate of uniform erosion, d is the droplet diameter, h is the liquid-film thickness defined by the following Eq. (2), and Hr is the relative Vickers hardness of the wall material with respect to that of the aluminum material.
h¼
Dq 4V
ð2Þ
where D is the specimen diameter. The experimental result indicates that the erosion depth increases almost linearly in the initial stage of erosion for Ed < 0.5 mm, while the growth rate of the erosion depth decreases gradually with an increase in the local volume flux qt. An apparent decrease in the growth rate is observed in the erosion depth Ed > 1 mm. This is expected to be due to the influence of the liquid-film thickness on the wall-thinning rate. An increase in liquid-film thickness on the wall reduces the impact pressure of the liquid droplet impingement and results in smaller wallthinning rate of the wall material (Fujisawa et al., 2013).
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(a)
(b)
Fig. 6. SEM observation on erosion surface. (a) Ed = 1 mm (b) Ed = 4 mm.
(a)
(b)
Fig. 7. Variation of maximum erosion depth Ed with local volume flux qt (P = 16 MPa, x = 270 mm). (a) Close-up view of small qt (b) whole field.
Fig. 8. Wall thinning rate versus erosion depth (data on Ed = 0 is obtained from Eq. (1) for uniform erosion).
With an increase in the maximum erosion depth, the wallthinning rate decreases more apparently in the larger erosion depth, as shown in the whole field in Fig. 7(b). This is due to the further increase in the liquid-film thickness in the deep erosion surface. It is expected that the increase in liquid-film thickness results in the reduction in impact pressure and the decrease in the wall-thinning rate in the deep erosion. The result shows that the growth rate of the wall-thinning rate increases with increasing the nozzle pressure P, which corresponds to the influence of droplet velocity on the wall-thinning rate.
Fig. 9. Attenuation factor f versus erosion depth Ed.
Fig. 8 shows the non-dimensional wall-thinning rates Vd (=DEd/qDt) with respect to the maximum erosion depth Ed, which is obtained from the experimental data for various nozzle pressures P = 16–28 MPa and the standoff distances x = 270 mm and 480 mm. Generally speaking, the wall-thinning rate Vd decreases with an increase in the erosion depth Ed, while there is a large scattering of the data in the small region of Ed. It seems that the wall-thinning rate Vd in this region increases with increasing the nozzle pressures, that is the droplet velocity. This result suggests that the wall-thinning rate can be expressed by a single parameter f (=Vd/Vdu), which is a ratio of the erosion rate Vd to that of the uniform erosion rate Vdu. The wall-thinning rate of uniform
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and the standoff distances x = 270 and 480 mm. The predicted wall-thinning rates are well correlated with the experimental data with the scattering of a factor of 2, while the scattering of the data is over a factor of 4 without introduction of uniform erosion rate Vdu. This result suggests that the introduction of the uniform erosion rate Vdu to the attenuation factor is very useful in predicting the wall-thinning rate by LDI in deep erosion. 4. Conclusions
Fig. 10. Correlation between experimental and predicted wall-thinning rates.
erosion Vdu can be obtained from Eq. (1) and the result is plotted in Fig. 8 on the line of Ed = 0. The introduction of attenuation factor f (=Vd/Vdu) implies that the damping effect of wall-thinning rate can be formulated as a function of the maximum erosion depth Ed, which is shown in Fig. 9 for various nozzle pressures and the standoff distances. All the data collapse on a single curve in Fig. 9 and is approximated by the following equation,
f ¼ exp c1 Em d
for Ed < 0:7 mm ðc1 ¼ 1:4; m ¼ 0:5Þ for Ed > 2 mm ðc1 ¼ 1:7; m ¼ 0:6Þ
ð3Þ
f ¼ aE2d þ bEd þ c for 0:7 mm < Ed < 2 mm ða ¼ 0:077;
b ¼ 0:39; c ¼ 0:54Þ
Acknowledgements
ð4Þ
where the constants c1 and m are obtained from the least square fitting of all the experimental data, and the constants a, b and c are determined to connect smoothly these equations. It should be mentioned that the role of the attenuation factor f is to attenuate the wall-thinning rate with increasing the maximum erosion depth. This result indicates that the wall-thinning rate of the deep erosion can be evaluated correctly by the introduction of the attenuation factor f. 3.4. Erosion model The non-dimensional wall-thinning rate in the deep erosion can be formulated by the following equation.
