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Periscope infrared thermography for local wall thinning in tubes
ARTICLE IN PRESS NDT&E International 42 (2009) 275–282
Contents lists available at ScienceDirect
NDT&E International journal homepage: www.elsevier.com/locate/ndteint
Periscope infrared thermography for local wall thinning in tubes A. Vageswar a, Krishnan Balasubramaniam a,, C.V. Krishnamurthy a, T. Jayakumar b, Baldev Raj b a b
Center for Non Destructive Evaluation and Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, India
a r t i c l e in fo
abstract
Article history: Received 1 March 2008 Received in revised form 11 November 2008 Accepted 21 November 2008 Available online 24 December 2008
In this paper, a novel way to inspect local wall thinning in metal tubes with infrared thermography has been demonstrated. The first of its kind method utilizes a periscope-like reflector located deep inside a tube to mirror the radiated heat that flows across the tube thickness to an IR camera positioned outside the tube. Localized wall thinning was represented by partially drilled holes of different depths on a tube, of inner diameter 82 mm and outer diameter 91 mm. Feasibility studies were carried out through simulations using a finite element model. Experiments were performed to determine the thermal diffusivity of the material. Remaining thicknesses of the tubes in wall-thinned sections were found to be estimated reasonably well using measured time–temperature profiles obtained by flash method [Parker WJ, Jenkins RJ, Butler CP, Abbott GL. Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity. J Appl Phys 1961;32:1679–84]. The good correlation found between model calculations and measurements vindicated the utility of a model-based approach to applications of pulsed IR thermography. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Pulse thermography Thermal diffusivity Periscope approach Tube inspection Local wall-thinning defects
1. Introduction Local wall thinning of metals is of serious concern to several industries. Such local wall thinning can occur due to local pittingtype corrosion [2], hydride blistering [3], etc., during service of the component. The detection and sizing of the local wall thinning is required in order to assess the remaining life of the pipe/tube. One method for determining the wall thinning is to introduce a change in the temperature of the fluid inside the pipe/tube and observe the transient/static temperature response on the outer wall and correlate this to wall thickness [4,5]. In this work, a metal tube with possible wall thinning on the outer surface of the tubes is investigated with the constraints that only the inside tube is accessible for line of sight inspection and that the IR camera be located only at a tube end. Among several thermographic techniques such as pulse thermography [6–8], pulse-phase thermography [9,10], and lock-in thermography [11,12], pulse thermography technique appears to be feasible given the fairly high thermal diffusivity of the tube material and given that the tube thickness is not too large (of the order of 4 mm). Two approaches to providing the transient heating/cooling can be considered, since the location of the IR camera is fixed at one end of the tube. One approach would be to change the temperature on the outer surface through heating or cooling
Corresponding author. Tel.: +91 44 22574662; fax: +91 44 22570545.
E-mail address: [email protected] (K. Balasubramaniam). 0963-8695/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ndteint.2008.11.008
and observe the temperature change on the inner surface, i.e., in transmission mode. The other approach would be to change the temperature and observe from the inner surface, i.e., in reflection mode. Transmission mode provides better thermal contrasts even when flash energies are not too high. Reflection mode is preferred when inspecting near-surface defects. For deeper defects, flash systems with higher power become essential. In the present case of a not-too-thick tube of reasonable thermal diffusivity, both transmission and reflection modes are explored using simulations. Experiments in the transmission mode alone are carried out based on the trends and features that emerged from the model.
2. Modeling the thermal response Given the constraints of inspection and given the curvature of the specimen, it was decided to employ a finite element method (FEM)-based study to determine the applicability of the flash method for quantitative defect depth estimation through remaining thickness evaluation. A 3D model of a section of the tube along with the defect (wall thickness loss) was implemented using the transient heat conduction analysis option in FEMLAB 3.1. To simulate wall thinning, five local wall-thinning defects, each having a diameter of 4 mm and depth starting from 0.5 mm with a step of 0.5 mm up to a maximum of 2.5 mm were considered in a tube of 82 mm ID and 4.5 mm wall thickness. The model, depicted in Fig. 1, was meshed using tetrahedral elements to account for
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Fig. 1. FEM model of the tube with the defect.
tube curvature. From the initial trials, the maximum element size of meshing element was set at 0.0015 m and element growth rate at 1.2. Since transient thermal diffusion through the tube thickness is under investigation, the axial length of the tube was restricted to 20 mm. Keeping in mind the flash lamp system BALCAR FX 60 as the source and CEDIP IR camera as the sensor, the following boundary conditions were applied to the model:
1. The outer top half surface of the tube which contains the defect was subjected to heat flux of 6.7 MW/m2, for approximately 10 ms. Inner surface of the tube and the outer bottom half surface were subjected to convectional heat transfer with heat transfer coefficient, h ¼ 5 W/m2 K. The ambient temperature was set as 30 1C. 1 2. The total simulation time for a trial was 1.88 s with 3000 s as the computational time step.
Several features emerged from these simulations. The tube end effects were found to be negligible helping to keep the computational domain small. The curvature effects were insignificant enough to employ 1D analysis for quantifying heat diffusion across the tube thickness. Specifically, for a 1D thermal diffusion process, the thermal diffusivity (a) in m2/s is expressed as [1]
a¼
1:38L2 p2 t1=2
(1)
where L is the thickness of the sample in m, t1/2 is the characteristic time, in seconds, required for the back surface to reach half of the maximum temperature rise. Alternately, the thermal diffusivity can also be expressed as
a¼
0:48L2 p2 t x
(2)
where L is the thickness of the sample in m, and tx the characteristic time, in seconds, is the time-axis intercept of the time–temperature evolution profile. Both of these expressions are equivalent for a slab subject to spatially uniform flash heating. However, a closer look at the time–temperature evolution of the defect-free and defective regions revealed that while curvature was found to have a negligible role in the early part of the time–temperature evolution, it seemed to influence the later part of the time–temperature evolution. These trends in turn implied that between the t1/2 and tx methods used for quantitative analysis, the latter appeared to be more suitable for the case under investigation.
