Constant Wave Speed Research Articles

Investigation of delta-t mapping source location technique based on the arrival of A0 modes

The main assumptions made for traditional Time of Arrival (TOA) source location techniques are constant wave speed and straight wave path between the acoustic emission (AE) source and the sensors. However, because of material inhomogeneity and structural complexity, wave velocities may vary in different directions and a direct wave path may be very difficult to be achieved. Therefore, to solve these problems, researchers developed delta-T mapping source location technique, which has been shown to have good accuracy for source location in aerospace structure because complex geometric features are considered when training the mapping data and accurate wave speed data are not required. However, this technique relies on identifying the arrival time of S0 (extensional) Lamb mode, which may not be distinguished from background noise due to lowamplitude AE sources such as corrosion or large source-to-sensor distance. As shown in Figure 1, source location accuracy in a corrosion test on a simple plate was greatly improved after the velocity of A0 (flexural) Lamb mode was used in the source location algorithm. Therefore, identifying the arrival time of A0 modes and hence building delta-T maps are more feasible to solve the problem. Experiments have been carried out with an artificial AE source on a thin complex steel plate. A threshold crossing method based on wavelet coefficient was used to estimate the arrival time of A0 modes. The average error (3.9 mm) of the source locations predicted by delta-T mapping based on A0 arrival was larger than that (1.8 mm) of S0 arrival, which can be explained by the difficulties in accurately identifying the arrival of A0 modes.

Exploring the controlling mechanisms for gradient evolution in unsteady detonation flows

Proper characterization of the transient interaction between shock front motion and chemical energy release is the key for further understanding of unsteady detonation dynamics. We have shown that the gradients could be the adequate intermediate quantities to reflect the transient interaction between shock front motion and chemical energy release through the Lagrangian particle analysis of the simulated direct detonation initiation (DDI) process in H2–O2–Ar mixtures. Specifically, the “shock change equations” are verified to describe the direct relation between the shock front motion and the gradients immediately behind the shock. Moreover, given the time derivatives of shock speed, the gradient evolution in the induction zone can be reproduced by the gradient evolution equations that are deduced from the Euler equations, no matter if the shock front undergoes rapid deceleration or acceleration. While in the reaction zone where the heat release is significant, it is demonstrated that the evolutions of velocity, pressure, and their gradients can be described by the Zel'dovich–von Neumann–Döring model with a constant wave speed that is below the Chapman–Jouguet speed, no matter if the shock front undergoes rapid deceleration or acceleration. These two distinct controlling mechanisms are verified in both planar and spherical DDI processes, showing their general applicability. This work suggests a new perspective, in terms of gradient evolution, for further understanding the unsteady detonation dynamics.

Fast hyperbolic relaxation elliptic solver for numerical relativity: Conformally flat, binary puncture initial data

We introduce nrpyelliptic, an elliptic solver for numerical relativity (NR) built within the nrpy+ framework. As its first application, nrpyelliptic sets up conformally flat, binary black hole (BBH) puncture initial data (ID) on a single numerical domain, similar to the widely used twopunctures code. Unlike twopunctures, nrpyelliptic employs a hyperbolic relaxation scheme, whereby arbitrary elliptic partial differential equations (PDEs) are trivially transformed into a hyperbolic system of PDEs. As consumers of NR ID generally already possess expertise in solving hyperbolic PDEs, they will generally find nrpyelliptic easier to tweak and extend than other NR elliptic solvers. When evolved forward in (pseudo)time, the hyperbolic system exponentially reaches a steady state that solves the elliptic PDEs. Notably nrpyelliptic accelerates the relaxation waves, which makes it many orders of magnitude faster than the usual constant wave speed approach. While it is still $\ensuremath{\sim}12\mathrm{x}$ slower than twopunctures at setting up full-3D BBH ID, nrpyelliptic requires only $\ensuremath{\approx}0.3%$ of the runtime for a full BBH simulation in the einstein toolkit. Future work will focus on improving performance and generating other types of ID, such as binary neutron stars.