V d ¼ c1 H3:3 V 7 f1 þ c2 ðh=dÞg 3 f r c
The wall-thinning rate of deep erosion by liquid droplet impingement is studied experimentally using a spray jet apparatus. The experiment is carried out for the specimen diameter larger than the spray size for various combinations of droplet velocities and standoff distances, and the measurements are conducted on the erosion surface contour, the wall-thinning rate and the erosion surface observation by SEM. The surface contour in the deep erosion is featured by the sharp groove penetrating into the wall material, which is due to the larger thinning rate on the center of the groove than that on the side surface of the groove. The wallthinning rate in the deep erosion is greatly decreased with an increase in the erosion depth. This is due to the damping effect of the liquid film on the wall-thinning rate and the influence of side jet of the liquid droplet impingement. The erosion model for predicting the wall-thinning rate of deep erosion is proposed in this study by introducing the attenuation factor with a function of erosion depth. The introduction of uniform erosion rate to the attenuation factor shows a better correlation with the experimental data, and the accuracy of correlation is improved by a factor of 2.
ð5Þ
where d is a droplet diameter, h is a liquid-film thickness, Hr is a relative Vickers hardness with respect to pure aluminum, V is a droplet velocity and f represents the attenuation factor in the deep erosion. The empirical constants are c1 = 4.0 1020, c2 = 92.2, and c3 = 1.30. It should be mentioned that Eq. (1) is derived from the uniform erosion experiments for various droplet velocities and liquid-film thicknesses under the assumption that the spray size is much larger than the specimen diameter, while the attenuation factor f in Eq. (5) introduced here is to express the attenuation of the wall-thinning rate in the deep erosion. In the shallow erosion stage, the attenuation factor is almost unity as is the case of uniform erosion of thin liquid film, while it is a function of the erosion depth in deep erosion and it decreases sharply with an increase in the erosion depth. Fig. 10 shows the comparison between the experimental wallthinning rate and the prediction by Eq. (5), which is obtained from the present experiment for various nozzle pressures P = 16–28 MPa
This research was supported by the Grant-in-aid for Scientific Research B (No. 24360391) in the fiscal years 2012 to 2014. The authors would like to express thanks to Dr. Inada and Dr. R. Morita from Central Research Institute of Electric Power Industry for their helpful suggestions during the course of this study. References Ferng, Y.M., 2008. Predicting local distributions of erosion–corrosion wear sites for the piping in the nuclear power plant using CFD models. Ann. Nucl. Energy 35, 304–313. Field, J.E., Lesser, M.B., Dear, J.P., 1985. Studies of two-dimensional liquid-wedge impact and their relevance to liquid-drop impact problems. Proc. R. Soc. Lond. A 401, 225–249. Fujisawa, N., Yamagata, T., Hayashi, K., Takano, T., 2012a. Experiments on liquid droplet impingement erosion by high-speed spray. Nucl. Eng. Des. 250, 101– 107. Fujisawa, N., Morita, R., Nakamura, A., Yamagata, T., 2012b. Critical consideration on wall thinning rate by liquid droplet impingement erosion. E J. Adv. Maintenance 4, 79–87. Fujisawa, N., Yamagata, T., Saito, K., Hayashi, K., 2013. The effect of liquid film on liquid droplet impingement erosion. Nucl. Eng. Des. 265, 909–917. Fujisawa, N., Yamagata, T., Takano, S., Saito, K., Morita, R., Fujiwara, K., Inada, F., 2015. The influence of material hardness on liquid droplet impingement erosion. Nucl. Eng. Des. 288, 27–34. Hattori, S., Takinami, M., 2010. Comparison of cavitation erosion rate with liquid impingement erosion rate. Wear 269, 310–316. Heymann, F.J., 1969. High-speed impact between a liquid drop and a solid surface. J. Appl. Phys. 40, 5113–5122. Heymann, F.J., 1979. Conclusions from the ASTM interlaboratory test program with liquid impact erosion facilities. In: Proc. 5th Int. Conf. on Erosion by Solid and Liquid Impact, 20–1 to 20–10. Ikohagi, T., 2011. On evaluation of LDI erosion rate based on fluid/solid coupled simulation. In: Proc. 8th Int. Conf. Flow Dynamics, pp. 402–403. Ishimoto, J., Akiba, S., Tanji, K., Matsuura, K., 2011. Integrated super computational prediction of liquid droplet impingement erosion. Prog. Nucl. Sci. Technol. 2, 498–502. Isomoto, Y., Miyata, H., 2008. Erosion phenomenon caused by water droplet impingement and life prediction of industrial materials, Part 2 establishment of predictive equations and evaluation of material performance. Zairyo-to-Kankyo 57, 146–152.