2.1. Simulation results Simulations were carried out on the pipe both in the transmission mode and the reflection mode for various defects. Fig. 2 shows the results of the transmission mode simulations as color plots of snap shots at different times from the start of the flash heating pulse. It can be observed that the defect indication appears early at t ¼ 0.14 s and that the temperature contrast for the 1-mm-deep defect was of the order of 2 1C. An important and characteristic feature of the defective regions in the thermograms is the emergence of the ‘‘hot spot’’ in time—a spatial domain whose thermal contrast with respect to the non-defective regions is a function of time. Since the defect signature is spread over a finite number of pixels, the thermal contrast as a function of time of the central portion of the ‘‘hot spot’’ differs from that near its edge. This blurred image of the defect arises from thermal diffusion effects in two and three dimensions and provides information about the lateral extent of the defect as well as the defect depth. From several simulations it was found that the thermal contrast of the central core region comprising about 50% of the ‘‘hot spot’’ is sufficient to provide quantitative assessment of both the lateral extent of the defect and the remaining thickness in the defective region. Although a more precise estimate can be determined from simulations, the assessment based on the central 50% portion of the ‘‘hot spot’’ was adopted for all the simulated and measured profiles as it is a feasible procedure in practice. The time–temperature evolution plots for the two shallow defects are shown in Fig. 3 that includes the time-axis intercepts. Remaining thickness estimates of defect 1 is 4.15 mm with an error of 3.75%. Similarly, remaining thickness estimates of defect 2 is 3.59 mm with an error of 2.57%. The depth estimates and ‘‘errors’’ with respect to the actual depths are tabulated for all the five defects in Table 1. It was found that the estimates were accurate for deep defects and were reasonable for the shallowest defects. Since the remaining thickness estimates utilize the 1D heat diffusion model, the effects of thermal diffusion in higher dimensions would be more significant for shallow defects than for deeper defects consistent with the trends seen in Table 1. Fig. 4 shows the FEM simulation results for defect 2 in the reflection mode. These snap shots show that when compared to the transmission mode, for the reflection mode, (a) the defect indications appear much later in time (approximately t ¼ 0.6 s) as expected from two-way heat diffusion, and (b) the temperature contrast obtained between a non-defective region (far from the defect) and the defective region is relatively small, approximately 0.5 1C. Although this change would be measurable with current IR cameras, the minimum depth of the defect that can be evaluated and the accuracy of such estimations would both not be comparable to the transmission mode.
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277
Fig. 2. FEM simulation results at different time frames after the flash for defect 2 in the transmission mode.
Fig. 3. Early part of the time–temperature plots in the transmission mode for defective and non-defective regions from FEM simulations. The plots also show the tx method being used for estimating the remaining thickness for (a) the 0.5 mm defect 1 and (b) the 1 mm defect 2.
3. The experimental approach The experimental setup for the transmission mode is depicted in Fig. 5. High power flashes (BALCAR FX 60), which give 6.4 kJ of energy for approximately 10 ms is used as the heat source.
Acquisition of thermal images is carried out using a CEDIP infrared camera which works in the range 7–10 mm, with a 320 240 pixels array having maximum acquisition frequency of 228 Hz. The acquisition frequency is set at 1150 Hz by sub-windowing the size to 72 94 pixels.
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A Zircaloy-2 tube having 82 mm inner diameter and 91 mm outer diameter was used in both the simulations and experiments. Five flat-bottomed holes were carefully drilled to simulate the localized wall-thinning defects, each having a diameter of 4 mm and off depths starting from 0.5 to 2.5 mm in steps of 0.5 mm. For accessing the inner surface of the tube, a novel periscopic approach was taken by employing an aluminum reflector to reflect the tube’s inner diameter surface thermal emissions to an IR camera placed outside the tube at one end of the tube. The aluminum reflector is a solid aluminum rod machined at an angle of 451 to the axis with the surface mirror polished by using buffing operation. The diameter of the rod was chosen to be 80 mm in order for this reflector to be able to slide inside the tube. The reflecting surface was rotated (about its axis) to an offset angle of 22.51 to avoid the cold spot of the camera merging with the region of observation in the tube. Thermographic data were collected by a PC and processed using MATLABs. The temperature contrast, i.e., the difference between the temperature on the surface (at any given time) above the defective region to that above a non-defective region (located far from the defect region), was computed in both the cases. The thermal diffusivity of the tube material and the remaining thickness in the defect region were both determined by applying Eq. (2) to the early history of the measured time–temperature profiles. Consistent with simulations, thermal diffusivity estimates based on Eq. (1) were found to produce significant errors, and hence were not pursued.