Amplitude-initiated open hysteresis loop of <i>P</i>-wave attenuation in sandstone: experimental study

In the area of solid state physics and materials science, new knowledge has been attained in recent years about micro-nano-plasticity using high-precision measurements at low stresses and strain. Rock microplasticity is currently poorly understood, but in the future it may prove useful in resolving problems of a fundamental and applied nature. This study examines the effect of cyclically varying pulse amplitude and wave velocity on the attenuation parameters of longitudinal wave (P-wave) in sandstone. Laboratory measurements were performed on rock specimens using the reflected wave method in the frequency range of 0.5–1.4 MHz at five values of strain amplitude ~ (0.5-2.0)10 –6 . Trial simulations were performed, in order to establish the effect of amplitude-dependent wave velocity on the parameters of wave attenuation in the sandstone. Wave attenuation behavior under combined action of the amplitude-dependent factor and wave velocity deviation is complex. The change in strain amplitude shifts the attenuation peak 1/ Q p ( f ) in the attenuation-frequency coordinates. The maximum change in peak attenuation value due to the amplitude factor and wave velocity deviation reaches 3–4 %. An open wave attenuation hysteresis loop was identified as a consequence of the closed amplitude cycle A1(+) --- A1(+) --- A1(–), where A1(+) = A1(–). Open attenuation hysteresis occurs both in the cases of constant and variable wave velocities. The length of the open part of the attenuation hysteresis loop relative to the peak value of the attenuation is as follows: for constant wave speed, 62.63 %, in the mode of increasing wave speed, 91.58 %; and, in the mode of decreasing wave speed, 47.01 %. The effect of open hysteresis of wave attenuation in sandstone can be explained by the action of microplastic deformation detected in the experiments.

Scaling Law for Boundary Layer Inner Eyewall Pumping in Concentric Eyewalls

AbstractThis study explains why observed storms with long concentric eyewall (CE) duration often have a large moat size. A series of slab boundary layer model experiments are conducted with the free atmosphere forcing from different CE structures. The experimental results indicate that the inner eyewall pumping (IEP), the maximum vertical motion at the inner eyewall region, increases with the increase in moat size d and vortex maximum wind vm, the decrease in the inner eyewall radius rm, and increase in inner eyewall vorticity. A scaling law is derived from hundreds of SBL experiments with four variables: IEP win, vortex inner radius rm, vortex maximum wind vm, and moat size d. The dimensionless scaling law is where w∗ = win/vm, d∗ = ζd/c, ζ is the vorticity 2vm/rm, and c is a constant gravity wave speed. The moat size divided by the Rossby length c/ζ, the dimensionless moat size d∗, combines the effect of the moat size and the vortex pressure gradient force to accelerate the inflow and to enlarge the IEP for inner eyewall convection maintenance. A phase diagram of IEP with vortex structure dimensionless moat ζd/c and vortex intensity vm is constructed based on the scaling law for the aircraft and satellite observations. The eyewall replacement cycle may be viewed as the process to reduce the IEP from the decrease of the vortex intensity and the vortex size of the dimensionless moat. This leads to the ultimate disappearance of the inner eyewall.

Stability for a Formally Determined Inverse Problem for a Hyperbolic PDE with Space and Time Dependent Coefficients

We prove stability for a formally determined inverse problem for a hyperbolic PDE where the coefficients depend on space and time variables. The hyperbolic operator has constant wave speed and we study the recovery of zeroth order and first order coefficients and the space dimension can be one or higher. We use a modification of the Bukhgeim-Klibanov method to obtain our results.

