E-Journal of Advanced Maintenance Vol.4 No.2 (2012) 79-87
Japan Society of Maintenology

Critical Consideration on Wall Thinning Rate by Liquid Droplet
Impingement Erosion
Nobuyuki FUJISAWA1,*, Ryo MORITA2, Akira NAKAMURA3 and Takayuki
YAMAGATA 1
1

Visualization Research Center, Niigata University, Niigata 950-2181, Japan
Central Research Institute of Electric Power Industry, Tokyo, 201-0004, Japan
3
Institute of Nuclear Safety System Inc., Fukui, 919-1205, Japan
2

ABSTRACTIn this paper, the experiments on the wall thinning rate by the liquid droplet impingement in literature arestudied by examining the erosion process, the method of erosion tests and the measurement accuracy of droplet
velocity. Although the wall thinning rates scatter among the researchers, they come to a consistent result whenthe experimental conditions are considered. The power index of droplet velocity in the wall thinning rate ranges
from 6 to 8 for the water jet and spray tests, while that of the rotating disk test shows smaller power index 5.8,
which is closer to the theoretical value 5. The difference in the power indices is expected to be due to the
influence of liquid film over the test specimen.
KEYWORDS

ARTICLE INFORMATION

Liquid droplet impingement, Erosion, Droplet velocity, Metal material,
Wall thinning rate, Nuclear power plant

Article history:
Received 3 April 2012
Accepted 7 July 20121.

Introduction

Liquid droplets are often generated in a cooling pipe of nuclear power plant due to theentrainment of liquid water from the upstream and also by the heat transfer through the pipe wall. In
the region behind the orifice and the valve in the pipeline, the velocity of the droplets is highly
accelerated due to the contraction effect. This results in the occurrence of high impact pressure on the
inner surface of the pipe due to the liquid droplet impingement. The impact pressure of the droplets
increases as high as several hundred MPa, which is beyond the elastic limit of the pipe-wall material,so that the pipeline is often damaged by the impact pressure of droplets. This phenomenon is calledliquid droplet impingement (LDI) erosion, which is known as one of the major causes of pipeline
leakage in the plants. In general, the LDI occurs on the dorsal side of the elbow in the pipe, where thedroplets cannot follow the steam flow due to the inertia of the droplets. A schematic illustration of
LDI can be seen in Fig. 1, which demonstrates the combined geometry of the flow acceleration by theorifice and the droplet impact on the outer wall of the elbow. The T-type joint and the various types ofvalves are other examples of the leakage due to LDI reported in literature [1], [2].
The impact pressure generated by LDI has been studied first by the theory of water hummer [3].
The theoretical study on the impact pressure is further extended by Heymann [4], who takes into
account the generation of shock wave by the impingement of droplets and the propagation of thepressure wave to the spreading edge of the contact point, which results in the pressure about threetimes the normal impact pressure. Later, Field et al. [5] study the process of LDI experimentally byusing the high-speed photography, and confirm the theoretical considerations on the LDI in literature.
The process of LDI consists of the generation of shock wave, the pressure wave propagation and theoccurrence of side jet (flow parallel to the surface), which speeds up to 10 times the impact speed ofthe droplets.
In order to predict the LDI erosion, the erosion model has to be established, which expresses therelationship between the erosion rate and the droplet parameters (the velocity, the diameter and the*Corresponding author, E-mail: fujisawa@eng.niigata-u.ac.jp

ISSN-1883-9894/10 © 2010 – JSM and the authors. All rights reserved.

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N. Fujisawa, et al./ Critical Consideration on Wall Thinning Rate

Fig. 1. Schematic illustration of liquid droplet impingement erosion

number of impinging droplet). Since the pioneering work by Heymann [6], there have been several
experimental studies on liquid droplet impingement erosion, such as Ito-Okabe [7], Miyata-Isomoto[8], Isomoto-Miyata [9], Hattori-Takinami [10], Hama et al. [11] and Hayashi et al. [12]. However, it
is known that these experimental results on the wall thinning rate are scattering widely. Therefore, theinvestigation into the causes of data scattering among the experiments are necessary.
In the present paper, the wall thinning rate by the LDI erosion is studied by examining theerosion process, the method of experimental tests and the accuracy of velocity measurement.

