Analytical model of a T-core coil above a multi-layer conductor with hidden hole using the TREE method for nondestructive evaluation

Purpose In eddy current nondestructive testing, a probe with a ferrite core such as an E-core coil is usually used to detect and locate defects such as cracks and corrosion in conductive material. However, the E-core coil has some disadvantages, such as large volume and difficulty in the process of winding the coils. This paper aims to present a novel T-core probe and its analytical model used for evaluating hidden holes in a multi- layer conductor. Design/methodology/approach By using a cylindrical coordinate system, the solution domain is truncated in the radial direction. The magnetic vector potential of each region excited by a filamentary coil is derived, and the expansion coefficients of the solutions are obtained by matching the boundary and interface conditions between the regions. By using the truncated region eigenfunction expansion method, the final expression in closed form for the impedance of the multi-turn coil is worked out, and the impedance calculation is performed in Mathematica. For frequencies ranging from 100 Hz to 100 kHz, both the impedance changes of the T-core coil above the multi-layer conductor without a hidden hole and in the absence of the layered conductor were calculated, and the influence of a hidden hole in the multi-layer conducting structure on the impedance change was investigated. Findings The correctness of the analytical model of the T-core coil was verified by the finite element method and experiments. The proposed T-core coil has higher sensitivity than an air-core coil, and similar sensitivity and smaller size than an E-core coil. Originality/value A new T-core coil probe and its accurate theoretical model for defect evaluation of conductor were presented; probe and analytical model can be used in probe design, detection process simulation or can be directly used in defect evaluation of multi-layer conductor.

A Theoretical Study of the Hydrodynamic Performance of an Asymmetric Fixed-Detached OWC Device

The chamber configuration of an asymmetric, fixed-detached Oscillating Water Column (OWC) device was investigated theoretically to analyze its effects on hydrodynamic performance. Two-dimensional linear wave theory was used, and the solutions for the associated radiation and scattering boundary value problems (BVPs) were derived through the matched eigenfunction expansion method (EEM) and the boundary element method (BEM). The results for the hydrodynamic efficiency and other important hydrodynamic properties were computed and analyzed for various cases. Parameters, such as the length of the chamber and the thickness and submergence of the rear and front walls, were varied. The effects on device performance of adding a step under the OWC chamber and reflecting wall in the downstream region were also investigated. A good agreement between the analytical and numerical results was found. Thinner walls and low submergence of the chamber were seen to increase the efficiency bandwidth. The inclusion of a step slightly reduced the frequency at which resonance occurs, and when a downstream reflecting wall is included, the hydrodynamic efficiency is noticeably reduced at low frequencies due to the near trapped waves in the gap between the OWC device and the rigid vertical wall.

Theoretical Hydrodynamic Analysis of a Surface-Piercing Porous Cylindrical Body

In the present study, the diffraction and the radiation problems of water waves by a surface-piercing porous cylindrical body are considered. The idea conceived is based on the capability of porous structures to dissipate the wave energy and to minimize the environmental impact, developing wave attenuation and protection. In the context of linear wave theory, a three-dimensional solution based on the eigenfunction expansion method is developed for the determination of the velocity potential of the flow field around the cylindrical body. Numerical results are presented and discussed concerning the wave elevation and the hydrodynamic forces on the examined body for various values of porosity coefficients. The results revealed that porosity plays a key role in reducing/controlling the wave loads on the structure and the wave run-up, hence porous barriers can be set up to protect a marine structure against wave attack.

Locating Defects in Conductive Materials Using the Eddy Current Model of the Filamentary Coil

This article presents an innovative technique for detecting flaws in conductive materials by using an ideal filamentary coil. To characterize such a coil accurately and explicitly, it is sufficient to be in possession of merely two parameters: the radius of the circle within which all the turns are located and the distance of the coil from the tested surface. The mathematical model derived using the truncated region eigenfunction expansion method enables the calculation of the changes in the components of the filamentary coil impedance that are the result of positioning the coil close to the conductive material with a hole. Because of this, the air-cored coil model can be replaced with a much simpler filamentary coil model. This solution makes it is possible to detect various types of holes (internal, surface, subsurface or through) occurring in both multilayer magnetic and non-magnetic materials. The derived results were verified by means of measurements and numerical calculations based on the finite element method. Very good agreement was observed in both cases. The paper contains the source code implemented in Matlab, which is used to for calculations.

