E-Journal of Advanced Maintenance Vol.3-3 (2011) 92-101
Japan Society of Maintenology

Simulation and visualization of guided wave propagation by large-scale 3DFEM
Takashi FURUKAWA*and Ichiro KOMURAJapan Power Engineering and Inspection Corporation, 14-1 Bentencho, Tsurumi-ku, Yokohama
230-0044, Japan(Received; For the use of JSM)
Abstract. Ultrasonic guided waves have been widely applied to the long-range inspection of straight piping.
The interpretation of the guided wave ultrasonic testing data beyond welds and elbows is challenging because
there are many wave modes with different sound velocity. One of the key techniques to examine the beam pathof each guided wave mode is the visualization of ultrasonic wave propagation. The authors have employed alarge-scale FEM code for bulk wave propagation to the interpretation of UT data, analysis of suitable UT
condition and training of UT. This paper describes the simulation and visualization of guided wave propagationin pipes and beyond elbows and welds via a large-scale 3D pure FEM code, which has over one billion elements
and parallel computing system. This study presents the comparisons between the simulated and experimentalresults.

KEYWORDS: Ultrasonic guided wave, Wave propagation, FEM, Piping, Elbow, Welds

1.

Introduction

Ultrasonic guided waves are suitable for the long-range inspection and online monitoring ofpipes [1-4]. Guided waves in piping are a combination of various wave modes. Each wave mode has adifferent sound velocity that depends on frequency except for T(0,1) mode. Therefore, guided wave
inspection results are difficult to interpret, i.e., a beam path is difficult to extract from observedechoes. Theoretical analyses tools, such as modal analyses, mathematical calculation [5], andsemi-analytic numerical calculation [6] help in the planning the inspection setup as well as theinterpretation of the inspection results for simple situations. However, the use of a large-scale FEM
code is the most effective method for solving the guided wave propagation problem for more
complicated situations involving welding, elbows, and defects. The purpose of this research is toconfirm the applicability of a large-scale FEM code and a parallel computing technique for thesimulation of guided wave propagation and the prediction of echoes in the presence of complex
geometries. This paper presents a guided wave transmitting and receiving FEM for guided wave
propagation and echo prediction, and compares simulation, theoretical, and experimental results.
2.

FEM code and modeling2.1. FEM code and computing system
A commercial FEM code ComWAVE [7] developed by ITOCHU Techno-Solutions forlarge-scale 3D analysis was selected to calculate to numerically solve the guided wave propagation
problem. A 12-core PC with 96GByte memory and 60-core cluster computing system with 124GByte
memory were employed to perform the necessary computations.

*Corresponding author, E-mail: furukawa-takashi@japeic.or.jp
ISSN – 1883 – 9894/10 © 2010 JSM and the authors. All rights reserved.

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T. Furukawa et al./ Simulation and visualization of guided wave propagation by large scale 3D FEM

2.2. Guided wave excitation and receiving model
Figure 1 shows the bird views of the FEM mode of pipe (blue area) and probe element(s) (redarea). Figure 1(a) shows a single ring-type probe element and Fig. 1(b) shows array-type probeelements. The model was excited by applying the initial displacement vector at all FEM meshed ofeach probe element(s); examples of the excitation model are shown in Fig. 2. The white arrows
indicate the direction of the initial displacement vector. Figure 2(a) shows an excitation model of thetorsional mode (T-mode) and Fig. 2(b) and 2(c) show excitation models of the longitudinal mode(L-mode).
The receiving of the model was realized by detecting the 3D displacement waveform at any FEM
mesh, corresponding to the receiver position.
Probe elements

Probe element

Pipe

Pipe

(a) Single ring element(b) Array-type elements
Fig. 1. Model of probe element(s) for guided wave excitation
Probe element

Pipe
Direction of displacement(a) T-mode excitation by single ring or array type element(s) applying circumferential vibration
Probe element

