The influence of support plate on MFL testing for a heat exchanger tube

Abstract

Defects are usually developed on the outside of heat exchanger tubes due to large friction between the support plate and the tube. In this paper, in order to improve the accuracy of the MFL (magnetic flux leakage) testing for heat exchanger tubes, the influence of support plate on MFL testing is investigated. Firstly, the influence of support plate on the magnetization status is theoretically analyzed by magnetic circuit analysis. Then, numerical simulations are conducted to investigate the magnetization intensity of the tube at different locations. Finally, MFL experiments for heat exchanger tubes are performed, in which a differential induction coil array is proposed to eliminate the background signal caused by support plate. The testing results show that the MFL signal amplitude is increasing with the defect moving from the center of the support plate to the edge, which should be taken into consideration in the evaluation of heat exchanger tubes.

Keywords

Heat exchanger tube support plate MFL (magnetic flux leakage) testing magnetization intensity

1. Introduction

With rapid developments of petrochemical industry, heat exchangers are widely used due to the efficient operation [1]. However, defects such as corrosion, erosion, pitting and cracks are inevitably developed in heat exchanger tubes by corrosive water and gas [2,3]. Specifically, these heat exchanger tubes are tightly held together by support plate, as a result, corrosions or defects are usually developed on the outside of the tubes due to large friction between the support plate and the tube [4–7].

In order to ensure the safety of heat exchanger, nondestructive testing (NDT) techniques are applied to inspect the heat exchanger tubes [4–11], such as eddy current testing (ECT), remote field eddy current testing (RFECT), pulsed eddy current testing (PCET), ultrasonic-internal rotary inspection (UT), ac magnetic flux leakage testing (ac MFL) and dc magnetic flux leakage (dc MFL). Since the block effect of external support plates, MFL probes are moved inside the tube to inspect the defects. Alternative electromagnetic excitation based testing methods such as the ECT methods and ac MFL have a limited sensitivity to these defects on the outside of the tubes due to the skin effect [12]. Besides, heat exchanger tubes are made of ferromagnetic materials, whose permeability cannot be held to a constant value, thus, ECT could be influenced by the variable permeability, which is another restriction for the ECT application. Additionally, UT method is not sensitive for the surface defects, the material surface needs couplant, and the low repetition frequency limits the testing speed.

As a powerful and highly efficient NDT technology [13–17], the dc MFL testing has been widely used for elongated ferromagnetic objects, such as the pipelines [18,19], rails [20], steel wires [21,22] and heat exchanger tubes [6]. In the MFL application for heat exchanger tubes, the big challenge is the detection of defects underneath or near the support plate caused by the friction. The support plate generates detection signals even without any defect, since some of the magnetic flux is absorbed into the support plate, which has been analyzed in previous papers [6]. On the other hand, the defects of same size but located at different places respect to the support plate generate different MFL signal amplitudes, which has been overlooked in the previous studies.

Hence, in this paper, in order to improve the accuracy of the MFL testing for heat exchanger tubes, the influence of the support plate is investigated by theoretical analysis, numerical simulations and MFL experiments. The rest of this paper is organized as follows: Section 2 analyzes the influence of support plate on magnetization intensity of the tubes by magnetic circuit analysis; Section 3 conducts numerical simulations to investigate the magnetization intensity and MFL signal amplitudes; Section 4 performs MFL experiment for heat exchanger tube; and Section 5 presents the conclusion.

2. The MFL testing for heat exchanger tube with a support plate

A MFL testing probe for heat exchanger tubes is illustrated in Fig. 1(a), which consists of a permanent magnet and a differential induction coil array. As displayed in Fig. 1(b), the permanent magnet generates a magnetomotive force, which drives magnetic flux through the air gap and the tube, as indicated by dotted lines. In the MFL application, the probe is moved inside heat exchanger tubes. If there is any defect in the tube, magnetic flux 𝜙_mfl will leak into the air and be detected by induction coils [23]. However, for the defects on the outside of the tube underneath or close to the support plate, the magnetic flux distribution is different, as displayed in Fig. 1(c). Due to the high permeability of the support plate, some of the magnetic flux 𝜙_s prefers the support plate path, weakening the magnetization intensity of the tube and the leaked magnetic flux 𝜙_mfl.

