NDT.net • Nov 2005 • Vol. 10 No.11 
Diagnostics of multilayer cylindrical structures based on wave’s interferenceV. Volkovas, V. SukackasKaunas University of Technology Technological Systems Diagnostics Institute Published in ISSN 13922114 ULTRAGARSAS, Nr.2(55) 2005 AbstractThe paper analyses the mechanism of asymmetric Lamb wave interference and the features of the phenomenon, dependent on the state of multilayered cylindrical structure. It is shown that the state of cylindrical structure, which is characterized by sediment layer, formed during technological processes, can be controlled by analyzing amplitude frequency function of the structure. The proposed means are averaging method, correlation function and Fourier methods.IntroductionA layer of the sediment forms and firmly sticks to the wall of different cylindrical structures, for example, on pipelines during the operation in chemical, oilprocessing industries and in power plants. The layer makes technical performance of devices considerably worse. Thus, diagnostics of technical state of pipes is an important problem. Diagnostics of the condition of internal cavity of pipes should answer the following questions:
b) if not, what is at the internal walls: liquid or solid; c) if there is a solid layer, what is the thickness of it. In this case wellknown ultrasonic, impulse and resonance methods of thickness measurements are nonefficient. As a rule, the surface of a sediment layer is nonuniform and porous thus hindering a sufficient reflection of ultrasonic waves necessary for the functioning of the thickness measuring instruments. The sediment is nonhomogeneous and is notable for the absorption and scattering of ultrasonic waves. In addition, conventional measuring instruments can merely measure the local thickness. In our case it would be necessary to make a number of measurements of the same diameter of the pipe. It is very promising to develop a method that would enable us to measure some generalized thickness of a sediment. We suggested new principles of diagnostics that can answer these questions and enable development of original measuring instruments and indicators for sediment layer thickness and liquid level sensors in pipelines. One integral value of the measured unit in one crosssection of the pipe is enough for these instruments. Therefore, measurements in a number of crosssection points are not necessary and measuring effectiveness is considerably increased. For obtaining the integral value it is purposeful to use waves of the same order or longer than wall thickness and longer than the measured sediment thickness. We used antisymmetric Lamb’s waves of the zero order 1. Waves propagating within the cylindrical structure and interference phenomenonAmong variety of cylindrical structures there are the pipelines for which d << R, where: d is the thickness of the wall, R is the average radius of the wall. The segment of the wall (Fig. l) slightly differs from the plate with the thickness d when symmetrical and asymmetrical Lamb waves are easily excited:
The coordinate system is shown in Fig. 1. It is characteristic of the functions F_{s} and F_{a} that their values are not equal to "0" in the surfaces of the wall when z = d/2. The latter circumstance is very important in our case, when a layer of the sediment is formed and it firmly sticks to the wall. The waves excite displacements also in the direction of axis x, that will not be taken into account when considering the excitation and the reception of the waves we use. Without any restriction, i.e. for any d there exist and, therefore, can be easily excited only the Lamb waves of the lowest order: the symmetrical U_{sz} and asymmetrical U_{az}, when m_{s} = m_{a} = 0, the above mentioned waves differ in the distribution of displacements. They are symmetrically distributed in the wave U_{sz} with respect to the plane z = 0 and when d → 0, this wave becomes longitudinal. On the contrary, the displacement (of one sign) in the thickness of the plate is characteristic of the wave U_{az}, when d → 0, it becomes flexural.
Both waves differ in absolute values of the wave velocity and in the dispersion dependence on the frequency. The velocity of the waves has been measured by two methods: interferometric and impulse. One of the transducers is excited by the alternating voltage while measuring with the interferometry method. The longitudinal waves propagate along the wall and are transformed into the Lamb waves spreading in all directions (in the plane z = 0, Fig. 1). Standing waves are formed in the wall, if the phases of the sending signal and the signal propagating a round the wall in both directions coincide. These waves interfere and are registered by another transducerreceiver (Fig.2).