4. Results and discussion 4.1. Defect visualization The grey-scale images (screen shots of the thermal image at different time frames) obtained using the periscope pulse thermography experimental setup is shown in Fig. 6 for the 2 shallow defects (denoted by 1 and 2). The acquisition frequency of the camera is set at 1150 fps, and thermographic images were captured at intervals of 0.043 s from the time of flash. The defect, representing a higher temperature region, is clearly visible on the thermographic image after flashing 3.2 kJ of energy on the outer surface of the tube. From the thermographic images, particularly the snapshots at 0.087 and 0.13 s, it is seen that flash energy plays a key role in distinguishing the defects from the sound region at early times. With increase in flash energy, defect contrast with respect to the non-defective region increases that aids in the improved visualization of the defects. That the contrast is improved when using higher flash energy can be seen comparing Fig. 6a with b for defect 1 and Fig. 6c with d for defect 2. In Fig. 6c and d, the temperature contrast in the images at time 0.130 s is about 0.4 1C more in Fig. 3d using the 6.4 kJ when compared to Fig. 6c. The trends seen in simulated thermograms, namely, the emergence of the ‘‘hot spots’’ and the times at which thermal contrasts are maximum are manifest in measurements as well. Fig. 7 shows how closely the simulation compares with experiment in determining the times of maximum thermal contrast for all the defects.
Table 1 Remaining thickness estimates using simulation data in the transmission mode.
BALCAR Flash Lamp
4.5 mm
Defect Defect Defect Defect Defect
1 2 3 4 5
Remaining thickness of defects (mm)
Estimates using simulated data
Percent error (FEM)
4.0 3.5 3.0 2.5 2.0
4.15 3.59 2.995 2.49 2.01
3.75 2.57 0.17 0.40 0.50
IR Camera Aluminum Reflector
Fig. 5. Schematic diagram of the experimental setup for transmission mode measurements.
Fig. 4. FEM simulation results for defect 2 in the reflection mode at different time frames after the flash.
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279
Defect
a 0 sec
0.043sec
0.087sec
0.13sec
0.174sec
0.217sec
0.26sec
0.304sec
0 sec
0.043sec
0.087sec
0.13sec
0.174sec
0.217sec
0.26sec
0.304sec
0 sec
0.043sec
0.087sec
0.13sec
0.174sec
0.217sec
0.26sec
0.304sec
0 sec
0.043sec
0.087sec
0.13sec
0.174sec
0.217sec
0.26sec
0.304sec
b
c
d Fig. 6. The thermographic images of 4-mm-diameter defects, in the transmission mode, obtained using the periscope approach at different time frames captured at 1150 fps. The sequences labeled (a) and (b) are the responses obtained using 3.2 and 6.4 kJ of flash energy, respectively, on defect 1 (0.5 mm deep). The sequences labeled (c) and (d) are the responses obtained using 3.2 and 6.4 kJ of flash energy on defect 2 (1 mm deep).
0.18
From a group of pixels representing the defect-free region of the thermogram, the normalized time–temperature plots are obtained and the characteristic time tx is determined as illustrated in Fig. 8. The tx estimated from the defect-free region was found to be 0.1235 s for a nominal wall thickness of the tube L( ¼ .0045 m). Hence, from Eq. (2), the thermal diffusivity constant of the material was determined as a ¼ 7.97 106 m2/s which compares well with the literature value for Zircaloy-2 of 7.2 106 m2/s [14]. It was found that the thermal diffusivity assessment was not influenced by errors in tx estimates in any significant manner. Further, it may be noted that although the estimated thermal diffusivity value differs from the reported value, the same method is used for estimating defect characteristics as well.
For a defective region of the material, the characteristic time tx is proportional to the square of the remaining thickness l 2
0.16
• Simulation
0.14
ο Experiment
0.12 0.1 0.08 0.06 0.04 0.02 0
1
2
3
4
5
Defect Depth (mm)
4.3. Remaining thickness estimation
tx / l
Characteristic time (s) of max thermal contrast
4.2. Thermal diffusivity estimation
Fig. 7. Comparison between simulations and experiments of the times of maximum thermal contrast, in the transmission mode, as a function of defect depth.
(3)
Therefore, the technique is quite robust to small errors in the measurement of the characteristic time for the evaluation of the remaining wall thickness, once the thermal diffusivity constant has been reliably measured. The remaining wall thicknesses in the defective regions were determined from the time–temperature evolution of the central 50% portion of the ‘‘hot spot’’ corresponding to the defective regions in the thermograms. The normalized time–temperature profiles of two shallow defects are shown in Fig. 9. Remaining
thickness of defect 1 was determined to be 4.23 mm with an error of 5.75%. Similarly, the remaining thickness of defect 2 was computed to be 3.48 mm with an error of 0.57%. The results for all the five defects along with estimates are shown in Table 2. It may be observed from this table that the trends shown by estimates based on measurements follow closely the trends indicated in simulations for all defects except defect 2. For defect
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2, measured data appears to be better than simulated data although some error is expected for this not-too-deep defect judging from the errors seen for defect 1. 4.4. Lateral sizing of defects To determine the lateral size of the defect, the image at the time frame corresponding to the maximum temperature contrast is
Table 2 Comparison of remaining thickness estimates using transmission mode data from simulation and experiment.
Fig. 8. Early history of the time–temperature evolution plot, in the transmission mode, for obtaining the time-axis intercept, tx, that relates the wall thickness (L) and the thermal diffusivity constant of the material.
Defect Defect Defect Defect Defect
1 2 3 4 5
Estimates using Remaining measured data thickness of defects (mm) using 6.4 kJ flash excitation
Percent error (Expt.)
Estimates using simulated data
Percent error (FEM)
4.0 3.5 3.0 2.5 2.0
5.75 0.57 0.33 0.40 0.50
4.15 3.59 2.995 2.49 2.01
3.75 2.57 0.17 0.40 0.50
4.23 3.48 3.01 2.51 1.99
Fig. 9. Remaining thickness estimation in the transmission mode (a) the 0.5 mm shallow defect 1 and (b) the 1.0 mm shallow defect 2, along with the corresponding temperature–time history profiles for the defect-free (sound) regions. Data obtained using 6.4 kJ flash excitation.