Pipe
Pipe

Direction of displacement(b) L-mode excitation by single ring or array type element(s) applying axial vibration(c) L-mode excitation by single ring or array type element(s) applying radial vibration
Fig. 2. Guided wave excitation model2

T. Furukawa et al./ Simulation and visualization of guided wave propagation by large scale 3D FEM

2.3. FEM model and simulation conditions
The structure of model was divided into cubic elements, with the maximum size of the elements
less than one-fifteenth of the wavelength. Figure 3 shows the straight pipe model that was used toverify the modeling by comparing the theoretical and experimental results. Figure 3(a) shows a small
two-pipe model of the same dimensions. The dimensions of each pipe are 150 mm in length, 5 mm inouter diameter and 1mm in thickness. The ring-type model, shown in Fig. 2(b), excited the L-modeguided wave. The waveforms of the initial displacements were tone burst signals with five cycles at200 kHz and 1,000 kHz. Figure 3(b) shows a straight pipe model which dimensions are 2,000 mm inlength, 34 mm in outer diameter and 3.2 mm in thickness. Tone burst signals at 200 kHz were emitted
from the probe element in the pipe model. The probe element generated the L-mode guided wave asshown in Fig.2(c). The echo signal was detected at outer surface of the pipe near the probe element.
The distance between the probe element and receiver was 50 mm. This setup was a model of anexperimental setup conducted by Matsuo and Cho [8].
Figure 4 shows the straight pipes and 90° elbow model with two welds. The outer diameter andthickness of model are 60 mm and 4 mm, respectively. Figure 4(a) shows an overview of the modeland Fig. 4(b) shows an enlarged view of the elbow and welds. Five cycles of wave, which had center
frequency of 30 kHz and 50 kHz, were used for the T-mode excitation of this model, as shown in Fig.
2(a). After traveling about 900 mm beyond the elbow, guided waves are received at eight positions on
the outer surface of pipe, as shown in Figs. 4(a) and 4(c).
The material parameters used in the calculation are listed in Table 1.
mm

50Length = 150 mm
Outer diameter = 5 mm
Thickness = 1 mm

015

Probe element
010Two pipes(a) Overview of small two pipes model (Model 1)

Probe element
50

Receiver00
2,0

Enlarged view50
1,0

Length = 2,000 mm
Outer diameter = 34 mm
Thickness = 3.2 mm(b) Overview of stainless pipe model (Model 2)
Fig. 3. Straight pipes model for verification (Mode1 1 and 2)

3

T. Furukawa et al./ Simulation and visualization of guided wave propagation by large scale 3D FEM(b) Enlarged view of elbow and welds

DCEElbow

Straight pipe

AF

Outer diameter = 60mm
Thickness = 4 mm

BHG

8 positions;
A: Inner side, E: Outer side

Transmitters(Probe Elements)(a) Overview of model(c) Positions 8 receivers
Fig. 4. Two pipes and elbow model with two welds for prediction of T-mode guided wave propagation
beyond elbow and welds (Model 3)
Table 1 Material parameters and simulation conditions
Material (Soundvelocity anddensity)
Dimensions
Center frequency
Element size

3.

Model 1Model 2Model 3

Aluminum alloy base metal(Vl = 6.0 km/s, Vs = 3.04 km/s,density = 2.7 × 103 kg/m3)
OD = 5 mm, t = 1 mm
200 kHz, 1,000 kHz
0.1 mm × 0.1 mm × 0.1 mm

Type 304 stainless steel base metal(Vl = 5.7 km/s, Vs = 3.1 km/s, density =7.9 × 103 kg/m3)
OD = 34 mm, t = 3.2 mm
200 kHz0.2 mm × 0.2 mm × 0.2 mm

Aluminum alloy base metal(Vl = 6.0 km/s, Vs = 3.04 km/s,density = 2.7 × 103 kg/m3)
OD = 60 mm, t = 4 mm
30 kHz, 50 kHz
0.5 mm × 0.5 mm × 0.5 mm

