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The sem images showthe similar grain-boundary shape ldi ero-sion

EROSION OF A SOLID SURFACE can be resulting in the generation of an expansion

changes take place in the wall material. This

(b) Shock wave Jetting

(c)

(d)

Reflection

(e)
the material surface (Fig.15c and d

in

Ref 29). It is noted that the LDI erosion in

Liquid Droplet Impingement Erosion / 765

LDI Erosion Rate index n ranges from 6 to 7.4 in waterjet tests
(Ref 29) and from 6.6 to 7.0 in spray tests
In predicting the lifetime of pipe-wall thin- (Ref 30, 31), while it shows a lower value, n =
2 to 6 (Ref 25, 27), for the spray test. One reason
ning of nuclear/fossil power plants, the erosion
for this difference is that power index n may
rate is an important factor to be considered.
come from the influence of the liquid film and
Therefore, several experimental studies were

nuclear/fossil power plants. The erosion rate in

the accuracy of the measurement of droplet
carried out in the literature for various ranges

the terminal stage was evaluated in a spray-

velocity, while the experimental condition, such
of droplet velocity, diameter, and wall materi-
as the droplet diameter and material itself, may
als, which are summarized in Table 1. It is
change the power index (Ref 35). It is expected
noted that the power index, n, in Table 1 comes
that the experiments with relatively thicker liq-
from the erosion-rate formulation Vm ~ Vn.
uid film will result in a larger power index value.
The rotating-disk test of LDI shows the power

LDI erosion (Ref 31). The spray consists of

This result agrees qualitatively with the numeri-
index n = 5.8 (Ref 22), which is approximately

liquid droplets of an average diameter of

cal results (Ref 11), in which the power index
equal to the theoretical value of 5 (Ref 23). How-
increases from 5.3 to 7.7 with increasing liq-
ever, a bit higher power index, n = 6 to 8, is
uid-film thickness on the material surface. These
observed in other rotating-disk testing (Ref 24). pure
(A1070), aluminum
experimental erosion-rate results indicate that
It is noted that the minor influence of the liquid

(A5056), brass (C3604), carbon steel (S20C),

power index n scatters in the range 2 to 8 due
film can be observed in this type of experiment, mild steel (SS400), and

stainless

steel
to the influence of experimental conditions
because of the high centrifugal forces in the
rotating-disk test. On the other hand, the power
Crack

mental results of power index n are shown in

Table 2. Although there is a minor variation

Fig. 2
Table 1

Droplet velocity

6–8 (terminal stage) Rotating disk
1310, 1575 195–269 12Cr steel, cobalt-base alloy, titanium alloy
speed) (rotating speed)

sampling method

3.3–5
366–580 1200–1900 90 X20Cr13, X5CrNiMoCuNb 14-5, Ref 26
5.5–6 (<100 m/s, or 330 ft/s)2–3

Spray

85–256 (impact force)

280–840
Ref 27
45–130 MgO, Al2O3, Si3N4, SiC, ZrO2, GS, TiN,
410J1

sampling method

Table 2 Power index, n, for droplet velocity dependence

Material n (D = 1.5 mm, or 0.06 in.) n (D = 2.5 mm, or 0.10 in.)
A1070 7.0 (±0.4) 7.4
A5056 9.0 (±0.5) 8.9
C3604 5.6 (±0.9) 4.9
SS400 7.0 (±0.4) 6.8
S20C 6.6 (±0.5) 7.0
Average 7.0 7.0

Source: Ref 34

erosion depth, the erosion rate

h [ – ]

1.2

Present (a = 3.52, b = 0.5)
sharply, and the gradient of the erosion rate
decreases gradually with further increasing of
Sasaki et al. (2016)
the erosion depth. In the asymptotic condition
of erosion depth larger than 5 mm (0.2 in.),
Xiong et al. (2010)
the erosion rate approaches almost zero. This Present (100 m/s)
indicates that erosion is highly damped by the
Present (200 m/s)
effect of the liquid pool in the deep cavity,
and erosion cannot proceed further. Present (300 m/s)
of surface roughness on LDI erosion and the Fig. 5 Variation of damping coefficient, Z, with nondimensional liquid-film thickness, k. Note that the range
complexity of the erosion mechanism of the
bar indicates the minimum to maximum of Z in Sasaki et al. (2016) in the velocity range from 100 to
wall material under the combined influence of
surface roughness and liquid film. However,
This result indicates that the influence of sur-face roughness is to reduce the incubation