ARTICLE IN PRESS A. Vageswar et al. / NDT&E International 42 (2009) 275–282
b Normalized temperature
a
281
1
Horizontal direction 0.5 0
5
10
15
Vertical direction
0 Diameter(mm)
Fig. 10. (a) Cross-sectional profiles used for sizing of the defect; (b) two profile plots drawn across the defect and used for sizing.
7
5. Conclusions
ο Experiment • Simulation
FWHM (mm)
6 5 4 3 2 1
2
3 Defect depths (mm)
4
5
Fig. 11. Defect sizing estimates based on FWHM. Comparison between simulations and experiments in the transmission mode.
chosen. Fig. 10 shows the sub-windowed defective region along with the line profiles of temperature across the defect in two perpendicular directions. As the IR camera has an aspect ratio of unity (square-shaped pixels), identical scale factors in both vertical and horizontal directions of the window in terms of actual dimensions were included in the size estimation. The diameter of the defect was estimated from the 6 dB drop of the FWHM [13]. It was determined that at the working distance employed in the experiment, each pixel of the sub-windowed thermographic image represented approximately 0.41 mm 0.41 mm area. Fig. 11 shows a comparison between the FWHM estimates obtained from simulated and measured thermograms for all the defects. The FWHM estimates are seen to be better as the remaining thickness decreases. This is expected since in the transmission mode thermal diffusion causes greater blurring with increasing distance from the back surface. While there is a definite trend shown by simulations, the experiments indicate some scatter. Bearing in mind that one pixel corresponds to 0.41 mm, and the difficulty in maintaining true focus on every defect, the scatter appears to be within a couple of pixels. The determination of the actual size from the blurred image is similar but not identical to what is usually done in optics and forms the subject of a forthcoming publication. It must be noted that if the experiments were conducted in the reflection mode, as in Ref. [13], the FWHM trends will be opposite to the one observed here, i.e., the measured defect sizes will be smaller than the actual size.
The novel periscope pulsed thermography technique reported in this paper, using a polished aluminum mirror, is capable of detecting and quantifying defects in metal tubes, without the need for the IR camera to be inserted into the tube. Thermal diffusivity of the material was experimentally estimated, which compares well with the reported value, using the 1D heat diffusion analysis, the remaining thicknesses for different defect regions were estimated and found to be accurate within a maximum error of 5.75% in experiments and 3.75% in FEM simulations when compared with actual thickness. The error is significantly small (less than 0.5%) for defects that are relatively deeper and more than 1/3rd of the total wall thickness. This proposed method of inspection proves to be reliable for (a) detecting local wall-thinning defects of 10% of wall thickness or more and (b) sizing of defects with minimum defect depth of 33% of wall thickness or higher. While the transmission mode was demonstrated in the present work, it appears that the reflection mode could also be employed using the periscope approach but with a higher flash energy as input.
Acknowledgement The authors wish to acknowledge BRNS, Mumbai, for funding this work. References [1] Parker WJ, Jenkins RJ, Butler CP, Abbott GL. Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity. J Appl Phys 1961;32:1679–84. [2] USNRC report. An approach for plant specific, risk-informed decision making: in-service inspection of piping. Draft Regulatory Guide DG-1063, Washington, DC: US Nuclear Regulatory Commission, 1997. [3] Perovic V, Weatherly GC. The nucleation of hydrides in a Zr-2.5 wt% Nb alloy. J Nucl Mater 1984;126:160–9. [4] Wurzbach RN, Seith DA. Infrared monitoring of power plant effluents and heat sinks to optimize plant efficiency. In: Proceedings of SPIE—The International Society for Optical Engineering. Thermosense XXII, Orlando, FL, USA, April 24–27, 2000. [5] Shen G, Chen G, Li T, Li C. Infrared thermography test for high temperature pressure pipe, 10th Asia-Pacific Conference on Non-Destructive Testing, Brisbane, Australia, September, 2001, /http://www.ndt.net/apcndt2001/ papers/1033/1033.htmS. [6] Sun JG. Analysis of pulsed thermography methods for defect depth prediction. J Heat Transfer 2006;128:329–38. [7] Ringermacher HI, Archacki Jr. RJ, Veronesi WA. Nondestructive testing: transient depth thermography. US Patent no. 5,711,603, 1998. [8] Shepard SM, Lhota JR, Rubadeux BA, Wang D, Ahmed T. Reconstruction and enhancement of active thermographic image sequences. Opt Eng 2003;42: 1337–42.
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[9] Maldague X, Marinetti S. Pulse phase infrared thermography. J Appl Phys 1996;79(5):2694–8. [10] Maldague X, Marinetti S, Couturier JP. Applications of pulse phase thermography. In: Thompson DO, Chimenti DE, editors. Review of progress in QNDE, vol. 16. NY: Plenum Press; 1997. p. 339–44. [11] Maldague X, Ibarra-Castanedo C, Gonzalez D, Klein M. Infrared image processing and data analysis. Infrared Phys Technol 2004;46:75–83.
[12] Maldague X. Infrared and thermal testing. Nondestructive testing handbook, vol. 3. Columbus, OH, USA: ASNT Publications; 2001. [13] Saintey MB, Almond DP. Defect sizing by transient thermography II: a numerical treatment. J Phys D: Appl Phys 1995;28:2539–46. [14] Report on thermal properties of zircaloy, International Nuclear Safety Centre, Argonne National Laboratory, 1997.
