E-Journal of Advanced Maintenance Vol.4 No.2 (2012) 88-95
Japan Society of Maintenology

Method for Thinning Shape Evaluation of Elbow due to LDI and
Representative Thinning Shape for Seismic Evaluation of Eroded Elbow
Ryo MORITA1,*, Fumio INADA1, Michiya SAKAI2, Shin-ichi MATSUURA2,
Shigenobu ONISHI3 and Mitsuo KUGIMOTO3
1

Central Research Institute of Electric Power Industry, 2-11-1, Iwado-Kita, Komae-shi , Tokyo
201-8511, Japan
2
Central Research Institute of Electric Power Industry, 1646, Abiko, Abiko-shi, Chiba, 270-1194,
Japan
3
Chubu Electric Power Company, 1, Higashi-shincho, Higashi-ku, Nagoya, Aichi, 461-8680, Japan
ABSTRACT
For more realistic seismic safety evaluation of elbow with local thinning shape due to liquid droplet
impingement erosion (LDI), a determination method of the thinning shape of the elbow due to LDI wasdeveloped, and a representative thinning shape for seismic evaluation of eroded elbows was proposed in thisstudy. For the mechanistically-based determination of the thinning shape due to LDI, calculations of the droplet
behavior and the thinning rate of the elbow were conducted. In addition, with this approach, the thinning shapes
in various flow and piping size conditions were evaluated, and the enveloping thinning shape of those thinningshapes with a safety factor is considered as a representative thinning shape for seismic evaluation of eroded
elbows.
KEYWORDS
Liquid droplet impingement erosion, Seismic evaluation, Thinning shape

1.

ARTICLE INFORMATION
Article history:
Received 3 April 2012
Accepted 9 July 2012

Introduction

Liquid droplet impingement erosion (LDI, see Fig.1) is defined as the erosion caused by thecollision of high-speed droplets in a steam flow. In a power plant, pipe wall thinning by LDI isobserved in steam piping systems such as the vent line. LDI is usually observed very locally and isdifficult to detect.
Recently, for seismic safety of piping system with wall thinning, uniform thinning over the full
pipe circumference was assumed for the safety analysis [1]. Generally, the piping strength for theseismic evaluation is reduced when the piping wall thickness becomes thinner and wider. For thisreason, the assumption of overall uniform thinning is thought of as giving a conservative evaluation
result. However, at an elbow section, LDI is often observed at the elbow extrados because of its
mechanism, and the local thinning shape is generated. Because of the difference of the thinning shape
between the overall uniform thinning assumption and actual local thinning, the seismic evaluation oferoded elbows with uniform thinning gave a different result from that with an actual thinning shape[2]. Though the influences of the local thinning of the elbow to the fatigue characteristics areinvestigated, the thinning shape was not decided mechanistically [3]. For more realistic seismic
evaluation of the eroded elbow due to LDI, it is necessary to determine more realistic thinning shapeof the elbow with the LDI mechanism.
In this paper, the determination method of the thinning shape of the elbow due to LDI with its
mechanism, including calculations of the droplet behavior and the thinning rate, has been developed.
In addition, a representative thinning shape, which covers the thinning shape due to LDI in an actual
plant, is proposed for the seismic safety evaluation.

*

Corresponding author, E-mail: ryo@criepi.denken.or.jp

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

88

R. Morita, et al./ Proposal of Method for Thinning Shape Evaluationof Elbow due to LDI and Representative Thinning Shapefor Seismic Evaluation of Eroded Elbow

Erosionbydropletcollision

Steam+ Droplet

Accelerated
DropletFig.1 Schematics of Liquid Droplet Impingement Erosion in Piping System
1. Evaluation of Droplet Behavior/Collision Points Distributions/Collision Velocity

2. Evaluation of Thinning Shape
Relative Thinning ShapeOperation of Step 1. and 2.
in Various Flow Conditions
Enveloping Surface

Determination ofRepresentative Thinning ShapeFig.2 Flowchart of LDI Thinning Shape Determination2.

