#### Simulation for the Assessment of Wall Thinning using Eddy Current Method

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1.INTRODUCTION

The failure in pipelines in power plants, zmical plants, and other related industry systems counts for huge economic loss . In order to ensure e integration of the piping system, pipe-wall nning needs to be monitored appropriately. As ustrated in Fig. 1, the pipes are usually made of rbon steel which is thermal insulated and otected by aluminum, stainless steel, or lvanized steel cladding. The possible inspection ethods are ultrasonic or radiographic testing. owever, the conventional ultrasonic inspection quires the removal and reinstallation of insulation d cladding, good coupling between the sensor d the pipe, etc., which accounts for huge expense. aide-wave ultrasonic inspection is fast but is garded of suit for screening of corrosion area her than exact assessment of the thinning rate d location. Radiograph inspection is slow and ceful safety precaution is required. All in all, it mains a challenge for NDE to assess pipe-wall nning efficiently and precisely.Eddy current testing is well recognized for its oid inspection speed. On the other hand, nocontact with the test piece is required. This meets the request of no removal of insulation and cladding for pipe-wall thinning measurement. However, owing to the presence of insulation and electrically conductive cladding, eddy current induced in pipe is relatively weak, which makes the eddy current measurement of pipe-wall thinning a challenge comparing with conventional eddy current inspection. This study investigates the capability of eddy current method regarding pipe-wall thickness measurement via numerical simulation. In the primary stage, the piping system is modeled as a multi-layered structure. Analytical solutions of magnetic flux density of both sinusoidal and pulsed eddy current measurements are deduced. Parameters of the pipe structure and the measurement condition are studied via simulation.

2. MODELING AND ANALYTICAL SOLUTIONS2.1 Analytical SolutionIf the diameter of a pipe is large enough, the pipe with insulation and cladding can be approximated by a four-layered structure illustrated in Fig. 2. From the top to bottom they are respectively the protective cladding, the thermal insulation, the pipe-wall, and the air inside. Their electrical conductivity and magnetic permeabilityst: FE , T 230-0044 (lt) WEBM ilirA, NDE E ? -, : 045-511-1376 mail: cheng-weiying@.japeic.or.jp- 308 -48 : , T230-0044 (H)ili , NDE tzv , : 045-511-1376 -mail: cheng-weiying@.japeic.or.jp e respectively denoted by 0; and M; (i=1,4).insulationpipe wallcircular coil is positioned z, above the cladding,air insidee inner and outer radius of the excitation coil arespectively r and ra, and the thickness of theFig. 1 Top view of a pipe with insulation and cladding.

04/14 mubstituting the coefficients C and B into equation 1). The other parameters, such as eddy current ensity, magnetic flux density, etc., can be alculated after A.The magnetic flux density is also regarded as ne summation of magnetic flux density resulted rom the excitation current in the coil loop and the ddy current in the conductive layers, that is even uw wavivuun vuru w WU von ivvy uuu my Eddy current in the conductive layers, that is B = B, +Bec By, the magnetic flux density

esulted from the excitation current, does not =hange as far as the excitation coil and excitation+ b k sin( kot)] where N is total number of summation,sin(ka IN) is the Gibbs factor to reduceka/N the Gibb's phenomenon, and

current are settled; while Bec , the magnetic fluxesulted from the excitation current, does not -hange as far as the excitation coil and excitationlensity resulted from the eddy current, changes vith the conductive layers, and therefore is a uusity itsuncu vom me euuy current, changesvith the conductive layers, and therefore is a parameter to assess pipe thinning. Bec can be

Therefore, the response of magnetic flux density can be calculated bycalculated by the following equation,

n whichwhere BK and Ak are respectively the absolutevalue and the phase angle of the kth order magnetic

(9) summation,Fig.3 Pulsed excitation current. ulated with2.1 Validation of the Analytical Solution excited by a The analytical solutions are validated by 3D(9) By choosing an appropriate number of summation, the magnetic flux density can be calculated with satisfied accuracy.In case that the multi-layer system is excited by a pulse wave illustrated in Fig. 3, where T is the cycle of pulse, I the ratio of occupation, the excitation pulse expressed by 1. 0

