Time-domain Numerical Model Research Articles

Ultrasound propagation in trabecular bone: a numerical study of the influence of micro-cracks

The accumulation of microdamage in trabecular bone tissue is suspected of being a predictive indicator of osteoporosis diagnosis. To quantify this microdamage, the Dynamic AcoustoElastic Testing (DAET) method measures the time of flight (TOF) and amplitude variations of transmitted ultrasound (US) pulses, while the bone sample is submitted to a low frequency pressure (opening/closing of microcracks). However, DAET is both sensitive to viscoelastic properties changes and microcracks density. To estimate the microcraks density contribution, a numerical approach is proposed, allowing simulations of different levels of microdamaged media. A 2D pseudo-spectral time domain numerical model was then developed to simulate linear wave propagation in heterogeneous solids including thermo-viscous attenuation. The influence of the microcracks number, size and orientation on the US TOF and amplitude was particularly investigated. Results are discussed and compared with experimental data extracted from DAET measurements in trabecular bone samples.

Spindle speed variation in turning: technological effectiveness and applicability to real industrial cases

Spindle speed variation is a well-known technique to suppress regenerative machine tool vibrations especially for low spindle speeds. Although a lot of research effort was made over the years the technique is not widespread in real turning applications. In this paper, the reasons that can limit the diffusion of the spindle speed variation were investigated. Therefore, the analysis of spindle speed variation strategy was not only focused on its chatter suppression properties but also on some more general technological aspects: the surface quality of the machined components, the cutting edge-spindle bearings load and the thermal overload the electrical spindle motor is subjected to when the speed modulation is used. A time-domain numerical model of the turning process was developed and exploited to support the analysis. A lot of cutting tests were also performed both to validate the numerical model and to evaluate the effect of variable spindle speed on surface quality. Finally, some real industrial applications were analyzed focusing on thermal overload issue of the spindle motor.

NUMERICAL INVESTIGATION OF THE ACOUSTIC DAMPING OF PLANE ACOUSTIC WAVES BY PERFORATED LINERS WITH BIAS FLOW

Perforated liners are extensively used in aero-engines and gas turbine combustors to suppress combustion instabilities. These liners, typically subjected to a low Mach number bias flow (a cooling flow through perforated holes), are fitted along the bounding walls of a combustor to convert acoustic energy into flow energy by generating vorticity at the rims of the perforated apertures. To investigate the acoustic damping of such liners with bias flow on plane acoustic waves, a time-domain numerical model is developed to compute acoustic wave propagation in a cylindrical duct with a single-layer liner attached. The damping mechanism of the liner is characterized in real-time by using a 'compliance', developed especially for this work. It is a rational function representation of the frequency-domain homogeneous compliance adapted from the Rayleigh conductivity of a single aperture with mean bias flow in the z-domain. The liner 'compliance' model is then incorporated into partial differential equations of the duct system, which are solved by using the method of lines. The numerical results are then evaluated by comparing with the numerical results of Eldredge and Dowling's frequency-domain model. Good agreement is observed. This confirms that the model and the approach developed are suitable for real-time characterizing the acoustic damping of perforated liners.

Structural analysis of the Roman Bibei bridge (Spain) based on GPR data and numerical modelling

There are many ancient masonry arch bridges still in use within the actual transportation. Some of these bridges are in need of special attention because they are subject to potentially destructive conditions, such as increased traffic loads and intense vibrations produced by their new functions, and these stresses are compounded by their age. To preserve these functional structures, structural assessment is necessary or, at least, highly recommended. However, many of the details of these structures are underground and are therefore hidden from view. In recent decades, ground-penetrating radar (GPR) has shown potential for internal bridge evaluation. The Roman Bibei bridge (Spain) was surveyed with GPR to analyse its inner state of conservation. The GPR survey was conducted using 250 and 500 MHz antennas. The interpretation and analysis of the GPR data were supported by finite-difference time domain numerical modelling based on the precise external geometry provided by three-dimensional laser scanning methods. Both real and synthetic results reveal that GPR evaluation provides unknown structural details and possible modifications over time. The internal ring stone thickness was also measured, which represents valuable information for engineers to perform an exhaustive assessment of the load carrying capacity of the bridge.

