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Nuclear Engineering and Design 265 (2013) 909– 917
Contents lists available at ScienceDirect
Nuclear Engineering and Design
j ourna l h om epa ge: www.elsev ier .com/ locate /nucengdes
he effect of liquid film on liquid droplet impingement erosion
obuyuki Fujisawaa,∗, Takayuki Yamagataa,∗, Kengo Saitob, Kanto Hayashib
Visualization Research Center, Niigata University, 8050, Ikarashi 2-Nocho, Nishi-ku, Niigata 950-2181, JapanGraduate School of Science and Technology, Niigata University, 8050, Ikarashi 2-Nocho, Nishi-ku, Niigata 950-2181, Japan
i g h l i g h t s
Liquid droplet impingement erosion is studied experimentally using high-speed conical spray.Erosion rate is increased with decreasing the liquid film thickness.Erosion model is proposed considering the influence of liquid film thickness.
r t i c l e i n f o
rticle history:eceived 9 April 2013eceived in revised form 16 July 2013ccepted 23 July 2013
a b s t r a c t
In the present paper, the pipe-wall thinning due to liquid droplet impingement erosion is studied exper-imentally by using a high-speed conical spray under the influences of liquid film on the target specimen.The size of the droplets considered is an order of tens of micrometers in diameter, which is the sameorder as those expected in the pipeline of nuclear/fossil power plants. In order to evaluate the erosionrate by the liquid droplet impingement under the influence of liquid film, the experiments are conductedby various combinations of the specimen diameters and the standoff distances of the spray from the noz-zle. The experimental results show that the erosion depth increases linearly with the local flow volume,indicating the presence of terminal stage of erosion. The present results indicate that the erosion rate
increases with decreasing the specimen diameter and increases slightly with increasing the standoff dis-tance. This result combined with the theoretical consideration of the liquid film on the specimen leads tothe conclusion that the erosion rate increases with decreasing the liquid film thickness, which supportsthe numerical result of liquid droplet impingement erosion in literature. Then, the erosion model forpredicting the erosion rate by the liquid droplet impingement is proposed considering the influence ofthe liquid film.. Introduction
The pipe-wall thinning in a pipeline of nuclear/fossil powerlant is an important topic of interests for the maintenance andhe safety management of the power plants. The pipe-wall thin-ing due to the liquid droplet impingement erosion often occurs inlbows, T junctions and the pipe walls downstream of the orifice inhe pipelines, where the flow velocity through the pipeline is highlyccelerated. In order to understand the liquid droplet impingementrosion, the experimental and theoretical studies have been carriedut and the mechanism of the erosion and the prediction method of
he erosion rate were studied both from the fluid and solid mechan-cs for the maintenance and the safety management of the pipelinesn the nuclear/fossil power plants (JSME, 2005, 2012).∗ Corresponding authors.E-mail addresses: [email protected] (N. Fujisawa),
[email protected] (T. Yamagata).
029-5493/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.nucengdes.2013.07.039
© 2013 Elsevier B.V. All rights reserved.
When the liquid droplets impinge on a solid wall, the liquiddroplet deforms the shape in a very short time in an order of microseconds, which results in the generation of high impact pressure onthe surface. As the impact pressure is proportional to the dropletvelocity (Heymann, 1969), the impact pressure of the droplet caneasily increase beyond the critical strength of the carbon steelby the impingement of droplets at velocity higher than 100 m/s,which is often observed in the actual pipelines. The liquid dropletimpingement erosion is not only dependent on the droplet veloc-ity, but also on the diameter and the number of impinging dropletsin the steam flow (Sanchez-Caldera, 1984). It is known that thedeformation of the droplet causes the local shock wave on the pipewall, its reflection on the droplet’s surface, which is followed bythe occurrence of side jet having the maximum velocity of about10 times faster than the impact velocity of the liquid droplet (Field
et al., 1985). Although the result suggests the difference in theimpact phenomenon of the liquid droplet impingement from thesolid one, the physical mechanism of the liquid droplet impinge-ment erosion has not been fully clarified yet due to the difficulty in
910 N. Fujisawa et al. / Nuclear Engineering and Design 265 (2013) 909– 917
Nomenclature
c, cs speed of sound in air and solid, respectively, Eq. (3)c1, c2, c3, c4 constants, Eqs. (3) and (5)d droplet diameterdi inner diameter of sampling probeEd erosion depthf volume density distribution of dropletsHv Vickers hardness of the solid materialHvAl Vickers hardness of aluminumn power index, Eq. (3)nm number of impinging droplets in unit area and unit
timep hardness of materialP pump pressuret timeQ0 bulk flow rateq local volume fluxV droplet velocityV0 velocity at nozzle exitVm erosion rateVme experimental erosion rateVmp predicted erosion rateVr radial velocity at end of specimenx coordinate along spray centerliney vertical coordinate normal to axial directionz horizontal coordinate normal to axial direction� density of liquid� kinematic viscosity of air
ts
ittrimo(ipatwasr(2IAlilamtidrs
2. Experimental apparatus
he observation of liquid droplet impingement, because it is a veryhort time phenomenon within 1 �s.
