CM NDT-98, 20-23 October, 1998, Minsk, Belarus.
2nd International Conference on Computer Methods and
Inverse Problems in Nondestructive Testing and Diagnostics.
Proceedings published by DGZfP
TABLE OF CONTENTS |
Axi-symmetric finite element model has been applied to the analysis of remote field eddy current test technique for investigating weld connecting sleeve with main tube. Such welding is used in heat exchangers as a repair method for corrosion damaged non-ferromagnetic tubes. Numerical calculations have been used for analysis of eddy current field distribution in weld region as well as for prediction of receiver signal phase dependence on influencing factors (electrical conductivity of components, filling coefficient), and for selection of test frequency.
A remote field eddy current (RFEC) technique is one of the newly used method for examining tubes in steam generators. In pipeline inspection operation, this method allows to test both the interior and the exterior surface of the piece [1,2]. One of the limitations inherent in this testing is the low level of the response signal to a test variables when the probe moves along the tube. It is therefore important, at first, to evaluate a possibility to use this technique in difficult test situations. It is obvious, that in order to get a better knowledge of the phenomena and to improve the performances of the RFEC method, the use of a numerical field calculation can provide a large help.
Numerical modeling of physical phenomena in many testing situations is of significant importance especially for the nuclear industry where heavy reliance on classical as well as on remote field eddy current techniques is encountered. In some situations here, the numerical process is the only feasible way to analyze the testing situation, in particular, in the case of testing quality of welding between two coaxial tubes. The use of a model allows to extend the range of application of RFEC technique to situations where the components are intrinsically quite difficult to inspect.
Heat exchanger tubes in nuclear power plants, when damaged by corrosion attack have to be plugged if the reduced wall thickness has reached a certain limit. Efficiency of the heat exchanger component gets poor, if too many tubes are closed. An alternative repair method is done by inserting a second tube in order to cover the damaged regions. This inserted sleeve is welded to the first tube by laser beam [3]. Afterwards, this welding has to be proofed by one of non-destructive techniques.
Up to date, the possible way to non-destructive examine such difficult situation was to use ultrasonics. Ultrasonic testing works quite well but it is slow and requires a lot of preparation prior to testing. Besides of this, the ultrasonic results show clearly the importance of the level of weld-surface waving in relation to welding size to be tested. Quite good results were obtained only in case if this level is small enough and no more than the order of a gap between tubes.
Current reseach work relates to numerical investigation of the feasibility of the RFEC testing procedure for examination of weld between two coaxial non-magnetic tubes. A key part of this effort is concerned with the use of finite element model for predicting the RFEC probe induced signal (resistive and reactive components). The particularity of this model and of the related package MagNum [4], is to be oriented towards the NDE modelisation.
In the RFEC technique, the excitation and the measurement coils are quite far from each other (the distance between these two coils is several pipe diameters) [1,2]. The receive coil measures an induced voltage that is generated by two different magnetic fields:
In the vicinity of the excitation coil, the direct field is dominant; far from the excitation coil, the remote field is dominant. For this reason, in a remote field operation, the receive coil is placed several pipes diameters far from the excitation coil. In this case, the field measured by the receive coil is a field generated by the induced eddy currents. They are affected by presence of welding connecting two tubes and the related magnetic field is also affected.
All the electromagnetic phenomena that occur in such operation can be modelized by a classical numerical method - finite element method, and the associated package must present some particularities:
The values of the measured fields are very small, so the experimental system has to be performant. And, as it will be seen below that this little value of the measured voltage in the receive coil will dictate our choice of the modelization technique.
In order to simulate the physical behavior of our system, we have to compute the eddy currents inside the tube wall. For this, some assumptions can be made according to geometry - all components of system (two coaxial tubes, excite and receive coils, as well the weld structure) have an axi-symmetric geometry. One of the classical complex equations governing the electromagnetic phenomena in axi-symmetric geometries was formulated for the magnetic vector potential. The finite element approach we used was a classical variational formulation - the solution of the equation is equivalent to the minimization of the appropriate energy functional [5].
