An in-bore magnetostrictive transducer is designed for the steam generator tubes of Prototype fast breeder reactor for the generation of L(0,2) modes of frequencies in the range of 250-350 kHz. Towards this, axi-symmetric finite element models are developed to optimize the coil parameters. The optimized length of the transmitter and the receiver coils turns out to be 10 mm (~half the wavelength) for the frequency of 300 kHz. The optimized width of the coils turns out to be 0.46 mm. FE models also show the generation, propagation and reception of L(0,2) modes in the frequency range of 250-350 kHz. The role of skin effect in the magnetostrictive based-generation of L(0,2) modes with frequency is also discussed. A transducer is designed based on the FE results. The transducer is tested for the generation of L(0,2) mode in the frequency range of 250-350 kHz in a 1 m long steam generator tube segment. A good agreement is observed between FE and experimental normalized amplitudes and the times of flight for different frequencies. L(0,2) modes are found to generate and propagate and received, as predicted by the finite element simulations. An excellent agreement is observed between the experimentally measured group velocities with those obtained from the dispersion curves in this frequency range. Experiments show the signal to noise ratio to be better than 15 dB. To ascertain the utility of the transducer in steam generator tubes for the long range testing, L(0,2) mode at 300 kHz frequency is propagated in a 1.5 m long tube. The resulted multiple end reflections amount to the propagation of 51 m distance. To check the capability of detection of defects, a short tube with a full circumferential defect of depth 0.46 mm (20%WT) and a short tube with a pin hole of 1.5 mm diameter are considered. Further, FE results for the case of the axi-symmetric circumferential defect are validated experimentally. For the case of the pinhole (non-axi-symmetric), the experimental signal to noise ratio turns out to be 6 dB, which is only 6 dB lower as compared to that obtained using a piezo based ultrasonic transducer of frequency 300 kHz coupled to the end of the tube.

中文翻译：

---

PFBR蒸汽发生器管超声导波检测用内孔磁致伸缩换能器的研制

内径磁致伸缩换能器是为原型快增殖堆的蒸汽发生器管设计的，用于产生 250-350 kHz 范围内的 L(0,2) 模式频率。为此，开发了轴对称有限元模型来优化线圈参数。对于 300 kHz 的频率，发射器和接收器线圈的优化长度为 10 毫米（~波长的一半）。结果证明，线圈的优化宽度为 0.46 毫米。FE 模型还显示了 L(0,2) 模式在 250-350 kHz 频率范围内的生成、传播和接收。还讨论了趋肤效应在基于磁致伸缩的 L(0,2) 模式频率生成中的作用。基于有限元结果设计换能器。测试换能器的 L(0, 2) 250-350 kHz 频率范围内的模式，在 1 m 长的蒸汽发生器管段中。在 FE 和实验归一化振幅以及不同频率的飞行时间之间观察到了很好的一致性。正如有限元模拟所预测的那样，发现 L(0,2) 模式产生、传播和接收。在实验测量的群速度与从该频率范围内的色散曲线获得的群速度之间观察到极好的一致性。实验表明信噪比优于15 dB。为了确定换能器在蒸汽发生器管中用于远程测试的效用，300 kHz 频率的 L(0,2) 模式在 1.5 m 长的管中传播。由此产生的多端反射相当于 51 m 距离的传播。检查缺陷检测能力，考虑了深度为 0.46 mm (20%WT) 的全圆周缺陷的短管和直径为 1.5 mm 的针孔的短管。此外，轴对称圆周缺陷情况下的有限元结果通过实验得到验证。对于针孔（非轴对称）的情况，实验信噪比为 6 dB，与使用频率为 300 kHz 的压电超声换能器耦合到管子的末端。