A 3-D time-domain coupled model for nonlinear waves acting on a box-shaped ship fixed in a harbor

A 3-D time-domain numerical coupled model is developed to obtain an efficient method for nonlinear waves acting on a box-shaped ship fixed in a harbor. The domain is divided into the inner domain and the outer domain. The inner domain is the area beneath the ship and the flow is described by the simplified Euler equations. The remaining area is the outer domain and the flow is defined by the higher-order Boussinesq equations in order to consider the nonlinearity of the wave motions. Along the interface boundaries between the inner domain and the outer domain, the volume flux is assumed to be continuous and the wave pressures are equal. Relevant physical experiment is conducted to validate the present model and it is shown that the numerical results agree with the experimental data. Compared the coupled model with the flow in the inner domain governed by the Laplace equation, the present coupled model is more efficient and its solution procedure is simpler, which is particularly useful for the study on the effect of the nonlinear waves acting on a fixed box-shaped ship in a large harbor.

A FDTD Modeling Approach to Investigate Critical Refraction from Crosswell Radar

First arrival travel times (FATTs) from critically refracted waves in crosswell radar applications have been known to cause incorrect estimates of electromagnetic wave velocities, if these waves are assumed to be a direct arrival. This is a particular problem when the FATTs are acquired from radar antennae placed near the ground surface. One way to accommodate critically refracted waves at the air-ground interface is to remove the upper [Formula: see text] of data and assume that the remaining FATTs within the profile travel directly from transmitter to receiver. An alternative method is to use simple ray-based inverse models that accommodate critically refracted waves to back calculate the near-surface electromagnetic wave velocity. In this work, we show the validity of these ray-based models in regions where critical refractions will occur, by first generating FATTs with a finite-difference time domain (FDTD) numerical model and assuming zero-offset profiling mode of acquisition. The ray-based inverse models were shown to reproduce the original electromagnetic wave velocity of the numerical model. A second test was also run using FDTD modeling, where an infiltrating wetting front moves past a set stationary antennae and the time series of FATTs were recorded for the duration of the infiltration experiment. The critically refracted waves occurring at the edge of the moving wetting front actually benefits the calculation of the hydraulic conductivity controlling the speed of the wetting front. Additionally, the sharper the wetting front, the more accurate the prediction for hydraulic conductivity. With the work presented here and elsewhere, obtaining reasonable estimates of electromagnetic wave velocity where critical refraction is known to occur should be easily applied and defended.

Time domain numerical modeling of wave propagation in 2D heterogeneous porous media

This paper deals with the numerical modeling of wave propagation in porous media described by Biot’s theory. The viscous efforts between the fluid and the elastic skeleton are assumed to be a linear function of the relative velocity, which is valid in the low-frequency range. The coexistence of propagating fast compressional wave and shear wave, and of a diffusive slow compressional wave, makes numerical modeling tricky. To avoid restrictions on the time step, the Biot’s system is splitted into two parts: the propagative part is discretized by a fourth-order ADER scheme, while the diffusive part is solved analytically. Near the material interfaces, a space–time mesh refinement is implemented to capture the small spatial scales related to the slow compressional wave. The jump conditions along the interfaces are discretized by an immersed interface method. Numerical experiments and comparisons with exact solutions confirm the accuracy of the numerical modeling. The efficiency of the approach is illustrated by simulations of multiple scattering.

Comparisons of internal solitary wave and surface wave actions on marine structures and their responses

In this paper, a time-domain numerical model is established for computing the action of internal solitary wave on marine structures and structure motion responses. For a cylindrical structure, its side and bottom are discretized by pole and surface elements, respectively. The drag and inertial forces in the perpendicular direction of the structure are computed by the Morison equation from the pole elements, and the Froude–Krylov force in the axial direction of the structure due to internal wave motion is computed by integration of the dynamic pressure over the surface elements. The catenary theory is used to analyze the reaction force due to mooring lines, and the motion equation of the marine structure is solved by the fourth-order Runge–Kutta method in the time domain. The model is used to calculate the interaction of the internal solitary wave with a Spar platform with mooring system, and the surface wave action with the platform has also been computed by a frequency-domain boundary element method for comparison. Through the comparison based on a practical internal wave and surface wave states, it can be concluded that the internal wave force on the structure is only 9% of the one due to surface waves. However, the motion response due to the internal wave is much greater than the one due to the surface waves. It shows that the low-frequency effect of internal solitary waves is a great threat to the safety of marine structures.