N. Fujisawa et al. / Annals of Nuclear Energy 88 (2016) 151–157 Itoh, H., Okabe, N., 1993. Evaluation of erosion by liquid droplet impingement for metallic materials. Trans. JSME (A) 59, 2736–2741. Kiuchi, M., Fujisawa, N., Tomimatsu, S., 2005. Performance of PIV system for combusting flow and its application to a spray combustor model. J. Visual. 8, 269–276. Li, R., Pellegrini, M., Ninokata, H., Mori, M., 2011. A numerical study on turbulence attenuation model for liquid droplet. Ann. Nucl. Energy 38 (2011), 1279– 1287. Miyata, H., Isomoto, Y., 2008. Erosion phenomenon caused by water droplet impingement and life prediction of industrial materials, Part 1 – investigation of droplet impingement factors and erosion testing methods. Zairyo-to-Kankyo 57, 138–145. Morita, R., Uchiyama, Y., 2011. Proposition of a wall thinning model for liquid droplet impingement erosion. CRIEPI Research Report, No. L10018.
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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Attenuation of wall-thinning rate in deep erosion by liquid droplet impingement Nobuyuki Fujisawa a,⇑, Takayuki Yamagata a,⇑, Keitaro Wada b a b
Visualization Research Center, Niigata University, 8050, Ikarashi 2-Nocho, Nishi-ku, Niigata 950-2181, Japan Graduate School of Science and Technology, Niigata University, 8050, Ikarashi 2-Nocho, Nishi-ku, Niigata 950-2181, Japan
a r t i c l e
i n f o
Article history: Received 16 January 2015 Received in revised form 7 September 2015 Accepted 21 October 2015 Available online 14 November 2015 Keywords: Wall thinning Liquid droplet impingement Erosion Erosion model Power plant Pipeline
a b s t r a c t This paper describes an experimental study on the wall-thinning rate in deep erosion by liquid droplet impingement (LDI) in a pipeline for application to nuclear/fossil power plant. The experiment is carried out in a spray jet apparatus, which allows the evaluation of local wall-thinning rate by the LDI erosion. The surface contour of erosion and the wall-thinning rate are measured and the observation by scanning electron microscope (SEM) is carried out in this experiment. The experimental result indicates that the wall-thinning rate is highly attenuated and the macro structure on the erosion surface grows with an increase in the erosion depth, which is due to the influence of the liquid film over the erosion surface. The erosion model for predicting the wall-thinning rate in deep erosion is proposed by introducing the attenuation factor with a function of erosion depth. The introduction of attenuation factor with liquidfilm effect shows a better correlation with the experimental data, and the accuracy of correlation is improved by a factor of 2. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Liquid droplet impingement (LDI) erosion is one of the causes of pipeline damage in nuclear/fossil power plants. The mechanism of the LDI erosion has been investigated experimentally and numerically both from the points of plant engineering and flow physics in literature. The fundamental of the LDI erosion is a single droplet impact on solid surface and the physics of the droplet impact has been studied by Field et al. (1985) using the high-speed observation of gelatin impact. The result indicates that the shock wave is generated at the instant of droplet impact on the solid wall, which propagates through the liquid medium and reflects at the free surface of the droplet and the reflected pressure wave focuses near the wall material leading to the occurrence of cavitation, while the droplet impact produces a side jet along the wall in radial direction. The side jet produces a thin film of liquid flowing over the wall with much faster velocity than that of the impact velocity of the liquid droplet. In spite of such a complex phenomenon of liquid droplet impingement on a wall, the impact pressure of the droplet roughly approximated by the impact formula, which indicates that the impact pressure is proportional to the products of the droplet density, acoustic velocity and droplet velocity (Heymann, 1969; ⇑ Corresponding authors. E-mail addresses: [email protected] (N. Fujisawa), yamagata@eng. niigata-u.ac.jp (T. Yamagata). http://dx.doi.org/10.1016/j.anucene.2015.10.024 0306-4549/Ó 2015 Elsevier Ltd. All rights reserved.