Contents lists available at ScienceDirect
NDT&E International journal homepage: www.elsevier.com/locate/ndteint
Periscope infrared thermography for local wall thinning in tubes A. Vageswar a, Krishnan Balasubramaniam a,, C.V. Krishnamurthy a, T. Jayakumar b, Baldev Raj b a b
Center for Non Destructive Evaluation and Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, India
a r t i c l e in fo
abstract
Article history: Received 1 March 2008 Received in revised form 11 November 2008 Accepted 21 November 2008 Available online 24 December 2008
In this paper, a novel way to inspect local wall thinning in metal tubes with infrared thermography has been demonstrated. The first of its kind method utilizes a periscope-like reflector located deep inside a tube to mirror the radiated heat that flows across the tube thickness to an IR camera positioned outside the tube. Localized wall thinning was represented by partially drilled holes of different depths on a tube, of inner diameter 82 mm and outer diameter 91 mm. Feasibility studies were carried out through simulations using a finite element model. Experiments were performed to determine the thermal diffusivity of the material. Remaining thicknesses of the tubes in wall-thinned sections were found to be estimated reasonably well using measured time–temperature profiles obtained by flash method [Parker WJ, Jenkins RJ, Butler CP, Abbott GL. Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity. J Appl Phys 1961;32:1679–84]. The good correlation found between model calculations and measurements vindicated the utility of a model-based approach to applications of pulsed IR thermography. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Pulse thermography Thermal diffusivity Periscope approach Tube inspection Local wall-thinning defects
1. Introduction Local wall thinning of metals is of serious concern to several industries. Such local wall thinning can occur due to local pittingtype corrosion [2], hydride blistering [3], etc., during service of the component. The detection and sizing of the local wall thinning is required in order to assess the remaining life of the pipe/tube. One method for determining the wall thinning is to introduce a change in the temperature of the fluid inside the pipe/tube and observe the transient/static temperature response on the outer wall and correlate this to wall thickness [4,5]. In this work, a metal tube with possible wall thinning on the outer surface of the tubes is investigated with the constraints that only the inside tube is accessible for line of sight inspection and that the IR camera be located only at a tube end. Among several thermographic techniques such as pulse thermography [6–8], pulse-phase thermography [9,10], and lock-in thermography [11,12], pulse thermography technique appears to be feasible given the fairly high thermal diffusivity of the tube material and given that the tube thickness is not too large (of the order of 4 mm). Two approaches to providing the transient heating/cooling can be considered, since the location of the IR camera is fixed at one end of the tube. One approach would be to change the temperature on the outer surface through heating or cooling
Corresponding author. Tel.: +91 44 22574662; fax: +91 44 22570545.
E-mail address: [email protected] (K. Balasubramaniam). 0963-8695/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ndteint.2008.11.008
and observe the temperature change on the inner surface, i.e., in transmission mode. The other approach would be to change the temperature and observe from the inner surface, i.e., in reflection mode. Transmission mode provides better thermal contrasts even when flash energies are not too high. Reflection mode is preferred when inspecting near-surface defects. For deeper defects, flash systems with higher power become essential. In the present case of a not-too-thick tube of reasonable thermal diffusivity, both transmission and reflection modes are explored using simulations. Experiments in the transmission mode alone are carried out based on the trends and features that emerged from the model.
2. Modeling the thermal response Given the constraints of inspection and given the curvature of the specimen, it was decided to employ a finite element method (FEM)-based study to determine the applicability of the flash method for quantitative defect depth estimation through remaining thickness evaluation. A 3D model of a section of the tube along with the defect (wall thickness loss) was implemented using the transient heat conduction analysis option in FEMLAB 3.1. To simulate wall thinning, five local wall-thinning defects, each having a diameter of 4 mm and depth starting from 0.5 mm with a step of 0.5 mm up to a maximum of 2.5 mm were considered in a tube of 82 mm ID and 4.5 mm wall thickness. The model, depicted in Fig. 1, was meshed using tetrahedral elements to account for
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Fig. 1. FEM model of the tube with the defect.
tube curvature. From the initial trials, the maximum element size of meshing element was set at 0.0015 m and element growth rate at 1.2. Since transient thermal diffusion through the tube thickness is under investigation, the axial length of the tube was restricted to 20 mm. Keeping in mind the flash lamp system BALCAR FX 60 as the source and CEDIP IR camera as the sensor, the following boundary conditions were applied to the model:
1. The outer top half surface of the tube which contains the defect was subjected to heat flux of 6.7 MW/m2, for approximately 10 ms. Inner surface of the tube and the outer bottom half surface were subjected to convectional heat transfer with heat transfer coefficient, h ¼ 5 W/m2 K. The ambient temperature was set as 30 1C. 1 2. The total simulation time for a trial was 1.88 s with 3000 s as the computational time step.
Several features emerged from these simulations. The tube end effects were found to be negligible helping to keep the computational domain small. The curvature effects were insignificant enough to employ 1D analysis for quantifying heat diffusion across the tube thickness. Specifically, for a 1D thermal diffusion process, the thermal diffusivity (a) in m2/s is expressed as [1]
a¼
1:38L2 p2 t1=2
(1)
where L is the thickness of the sample in m, t1/2 is the characteristic time, in seconds, required for the back surface to reach half of the maximum temperature rise. Alternately, the thermal diffusivity can also be expressed as
a¼
0:48L2 p2 t x
(2)
where L is the thickness of the sample in m, and tx the characteristic time, in seconds, is the time-axis intercept of the time–temperature evolution profile. Both of these expressions are equivalent for a slab subject to spatially uniform flash heating. However, a closer look at the time–temperature evolution of the defect-free and defective regions revealed that while curvature was found to have a negligible role in the early part of the time–temperature evolution, it seemed to influence the later part of the time–temperature evolution. These trends in turn implied that between the t1/2 and tx methods used for quantitative analysis, the latter appeared to be more suitable for the case under investigation.