(a) Numerical result(b) Analytical result Fig. 4 Contour of the eddy current density on the cross section of a 10mm carbon steel plate.Fig. 4numerical code and the above mentioned analytical solution. The excitation frequency is 10Hz, and excitation current is 30AT. The excitation coil (denoted as EXCOIL-52.5 hereafter), whose inner and outer radius and the thickness are 50mm, 55mm and 10mm, respectively, is held lmm above the cladding. The cladding (denoted as cladding-M hereafter) whose conductivity and permeability are respectively 1.0x10°S/m and 100 is 0.8mm in thickness. The insulation is 29.2mm thick. The conductivity and permeability of the carbon steel (denoted as CBNSTL-A hereafter) are respectively 1.6 x 10°S/m and 1000. Casting aside the difference on color bar, Figs. 4(a) and 4(b) are efficiently identical. This identical on eddy current distribution validates the analytical solution of sinusoidal excitation and implies the applicability of the analytical method in this study.Fig. 5 shows the magnetic flux density B, at z=1mm along the axis of a circular coil whose inner and outer radius is respectively 13.25mm and 16.75mm, the coil is 10mm in thickness. The eddy current is initiated by a pulse current whose cycle and occupation rate are 500Hz and 10%, and I, is 30AT. The B, signal obtained at the plus half cycle is subtracted by the B, at the minus half cycle so that common noise is removed. The signal in Fig. 5 is of a half cycle. The signals calculated by the numerical method and the analytical method agree well, excepted at the point of time when excitation current changes dramatically. This mayNumerical and Analytical Solution of BzNumerical Analytical

Fig. 5 Pulsed ECT signal of Bz. be due to the modeling of pulse excitation in numerical calculation. The agreement implies that it is possible to calculate the pulsed eddy current response using analytical solution in Eq. (13).3. EDDY CURRENT MEASUREMENT OF A FOUR-LAYER STRUCTUREBy applying the analytically approximate solution deduced in last section, we can investigate the capability of eddy current method regarding wall thickness measurement, and see how the signal is affected by inspection conditions.Parameters reflecting the inspection condition and the multi-layer structure are: the electromagnetic property and thickness of each layer, the excitation current and frequency, and the occupation rate in case of pulse wave, etc.3110Bz (Im.) (Gauss)Bz at Z1, f=10Hz, Sinusoidal Excitation 0.5 1.0 1.5 2.0_ 2.5 {*NOCLD-W(30-40)NOCLD-W(35-40) no cladding insulation 30mm insulation 10mm A NOCLD-W(30-35)XCLD-M-W(30-40) cladding-MXCLD-M-W(35-40)CLD-M-W(30-35)+ CLD-C-W(30-40) c .)O CLD-C-W(35-40)CLD-C-W(30-35) cladding-COCLD-M-W{10-20) O CLD-M-W(15-20)A CLD-M-W10-15) Bz (Re.) (Gauss)Fig. 6 Simulation of Bz signal obtained from low frequency eddy current measurement.3.1 Low frequency eddy current methodMagnetic flux densities resulted from the eddy current are calculated along the axis of the circular coil. Fig. 6 shows the normal component ofmagnetic flux density B? at position Z=1mm,with respect to different cladding layers and insulation/wall thickness. The pipe is made of carbon steel CBNSTL-A. In this figure, NOCLD means without cladding layer, and CLD-M and CLD-C stand for cladding-M and cladding-C, respectively. The XX1 and XX2 in W(XX1-XX2) stand for dz and d4 in Fig. 2. The thickness of the wall is XX1-XX2, and is xx1 below the surface of cladding layer. W(30-40) stands for the normal situation that the wall is 10mm thick and 30mm below the cladding. W(35-40) and W(30-35) represent outer and inner thinning respectively, while the wall is 5mm thick.No significant difference is observed on Bz signals of W(30-40) and W(30-35). It implies that it is difficult to measure the wall thinning on the inner side of a pipe. However, the difference on the Bz signals of W(30-40) and W(35-40) shows the possibility of measuring the wall thinning on the outer side of a pipe using sinusoidal eddy current method.The difference between the Bz signals of W(30-40) and W(35-40) with magnetic lagging CLD-M is smaller than that of with non-magnetic lagging CLD-C. Therefore, it is more challengeableBz at 21 (Cladding-M, f=5Hz, tou=10%)

