Steam generator tube integrity program: Annual report, August 1995--September 1996. Volume 2 Page: 64 of 198
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be very helpful in understanding and interpreting the response of an EC probe to complex
tube/defect geometries associated with the ISI of SG tubing. To establish the validity of the
model, theoretical and experimental responses of an absolute bobbin probe to two types of
calibration standard defects are compared. Modeling results from a theoretical study of
the effect of length, width, and ligament size in axial cracks on EC indications with
conventional ISI bobbin probes are also presented.
In the FEM model, governing EM field equations in terms of magnetic-vector and
electric-scalar potentials in conducting media and reduced or total scalar potentials in
nonconducting regions are solved by using finite-element discretization. A more detailed
analysis can be found in the proceedings of the 24th Water Reactor Safety Information
Meeting (WRSM).12 Probe impedance is determined through energy and power
calculations. The signal trajectory in the impedance plane, due to probe motion, is
determined by calculating the response at discrete points along the tube axis.
Representative test cases that simulate steady-state solutions with both differential and
absolute bobbin coils are presented here.
3.1.2.1 Numerical and Experimental Results
A series of test case simulations was initially carried out to verify the accuracy of the
FEM solutions by comparing the results with detailed experimental measurements. The
experimental EC data, supplied by C. V. Dodd, formerly of ORNL, were obtained using a
large aluminum tube that contained throughwall holes and axial slits. Measurements were
made at three frequencies with a Hewlett-Packard impedance analyzer and a specially
constructed absolute bobbin coil (SN480A). Here, we compare the experimental data for a
throughwall hole and an axial slit with the FEM calculations. The results are expressed in
terms of both calculated impedance variations as a function of probe position inside the
tube and impedance-plane plots that simulate conventional EC instrument display.
Figure 28 shows the lumped element equivalent circuit for the probe and test sample
(tube) interaction modeled as primary and secondary sides of a transformer circuit. Also
shown, within the dashed rectangle, is the part of the circuit modeled by the FEM problem
space. It should be noted that, in this figure, the final solutions are normalized to
eliminate explicit dependence of the parameters on the coil/cable resistance Ro. These
normalized parameters are experimentally determined as
Xn=- (1)
Xo
and
Rn = R -RO , (2)
X0
where
Xo = coko (3)NUREG/CR-6511, Vol. 2
32
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Diercks, D. R.; Bakhtiari, S.; Kasza, K. E.; Kupperman, D. S.; Majumdar, S.; Park, J. Y. et al. Steam generator tube integrity program: Annual report, August 1995--September 1996. Volume 2, report, February 1998; Washington D.C.. (https://digital.library.unt.edu/ark:/67531/metadc697371/m1/64/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.