Results

3.1. Simulation results of Model 1 (L-mode guided wave propagation of differentfrequency)
Figure 5 shows the visualization results of the guided wave propagation in two pipes. The color
bar indicates the magnitude of the absolute value of the displacement vector. The amplitude of thedisplacement vector of each wave packet in Fig. 5 is axisymmetric. Therefor, all wave packets
propagate along the pipe axially symmetric. Figure 6 shows the group velocity dispersion curves of
the L-mode propagating in a 5 mm outer diameter and 1 mm thickness aluminum pipe. The vertical
black-dotted lines indicate the excitation frequencies, at 200 kHz and 1,000 kHz. Considering thedispersion curves in Fig. 6, a wave packet at 200 kHz seems to be the L(0,1) mode. A faster wave
packet at 1,000 kHz seems to be the L(0,2) and a slower wave packet seems to be the L(0,1) mode.
Figure 7 shows an axial section of the Model 1. Details of the displacement vector of each wave
packet are shown in Fig. 7. The red-dotted lines indicate the deformation of outer and inner surface.
The green arrows indicate the displacement vector. The deformation of the pipe by the wave packet at
200 kHz was axisymmetric (The snapshot showed the wave packet expanded the diameter of thepipe.). Because the outer and inner surfaces of the pipe deformed in the same direction, thedeformation in the wall direction was asymmetric. Therefore, this wave packet was identified as theL(0,1) mode [9][10]. The slower wave packet at 1,000 kHz was also identified as the L(0,1) mode.

4

T. Furukawa et al./ Simulation and visualization of guided wave propagation by large scale 3D FEM

The deformation of the pipe by the faster wave packet at 1,000 kHz was axisymmetric. However, in
this case, the outer and inner surfaces of the pipe deformed in opposite directions, and the deformationin the wall direction was symmetric. Therefore, this wave packet was identified as the L(0,2) mode
[9][10]. The wave modes of all wave packets were identified. Good agreement between FEM results
and theoretical prediction through dispersion curves was obtained.

1,200kH00
z0k
Hz

Probe element

200k
1,00 Hz0kHz

Probe element

L(0,1)
L(0,1)
L(0,2)

Probe element

1,1,0200k
H00
z0k
Hz

Probe element(b) at 8 μsec. after wave generation
200k
Hz00kHz(a) at 4 μsec. after wave generation

L(0,1)
L(0,1)
L(0,1)
L(0,1)

L(0,2)(c) at 12 μsec. after wave generation(d) at 16 μsec. after wave generation
Fig. 5. Simulation results of L-mode guided wave propagation in Model 1 (200 kHz and 1,000 kHz)

Excitation mode

Group Velocity (m/s)

6000

L(0,1)
L(0,2)

5000
4000
3000
2000
1000
00500

1000

1500

2000

Frequency(KHz)

Fig. 6. Group velocity dispersion curves of L-modes propagating in a 5 mm outer diameter and 1 mm
thickness aluminum alloy pipe

1,200k
H00z0kHz

Probe element
L(0,1)

L(0,1)
L(0,2)

Fig. 7. Displacement vector of wave packets in Model 1 (axial section of the pipes)

5T. Furukawa et al./ Simulation and visualization of guided wave propagation by large scale 3D FEM