L-Sweeps: A scalable, parallel preconditioner for the high-frequency Helmholtz equation

We present the first fast solver for the high-frequency Helmholtz equation that scales optimally in parallel for a single right-hand side. The L-sweeps approach achieves this scalability by departing from the usual propagation pattern, in which information flows in a 180∘ degree cone from interfaces in a layered decomposition. Instead, with L-sweeps, information propagates in 90∘ cones induced by a Cartesian domain decomposition (CDD). We extend the notion of accurate transmission conditions to CDDs and introduce a new sweeping strategy to efficiently track the wave fronts as they propagate through the CDD. The new approach decouples the subdomains at each wave front, so that they can be processed in parallel, resulting in better parallel scalability than previously demonstrated in the literature. The method has an overall O((N/p)log⁡ω) empirical run-time for N=nd total degrees-of-freedom in a d-dimensional problem, frequency ω, and p=O(n) processors. We introduce the algorithm and provide a complexity analysis for our parallel implementation of the solver. We corroborate all claims in several two- and three-dimensional numerical examples involving constant, smooth, and discontinuous wave speeds.

Bifurcations of Solitary Waves of a Simple Equation

In this paper, we consider a simple equation which involves a parameter [Formula: see text], and its traveling wave system has a singular line. Firstly, using the qualitative theory of differential equations and the bifurcation method for dynamical systems, we show the existence and bifurcations of peak-solitary waves and valley-solitary waves. Specially, we discover the following novel properties: (i) In the traveling wave system, there exist infinitely many periodic orbits intersecting at a point, or two points and passing through the singular line, and there is no singular point inside a homoclinic orbit. (ii) When [Formula: see text], in the equation there exist three types of bifurcations of valley-solitary waves including periodic wave, blow-up wave and double solitary wave. (iii) When [Formula: see text], in the equation there exist two types of bifurcations of valley-solitary wave including periodic wave and blow-up wave, but there is no double solitary wave bifurcation. Secondly, we perform numerical simulations to visualize the above properties. Finally, when [Formula: see text] and the constant wave speed equals [Formula: see text], we give exact expressions to the above phenomena.

Inverse scattering for the one-dimensional Helmholtz equation with piecewise constant wave speed

This paper analyzes inverse scattering for the one-dimensional Helmholtz equation in the case where the wave speed is piecewise constant. Scattering data recorded for an arbitrarily small interval of frequencies is shown to determine the wave speed uniquely, and a direct reconstruction algorithm is presented. The algorithm is exact provided data is recorded for a sufficiently wide range of frequencies and the jump points of the wave speed are equally spaced with respect to travel time. Numerical examples show that the algorithm works also in the general case of arbitrary wave speed (either with jumps or continuously varying etc) giving progressively more accurate approximations as the range of recorded frequencies increases. A key underlying theoretical insight is to associate scattering data to compositions of automorphisms of the unit disk, which are in turn related to orthogonal polynomials on the unit circle. The algorithm exploits the three-term recurrence of orthogonal polynomials to reduce the required computation.

Effective grain orientation mapping of complex and locally anisotropic media for improved imaging in ultrasonic non-destructive testing

Imaging defects in austenitic welds presents a significant challenge for the ultrasonic non-destructive testing community. Due to the heating process during their manufacture, a dendritic structure develops, exhibiting large grains with locally anisotropic properties which cause the ultrasonic waves to scatter and refract. When basic imaging algorithms, which typically make constant wave speed assumptions, are applied to datasets arising from the inspection of these welds, the resulting defect reconstructions are often distorted and difficult to interpret correctly. However, knowledge of the underlying spatially varying material properties allows correction of the expected wave travel times and thus results in more reliable defect reconstructions. In this paper, an approximation to the underlying, locally anisotropic structure of the weld is constructed from ultrasonic time of flight data. A new forward model of wave front propagation in locally anisotropic media is presented and used within the reversible-jump Markov chain Monte Carlo method to invert for the map of effective grain orientations across different regions of the weld. This forward model and estimated map are then used as the basis for an advanced imaging algorithm and the resulting defect reconstructions exhibit a significant improvement across multiple flaw characterization metrics.

Ultrasonic Synthetic-Aperture Interface Imaging.

