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The Analysis of Guided Wave Propagating on Elbow Pipe
Shiuh-Kuang Yang 1,a
, Hong-Yi Chen 1, Jyin-Wen Cheng
2, Ping-Hung Lee
3, Jin-Jhy
Jeng 4 and Chi-Jen Huang
3
1Department of Mechanical and Electro-Mechanical Engineering, National Sun Yat-sen University,
Kaohsiung, 80424, Taiwan 2Cepstrum Technology Corporation, Kaohsiung, 80245, Taiwan
3Taiwan Metal Quality Control Corporation, Kaohsiung, 81256, Taiwan
4CPC Corporation, Kaohsiung, 81126, Taiwan
aemail: [email protected]
Keywords: Guided Wave, Elbow, Interference, ANSYS
Abstract. Guided wave technique is widely used in the petrochemical plant for pipes inspection. The
technique detects corrosion and defects on straight pipes easily. However, pipe bends or elbows are
known to distort the guided waves due to its anti-symmetric natures in geometry. The interference of
the propagating guided waves occurred inside and beyond the elbow could lead to complicated signals
from features reflection. It may cause missing detections or fault calls of flaws on and beyond the
elbow pipe. This paper focuses on the above-mentioned interference phenomena through pipeline
with elbows. A finite element method, ANSYS, was used to obtain the transient solution for the
travelling guided waves along a pipe elbow without defect. The reflection signals of the guided wave
mode T(0,1) and its converted modes were analyzed. The results were also verified with experiments
by a commercial guided wave system on a 6-inch diameter, schedule 40 steel pipe. The comparisons
between the simulated and experimental results were in good agreement.
Introduction
The advantage of using guided wave method for pipelines inspection lies in its short testing time
and long-rang detection ability. Pipes are commonly nested in the field of refinery and petrochemical
plants. The pipe elbows are usually used to change the path of the pipeline for manufacturing process
and space requirements. However, the geometry of elbow makes the guided wave path is no longer
completely axially symmetry and the mode conversion of the guided wave occured. Results of the
mode conversion also cause the signal of guided waves become more complex and difficult to
identify for analysis. It may also lead to missing detections or fault calls of flaws on and beyond the
elbow pipe.
For guided waves used in the field, Rose et al. [1-6], Alleyne et al. [7-12] published a number of
researchs in recent years to study the feasibility of guided waves used in pipeline detection technology.
In 2001, Rose et al. [13] excited the high-order and non-axisymmetrical modes propogating on the
straight tube to find defects 360。around the circumferences. In 2005, Hayashi et al. [14] used
simulation method to excite a point source on a straight pipe to discuss its wave propagation and
interference behavior. Sun et al. [15] generated a flexural torsional guided wave on the straight pipe in
experiments to study its wave propagation and interference status. At the year of 2005, Rose et al. [16]
reported an automatic interference low frequency guided wave experiment for the detection of defects
beyond elbows. In 2011, Nishino et al. [17] studied the ring-shaped array on an aluminum pipe to
analyze the transmission signal after elbow by pitch and catch method. The transducers were fixed
before and after elbow and generated 30 to 80 kHz frequency range in experiment. The time-domain
signals were received to identify varity modes by phase characteristic analysis. They successfully
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separated different order of torsional modes which come from pipe elbow.
Finite element set up
A finite element software package ANSYS is used to simulate the T(0,1) guide wave propagation
behavior in this paper. A 6 inches with schedule 40 elbow steel pipe is given in ANSYS analysis. The
pipe generally consists of two straight with an elbow welded together. The outer diameter of pipe is
168-mm, internal diameter is 154-mm, Young's modulus is 216.9 GPa, density is 7932 3
mkg , and
Poisson's ratio is 0.2865, respectively, are applied for simulation. The dimensions of elbow are
obtained from American National Standards Institute. The radiu of bend is set to 90 degrees, the
curvature is 229-mm. The centerline length of bend approximately 360-mm is calculated by geometry
of bend. The arc length of the inner pipe 228-mm and the arc length of lateral 492-mm are also
obtaibed from geometry calculation. The sources, a series of 30 kHz, 5 cycles Hanning-windowed
tune burst signal, generated as displacement load are applied along the θ-axis of the cylindrical
direction since T(0,1) is a axisymmetric torsional mode. It is uniformly applied on the pipe to generate
T(0,1) mode propagating on the pipe. Furthermore, to understand the interference of guide waves on
the elbow, the output time-domain signals of nodes (total of 60 nodes) on the circumferential
direction will be calculated. The results of time domain analysis can be presented on the polar plot as
the guided wave interference pattern of the elbow pipe.