3.2. Simulation results of Model 2 (Echo simulation from the pipe edge of L-mode
guided wave)
Figure 8 shows simulation results, group velocity dispersion curves of the L-mode propagating in
the pipe, and an experimental result of a received waveform [8]. Figure 8(a) shows the simulation
result of a received waveform and Fig. 8(b) shows a visualization of the L-mode guided wave
propagation that is indicated in the dispersion curves as shown in Fig. 8(c). The vertical red-dottedline indicates the excitation frequency. In this case, simulation results show that two types of theL-mode guided waves propagated toward the edges of the pipe, as shown in Fig. 8(b), and reflected atboth the edges. Furthermore, echo signals were received as indicated in Fig. 8(a). The time of flight of
the faster echo was around 400 μs and that of the slower echo was around 700 μs. Figure 8(d) shows
an experimentally received waveform that was detected using a special optical fiber sensor [8].
Figures 8(a) and 8(d) show that the time of flight of each echo in the simulated andexperimentally received waveform was almost equal. We have not modeled characteristics of theoptical fiber sensor yet. Therefor, the simulation does not predict the amplitude of echoes completely.
Comparisons between the FEM simulation and the experimental results show that the FEM simulation
corresponds very well to the state (the two modes having different propagation times and amplitudes)of guided wave propagation in the actual piping.
radial (out-of-plane) displacement
axial (in-plane) displacementRelative amplitude

0.4

L(0,2)
Probe Element

0.2
0.0-0.2

L(0,1)

L(0,2)

L(0,1)

-0.4
0200

400

600

800-6Time (10 sec.)(a) Simulation result of received waveform

L(0,1) mode
Group Velocity. m/s

at 20 μsec.

(b) Visualization of L-mode guided wave propagation

L(0,2) mode

6000

4000

after 20μsec. of wave generation

Excitation mode

2000

L(0,1) mode
00500

1000

Frequency, kHz(c) Group velocity dispersion curves(d) Experimental received waveform
Fig. 8. Simulation results, group velocity dispersion curves of L-modes propagating in a 34 mm outer
diameter and 3.2 mm thickness stainless steel pipe, and experimental received waveform[8]3.3. Simulation results of Model 3 (T-mode guided wave propagation beyond welds andelbow piping)
Figures 9(a) and 9(b) show simulation results of received waveforms at eight different positions
as shown in Fig. 4(c). These waveforms are circumferential components of the displacement vector.
The signals at the top of the figures are sums of the eight signals, that are fundamental T(0,1) mode. In
Fig. 9(a), the echo of the fundamental T(0,1) mode appears only around at 500 μs. Each waveform6T. Furukawa et al./ Simulation and visualization of guided wave propagation by large scale 3D FEM

also has large echo amplitude at a propagation time of around 500 μs. The echo durations of positions
A, B, D, E, F, and H are longer than those of the fundamental T(0,1) mode. The delayed part of theecho may be a different mode from the T(0,1) mode. Sound velocity of the mode is slower than that ofthe T(0,1) mode. Because the phases of the waveforms at around 600 μs of positions A and E areopposite in direction, an asymmetric mode may be generated beyond the elbow.
In Fig. 9(b), large echo amplitude appears at 50 kHz at a propagation time of around 450 μs. A
delayed echo clearly appears at a propagation time of around 600 μs in positions A, C, E, and G at
50kHz. The waveforms at around 600 μs of positions A and E have a coordinate phase. The phases ofthe waveforms at around 600 μs of positions A and C are opposite in direction. Therefore, asymmetricmodes may be generated beyond the elbow at 50 kHz. Figure 10 shows snapshots of the displacement
vector, which are cross-sectional views of the receiver position; at propagation times of around 450and 600 μs. Figure 10(a) shows symmetrical and circumferential displacement vectors at 450 μs.
Circumferential displacement vectors are shown in Fig. 10(b) corresponding to the receiver positions
A, C, E, and G at 603 μs. This mode seems to be a higher order of T-mode [11].
0200400060030kHz

4040060050kHz4All200All0-4-41.0
0.5
0.0
-0.5
-1.0
1.0
0.5
0.0
-0.5
-1.0
1.0
0.5
0.0
-0.5
-1.0
1.0
0.5
0.0
-0.5
-1.0
1.0
0.5
0.0
-0.5
-1.0
1.0
0.5
0.0
-0.5
-1.0
1.0
0.5
0.0
-0.5
-1.0
1.0
0.5
0.0
-0.5
-1.0