2.1. Simulation results Simulations were carried out on the pipe both in the transmission mode and the reflection mode for various defects. Fig. 2 shows the results of the transmission mode simulations as color plots of snap shots at different times from the start of the flash heating pulse. It can be observed that the defect indication appears early at t ¼ 0.14 s and that the temperature contrast for the 1-mm-deep defect was of the order of 2 1C. An important and characteristic feature of the defective regions in the thermograms is the emergence of the ‘‘hot spot’’ in time—a spatial domain whose thermal contrast with respect to the non-defective regions is a function of time. Since the defect signature is spread over a finite number of pixels, the thermal contrast as a function of time of the central portion of the ‘‘hot spot’’ differs from that near its edge. This blurred image of the defect arises from thermal diffusion effects in two and three dimensions and provides information about the lateral extent of the defect as well as the defect depth. From several simulations it was found that the thermal contrast of the central core region comprising about 50% of the ‘‘hot spot’’ is sufficient to provide quantitative assessment of both the lateral extent of the defect and the remaining thickness in the defective region. Although a more precise estimate can be determined from simulations, the assessment based on the central 50% portion of the ‘‘hot spot’’ was adopted for all the simulated and measured profiles as it is a feasible procedure in practice. The time–temperature evolution plots for the two shallow defects are shown in Fig. 3 that includes the time-axis intercepts. Remaining thickness estimates of defect 1 is 4.15 mm with an error of 3.75%. Similarly, remaining thickness estimates of defect 2 is 3.59 mm with an error of 2.57%. The depth estimates and ‘‘errors’’ with respect to the actual depths are tabulated for all the five defects in Table 1. It was found that the estimates were accurate for deep defects and were reasonable for the shallowest defects. Since the remaining thickness estimates utilize the 1D heat diffusion model, the effects of thermal diffusion in higher dimensions would be more significant for shallow defects than for deeper defects consistent with the trends seen in Table 1. Fig. 4 shows the FEM simulation results for defect 2 in the reflection mode. These snap shots show that when compared to the transmission mode, for the reflection mode, (a) the defect indications appear much later in time (approximately t ¼ 0.6 s) as expected from two-way heat diffusion, and (b) the temperature contrast obtained between a non-defective region (far from the defect) and the defective region is relatively small, approximately 0.5 1C. Although this change would be measurable with current IR cameras, the minimum depth of the defect that can be evaluated and the accuracy of such estimations would both not be comparable to the transmission mode.
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Fig. 2. FEM simulation results at different time frames after the flash for defect 2 in the transmission mode.
Fig. 3. Early part of the time–temperature plots in the transmission mode for defective and non-defective regions from FEM simulations. The plots also show the tx method being used for estimating the remaining thickness for (a) the 0.5 mm defect 1 and (b) the 1 mm defect 2.
3. The experimental approach The experimental setup for the transmission mode is depicted in Fig. 5. High power flashes (BALCAR FX 60), which give 6.4 kJ of energy for approximately 10 ms is used as the heat source.
Acquisition of thermal images is carried out using a CEDIP infrared camera which works in the range 7–10 mm, with a 320 240 pixels array having maximum acquisition frequency of 228 Hz. The acquisition frequency is set at 1150 Hz by sub-windowing the size to 72 94 pixels.
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A Zircaloy-2 tube having 82 mm inner diameter and 91 mm outer diameter was used in both the simulations and experiments. Five flat-bottomed holes were carefully drilled to simulate the localized wall-thinning defects, each having a diameter of 4 mm and off depths starting from 0.5 to 2.5 mm in steps of 0.5 mm. For accessing the inner surface of the tube, a novel periscopic approach was taken by employing an aluminum reflector to reflect the tube’s inner diameter surface thermal emissions to an IR camera placed outside the tube at one end of the tube. The aluminum reflector is a solid aluminum rod machined at an angle of 451 to the axis with the surface mirror polished by using buffing operation. The diameter of the rod was chosen to be 80 mm in order for this reflector to be able to slide inside the tube. The reflecting surface was rotated (about its axis) to an offset angle of 22.51 to avoid the cold spot of the camera merging with the region of observation in the tube. Thermographic data were collected by a PC and processed using MATLABs. The temperature contrast, i.e., the difference between the temperature on the surface (at any given time) above the defective region to that above a non-defective region (located far from the defect region), was computed in both the cases. The thermal diffusivity of the tube material and the remaining thickness in the defect region were both determined by applying Eq. (2) to the early history of the measured time–temperature profiles. Consistent with simulations, thermal diffusivity estimates based on Eq. (1) were found to produce significant errors, and hence were not pursued.
