Ultrasonic Beam Propagation Research Articles

New submodels describing attenuation of the ultrasonic beams in 3-d cubic nonlinear medium in the absence of dissipation

For a three-dimensional generalized model of nonlinear hydroacoustics by Khokhlov–Zabolotskaya–Kuznetsov in a cubic nonlinear medium in the absence of dissipation, we studied the attenuation of ultrasonic beams after the formation of shock fronts. Earlier, in the work of one of the authors for this model, submodels were obtained and studied, described by non-stationary solutions, invariant with respect to some three-dimensional subgroups of the main ten-parameter group of the differential equation that defines this model. In our paper we obtained and studied four non-stationary submodels of this model that are invariant with respect to four-parameter subgroups of the main group of this differential equation. These submodels are new submodels and have not been previously noted in the literature. They are given by invariant solutions of rank 1. Among these 4 submodels, 2 submodels describe axisymmetric ultrasonic beams, the remaining 2 describe one-dimensional ultrasonic beams. The search for invariant solutions that define these 4 submodels is reduced to solving of nonlinear integral equations, the implicit solutions of which are obtained in the form of nonlinear algebraic equations containing transcendental functions. These submodels are used to study the propagation of ultrasonic beams, for which either the acoustic pressure and its rate of change or the acoustic pressure and its gradient are given at the initial time at a fixed point. Conditions are obtained that ensure the existence and uniqueness of solutions to boundary value problems describing these processes. This makes it possible to correctly carry out numerical calculations in the study of these processes. As a result of the numerical solution of these boundary value problems for some values of the parameters characterizing these processes, pressure distribution graphs were obtained. In all cases, ultrasonic beams are weaken monotonically with time and completely fade away in a finite time. At each point, the time of complete attenuation of ultrasonic beams is found.The obtained and studied new submodels are another step towards the creation of a database of physically significant submodels of the three-dimensional generalized model of nonlinear hydroacoustics by Khokhlov–Zabolotskaya–Kuznetsov in a cubic nonlinear medium in the absence of dissipation, which describes the attenuation of ultrasonic beams after the formation of shock fronts.

Research on ultrasonic process fusing tomography for numerical and laboratory imaging in liquid-background two-phase flow

Real-time ultrasonic process tomography (UPT) could be suitable for the conditions including various sizes and locations as well as amount of the interesting targets and different pipelines. However, the difficulty in determining flow-pattern segmentation in the back-projection for both transmission mode and reflection mode was not overcome for real-time imaging. This work focused on an ultrasonic process fusing tomography (UPFT) for implementing both reflection-mode and transmission-mode tomography draw support from an 8-channel scanning technique. The behavior of fan-shaped ultrasonic beam propagation and the characteristics of acoustic field in two phases had been studied, by which the tomographic size resolution about UPFT had been analyzed numerically. The resultant impact on reconstructed image quality due to the operation conditions was discussed in detail. Transmitted waves were adopted as a base of imaging, and reflected waves were integrated as supplementary information to execute threshold optimization. To carry out a validation, a digital 8-channel prototype of UPFT was developed for the laboratory investigation of stratified flow with continuous injection of water. It was found that such ultrasonic tomography yielded significant improvements in reconstruction, compared to single-mode imaging merely using transmitted or reflected waves. At the same time, quantitative results showed that the proposed method facilitated automatic and reasonable flow-pattern identification, and the developed system represented a fast data acquisition and processing as well as strong noise resistance capability.

Research on ultrasonic phased array detection algorithm for TA15/Ti2AlNb multi-layer gradient material structure

Conventional ultrasonic detection methods can detect a TA15/Ti2AlNb gradient material multi-layer structure with many layers; the reflection and refraction phenomena of ultrasonic waves at the partition interface result in considerable attenuation of ultrasonic energy. It is difficult to achieve accurate focusing control of multi-array element synthetic beams, and internal defects cannot be detected. We explored the ‘ultrasonic velocity scale coefficient K’ algorithm to determine the ultrasonic beam propagation refraction path of a multi-layer gradient material structure. The algorithm makes full use of the refraction characteristics of ultrasonic waves on each material layer interface, establishes the acoustic ray-tracing model, analyzes the acoustic ray-tracing propagation path of each array element, and quickly obtains the focusing law. A TA15/Ti2AlNb gradient material specimen was prepared using laser melting deposition (LMD) technology, and a multi-layer structure model was established based on the finite difference time domain (FDTD) method to verify the focusing law. The experimental results of the ultrasonic phased array showed that the proposed algorithm effectively improved the defect detection signal-to-noise ratio (SNR) and imaging quality of the TA15/Ti2AlNb gradient material.