This paper analyzes the guided waves propagating through elbow on the pipe to understand the
interference behavior of the wave modes occurred from mode conversion. Thus, the signals on and
beyond elbow will be analyzed. A schematic diagram of simulation model setup is shown in Fig. 1 (a)
where the elbow is divided into six parts by the 15 °, 30 °, 45 °, 60 ° and 75 ° cutting, respectively. To
make the comparison between the pipe with elbow and a straight pipe, the 1λ to 20λ meshing beyond
elbow and the analog position of the straight pipe are meshed and shown at the lower part of Fig. 1 (a),
where λ is the wavelength. There are two welds on the straight pipe to correspond with the welds
before and after elbow. In addition, the cross-section of the pipe shown in Fig. 1 (b) is divided into 12
positions to identify the location of circumferential direction on the pipe. The 3- and 9-, 0- and
12-o’clock positions represent the inner and outer side of curvature center, the top and button position
of the pipe, respectively.
To make the comparison easier, the signals obtained from the straight pipe are used to normalize
the signals obtained from the elbow pipe. The amplitude ratio is calculated as follow
(a) (b)
Fig. 1 A schematic diagram of simulation model set up
pipestraightonamplitude
pipeelbowonamplituderatioamplitude = う1え
Interference behavior of guided waves on the elbow
Fig. 2 shows the interference pattern of guided waves at the cross-sections of the elbow cutting at
different degrees as shown in Fig. 1 when a 30 kHz symmetric T(0,1) guided wave is incident from
the left end of the pipe. The amplitude ratio of the total traveling waves, i.e., the T(0,1) and the other
converted waves, on the cross-sections can be seen in the figure. It remains symmetric at 10o
cross-section since mode conversion does not happen at the beginning, then starts focusing on the
outer part of the elbow after 30° of the elbow, and then becomes focusing at multiple directions. At
directions other than the focusing locations, the amplitude ratios are significantly reduced. Noted that
the amplitude ratio can even up to 2 times compared to the straight pipe.
The ANSYS simulated propagating guided waves on the pipe are displayed in Fig. 3. The figure
shows that when a T(0,1) guided wave is entering the elbow at the beginning, the amplitude ratio
distributes uniformly on the pipe. However, when wave comes to the deeper elbow location, the
amplitude ratio of waves concentrates at the outer side of elbow. It became evident that the focus
phenomenon is displaying on the elbow. The focus area is even more concentrated until the wave goes
through the elbow as shown in Fig. 3 (e) - (h).