A TIME-DOMAIN ANALYSIS OF WAVE FORCE ON SMALL-SCALE CYLINDERS OF OFFSHORE STRUCTURES

To get the accurate wave loads on the small-scale cylinders on the platforms, not only the incident wave but also the diffraction and radiation wave should be considered. By taking the wave diffraction from a fixed large-scale cylinder as an example, wave loads on small-diameter cylinders in the diffraction wave field are calculated by Morison formula in this paper. A time-domain numerical model on wave diffraction from large-scale structures is developed with a higher-order boundary element method (HOBEM). Then the velocity and acceleration of any water particle in the fluid domain can be produced from the solved diffraction potential. Results show that the incident wave force is even equal to diffraction wave force when the diameter of the large-scale cylinder is 8 times as great as the small-scale one; And the total force is different with the locations of the small-scale cylinder. The maximum total force is 1.57 times as great as only the incident wave force. Therefore, the wave force on the stake produced by the diffraction waves due to the existence of upper structures should be considered in the practical engineering.

Ground‐penetrating radar assessment of the medieval arch bridge of San Antón, Galicia, Spain

AbstractSeveral arched masonry bridges are listed historical monuments in Spain, which are valued tourist attractions or local landmarks. They are maintained by several organizations dedicated to the cultural heritage such as the International Council on Monuments and Sites (ICOMOS). Many of these important structures are the oldest constructions still in use within the transportation infrastructure and as a result of the increase in traffic loads and their age they have undergone some structural decay. Ground‐penetrating radar (GPR) has been shown to be valuable in evaluating the state of conservation of the San Antón medieval bridge in order to help preserve its historical character. This bridge was surveyed by using the 200, 250 and 500 MHz antennas. Interpretation and analysis of GPR reflection data were supported by finite‐difference time domain numerical modelling, based on the accurate external geometry obtained with three‐dimensional laser scanning methods. Results show that GPR mapping provides valuable information for detecting an internal structural element used for reinforcement as well as a possible interior hidden arch that remains from ancient times. This information is noteworthy for archaeologists and civil engineers as it can be used to make decisions about stability and for future strengthening measures. Copyright © 2010 John Wiley & Sons, Ltd.

An investigation into parametric roll resonance in regular waves using a partly non-linear numerical model

A partly non-linear time-domain numerical model is used for the prediction of parametric roll resonance in regular waves. The ship is assumed to be a system with four degrees of freedom, namely, sway, heave, roll and pitch. The non-linear incident wave and hydrostatic restoring forces/moments are evaluated considering the instantaneous wetted surface whereas the hydrodynamic forces and moments, including diffraction, are expressed in terms of convolution integrals based on the mean wetted surface. The model also accounts for non-potential roll damping expressed in an equivalent linearised form. Finally, the coupled equations of motion are solved in the time-domain referenced to a body fixed axis system. This method is applied to a range of hull forms, a post-Panamax C11 class containership, a transom stern Trawler and the ITTC-A1 containership, all travelling in regular waves. Obtained results are validated by comparison with numerical/experimental data available in the literature. A thorough investigation into the influence of the inclusion of sway motion is conducted. In addition, for the ITTC-A1 containership, an investigation is carried out into the influence of tuning the numerical model by modifying the numerical roll added inertia to match that obtained from roll decay curves.

Using a time-domain higher-order boundary element method to simulate wave and current diffraction from a 3-D body

To study wave-current actions on 3-D bodies a time-domain numerical model was established using a higher-order boundary element method (HOBEM). By assuming small flow velocities, the velocity potential could be expressed for linear and higher order components by perturbation expansion. A 4th-order Runge-Kutta method was applied for time marching. An artificial damping layer was adopted at the outer zone of the free surface mesh to dissipate scattering waves. Validation of the numerical method was carried out on run-up, wave exciting forces, and mean drift forces for wave-currents acting on a bottom-mounted vertical cylinder. The results were in close agreement with the results of a frequency-domain method and a published time-domain method. The model was then applied to compute wave-current forces and run-up on a Seastar mini tension-leg platform.