Description of the attenuation of invariant ultrasonic beams after formation of the shock fronts in a cubic nonlinear medium in the absence of dissipation

In the framework of a three-dimensional generalized Khokhlov–Zabolotskaya–Kuznetsov model of nonlinear hydroacoustics in a cubic nonlinear medium in the absence of dissipation, the attenuation of ultrasonic beams after the formation of shock fronts is investigated. For the main group of the equation of the investigated model, an optimal system of three-parameter subgroups that do not contain the time transport transformation is constructed. This system contains 68 subgroups. As a result, it is possible to construct 68 nonstationary submodels that are invariant with respect to these subgroups. We have built and studied five submodels. For three submodels, equations are obtained that implicitly determine the acoustic pressure in ultrasonic beams. Namely, for two of them, the pressure is implicitly determined from transcendental equations, and for one submodel, the pressure is implicitly determined from an algebraic equation. Among these five sub-models, two sub-models describe axisymmetric ultrasonic beams, two others describe planar ultrasonic beams, and one describes a one-dimensional ultrasonic beam. Using these submodels, the propagation of ultrasonic beams is investigated, for which either the acoustic pressure and the rate of its change, or the acoustic pressure and its gradient are set at the initial moment of time at a fixed point. The existence and uniqueness of solutions to boundary value problems describing these processes is established. For some values of the parameters characterizing these processes, using a numerical solution, graphs of the distribution of the dynamic component of the acoustic pressure are obtained. From these graphs it follows that the ultrasonic beams monotonically weaken with a time and completely disappear in a finite time.

A Fast Finite Element Simulation Method of Phased Array Ultrasonic Testing and Its Application in Sleeve Fillet Weld Inspection

Numerical simulation can provide quantitative information on ultrasonic beam propagation and plays an important role in analyzing its detection ability and in optimizing the corresponding parameters of the phased array ultrasonic testing (PAUT). In this paper, a fast finite element simulation method of PAUT is developed using an improved explicit integration algorithm and a non-zero element compressed storage method. The new method is applied for the simulation of PAUT of a type-B sleeve weld, and compared with the commercial finite element software and experiment results. We found that the computation time and memory consumption of the new method is only about a 15th and a 40th of the commercial finite element software, respectively.

Simulation and experiment of ultrasonic phased array for additive manufacturing titanium alloy with columnar crystal structure

The influence of the grain structure of titanium alloys, used for additive manufacturing (AM), on the propagation of ultrasonic beams is of great significance for the non-destructive testing of components manufactured from this material. In order to explore the issues related to ultrasonic testing, such as low signal-to-noise ratio (SNR) and large imaging error of internal defects, an ultrasonic phased array C-scan image was obtained and the measurements of ultrasonic noise level and defect distortion caused by columnar crystals were analysed. Ultrasonic wave theory was combined with the Voronoi algorithm to establish a finite element (FE) model of the AM titanium alloy with a columnar crystal structure. The focusing and scattering of ultrasonic beams in different grain structures was studied and the defect echo signals from the FE model and the experimental results were extracted and compared. Comparisons of the signal-to-noise ratio and the background noise of three typical sections were in good agreement, which shows that the proposed simulation model can be used to analyse the propagation and scattering of beams for the inspection of AM titanium alloys. Finally, suggestions to improve the ultrasonic detection results of AM titanium alloy components and the applicability of the wave simulation model for other polycrystalline materials are discussed.

An Accelerated Post-processing Calculation Method of Curved Surface Profile Extraction Based on the Total Focusing Method of Ultrasonic Phased Array

Surface profile extraction is a significant process for determining the ultrasonic beam propagation path based on the Fermat’s principle while applying the total focusing method (TFM) of ultrasonic phased array on a curved component immersed in water. However, TFM calculation is time consuming due to the large amounts of data post-processing. Hence, a trade-off between computation cost and precision of result image is must to be made. In this paper, an accelerated total focusing method (ATFM) was proposed to extract the surface profile of an arc-shaped component. The experimental results show that compared with TFM, ATFM could shorten the imaging time by more than 70% under various conditions of grid spacing. Meanwhile, the maximal error of extracted surface profile compared to the practical profile curve is about 0.7mm and the surface extraction errors near the central area are less than 0.1mm. It shows that the proposed ATFM can significantly improve the computation efficiency while ensuring the accuracy of surface extraction.

