Dominique Placko

Modeling of phased array transducers

Phased array transducers are multi-element transducers, where different elements are activated with different time delays. The advantage of these transducers is that no mechanical movement of the transducer is needed to scan an object. Focusing and beam steering is obtained simply by adjusting the time delay. In this paper the DPSM (distributed point source method) is used to model the ultrasonic field generated by a phased array transducer and to study the interaction effect when two phased array transducers are placed in a homogeneous fluid. Earlier investigations modeled the acoustic field for conventional transducers where all transducer points are excited simultaneously. In this research, combining the concepts of delayed firing and the DPSM, the phased array transducers are modeled semi-analytically. In addition to the single transducer modeling the ultrasonic fields from two phased array transducers placed face to face in a fluid medium is also modeled to study the interaction effect. The importance of considering the interaction effect in multiple transducer modeling is discussed, pointing out that neighboring transducers not only act as ultrasonic wave generators but also as scatterers.

Ultrasonic field modeling: a comparison of analytical, semi-analytical, and numerical techniques

Modeling ultrasonic fields in front of a transducer in the presence and absence of a scatterer is a fundamental problem that has been attempted by different techniques: analytical, semi-analytical, and numerical. However, a comprehensive comparison study among these techniques is currently missing in the literature. The objective of this paper is to make this comparison for different ultrasonic field modeling problems with various degrees of difficulty. Four fundamental problems are considered: a flat circular transducer, a flat square transducer, a circular concave transducer, and a point focused transducer (concave lens) in the presence of a cavity. The ultrasonic field in front of a finite-sized transducer can be obtained by Huygens-Fresnel superposition principle that integrates the contributions of several point sources distributed on the transducer face. This integral which is also known as the Rayleigh integral or Rayleigh-Sommerfeld integral (RSI) can be evaluated analytically for obtaining the pressure field variation along the central axis of the transducer for simple geometries, such as a flat circular transducer. The semi-analytical solution is a newly developed mesh-free technique called the distributed point source method (DPSM). The numerical solution is obtained from finite element analysis. Note that the first three problems study the effect of the transducer size and shape, whereas the fourth problem computes the field in presence of a scatterer.

Ultrasonic Field Modeling in Multilayered Fluid Structures Using the Distributed Point Source Method Technique

In the field of nondestructive evaluation (NDE), the newly developed distributed point source method (DPSM) is gradually gaining popularity. DPSM is a semi-analytical technique used to calculate the ultrasonic field (pressure and velocity fields) generated by ultrasonic transducers. This technique is extended in this paper to model the ultrasonic field generated in multilayered nonhomogeneous fluid systems when the ultrasonic transducers are placed on both sides of the layered fluid structure. Two different cases have been analyzed. In the first case, three layers of nonhomogeneous fluids constitute the problem geometry; the higher density fluid is sandwiched between two identical fluid half-spaces. In the second case, four layers of nonhomogeneous fluids have been considered with the fluid density monotonically increasing from the bottom to the top layer. In both cases, analyses have been carried out for two different frequencies of excitation with various orientations of the transducers. As expected, the results show that the ultrasonic field is very sensitive to the fluid properties, the orientation of the fluid layers, and the frequency of excitation. The interaction effect between the transducers is also visible in the computed results. In the pictorial view of the resulting ultrasonic field, the interface between two fluid layers can easily be seen. DOI: 10.1115/1.2164516 Ultrasonic nondestructive evaluation NDE generally has two objectives: to detect defects in structures and to determine the material properties of the structure, without damaging it. Ultrasonic transducers are commonly used to generate ultrasonic waves used in NDE experiments. Transducers are used both as transmitters and receivers. Multilayered fluid systems excited by multiple transducers are modeled in this paper. Multilayered fluid structure is not that uncommon in nature. For example, in the early stage of pregnancy, in the human female body the embryo grows in layered fluid surroundings. The plasma of any cell, suspended in a fluid inside or outside of an animal body, is also an example of a layered fluid system. Human eye lenses also behave almost like layered fluid structures. Elastic properties of biological materials are needed for understanding their interaction with implant materials. Layers of crude oil in sea water, as seen after an oil spill in the ocean, are another example of layered fluid structure. Ultrasonic nondestructive testing can be used to find the acoustical properties and thickness of different fluid layers in a multilayered fluid structure. With these applications in mind, an efficient semi-analytical tool has been developed in this paper to model the ultrasonic field in multilayered fluid structures. The method is based on the DPSM distributed point source method technique originally developed to model ultrasonic or eddy current fields, i.e., pressure and velocity fields or magnetic fields generated by ultrasonic or eddy current transducers. DPSM technique for ultrasonic field modeling was first developed by Placko and Kundu 1. They used this technique to model ultrasonic fields

Physical modeling of an eddy current sensor designed for real time distance and thickness measurement in galvanization industry

An analytical model of an eddy current sensor designed for noncontact thickness and distance measurement is presented. A dipolar model allows the external physical parameters (conductivity and permeability of alloys) to be taken into account. Analysis of an iron sheet coated with a conductive material gives an accurate interpretation of the detected signals, useful for optimization of the sensor design. Experimental and theoretical data are compared for a galvanization line, demonstrating the potential of this system for nondestructive continuous evaluation. >