Heymann (1979) reported the summary of the liquid dropletmpingement tests conducted at some research institutes. Most ofhe tests were carried out using an experimental apparatus usinghe rotating disk, which is featured by the evaluation of highly accu-ate droplet velocity by rotating the arm with the test specimen ont. The droplet diameter tested was larger than 1 mm, which was
uch larger than that expected in the actual pipelines of an orderf tens of micrometers, evaluated in the steam flow test by Morita2007). It is reported that the erosion rate of the metal materials proportional to 4.8th power of the droplet velocity and 3.67thower of the droplet diameter using the multiple linear regressionnalysis (ASTM G73-98, 2005). Note that the power dependence onhe droplet diameter is slightly larger than the theoretical value 3,hich may reflect the inaccuracy in droplet diameter measurement
nd the number of impinging droplets in the analysis. Since then,everal experimental studies on the erosion rate of metal mate-ials have been carried out by using the rotating disk apparatusItoh and Okabe, 1993), water-jet apparatus (Hattori and Takinami,010), and spray-jet apparatus (Shinogaya et al., 1987; Miyata and
somoto, 2008; Isomoto and Miyata, 2008; Fujisawa et al., 2012b).mong these tests, the spray-jet apparatus allows the evaluation of
iquid droplet impingement erosion of small droplet diameter hav-ng an order of tens of micrometers and in a similar situation of theiquid film on the actual pipeline (Fujisawa et al., 2012b), so that thispparatus has a potential to be used as the liquid droplet impinge-ent test for application to the pipe-wall thinning study. Although
he droplet diameter in the erosion tests is an important parameter,t was not always measured in the previous experimental studies
ue to the difficulty in the measurement with high accuracy. It isecommended that the droplet diameter near the droplet impacthould be measured by optical techniques (Takano et al., 2011)Fig. 1. Experimental apparatus for liquid droplet impingement erosion.
for future use of the experimental data in the prediction of liquiddroplet impingement erosion (Li et al., 2012).
According to the theoretical consideration on the liquid dropletimpingement erosion, the erosion rate is proportional to 4thpower of the droplet velocity (Sanchez-Caldera, 1984), while thepower index is reported as 4.8 in the experiments summarizedby Heymann (1979). When the contribution of the flow rate onthe erosion rate is taken into account, these power indices mayincrease to 5 and 5.8, respectively, assuming that the flow rateis proportional to the droplet velocity. On the other hand, thepower indices in recent experimental studies are reported as 6–8by Itoh and Okabe (1993), 4 by Miyata and Isomoto (2008), 6–7.4by Hattori and Takinami (2010), 7 by Fujisawa et al. (2012b). Thus,there is a large scattering of the power indices among the experi-ments in literature, which might be caused by the variations of theexperimental conditions, such as the type of experimental appara-tus, droplet properties, erosion stages, test materials, and so on. Itshould be mentioned that erosion rate in the terminal stage, whichwas most important parameter in the pipe-wall thinning, had onlybeen measured by Itoh and Okabe (1993), while the maximum ero-sion rate was used for the representative of the thinning rate byother researchers. This may be due to the time consuming tests oferosion to acquire the experimental data in the terminal stage oferosion. According to the critical examination of the previous stud-ies of liquid droplet impingement erosion (Fujisawa et al., 2012a),the difference in the power indices of droplet velocity is expectedto be due to the influence of the liquid film over the test specimen.On the other hand, the influence of liquid film on the erosion ratehas been numerically studied by Ikohagi (2011) and Xiong et al.(2011), using the coupled analysis of a single droplet impingementon a solid plate considering the propagation of the pressure wavein the solid. The numerical result by Ikohagi (2011) shows that thepower index of the droplet velocity on the erosion rate is increasedfrom 5.3 (dry) to 7.7 (wet) by the presence of liquid film sprayedover the test specimen. However, it has not been validated yet byexperiment.
