Gap width measurements in fuel elements

Gap width measurements in fuel elements Y. Segal and F. Trichter The analysis of 11 neutron radiographs, five of pin CEP-E1 no. 4 and six of pin CEP-E1 no. 7 are presented. The dimensions of the gaps between adjacent pellets were determined by three methods: projection microscopy measurements, the derivative method and the convolution method. The errors associated with the gap width measurements were in some cases over 100%.

Keywords: neutron radiography, fuel element pellets, gap width measurement Neutron radiography is very important in determining the condition of nuclear fuel elements. Quantitative information on cracks, voids, swellings and dimensions enables prediction of the possible allowable lifetime of a fuel element in a reactor core. A significant amount of work has been done in the quantitative interpretation of neutron radiographs [1-2°1. An important step towards a world-wide standardization and comparison of quantitative neutron radiography of fuel elements has been made by Euratom tl ~]. In this programme t91, three test patterns are suggested, two for determining the quality of the neutron beam and the third for determining the resolution of the neutron radiography system, including film and screens etc. As the project was related to a nuclear fuel element, the image quality indicator (IQI) adopted was a simulation of a fuel pin with calibrated radial and longitudinal gaps (see Figure 1). Several pins were produced and distributed to various laboratories. The pins were neutron radiographed by the laboratories, using different facilities and techniques. Details of five neutron radiographs of fuel pin CEP-E1 no. 4 and six neutron radiographs of pin CEP-E1 no. 7, as well as their weights and measurement certificates, are presented in Tables 1 and 2. Each of the 11 neutron radiographs was obtained by a different technique (see Table 3). These neutron radiographs were thoroughly examined by us.

Profile projecton microscopy measu rements This method is relatively simple. A projection microscope (Nikon profile projector V-12) was used. The digital x - y coordinate table has a resolution of 1 /~m. This method is subjective as the operator must decide between which two coordinates the width of the gap extends. The results of these measurements are presented in Table 4. They show that: • For most neutron radiographs and gaps, the measured values are larger than the true ones. Exceptions to this are radiograph no. 101, and gaps of 316, 250 and 208 pm.

• The largest relative errors appear in the case of the narrowest gap, which has a nominal width of 50 #m. In an extreme case, an error factor of approximately 7 was obtained. The average is around 240/~m, ie a factor of almost 5. • For wider gaps the relative error decreases: for a nominal gap width of 100 /~m the average is over 200 /~m, ie a factor of approximately 2. For the widest gap, of nominal width 300/tm, the average is below 400/~m, ie an error of 30 %. • Analysis of specific neutron radiographs shows that a large error in the measurement of a narrow gap does not imply a large error in a wider gap (neutron radiographs 103 and 106). The gaps were measured by several people using the same projection microscope, and every person obtained different results; however, the general trend remained the same. The reason is that every person interpreted differently the location of the edges. The differences increases if the operator does not know in advance the expected gap widths.

Computerized microdensitometer measurements The projection microscopy measurements are, to a certain extent, operator dependent, whereas a density profile obtained by a digitizing microdensitometer is free from this limitation. The neutron radiographs were scanned using a computer-controlled Photomation 1700 microdensitometer (manufactured by Optronics Ltd). The pixel size was 25 x 25 #m. A typical result is presented in Figure 2. The spikes on the graph are due to the controlled gaps between the pellets. The holes drilled in the pellets can also be identified. The gap widths were derived by evaluation of the spikes. The derivative and the convolution methods were used to determine the gap widths.

The derivative method In this method, the derivative of the film density profile is taken (see Figure 3 ). The width of the gap is determined

0308-9126/89/040222-07/$03.00 © 1989 Butterworth & Co (Publishers) Ltd 222

NDT International Volume 22 Number 4 August 1989

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T a b l e 2. G a p w i d t h s

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299 299 297 298

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E2

E3

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E5

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51 50 50 50

101 100 101 101

148 145 145 146

201 196 195 197

250 251 250 250

301 296 295 297

(1)

where a, b and c are parameters and i is the distance of the pixel from the middle of the filter window.

