Modelling III

Numerical Simulation of Guided Wave Propagation using Large Scale FEM Code T. Furukawa, I. Komura, Japan Power Engineering and Inspection Corporation, Japan

ABSTRACT

Ultrasonic guided waves are being widely applied to the long range inspection of piping. The

interpretation of the guided wave ultrasonic testing data is challenging because guided waves contain

many wave modes with different sound velocities. In order to understand the beam path of each

guided wave mode, one of the key issues is to visualize ultrasonic wave propagation. JAPEIC NDE

Center has applied the experimental ultrasonic wave visualization technique and the numerical

simulation technique of bulk wave propagation to the interpretation of UT data, the analysis of suitable

UT condition and the education/training of UT. This paper describes the numerical simulation results

of guided wave propagation in pipes by using a large scale three-dimensional FEM code, which can

analyze over one billion elements and can use parallel computing system. Procedure of modelling for

guided wave generation and the comparison between simulation and experiment are described.

KEYWORDS: Ultrasonic Testing (UT), Guided Wave, Piping, Wave Propagation, FEM, Parallel

computing

INTRODUCTION

Ultrasonic guided wave technology is expected to apply to the online inspection, monitoring, and the

long range inspection[1-4]. Guided wave has various wave modes with different sound velocity

depend on frequency. Therefore, guided wave inspection results are very complicated to interpret the

beam path of observed echoes. So, the theoretical analyses, such as modal analyses, mathematical

calculation[5], and semi-analytic numerical calculation[6], help us to plan the inspection setup and to

interpret the inspection results for simple or basic problems. For practical problems, for example

welding, defects, piping support, and flanges, one of the most effective solutions to analyze the guided

wave propagation is the calculation by pure FEM.

The purpose of this research is to confirm the applicability of a large scale FEM and a parallel

computing technique for simulation of guided wave propagation and prediction of echoes, and to

confirm the capability of the FEM code as a simulation tool for complex geometries. This paper

presents the guided wave generation model. FEM simulation of guided wave propagation and

prediction of echoes are shown. Comparison between simulation results, theoretical results, and

experimental results is also discussed.

SIMULATION CODE AND MODELS

A commercial FEM code for large scale three dimensional analysis, which was developed by ITOCHU

Techno-Solutions; named COM WAVE[7], was selected to calculate guided wave propagation along

tubes and pipes. A parallel computing system which has 60 cores and 124 GByte memories was

employed for this computation.

In the present situation of wave generation model, the electrical-mechanical-acoustic problem was not

modeled yet. The direction of displacement vector generated by the transmitter was modeled. A

schematic diagram of the guided wave generation model in present simulation is shown in Figure 1.

This figure shows the cross sections of tubes and probe elements. The blue and red areas are tube and

the probe elements respectively. The initial displacement waveform was applied to all surface FEM

meshes of tube at each probe element. The directions of displacement vector are indicated by black

arrows. Figure 1(a) shows a longitudinal mode (L-mode) excitation model and Figure 1(b) shows a

torsional mode (T-mode) excitation model. The receiving model are now under developing. In the

present simulation, the receiving information was modeled to detect the displacement waveform of

surface FEM meshes corresponding to the receiver position.

The structure of tube model was divided into cubic elements with the maximum size of the elements

less than one-fifteenth of the wavelength. Figure 2 shows the straight tubes and pipe model which are

used to verify our modeling by comparing the both theoretical and experimental results. Figure 2(a)

shows small three tubes model of the same dimensions. The dimensions of each tube are 450mm

length, 5mm outer diameter and 1mm thickness. Five cycles of wave which has the center frequency

of 1MHz, 500kHz and 200kHz was used for the L-mode excitation in each three tubes. Figure 2(b)

shows a pipe model which dimensions are 2,000mm length, 34mm outer diameter and 3.2mm

thickness. Five cycles of wave which has the center frequency of 200kHz was used for the L-mode

excitation of this pipe. The material parameters used in the calculation is listed in Table 1.