The purpose of this paper is to study the relationship betweenthe erosion rate and the droplet properties using the high-speedconical spray jet under various liquid film conditions. The erosionrate is measured in the terminal stage by the high-speed sprayimpinging on the test specimen of various diameters and stand-off distances to understand the influence of the liquid film. Thesevariations in experimental conditions allow the evaluation of liquidfilm thickness distributed on the test specimen. Then, the influenceof the liquid film on the erosion rate is studied theoretically andthe erosion model for predicting the liquid droplet impingementerosion is proposed.
Fig. 1 shows the experimental apparatus for the study of liq-uid droplet impingement erosion. This apparatus consists of high
N. Fujisawa et al. / Nuclear Engineering and Design 265 (2013) 909– 917 911
pnitoj
dt3czieC2sru
a5sbtefgw
3
3
s(ft6iant4
Fig. 2. Structure of conical spray nozzle.
ressure plunger pump (maximum pressure 35 MPa), conical sprayozzle, test specimen of aluminum material and water tank (0.58 m
n diameter and 0.84 m in height). Note that the filter is placed inhe upstream of the pump to remove the dust in the working fluidf water. The pump pressure is measured by pressure meter locatedust downstream of the pump.
The conical spray nozzle used in this experiment is newlyesigned for the present experiment. It consists of a fan type sprayip combined with the straight pipe section (3 mm in diameter and0 mm long), which is shown in Fig. 2. The present nozzle designomes from the fact that there is no commercial conical spray noz-le available for the droplet velocity higher than 200 m/s expectedn the actual pipeline. The commercial fan type spray tip has anlliptic exit shape having a minimum dimension of 0.6 mm (Ikeuchio., VNP 2525), which can provide the droplet velocity larger than00 m/s. The spray pattern changes from the fan to conical in thetraight pipe section downstream of the nozzle. The volume flowate of the spray is evaluated from the direct measurement of vol-me flow rate of water to the tank.
The test specimen is made of aluminum material (A1070). It has cylindrical geometry having a diameter ranging from 2.5 mm to
mm with the same height 10 mm, as shown in Fig. 2. The erosionurface of the test specimen is machined smoothly and polishedy sandpaper #1000. In order to remove the work hardening ofhe test specimen, the heat treatment was carried out before therosion experiment. The test specimen was heated in an electricurnace at the temperature 470 K for 1 h, which is followed by theradual cooling in the furnace. The hardness of the test specimenas found to be Hv = 30 in Vickers hardness.
. Measurements of droplet properties
.1. Droplet velocity
The measurement of droplet velocity was carried out using thetandard PIV system, which consisted of pulsed Nd:YAG lasers50 mJ/pulse), a high speed CMOS camera with frame straddlingunction (1280 × 1024 pixels with 8 bits) and a pulse genera-or for synchronizing the camera and lasers. The target area is0 mm × 50 mm to cover the whole area of interests in the spray. An
llumination was provided to visualize the central cross-sectional
rea along the spray axis using a laser sheet of 1 mm in thick-ess. The sequential two images of the spray were captured in aime interval of 1 �s, which allows the maximum displacement of–5 pixels of the droplet images.Fig. 3. Experimental setup for measurement of droplet diameter.
The droplet velocity is evaluated from the direct cross-correlation analysis using the two sequential images. Theinterrogation area in the analysis is set to 31 × 31 pixels, and thesub-pixel analysis is introduced to obtain a high accuracy in thevelocity measurement (Kiuchi et al., 2005). A number of invalidvelocity vectors were found less than 1% of the measured veloci-ties of the spray, and the uncertainty of velocity measurement wasestimated to 3% of the maximum velocity in the image.