Rochester and Brunton, 1974). The result implies that the impact pressure is independent of the droplet diameter and becomes larger than the yield stress of the carbon steel, when the droplet velocity is above 100 m/s. This condition applies to the flow through the pipeline of nuclear/fossil power plant. Therefore, the main cause of LDI erosion in the power-plant pipeline is considered to be due to the high impact pressure of the liquid droplet in the high-speed steam flow. In order to estimate the lifetime of the pipeline in the power plant, the prediction of the wall-thinning rate due to the LDI erosion is becoming an important topic of interests in recent years (Ferng, 2008; Li et al., 2011; Morita and Uchiyama, 2011). For this to be done, experimental erosion models are fundamental and they are summarized in Table 1, which includes Heymann (1979), Sanchez-Caldera (1984), Itoh and Okabe (1993), Oka et al. (2007), Miyata and Isomoto (2008), Isomoto and Miyata (2008), Hattori and Takinami (2010), Ishimoto et al. (2011) and Fujisawa et al. (2012a, 2013, 2015). Using these erosion models, the wallthinning rate is evaluated from the droplet parameters, such as the droplet velocity, droplet diameter, number of droplets, and the material hardness, while the influence of the liquid-film thickness on the wall-thinning rate is found to be another important factor by the recent numerical studies of Ikohagi (2011) and Xiong et al. (2011). Later, the influence of liquid film on the wallthinning rate is experimentally studied by Fujisawa et al. (2013),
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Nomenclature c1, c2, c3 d Ed f Hr n P t Qo
constants, Eq. (1) droplet diameter maximum erosion depth attenuation factor, Eqs. (3) and (4) relative Vickers hardness with respect to aluminum power index for droplet velocity dependency pump pressure time bulk flow rate
pure
q V Vo Vd Vde Vdp Vdu x
q m
local volume flux droplet velocity velocity at nozzle exit non-dimensional erosion rate experimental erosion rate predicted erosion rate uniform erosion rate, Eq. (1) coordinate along spray centerline density of liquid kinematic viscosity of air
Table 1 Summary of previous experiments on LDI.
Heymann (1979) Itoh and Okabe (1993) Isomoto and Miyata (2008), Miyata and Isomoto (2008) Hattori and Takinami (2010) Fujisawa et al. (2012a) Fujisawa et al. (2013) Fujisawa et al. (2015)
Power index n
Test method
Droplet velocity V (m/s)
Droplet diameter (lm)
Test material
5.8 (maximum rate point) 6–8 (terminal stage)
Rotating disk Rotating disk Spray
810–2000 195–269 immersion drop sampling method 20–200 immersion drop sampling method 60–120
A1100-0, A6061-T6, Ni270, SUS316 12 Cr steel, cobalt base alloy, titanium alloy A5083, SS400, SUS410 J1, SUS304 SK3 S15C, STPA24, SUS304
Spray
93–400 (rotating speed) 400,480 (rotating speed) 40,300 (impact force) 80–184 (nozzle pressure) 130–160 (PIV)
60–120 shadowgraph
A1050
Spray Spray
140–175 (PIV) 140–180 (PIV)
30 shadowgraph 30 shadowgraph
A1070 A1070, A5056, C3604, SS400, S20C, SUS304
6 (<100 m/s) 2 (>150 m/s) 6.0–7.4 (maximum rate stage) 7 (maximum rate point) 6.6 (terminal stage) 7 (terminal stage)
Water jet
leads to a leak of the steam flow to the outside, as was the case of Onagawa power plant in 2007. In the case of deep erosion, the wall-thinning rate may be influenced by the erosion depth, while the details of such a deep erosion have not been studied in literature. In the present study, the deep LDI erosion is experimentally studied using a high-speed spray jet for characterizing the influence of erosion depth on the wall-thinning rate. An attention is placed on the deep LDI erosion model including the influence of erosion depth.
Fig. 1. LDI erosion in bent pipe downstream of orifice.