Invariant submodels describing a propagation of the ultrasonic beams in a cubically nonlinear medium without dissipation after self-focusing

Recently, for high-power ultrasonic beams, it was experimentally found that as a result of self-action, their self-focusing occurs. With self-focusing, a powerful ultrasonic beam is noticeably narrowed, has a nonlinear narrowing, and it is significantly amplified at the focus. A generalization of the three-dimensional Khokhlov–Zabolotskaya–Kuznetsov model in a cubic nonlinear medium in the presence of dissipation with a special nonlinearity coefficient describes the propagation of ultrasonic beams after self-focusing. This work is devoted to the study of submodels of this model without dissipation, which are invariant with respect to four-parameter subgroups of the main group of the equation of this model. These submodels are defined by invariant solutions of rank 0 or 1, which describe one-dimensional, plane and axisymmetric ultrasonic beams. Solutions of rank 0 and some solutions of rank 1 are found explicitly. Some of them, at each fixed moment of time, contain a destroying element in the form of an ultrasonic needle or an ultrasonic knife, which at each fixed moment of time are localized in a limited domain, on the surface of which the acoustic pressure is zero. These submodels describe one-dimensional, plane, or axisymmetric ultrasonic beams. Finding other invariant solutions of rank 1 is reduced to solving nonlinear integral equations. These invariant solutions are used to study the propagation of ultrasonic beams after self-focusing, for which either the acoustic pressure and its gradient, or the acoustic pressure and the rate of its change are given at the initial moment of time at a fixed point. Under certain additional conditions, the existence and uniqueness of the solutions to boundary value problems describing these processes are established. This makes it possible to correctly carry out numerical calculations when studying these processes. The graphs of the pressure distribution obtained as a result of the numerical solution of these boundary value problems for some values of the parameters characterizing the indicated processes are presented. These graphs show that for these submodels in the ultrasonic beams a monotonic increase in acoustic pressure occurs over time.

Simulation of Ultrasonic Beam Propagation From Phased Arrays in Anisotropic Media Using Linearly Phased Multi-Gaussian Beams.

Phased array ultrasonic testing is widely used to test structures for flaws due to its ability to produce steered and focused beams. The inherent anisotropic nature of some materials, however, leads to skewing and distortion of the phased array beam and consequently measurement errors. To overcome this, a quantitative model of phased array beam propagation in such materials is required, so as to accurately model the skew and the distortion. The existing phased array beam models which are based on exact methods or numerical methods are computationally expensive or time consuming. This article proposes a modeling approach based on developing the linear phased multi-Gaussian beam (MGB) approach to model beam steering in anisotropic media. MGBs have the advantages of being computationally inexpensive and remaining non-singular. This article provides a comparison of the beam propagation modeled by the developed ordinary Gaussian beam and linear phased Gaussian beam models through transversely isotropic austenitic steel for different steering angles. It is shown that the linear phased Gaussian beam model outperforms the ordinary one, especially at steering angles higher than 20° in anisotropic solids. The proposed model allows us to model the beam propagation from phased arrays in both isotropic and anisotropic media in a way that is computationally inexpensive. As a further step, the developed model has been validated against a finite element model (FEM) computed using COMSOL Multiphysics.

Prediction of grain orientation in dissimilar metal weld using ultrasonic response of numerical simulation from deliberated scatterers

Ultrasonic nondestructive testing plays an important role in structural integrity monitoring of dissimilar metal weld (DMW) structures in pressure vessels and piping of nuclear power plants. Inspection of DMW components is too complicated due to its anisotropic behavior to ultrasonic beam propagation. Many researchers are working rigorously to model the grain orientation and ultrasonic beam skewing in DMW structures but still not completely resolved yet. This paper is intended to estimate the grain orientation with the help of numerical simulation for a given asymmetric DMW component with specified scatterers. The DMW is fabricated from austenite stainless steel and carbon steel base metals with austenite stainless steel filler metal using Gas Tungsten-Arc Welding. To study this research a finite element method (FEM) based numerical simulation has been used to exactly evaluate the grain structure. This model mainly depends on the elasticity matrix which is a function of the grain orientation and attenuation of ultrasonic energy of the weld. Iterative measurement of grain orientation using macrograph of the etched weldment with 5 × 5mm mesh size was carried out then the attenuated elasticity matrix was fed into the FEM COMSOL software model as input parameter. Result obtained from numerical simulation (time of flight and amplitude) are validated with the experimental result and good agreement (above 0.8 correlation coefficient) have been observed at higher iterations. This macro-graphic information based numerical model shows the potential to predict the grain orientation of DMW.