3.2. Droplet diameter
The measurement of droplet diameters of the spray was carriedout using the shadowgraph technique combined with the digitalimage analysis (Fujisawa et al., 2012b). The experimental setupis shown in Fig. 3(a) and (b). The illumination was provided fromthe in-line arrangement of the pulsed Nd:YAG lasers (50 mJ/pulse).After expanding the laser beam conically, the volume of light passedthrough the frosted glasses before entering into the test section. Thein-line images were taken by the CCD camera (1008 × 1018 pixelswith 8 bits) with a long-focal-length-lens (F4.5, f310 mm). The tar-get area of measurement was 2 mm × 2 mm, so that the depth offocus in the test section was 90 �m (Raffel et al., 1998). The exper-imental setup for shadowgraph method is basically the same asthat reported by Fujisawa et al. (2012b). The main difference in thepresent experiment comes from the conical development of thespray, while it is in a fan-like development of the spray in the pre-vious study (Fujisawa et al., 2012b). Due to the difference in thespray geometry, a large number of spray droplets blocked the in-line observation of the droplets near the spray axis in the presentexperiment. In order to overcome this difficulty, a slit is designedto remove the outer spray structure, which acts as a noise in themeasurement of droplet diameter near the spray axis. The dropletsremoved by the slit structure are separated from the core of thespray jet by the triangular rods attached on both sides of the slitbefore passing through the slit. Note that the slit width is 5 mmand the height of the triangular rods is 10 mm, which are illus-trated in Fig. 3(b). It should be mentioned that the shadowgraphimages having lower gray level intensity are removed in the analy-sis, because they often acted as a noise in the analysis of the droplet
sizing. After these improvements in the experimental method andthe analysis, the measurements of droplet diameters near the sprayaxis of the conical spray are successfully carried out in the presentexperiment. It should be mentioned that 1000 images were taken
9 ering and Design 265 (2013) 909– 917
add
3
usdttitltbn(
q
EpiieemtTittwv
3
dfl
V
Tgtowbse
4
4
(scccid
Fig. 4. Spray images: (a) side view; (b) top view.
pressures ranging from P = 24 to 33 MPa. The experimental resultshows that the droplet velocity decreases gradually downstreamdue to the drag force acting on the droplets in the air, while thenormalized droplet velocity increases slightly with an increase in
Table 1Nozzle exit velocity V0 and bulk flow rate Q0 for various nozzle pressures P.
P (MPa) V0 (m/s) Q0 (m3/s)
12 N. Fujisawa et al. / Nuclear Engine
t every 1 s for the statistical analysis of the droplet diameter. Theetails of the image analysis to obtain the droplet diameter wereescribed in Fujisawa et al. (2012b).
.3. Local volume flux
The local volume flux q of the high-speed spray was measuredsing the sampling probe method (Fujisawa et al., 2012b). Theampling probe was made of a stainless steel pipe having an inneriameter di = 2 mm with 30 mm in length. This probe was placed onhe spray-jet axis to measure the local volume flux. The probe wasraversed in horizontal and vertical directions using the travers-ng mechanism. The local volume flux was evaluated by measuringhe net weight of the water flow through the probe. The samp-ing time was set to 10–20 s to obtain enough sampling volume forhe measurement of local volume flux. The local volume flux q cane expressed by the mean droplet volume �/6d3 (mm3) times theumber of impinging droplets in a unit area and a unit time nm
1 mm–2/s), which is written as follows:
= �
6d3nm (1)
q. (1) implies that the local volume flux combines two dropletarameters, such as the droplet diameter d and the number of
mpinging droplets nm, which are difficult to measure accurately,nto one parameter. This suggests that the local volume flux is anffective parameter for the study of the liquid droplet impingementrosion. The uncertainty in the measurement of local volume fluxay arise from the friction loss through the sampling probe and
he pressure loss due to the secondary flow in the curved section.herefore, the pipe diameter and the length are considered to bemportant parameters in the probe design. It should be mentionedhat the measurement of volume flux was almost independent ofhe pipe diameter of the sampling probe in the range of 1.5–2.5 mm,hich supported the validity in the present measurement of local
olume flux (Fujisawa et al., 2012b).