2. Erosion Process by Liquid Droplet Impingement
Typical erosion process of solid materials by the liquid droplet impingement is shown in Figs.
2(a), (b). The time variations of the erosion depth are shown in Fig. 2(a), and the wall thinning rate(the gradient of the erosion depth with time) is indicated in Fig. 2(b). These results are obtained byassuming that the test material is 12Cr steel (Vickers hardness: Hv450) and cobalt metal (Hv450) in
the empirical equations proposed by Ito-Okabe [7], which is written as follows:E  (a  bt )[1  exp{(t  t 0 ) / t s ) }](1)

where E: erosion depth, t: time and a, b, α, t0, ts are material constants. The material constants are set
to a = 0.55, b = 3.2×10-3, α = 1.2, t0 = 2, ts = 10.7 for the 12Cr steel and a = 0.38, b = 2.5×10-3, α =2.05, t0 = 0, ts = 38.2 for the cobalt metal in reference to Ito-Okabe [7]. Note that the wall thinning rate
is obtained by the time derivative of Eq.(1). These results indicate that the erosion process by LDI canbe categorized into four stages. In the incubation stage, the material surface does not change by the
LDI because of the elastic deformation of the material. In the acceleration stage, the erosion initiates
on the surface by the stress concentration beyond the fatigue limit of the material, and the wall
thinning rate increases rapidly. Then, the wall thinning rate reaches a maximum value (maximum rate
point). When the material surface becomes rough by the plastic deformation due to the LDI, the wall
thinning rate is decreased due to the cushioning effect by the presence of the liquid film over therough surface (deceleration stage). Thereafter, the wall thinning rate approaches the terminal stage,
where the erosion rate becomes a constant with respect to the time. Note that the period of the
incubation stage to the maximum rate point depends on the characteristics of the metal materials. In
the actual erosion process, the period of incubation stage to maximum rate point is considered small incomparison with the very long plant operation time. Therefore, the LDI erosion in the pipe is mostly
governed by the wall thinning rate in the terminal stage. In the past, the wall thinning rate is definedby the maximum erosion rate or the erosion rate in the terminal stage. The former definition of thewall thinning rate does not represent the average erosion rate of the pipe-wall thinning in the pipe.
Furthermore, the maximum wall thinning rate cannot be determined accurately, because the thinning
rate varies rapidly near the maximum rate point. The wall thinning rate in the terminal stage is,therefore, considered as the representative of the wall thinning rate of the LDI erosion.

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3.

Theoretical Consideration on Wall Thinning Rate

The wall thinning rate by LDI is governed by the droplet velocity V, the droplet diameter d andthe number of impinging droplets in a unit area Nm. According to the dimensional analysis by
Sanchez-Caldera [13], the wall thinning rate Vm, defined by the time variation of the erosion depth, isexpressed as follows;Vm C drop mdropV 4 N m
p 2 C 2(2)

where C: empirical constant, ρdrop : droplet density, mdrop : droplet mass, p: hardness of oxide layer, εC:
cumulative strain to damage oxide layer. Note that the number of impinging droplets in a unit area Nm
can be expressed by the number density of droplet nm multiplied by the droplet velocity V, as follows;N m  nmV

(3)

Therefore, the wall thinning rate Vm is proportional to the 5th power of the droplet velocity V andgrows linearly with the number density of droplets nm. While, the wall thinning rate Vm is proportional
to the 3rd power of the droplet diameter d, because the droplet mass is expressed as
mdrop   drop d 3 / 6 . Therefore, the droplet velocity V is considered as the most influential parameter tothe wall thinning rate Vm by LDI. It should be noted that the liquid film over the material surface is notconsidered in the theoretical analysis. However, the liquid film exists on the actual material surface of
LDI in the plant. To clarify the influence of the liquid film, the impact pressure on the solid material
by the impingement of one droplet coupled with the pressure wave propagation in the material isnumerically studied by Ikohagi [14]. He found that the impact pressure due to LDI was drasticallyreduced by the cushioning effect of the liquid film. It is also shown that the plastic volume, which
exceeds the fatigue limit of the material, is proportional to the droplet velocity to the power of 5.3
without any liquid film over the material. However, this power index increases to 7.7 by the presenceof a liquid film of 2.5 μm in thickness with respect to the droplet diameter of 100 μm [14]. This meansthat existence of the liquid film may change the dependency of the droplet velocity (power index) on
the wall thinning rate. However, the assumption on the wall thinning rate and the volume of theplastic deformation is not clarified in the present state of the art.

(a) Erosion loss versus time81

N. Fujisawa, et al./ Critical Consideration on Wall Thinning Rate(b) Erosion rate versus time
Fig. 2. Erosion process by liquid droplet impingement

4.