Fig 1: Outline of the finite element model used in the investigation of influence of frequency on difference signal Fig 2: Zoom-in of the mesh in the region of the weld-model |
Fig 3: The magnetic flux distribution at one time step presented for fixed weld position and for frequency 5 kHz Fig 4: The magnetic flux distribution at one time step presented for fixed weld position and for frequency 7 kHz. |
Fig 4a: Calculated influence of frequency on difference signal phase |
Fig 5: Calculated influence of welding conductivity variation on difference signal phase(tube material conductivity 2 MCm/m, frequency 425 kHz) Fig 6: Calculated influence of welding conductivity variation on difference signal phase(welding conductivity 2 MCm/m, frequency 425 kHz) |
Fig 7: Calculated influence of filling factor on difference signal phase (frequency 425 kHz) |
The analysis domain includes sleeve tube (with inner diameter 16.6 mm, wall thickness 1.2 mm, conductivity 2 MSm/m) inside another one (with inner diameter 19.5 mm, wall thickness 1.25 mm, conductivity 2 MSm/m), the gap 0.25 mm between the two tubes, excite and receive coils (each with inner 12 mm and outer 16 mm diameters and length 2 mm) distanced by 42..50 mm. All calculations in each investigation series were performed on the same mesh (usually consisting of about 10000 finite elements) with only the materials allocations changing in the welding region, where some of the triangular elements were specified sometimes as weld or air, and sometimes as tube material.
The finite element mesh used in the simulation is very important for the quality of results. In case for modeling probe displacement in coaxial tube system with a welding, we imposed a fixed position for the excitation coil and simulated a weld displacement. All the next weld positions were defined and were considered like different "materials" with appropriate values of electric conductivity. All these positions were identified by a genetic name. This procedure implied a mesh with bigger number of nodes, but this discretization mesh was made once for each series.
In other investigation cases of the automatic solution, only one position of the weld was taken into account, while the others were "masked" by modifying the electromagnetic properties of these "materials". A single mesh including one position of the weld, was generated and the different calculations were made with and without weld in order to give absolute and relative variations in relation to coaxial tubes without weld. We supposed that the receive coil was connected to an infinite impedance, therefore, this coil did not modify the flux lines distribution. So, its position was not included in the mesh and the flux through the receive coil was directly calculated from the solution of equation system. Just after automatic simulation, the various possible positions of the receive coil and its parameters (dimensions, number of turns, distance from excitation coil) can be defined.Geometric details of the solution domain for investigation are shown in Figure 1. In order to improve accuracy and provide resolution in the region of weld, the mesh density here was made high. To give an impression of the refinement of the mesh (in case of investigation of influences), this region is shown in Figure 2.
Influence of frequency on flux redistribution
The classical flux lines at one time step are presented for fixed weld position and for two different frequencies (figures 3 and 4). We can notice that the flux lines concentrate around different "secondary" centers in each case, but its perturbation near receive coil is not clearly visible. So, only the numerical values of flux through receive coil can be considered in order to study the influence of the different frequencies.
Influence of frequency on signal phase
It was the most interesting to investigate influence of frequency on phase of receiver signal.In this case we calculated the difference signals generated by the tested situation taking the signal calculated for a particular weld parameters and subtracting from it the signal obtained for the weld-free case to give just the required value. This difference signal phase was evaluated for various frequencies and for different distance between exciter and receiver, and the most suitable frequency (approximately 425 kHz) was selected as optimal considering the maximum of this difference signal phase for distance 40 mm (see figure 4).
Influence of component conductivity on signal phase
In this case we calculated the difference signal phase for various values of component conductivities (weld material and tube material) and, as in previous case, for different distances between exciter and receiver. Figure 5 shows influence of welding conductivity (with fixed value for tube material conductivity) and Figure 6 - influence of tube conductivity comparable to constant value of conductivity of weld (tested frequency was selected as 425 kHz). From the obtained results, we can conclude that the selection of operating frequency is sensitive to electrophysical parameters of components and geometrical parameters of detector.
Influence of filling factor on signal phase
In this case we calculated the difference signal phase for various relative values of receiver diameter (so-called, filling factor) and for different distances between exciter and receiver. Figure 7 shows influence of such factor on obtained results, which demonstrates sensitivity of selected operating frequency.
Some numerical results of this investigation demonstrate how the RFEC technique can be used to evaluate welding parameters between two coaxial tubes in heat exchanger tubes. The possible RFEC response signals were obtained using finite element software package MagNum. The numerical analysis was used to examine the effect of weld parameters and some influencing factors on the induced voltage in receive coil.
Considerable work still remains to be done before realistic welding shapes can be handled in three dimensions, but nevertheless, these initial results do give an indication of the power of the finite element method to predict RFEC signal.
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