Fig. 1.

The MFL testing principle for heat exchanger tubes. (a) The MFL testing probe; (b) magnetic flux distribution of the defect without support plate; (c) magnetic flux distribution of the defect with a support plate.

In order to analyze the influence of support plate on MFL testing, a simplified magnetic circuit is built. As displayed in Figs 2(a) and (b), the magnetic flux generated by the permanent magnet firstly passes through the air R ₀, then the tube body R ₁, and finally the combined area of the tube R ₂ and the support plate R _s.

Fig. 2.

The magnetic circuit model of the heat exchanger tubes with support plate. (a) Magnetic elements of the magnetization circuit; (b) the simplified magnetic circuit.

Based on the Hopkinson’s law, the magnetic flux 𝜙_t passing through the tube is expressed as follow [24]: $\begin{eqnarray}\displaystyle {\phi}_{\text{t}}=\frac{F}{(2R_{0}+2R_{1})+R_{2}+{\displaystyle \frac{(2R_{0}+2R_{1})R_{2}}{R_{\text{s}}}}} & & \displaystyle\end{eqnarray}$ (1) where F denotes the magnetomotive force depending on the permanent magnet; R ₀, R ₁, R ₂ and R _s denote the magnetic reluctance of magnetic elements, respectively.

The magnetic reluctance is expressed as follows [24]: $\begin{eqnarray}\displaystyle R=\frac{l}{{\mu}A} & & \displaystyle\end{eqnarray}$ (2) where l is the length of the magnetic circuit element, 𝜇 is the relative permeability of the material, and A is the cross-sectional area of the magnetic circuit element, respectively.

Based on the Eqs (1) and (2), high-permeability support plate has a small magnetic reluctance R _s, and the small R _s will lead to a weakened magnetic flux 𝜙_t in the tube and thereafter generate a weak MFL signal. On the other side, from the center of the support plate to the edge, the increased R _s will enhance the magnetic flux 𝜙_t in the tube and thereafter leads to an increasing MFL signal amplitude.

3. Simulation study of MFL testing for heat exchanger tube with a support plate

In order to obtain an accurate influence of support plates on MFL testing, numerical simulations are conducted to investigate the magnetization intensity and MFL signal amplitudes by the electromagnetic simulation software ANSOFT. The simulation model is built and displayed in Fig. 3. A tiny crack (0.20 mm in width and 0.6 mm in depth) is made at the combined area of heat exchanger tube and the support plate. The conductivity and relative permeability of the tube and support are 2 × 10⁶ S/m and 700, respectively. In mesh operation for heat exchanger tube, the maximum size of elements is restricted to 0.01 mm. Firstly, magnetization intensities of the tube with different distances d from the support plate center are simulated, as shown in Fig. 4. It can be seen that with the increase of the distance d from 0.0 mm (at the support plate center) to 8.0 mm (at the support plate edge), the magnetization intensity of the tube is increasing; after that, the magnetization intensity has a slow decreasing trend, which matches well with the Eq. (1).

Fig. 3.

The simulation model for heat exchanger tube (unit: mm).

Fig. 4.

The magnetization intensity of the tube at different locations from the support plate center.

Then, the magnetic flux densities around the defect affected by the support plate are simulated. In the simulation, for the defects located at different positions respect to the support plate, the permanent magnet is always placed to make the defect located at the center of the magnet Fig. 5(a) shows the magnetic flux density in the tube without support plate; then, the defect of same size but located at the support plate center is simulated, as displayed in Fig. 5(b). Compared to Fig. 5(a), it can be seen that there is an obvious decrease of the magnetic flux density around the defect. Further, the defects located at distances of 3.0 mm and 6.0 mm from the support plate center are simulated, as shown in Figs 5(c) and (d). From the Figs 5(a), (b), (c) and (d), it can be concluded that the support plate reduces the magnetization intensity. In particular, from the center of the support plate to the edge, the magnetization intensity of the tube is increasing.

Fig. 5.

The magnetic flux density around the defects of same size but at different locations. (a) The defect without support plate; (b) the defect located at the support plate center; (c) the defect located at distance of 3.0 mm from the support plate center; (d) the defect located at distance of 6.0 mm from the support plate center.