Development of Determination Method

2.1. Evaluation of Droplet Behavior
The evaluation flowchart of LDI thinning shape determination for the seismic tests(representative thinning shape) is shown in Fig.2. At first, the droplet behavior from the elbow inlet tothe collision point is calculated to evaluate the distributions of the collision point and collisionvelocity.
Figure 3 shows the concept of the droplet behavior calculations. Steam flow velocity ug
distributions in the elbow are assumed as uniform in the flow direction and no secondary flow.
u g ,  u in,
u g , r  u g ,  0

u: Flow Direction Velocity, ur: Radial Direction Velocity,u: Circumferential Direction Velocity(1)

For more accurate droplet behavior calculation, a 3-dimensional flow calculation is applied toobtain the velocity distributions in the elbow. This procedure with 3D calculations can be estimatedactual data reasonably as mentioned after. However, in this study, as a lot of parametric study isnecessary, it is not realistic to apply 3D calculations.
Droplets are assumed uniform distributions at the elbow inlet, and section area S is assigned.
Then, the behavior of each droplet is calculated until it collides with the elbow wall (or it passes
through the elbow). The droplet is transferred by a drag force from steam flow, and displacement dx
for a certain time step dt is calculated as follows.
dx = 0.5l(ul-ug)| ul-ug |Cd A dt,
A: Projected Area of Droplet (=d2/4), Cd: Drag Coefficient of Droplet(2)89

R. Morita, et al./ Proposal of Method for Thinning Shape Evaluationof Elbow due to LDI and Representative Thinning Shapefor Seismic Evaluation of Eroded Elbow

A-A’
Area:Sdrd
0°

Dropletuin

Pipe Diameter：D

0°V’
V”
φ

A’

Steam

DropletDensity:ρl, Diameter:dDrag Coeff.:Cd
Velocity：ul

V’
V

ur
θ A
O

Steam
Density：ρg, Velocity:uguθ

Fig.3 Concept of Droplet Behavior Calculations

θ：0°Flow dir.: θAView A
Elbow dorsal
：0°

Circum dir.: θ：90° ：-90°

：90°：Evaluation Region(0°<θ<90°，-90°<<90°)
Fig.4 Evaluation Region of LDI Thinning ShapeA droplet at position xn in time t moves to a new position xn+1=xn+dx in t+dt with flow conditions
at xn. Then, the flow conditions are updated to the values at xn+1, and new displacement dxn+1 is
calculated. This procedure is conducted in x, y, z directions and repeated until the droplet collides withthe elbow or passes through the elbow section. Figure 4 shows evaluation region of the droplet
collision and LDI thinning shape. The evaluation region is along the elbow extrados, and is divided
into 30 sections both in the flow direction () and the circumferential direction ().
When the droplet collides with elbow wall, the position (, ) and the collision velocity arerecorded. Applying this operation to all droplets, distributions of the collision point and the averagecollision velocity are obtained.
In this study, the droplet behavior calculation and thinning shape evaluation has been conducted
for various flow and geometry conditions to evaluate a representative thinning shape. The parametersof the calculations and the reason why the parameter range was chosen are as follows.
1. Steam velocity, u: 100, 200, 400 m/s
Reason: Lower limit velocity of LDI has been reported around 100m/s [4]. Steam velocity in thepiping is assumed below sonic speed (about 450m/s in wet steam).
2. Pressure, p: 0.005, 0.01, 0.1, 1.0, 7.0 MPa
Reason: Range of pressure in main steam piping to condenser pressure.
3. Droplet Diameter, d: 1.0, 2.0, 5.0, 10, 20, 50 m
Reason: From droplet diameter measurement tests in CRIEPI [5], the average diameter was within
1-20m and 99% of droplet diameters were bound by twice the average.
4. Pipe Diameter, D: 50, 100, 150, 300, 400 mm
Reason: Typical of the wet steam piping diameter in actual power plants.
Distributions of the collision point and the average collision velocity are evaluated in all
combinations of these parameters (total 450 conditions).
2.2. Evaluation of Thinning Shape
After the droplet behavior calculations with the method described in 2.1, the thinning shape on

90

R. Morita, et al./ Proposal of Method for Thinning Shape Evaluationof Elbow due to LDI and Representative Thinning Shapefor Seismic Evaluation of Eroded Elbow

the elbow was estimated with LDI thinning rate model. The Sanchez model [5] was used in this study.
The Sanchez model equation is expressed as follows.
T .R . 