Wave-current interactions with three-dimensional floating bodies

A Time-domain Higher-Order Boundary Element Method (THOBEM) is developed for simulating wave-current interactions with 3-D floating bodies. Through a Taylor series expansion and a perturbation procedure, the model is formulated to the first-order in the wave steepness and in the current velocity, respectively. The boundary value problem is decomposed into a steady double-body flow problem and an unsteady wave problem. Higher-order boundary integral equation methods are then used to solve the proposed problems with a fourth-order Runge-Kutta method for the time marching. An artificial damping layer is adopted to dissipate the scattering waves. Different from the other time-domain numerical models, which are often focused on the wave-current interaction with restrained bodies, the present model deals with a floating hemisphere. The numerical results of wave forces, wave run-up and body response are all in a close agreement with those obtained by frequency-domain methods. The proposed numerical model is further applied to investigate wave-current interactions with a floating body of complicated geometry. In this work, the regular and focused wave combined with current interacting with a truss-spar platform is investigated.

Aerodynamic instability of a bridge deck section model: Linear and nonlinear approach to force modeling

The aerodynamic behavior of a bridge deck section model with a simple single-box shape was characterized in wind tunnel. At large nose-up mean angles of attack, a torsional instability arises, outlining a situation in which nonlinear aeroelastic effects may be critical. Such condition represents an interesting case to develop and validate nonlinear models for the aeroelastic problem. The experimental campaign allowed both to characterize the aerodynamic forces using forced motion tests and to study the aeroelastic behavior of the section model, when excited by actively generated turbulent wind. These aeroelastic tests are used to validate a numerical time-domain model for aerodynamic forces that takes into account the nonlinearities due to the reduced velocity and to the amplitude of the instantaneous angle of incidence. Results are critically analyzed and compared with those obtained with a linear model.

An E-J Collocated 3-D FDTD Model of Electromagnetic Wave Propagation in Magnetized Cold Plasma

A new three-dimensional finite-difference time-domain (FDTD) numerical model is proposed herein to simulate electromagnetic wave propagation in an anisotropic magnetized cold plasma medium. Plasma effects contributed by electrons, positive, and negative ions are considered in this model. The current density vectors are collocated at the positions of the electric field vectors, and the complete FDTD algorithm consists of three regular updating equations for the magnetic field intensity components, as well as 12 tightly coupled differential equations for updating the electric field components and current densities. This model has the capability to simulate wave behavior in magnetized cold plasma for an applied magnetic field with arbitrary direction and magnitude. We validate the FDTD algorithm by calculating Faraday rotation of a linearly polarized plane wave. Additional numerical examples of electromagnetic wave propagation in plasma are also provided, all of which demonstrate very good agreement with plasma theory.

FUNDAMENTAL PERFORMANCE OF A HYDRAULICALLY ACTUATED FRICTION DAMPER FOR SEISMIC ISOLATION SYSTEM BASED ON THE SKYHOOK THEORY

A seismic-isolation damper system consisted of a water tank and a high-porosity porous media has been proposed, and its fundamental performance is investigated by numerical computations and model experiments. A time-domain numerical model, coupled with CFD to consider the interaction between the porous media with the fluid motions, was newly developed. Shaking-table experiments with a water tank were conducted to confirm the damper's performance and to verify the validity of the numerical model. Results of the forced vibration tests showed the immobility of fluid inside the stationary porous media that highlighted an established passive damping control strategy which is based on the skyhook damper theory. The frequency-sweep studies confirmed the characteristics of the damper such as the non-increase of acceleration responses of building in the high frequency region as a basic characteristic of the skyhook damper. Numerical parametric studies with the variation of the fiber diameters of the porous media and the dimensions of water tank were also carried out to clarify the region of the immobility of fluid inside the porous media.

A versatile thermoelectric temperature controller with 10 mK reproducibility and 100 mK absolute accuracy

We describe a general-purpose thermoelectric temperature controller with 1 mK stability, 10 mK reproducibility, and 100 mK absolute accuracy near room temperature. The controller design is relatively simple and could be readily modified for use in different experimental circumstances. We also describe a time-domain numerical model that allows one to characterize the stability and transient behavior of the system being controlled, even in the presence of elements with highly nonlinear responses.

