Moving Point Source Research Articles

Modeling of a moving point source in inhomogeneous and turbulent media - Application to aircraft noise

Engineering solutions for the modeling of aircraft noise often rely on simplified approaches that consider quasi-static sources and homogenous propagation conditions. These hypothesis may lead to significant inaccuracies on sound pressure level predictions in certain configurations, especially for source traveling at high mach number and at several hundred meters from the receiver. In order to overcome these limitations, an efficient numerical model based on the coupling of a heuristic formulation and a ray-tracing model is proposed. The modeling takes into account source motion effect (Doppler effect and convective amplification), as well as the sound propagation phenomena in inhomogeneous media (waves refraction and scattering by atmospheric turbulence). Several case study related to aircraft noise are presented, for which wind and temperature profiles correspond to experimental measurements. The influence of atmospheric turbulence for such configuration is finally discussed. This work is part of the program MAMBO (Advanced methods for engine and aicraft noise modelling" coordinated by Airbus SAS and supported by the Direction Générale de l'Aviation Civile (DGAC).

Imaging a Moving Point Source from Multifrequency Data Measured at One and Sparse Observation Points (Part II): Near-Field Case in 3D

Imaging a Moving Point Source from Multifrequency Data Measured at One and Sparse Observation Points (Part II): Near-Field Case in 3D

An improved 27-point frequency-domain elastic-wave average-derivative method with applications to a moving point source

Exploration seismology based on moving sources such as high-speed trains has attracted increasingly great attention. It is an important task to perform near-surface seismic imaging and inversion using moving sources. In this context, an accurate and efficient forward-modeling engine for moving sources is crucial. We initially consider a single moving point source. To implement the numerical simulation in terms of a moving point source, two aspects need to be considered: (1) the numerical discretization strategy of the seismic-wave equation and (2) the discrete representation of the moving point source. For the 3D heterogeneous elastic-wave equation, we develop an improved frequency-domain average-derivative numerical method (ADM) by introducing the weighted average of four sets of grid points for the mass-acceleration term. Due to the numerical discretization template, the continuously moving point source is discretized as a series of fixed sources located at different grid points and excited at different times. The corresponding discrete representation of spatio-temporal variation is given by modifying the right-hand side of the resulting linear system of equations. A numerical experiment in a 3D homogeneous half-space model validates the higher computational accuracy of the improved ADM and the feasibility of the numerical simulation scheme for a moving point source. Furthermore, we test the performance of the moving-point-source numerical simulation scheme in the 3D heterogeneous overthrust model. The successful implementation of the 3D frequency-domain numerical simulation for a moving point source establishes a foundation for subsequent practical applications of moving sources in seismic imaging to be performed in the future.

Theoretical study on bubble dynamics under hybrid-boundary and multi-bubble conditions using the unified equation

This paper aims to use the unified bubble dynamics equation to investigate bubble behavior in complex scenarios involving hybrid free surface/wall boundaries and interactions between multiple bubbles. The effect of singularity movement on the unified equation’s form is analyzed after deriving the bubble pulsation equation using a moving point source and a dipole, followed by discussions on the effect of migration compressibility-related terms on the bubble dynamics. In addition, the present study accounts for the impact of hybrid boundaries, including crossed and parallel boundaries, by introducing a finite number of mirror bubbles for the former and an infinite number of mirror bubbles for the latter. Spark bubble experiments and numerical simulation are conducted to validate the present theory. The application of the unified equation in multi-bubble interactions is exemplified by computing a spherical bubble array containing more than 100 uniformly distributed cavitation bubbles under different boundary conditions. The bubble cluster-induced pressure peak can reach nearly two times or even higher than that of an individual bubble, highlighting the damage potential caused by cavitation bubble clusters.

Imaging a Moving Point Source from Multifrequency Data Measured at One and Sparse Observation Directions (Part I): Far-Field Case

Imaging a Moving Point Source from Multifrequency Data Measured at One and Sparse Observation Directions (Part I): Far-Field Case

Synthesis of sound field from moving complex sources with arbitrary trajectories by linear and spherical loudspeaker arrays.

The spectral division method (SDM) and near-field compensated higher order ambisonics (NFC-HOA) are sound field synthesis techniques based on the spatial Fourier representation of sound fields. Previous studies have derived the driving functions of SDM for sound field synthesis with consideration to uniformly moving point sources and moving point sources with arbitrary trajectories. However, the driving functions of NFC-HOA for synthesizing sound fields from moving sound sources have not been proposed to date. For a more realistic auditory experience, the synthesis of a sound field produced by a moving sound source with a complex radiation property is required. This study focused on deriving the driving functions for synthesizing sound fields produced by moving sound sources with arbitrary trajectories and radiation properties. Sound fields were formulated in the angular spectrum and spherical harmonic domains and applied to SDM and NFC-HOA, respectively. Numerical and measurement experiments were conducted to evaluate the proposed method. The results reveal that the proposed method can synthesize the desired sound fields.

