A Multiple-Frequency Eddy Current Testing Method for of Multi-Layer Heterogeneous Membrane Stacks Measurement in Nuclear Fuel Cladding Tube
Huang Pu1, Han Zheng2, Peng Lisha2, Wen Yinghong1, Huang Songling2
1. School of Automation and Intelligence Beijing Jiaotong University Beijing 100044 China; 2. Department of Electrical Engineering Tsinghua University Beijing 100084 China
Abstract：Within the extreme operational environment of a nuclear reactor, the fuel assembly functions as the cornerstone of nuclear safety, acting as the first physical barrier against radioactive release. The zirconium alloy cladding tube, serving as the pressure boundary, must maintain impeccable structural integrity to effectively contain fission products, prevent the leakage of radioactive materials, and provide long-term mechanical support for the fuel pellets. However, prolonged exposure to high-temperature, high-pressure coolant flow induces persistent thermo-chemical interactions. These interactions lead to oxidation reactions that consume the metallic matrix, resulting in the formation of a heterogeneous oxide film on the outer cladding surface. This corrosion phenomenon not only reduces the effective load-bearing wall thickness but also severely compromises the mechanical properties—particularly the strength and toughness—of the fuel assembly, thereby elevating the risk of functional failure. Consequently, the accurate assessment of the cladding’s structural state necessitates the high-precision, non-destructive measurement of multiple coupled parameters, specifically the oxide film thickness, the wall thickness, and the electromagnetic properties induced by irradiation and corrosion. Traditional single-frequency eddy current testing (ECT) methods are fundamentally limited in this context, as the lift-off, thickness, and conductivity are highly intertwined, creating a complex inverse problem that hinders decoupled measurement. To surmount these limitations, this paper proposes a novel multi-layer heterogeneous film characterization methodology utilizing a stacked-array multiple-frequency eddy current testing technique. The core innovation lies in the synergistic integration of a bespoke sensor architecture and an advanced inversion algorithm. First, a specialized stacked-array eddy current sensor was designed and fabricated, comprising three coaxial coils arranged in a compact, layered configuration. This unique geometry optimizes the spatial sensitivity distribution, enabling the simultaneous acquisition of electromagnetic responses at varying penetration depths. Correspondingly, an analytical forward model was established based on the electromagnetic theory of a two-layer composite medium, representing the conductive metallic cladding substrate and the relatively non-conductive oxide film layer. By solving Maxwell’s equations under quasi-static conditions, the mutual inductance expressions governing the interactions between the excitation and pickup coils were rigorously derived. These formulations establish the complex mathematical relationship between the measured coil impedance and the target material parameters—namely, oxide thickness, cladding thickness, and electrical conductivity—across a broad spectrum of excitation frequencies. Subsequently, a multi-parameter stepwise decoupling inversion method was developed to resolve the ambiguities inherent in the coupled signals. This strategy strategically exploits the frequency-dependent skin effect: high-frequency eddy currents are confined primarily to the surface region, rendering them highly sensitive to the oxide film but insensitive to the substrate, whereas low-frequency currents penetrate deeper, carrying information about the metallic matrix. Specifically, the high-frequency response signals are first utilized to invert the thickness of the surface oxide film layer, effectively isolating surface effects from the underlying substrate. Once the oxide thickness is accurately determined, the low-frequency response signals are processed in conjunction with the spatial sensitivity characteristics of the coil array. This allows for the subsequent decoupled reconstruction of the cladding thickness and the conductivity. This stepwise approach transforms a traditionally ill-posed multi-variable optimization problem into a sequence of stable, single-variable estimations, significantly enhancing the robustness of the inversion process. Finally, the proposed method is validated through finite element numerical simulations and experiments. Parametric FEM simulations are conducted to analyze the sensitivity coefficients of various frequencies to the target parameters, confirming the theoretical basis for frequency selection. Furthermore, experimental tests are performed on zirconium alloy cladding tube specimens with artificially prepared oxide layers with varying thicknesses. The results demonstrate that accurate estimation of all three heterogeneous film parameters can be achieved by analyzing the differential multi-frequency responses based on the eddy current skin effect in stacked arrays. Quantitative analysis indicates that the average relative error for the oxide film thickness, cladding thickness, and electrical conductivity was maintained below 3.5%. This level of precision effectively proves the feasibility and accuracy of the proposed method, offering a robust technical solution for the in-situ, high-precision evaluation of fuel cladding degradation and contributing significantly to the predictive maintenance and safety assessment of nuclear power plants.
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2026, Vol. 41 