Application of Immersion Ultrasonic Testing For Non-Contact Quality Evaluation of Magnetically Impelled Arc Butt Welded Drive Shafts of Motor Vehicles

The article presents contemporary ultrasonic methods that can be applied to evaluate the quality of transmission drive components of motor vehicles. The issues of non-destructive analysis of discontinuities in manufactured drive shafts, consisting currently of thin-walled tubes, were investigated in this study. The driveshaft elements were joined by using innovative method called Magnetically Impelled Arc Butt Welding (MIAB). For many years, a major challenge for engineers working with ultrasonic techniques was joining of thin-walled components (having thickness below 3 mm). In addition of this limitation, the problem of variable geometry of the weld flash on the weld perimeter was highlighted. To reduce the impact of mentioned factors the pseudo-surface waves (also known as lateral waves) have been applied in this study. In order to select optimal parameters of the ultrasonic beam propagation and to understand the physical-acoustic phenomena, the Finite Elements Method modelling was performed. The phenomena of wave transformation on medium boundary and reflections from artificial flaw have been analyzed by numerical modelling. The results of numerical analysis were confirmed by UT experimental research. The manufactured MIAB welded joints were tested with using in-house made experiment set-up. The selected configurations with various shapes and dimensions of samples, and various process parameters have been investigated. The results confirm the usefulness of pseudo-surface ultrasonic waves in UT quality evaluation of MIAB welded elements of drive shafts of motor vehicles.

Simulation of hemispherical transducers for transcranial HIFU treatments using the hybrid angular spectrum approach

Transcranial focused ultrasound is emerging as a promising treatment modality for a variety of disorders including essential tremor and glioblastoma. However, traditional full-wave methods of simulating ultrasound pressure fields for these treatments, such as FDTD, are computationally intensive. The situation is exacerbated by the large area insonified by the transcranial transducers, which are typically hemispherical to spread the intensity over a large area of the skull and prevent burns. The Hybrid Angular Spectrum (HAS) approach [1] has been used to rapidly model ultrasonic beam propagation. Here we present a method for adapting the HAS technique to hemispherical transducers.

Ultrasonic beam propagation in highly anisotropic materials simulated by multi-Gaussian beams

The necessity of nondestructively inspecting fiber-reinforced composites, austenitic steels, and other inherently anisotropic materials has stimulated considerable interest in developing beam models for anisotropic media. The properties of slowness surface play a key role in the beam models based on the paraxial approximation. In this paper, we apply a modular muiti-Gaussian beam (MMGB) model to study the effects of material anisotropy on ultrasonic beam profile. It is shown that the anisotropic effects of beam skew and excess beam divergence enter into the MMGB model through parameters defining the slope and curvature of the slowness surface. The overall beam profile is found when the quasilongitudinal (qL) beam propagates in the symmetry plane of a transversely isotropic gr/ep composite. Simulation results are presented to illustrate the effects of these parameters on ultrasonic beam diffraction and beam skew. The MMGB calculations are also checked by comparing the anisotropy factor and beam skew angle with other analytical solutions.

Experimental validation for the diffraction effect in the ultrasonic field of piston transducers and its influence on absorption and dispersion measurements.

The aim of this work was to study the diffraction effects in the ultrasonic field of piston source transducers and their importance for accurate measurements of attenuation and dispersion in viscoelastic materials. In laboratory measurements, the diffraction phenomena are mainly due to the beam spread of the ultrasonic wave propagating in viscoelastic materials. This effect is essentially related to the estimated attenuation and dispersion in the material. In this work, a frequency domain system identification approach, using the maximum likelihood estimator (MLE), was applied to the measured data in order to determine a function for correcting the diffraction losses in both normal and oblique incidences for a large frequency band (300 kHz to 3 MHz). The effective radius of the used transmitter was determined by the inverse problem when ultrasonic beam propagation was investigated in a water medium. Using the estimated radius, the propagation through viscoelastic materials was established, and the acoustic parameters of these materials were estimated. Attention was paid to the determination of the attenuation and dispersion in the materials. These quantities were compared to those obtained without diffraction correction in order to see the influence of introducing the diffraction correction into the propagation model.