as the liquid-film thickness prevailing over

the wall material. Fig. 6

Attenuation factor, f, versus erosion depth, Ed. Source: Ref 36

Kirols et al. carried out an SEM observation
roughness (D/d = 0.5) of the V-groove is Fig. 7

sandpaper grit number

Sandpaper grit number Dmax, mm
30
50
100
500
1000
Smooth

shown in Fig. 8, which shows SEM images of

the V-groove after the start of the erosion test. Fig. 8 Scanning electron microscopy observation of single V-groove of small relative roughness (D/d = 0.5).
The groove depth is D = 15 mm and the width
is 30 mm, while the droplet diameter is d = 30
mm (see the scale bars on the images). After
be mentioned that there were several microme-
ter-order grooves on the smooth surface due to
the milling machine surface tracers, although

they did not influence the erosion pattern. This

Flow
meter

Super-
heater

Control
valve

T P T Q 2. Cooling system (wetness control)
Q

eroded wall highly suppresses the erosion rate,

which is different from the thin liquid film, and

Heat exchanger
Wet steam

water heater, an orifice was installed at the inlet of the pipeline, and some elbows were

placed downstream of the orifice. The diameter
of the bent pipe was approximately 150 mm
(6 in.), and the thickness was 7.1 mm (0.28
in.). The details of the piping geometry and
flow conditions of the vent line are summar-

Table 4

Summary of liquid droplet impingement erosion models

Equation of empirical model Reference
log(Re) = 4.8log(V) + 0.67log(d) � log(NER) + ch Re: rationalized erosion rate

Heymann (1979) (Ref 22)

ec: critical strain to fracture of oxide layer (Ref 61) T.R. = ci q HV�2.75V2
q: droplet flow rate

Isomoto and Miyata (2008) (Ref 25)

HV: Vickers hardness
V: velocity

Condenser

11 mm

Orifice

Morita and Uchiyama (2011) Fig. 11 Geometry of steam vent line in Japanese

n: 7.0 (Ref 34)

power plant and erosion-hole geometry.
T.R. = cm qHV�2.75V2fm(h/d)

Source: Ref 62

(Ref 56)

770 / Wear Failures

or 920 ft/s) at the orifice, which is due to the higher power index of the velocity and no liq-
entrainment of condensed water droplets from uid-film effect. This resulted in much higher
the heater. These conditions resulted in erosion erosion in the numerical prediction. The pre-
on the first elbow downstream of the orifice and dictions by Morita and Uchiyama (Ref 56)
then led to the pinhole leak. An enlarged view and Fujisawa et al. (Ref 36) showed a lower
in Fig. 11 shows the geometry of the erosion hole erosion rate than the others. This may be due

the influence of liquid film and surface rough-

in the elbow. This hole was situated at an angle to the influence of the liquid film, which was

ness, and also the prediction of LDI erosion

of 42�from the elbow inlet and had dimensions
of 11 mm (0.43 in.) in the axial direction and
9 mm (0.36 in.) in the circumferential direction

nism of erosion damage is thoroughly under-

of the elbow. Note that the inner surface around

stood and is applicable to the prediction of

the hole showed a sawtoothlike pattern spread
over the outer bent wall.
The numerical prediction of erosion in the occur at the location of high-speed steam flow
pipeline was carried out by Fujisawa et al. with a flow direction change, such as an elbow,

ing-edge erosion on turbine blades under the

(Ref 49), who showed the erosion-rate distri- downstream of a valve and orifice, or at a

influence of surface roughness. For this to be

butions of this flow geometry. The prediction T-junction. Moreover, even if the flow is a sin-
was carried out using various empirical erosion gle-phase water flow, droplet impingement
models, such as Heymann (Ref 22), Isomoto may occur downstream of the valve or orifice
and Miyata (Ref 25), Morita and Uchiyama due to flashing when the local pressure is
(Ref 56), and Fujisawa et al. (Ref 36). In the lower than the vapor pressure. Erosion-rate

porosity, cracks, or erosion craters). The phys-

numerical simulations, the flow fields were prediction is becoming an important tool

ics of the initiation of LDI erosion and the

because it can provide the location and
evaluated from three-dimensional single-phase
expected erosion depth in advance. How to
numerical simulations with the aid of a stan-
avoid erosion initiation and further develop-
dard k-e turbulence model, and the droplet
ment of the erosion rate in the pipeline is the
parameters, such as the droplet velocity, num-

next consideration.