Study on Dynamic Stability of Single Floating Pier Under Waves

Considering the upper structure restraint effect of the floating bridge, the diffraction effect and radiation effect of linear monochromatic waves, the dynamic response equation of floating pier is derived and the factors affecting the dynamic stability of the floating pier are analyzed in this paper. Based on the theory of potential flow, the calculation domain is divided into the interior region and the exterior region. The wave diffraction and radiation problems are solved by the matched eigenfunction expansion method (MEEM). After obtaining the wave excitation force, additional mass and radiation damping coefficient, considering the restraint effect of the upper structure of the floating bridge, the motion differential equation of the floating pier is established, and the response amplitude operator (RAOs) of the floating pier is obtained. The effects of span, mass and stiffness of upper structure, as well as the draft depth, size and net height of floating pier on dynamic stability of floating pier under wave are analyzed. The results show that the increase in the span of upper structure will significantly increase the peak RAOs of sway and heave, and the increase in stiffness is helpful to reduce the peak RAOs of sway and heave. The increase of the floating pier radius can reduce the heave RAO, and the net height on the water surface of the floating pier increases the heave and roll.

Sizes and Shapes of Sea Ice Floes Broken by Waves–A Case Study From the East Antarctic Coast

The floe size distribution (FSD) is an important characteristics of sea ice, influencing several physical processes that take place in the oceanic and atmospheric boundary layers under/over sea ice, as well as within sea ice itself. Through complex feedback loops involving those processes, FSD might modify the short-term and seasonal evolution of the sea ice cover, and therefore significant effort is undertaken by the scientific community to better understand FSD-related effects and to include them in sea ice models. An important part of that effort is analyzing the FSD properties and variability in different ice and forcing conditions, based on airborne and satellite imagery. In this work we analyze a very high resolution (pixel size: 0.3 m) satellite image of sea ice from a location off the East Antarctic coast (65.6°S, 101.9°E), acquired on February 16, 2019. Contrary to most previous studies, the ice floes in the image have angular, polygonal shapes and a narrow size distribution. We show that the observed FSD can be represented as a weighted sum of two probability distributions, a Gaussian and a tapered power law, with the Gaussian part clearly dominating in the size range of floes that contribute over 90% to the total sea ice surface area. Based on an analysis of the weather, wave and ice conditions in the period preceding the day in question, we discuss the most probable scenarios that led to the breakup of landfast ice into floes visible in the image. Finally, theoretical arguments backed up by a series of numerical simulations of wave propagation in sea ice performed with a scattering model based on the Matched Eigenfunction Expansion Method are used to show that the observed dominating floe size in the three different regions of the image (18, 13 and 51 m, respectively) agree with those expected as a result of wave-induced breaking of landfast ice.

Wave Interaction With a Pair of Submerged Floating Tunnels in the Presence of An Array of Submerged Porous Breakwaters

In this article, a coupled model is proposed for wave interaction with a pair of submerged floating tunnels in the presence of an array of bottom-standing trapezoidal porous breakwaters. The theory of Sollitt and Cross is adopted to govern the fluid flow inside the porous medium. For constant water-depth, the eigenfunction expansion method is employed, whereas for varying water-depth, the eigenfunction expansion method along with the mild-slope approximation is employed. The solutions, thus derived, are matched at the shared boundaries under defined physical conditions. First, the performance of a single breakwater of impermeable and permeable type in reducing wave forces on tunnels is analyzed. Next, the performance of two and three submerged breakwaters is studied. The reflection and transmission coefficients of waves are high in the absence of the submerged breakwater and in the presence of an impermeable breakwater. These coefficients significantly reduce in the presence of the submerged porous breakwater. As a result, the horizontal and vertical forces acting on bridges and tunnels are substantially subsided. Wave forces on tunnels reduce with an increase in the angle of incidence. Multiple porous breakwaters show better performance in mitigating wave forces on tunnels. Higher wave force on tunnels is noticed in intermediate water-depth. The findings can enhance the knowledge of submerged porous breakwaters’ performance in reducing wave loads on bridges and tunnels.

Power take-off damping control performance on the power conversion of oscillating-buoy wave energy converter

The power take-off (PTO) damping mechanism is very important to the motion and power conversion for the wave energy converters. Based upon the potential flow theory, the series expression with unknown Fourier coefficients of velocity potential function of the basin where the cylindrical floating buoy is located is obtained by using the eigenfunction expansion method. According to the characteristics of the PTO damper, the motion and wave energy conversion characteristics of the float under the linear and non-linear PTO damping are studied, respectively, and the over-damping problem under the linear PTO damping is emphatically explored. The results show that the influence of PTO system with low velocity index on the motion of the device is mainly reflected in the PTO damping coefficient. With the increase of damping coefficient, the resonance frequency of the wave energy device decreases gradually, but the decrease amplitude is very small. The non-linear characteristics of PTO system cannot change the optimal capture width ratio of the float, but the large velocity index can effectively improve the damping capacity of PTO system. At lower and higher frequencies, the optimal PTO damping obtained by the analytic algorithm will make the device in an over-damped state. The highest frequency in the low frequency part and the lowest frequency in the high frequency part which need to be modified will gradually decrease with the increase of radius and draught.