Synthetic-aperture (SA) imaging is a popular method to visualize the reflectivity of an object from ultrasonic reflections. The method yields an image of the (volume) contrast in acoustic impedance with respect to the embedding. Typically, constant mass density is assumed in the underlying derivation. Due to the band-limited nature of the recorded data, the image is blurred in space, which is quantified by the associated point spread function. SA volume imaging is valid under the Born approximation, where it is assumed that the contrast is weak. When objects are large with respect to the wavelength, it is questionable whether SA volume imaging should be the method-of-choice. Herein, we propose an alternative solution that we refer to as SA interface imaging. This approach yields a vector image of the discontinuities of acoustic impedance at the tissue interfaces. Constant wave speed is assumed in the underlying derivation. The image is blurred in space by a tensor, which we refer to as the interface spread function. SA interface imaging is valid under the Kirchhoff approximation, where it is assumed that the wavelength is small compared to the spatial dimensions of the interfaces. We compare the performance of volume and interface imaging on synthetic data and on experimental data of a gelatin cylinder with a radius of 75 wavelengths, submerged in water. As expected, the interface image peaks at the gelatin-water interface, while the volume image exposes a peak and trough on opposing sides of the interface.

Acoustic interface contrast imaging

In acoustic reflectivity imaging, we infer the internal reflectivity of an unknown object from reflected waveforms. A common assumption is that the mass density is constant and that the recorded pressure field is related to a volume contrast in the wave speed by a nonlinear volume-integral representation. This representation is typically linearized under the Born approximation and solved for the volume contrast by iterative inversion. We propose an alternative methodology, which we refer to as interface contrast imaging. In our derivation, we assume a medium with constant wave speed, which contains discontinuities of the acoustic impedance at a collection of interfaces between piecewise-homogeneous subdomains. A linear relationship is established between the recorded data and the gradient of the acoustic impedance at the interfaces, which we refer to as an interface contrast. This contrast can be solved for by iterative inversion. With this procedure, acoustic interfaces can be delineated with superior resolution compared to volume contrast imaging. Since the convergence speed is relatively fast and a reasonable image can already be obtained after a single iteration, real-time applications seem feasible. If necessary, the acoustic impedance can also be imaged by integrating the retrieved reflectivity contrast over space.

Distributed acoustic emission sensing for large complex air structures

The vast majority of existing work on acoustic emission–based structural health monitoring is for geometrically simple structures with uninterrupted propagation path and constant wave speed. Realistic systems such as a full-scale fuselage, however, are built from interconnected pieces of acoustically mismatched parts such as sandwich core panels, stringer stiffened skin, and fastener holes. The geometric complexity and dynamic operating environment of realistic systems mean that the acoustic emission wave undergoes multiple reflections, refractions, and mode changes resulting in overlapped transducer outputs with no clear beginning and end. The objective of this paper is to outline the fundamental limitations of acoustic emission as applied to complex systems and present a new distributed data-centric acoustic emission sensing network for durability health monitoring and damage tolerance applications in large and complex systems. The study considers the case of a full-scale composite rotorcraft fuselage to introduce several new concepts on acoustic emission data acquisition time control for alleviating effects of wave distortion as well as methods for improving event location analysis in large quasi-isotropic materials. Methods for adaptive front-end signal processing and data volume control are presented. Despite the size and complexity of realistic full-scale systems and the acoustic emission data, we show that it is possible to locate damage with acceptable accuracy.

Cavitation Influence in 1D Part-load Vortex Models

Residual swirl in the draft tube of Francis turbines may cause annoying low- frequency pulsation of pressure and power output, in particular during part-load operation. A 1D analytical model for these dynamic phenomena would enable simulation by some conventional method for computing hydraulic transients. The proper structure of such a model has implications for the prediction of prototype behaviour based on laboratory tests.The source of excitation as well as the dynamic transmission behaviour of the draft tube flow may both be described either by lumped or distributed parameters. The distributed version contains more information and, due to limited possibilities of identification, some data must be estimated. The distributed cavitation compliance is an example for this dilemma. In recent publications, the customary assumption of a constant wave speed has produced dubious results. The paper presents a more realistic model for distributed compressibility. The measured influence of the Thoma number is applied with the local cavitation factor. This concept is less sensitive to modelling errors and explains both the Thoma and Froude number influence.The possible effect of the normally unknown non-condensable gas content in the vortex cavity is shortly commented. Its measurement in future tests is recommended. It is also recommended to check the available analytical vortex models for possible dispersion effects.

