Eddy Current Measurement of Electrical Resistivity in Heat-Treated Zr-2.5%Nb Pressure Tubes
Zr-2.5%Nb pressure tubes (PTs) house uranium fuel bundles in the fuel channels of CANDU<sup>®</sup> nuclear reactors. Preventing a failure mode caused by contact of the PT with an outer calandria tube (CT) is performed by inspection using eddy current (EC) testing and ultrasonic testing...
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MDPI AG
2024-11-01
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| author | W. G. Thorpe P. R. Underhill T. W. Krause |
| author_facet | W. G. Thorpe P. R. Underhill T. W. Krause |
| author_sort | W. G. Thorpe |
| collection | DOAJ |
| description | Zr-2.5%Nb pressure tubes (PTs) house uranium fuel bundles in the fuel channels of CANDU<sup>®</sup> nuclear reactors. Preventing a failure mode caused by contact of the PT with an outer calandria tube (CT) is performed by inspection using eddy current (EC) testing and ultrasonic testing (UT) to measure the PT-CT gap. EC gap measurements are particularly sensitive to circumferential variation of the PT’s electrical resistivity due to microstructural variations. A full-factorial experiment was performed to examine the statistical significance of variations in the EC test parameters and manufacturing conditions on the average circumferential electrical resistivity of as-manufactured PTs. It was found that 79% of the variance in the data could be attributed to variations caused by any of the test factors or combinations of test factors. The parameters that accounted for the majority of the variance were: (1) heat treatment (HT); (2) HT and EC frequency; (3) probe inner or outer surface placement; and (4) EC frequency. Measurements of circumferential resistivity showed up to ±2.3% variation from the average of either surface. HT caused the average PT resistivity to decrease at a rate of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.53</mn><mo>±</mo><mn>0.08</mn><mo> </mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="sans-serif">μ</mi><mi mathvariant="sans-serif">Ω</mi><mo>·</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">m</mi></mrow><mrow><mrow><mrow><mi mathvariant="normal">log</mi></mrow><mo></mo><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">h</mi><mi mathvariant="normal">r</mi></mrow></mfenced></mrow></mrow></mrow></mfrac></mstyle></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.1</mn><mo>±</mo><mn>0.4</mn><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="sans-serif">μ</mi><mi mathvariant="sans-serif">Ω</mi><mo>·</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">m</mi></mrow><mrow><mrow><mrow><mi mathvariant="normal">log</mi></mrow><mo></mo><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">h</mi><mi mathvariant="normal">r</mi></mrow></mfenced></mrow></mrow></mrow></mfrac></mstyle></mrow></semantics></math></inline-formula> for inner and outer PT surfaces, respectively. The results are correlated with differences reported in the literature in the average <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>β</mi></mrow><mrow><mi>Z</mi><mi>r</mi></mrow></msub></mrow></semantics></math></inline-formula> ribbon thickness in the axial-transverse cross-section between inner and outer PT surfaces. The results demonstrate potential for EC-based resistivity measurements to characterize variations and changes in the microstructure of Zr-2.5%Nb PT material. |
| format | Article |
| id | doaj-art-649e4ea8ac994c7bbdc59ebe67a8d081 |
| institution | DOAJ |
| issn | 1424-8220 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
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| series | Sensors |