Passive Velocity Estimation of a Distant Harmonic Source in a Pekeris Waveguide Based on Modal Doppler Shifts

The acoustic field generated by a moving point source in terms of normal modes predicts that each mode has a different Doppler shift, i.e., modal Doppler shifts, which contains the velocity information of the moving source. This paper presents a method to estimate the velocity of a distant harmonic source in a Pekeris waveguide passively based on modal Doppler shifts. Combined with the fact that the modal depth function varies slowly with frequency, a cost function is designed to realize the velocity estimation of a distant harmonic source with a single hydrophone when the bottom parameters are unknown. The effectiveness of the method is validated by simulations.

A point particle source model for conjugate heat and mass transfer in dispersed two-phase flows by BEM based methods

The paper reports on development of a Boundary Element Method (BEM) based two phase dispersed flow model, that allows an accurate and efficient heat and mass transfer coupling by using a moving point source model to account for particle–fluid interaction. The two-way coupling model highlights the efficient use of the elliptic fundamental solution and the Dirac delta distribution properties to accurately evaluate the heat and mass point particle source impact on the continuous phase, solved by the Boundary Domain Integral Method (BDIM). In addition to the BDIM model of the particle–fluid heat and mass transfer interaction, the two-phase flow case under consideration is extended to the case of porous spherical particle drying with internal moving drying front, which is solved by the Boundary Element Method. As the two-phase flow is considered to be dilute, the particle–fluid momentum exchange is covered by a one-way coupling algorithm, with Lagrangian particle tracking used for determination of particle positions and velocities in the flow. Two computational cases are presented, where 1000 and 10000 particles are dried in a stream of hot air. Comparison between the obtained drying times for the cases of the one-way and the two-way heat and mass transfer coupling results shows, that the developed two-way coupling model accurately captures the effect of moisture accumulation and temperature decrease in the fluid phase, leading to realistic computations of drying rates of particles in the flow.

Identification of the Trajectory of a Moving Point Source when Heating a One-Dimensional Rod

Identification of the Trajectory of a Moving Point Source when Heating a One-Dimensional Rod

Inverse moving point source problem for the wave equation

In this paper, we consider the problem of identifying a single moving point source for a three-dimensional wave equation from boundary measurements. Precisely, we show that the knowledge of the field generated by the source at six different points of the boundary over a finite time interval is sufficient to determine uniquely its trajectory. We also derive a Lipschitz stability estimate for the inversion.

Understanding the effects of temporal waveform modulation of the laser emission power in laser powder bed fusion: Part I - Analytical modelling

The architecture of contemporary fiber laser sources enables users a wide choice in terms of spatial and temporal profiles during the laser powder bed fusion (LPBF) process. Given the range of possibilities, the need for analytical modelling approaches to predict the consequences of waveform modulation in terms of both thermal and fluid-dynamic aspects over the powder bed, process dynamics and resulting part quality is of great interest. Within the present investigation a moving point source analytical model was developed to study the effect of temporally modulated laser beams over the temperature distribution and recoil pressure induced over the molten region during single track LPBF depositions. This study configures as the first part of an investigation on the topic presented with the aim of developing the modeling framework to predict the effects of temporal waveform modulation in the LPBF process. The model developed was implemented numerically to simulate the single track LPBF deposition of stainless steel AISI316L with different waveform shapes ranging from the conventional Square Wave emission to Ramp Up, Ramp Down and Triangle waveforms. Modulation at different amplitude levels and different waveform frequencies were also investigated. Results show that temperature variations followed the temporal profile of the power exposed over the material. Consequently, recoil pressure oscillations over the melt region exhibited a periodic profiles correlated to the waveform modulation of the laser power indicating that melt flow may be controlled by means of such techniques. Peak values of recoil pressure, which might be symptomatic of melt pool instabilities, could be reduced employing higher levels of modulation frequency or lower oscillation amplitudes between non-zero values of the emission power.