N D T International A u g u s t 1989

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by the distance between the negative and the positive peaks [211. However, owing to noise, it is impossible to take a meaningful derivative of a directly measured density profile. Therefore, the density profile was smoothed using a low-pass filter based on a second-order polynomial of the type y i = ai 2 + bi + c

no. 4 a c c o r d i n g

The parameters a, b and c are obtained by least-squares fitting. A typical result is presented in Figure 3. The results obtained by the derivative method are summarized in Table 5. The diversity of the results obtained by the derivative method is no better than that obtained with the projection microscope. The

convolution

method

If it is assumed that the gap is rectangular and the radiation beam is unidirectional and parallel to the gap's

223

Table 3. Techniques and facilities for the radiographs studied Radiograph number

Radiograph marking

Pin number

Radiography facility

Screen type

Film type

100 101 102 103 104 105 106 107 108 109 110

DYD4HW(RI) DYMHW(RI) DYSRHW(RI) GDSRHW(RI) DYMHW(RI) DYSRRI (T) DYD4RI (T) DYMRI(T) GDSRRI(T) GDD4RI(T) GDMRI(T)

4 4 4 4 4 7 7 7 7 7 7

Harwell Harwell Harwell Harwell Harwell RISO RISQ RISO RISO RISO RISO

Dysprosmm Dysprosium Dysprosmm Gadolinium Dysprosium Dysprosium Dysprosmm Dysprosmm Gadolinium Gadolinium Gadolinium

D4 M SR SR M SR D4 M SR D4 M

Table 4. Results of measurements with the profile projector microscope

0.75

Radiograph number Gap width (pm) True gap width

Pin no 4

100 101 102 103 104

316 260 208 156 108 321 225 448 434 466

216 152 316 338 249

198 155 296 277 268

233 163 271 329 271

206 140 210 225 177

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105 106 107 108 109 110

303 250 204 148 104 55 395 423 426 318 373 416

383 285 334 315 300 268

346 310 225 284 264 254

319 321 387 201 339 255

361 263 537 110 181 192

385 342 327 141 247 200

0.06

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2.22

2.33

2.45

2.57

pixel numberx107 Fig. 3 The upper curve is a typical density profile of a gap between two pellets. The higher density on the right is due to the hole in the right pellet. To reduce noise, 40 lines of 50 x 50/~m pixel scans were summed. The line obtained was smoothed using a low-pass filter. The lower curve is the derivative of the smoothed density profile

walls, the ideal density profile will have the shape of a square wave. However, in practice, blurring occurs and a diffuse picture is obtained. Blurring may be represented by an exponential line spread function (LSF) [22]. Therefore, the shape of the density profile will be the convolution of the ideal response with an exponent [14'23'242 D~ = D,* LSF L Fig. 2 Profile scans of fuel element sample: CN BN RI 50 T, 50 /lm aperture 0-2 D scanned with P-1700 microdensitometer under IPS version 2.O. Top: Original segment of scanned image, 300 lines × 2000 samples/line. Centre: Profile of density through centre of element, averaged over 40 lines ( equivalent aperture size is 50 l=m by 2 mm). Distance between vertical grid lines represents 400 pm; horizontal grid lines represent a density change of little more than 0.06 D (2.0/32). Bottom: Off-centre profile of the neutron radiograph

224

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NDT International August 1989

Table 5. Results of gap width measurements by the derivative method

Table 6. Least-squares fitted parameters obtained by the convolution method for radiograph no. 100 of pin 4

Radiograph number Gap width (pm) True gap width

Pin no 4

316 260 208 156 108

100 101 102 103 104

350 225 575 600 450

True gap width

300 200 450 425 350

200 175 375 350 250

275 200 350 325 275

51

175 175 250 275 250

150 300 275 225 200

303 250 204 148 104

55

True gap widths (/~m)

2a(#m)

2(pm -1)

H1

H2

316 260 208 156 108 51

320 254 188 180 144 120

0.00676 0.00781 0.00808 0.00800 0.00832 0.00604

0.320 0.317 0.315 0.313 0.222 0.182

0.201 0.212 0.216 0.232 0.141 0.117

where ~ is the coordinate in the x direction; R o is the minimum density level; H is the ideal density level above Ro; x o is the middle of the gap; 2a is the width of the gap and h(x) is the Heaviside function.