Every time such resonances are repeated, when
Investigation [3, 4] shows that the asymmetrical Lamb wave of the lowest order propagates in an empty wall and another wave that can be excited is symmetrical of the lowest order and differs very much in the character of speed values and dispersion. Waves of the higher orders are not excited below the critical values of d · f. The frequency response of an empty steel pipe is shown in Fig.3 (straight line). Its exterior radius is R = 76 mm, the thickness of the wall is d = 8 mm. The resonance frequency that is rounded to kHz is marked by the resonance upper parts. It is obtained by comparatively narrowband transducers. The measurements were carried out using wideband nonresonance transducers, with the above mentioned pipes and also different pipes, their radius being R = 25 mm and d=3.5 mm. 2. Discussion of the resultsThe measurements were carried out when the parameter f·d=(40160) kHz·cm. The values of the speed (m/s) and the character of dispersion, (considerable increase of the speed), while increasing "f·d" (f is frequency), especially at f·d=150 kHz cm, show that the asymmetrical Lamb wave of the lowest order is excited in the wall. The frequency response of the pipe having a 1.5 2.0 cm layer of sediment is marked by the dotted line (Fig.3). The pipe has been used for oilrefining at high temperatures. One can see that the interference is considerably reduced. Experiments have shown that the interference is also reduced by the liquid that is in a pipe and this fact must be taken into consideration.This reduction interferes with the use of the interferometric method of velocity measurement. While using the impulse method for the pipe, its radius being R=25 mm and d=3.5 mm, it is proved that, when a layer of sediment changes within the limits of 0 – 10 mm, the velocity of waves changes not more than 10%. It allows drawing a conclusion that another type of waves do not occur. If they occurred, the difference among the speeds would be greater because the expected velocities of waves in sediment are at least twice less than in steel. We managed to evaluate only the velocity of longitudinal waves in sediment, when is 2700 m/s. Therefore, the sediment plays an effective role of a damper. It allows expecting a great sensitivity of the method with negligible thickness. On the contrary, with greater thickness we expect lower sensitivity. The experiment showed that due to the attached mass layer of liquid or solid having an acoustic contact with the internal surface of the pipe changes the velocity of waves and increases their absorption. Each of these effects was applied in different fields [5]. Correlation between the condition of the pipe and characteristics of interference is another important question in investigation of the problem. It is possible for different thickness of the sediment in the pipe to carry out the measurement of the parameters of interference. But for that case we must to develop a method that would enable us to determine diagnostic parameters which are reliable enough. We apply the autocorrelation function of the frequency response, which is measured using the transducerreceiver configuration (Fig.2). The autocorrelation function easy shows the differences – maximum steepness of that function in the internal units its first local trough is strictly related to the attenuation of waves in the wall of resonance pipe (see Fig.4).
Investigation [6] showed that the envelope function of the received pulse u = u(f, t) depends on a sediment’s layer. We apply 2D FFT for analysis of that function (see Fig.5). The results show that decrease of the velocity of peaks of the mapped signals is the measure of wave absorption in the pipe’s wall an can be characteristics of sediment‘s value inside the pipe. Using this method, the measurement time decreases, in comparison with the correlation method. ConclusionsThe mechanism of the mentioned phenomenon is not completely clear and investigations are being continued. The dispersion of the velocity is chaotically scattered in the way of waves, when the layer of sediment is not thick enough. This fact appears because of the unevenness of the total sum thickness. A portable indicator of sediment is being developed [3]. It operates according to the method described above. The transducer is excited by the voltage and the frequency is modulated according to the "triangle" law within the limits of 110150 kHz.The ratio of the maximum of the received signal and its average value are approximately proportional to the quality factor of the system and changes from tens in an empty pipe to ones in a pipe with some sediment. That was the main information about the processing algorithm in the device. The correlation function has characteristic dependence that allows development of new measuring instruments for estimation of sediment layer thickness. The described interference method may be developed using another processing method of the frequency response, e.g., 2D FFT. References

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