Fluid simulation of dispersive and nondispersive ion acoustic waves in the presence of superthermal electrons

One-dimensional fluid simulation is performed for the unmagnetized plasma consisting of cold fluid ions and superthermal electrons. Such a plasma system supports the generation of ion acoustic (IA) waves. A standard Gaussian type perturbation is used in both electron and ion equilibrium densities to excite the IA waves. The evolutionary profiles of the IA waves are obtained by varying the superthermal index and the amplitude of the initial perturbation. This simulation demonstrates that the amplitude of the initial perturbation and the superthermal index play an important role in determining the time evolution and the characteristics of the generated IA waves. The initial density perturbation in the system creates charge separation that drives the finite electrostatic potential in the system. This electrostatic potential later evolves into the dispersive and nondispersive IA waves in the simulation system. The density perturbation with the amplitude smaller than 10% of the equilibrium plasma density evolves into the dispersive IA waves, whereas larger density perturbations evolve into both dispersive and nondispersive IA waves for lower and higher superthermal index. The dispersive IA waves are the IA oscillations that propagate with constant ion plasma frequency, whereas the nondispersive IA waves are the IA solitary pulses (termed as IA solitons in the stability region) that propagate with the constant wave speed. The characteristics of the stable nondispersive IA solitons are found to be consistent with the nonlinear fluid theory. To the best of our knowledge, this is the first fluid simulation study that has considered the superthermal distributions for the plasma species to model the electrostatic solitary waves.

Acoustic emission source location in complex structures using full automatic delta T mapping technique

An easy to use, fast to apply, cost-effective, and very accurate non-destructive testing (NDT) technique for damage localisation in complex structures is key for the uptake of structural health monitoring systems (SHM). Acoustic emission (AE) is a viable technique that can be used for SHM and one of the most attractive features is the ability to locate AE sources. The time of arrival (TOA) technique is traditionally used to locate AE sources, and relies on the assumption of constant wave speed within the material and uninterrupted propagation path between the source and the sensor. In complex structural geometries and complex materials such as composites, this assumption is no longer valid. Delta T mapping was developed in Cardiff in order to overcome these limitations; this technique uses artificial sources on an area of interest to create training maps. These are used to locate subsequent AE sources. However operator expertise is required to select the best data from the training maps and to choose the correct parameter to locate the sources, which can be a time consuming process.This paper presents a new and improved fully automatic delta T mapping technique where a clustering algorithm is used to automatically identify and select the highly correlated events at each grid point whilst the “Minimum Difference” approach is used to determine the source location. This removes the requirement for operator expertise, saving time and preventing human errors. A thorough assessment is conducted to evaluate the performance and the robustness of the new technique. In the initial test, the results showed excellent reduction in running time as well as improved accuracy of locating AE sources, as a result of the automatic selection of the training data. Furthermore, because the process is performed automatically, this is now a very simple and reliable technique due to the prevention of the potential source of error related to manual manipulation.

Scattering mean free path in continuous complex media: beyond the Helmholtz equation.

We present theoretical calculations of the ensemble-averaged (or effective or coherent) wave field propagating in a heterogeneous medium considered as one realization of a random process. In the literature, it is usually assumed that heterogeneity can be accounted for by a random scalar function of the space coordinates, termed the potential. Physically, this amounts to replacing the constant wave speed in Helmholtz' equation by a space-dependent speed. In the case of acoustic waves, we show that this approach leads to incorrect results for the scattering mean free path, no matter how weak the fluctuations. The detailed calculation of the coherent wave field must take into account both a scalar and an operator part in the random potential. When both terms have identical amplitudes, the correct value for the scattering mean free paths is shown to be more than 4 times smaller (13/3, precisely) in the low-frequency limit, whatever the shape of the correlation function. Based on the diagrammatic approach of multiple scattering, theoretical results are obtained for the self-energy and mean free path within Bourret's and on-shell approximations. They are confirmed by numerical experiments.