2 must be more or less constant. This situation must be fulfilled at least at different points on a given radiograph. However, least-squares values of 2 for different gaps on the same radiograph are different (see Table 6). To avoid this anomaly, the value of 2 was fixed for each radiograph. This step also reduced the number of fitted parameters and therefore a better accuracy is expected. For each radiograph two values of 2 were calculated, both based on Equation (6). The first was calculated by imposing on 2a the known central void in one of the pellets. The dimensions of the holes are about 4 mm, which is large compared with the edge effect of the LSF. The second value of 2 was obtained by imposing on 2a the nominal 300/tm gap width. The results are presented in Tables 7 and 8, respectively. This step significantly improved the situation. This step uses a selected dimension on the neutron radiograph to characterize or calibrate the neutron radiography system by determining the value of 2, ie the LSF.

Equation (4) represents the situation where the density level at the two sides of the gap is equal. However, the fuel pin is composed of pellets having a partial central hole (see Figure 1). Therefore, the density level is different at each side (see Figures 2 and 3). In this case, instead of Equation (4), we obtain

For convenience, the results presented in Tables 4-8 are summarized in Figure 4 for pin no. 4 and in Figure 5 for pin no. 7. A logarithmic scale is used and, for each gap, the measured width is presented in units of its true width. For all methods the diversity is large and increases with decreasing gap width.

Dl= Hlh(x- Xo + a)- H2h(x- x o-a)+ Rol - Ro2

The best values were obtained by the 'locked' convolution method. It is interesting that in certain cases the measured values are smaller than the true ones. Equation (6) shows that blurring can only widen the gaps as they appear on the neutron radiograph. Therefore, some other mechanism must be responsible for the narrowing effect, which could be due to an oblique neutron radiography geometry.

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105 106 107 108 109 110

550 450 500 425 450 450

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450 225 450 325 450 475

450 375 450 475 475 325

975 450 800 750 550 425 425 575 725 600

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NDT International August 1989

If the radiation beam is not parallel to a gap wall, a shadow will appear. If the inclination angle is large enough, the shadow will mask the gap completely. One may define a critical angle as one in which the oblique ray hits the upper and lower edges of the gap. In our case, the critical angles for the gaps of width 300, 250, 200, 150, 100 and 50/am are 1.36°, 1.13 o, 0.91 °, 0.68 °, 0.45 ~ and 0.23 °, respectively. These angles are very small. Generally, radiographers do not position their samples with such a high accuracy. An exaggeration of the phenomenon is demonstrated in Figure 6. Fuel pin no. 14 CFP-E1 (its weights and measures certificate is presented in Table 9) was X-radiographed three times. First, the focus of the X-ray machine was located above the 300 /tm gap, secondly over the 100 #m gap and thirdly over the 50 pm gap (see Figures 6a-c). Although all three

225

Table 7. Gap widths obtained through the locked Z convolution method Radiograph number

Gap width (/~m)

True gap width

316

260

100 101 Pin no. 4 102 103 104

334 397 396 352 378

True gap width

303

250

105 106 107 Pin no. 7 108 109 110

499 _+ 7 486 +_ 8 487 + 16 368 -+ 8 349 -+ 13 497_+11

424 425 497 304 303 441

_+ 11 _+ 6 _+ 13 _+ 8 _+ 8

282 205 250 297 303

208 + 4 _+ 5 _+ 19 _+ 9 _+ 5

_+ 4 _+ 7 -+ 11 -+ 3 -+ 5 _+6

219 227 331 248 235

156 -+ 5 _+ 5 _+ 3 _+7 _+ 6

202 210 382 247 226

108 _+ 7 _+ 6 _+ 1 5 _+ 5 _+ 10

130 116 344 134 136

51 _+ 5 + 6 _+ 21 _+ 6 _+ 6

204

148

104

309 _+ 3 295 _+ 7 374 _+ 8 236 + 5 243 _+4 324_+7

280 _+ 6 279 + 6 266 -+ 9 225 -+ 5 235 _+ 8 313+8

119 _+ 7 109 + 4 -95 -+ 3 135 _+ 12 112_+9

m

93_+7 131 _+24 117_+6 109_+13 55 -90 -+ 9 -72 _+ 3 163 _+ 9 53_+6

At first, 2 was calculated by inserting the known value of the length of the central hole in one of the pellets. This calculated value was used as a known value while all the other parameterswere obtained by least-squaresfitting.