C 0  l m tot  u l 4 Fe FhMAT 2 AC,
T.R.: Thinning Rate, C0: Coefficient(=1.1e-6 [6]), mtot: Mass Flow Rate, : Wetness
ul: Collision Velocity, Fe: Entrainment Factor, Fh: Hitting Factor
MAT: Material Factor (Strength of Oxide Film on Material Surface), AC: Collision Area

(3)

Sanchez model is proportional to the 4th power of the collision velocity. This tendency was sameas observed in Rochester’s research [7].
For the validation of the basic parts of the droplet behavior evaluations (all concepts except
velocity distributions (eq.(1))) and LDI thinning rate model, the comparison between actual LDI data
and thinning shape evaluation with 3-dimensional calculation was conducted. Figure 5 shows athinning shape of 1st elbow of an orifice downstream in a vent line of an actual power plant, and Fig. 6
shows the velocity distributions around this elbow and evaluated thinning shape of the elbow with
3-dimensional flow calculation. The thinning rate is normalized with maximum thinning rate of eachdata. Because the wall thickness (absolute value of the erosion rate) will be given as the parameter inthe seismic tests, it is necessary to evaluate the normalized (relative) thinning shape in this study.
Therefore, a relative thinning rate was compared.
From these figures, a jet flow was observed because of the orifice and the flow structure becomesvery complex. However, both thinning shape were distributed almost same region ((, ) = (30~60
deg., -40~40 deg.)). And also, Fig. 7 shows the comparison of the thinning shape distributions ofsections A and B in Fig.5. Sections A and B were the sections which maximum thinning rate isobserved in actual data. It is shown that the evaluated thinning shape with 3-dimensional calculationagrees well with actual data qualitatively, and we have confirmed the basic parts of the evaluation
method.

0.1 ‐0.2
0.6 ‐0.7

0.2 ‐0.3
0.7 ‐0.8A

0.3 ‐0.4
0.8 ‐0.9

0.4 ‐0.5
0.9 ‐1.0
70.2
65.5
60.2
55.6

B

50.4
45.1
40.5
35.2
30.6

Flow Direction Angle，θ[°]0.0 ‐0.1
0.5 ‐0.6

25.4
20.1

‐48 ‐34 ‐20 ‐11 ‐5 0 14 28 42 56 69
Circumferential Direction Angle，φ[°]Fig.5 Relative Thinning Shape at Elbow on Actual Plant( 1st Elbow of Orifice Downstream in Vent Line, Case 1)

91

R. Morita, et al./ Proposal of Method for Thinning Shape Evaluationof Elbow due to LDI and Representative Thinning Shapefor Seismic Evaluation of Eroded Elbow

0.0 ‐0.1
0.5 ‐0.6

0.1 ‐0.2
0.6 ‐0.7

0.2 ‐0.3
0.7 ‐0.8

0.3 ‐0.4
0.8 ‐0.9

0.4 ‐0.5
0.9 ‐1.0
72

60
54
48
42
36
30

Flow Direction Angle，θ[°]

66

24
18

‐60 ‐48 ‐36 ‐24 ‐12 0 12 24 36 48 60 72
Circumferential Direction Angle，φ[°]Relative Thinning Rate[‐]1.0

Actual Data 1
Evaluation (3D calc.)

0.8
0.6
0.4
0.2

Relative Thinning Rate[‐](a) Velocity Distribution with 3D Flow Calculation(b) Thinning ShapeFig.6 Evaluated Thinning Shape at Elbow obtained from 3D Calculation Method
1.0

Actual Data 1

0.8

Evaluation (3D calc.)