Propagation of ultrasonic beams in paratellurite crystal

Analytical expressions have been obtained of the main curvatures of the concavity of the wave vector surface, corresponding to the quasi-transverse wave, versus anisotropy parameter C= C 11− C 12−2 C 66 of the paratellurite crystal. Changes in the form of the sound beam on scanning in the direction of its propagation in the (001) and (11̄0) planes have been investigated. It has been found that near the acoustic axis lying in (001) considerable transformation of the beam takes place; initially extended, it becomes squeezed along the [001] axis. The conditions for focusing and channelling of ultrasound radiation have been determined. The propagation directions at which anisotropy of the paratellurite crystal does not influence the beam divergence have been found. It is shown that, for a wide range of deviation angles θ of the wave normal from the [001] axis in the symmetry plane (11̄0) ( θ≤50°), the presence of anisotropy leads to weaker diffraction broadening. The character of variation in the direction and divergence of the sound beam on scanning in the vicinity of the [110] direction has been studied experimentally.

Integral approximation method for calculating ultrasonic beam propagation in anisotropic materials

Plane-wave solutions to the acoustic wave equations in a generally anisotropic solid are reviewed, along with their connection to geometric ray theory. A Fourier-transform formulation of the field of a focused beam (coherent point source) passed from a liquid couplant to an anisotropic specimen through a plane surface is derived. The integral is approximated asymptotically using the stationary-phase method. The result for isotropic media is derived analytically to facilitate a direct comparison to the ray theory. The application of this method to the anisotropic case is illustrated, using the real-world example of the austenitic stainless-steel weld.

Doppler Velocimetry in Cavitating Media

A numerical model has been developed to simulate propagation of ultrasonic beams in inhomogeneous moving media. The model is based on the ray theory of propagating waves, valid in the limit of high frequencies. The resulting equations depend only on local values of the velocity field and the speed of sound. In its implementation, the model assumes that the interactions of sound with the surrounding flow field are decoupled. This allows for applying the model in a post processing mode to flows computed by other means. The model was used to investigate beam behavior in unsteady cavitating flows. The study was motivated by reports of cavitation occurring in mitral bi-leaflet mechanical heart valves. The flow field and cavitation physics were simulated using a general purpose computer code, CFD-ACE. The ultrasonic beam model was then used to calculate the beam path, orientation, and frequency changes in the transient cavitating region. Results show that the presence of cavitation can fundamentally alter the beam propagation characteristics. Simple models that assume rectilinear propagation cannot, by definition, handle such flows. Cavitation incurs very large variations in the local sound speed, which in turn can induce very large distortions in the beam. This fact has strong ramifications regarding the accuracy of ultrasonic velocimetry when simple models are used to interpret Doppler data gathered under such flow conditions.

Increased off-axis energy deposition due to diffraction and nonlinear propagation of ultrasound from rectangular sources

An existing model, the Bergen code, is used to simulate the propagation of ultrasonic beams of finite amplitude, due to rectangular and square sources. It is found that the edges of the source give rise to peaks in the diffraction pattern at the fundamental frequency, which can cause the strongest shockwaves to form off-axis. These tend to be sharply bounded, causing rapid variation in heat deposition and streaming pressure across even an unfocused beam, and suppressing axial maxima in the pressure field.

Ultrasonic beam propagation through a bimetallic weld — a comparison of predictions of the Gauss-Hermite beam model and finite element method : Minachi, A.; Mould, J.; Thompson, R.B. Journal of Nondestructive Evaluation, Vol. 12, No. 2, pp. 151–158 (Jun. 1993)

Ultrasonic beam propagation through a bimetallic weld — a comparison of predictions of the Gauss-Hermite beam model and finite element method : Minachi, A.; Mould, J.; Thompson, R.B. Journal of Nondestructive Evaluation, Vol. 12, No. 2, pp. 151–158 (Jun. 1993)

Ultrasonic beam propagation through a bimetallic weld?A comparison of predictions of the Gauss-Hermite beam model and finite element method

Ultrasonic beam propagation through a bimetallic weld?A comparison of predictions of the Gauss-Hermite beam model and finite element method