who carried out an experiment using the spray jet. They found that the wall-thinning rate is strongly attenuated by increasing the liquid-film thickness over the specimen surface. On the other hand, the wall-thinning rate has been formulated by a power law of droplet velocity with a constant power index n = 7, while it is scattering in a range from 3 to 8, as seen in Table 1. It should be mentioned that the power index n = 5 is derived from the dimensional analysis by Sanchez-Caldera (1984). Such large scattering of the power index can be explained by the influence of experimental conditions, erosion stage, material hardness, droplet diameter, liquid-film thickness and so on, while the reason of the scattering is still not clear due to the limitation of experimental study in literature (Fujisawa et al., 2012b). The LDI erosion often occurs in a steam pipeline of the nuclear/ fossil power plant, where the steam flow is highly accelerated downstream of the orifice and it impinges on the bent pipe downstream, as illustrated in Fig. 1. Once the erosion on the pipe wall is highly accelerated, the LDI erosion may cause deep erosion. This
2. Experiment Fig. 2 shows a schematic illustration of the experimental apparatus, which consists of a straight nozzle and a pure aluminum test specimen (Al070), which is a circular plate of 40 mm in diameter with a thickness of 8 mm. The nozzle exit diameter is 0.8 mm and it generates a straight liquid column at the nozzle exit (MCP08, Ikeuchi Co.), while the liquid column changes to a spray jet immediate downstream due to the instability of the liquid-air interface associated with the entrainment of the surrounding air. The erosion experiment was carried out by impinging the jet on the test specimen from the top in the present study. Note that the erosion rate in vertical impingement agrees with that in horizontal impingement, which suggests negligibly small influence of the gravity on the erosion rate. The spray image taken by a digital camera with strobe-flush is shown in Fig. 3, which is an instantaneous spray image covering the spray jet of a distance 500 mm downstream of the nozzle exit. It is seen that the flow of liquid column is limited near the nozzle and the flow spreads almost linearly from the nozzle downstream. The detail observation of the spray jet indicates that the transition of the liquid column to the spray
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cross-correlation algorithm combined with the sub-pixel analysis (Kiuchi et al., 2005). The interrogation window size was set to 31 31 pixels and was set to satisfy 50% overlap condition. The measurement of droplet diameter was made by the shadowgraph technique combined with the image processing (Fujisawa et al., 2012a). The shadowgraph is an inline imaging technique illuminated by the Nd:Yag pulse laser with an optics for laser and the images are captured by a CCD camera with a spatial resolution of 1008 1018 pixels. The target area of measurement is set to 10 mm 10 mm. Then, the droplet diameter was found to be 25 ± 5 lm in the volume average diameter at x = 270 mm and 480 mm downstream of the nozzle, which is a slightly smaller diameter in comparison with the former spray nozzle used in the uniform erosion (Fujisawa et al., 2013). The details of the measurement technique for the droplet diameter have been described by Fujisawa et al. (2012a).
Fig. 2. Experimental apparatus for LDI erosion.
jet is completed within a distance of 200 mm from the nozzle and the flow is considered as spray jet further downstream. Therefore, the LDI experiments have been carried out in the standoff distances x = 270 mm and 480 mm from the nozzle, where the fully developed spray structure is observed. This condition can be applied to the real pipeline, such as the Onagawa power plant (NUCIA, 2007). The LDI experiments on the test specimen were carried out by changing the nozzle pressure from 16 to 28 MPa. The wall-thinning rate of the test specimen was evaluated by measuring the maximum erosion depth Ed, which is measured near the center of the specimen by using the scanning optical microscope with an accuracy of 0.01 mm. Note that the scanning optical microscope allows the measurement of the maximum erosion depth as well as the whole contour of erosion surface in the area of observation. It should be mentioned that the maximum erosion depth is the major concern, so that the local depth on the groove slope is not studied here. The non-dimensional erosion rates Vd (=DEd/qDt) were evaluated from the present measurement, where DEd is the variation of maximum erosion depth, q is the local volume flux and t is an elapsed time. The local volume flux q was measured by a sampling probe with an inner diameter of 1.18 mm (Fujisawa et al., 2012a). The droplet velocity was measured by the particle image velocimetry (PIV) without adding any tracer particles (Fujisawa et al., 2012a). Note that the pattern of droplet images are considered as the tracers in the measurement. The standard PIV system is used for the measurement. It consists of a CCD camera (spatial resolution of 1008 1018 with 8 bits), the Nd:Yag double pulse laser of 50 mJ and the pulse controller. The target area of measurement is 10 mm 10 mm. The droplet velocity was obtained by time-averaging 1000 instantaneous velocity fields measured from the PIV images taken in every 1/5 s time interval. It should be mentioned that the PIV analysis was carried out using the
3. Results and discussions 3.1. Droplet velocity and local volume flux The experiments on LDI erosion are carried out for various nozzle pressures P = 16–28 MPa to evaluate the wall-thinning rate in the deep LDI erosion. The experimental conditions of total flow rate Q0 and nozzle exit velocity V0 for various nozzle pressures P are shown in Table 2. Note that the total flow rate Q0 was evaluated from the bulk volume measurement of water in a storage tank in a unit time, while the nozzle exit velocity V0 was evaluated from Q0 using the continuity equation, which agrees closely with that from the nozzle pressure measurement by the Bernoulli equation. The local droplet velocity V/V0 and local volume flux q/Q0 in the spray centerline are measured by particle image velocimetry (PIV) and sampling probe, respectively, and they are summarized in Table 2 for both standoff distances of x = 270 mm and 480 mm. Generally speaking, the droplet velocity V/V0 and the local volume flux q/Q0 decrease downstream in a fixed nozzle pressure, though they increase with increasing the nozzle pressure. Note that the droplet velocity in this experiment agrees with those of the prototype power plant. 3.2. Depth distribution on erosion surface Fig. 4 shows an example of the cross-sectional surface contour of LDI erosion at x = 270 mm, which is measured by a scanning optical microscope. The measurement is done in the nozzle pressure 16 MPa. The observation of erosion surface in the initial stage is featured by the smaller erosion depth than the spray size, which is the condition of the previous studies summarized in Table 1. With the progress of erosion, the depth of erosion increases and the maximum erosion depth becomes comparable to the spray size. This is the case of the deep erosion and is the case of this
Fig. 3. Spray image.