4. Results and discussion 4.1. Defect visualization The grey-scale images (screen shots of the thermal image at different time frames) obtained using the periscope pulse thermography experimental setup is shown in Fig. 6 for the 2 shallow defects (denoted by 1 and 2). The acquisition frequency of the camera is set at 1150 fps, and thermographic images were captured at intervals of 0.043 s from the time of flash. The defect, representing a higher temperature region, is clearly visible on the thermographic image after flashing 3.2 kJ of energy on the outer surface of the tube. From the thermographic images, particularly the snapshots at 0.087 and 0.13 s, it is seen that flash energy plays a key role in distinguishing the defects from the sound region at early times. With increase in flash energy, defect contrast with respect to the non-defective region increases that aids in the improved visualization of the defects. That the contrast is improved when using higher flash energy can be seen comparing Fig. 6a with b for defect 1 and Fig. 6c with d for defect 2. In Fig. 6c and d, the temperature contrast in the images at time 0.130 s is about 0.4 1C more in Fig. 3d using the 6.4 kJ when compared to Fig. 6c. The trends seen in simulated thermograms, namely, the emergence of the ‘‘hot spots’’ and the times at which thermal contrasts are maximum are manifest in measurements as well. Fig. 7 shows how closely the simulation compares with experiment in determining the times of maximum thermal contrast for all the defects.
Table 1 Remaining thickness estimates using simulation data in the transmission mode.
BALCAR Flash Lamp
4.5 mm
Defect Defect Defect Defect Defect
1 2 3 4 5
Remaining thickness of defects (mm)
Estimates using simulated data
Percent error (FEM)
4.0 3.5 3.0 2.5 2.0
4.15 3.59 2.995 2.49 2.01
3.75 2.57 0.17 0.40 0.50
IR Camera Aluminum Reflector
Fig. 5. Schematic diagram of the experimental setup for transmission mode measurements.
Fig. 4. FEM simulation results for defect 2 in the reflection mode at different time frames after the flash.
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Defect
a 0 sec
0.043sec
0.087sec
0.13sec
0.174sec
0.217sec
0.26sec
0.304sec
0 sec
0.043sec
0.087sec
0.13sec
0.174sec
0.217sec
0.26sec
0.304sec
0 sec
0.043sec
0.087sec
0.13sec
0.174sec
0.217sec
0.26sec
0.304sec
0 sec
0.043sec
0.087sec
0.13sec
0.174sec
0.217sec
0.26sec
0.304sec
b
c
d Fig. 6. The thermographic images of 4-mm-diameter defects, in the transmission mode, obtained using the periscope approach at different time frames captured at 1150 fps. The sequences labeled (a) and (b) are the responses obtained using 3.2 and 6.4 kJ of flash energy, respectively, on defect 1 (0.5 mm deep). The sequences labeled (c) and (d) are the responses obtained using 3.2 and 6.4 kJ of flash energy on defect 2 (1 mm deep).
0.18
From a group of pixels representing the defect-free region of the thermogram, the normalized time–temperature plots are obtained and the characteristic time tx is determined as illustrated in Fig. 8. The tx estimated from the defect-free region was found to be 0.1235 s for a nominal wall thickness of the tube L( ¼ .0045 m). Hence, from Eq. (2), the thermal diffusivity constant of the material was determined as a ¼ 7.97 106 m2/s which compares well with the literature value for Zircaloy-2 of 7.2 106 m2/s [14]. It was found that the thermal diffusivity assessment was not influenced by errors in tx estimates in any significant manner. Further, it may be noted that although the estimated thermal diffusivity value differs from the reported value, the same method is used for estimating defect characteristics as well.
For a defective region of the material, the characteristic time tx is proportional to the square of the remaining thickness l 2
0.16
• Simulation
0.14
ο Experiment
0.12 0.1 0.08 0.06 0.04 0.02 0
1
2
3
4
5
Defect Depth (mm)
4.3. Remaining thickness estimation
tx / l
Characteristic time (s) of max thermal contrast
4.2. Thermal diffusivity estimation
Fig. 7. Comparison between simulations and experiments of the times of maximum thermal contrast, in the transmission mode, as a function of defect depth.
(3)
Therefore, the technique is quite robust to small errors in the measurement of the characteristic time for the evaluation of the remaining wall thickness, once the thermal diffusivity constant has been reliably measured. The remaining wall thicknesses in the defective regions were determined from the time–temperature evolution of the central 50% portion of the ‘‘hot spot’’ corresponding to the defective regions in the thermograms. The normalized time–temperature profiles of two shallow defects are shown in Fig. 9. Remaining
thickness of defect 1 was determined to be 4.23 mm with an error of 5.75%. Similarly, the remaining thickness of defect 2 was computed to be 3.48 mm with an error of 0.57%. The results for all the five defects along with estimates are shown in Table 2. It may be observed from this table that the trends shown by estimates based on measurements follow closely the trends indicated in simulations for all defects except defect 2. For defect
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2, measured data appears to be better than simulated data although some error is expected for this not-too-deep defect judging from the errors seen for defect 1. 4.4. Lateral sizing of defects To determine the lateral size of the defect, the image at the time frame corresponding to the maximum temperature contrast is
Table 2 Comparison of remaining thickness estimates using transmission mode data from simulation and experiment.
Fig. 8. Early history of the time–temperature evolution plot, in the transmission mode, for obtaining the time-axis intercept, tx, that relates the wall thickness (L) and the thermal diffusivity constant of the material.
Defect Defect Defect Defect Defect
1 2 3 4 5
Estimates using Remaining measured data thickness of defects (mm) using 6.4 kJ flash excitation
Percent error (Expt.)
Estimates using simulated data
Percent error (FEM)
4.0 3.5 3.0 2.5 2.0
5.75 0.57 0.33 0.40 0.50
4.15 3.59 2.995 2.49 2.01
3.75 2.57 0.17 0.40 0.50
4.23 3.48 3.01 2.51 1.99
Fig. 9. Remaining thickness estimation in the transmission mode (a) the 0.5 mm shallow defect 1 and (b) the 1.0 mm shallow defect 2, along with the corresponding temperature–time history profiles for the defect-free (sound) regions. Data obtained using 6.4 kJ flash excitation.