Ground penetrating radar imaging and time-domain modelling of the infiltration of diesel fuel in a sandbox experiment

Ground penetrating radar (GPR) is a non-destructive method which, over the past 10 years, has been successfully used not only to estimate the water content of soil, but also to detect and monitor the infiltration of pollutants on sites contaminated by light non-aqueous phase liquids (LNAPL). We represented a model water table aquifer (72 cm depth) by injecting water into a sandbox that also contains several buried objects. The GPR measurements were carried out with shielded antennae of 900 and 1200 MHz, respectively, for common mid point (CMP) and constant offset (CO) profiles. We extended the work reported by Loeffler and Bano by injecting 100 L of diesel fuel (LNAPL) from the top of the sandbox. We used the same acquisition procedure and the same profile configuration as before fuel injection. The GPR data acquired on the polluted sand did not show any clear reflections from the plume pollution; nevertheless, travel times are very strongly affected by the presence of the fuel and the main changes are on the velocity anomalies. We can notice that the reflection from the bottom of the sandbox, which is recorded at a constant time when no fuel is present, is deformed by the pollution. The area close to the fuel injection point is characterized by a higher velocity than the area situated further away. The area farther away from the injection point shows a low velocity anomaly which indicates an increase in travel time. It seems that pore water has been replaced by fuel as a result of a lateral flow. We also use finite-difference time-domain (FDTD) numerical GPR modelling in combination with dielectric property mixing models to estimate the volume and the physical characteristics of the contaminated sand.

Utilizing High-Frequency Acoustic Backscatter to Estimate Bottom Sand Ripple Parameters

In some applications of underwater acoustics, it is important to know the ripple structure on shallow-water sediments. For example, the prediction of buried target detection via sound scattering by ripples depends critically on the ripple height and spatial wavelength. Another example is the study of sediment transport, where knowing the ripple structure and its evolution over time helps to understand the forcing on the bottom and the response of sediments. Here, backscatter data from a 300-kHz system are used to show that ripple wavelength and height can be estimated from backscatter images via a simple inversion formula. The inversion results are consistent with in situ measurements of the ripple field using an independent measurement system. Motivated by the backscatter data, we have developed a time-domain numerical model to simulate scattering of high-frequency sound by a ripple field. This model treats small-scale scatterers as Lambertian scatterers distributed randomly on the large-scale ripple field. Numerical simulations are conducted to investigate the conditions under which remote sensing of bottom ripple heights, wavelength, and its power spectrum is possible.

Radar Response of Firn Exposed to Seasonal Percolation, Validation Using Cores and FDTD Modeling

We use ground-penetrating radars (GPRs), firn cores, and electromagnetic finite-difference time-domain (FDTD) numerical modeling to characterize the GPR response to a frozen high-arctic firn pack. As a result of extensive summertime percolation, the firn pack comprises a high fraction of ice layers, lenses, and vertical glands. We show that the GPR response on the firn pack mainly depends on the following: (1) the thickness of the ice layers; (2) the distance between layers; (3) the layer roughness; and (4) the presence or absence of elliptical ice lenses. Using 3-D FDTD modeling, we show that the GPR is not sensitive to typical ice glands, which implies that the GPR underestimates firn heterogeneity, such that firn stratigraphy in percolation and wet-snow zones could be incorrectly interpreted as being better preserved than it actually is. We find that thin ice layers (< 0.05 m) or multiple thin ice layers give a strong response. Thicker ice layers typically give a weaker backscatter per unit area, mainly due to the lack of interference of the reflections from the upper and lower interfaces, but are, due to their continuity, easily trackable. Ice layers with a thickness comparable to the GPR wavelength give 180deg phase-shifted upper and lower reflections and are, in general, separated by a band of low GPR response, due to the lack of permittivity contrast within the ice layers. Despite the ice lenses' relatively short horizontal correlation length, as inferred from cores, bands of high-amplitude clutter caused by these features can be traced over several kilometers in GPR profiles.