Elsevier

Ultrasonics

Volume 116, September 2021, 106508
Ultrasonics

Simulation and performance study of circular ultrasonic array for tubes’ internal inspection

https://doi.org/10.1016/j.ultras.2021.106508Get rights and content

Highlights

  • The proposed circular linear array is competent to implement internal inspection of small diameter tubes.

  • The detection sensitivity of the array reaches 0.2 mm in circumferential and 0.1 mm in radial direction.

  • The delay law for curve interface is derived from Snell’s law which is expressed as a quartic polynomial.

  • Acoustic beam profiles in the tube wall are simulated to select preferable parameters.

  • Reflector response simulations are achieved to predict the circular linear array’s detection sensitivity.

Abstract

A circular array (CA) transducer is developed and validated to implement internal inspection of the small diameter tubes, one of whose potential application targets is the heat exchanger tubes in Modular High Temperature Gas-cooled Reactor. A geometric model of the transducer and the delay law are proposed according to the inspection setup. Using k-Wave, an open source acoustic simulation toolbox, the beam profiles of various aperture sizes are analyzed to select a suitable aperture. The beams with different focal depths are compared to verify the delay law and to choose a preferable focus. Reflector responses are simulated to predict the transducer’s detection sensitivity. To validate the simulation results, a prototype transducer composed of 64 elements is fabricated. Its electrical and acoustical performances are acquired with a pulser-receiver. A 4-element aperture with the focal depth of 1.0 mm is selected to perform internal inspection experiment according to the simulation results. The eight longitudinal grooves with widths of 0.2, 0.3, 0.4, and 0.5 mm on inner and outer tube walls are applied as typical reflectors to test circumferential detection sensitivity. The other five grooves with depths from 0.1 mm to 0.5 mm are chosen to verify radial detection sensitivity. The experiment results demonstrate the detection sensitivity of the CA transducer reaches at least 0.2 mm in circumferential direction and 0.1 mm in radial direction. The CA is proven capable of inspecting small diameter tubes.

Introduction

Tubes of steam generator (SG) in nuclear power plant play a vital function in ensuring the integrity of pressure boundary [1]. They work at high temperature and under high pressure with complex stress, strain and corrosion conditions. The tubes should be inspected during manufacture, pre-service and in-service in order to track its status according to ASME code [2]. In-service induced flaws such as corrosion and thinning must be monitored periodically in order to prevent injury and protect environment. In this paper, the SG heat exchanger tubes in Modular High Temperature Gas-cooled Reactor (HTGR) [3] are taken as the inspection samples. The size of the tubes is Φ19 × 3 mm. Inspection from external of the tubes is inaccessible due to limited space and radioactivity. Internal inspection is the most possible way to track potential dangers in the SG.

The conventional popular internal inspection methods for tubes is eddy current testing (ET) [4], which is competent to detect and characterize surface and sub-surface flaws in conductive materials [5]. However, evaluation of small flaws like pits can be difficult for ET [6]. Ultrasonic testing (UT) is a representative volumetric inspection method and its advanced phased array technology have attracted increasing attention [7]. It has advantages of high sensitivity, flexibility, and effectiveness for a variety of materials. The ultrasonic wave propagation in the tube wall was studied by Choi et al. [8]. Yi-Mei Mao and Pei-Wen Que [9] compared ultrasonic signals reflected from various defects on the tube. Elfgard Kühnicke [10] studied the curved array’s harmonic and transient sound fields in water to analysis and eliminate grating lobes. The internal rotating ultrasonic inspection (IRIS-UT) system developed by Pan American Industries Inc. and OLYMPUS Inc. used a single element probe and a rotating mirror to achieve circumferential scanning [11], [12]. Karpelson [13] discussed array transducers used in internal inspection and proposed a transducer which called cone-probe. ANSALDO proposed the POSITEUS system and circular transducer [14].

However, the methods like IRIS-UT only use single element to imaging, the directivity and energy of the ultrasonic beam were relatively limited [15]. In addition, large curvature of the tube wall has adverse influences on focusing, and limited space makes acoustic beam focus poorly in the circumferential direction [16]. Phased array ultrasonic testing (PAUT) is able to overcome above shortcomings by delaying the elements’ excitation signals with a proper focal law, which can achieve varieties of steering or focusing beams [17].

In this paper, a circular array (CA) transducer is developed, whose schematic is shown in Fig. 1. The elements are arranged circumferentially on a cylinder. The transducer is arranged inside the tube and moves in axial direction, focused beam is formed with proper active aperture and designed delay law. The gap between the tube and the transducer is filled with water as coupling agent.

The structure of this paper is arranged as follow. In Section 2, a geometric model of the CA and the delay law is first described according to the specific inspection setup. The mathematic model of CA’s delay law is proposed. The computation toolbox and models of simulations are stated. The fabrication procedure and test methods of the prototype transducer are finally given. 3.1 Beam simulations of different apertures, 3.2 Focal point control simulations and focus selection, 3.3 Reflector response simulation results are simulation results: the beams formed by different apertures are analyzed in 3.1, the beams with different focal depth are compared in 3.2, and the reflector response simulations are carried in 3.3 to predict the detection sensitivity of the CA. 3.4 Prototype transducer tests, 3.5 Internal inspection experiment results show experiment results of the prototype transducer: the electrical and acoustical performances can be found in Section 3.4, and the internal inspection results are shown in Section 3.5.

Section snippets

Inspection setup and geometric model of the transducer

The tube with the inner diameter (2Ri in Fig. 1) of 13 mm and with a wall thickness (Dtw) of 3 mm is taken as the inspection objective. The whole wall thickness (WT) is the region of interest. The volumetric flaws like corrosion, pitting and thickness thinning with circumferential or radial dimensions beyond 10% WT (0.3 mm in this case) should be detected according to ASME codes. Therefore, a uniform, focused, and with high acoustic pressure beam along the whole thickness of the tube wall is

Beam simulations of different apertures

The normalized beam simulations of different apertures in circumferential-axial plane are displayed in Fig. 10. Only the area inside the tube wall is concerned, so the other areas’ acoustic pressure is set to 0. The beams’ parameters are listed in Table 5. Fig. 11 shows the acoustic pressure profiles along beam axis. The beams of single element aperture (Fig. 10(a)) and 2-element aperture (Fig. 10(b)) are unfocused, acoustic pressure mainly concentrate at near inner wall while the pressure at

Discussion

The selection of the array parameters should be further discussed. The determination of central frequency, element number, pitch, width and length is a trade-off between acoustic performance and present machining cost. Generally, there should be an optimized configuration which is able to achieve the best beam profile: higher pressure in the main lobe, lower level of the side lobes, without grating lobes, and more uniform in the region of interest, etc. However, first, as stated in Section 2.5,

Conclusion

A circular array transducer is developed and validated to implement internal inspection of the small diameter tubes. We first demonstrated that the CA transducer and the designed delay law can be applied to generate controllable and focused beams in tube wall by simulations. The beams and pressure profiles are analyzed and the parameters are carefully determined. The 4-element aperture with the focal depth at 1 mm depth in tube wall is chosen to implement defect response simulation and

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

This work has been supported by the Chinese National S&T Major Project (Grant No. ZX069).

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