SIMULATION RESULTS

Model A

The simulation results of guided wave propagation in model A is shown in Figure 3. The color bar

indicates the amplitude of deformation of the outer surface. In Figure 3, each four result is the

snapshots after 2 micro second, 10.2 micro second, 16.6 micro second, and 24 micro second of wave

generation respectively. Figure 4 shows the group velocity dispersion curves of Model A in L(0,1) and

L(0,2) mode. As pointed out by the white arrow in Figure 3, all waves are axially symmetric modes.

Considering the dispersion curves in Figure 4, a wavelet at 200kHz seems to be L(0,1) mode. Two

wavelets are shown at 1MHz. Faster and slower wavelet seems to be L(0,2) and L(0,1) mode,

respectively. Details of deformation and vibration of each wavelet are shown in Figure 5. The red

dotted lines indicate the deformation of outer and inner surface. The green arrows indicate the

displacement vector. Figure 5(a) shows a close-up view of the wavelet at 200kHz. This wavelet was

axially symmetric and the vibration in the wall direction was asymmetric. Therefore, this wavelet is

identified as L(0,1) mode. Figure 5(b) shows a close-up view of the faster wavelet at 1MHz. This

wavelet was axially symmetric and the vibration in the wall direction was symmetric. Therefore, this

wavelet is identified as L(0,2) mode. Figure 5(c) shows a close-up view of the slower wavelet at

1MHz. This wavelet was axially symmetric and the vibration in the wall direction was asymmetric.

Therefore, this wavelet is identified as L(0,1) mode.

The wave modes of all wavelets were identified. Good agreement between FEM results and

theoretical prediction through dispersion curves was obtained.

Model B

In the case of model B, Figure 6 shows an experimental result of received waveform[8] and a

calculated result by FEM. As shown in Figure 6, the time of flight of echoes in the simulated and

experimental received waveform was almost equal. Simulated received waveform was similar to the

experimental result except for signal amplitude and noise level which had not been modeled in this

simulation. Figure 7 shows wave propagation behavior and theoretical dispersion curves of L-Mode.

Comparison between FEM simulation and experimental results shows that the FEM simulation

corresponds very well to the state of guided wave propagation in actual piping.

TRIAL APPLICATION TO U-BENT MODEL

Figure 8 shows a result of trial FEM simulation on U-bent tube model. The outer diameter and

thickness of the tube are 5mm and 1mm. The model structure is shown in Fig. 8(a). Five cycles of

wave which has the center frequency of 500kHz was used in the T-mode excitation. The material

parameters and simulation conditions used in this simulation is the same as that of Model A. Guided

wave propagation through U-bent tube are shown in Figure 8(b) to Figure 8(f). It was recognized that

T-mode was mode-converted to a flexural mode (F-mode) at U-bent.

CONCLUSION

As the results of present study, it was found that the large scale FEM simulation is applicable and

capable to the simulation of guided wave propagation and "echo" prediction. The research is in

progress. As the next stage, we are trying to challenge the simulation of complex geometry model such

as the piping which has a welding, an elbow, and defects.

REFERENCES

1) Joseph L. Rose, "Ultrasonic Guided Waves: An Introduction to the Technical Focus Issue,"

Materials Evaluation, Vol. 61, 2003, p.65

2) C H P Wassink, M A Robers, J A de Raad and T Bouma, "Condition monitoring of

inaccessible piping," Insight, Vol. 43, pp.86-88

3) P. Cawley, M.J.S. Lowe, D.N. Alleyne, B. Pavlakovic and P. Wilcox, "Practical Long Range

Guided Wave Testing: Applications to Pipes and Rail," Materials Evaluation, Vol. 61, 2003,

pp.66-74

4) Hegeon Kwun, Sang Y. Kim and Glenn M. Light, "The Magnetostrictive Sensor Technology

Long Range Guided Wave Testing and Monitoring Structures," Materials Evaluation, Vol. 61,

2003, pp.80-84

5) Joseph L. ROSE, Jing MU, Younho CHO, "Recent Advances on Guided Waves in Pipe

Inspection," 17th WCNDT, 25-28 Oct. 2008

6) Hayashi and Joseph L. Rose, "Guided Wave Simulation and Visualization by a Semianalytical

Finite Element Method," Materials Evaluation, Vol. 61, 2003, pp.75-79

7) http://www.ctc-g.co.jp/

8) T. Matsuo, H. Cho and M. Takemoto, "Evaluation of Corrosion-induced Wall Reduction of