Ultrasonic field computation in the presence of a scatterer of finite dimension

A recently developed semi-analytical technique called DPSM (Distributed Point Source Method) is improved and used to model the ultrasonic field in a fluid generated by an ultrasonic transducer and scattered by a solid plate of finite dimension. Earlier works on the ultrasonic field modeling by the DPSM technique have been limited to homogeneous fluids or nonhomogeneous media with infinite interfaces. This is the first attempt to model the complete ultrasonic field consisting of incident, reflected, transmitted and diffracted fields by a finite scatterer of any shape or size. No closed form analytical solution exists for ultrasonic field computation in presence of a scatterer and an ultrasonic transducer, both of which can have finite dimensions and any shape. Finite element solution for wave propagation analysis is very time consuming; hence, the semi analytical technique used here appears to be the method of choice for solving such practical problems. The paper shows how the scattered field varies as the acoustic properties and dimensions of the scatterer change.

Theoretical computation of acoustic pressure generated by ultrasonic sensors in the presence of an interface

DPSM (Distributed Point Source Method) is a computational technique that can be used to model the pressure field generated by ultrasonic acoustic transducers. This technique involves discretization of the transducer face of any geometrical shape, into a number of elemental surface areas. Point sources are placed at the centroids of the elemental surface areas. The strengths of the point sources are proportional to the surface areas. Pressure field at a given point is the cumulative effect of the pressure fields generated by all point sources. The accuracy of the computational technique depends on the sensor surface discretization. In this paper, circular transducers are modeled using the DPSM technique. This technique is applied to calculate the pressure field distribution in non- homogeneous fluids with interface. The non-homogeneous fluid is composed of two fluid half-spaced with the interface in front of the transducer face parallel or inclined to the transducer face. Pressure fields in both fluids for normal and angular incidence of the ultrasonic beam have been calculated using DPSM technique.

Ultrasonic field modeling by distributed point source method for different transducer boundary conditions

Several investigators have modeled ultrasonic fields in front of transducers by Huygens-Fresnel superposition principle that integrates the contributions of a number of point sources distributed on the transducer face. This integral solution, also known as the Rayleigh integral or Rayleigh-Sommerfeld Integral solution, assumes the strengths of the point sources distributed over the transducer face. A newly developed technique called distributed point source method (DPSM) offers an alternative approach for modeling ultrasonic fields. DPSM is capable of modeling the field for prescribed source strength distribution as well as for prescribed interface conditions with unknown source strengths. It is investigated how the ultrasonic field in front of the transducer varies in different situations: (1) when the point source strengths are known, (2) when the point source strengths are unknown but obtained from the interface condition that only the normal component of the transducer velocity is continuous across the fluid-solid interface, (3) when all three components of velocity are assumed to be continuous across the interface for the no-slip condition, and (4) when the pressure instead of the velocity is prescribed on the transducer face. Results for these different interface conditions are compared with the analytical solutions along the central axis.

Localization of defects in steam generator tubes using a multi-coil eddy current probe dedicated to high speed inspection

Steam generator (SG) tubing of pressurized water reactor in nuclear plants must be rapidly and accurately checked in order to detect defects in their early stages. In this paper, the authors present a multi-coil eddy current (EC) probe allowing both high speed inspection and circumferential localization of defects in the tube wall. A method of multi-coil EC signal processing, based on a continuous wavelet transform combined with a maximum likelihood diagnosis, is elaborated in order to enhance the detection performances and to provide automatic localization of defects. The inspection of SG tube samples shows good localization performances for defects as small as 10% deep, 15 mm long and 100 μm wide outer diameter notches, of both circumferential and axial orientations.

Wall thickness evaluation of single-crystal hollow blades by eddy current sensor

Advanced high-pressure turbine blades of jet engines are hollow and monocrystalline. The external wall thickness of these blades has to be checked systematically and quickly after manufacturing in order to guarantee the blade strength. Thickness evaluation is made difficult by the presence of internal partitions and by the crystalline anisotropy of the superalloy used in blade manufacturing. In this paper, the authors present the advantages of the eddy current (EC) technique in comparison to other non-destructive evaluation (NDE) techniques for wall thickness evaluation. A dedicated EC sensor was developed and implemented. The thickness evaluation was carried out with a neural network inverse model, and the results show the high accuracy and reliability of the proposed method.

An original approach to eddy current problems through a complex electrical image concept

In this paper, we propose an original method for the physical analysis of electromagnetic interactions between an inductive sensor and any homogeneous conducting plane target. In the first part of this paper, the basic principles of inductive sensors are recalled. Then, we solve Maxwells equations in order to obtain an analytical model for the relationship between the target properties and the electrical signals for a U-shaped sensor. Next, we emphasize the fact that our analytical relations can be interpreted as an extension of the electrical image method, even in the most difficult case of conducting and magnetic targets. In the last part, we present some measurements illustrating this new electrical image concept.