Table 8. G a p widths obtained by the convolution method Radiograph number True gap width

Pin no. 4

100 101 102 103 104

True gap width

Pin no. 7

105 1 06 1 07 108 109 110

Gap width (#m) 316

260

208

156

108

317_+3 316 _+ 3 327 _+ 7 337 _+ 8 322_+4

269+4 247 _+ 5 227 -+ 5 278 _+ 7 262_+5

209+5 193 + 5 284 -+ 22 232 -t- 7 212_+5

194_+7 178 _+ 5 320 + 34 229 -+ 5 210_+8

126_+7 105 _+ 5 288 -+ 18 125 -t- 8 127_+5

303

250

204

148

104

305 + 3 306 _+ 3 305 + 3 307 __+4 305+3 306_+3

262 +_ 4 253 _+ 3 321 + 6 254 + 3 265__+5 271 _+4

203 + 4 1 90 ___3 248 __ 6 200 -I- 4 213_+4 216_+5

1 89 + 5 1 82 + 4 188 + 5 191 + 5 207_+7 206_+6

-77 + 3 -87 +__2 120_+11 121 _+4

51 -86 _+ 7 86 _+ 19 100 + 7 117+9 55 ---67 + 2 144_+8 96+4

At first 2 was calculated by inserting the known value of the 316 #m gap for Pin 4 (for Pin 7 this was 303/~m). This value of 2 was inserted as a known value while all other parameters were obtained through least squaresfitting.

radiographs are of the same pin, the gap widths extracted from each radiograph will be different. In the first radiograph, the 50/~m and 100 #m gaps are not seen, but in the third radiograph the wider gaps of 150 #m, 200 pm, 250 pm and 300 #m almost disappear while the 50 p m and 100 pm gaps are seen clearly. This is due to the very small critical angles, in the range 0.23-1.36 °. The neutron radiographs were obtained using geometries in which the neutron beams were parallel to the gap walls. However, as the critical angles are very small, a deviation of even a fraction of a degree may lead to a considerable narrowing of a gap width. The oblique mechanism causes the reverse effect to blurring and in certain combinations the influence of the oblique geometry will overcome the widening due to blurring. A more detailed analysis of the oblique effect is given elsewhere Cz5'26].

226

Conclusions The extraction of sub-millimetre dimensions from radiographs is a problem. If not approached carefully, errors of a factor of 2 may be obtained. The error may give narrower or greater widths than the true value. Accurate measurements require a precise knowledge of radiography angles and the LSF of the system. Natural cracks tend to change direction randomly. Therefore, one has to be very careful in relating quantitative values to a measured crack width.

Acknowledgement The authors are very grateful to Mr J.C. D o m a n u s from the RISO Research Establishment for providing the neutron radiographs and certificates essential to the