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Table 2 Summary of experimental conditions. Nozzle pressure P (MPa)
Bulk flow rate Q0 (mm3/s)
Nozzle exit velocity V0 (m/s)
16 20 24 28
1.03 105 1.10 105 1.22 105 1.29 105
179 200 219 237
Local volume flux q and velocity V at x = 270 mm
Local volume flux q and velocity V at x = 480 mm
q (mm/s)
V (m/s)
q (mm/s)
V (m/s)
3.50 103 3.78 103 4.08 103 4.38 103
159 174 189 207
2.10 103 2.14 103 2.27 103 2.36 103
146 158 170 178
Fig. 4. Cross-sectional contours of LDI erosion (P = 16 MPa, x = 270 mm).
study. The time variation of the erosion distribution indicates that the growth rate of erosion is larger in the groove center than in the surrounding, so that the erosion distribution becomes sharper near the groove center with increasing the elapsed time. Therefore, the growth of the groove may lead to a pin-hole type erosion with an increase in the elapsed time, which results in the leak of steam flow in the pipeline as observed in Onagawa power plant (NUCIA, 2007). It should be mentioned that the erosion surface distribution is fluctuating with time due to the randomness of the erosion damage by LDI. Fig. 5 shows the angle of erosion groove h plotted against the depth of maximum erosion Ed near the center of the groove. It should be mentioned that all the experimental results of nozzle pressures P = 16–28 MPa and standoff distances (x = 270 mm, 480 mm) are plotted in this figure. Note that the groove angle is obtained from the volume loss of the material and the maximum erosion depth assuming the cone-shape erosion contour. The groove angle corresponds to the average gradient of the grove surface with respect to the non-eroded surface. The results indicate that the groove angle increases gradually with an increase in the maximum erosion depth, which is almost independent of the nozzle pressure and only weakly dependent on the standoff distance. Fig. 6 shows the SEM observation on the surface of shallow erosion at Ed = 1 mm (a) and that of deep erosion at Ed = 4 mm (b) in the nozzle pressure P = 16 MPa and the standoff distance x = 270 mm. The surface images are taken by the SEM with a magnification factor 20. The image of shallow erosion shows that the macro structure with a scale of 200–300 lm exists on the erosion surface, which is similar to that observed on the uniform erosion surface (Fujisawa et al., 2013). The size of the macro structure on the erosion surface decreases near the edge of the erosion, where the direct impingement of liquid droplets is weakened and the side jet effect is expected. On the other hand, a large-scale structure of several hundreds of lm appears near the center of the groove in deep erosion (b), while the scale of the structure decreases on the side wall of the groove and a small structure appears near the edge of the erosion surface. The occurrence of large-scale structure near the deep-groove center may be due to the influence of the thick liquid film on the groove surface. It should be mentioned that the SEM observation with a magnification factor 200, which was not shown here, showed similar scale of micro structure on
Fig. 5. Variation of groove angle.
the erosion surface independent of the erosion depth, as was the case of uniform erosion (Fujisawa et al., 2013). This result suggests that the macro structure of the erosion surface is modified in the deep LDI erosion, while the micro structure does not change with the erosion depth. 3.3. Depth variation of wall-thinning rates Fig. 7 shows the variation of maximum erosion depth Ed with the local volume flux qt of the spray jet in the nozzle pressure ranging from P = 16 to 28 MPa and the standoff distance of x = 270 mm. The close-up view of small qt is shown in Fig. 7(a) and the whole field is described in Fig. 7(b). A linear growth rate of uniform erosion of the test specimen of 2.5 mm diameter is evaluated from the following Eq. (1) by Fujisawa et al. (2013) and the results are shown by the straight lines in Fig. 7(a) for comparative purposes.