NONUNIQUENESS AND INSTABILITY OF CLASSICAL FORMULATIONS OF NONASSOCIATED PLASTICITY, I: CASE STUDY

A dynamic instability, which is relatively unexplored in the literature despite having been long ago previously asserted to exist for any conventional nonassociated plastic flow model, is illustrated by means of an example problem. This instability is related to a condition known as achronicity, in which the wave speed in plastic loading is greater than that in elastic unloading (making it absolutely not related to the well-studied phenomena of localization and flutter). The one-dimensional example problem initializes an elastic-plastic half-space to a initially quiescent uniform state of prestress that places it in an achronic condition if a nonassociated flow rule is used. The initial stress state is perturbed by an axial stress pulse applied at the surface. The problem is first solved analytically for the case of constant wave speeds, and it is shown to possess a two-parameter family of nonunique solutions. These solutions are unstable in that both the amplitude and the width of the propagating pulse increase linearly with time. The casestudy problem technically represents spontaneous motion from a quiescent state, but it does not violate thermodynamics (as the energy driving the instability is available from elastic stored energy of the initial prestress). The example problem is additionally solved numerically for both constant and nonconstant plastic wave speeds, where the instability is observed in either case. Furthermore, it is shown that neither the constant nor the nonconstant wave speed solution converges with mesh refinement, which therefore represents a numerical inadmissibility associated with the underlying loss of uniqueness of solution. It is the nonuniqueness of the unstable solution, not the existence of the instability itself, that is of primary concern. Unlike conventional localization instability, this achronic instability is not yet known to be a real phenomenon. This case-study problem illustrates the need for novel laboratory testing methods sufficient to determine if the instability is truly physical, or merely an anomalous shortcoming of classical nonassociated plasticity formulations. Some guidance for appropriate laboratory testing is presented, with emphasis on why such testing is highly nontrivial as a result of irreducible uncertainty in direct validation of a regular flow rule.

Stable Determination of Polyhedral Interfaces from Boundary Data for the Helmholtz Equation

We study an inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map. We consider piecewise constant wave speeds on an unknown tetrahedral partition and prove a Lipschitz stability estimate in terms of the Hausdorff distance between partitions.

Spinning detonation, cross-currents, and the Chapman–Jouguet velocity

AbstractInterestingly, the Chapman–Jouguet detonation velocity ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}D_{CJ}$) based on a one-dimensional and steady model compares well with the measured data. For the spinning detonation, in particular, this agreement is particularly notable, since the flow is highly three-dimensional and unsteady; perpendicular to the leading shock front, a transverse detonation wave (TDW) spins periodically. In the wake of this TDW, a secondary flow, called here the cross-current, appears which is orthogonal to the leading shock. Despite the presence of these cross-currents, the $D_{CJ}$ agreement remains remarkably satisfactory, and we investigate the reason for this, for spinning detonation in a tube. First, we focus on the origin of the cross-current. The cross-current, driven by the shock pressure, arises initially across a warped shock frontal surface, and both its sign and magnitude depend on the local slopes of the shock surface. The cross-current undergoes further pressure-driven transitions, with its magnitude eventually diminishing downstream and reducing the flow to a quasi-one-dimensional one. Second, regarding the unsteadiness, under the assumptions that the TDW spins at constant angular wave speed and the flow is steady in the frame rotating with it, the unsteady energy equation becomes integrable, resulting in the invariance of the so-called rothalpy. Also, in the integral forms of the mass and momentum balance, the unsteady terms drop out. Taken together, in the far field the governing equations are reduced to being one-dimensional and steady. From these the $D_{CJ}$ follows immediately, which appears to be the reason for the enduring usefulness of the $D_{CJ}$. The results of the analysis are confirmed with computational fluid dynamics (CFD). Additionally, the area-averaged flow profiles are found to display more than a passing resemblance to the Zeldovitch–Von Neumann–Doering (ZND) model.