.4. Erosion rate
The non-dimensional erosion rate Vm is defined by the erosionepth Ed of the test specimen in a unit time t over the local volumeux q, which is expressed by the following equation:
m = Ed
qt(2)
he non-dimensional erosion rate Vm is directly obtained from theradient of the erosion depth Ed versus the local flow volume qt ofhe spray. Therefore, Vm can be evaluated without the informationf droplet diameter d and the number of impinging droplets nm,hich are rather difficult to measure with high accuracy. It should
e mentioned that the erosion depth Ed is evaluated from the mea-urement of the weight loss of the specimen using a high precisionlectric weight-meter having an accuracy of 0.1 mg.
. Results and discussion
.1. Spray images
Fig. 4(a) and (b) shows the spray images taken by a CCD camera1018 × 1008 pixels) located in orthogonal directions normal to thepray axis, which allows the visualization of horizontal and verti-al images of the spray, respectively. Note that the observation was
arried out at the nozzle pressure 24 MPa. These images show theircular development of spray downstream of the nozzle, cover-ng the distance x = 0–300 mm. The spray spreads in a small angleownstream of the nozzle with almost the same spreading angles inFig. 5. Downstream variations of droplet velocity V/V0.
horizontal and vertical directions, which suggests the modificationsof the fan type spray to the conical one by the straight pipe sectionattached to the spray tip. It should be mentioned that the originalspray angle of the fan type spray tip was 25◦ in vertical direction and2◦ in horizontal direction (Fujisawa et al., 2012b). The downstreamdevelopment of the spray indicates that the number of impingingdroplets in a unit area decreases downstream, on the condition thatthe merging and separation of the droplets does not occur in thespray. It should be mentioned that the width of the spray increasedfrom 3 mm to 15 mm in the development of 150 mm downstream ofthe nozzle. Therefore, the size of the test specimen 2.5–5 mm testedin this experiment is considered small enough compared with thespray width in the test section (x = 150–240 mm) downstream ofthe nozzle.
4.2. Droplet characteristics
Fig. 5 shows the downstream variations of the droplet velocityalong the spray centerline measured by PIV. The droplet veloc-ity is normalized by the nozzle exit velocity V0 evaluated fromthe Bernoulli equation using the nozzle pressure, which is shownin Table 1. The experiments were carried out for various nozzle
24 219 1.13 × 10−4
27 232 1.24 × 10−4
30 245 1.32 × 10−4
33 257 1.38 × 10−4
N. Fujisawa et al. / Nuclear Engineering and Design 265 (2013) 909– 917 913
F
tcptp
dzmiptc∼two
vnbwuia3uvivv
ig. 6. Volume density distribution f for various standoff distances (P = 24 MPa).
he nozzle pressures, which might be due to a decrease in the dragoefficient of droplets at higher Reynolds numbers. Note that theresent results indicate that the droplet velocity ranges from 145o 168 m/s in the test section, which agrees with that of the actualipelines.
Fig. 6 shows the volume density distribution of the sprayroplets at various standoff distances x = 150–240 mm at noz-le pressure P = 24 MPa, which is measured by the shadowgraphethod. The result shows that the droplet diameter of the spray
s ranging from 0 to 100 �m and the distribution is almost inde-endent of the standoff distance (x = 150–240 mm). It is found thathe volumetric median diameter, which corresponds to 50% in theumulative volume number density distribution, is estimated as30 �m in the range of the present experiment. It should be men-
ioned that the volume density distribution of the spray dropletsas found to be independent of the nozzle pressures in the range
f P = 24–33 MPa.Fig. 7 shows the downstream variations of the normalized local
olume flux q/Q0 of the droplets along the jet centerline for variousozzle pressures P ranging from 24 to 33 MPa, which is measuredy the sampling probe. Note that Q0 is a bulk flow rate of the spray,hich is shown in Table 1. These results indicate that the local vol-me flux q/Q0 along the spray centerline decreases about 30% by
ncreasing the distance from x = 150–240 mm, while they increasebout 15% with increasing the nozzle pressures P from 24 MPa to3 MPa. It should be mentioned that the decay rate of the local vol-me flux (Fig. 7) is about 8 times larger than that of the dropletelocity (Fig. 5). This result suggests that the number of imping-
ng droplets decreases downstream much faster than the dropletelocity due to the lateral spreading of the spray, because the localolume flux q is proportional to the number of impinging dropletsFig. 7. Downstream variations of local volume flux q/Q0.