Experimental Consideration on Wall Thinning Rate

Most of the experiments on wall thinning rate by LDI have been conducted by one of thefollowing methods, such as the rotating disk test (Fig. 3(a)), the water jet test (Fig. 3(b)) and the spraytest (Fig. 3(c)). In the rotating disk test [6, 7], a test specimen is set on an edge of the rotating disk.
The LDI erosion occurs when the test specimen go through the spray or falling droplets during therotation of the disk. The merit of this experimental method is to evaluate directly the droplet velocity
from the rotating speed of the test specimen, so that the measurement of droplet velocity can be
conducted with high accuracy. However, it is difficult to evaluate the other droplet parameters (droplet
diameter and number density of droplets), because they are not uniform in the spray. In case of falling
droplets, the diameter of the droplets becomes as large as an order of mm, which is much larger thanthe droplets in actual plants (less than 100 μm in diameter). It should be mentioned that the thicknessof the liquid film over the material surface in the rotating disk test becomes thinner than that of theactual plant condition due to the strong centrifugal forces.
The water jet test [10] and the spray test [8, 9, 11, 12] are carried out using the high-speed water
jet injected from the high-pressure pump to wear the test specimen. The difference between water jet
test and spray test comes from the liquid structure impinging on the test specimen, which depends on
the nozzle geometry and the distance from the nozzle. In the water jet test, a circular straight nozzle isused and the water jet impinges on the test specimen instead of the droplets. Therefore, the jet column
is assumed equivalent to the droplets. Note that the droplet diameter is represented by the jet diameterin this test. The jet velocity is evaluated accurately from Bernoulli equation with the pump pressure,or from the continuity equation with the flow rate. On the other hand, the spray test has been carriedout by impinging the droplets injected from the spray nozzle [11, 12, 15]. The water jet breaks up into
the droplets in a short distance from the spray nozzle, and they hit on the test specimen. The elliptic
nozzle is effective to generate a high-speed mist flow. However, it is difficult to evaluate the droplet
velocity from the pump pressure or flow rate, because the local velocity increases near the nozzle exit
by the influence of cavitation in the nozzle, and the droplet velocity decreases gradually further
downstream due to the drag force acting on the droplet. Therefore, it is necessary to measure the local
velocity near the test specimen by non-intrusive measurement techniques, such as LDV or PIV [16].
To simulate the LDI erosion, a wet steam flow test is also conducted [17]. This method uses thewet steam flow, which is closer to the flow condition in the plant. Therefore, it is suited for the LDI
test, but the experimental cost is higher than other methods due to the necessity of the steam boiler.

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N. Fujisawa, et al./ Critical Consideration on Wall Thinning Rate(a) Rotating-type apparatus(b) Water jet(c) Spray

Fig. 3. Experimental apparatus for liquid droplet impingement erosion

5.

Dependency of Droplet Velocity on Wall Thinning Rate

The experimental results on the dependency of the droplet velocity on the wall thinning rate arereported by Heymenn [6], Miyata-Isomoto [8], Isomoto-Miyata [9], Hattori-Takinami [10], Hama etal. [11] and Hayashi et al. [12]. These results are summarized in Table 1.
Heymann [6] reported the conclusions from the LDI experiments conducted by the rotating disk
tests with spray and jet at 10 laboratories, and found that the wall thinning rate was proportional to the
5.8th power of the droplet velocity. However, the droplet diameters used in these experiments arelarger than 0.8 mm, which is much larger than the actual droplet diameters in the plants. In this test,
the thinning rate is evaluated at the maximum rate point of LDI erosion.
Ito and Okabe [7] reported the wall thinning rate of three materials, 12Cr-steel, cobalt base alloy
and Ti base alloy using the rotating disk test with spray. They reported that the wall thinning rate in
the terminal stage was proportional to the droplet velocity with the power index ranging from 6 to 8.
The experiments were conducted in two droplet velocities 400 m/s and 480 m/s, and the droplet
diameters were found to be 195 μm and 269 μm in Sauter mean diameter. However, the power index
of droplet velocity may have large uncertainty, because it is obtained from the measurements at only
two droplet velocities.
Miyata and Isomoto [8] reported the wall thinning rate from the spray test with a high pressure
pump. Although they used a circular straight nozzle with 0.4 mm in diameter, the standoff distance
was set as far as 200 mm from the nozzle to obtain the spray condition. The droplet diameter is about
100 μm, which is measured by the immersion drop sampling method. The experimental results showthat the wall thinning rate of the maximum erosion depth is proportional to the 4th power of thedroplet velocity in the terminal stage. However, the droplet velocity may not be evaluated correctly,
because it is calculated from the impact force measurement combined with the momentum theory,
which cannot be applied to the droplet impingement. They also conducted the LDI test with various
materials, carbon steel, stainless steel and brass and so on, and reported the wall thinning rate wasproportional to the Vickers hardness to the power -2.75 [9].
Hattori and Takinami [10] conducted the water jet test to simulate the LDI erosion with a circularstraight nozzle of 0.4 mm in diameter. The standoff distance was short as 12 mm from the nozzle exit.
The experiments are carried out for carbon steel, low alloy steel and stainless steel. They reported thatthe power index of the velocity was ranging from 6.0 to 7.4.
Hama et al. [11] conducted the spray test in a range of the droplet diameters from 50 μm to 120