Further, the MFL distribution generated by defects are simulated. As displayed in Fig. 5, along the line l with a liftoff distance of 0.5 mm from the tube surface, the radial and axial MFL components are calculated and plotted in Figs 6(a) and (b), respectively. It can be seen that the defects of same size but at different locations respect to the support plate generate different MFL signals due to the different magnetization status. For the defects located from the center of the support plate to the edge, the amplitudes of both radial and axial MFL components are increasing.

Fig. 6.

The MFL distribution generated by the defects at different locations. (a) Radial MFL component; (b) axial MFL component.

4. Experimental studies of heat exchanger tube with a support plate

To validate the influence of the support plate on the MFL testing, experimental studies are conducted. In order to eliminate background testing signals generated by support plate, a differential induction coil array is proposed, as displayed in Fig. 7(a). When the probe scans the tube underneath the support plate, the same background signal generated by the support will be collected by sensors S ₁ and S ₂, and then subtraction process is used to eliminate the same support signal. However, if a defect passes through the middle space between two nearby coils, a missing detection will occur [25,26]. To fulfill the 100% scanning coverage for defects, two columns of induction coils are arranged circumferentially. In each column there are six sensors, and one column is arranged in some azimuthal distance of π∕6 along the pipe axis to make up for the possible missing detection of the other column. The experiment setup and the probe are pictured in Figs 7(b) and (c), respectively. The MFL probe consists of a cylindrical permanent magnet (material: Nd2Fe14B) and a differential induction coil array, and the induction coils are fixed at the center of the magnet. In the experiment, the probe is moved inside the heat exchanger tube (external diameter: 16.0 mm, thickness: 1.5 mm) at a certain speed of 0.3 m/s. If there is any defect in the tube, MFL will be generated in the proximity of the defect and picked up by the induction coils. Three artificial defects C ₁, C ₂ and C ₃ with the same width of 0.2 mm and the same length of 5.0 mm but with different depths of 0.9 mm, 0.6 mm and 0.3 mm are made on the external surface of the tube.

Fig. 7.

The MFL experiment setup for heat exchanger tube. (a) Differential induction coils arrangement; (b) the MFL experiment setup; (c) the MFL probe for heat exchanger tube.

Fig. 8.

The MFL testing signals affected by the support plate. (a) Testing signals generated by C ₁, C ₂ and C ₃ without support plate; (b) testing signals generated by C ₁, C ₂ and C ₃ at the support plate center; (c) testing signals generated C ₂ with distances of 6.0 mm and 3.0 mm from the support plate center.

Figure 8(a) shows the testing signals generated by the three defects without support plate, which shows a decreasing trend of the MFL signal amplitude with respect to the defect depth. Then, a support plate is placed to cover the three defects. The testing signals generated by the defects located at the support plate center are obtained and displayed in Fig. 8(b). In contrast to Fig. 8(a), it can be seen that the support plate reduces the testing signal amplitude greatly. Besides, it can be seen that there is no baseline shift since the background signal generated by support plate has been removed by the subtraction process.

Further, the support plate is placed to make the defect C ₂ located with distances of 3.0 mm and 6.0 mm from the support plate center. The testing signals generated by C ₂ are obtained and displayed in Fig. 8(c). It can be seen that with the defect located from the center of support plate to the edge, the signal amplitude is increasing, which is accordant with the simulation results. It can be concluded that after eliminating the background signal by subtraction process, the support plate still causes sensitivity difference due to different magnetization status. In practical MFL inspection, this sensitivity difference could be eliminated by setting different amplification parameters according to defect locations.

5. Conclusion

In order to improve the MFL testing and evaluation for heat exchanger tube, the influence of the support plate on testing signals of defects at the combined area of the tube and support plate are analyzed. By theoretical analysis, numerical simulations and experimental studies, it is found that the support plate will weaken the magnetization intensity. Especially, from the edge of the support plate to the center, the weakening effect is enhanced. Since the support plate has different influences on the magnetization intensity at different locations, sensitivity differences are generated for the defects underneath or close to the support plate, which should be taken into consideration in the tube testing and evaluation.

Footnotes

Acknowledgements

This work was financially supported by National Natural Science Foundation of China (Grant No. 51505308), and Technology support program of Sichuan Province (Grant No. 2018JY0393).

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