Flow of a Viscous Incompressible Fluid from a Moving Point Source

The flow of a viscous incompressible fluid outflowing from a uniformly moving point source is considered. An exact solution to the problem is found in the way that the velocity decreases inversely with the radial coordinate. It is shown that a spherical volume of fluid is carried away by the source, the radius of which is inversely proportional with respect to the velocity of motion. In this case, a cylindrical discontinuity arises in the region of forming a wake behind the body, the dimensions of which are determined by the magnitude of the external pressure and do not depend on the velocity of the source. The obtained solutions are governed by hydrodynamical fields of flows which can be recognized as special invariants at symmetry reduction.

A neural network method for time-dependent inverse source problem with limited-aperture data

This paper is concerned with the mathematical design of a novel gesture-based input/instruction device with identification and prediction using a moving emitter. The emitter acts as a point source and there is a sensor monitoring the wave field emitted by the emitter away from it on a surface in real time. In practice, the emitter could be a ring worn on a finger of the human being who desires to interact/communicate with the computer, while the sensor could be mounted on a computer. The input/instruction can be recognized and predicted by identifying the moving trajectory of the emitter performed by the human being from the collected wave field data. The process can be modeled as an inverse moving source problem, that is, one identifies and predicts the trajectory of a moving point source by measuring the corresponding wave field. There are several salient features of our study. First, for the practical consideration, the dynamical wave field data are collected in a limited aperture and full aperture respectively. Second, we design a parameter inversion model by neural network (PIMNN) to reconstruct the trajectory of the moving point source. This model solves the problem of information loss caused by data acquisition in limited aperture and has certain robustness with respect to noise. The computing complexity of the PIMNN are calculated by the Multiply Accumulate. Third, we consider the trajectory prediction of the moving point source for the inverse source problem associated with the novel input/instruction approach, and construct a trajectory prediction model by neural network (TPMNN) to predict the trajectory of the moving point source. Numerical experiments show that the proposed device works effectively and efficiently in some practical scenarios.

A MODEL OF WELDING THERMAL PROCESSES WITH A LIMITED NUMBER OF FICTITIOUS POINT SOURCES

Analytical methods of calculation of thermal processes at welding enable to estimate operatively the influence of welding modes on parameters of a temperature field and to predict structural changes in a zone of thermal influence. In the mid-twentieth century it was suggested to calculate the heat processes in welded products with parallel boundary planes by summing up the temperature fields of the main and infinite number of fictitious point sources using thereflection method. However, due to computational difficulties, this method could not be brought to a state of wide practical application. Furthermore, since the schematization of heated bodies is conditional, the choice of the body scheme (plate, flat layer, semi-infinite body) and therefore the thermal calculation model is performed intuitively based on the accumulated experience. This uncertainty inevitably leads to discrepancy between the calculated and actual parameters of the thermal welding process. The purpose of this work is to adapt a model of thermal processes with a limited number of fictitious fast moving point sources to the calculation of thermal welding processes. The proposed model, solvable in Mathcad software, contains the equations of temperature field and temperature rate of change with account of the number
 of fictitious heat sources involved in the calculation. This model allows a reasonable limitation of the number of fictitious heat sources for providing the required accuracy of calculations, since as the fictitious heat sources move away from the product and their influence on the product heating decreases. In most cases for practical calculations 2 pairs of fictitious sources are enough for welding of 2 cm thick steel products, of 0.5 cm thick products ‒ 5 pairs, of 0.2 cm thick products ‒ 12 pairs. Comparison of the calculated values of the proposed model with actual temperature field measurements and known effects of cooling rate in the plate, plane layer and semi-infinite body within the accepted limits have confirmed its adequacy. The presented comparative results demonstrate versatility of the proposed model with a limited number of fictitious fast moving point sources, which can be applied sufficiently and successfully for analysis of the thermal welding processes of real industrial products of arbitrary thickness without discriminating into plate, plane layer and semi-infinite body models.

Development of a moving point source model for shipping emission dispersion modeling in EPISODE–CityChem v1.3

Abstract. This paper demonstrates the development of a moving point source (MPS) model for simulating the atmospheric dispersion of pollutants emitted from ships under movement. The new model is integrated into the chemistry transport model EPISODE–CityChem v1.3. In the new model, ship parameters, especially speed and direction, are included to simulate the instantaneous ship positions and then the emission dispersion at different simulation time. The model was first applied to shipping emission dispersion modeling under simplified conditions, and the instantaneous and hourly averaged emission concentrations predicted by the MPS model and the commonly used line source (LS) and fixed point source (FPS) models were compared. The instantaneous calculations were quite different due to the different ways to treat the moving emission sources by different models. However, for the hourly averaged concentrations, the differences became smaller, especially for a large number of ships. The new model was applied to a real configuration from the seas around Singapore that included hundreds of ships, and their dispersion was simulated over a period of a few hours. The simulated results were compared to measured values at different locations, and it was found that reasonable emission concentrations were predicted by the moving point source model.