ber density, and impingement angle, were

will trigger the laminar-turbulent transition of

evaluated from the flow computation. It is
velocity (flow rate) is highly effective, because
noted that the influences of droplet velocity
the velocity (flow rate) is the most influential
dependency, material hardness, and liquid-film
parameter on the erosion rate. This can be car-
thickness are major differences among these
ried out by increasing the pipe diameter.

ACKNOWLEDGMENTS

empirical models, and all are considered in
Decreasing the steam wetness (number density
the models of Morita and Uchiyama (Ref 56)
and Fujisawa et al. (Ref 36). of the droplet) by installing a separator or
Figure 12 shows a comparative study of the heater is another effective suppression method

This article was revised from R.H. Richman,

prediction results of maximum erosion depth for LDI erosion; this is because of the decrease
in the elbow for various empirical models. in droplet collision frequency. For a practical
All of the results indicate that the erosion countermeasure, a change in piping layout near
depth increases gradually with increasing the collision location, for example, installation
elapsed time; however, the absolute values of a target plate or thicker piping element, is

Research Institute of Electric Power Industry),

clearly deviate from each other. Heymann’s effective in decreasing the leak frequency due

Dr. T. Yamagata (Niigata University), and Dr.

model (Ref 22) indicated an erosion rate that to LDI erosion. A change of material can also
was much higher than those of the other mod- act to decrease the erosion rate; however, it is
els, which may be due to the assumption of a

and Prof. M. Medraj (Concordia University)
is also acknowledged. This work was carried
out during the first author’s stay at Brown Uni-

Book of ASTM Standards, ASTM Interna-

Fig. 12

Time variation of maximum erosion depth, Edm, for various erosion models. Source: Ref 49

46. V.N. Varavka and O.V. Kudryakov, Regu-

57. S. Hattori, R. Nakamura, and G. Lin,

larities of Steel Wear under the Impact of

Impingement Erosion, Trans. JSME, Vol

tial Stage of Droplet Impingement Erosion,

52. M.H. Keegan, D.H. Nash, and M.M. Stack,
J. Friction Wear, Vol 36, 2015, p 71–79
47. V.N. Varavka and O.V. Kudryakov, Regula-

Prediction of Erosive-Corrosive Wear in

rities of Steel Wear under the Impact of Dis-

D, Appl. Phys., Vol 46, 2013, p 383001
53. A. Sareen, C.A. Sapre, and M.S. Selig, IEEE Power
1987,

Developed Droplet Impingement Erosion, J.

Effects of Leading Edge Erosion on Wind

Friction Wear, Vol 36, 2015, p 153–162
48. R. Morita, K. Yoneda, and F. Inada,

Mitigation of Erosion-Corrosive Wear in

Development of Evaluation System for

54. A. Castorrini, A. Corsini, F. Rispoli, P.
Liquid Droplet Impingement Erosion,

duyar, Computational Analysis of Wind-

60. F.A. McClintock and

A.S.

Argon,
49. N. Fujisawa, K. Wada, and T. Yamagata,

son-Wiley, 1966, p 461

Numerical Analysis of Wall-Thinning 55. B. Amirzadeh, A. Louhghalam, M. Raessi,

61. R.G. Keck, “Prediction and Mitigation of

Framework for the Analysis of Rain-

Piping Systems,” Ph.D. thesis, Department of

Mechanical
50. Y.M. Ferng, Predicting Local Distribu-

Parts I and II, J. Wind Eng. Ind. Aerodyn.,

Institute of Technology, 1987

56. R. Morita and Y. Uchiyama, Development

Onagawa Nuclear Power Plant in 2007,”

Using CFD Models, Ann. Nucl. Energy,

Droplet Impingement Erosion, ASME
51. K. Yoneda, R. Morita, K. Fujiwara, and F.

Pressure Vessels and Piping Conference,

9373 (in Japanese)

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