0.6
0.4
0.2
0.0

0.0
0

10

20 30 40 50 60 70
Flow Direction Angle, [°]

80

‐90

90

‐60
‐30
0
30
60
90
Circum ferential Direction Angle, [°](a) Flow Direction (Line A at Fig.5)(b) Circumferential Direction (Line B at Fig.5)
Fig.7 Comparison of Thinning Rate Profile

2.3. Determination of Representative Thinning ShapeFigure 8 shows an example of the estimated thinning shape on the extrados side of the elbow.
Thinning rate is normalized with maximum thinning rate. In this condition, the erosion shape wasdistributed concentrically and the maximum erosion point was around ()=(0deg., 60deg.).
This evaluation procedure of the estimation of the relative thinning shape was repeated for allcases (450 cases) to evaluate the representative thinning shape. Figure 9 shows the evaluation imageof the representative thinning shape. As we thought the representative thinning shape needs to beencompassed all evaluated thinning shapes, the thinning rate of an enveloping shape T.R.env() was
evaluated as follows.
T .R.env  ,   T .R.u1 , p1 , d1 , D1  ,  ,





 T .R. u , p , d , D  ,  ,
i
j
k
l
,

 max .

T .R. u i , p j , d k , Dl 1  ,  ,






 T .R. u i max , p j max , d k max , Dl max  ,  












(4)

92

Relative
Erosion Rate by
ErosionRate[mm/yr]
Sanchez
Model

90
81
72
63
54
45
36
27
18
9
0

0.90‐1.00
0.80‐0.90
0.70‐0.80
0.60‐0.70
0.50‐0.60
0.40‐0.50
0.30‐0.40
0.20‐0.30
0.10‐0.20
0.00‐0.10

Flow Direction[deg.，Elbow Inlet:0deg.]

R. Morita, et al./ Proposal of Method for Thinning Shape Evaluationof Elbow due to LDI and Representative Thinning Shapefor Seismic Evaluation of Eroded Elbow‐90 ‐72 ‐54 ‐36 ‐18 0 18 36 54 72 90
Circumferential Direction[deg., Dorsal:0deg.]

Fig.8 Example of Estimated Thinning Shape( p:0.1MPa, u:400m/s, d:20mm, D:150mm )Thinning Shape Calculations in Various Conditions
Enveloping Surface

Relative
Erosion Rate by
ErosionModelRate[mm/yr]
Sanchez+

0.0 ‐0.2
90
81
72
63
54
45
36
27
18
9
0

0.90‐1.00
0.80‐0.90
0.70‐0.80
0.60‐0.70
0.50‐0.60
0.40‐0.50
0.30‐0.40
0.20‐0.30
0.10‐0.20
0.00‐0.10‐90 ‐72 ‐54 ‐36 ‐18 0 18 36 54 72 90‐90 ‐72 ‐54 ‐36 ‐18 0 18 36 54 72 90

Circumferential Direction[deg., Dorsal:0deg.]

Circumferential Direction[deg., Dorsal:0deg.]

0.2 ‐0.4

0.4 ‐0.6

0.6 ‐0.8
90
81
72
63
54
45
36
27
18
9
0

+… =

‐90 ‐72 ‐54 ‐36 ‐18 0 18 36 54 72 90
Circumferential Direction Angle，φ[°]Fig.9 Evaluation of Enveloping Thinning Shape

0.0 ‐0.2

0.2 ‐0.4

0.4 ‐0.6

0.6 ‐0.8
90
81
72
63
54
45
36
27
18
9
0

0.8 ‐1.0‐90 ‐72 ‐54 ‐36 ‐18 0 18 36 54 72 90
Circumferential Direction Angle，φ[°]Fig.10 Representative Thinning Shape(Enveloping Thinning Shape with Factor 2)

93

0.8 ‐1.0

Flow Direction Angle，θ[°]

90
81
72
63
54
45
36
27
18
9
0

Flow Direction Angle，θ[°]0.90‐1.00
0.80‐0.90
0.70‐0.80
0.60‐0.70
0.50‐0.60
0.40‐0.50
0.30‐0.40
0.20‐0.30
0.10‐0.20
0.00‐0.10

Flow Direction[deg.，Elbow Inlet:0deg.]

Erosion Rate by
Relative
Sanchez
ErosionModelRate[mm/yr]

Flow Direction[deg.，Elbow Inlet:0deg.]