NDT International August 1989

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References

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Basham, S.J., Grieser, D.R. and Ray, J.W. 'Dimensional measurements of cylindrical specimens using neutron radiography' Mat Eval (June 1970) p 140 Cutforth, D.C. 'Dimensioning reactor fuel specimens from thermal neutron radiographs' Nuclear Technology 18 (April 1973) p 67 Vary, A. and Bowles, K.J. 'Application of an electronic image analyser to dimensional measurements from neutron radiographs' Mat Eval (January 1974) p 7 Harms, A.A. 'Physical processes and mathematical methods in neutron radiography' Atomic Energy Review 15 143 (1977) Domanus, J.C. 'Accuracy of dimension measurements from neutron radiographs of nuclear fuel pins' RISO-M-1860 (March 1976) Domanus, J.C. RISO National Laboratory, B-497 (AugustSeptember 1980) Domanus, J.C. 'Standard defects and dimensional measurements in neutron radiography' RISO-M-2318 (October 1981) Osuwa, J.C. and Harms, A.A. 'The extremum-slope for precise dimensional measurements in neutron radiography' Proc First World Co•f Neutron Radiography San Diego, USA (1981) p 859 Domanus, J.C. 'Revised test program for testing of CFP-E1; ASTM (revised) BPI and SI and BPI-E' RISO B-512 (August 1981) Do°anus, J.C. 'Search for adequate quality standards for neutron radiography of nuclear fuel' Proc First World Conf in Neutron Radiography San Diego, California, USA (1981) p 1017 Do°anus, J.C. 'Euratom test program for image quality and accuracy of dimensions' Proc First World Conf. in Neutron Radiography San Diego, California, USA (1981) p 1025 Ruyter, I. and Leeflang, M. 'Dimensional measurement of the Petten calibration pin' Proc First World Con.[ in Neutron Radiography San Diego, California, USA (1981) p 867 Akopov, V.S., Golenischev, I.A., Graehev, A.V., Mayorov, A.N. and Petukhov, V.I. 'Fuel element radiographic inspection: the development of technique and apparatus complex' lOth World Conference on NDT Moscow USSR (August 1982) Snare, C. 'Dimensional measurements by means of neutron radiography image', GKSS 82/E 17 Harms, A.A. 'Dimensional neutron radiography' 4th Annual Meeting, Neutron Radiography Working Group EURATOM (May 1982) Trichter, F., Notea, A. and Segal, Y. 'Dimension measurement of gaps' Trans of l lth Annual Meeting of the Israel Nuclear Society (December 1983) pp 248-250

Fig. 5 Similar to Figure 4 but for pin no. 7. The general behaviour is the same for both pins

Fig. 6

Table

Three X-radiographs of pin no. 14

9. Gap

widths

Gap (#m)

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227

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23

Notea, A., Segal, Y. and Trichter, F. 'Gaps dimensions in fuel elements from neutron radiography' Proc 6th Int Conf on NDE in Nuclear Industry Zurich, Switzerland ( November-December 1983) p 433 Leetlang, H.P. 'Preliminary assessment of the NRWG test program performed with the Petten neutron radiography facility' ECN-83074, Petten, The Netherlands (May 1983) Wyman, D.R. and Harms, A.A. 'System transfer function applications in neutron radiographic object scattering', Nucl Sci Eng 88 522 (1984) Bnshlin, Y., Ingman, D. and Notea, A. 'Moment analysis method for the determination of dimensions from radiographs' Nuclear Technology 74 218(1986) lngman, D. and Notea, A. 'Derivative method for edge enhancement in radiographic testing' Nuclear Technology 72 99 (1986) Segal, Y., Gntman, A., Fishman, A. and Notea, A. 'Point spread functions due to neutron scattering in thermal neutron radiography of aluminium, iron, zircaloy and polyethylene objects' Nuclear Instrumentation Methods 197 557 (1982) Burch, S.F. 'Application of digital techniques to the restoration of

24 25

26

radiographic images' Material Physics Division, AERE-R10219 Harwell (September 1980) Bnshlin, Y. 'Extraction of quantitative information from noisy radiographs' MSc Research Thesis Technion, Haifa, Israel (October 1985) Triehter, F. 'Dimensional measurement by means of radiography in the submillimetric range' DSc Thesis Department of Nuclear Engineering, Technion-Israel Institute of Technology, Haifa, Israel 1986 (in Hebrew) Segal, Y. and Triehter, Y. 'Limitations in gap width measurements by X-ray radiography' NDTlnternational 21 (1988) 11-16

Authors T h e a u t h o r s are w i t h the D e p a r t m e n t of N u c l e a r E n g i n e e r i n g , T e c h n i o n - I s r a e l I n s t i t u t e of T e c h n o l o g y , H a i f a , Israel.

Paper received 20 May 1988. Revised 26 September 1988

228

NDT International August 1989