Pipe using both Optical Fiber AE System and Guided Wave Inspection Method," Zairyo

Shiken Gijutu, Vol.52, 2007, pp.154-161 (in Japanese)

(a) L-mode excitation (b) T-mode excitation

Figure 1 - Cross section of tube and probe elements

(a) Small three tubes model (Model A) (b) Pipe model (Model B)

Figure 2 - Schematic diagram of the straight pipe configuration

Model A Model B

Material

(Sound velocity)

Aluminum alloy base metal

(Vl=6.0km/sec., Vs=3.04km/sec)

Type 304 stainless steel base metal

(Vl=5.7km/sec., Vs=3.1km/sec)

Dimensions OD=5mm, t=1mm OD=34mm, t=3.2mm

Center frequency 200kHz, 500kHz, 1MHz 200kHz

Element size 0.1mm×0.1mm×0.1mm 0.2mm×0.2mm×0.2mm

Total number of the

elements

About 100 million About 3.3 million

Table 1 - Material parameters and simulation conditions

50.0

mm

50.0

mm

50.0

mm

200k

Hz

500k

Hz

1MHz

Transmitter

50.0

mm

50.0

mm

L(0,1)

L(0,2)

L(0,1)

(a) after 2.0sec. of wave generation (b) after 10.2sec. of wave generation

50.0

mm

50.0

mm

50.0

mm

L(0,1)

L(0,1)

200k

Hz

500k

Hz

1MHz

(c) after 16.6sec. of wave generation (d) after 24.0sec. of wave generation

Figure 3 - Simulation results of Model A

Figure 4 - Group velocity dispersion curves for L-Mode (OD=5.0mm,

t=1.0mm, Aluminum alloy tube)

0

1000

2000

3000

4000

5000

6000

0 500 1000 1500 2000

Frequency(KHz)

Gro

up

Ve

locity

(m

/s)

L(0,1)

L(0,2)

Wav

e pr

opag

ation

dire

ction

200kHz

L(0,1)

200kHz

500kHz

1MHz

(a) Details of 200kHz L(0,1) mode

Wav

e pr

opag

atio

n dire

ction

1MHz

L(0,2)

200kHz

500kHz

1MHz

(b) Details of 1MHz L(0,2) mode

Wav

e pr

opag

ation

dire

ction

1MHz

L(0,1)

200kHz

500kHz

1MHz

(c) Details of 1MHz L(0,1) mode

Figure 5 - Deformation and vibration display of wavelets

- 0. 4- 0. 20. 00. 20. 4Relative amplitude 8006004002000 Ti me ( 10- 6sec. )

radi al ( out - of - pl ane) di spl acement axi al ( i n- pl ane) di spl acementL(0,2)

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

L(0,1)

(a) Experimental Result [8] (b)Simulation result

Figure 6 - Comparison of received waveform

L(0,1) mode

0 500 10000

2000

4000

6000

Frequency, kHz

Gro

up V

elo

city.

m/s

L(0,1) mode

L(0,2) mode

0 500 10000

2000

4000

6000

L(0,1) mode

0 500 10000

2000

4000

6000

Frequency, kHz

Gro

up V

elo

city.

m/s

L(0,1) mode

L(0,2) mode

0 500 10000

2000

4000

6000

0 500 10000

2000

4000

6000

(a) after 20sec. of wave generation (b) Group velocity dispersion curves for L-Mode

(OD=34mm, t=3.2mm, Stainless steel piping)

Figure7 - Simulation result of Model B and group velocity dispersion curve

Transmitter (Probe Elements)

L(0,2)

L(0,1)

T-mode

excitation 1000

mm

Wav

e pro

pagat

ion

15R50

0 m

m

1000

mm

Wav

e pro

pagat

ion

15R50

0 m

m

Thickness =1mm

Diameter =5mm

T(0,1)-mode

(a) Structural Modelling (b) after 160sec. of wave generation

(c) after 167sec. of wave generation (d) after 171sec. of wave generation

(e) after 175sec. of wave generation (f) after 179sec. of wave generation

Figure 8 - Guided wave propagation through U-bent tube with T-mode excitation

F-mode