V du ¼ c1 H3:3 V 7 f1 þ c2 ðh=dÞg r
c3
ð1Þ
where Vdu is the wall-thinning rate of uniform erosion, d is the droplet diameter, h is the liquid-film thickness defined by the following Eq. (2), and Hr is the relative Vickers hardness of the wall material with respect to that of the aluminum material.
h¼
Dq 4V
ð2Þ
where D is the specimen diameter. The experimental result indicates that the erosion depth increases almost linearly in the initial stage of erosion for Ed < 0.5 mm, while the growth rate of the erosion depth decreases gradually with an increase in the local volume flux qt. An apparent decrease in the growth rate is observed in the erosion depth Ed > 1 mm. This is expected to be due to the influence of the liquid-film thickness on the wall-thinning rate. An increase in liquid-film thickness on the wall reduces the impact pressure of the liquid droplet impingement and results in smaller wallthinning rate of the wall material (Fujisawa et al., 2013).
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(a)
(b)
Fig. 6. SEM observation on erosion surface. (a) Ed = 1 mm (b) Ed = 4 mm.
(a)
(b)
Fig. 7. Variation of maximum erosion depth Ed with local volume flux qt (P = 16 MPa, x = 270 mm). (a) Close-up view of small qt (b) whole field.
Fig. 8. Wall thinning rate versus erosion depth (data on Ed = 0 is obtained from Eq. (1) for uniform erosion).
With an increase in the maximum erosion depth, the wallthinning rate decreases more apparently in the larger erosion depth, as shown in the whole field in Fig. 7(b). This is due to the further increase in the liquid-film thickness in the deep erosion surface. It is expected that the increase in liquid-film thickness results in the reduction in impact pressure and the decrease in the wall-thinning rate in the deep erosion. The result shows that the growth rate of the wall-thinning rate increases with increasing the nozzle pressure P, which corresponds to the influence of droplet velocity on the wall-thinning rate.
Fig. 9. Attenuation factor f versus erosion depth Ed.
Fig. 8 shows the non-dimensional wall-thinning rates Vd (=DEd/qDt) with respect to the maximum erosion depth Ed, which is obtained from the experimental data for various nozzle pressures P = 16–28 MPa and the standoff distances x = 270 mm and 480 mm. Generally speaking, the wall-thinning rate Vd decreases with an increase in the erosion depth Ed, while there is a large scattering of the data in the small region of Ed. It seems that the wall-thinning rate Vd in this region increases with increasing the nozzle pressures, that is the droplet velocity. This result suggests that the wall-thinning rate can be expressed by a single parameter f (=Vd/Vdu), which is a ratio of the erosion rate Vd to that of the uniform erosion rate Vdu. The wall-thinning rate of uniform
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and the standoff distances x = 270 and 480 mm. The predicted wall-thinning rates are well correlated with the experimental data with the scattering of a factor of 2, while the scattering of the data is over a factor of 4 without introduction of uniform erosion rate Vdu. This result suggests that the introduction of the uniform erosion rate Vdu to the attenuation factor is very useful in predicting the wall-thinning rate by LDI in deep erosion. 4. Conclusions
Fig. 10. Correlation between experimental and predicted wall-thinning rates.
erosion Vdu can be obtained from Eq. (1) and the result is plotted in Fig. 8 on the line of Ed = 0. The introduction of attenuation factor f (=Vd/Vdu) implies that the damping effect of wall-thinning rate can be formulated as a function of the maximum erosion depth Ed, which is shown in Fig. 9 for various nozzle pressures and the standoff distances. All the data collapse on a single curve in Fig. 9 and is approximated by the following equation,
f ¼ exp c1 Em d
for Ed < 0:7 mm ðc1 ¼ 1:4; m ¼ 0:5Þ for Ed > 2 mm ðc1 ¼ 1:7; m ¼ 0:6Þ
ð3Þ
f ¼ aE2d þ bEd þ c for 0:7 mm < Ed < 2 mm ða ¼ 0:077;
b ¼ 0:39; c ¼ 0:54Þ
Acknowledgements
ð4Þ
where the constants c1 and m are obtained from the least square fitting of all the experimental data, and the constants a, b and c are determined to connect smoothly these equations. It should be mentioned that the role of the attenuation factor f is to attenuate the wall-thinning rate with increasing the maximum erosion depth. This result indicates that the wall-thinning rate of the deep erosion can be evaluated correctly by the introduction of the attenuation factor f. 3.4. Erosion model The non-dimensional wall-thinning rate in the deep erosion can be formulated by the following equation.