| spelling | doaj-art-649e4ea8ac994c7bbdc59ebe67a8d0812025-08-20T02:50:36ZengMDPI AGSensors1424-82202024-11-012423742610.3390/s24237426Eddy Current Measurement of Electrical Resistivity in Heat-Treated Zr-2.5%Nb Pressure TubesW. G. Thorpe0P. R. Underhill1T. W. Krause2Department of Physics, Engineering Physics and Astronomy, Queen’s University Kingston, Kingston, ON K7L 3N6, CanadaDepartment of Physics and Space Science, Royal Military College of Canada, Kingston, ON K7K 7B4, CanadaDepartment of Physics and Space Science, Royal Military College of Canada, Kingston, ON K7K 7B4, CanadaZr-2.5%Nb pressure tubes (PTs) house uranium fuel bundles in the fuel channels of CANDU<sup>®</sup> nuclear reactors. Preventing a failure mode caused by contact of the PT with an outer calandria tube (CT) is performed by inspection using eddy current (EC) testing and ultrasonic testing (UT) to measure the PT-CT gap. EC gap measurements are particularly sensitive to circumferential variation of the PT’s electrical resistivity due to microstructural variations. A full-factorial experiment was performed to examine the statistical significance of variations in the EC test parameters and manufacturing conditions on the average circumferential electrical resistivity of as-manufactured PTs. It was found that 79% of the variance in the data could be attributed to variations caused by any of the test factors or combinations of test factors. The parameters that accounted for the majority of the variance were: (1) heat treatment (HT); (2) HT and EC frequency; (3) probe inner or outer surface placement; and (4) EC frequency. Measurements of circumferential resistivity showed up to ±2.3% variation from the average of either surface. HT caused the average PT resistivity to decrease at a rate of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.53</mn><mo>±</mo><mn>0.08</mn><mo> </mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="sans-serif">μ</mi><mi mathvariant="sans-serif">Ω</mi><mo>·</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">m</mi></mrow><mrow><mrow><mrow><mi mathvariant="normal">log</mi></mrow><mo></mo><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">h</mi><mi mathvariant="normal">r</mi></mrow></mfenced></mrow></mrow></mrow></mfrac></mstyle></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.1</mn><mo>±</mo><mn>0.4</mn><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="sans-serif">μ</mi><mi mathvariant="sans-serif">Ω</mi><mo>·</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">m</mi></mrow><mrow><mrow><mrow><mi mathvariant="normal">log</mi></mrow><mo></mo><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">h</mi><mi mathvariant="normal">r</mi></mrow></mfenced></mrow></mrow></mrow></mfrac></mstyle></mrow></semantics></math></inline-formula> for inner and outer PT surfaces, respectively. The results are correlated with differences reported in the literature in the average <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>β</mi></mrow><mrow><mi>Z</mi><mi>r</mi></mrow></msub></mrow></semantics></math></inline-formula> ribbon thickness in the axial-transverse cross-section between inner and outer PT surfaces. The results demonstrate potential for EC-based resistivity measurements to characterize variations and changes in the microstructure of Zr-2.5%Nb PT material.https://www.mdpi.com/1424-8220/24/23/7426Zr-2.5%Nbpressure tubeseddy current testingelectrical resistivityfuel channels |
| spellingShingle | W. G. Thorpe P. R. Underhill T. W. Krause Eddy Current Measurement of Electrical Resistivity in Heat-Treated Zr-2.5%Nb Pressure Tubes Sensors Zr-2.5%Nb pressure tubes eddy current testing electrical resistivity fuel channels |
| title | Eddy Current Measurement of Electrical Resistivity in Heat-Treated Zr-2.5%Nb Pressure Tubes |
| title_full | Eddy Current Measurement of Electrical Resistivity in Heat-Treated Zr-2.5%Nb Pressure Tubes |
| title_fullStr | Eddy Current Measurement of Electrical Resistivity in Heat-Treated Zr-2.5%Nb Pressure Tubes |
| title_full_unstemmed | Eddy Current Measurement of Electrical Resistivity in Heat-Treated Zr-2.5%Nb Pressure Tubes |
| title_short | Eddy Current Measurement of Electrical Resistivity in Heat-Treated Zr-2.5%Nb Pressure Tubes |
| title_sort | eddy current measurement of electrical resistivity in heat treated zr 2 5 nb pressure tubes |
| topic | Zr-2.5%Nb pressure tubes eddy current testing electrical resistivity fuel channels |
| url | https://www.mdpi.com/1424-8220/24/23/7426 |
| work_keys_str_mv | AT wgthorpe eddycurrentmeasurementofelectricalresistivityinheattreatedzr25nbpressuretubes AT prunderhill eddycurrentmeasurementofelectricalresistivityinheattreatedzr25nbpressuretubes AT twkrause eddycurrentmeasurementofelectricalresistivityinheattreatedzr25nbpressuretubes |