Thinning Shape atThinning Shape at
p:0.005MPa, u:200m/s, d:10μm p:0.1MPa, u:400m/s, d:20μm

R. Morita, et al./ Proposal of Method for Thinning Shape Evaluationof Elbow due to LDI and Representative Thinning Shapefor Seismic Evaluation of Eroded Elbow

Representative Thinning Rate [‐]

1

0.8

‐20%

0.6

0.4
Actual Data (Case 1)
0.2

Actual Data (Case 2)
Actual Data (Case 3)

0
0

0.2

0.4
0.6
0.8
Thinning Rate (Actual Data) [‐]1

Fig.11 Representative Thinning Rate vs. Thinning Rate of Actual LDI Cases(3 Cases, 1st Elbow of Orifice Downstream in Vent Line)

With this procedure, the enveloping surface was obtained. However, this enveloping shape isevaluated assuming uniform and no secondary flow as described above. In actual cases, LDI issometimes caused by non-uniform inlet flow condition, like LDI at a valve or downstream of anorifice (see Fig.6). Therefore, a factor 2 was applied to the relative thinning shape of the enveloping
surface and we adopt this thinning shape as the representative shape (Fig.10).
The representative thinning shape (enveloping surface with the safety factor 2 applied) for
seismic tests was then compared with actual LDI cases. Figure 11 shows the comparisons of thesection shape of the thinning rate with the actual data. Cases 1-3 are actual LDI cases of 1st elbow ofan orifice downstream in different vent lines, which are considered as the jet flows collide.
From the figure, it was observed that the representative thinning shape bounds almost actual dataconservatively (94.6% of all actual data, 99.8% of actual data with T.R.>0.1). As mentioned before,
the piping strength for the seismic evaluation becomes smaller when the piping wall thickness isthinner and wider. Therefore, it was thought that the representative thinning shape gave a conservative
result of the seismic evaluations. Although some non-conservative points were observed around thesmall thinning rate region (T.R.<0.1) and T.R.~0.8 (3 points only), it was considered that small
thinning rate region and a few points under-estimation of thinning rate have little effect tonon-conservativeness of seismic evaluation.
As a result of the comparison, it is clarified that the representative thinning shape estimated with
non-secondary uniform flow assumption can encompasses the actual data almost conservatively, andthe representative thinning shape is thought to be applicable to the seismic evaluation for the thinned
elbow.

3. Conclusion
For more realistic seismic safety evaluation, a determination method of LDI thinning shape at the
elbow in line with the LDI mechanism has been developed. The droplet behavior and thinning shapecalculation have been conducted under various flow and geometry conditions with an assumed
velocity distribution in the elbow. The enveloping shape with safety factor 2 on relative thinning rate
was considered as the representative thinning shape. As the representative thinning shape bounded94

R. Morita, et al./ Proposal of Method for Thinning Shape Evaluationof Elbow due to LDI and Representative Thinning Shapefor Seismic Evaluation of Eroded Elbow

actual LDI thinning shapes conservatively, it was thought that the representative thinning shape wasapplicable to the seismic evaluation for the thinned elbow due to LDI.

References[1] Nakamura, I., et al., “Tri-Axial Shake Table Test on the Thinned Wall Piping Model and Damage
Detection before Failure,” PVP2010-25839.
[2] Sakai, M., et al., “Seismic safety evaluation of piping systems with locally wall thinning by LDI(Part3) -Seismic performance effects of elbow pipes by loading tests-,” Procs. of 7th annual
meeting of Japan Society of Maintenology, A-4-5 (in Japanese).
[3] Balan, C., et al., “The effect of bi-directional loading on fatigue assessment of pressurized piping
elbows with local thinned areas,” Pressure Vessels and Piping, 82 (2005), 235-242.
[4] Shinogaya, T., Takemoto, M., “Erosion of Metals in High Speed Mist Flow Evaluation ofThreshold Velocity by Acoustic Emission System,” 10th Int. Congress on Metalic Corrosion,
vol.4,Sessions 14-19(1987), 4047-4054.
[5] Morita, R., “Droplet Diameter Measurements for the Prediction of Liquid Droplet Impingement
Erosion,” Proc. of ICONE 16 (2008).
[6] L.E. Sanchez-Caldera, “Mechanism of Corrosion-Erosion in Steam Extraction Lines of Power
Stations,” Ph.D. Thesis, Dep. Mech. Eng., Massachusetts Institute of Technology, (1984).
[7] M.C. Rochester, J.H. Brunton, “Influence of Physical Properties of the Liquid on the Erosion ofSolids,” ASTM STP 567(1974), 128-151

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