V d ¼ c1 H3:3 V 7 f1 þ c2 ðh=dÞg 3 f r c
The wall-thinning rate of deep erosion by liquid droplet impingement is studied experimentally using a spray jet apparatus. The experiment is carried out for the specimen diameter larger than the spray size for various combinations of droplet velocities and standoff distances, and the measurements are conducted on the erosion surface contour, the wall-thinning rate and the erosion surface observation by SEM. The surface contour in the deep erosion is featured by the sharp groove penetrating into the wall material, which is due to the larger thinning rate on the center of the groove than that on the side surface of the groove. The wallthinning rate in the deep erosion is greatly decreased with an increase in the erosion depth. This is due to the damping effect of the liquid film on the wall-thinning rate and the influence of side jet of the liquid droplet impingement. The erosion model for predicting the wall-thinning rate of deep erosion is proposed in this study by introducing the attenuation factor with a function of erosion depth. The introduction of uniform erosion rate to the attenuation factor shows a better correlation with the experimental data, and the accuracy of correlation is improved by a factor of 2.
ð5Þ
where d is a droplet diameter, h is a liquid-film thickness, Hr is a relative Vickers hardness with respect to pure aluminum, V is a droplet velocity and f represents the attenuation factor in the deep erosion. The empirical constants are c1 = 4.0 1020, c2 = 92.2, and c3 = 1.30. It should be mentioned that Eq. (1) is derived from the uniform erosion experiments for various droplet velocities and liquid-film thicknesses under the assumption that the spray size is much larger than the specimen diameter, while the attenuation factor f in Eq. (5) introduced here is to express the attenuation of the wall-thinning rate in the deep erosion. In the shallow erosion stage, the attenuation factor is almost unity as is the case of uniform erosion of thin liquid film, while it is a function of the erosion depth in deep erosion and it decreases sharply with an increase in the erosion depth. Fig. 10 shows the comparison between the experimental wallthinning rate and the prediction by Eq. (5), which is obtained from the present experiment for various nozzle pressures P = 16–28 MPa
This research was supported by the Grant-in-aid for Scientific Research B (No. 24360391) in the fiscal years 2012 to 2014. The authors would like to express thanks to Dr. Inada and Dr. R. Morita from Central Research Institute of Electric Power Industry for their helpful suggestions during the course of this study. References Ferng, Y.M., 2008. Predicting local distributions of erosion–corrosion wear sites for the piping in the nuclear power plant using CFD models. Ann. Nucl. Energy 35, 304–313. Field, J.E., Lesser, M.B., Dear, J.P., 1985. Studies of two-dimensional liquid-wedge impact and their relevance to liquid-drop impact problems. Proc. R. Soc. Lond. A 401, 225–249. Fujisawa, N., Yamagata, T., Hayashi, K., Takano, T., 2012a. Experiments on liquid droplet impingement erosion by high-speed spray. Nucl. Eng. Des. 250, 101– 107. Fujisawa, N., Morita, R., Nakamura, A., Yamagata, T., 2012b. Critical consideration on wall thinning rate by liquid droplet impingement erosion. E J. Adv. Maintenance 4, 79–87. Fujisawa, N., Yamagata, T., Saito, K., Hayashi, K., 2013. The effect of liquid film on liquid droplet impingement erosion. Nucl. Eng. Des. 265, 909–917. Fujisawa, N., Yamagata, T., Takano, S., Saito, K., Morita, R., Fujiwara, K., Inada, F., 2015. The influence of material hardness on liquid droplet impingement erosion. Nucl. Eng. Des. 288, 27–34. Hattori, S., Takinami, M., 2010. Comparison of cavitation erosion rate with liquid impingement erosion rate. Wear 269, 310–316. Heymann, F.J., 1969. High-speed impact between a liquid drop and a solid surface. J. Appl. Phys. 40, 5113–5122. Heymann, F.J., 1979. Conclusions from the ASTM interlaboratory test program with liquid impact erosion facilities. In: Proc. 5th Int. Conf. on Erosion by Solid and Liquid Impact, 20–1 to 20–10. Ikohagi, T., 2011. On evaluation of LDI erosion rate based on fluid/solid coupled simulation. In: Proc. 8th Int. Conf. Flow Dynamics, pp. 402–403. Ishimoto, J., Akiba, S., Tanji, K., Matsuura, K., 2011. Integrated super computational prediction of liquid droplet impingement erosion. Prog. Nucl. Sci. Technol. 2, 498–502. Isomoto, Y., Miyata, H., 2008. Erosion phenomenon caused by water droplet impingement and life prediction of industrial materials, Part 2 establishment of predictive equations and evaluation of material performance. Zairyo-to-Kankyo 57, 146–152.
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