Fig. 8. SEM observation on erosion surface (P = 24 MPa, x = 150 mm, D = 5 mm).
nm assuming that the droplet diameter d is kept constant in Eq.(1). Note that the measurement of local volume flux without testspecimen is used as that on the test specimen.
4.3. Observation of erosion surface
Fig. 8(a) and (b) shows the SEM observation on the erosion sur-face of the aluminum material in the liquid droplet impingementtest after the test period of 1 h. The visual observations are madeby SEM microscope with the magnification factor of 20 and 200,respectively. The erosion test was carried out using the high-speedspray at the nozzle pressure P = 24 MPa and the standoff distancex = 150 mm. Note that the diameter of the test specimen is 5 mmin diameter. These observations show that the erosion surface ismade of many pinholes of several tens of �m in diameter, whichis about the same size as the droplet diameter (Fig. 8(b)). On theother hand, they also indicate the presence of macro structure ofseveral hundreds of �m in diameter (Fig. 8(a)). It should be men-tioned that these structures on the erosion surface did not changeso much with the variations of nozzle pressures, standoff distances,and specimen diameters in the range of present experiment.
4.4. Non-dimensional erosion rate
Fig. 9 shows the variations of the erosion depth Ed of the testspecimen with the local flow volume qt of the spray jet at variousnozzle pressures P ranging from 24 to 33 MPa, where q is a localvolume flux in a unit area and t is a time. An example of the exper-
imental results is shown here at the standoff distance x = 150 mmand the specimen diameter 5 mm. It is found that the erosion depthincreases almost linearly with an increase in the local flow volumeqt except for the initial stage of erosion, where the erosion rate
914 N. Fujisawa et al. / Nuclear Engineering and Design 265 (2013) 909– 917
F(
ceedatUtegeermHssciwfap
tifiewa
Fx
ig. 9. Erosion depth Ed versus local flow volume qt for various nozzle pressures Px = 150 mm, D = 5 mm).
hanges gradually from zero to a constant gradient. Note that therosion surface changes from smooth to rough during the initialrosion stage. It is seen that the erosion rate reaches a constant gra-ient after the initial erosion stage and the erosion rate becomeslmost constant in the later stage of erosion. The result also showshat the erosion rate increases with the growth of nozzle pressures.sually, the erosion stage of the liquid droplet impingement goes
hrough the incubation, acceleration, maximum erosion rate, decel-ration before reaching the terminal erosion stage, where the linearrowth of erosion is observed (Itoh and Okabe, 1993). The initialrosion stage in the present experiment corresponds to the first 3rosion stages before approaching the terminal erosion stage. Theeason why the terminal stage is so clearly observed in this experi-ent is due to the use of aluminum material with smaller hardnessv = 30 than that of the carbon steel Hv = 150, which has often beentudied in the previous studies. It should be mentioned that the ero-ion rate in the liquid droplet impingement erosion of aluminuman be converted into that of the carbon steel with the use of exper-mental correlation with a hardness Hv (Miyata and Isomoto, 2008),
hich was developed from the experimental study of erosion ratesor various metal materials, such as carbon steel, stainless steel,luminum and so on, for the prediction of the erosion rate in therototype pipeline.
Fig. 10 shows the variations of the erosion depth Ed of theest specimen with respect to the local flow volume qt for var-ous standoff distances x = 150–240 mm. The nozzle pressure is
xed to 24 MPa and the specimen diameter is set to 5 mm. Thexperimental results show that all the erosion rates increasesith an increase in the local flow volume, while the erosion ratesre slightly influenced by the standoff distance x. It should be
ig. 10. Erosion depth Ed versus local flow volume qt for various standoff distances (P = 24 MPa, D = 5 mm).
Fig. 11. Erosion depth Ed versus local flow volume qt at various specimen diametersD (P = 24 MPa, x = 150 mm).
mentioned here that the local volume flux decreased with thestandoff distance increased (Fig. 7), because the number densityof droplets decreased at larger standoff distances. This suggests adecrease in the liquid film thickness on the test specimen at largerstandoff distances. The influence of the liquid film on the erosionrate will be discussed in Section 4.5.