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b Normalized temperature
a
281
1
Horizontal direction 0.5 0
5
10
15
Vertical direction
0 Diameter(mm)
Fig. 10. (a) Cross-sectional profiles used for sizing of the defect; (b) two profile plots drawn across the defect and used for sizing.
7
5. Conclusions
ο Experiment • Simulation
FWHM (mm)
6 5 4 3 2 1
2
3 Defect depths (mm)
4
5
Fig. 11. Defect sizing estimates based on FWHM. Comparison between simulations and experiments in the transmission mode.
chosen. Fig. 10 shows the sub-windowed defective region along with the line profiles of temperature across the defect in two perpendicular directions. As the IR camera has an aspect ratio of unity (square-shaped pixels), identical scale factors in both vertical and horizontal directions of the window in terms of actual dimensions were included in the size estimation. The diameter of the defect was estimated from the 6 dB drop of the FWHM [13]. It was determined that at the working distance employed in the experiment, each pixel of the sub-windowed thermographic image represented approximately 0.41 mm 0.41 mm area. Fig. 11 shows a comparison between the FWHM estimates obtained from simulated and measured thermograms for all the defects. The FWHM estimates are seen to be better as the remaining thickness decreases. This is expected since in the transmission mode thermal diffusion causes greater blurring with increasing distance from the back surface. While there is a definite trend shown by simulations, the experiments indicate some scatter. Bearing in mind that one pixel corresponds to 0.41 mm, and the difficulty in maintaining true focus on every defect, the scatter appears to be within a couple of pixels. The determination of the actual size from the blurred image is similar but not identical to what is usually done in optics and forms the subject of a forthcoming publication. It must be noted that if the experiments were conducted in the reflection mode, as in Ref. [13], the FWHM trends will be opposite to the one observed here, i.e., the measured defect sizes will be smaller than the actual size.
The novel periscope pulsed thermography technique reported in this paper, using a polished aluminum mirror, is capable of detecting and quantifying defects in metal tubes, without the need for the IR camera to be inserted into the tube. Thermal diffusivity of the material was experimentally estimated, which compares well with the reported value, using the 1D heat diffusion analysis, the remaining thicknesses for different defect regions were estimated and found to be accurate within a maximum error of 5.75% in experiments and 3.75% in FEM simulations when compared with actual thickness. The error is significantly small (less than 0.5%) for defects that are relatively deeper and more than 1/3rd of the total wall thickness. This proposed method of inspection proves to be reliable for (a) detecting local wall-thinning defects of 10% of wall thickness or more and (b) sizing of defects with minimum defect depth of 33% of wall thickness or higher. While the transmission mode was demonstrated in the present work, it appears that the reflection mode could also be employed using the periscope approach but with a higher flash energy as input.
Acknowledgement The authors wish to acknowledge BRNS, Mumbai, for funding this work. References [1] Parker WJ, Jenkins RJ, Butler CP, Abbott GL. Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity. J Appl Phys 1961;32:1679–84. [2] USNRC report. An approach for plant specific, risk-informed decision making: in-service inspection of piping. Draft Regulatory Guide DG-1063, Washington, DC: US Nuclear Regulatory Commission, 1997. [3] Perovic V, Weatherly GC. The nucleation of hydrides in a Zr-2.5 wt% Nb alloy. J Nucl Mater 1984;126:160–9. [4] Wurzbach RN, Seith DA. Infrared monitoring of power plant effluents and heat sinks to optimize plant efficiency. In: Proceedings of SPIE—The International Society for Optical Engineering. Thermosense XXII, Orlando, FL, USA, April 24–27, 2000. [5] Shen G, Chen G, Li T, Li C. Infrared thermography test for high temperature pressure pipe, 10th Asia-Pacific Conference on Non-Destructive Testing, Brisbane, Australia, September, 2001, /http://www.ndt.net/apcndt2001/ papers/1033/1033.htmS. [6] Sun JG. Analysis of pulsed thermography methods for defect depth prediction. J Heat Transfer 2006;128:329–38. [7] Ringermacher HI, Archacki Jr. RJ, Veronesi WA. Nondestructive testing: transient depth thermography. US Patent no. 5,711,603, 1998. [8] Shepard SM, Lhota JR, Rubadeux BA, Wang D, Ahmed T. Reconstruction and enhancement of active thermographic image sequences. Opt Eng 2003;42: 1337–42.
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[9] Maldague X, Marinetti S. Pulse phase infrared thermography. J Appl Phys 1996;79(5):2694–8. [10] Maldague X, Marinetti S, Couturier JP. Applications of pulse phase thermography. In: Thompson DO, Chimenti DE, editors. Review of progress in QNDE, vol. 16. NY: Plenum Press; 1997. p. 339–44. [11] Maldague X, Ibarra-Castanedo C, Gonzalez D, Klein M. Infrared image processing and data analysis. Infrared Phys Technol 2004;46:75–83.
[12] Maldague X. Infrared and thermal testing. Nondestructive testing handbook, vol. 3. Columbus, OH, USA: ASNT Publications; 2001. [13] Saintey MB, Almond DP. Defect sizing by transient thermography II: a numerical treatment. J Phys D: Appl Phys 1995;28:2539–46. [14] Report on thermal properties of zircaloy, International Nuclear Safety Centre, Argonne National Laboratory, 1997.