Fig. 2 The interference pattern of the total guided waves on different cross-sections of the elbow
Fig. 3 The ANSYS simulated waves is propagating on the elbow
(a)
(b)
(c)
(d)
(e)
Interference behavior of guided waves beyond the elbow
The interference pattern of the 30kHz guided waves beyond the elbow from 1λ to 20λ distance are
shown in Fig. 4. It shows that the interference behavior of the guided wave due to the elbow has a
dramatic change from 1λ to 5λ after passing through elbow shown in Fig. 4 (a)-(e). The phenomenon
results from that all modes are overlapping at that time. The interferences are still last even the waves
are 20λ away from the elbow as can be seen in Fig. 4 (f)-(t). The reason that the guided wave
interference occurred is mainly due to different modes propagated with similar velocity. For example,
when T(0,1) wave encounter a elbow during propagating at 30 kHz frequency. F(1,2)、F(2,2) and
F(3,2) are generated due to mode conversion as shown in the dispersion curve (Fig. 5). Fig. 6 shows
the time domain signals of each mode at positions 5λ, 10λ, 15λ and 20λ after the elbow. The group
velocity of F(2,2) and F(3,2) modes are close to T(0,1) mode; thus, the F-modes still overlap with
each other when T(0,1) wave has just left the elbow within the distance of 1λ to 5λ (Fig. 6 (a)). After
that short region, the longer the traveling distance, the less interference of the guided wave. This
phenomenon can be seen in Fig. 6 that the slowest F(3,2) mode is completely separated from the other
modes while T(0,1) and F(1,2) modes will still interfere with each other due to their similar group
velocity. However, the behavior of interference become much simpler due to fewer modes.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
(p)
(q)
(r)
(s)
(t)
Fig. 4 The interference pattern of the total guided waves at different distances beyond the elbow
Fig. 5 Dispersion curve. Phase velocity for left and group velocity for right
(a) 5λ (b) 5λ
(c) 15λ (d) 20λ
Fig. 6 Time domain signals of each mode at different places beyond elbow (m=2)
Experimental set up
This paper mainly investigates the behavior of interference when a guided wave T(0,1) mode
propagating through the elbow. The experiment therefore is setup as pitch-catch technique to measure
the transmission wave. A 6- inch schedule 40 (168-mm outer diameter, 7.1-mm wall thickness) steel
pipe with 90° elbow (229-mm bend radius) is used in the experiment. The schematic diagram of
experimental pipe is shown in Fig. 7. Two transducer rings are mounted on the pipe for guided wave
generation and transmission wave receiving, respectively. The distances between two rings are at
0.55-, 1.1-, 1.6- and 2.2-m, respectively. The transducer ring is divided into six segments as shown in
Fig. 8 for signal analysis in the circumferential direction of pipe. Fig. 8 shows that A1 and A6 are the
outer side of the elbow. The segment A3 and A4 are the inner side of the elbow. A Guided Ultrasonic
Ltd. wavemaker G3 instrument is used to generate an 8-cycle Hanning-windowed tone burst signal.
The transducer ring is excited at 14, 18, 24, 30 and 37 kHz, respectively, to propagate the torsional
T(0,1) mode on the pipe for elbow analysis. The guided wave is generated by transmmitting ring and
the signals after the elbow are analyzed by the receiving ring. The results of experiment will be
compared to the simulation.
Fig. 7 A schematic diagram of experimental pipe
Fig. 8 A schematic diagram of 6 segments are distributed
Experimental results
Both experiments and its simulations results are shown together in Fig. 9. Fig. 9 shows that there
is no interference behavior at low frequency, take 14 and 18 kHz for examples, both on experimental
results and simulations. It is found the amplitude pattern of 0.55-m has slight interference at inner side
of the elbow. This is because that there are fewer modes at low frequency as observe from Fig. 5 and
that the non-axisymmetric modes can be separated obviously. When the exciting frequencies are
increased to 24, 30 and 37 kHz the interference behavior becomes strong. It is evident that the mode
conversion phenomena observed and induce higher order non-axisymmetric modes at high frequency.
Also, the simulated and experimental results are in good agreement for the behavior of interference on
the elbow pipe as can be observed in Fig. 9.
Summary
This paper investigates the behavior of interference on T(0,1) mode propagating through the
elbow. A finite element method, ANSYS, was used to obtain the transient solution for the travelling
guided waves along an elbow without defect. The reflected signals of the guided wave mode T(0,1)
and its converted modes were analyzed. The results were also verified with experiments by a
commercial guided wave system on a 6-inch diameter, schedule 40 steel pipe. The interference
patterns of guided wave are demonstrated at each circumferential positions on the elbow pipe. When
the guided wave propagates on the elbow the mode conversion is occurred to generate higher order
non-axisymmetric modes. The comparisons between the simulated and experimental results were in
good agreement.
(a) (b) (c)
(d) (e)
Fig. 9 Experimental results compared with simulation results
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