High-resolution velocimetry technique based on the decaying streaks of phosphor particles.

This Letter introduces a new, to the best of our knowledge, particle streak velocimetry technique based on decaying streaks formed by individual phosphor particles following pulsed excitation. Tin-doped phosphor particles are dispersed into flows and excited by a pulsed UV laser light sheet. Emission streaks are recorded as a result of particle motion during the persistence of luminescence (here ∼27µs). The two components of the flow velocity are derived from the streaks without directional ambiguity by applying to each streak a two-dimensional fit describing a linearly moving point source with a mono-exponential decaying emission. This technique can achieve high spatial resolution compared to particle image velocimetry (PIV), while also requiring much fewer computational resources than particle tracking velocimetry (PTV) at high seeding densities. The wavelength-shifted luminescence also allows rejection of reflected laser light. The approach was validated in a free jet against simultaneous PTV and PIV and then successfully applied to measure a canonical boundary layer flow.

Нагруженные уравнения, возникающие при синтезе управления нагревом стержня движущимися источниками

The article proposes an approach to solving the problem of synthesis of motion and power control of lumped sources. For concreteness, the problem of linear feedback control of moving heat sources during heating of the rod is considered. The powers and motion of point sources, participating in the right-hand side of the differential equation of parabolic type, are determined depending on the measured values of the process state at the points of measurement. As a result, the right-hand side of the differential equation linearly depends on the values of the process state at the given points of the bar. Formulas for the components of the gradient of the functional with respect to the parameters of linear feedback are obtained, which make it possible to use first-order optimization methods for the numerical solution of synthesis problems.

MGEODAR-A Mobile Radar System for Detection and Monitoring of Gravitational Mass-Movements.

Radar measurements of gravitational mass-movements like snow avalanches have become increasingly important for scientific flow observations, real-time detection and monitoring. Independence of visibility is a main advantage for rapid and reliable detection of those events, and achievable high-resolution imaging proves invaluable for scientific measurements of the complete flow evolution. Existing radar systems are made for either detection with low-resolution or they are large devices and permanently installed at test-sites. We present mGEODAR, a mobile FMCW (frequency modulated continuous wave) radar system for high-resolution measurements and low-resolution gravitational mass-movement detection and monitoring purposes due to a versatile frequency generation scheme. We optimize the performance of different frequency settings with loop cable measurements and show the freespace range sensitivity with data of a car as moving point source. About 15 dB signal-to-noise ratio is achieved for the cable test and about 5 dB or 10 dB for the car in detection and research mode, respectively. By combining continuous recording in the low resolution detection mode with real-time triggering of the high resolution research mode, we expect that mGEODAR enables autonomous measurement campaigns for infrastructure safety and mass-movement research purposes in rapid response to changing weather and snow conditions.

Convexification and experimental data for a 3D inverse scattering problem with the moving point source

Inverse scattering problems of the reconstructions of physical properties of a medium from boundary measurements are substantially challenging ones. This work aims to verify the performance on experimentally collected data of a newly developed convexification method for a 3D coefficient inverse problem for the case of unknown objects buried in a sandbox. The measured backscatter data are generated by a point source moving along an interval of a straight line and the frequency is fixed. Using a special Fourier basis, the method of this work strongly relies on a new derivation of a boundary value problem for a system of coupled quasilinear elliptic equations. This problem, in turn, is solved via the minimization of a Tikhonov-like functional weighted by a Carleman weight function. Different from the continuous case, our weighted cost functional in the partial finite difference does not need the penalty term to gain the global convergence analysis. The numerical verification is performed using experimental data, which are raw backscatter data of the electric field. These data were collected using a microwave scattering facility at The University of North Carolina at Charlotte.

Numerical schemes to reconstruct three-dimensional time-dependent point sources of acoustic waves

This paper addresses the numerical simulation of three-dimensional time-dependent inverse source problems of acoustic waves. The reconstructions of both multiple stationary point sources and a moving point source are considered. The modified method of fundamental solutions (MMFS), which expands the solution utilizing the time convolution of Green’s function and the signal function, is proposed to solve the problem. Moreover, for the reconstruction of a moving point source, the MMFS is simplified as a simple sampling method at each time step. Numerical experiments are conducted to show the effectiveness of the proposed methods.