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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 1

Department of Mechanical and Electro-Mechanical Engineering, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan 2 Cepstrum Technology Corporation, Kaohsiung, 80245, Taiwan 3 Taiwan Metal Quality Control Corporation, Kaohsiung, 81256, Taiwan 4 CPC Corporation, Kaohsiung, 81126, Taiwan a

email: [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

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 kg m 3 , 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

amplitude ratio =

amplitude on elbow pipe amplitude on straight pipe

(a)

1

(b)

Fig. 1 A schematic diagram of simulation model set up

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).

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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

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.

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(f)

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(h)

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(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

(c) 15λ

(b) 5λ

(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.

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(b)

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Fig. 9 Experimental results compared with simulation results

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