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




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
LDI Erosion Rate	(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 =
In predicting the lifetime of pipe-wall thin-	2 to 6 (Ref 25, 27), for the spray test. One reason
ning of nuclear/fossil power plants, the erosion	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.	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	come from the influence of the liquid film and	nuclear/fossil power plants. The erosion rate in
Therefore, several experimental studies were	the accuracy of the measurement of droplet	nuclear/fossil power plants. The erosion rate in
carried out in the literature for various ranges	the accuracy of the measurement of droplet	the terminal stage was evaluated in a spray-
carried out in the literature for various ranges	velocity, while the experimental condition, such	the terminal stage was evaluated in a spray-
of droplet velocity, diameter, and wall materi-	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	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	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.	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	uid film will result in a larger power index value.	LDI erosion (Ref 31). The spray consists of
The rotating-disk test of LDI shows the power	This result agrees qualitatively with the numeri-	LDI erosion (Ref 31). The spray consists of
index n = 5.8 (Ref 22), which is approximately	This result agrees qualitatively with the numeri-	liquid droplets of an average diameter of
index n = 5.8 (Ref 22), which is approximately	cal results (Ref 11), in which the power index	liquid droplets of an average diameter of
equal to the theoretical value of 5 (Ref 23). How-	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	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).	uid-film thickness on the material surface. These	pure			(A1070),		aluminum
observed in other rotating-disk testing (Ref 24).	experimental erosion-rate results indicate that	pure			(A1070),		aluminum
It is noted that the minor influence of the liquid	experimental erosion-rate results indicate that	(A5056), brass (C3604), carbon steel (S20C),
It is noted that the minor influence of the liquid	power index n scatters in the range 2 to 8 due	(A5056), brass (C3604), carbon steel (S20C),
film can be observed in this type of experiment,	power index n scatters in the range 2 to 8 due	mild	steel	(SS400),		and	stainless	steel
film can be observed in this type of experiment,	to the influence of experimental conditions	mild	steel	(SS400),		and	stainless	steel
because of the high centrifugal forces in the	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
6–8 (terminal stage)	Rotating disk	speed)	(rotating speed)		12Cr steel, cobalt-base alloy, titanium alloy

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
5.5–6 (<100 m/s, or 330 ft/s)2–3				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	1.2	Present (a = 3.52, b = 0.5)
sharply, and the gradient of the erosion rate	1.2
decreases gradually with further increasing of
decreases gradually with further increasing of		Sasaki et al. (2016)
the erosion depth. In the asymptotic condition		Sasaki et al. (2016)
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 (100 m/s)
indicates that erosion is highly damped by the		Present (200 m/s)
effect of the liquid pool in the deep cavity,		Present (200 m/s)
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
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
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	Fig. 6

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
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
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,
Q									which is different from the thin liquid film, and
Heat exchanger
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)	Geometry of steam vent line in Japanese
		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)	Source: Ref 62

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)
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
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
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							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												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
of 11 mm (0.43 in.) in the axial direction and
9 mm (0.36 in.) in the circumferential direction
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												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												stood and is applicable to the prediction of
the hole showed a sawtoothlike pattern spread
over the outer bent wall.
over the outer bent wall.
The numerical prediction of erosion in the					occur at the location of high-speed steam flow
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,
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							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-							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
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
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
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
(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							porosity, cracks, or erosion craters). The phys-
					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					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					ried out by increasing the pipe diameter.
empirical models, and all are considered in					Decreasing the steam wetness (number density
the models of Morita and Uchiyama (Ref 56)					Decreasing the steam wetness (number density
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							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
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
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
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
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							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							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
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
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)
											9373 (in Japanese)