Fig. 11 shows the relationship between the erosion depth Edand the local flow volume qt for various specimen diameters D ran-ging from 2.5 mm to 5 mm at the nozzle pressure P = 24 MPa withthe standoff distance fixed to x = 150 mm. All the erosion depthsincrease linearly with an increase in the local flow volume exceptfor the initial stage of erosion. It is found from the present result thatthe erosion rate increases clearly with a decrease in the specimendiameter. Note that the variation of the erosion rate with spec-imen diameter in Fig. 11 is much larger than that with standoffdistance from x = 150 mm to 240 mm in Fig. 10. The variation of theerosion rate is expected to be due to the influence of liquid filmon the specimen surface, and the presence of thicker liquid filmwill damp the impact pressure of the droplets. For more details seeSection 4.5.
Fig. 12 shows the logarithmic relationship between the non-dimensional erosion rate and the droplet velocity for variousstandoff distances. Note that the results are shown for the spec-imen diameter D = 5 mm. The present results indicate that thenon-dimensional erosion rate increases in proportional to 6.6thpower of the droplet velocity, which is almost independent of thestandoff distances. It should be mentioned that the power index 6.6
was almost independent of the specimen diameters in the presentexperiment. The present power dependence is larger than that of4.8 by Heymann (1979) in the maximum erosion stage and that of 4Fig. 12. Erosion rate Vm versus droplet velocity V in logarithmic plot.
N. Fujisawa et al. / Nuclear Engineering and Design 265 (2013) 909– 917 915
btt
ne
V
wiECrbototst
maoiiidr
indicates that the liquid film thickness increases with the speci-
Fig. 13. Erosion rate Vm versus specimen diameter D.
y Sanchez-Caldera (1984) derived from the dimensional analysis,hough it is within the experimental scattering of the data 5–7 inhe terminal stage of erosion by Itoh and Okabe (1993).
According to the dimensional analysis by Ikohagi (2011), theon-dimensional erosion rate Vm can be expressed by the followingquation:
m = c1Vn(
�c
pcs
)n/2(3)
here c is speed of sound in liquid, cs is speed of sound in solid, ps hardness of material, � is density of liquid and c1 is a constant.q. (3) is similar to the non-dimensional erosion rate by Sanchez-aldera (1984), but it allows the use of arbitrary power index n withespect to the droplet velocity V. The power index n of Eq. (3) cane fixed to 6.6 in reference to the present experimental data. On thether hand, the erosion rate increases slightly with an increase inhe standoff distances, as seen in Fig. 12. This is due to the influencef the liquid film on the specimen surface. The damping effect ofhe droplet impact due to the liquid film becomes weak at largertandoff distance x = 240 mm, where the liquid film is thinner dueo the reduced number density of droplets.
Fig. 13 shows the variations of the erosion rate Vm with the speci-en diameter D. The results are shown for various nozzle pressures
t fixed standoff distance x = 150 mm (a) and for various stand-ff distances at fixed nozzle pressure P = 24 MPa (b). These resultsndicate that the erosion rate decreases with an increase in the spec-men diameter D, while the erosion rate increases with an increase
n the standoff distances. However, the influence of the standoffistance is marginal due to the experimental uncertainty. All theesults indicate that the erosion rate varies with the specimenFig. 14. Liquid film thickness versus specimen diameter D.
diameter and the standoff distance due to the influence of liquidfilm on the specimen diameter, as was mentioned in Figs. 10 and 11.
4.5. Effect of liquid film on erosion rate
In order to understand the influence of the liquid film on theerosion rate, the theoretical consideration is focused on the esti-mation of a liquid film thickness h. The liquid film thickness can beapproximated by the following equation, assuming that the totalvolume of the spray impinging on the specimen surface exits fromthe end of the specimen in radial direction from the conservationof mass:
h = Dq
4Vr(4)
where Vr is the radial velocity exits from the end of the specimen. Inthe framework of this study, the radial velocity Vr is assumed equalto the droplet velocity V impinging on the specimen surface as a firstorder approximation, because the major influence of the liquid filmcomes from the specimen diameter D and the local volume flux qin Eq. (4). It should be mentioned that the radial velocity is difficultto measure, because it is a thin film of an order of �m.