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μm, which was measured by the shadowgraph method combined with the image analysis [17]. The
droplet velocity was evaluated from PIV measurement near the test specimen. From the tests of
Aluminum material, they found that the wall thinning rate was proportional to the 5.5th power of thedroplet velocity in the terminal stage, while the power index increases to 7.5 in the maximum rate
point. The power index of droplet velocity in the maximum rate point is larger than the terminal stage.
More recently, Hayashi et al. [12] carried out the LDI test using the spray under the condition that thetest specimen is smaller than the sprayed area, which allows a uniform thinning rate of the test
specimen by the spray test. They found that the wall thinning rate of Aluminum is proportional to thedroplet velocity to the power 8.3 in the terminal stage. The difference in the power index of droplet
velocity between two tests may be caused by the influence of erosion depth distribution by LDI.
These considerations on the wall thinning rate indicate that the power index of droplet velocity isstrongly influenced by the erosion process, the method of erosion tests and the accuracy of thevelocity measurement. The wall thinning rates obtained from the erosion volume does not need tocorrespond to those of the maximum erosion depth. This is expected to be due to the cross-sectional
distribution of the erosion depth in the water jet and the spray tests in the terminal stage. Note that thedata of the maximum erosion depth scatters largely due to the local measurement of the erosion
surface.
Considering the experimental methods, the liquid film thickness on the test specimen is expected
to be different among the rotating disk, water jet and spray tests. The liquid film thickness in therotating disk test can be thinner than that in the water jet and the spray tests. The liquid film in therotating disk test may be blown off by the influence of centrifugal forces during the calm period ofliquid droplet impingement from the nozzle. On the other hand, thicker liquid film may exist on thematerial surface in the water jet and the spray tests. This experimental condition of liquid film in thewater jet and spray tests is closer to the actual condition of LDI than that of the rotating disk test.
In summary, it is rather difficult to compare the thinning rates reported in the past literatures
directly because of the difference in the droplet diameter and the liquid film thickness. However, thefollowing conclusions can be obtained. The rotating disk test by Heymann [6] showed that the powerindex of droplet velocity is 5.8, which is close to the theoretical value 5 by Sanchez-Caldera [13]. Thisis expected to be due to the negligible influence of liquid film on the material surface in the rotating
disk test. On the other hand, the power indices of droplet velocity in the water jet and the spray tests
range from 6 to 8, which is larger in magnitude than that of the rotating disk test except for the powerindex of Miyata-Isomoto[8], where the droplet velocity may not be evaluated correctly. One of thecauses of this difference in the value of power index may come from the influence of liquid film on
the material surface. Therefore, it is considered that the experiments with relatively thicker liquid film
may have larger power index of droplet velocity. This tendency agrees qualitatively with thenumerical results by Ikohagi [14], who found the growth of the power index from 5.3 to 7.7 by thepresence of liquid film on the material surface. Although the qualitative study is conducted in the wet
steam [17], the influence of the liquid film on the thinning rate has not been clarified quantitatively. It
is, therefore, recommended to study further the wall thinning rate combined with the accurate
measurements of the droplet velocity, the droplet diameter, the number density of droplets, and tounderstand the influence of the liquid film on the wall thinning rate comprehensively.

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N. Fujisawa, et al./ Critical Consideration on Wall Thinning Rate

6.

Conclusions

This paper presents the critical consideration on the wall thinning rate of the metal materials in
the liquid droplet impingement tests in literature. The experimental data are examined by taking into
account the erosion process, the method of erosion test and the measurement accuracy of droplet
velocity. Although the power indices of the droplet velocity scatter widely among the researchers,
they come to a consistent value, when the erosion process, the liquid film thickness and the accuracyof velocity measurement are considered. The power index of droplet velocity ranges from 6 to 8 in theexperiments of water jet and spray tests, while that of the rotating disk test indicates the smaller powerindex 5.8, which is close to the theoretical value of 5. The deviation of the velocity indices among
these tests is considered to be due to the influence of the liquid film on the test specimen, which
supports the larger value of power index in the water jet and the spray tests for the pipe-wall thinningprediction in actual plants.

Acknowledgement
The authors acknowledge Dr. F. Inada from Central Research Institute of ElectricPower Industry for his suggestion on this work.

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