Time (ms)(a) Bz versus time, carbon steel wall of different thickness under magnetic cladding.20*LOG(Bz)Bz at 21 (Cladding-M, f=5Hz, tou=10%)

Time (ms)TheFig. 8 The decayed Bz versus time. The frequency of excitation pulse is 100Hz.to measure the thickness of a pipe when the protective cladding layer is magnetic.Fig. 6 also shows that by reducing the thickness of insulation from 30mm to 10mm, the amplitude of Bz increases. The thicker the insulation layer, the more difficult to measure the wall thickness.3123.2 Pulsed eddy current methodThe eddy current is induced by the pulse current described in Fig.3.Fig. 7(a) show the Bz at Z1 of different thickness CBNSTL-A pipes under 0.8mm cladding-M. The cycle of excitation pulse is 5Hz, and the occupation rate is 10%. The difference on the maximum value of the Bz on Fig. 7(a) corresponding to different wall/insulation thickness is very small. However, significant difference is observed on the logarithm value of the decayed Bz. If the measurement equipment is sensitive enough, it is possible to measure the wall thickness using the decayed magnetic flux density signal. The decayed Bz signals of W(30-35) and W(35-40) are almost identical, it implies that the pulsed eddy current method is applicable regardless of inner or outer thinningFig. 8 shows the measurement of the same pipe thinning of Fig. 7 when the cycle of pulse is increased to 100Hz, and the occupation rate is 20%. However, the difference on the decayed signals of the W(30-40) and W(35-40) is much smaller than that at 5Hz. Therefore, it is advisable of using lower frequency pulsed excitation current.The cladding of Fig. 9 is a non-magnetic conductor whose conductivity is as high as 3.8x108 /m. 2mm wall thinning is detectable from the decayed signal. Comparing Fig. 9 to Fig. 7, we find that the Bz signal of the same pipe underBz at 21 (Cladding-Al, f=5Hz, tou=10%)

Time (ms)Fig. 9 Decay of Bz, carbon steel pipe under non-magnetic cladding.non-magnetic cladding is larger than that of under magnetic cladding-M. Therefore, the wall thinning under magnetic cladding is more difficult to measure.4. CONCLUSIONAnalytical solution is deduced on a cylindrically symmetric multi-layered conductive/magnetic structure. The solution is validated by 3D numerical solution, and applied to the simulation of wall thinning measurement using both sinusoidal eddy current and pulsed eddy current method. The simulation shows that low frequency sinusoidal eddy current is basically limited for the measurement of outer wall thinning, while pulsed eddy current is valid for both inner and outer wall thinning measurement. It is advisable to use a low cycle pulse for wall thickness measurement. The electromagnetic property of cladding affects the measurement significantly. Wall thinning under magnetic cladding layers are more difficult to measure than that under non-magnetic ones.** * [1] C.V.Dodd, W.E.Deeds, ““Analytical solutions toeddy-current probe-coil problems““, Journal ofApplied Physics, Vol. 39, No. 6, 2829-2838 (1968). [2] C.V.Dodd, C.C.Cheng, and W.E.Deeds, ““Indcutioncoils coaxial with an arbitrary number of cylindrical conductors““, Journal of Applied Physics,Vol. 45, No. 2, 638-649 (1974). [3] W. Cheng, I.Komura, ““Simulation of transienteddy-current measurement for the characterization of depth and conductivity of a conductive plate““, IEEE Tran. Mag, Vol.44, No. 11, 3281-3284 (2008).313“ “Simulation for the Assessment of Wall Thinning using Eddy Current Method“ “程 衛英,Weiying CHENG,古村 一朗,Ichiro KOMURA