1.0
0.5
0.0
-0.5
-1.0
1.0
0.5
0.0
-0.5
-1.0
1.0
0.5
0.0
-0.5
-1.0
1.0
0.5
0.0
-0.5
-1.0
1.0
0.5
0.0
-0.5
-1.0
1.0
0.5
0.0
-0.5
-1.0
1.0
0.5
0.0-0.5-1.0
1.0
0.5
0.0
-0.5
-1.0

Position H

Position G

Position F

Outer side
Position E

Position D

Position C

Position B

Inner side
Position A

0200400

Position H

Position G

Position F

Outer side
Position E

Position D

Position C

Position B

Inner side
Position A

0600

200400-6-6600

time (10 sec.)time (10 sec.)(a) at 30 kHz T-mode(b) at 50 kHz T-mode
Fig. 9. Waveforms received at eight positions and addition of eight waveforms beyond elbow and welds

7T. Furukawa et al./ Simulation and visualization of guided wave propagation by large scale 3D FEM

To investigate the cause of these phenomena, the visualization results of guided wave
propagation in elbow and beyond are displayed in Figs. 11 and 12. The color bar corresponds to theamplitude of the absolute value of the displacement. Symmetric wave packets are seen in Figs. 11(a)and 12(a). The simulation results indicated the mode-conversion to asymmetric modes beyond theelbow. The FEM results show that the difference between the traveling paths of the inner and outersides of the elbow is one of the major causes of the asymmetric modes.
When the 30 kHz T-mode guided wave propagated in the elbow, the amplitude of the inner side
was larger than that of the outer side as shown in Figs. 11(b) and (c) by natural focusing. In contrast,
natural focusing to the outer side of the elbow is shown in Figs. 12(b) and (c) at 50 kHz. The
visualization results of guided wave propagation revealed that the natural focusing position waschanged depending on the excitation frequency.

(a) at 450 μsec.
(b) at 603 μsec.
Fig. 10. Cross sectional snap shots of displacement vector at received position (50 kHz)Endview

Endview

Side view(a) at 90 μsec. after wave generation

Side view(b) at 190 μsec. after wave generation(c) at 210 μsec. after wave generation(d) at 270 μsec. after wave generation
Fig. 11. Visualized guided waves in elbow and beyond elbow region, at 30 kHz T-mode generation (Thewhite arrows indicate the guided wave focusing due to the elbow.)8

T. Furukawa et al./ Simulation and visualization of guided wave propagation by large scale 3D FEMEndview

Endview

Side view(a) at 90 μsec. after wave generation

Side view(b) at 140 μsec. after wave generation(c) at 160 μsec. after wave generation(d) at 270 μsec. after wave generation
Fig. 12. Visualized guided waves in elbow and beyond elbow region, at 50 kHz T-mode generation (Thewhite arrows indicate the guided wave focusing due to the elbow.)4.

Conclusion
3D large-scale FEM models were employed to simulate guided wave propagation in straightpipes and pipes with elbows. The accuracy of this FEM model was verified. The simulation results
showed that the higher-order of T-modes were generated beyond the elbow by mode-conversion. Thenatural focusing occurred in the elbow. The focal positions of 30 kHz and 50 kHz T-mode guided
wave were the inner side and the outer side, respectively. The simulation results also showed that thefrequency dependence of the natural focal position of the T-mode guided wave in the elbow.

Acknowledgement
We would like to thank Dr. H. Nishino of Tokushima University for the valuable discussions
during this investigation.

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Inspection", 17th WCNDT, 25-28 Oct. 2008
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Gijutu, Vol.52, 2007, pp.154-161 (in Japanese)[9] Joseph L. ROSE, " Ultrasonic waves in solid media", Cambridge Univ. press, 1999, pp.159-161[10] H. Nishino, S. Takahashi, F. Uchida, M. Takemoto and K. Ono, "Modal Analysis of Hollow
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