Fig. 14 shows the liquid film thickness h in relation to the spec-imen diameter D for various nozzle pressures at fixed standoffdistance x = 150 mm (a) and for various standoff distances at noz-zle pressure P = 24 MPa (b). Note that the liquid film thickness isobtained from Eq. (4) by assuming that the exit velocity Vr of theliquid film is equal to the droplet velocity V. The present result
men diameter D, while it increases with the droplet velocity V anddecreases with the standoff distance x. It should be mentioned thatthe increase in the liquid-film thickness results in larger damping
916 N. Fujisawa et al. / Nuclear Engineering
F
ois
4
le
V
wncatbmc−hirr(tl
dd
ig. 15. Correlation between experimental Vme and predicted erosion rates Vmp .
f the impact pressure. Therefore, the reduction in the erosion rates expected in thicker liquid film on the specimen surface, as wasuggested in the numerical simulation by Ikohagi (2011).
.6. Erosion model
The experimental erosion rate Vm of any solid material due to theiquid droplet impingement erosion is formulated by the followingquation considering the influence of the liquid film:
m = c2
(Hv
HvAl
)−3.3· V6.6 ·
{1 + c3
(h
d
)}c4
(5)
here c2, c3, c4 are empirical constants and Hv is the Vickers hard-ess of solid material and HvAl is that of aluminum. The empiricalonstants c2, c3, c4 are determined as c2 = 9.11 × 10−20, c3 = 92.2,nd c4 = −1.3 by fitting the experimental data. Note that the func-ional form of Hv was determined in reference to the experimentsy Miyata and Isomoto (2008), who carried out the erosion experi-ents for various kinds of metal materials, such as aluminum alloy,
arbon steel, stainless steel and mild steel, and found a power index2.75 with respect to the Vickers hardness for the droplet velocityigher than 100 m/s. This power index was slightly modified to −3.3
n the present study in considering the non-dimensional erosionate in Eq. (3). The damping function in Eq. (5) was introduced ineference to the study by Ikohagi (2011) and Morita and Uchiyama2011). It should be mentioned that the constant c3 was much largerhan 1, which might imply that the radial spreading velocity of the
iquid film on the test specimen was lower than the impact velocity.Fig. 15 shows the correlation between the experimental and pre-icted erosion rates obtained from Eq. (5) with and without theamping function. It is found that the correlation with the damping
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function (Fig. 15(a)) is well converged on a line within a factorof 1.3, while the predicted result diverged to a factor of 2 for thecorrelation without the damping function (Fig. 15(b)). This resultsuggests that the damping function plays an important role for theprediction of liquid droplet impingement erosion, which supportsthe reliability of the correlation formula given by Eq. (5).
5. Conclusions
The liquid droplet impingement erosion is experimentally stud-ied using the high-speed conical spray under the condition that thecircular specimen is smaller than the spray diameter. The erosionrate in the terminal stage of liquid droplet impingement erosion isevaluated from the experimental data. The influence of the liquidfilm is realized by varying the specimen diameter and the distancefrom the nozzle, which is closely related to the local volume flux ofthe spray. The characterization of the droplet properties is carriedout using the PIV for droplet velocity, the sampling probe for localvolume flux and the shadowgraph method for the droplet diam-eter. It is found that the erosion rate increases with decreasingthe specimen diameter and increasing the standoff distance. Theseexperimental results combined with the theoretical considerationon the characteristics of the liquid film lead to the conclusion thatthe erosion rate increases with the decrease in the liquid filmthicknesses. Based on the experimental data, the erosion model isproposed for the prediction of erosion rate due to the liquid dropletimpingement considering the influence of the liquid film. The pre-dicted erosion rate is well correlated with the experimental datawith a factor of 1.3, which is correlated much better than the pre-diction without the damping function, which is scattering with afactor of 2.
Acknowledgements
This research was supported by the project for the safety main-tenance of aged nuclear power plants by the Safety Board in thefiscal year 2007–2010 and also Grant-in-aid for Scientific ResearchB (No. 24360391) in the fiscal year 2012. The authors would liketo express thanks to Prof. T. Ikohagi from Institute of Fluid Sci-ence, Tohoku University, Dr. F. Inada and Dr. R. Morita from CentralResearch Institute of Electric Power Industry for the helpful discus-sion on this topic and also to Mr. D. Hama from Graduate Schoolof Science and Technology, Niigata University for the help in thepreliminary stage of experiment.
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