Surface Integral Method Research Articles

A novel pavement mean texture depth evaluation strategy based on three-dimensional pavement data filtered by a new filtering approach

Automatic pavement inspection is a reliable strategy to evaluate pavement conditions. Generally, the skid resistance of asphalt pavement is employed to characterize the pavement surface characteristics. The mean texture depth (MTD) of pavement is a crucial metric to characterize the macrotexture of asphalt pavement. The primary aim of this article is to evaluate pavement MTD. To evaluate this parameter based on three-dimensional (3-D) point cloud data extracted from a self-developed 3-D detection system, a novel filtering method and reference surface integral method were proposed. The novel filtering method was first employed to eliminate the isolated noise of the extracted 3-D point cloud data and was compared with the primary surface profile (PSP)-based filtering method. Then, a 3-D virtual model of pavement texture was generated based on the filtered 3-D data. Finally, a novel method, the reference surface integral, was proposed to evaluate the pavement MTD. The evaluated results were compared with the results measured via manual sand-patch testing. The results show that the novel filtering method performs better filtering performance than PSP-based filtering. The error between the evaluated MTD and the measured MTD is within 3.28%, which demonstrates that the proposed filtering method and MTD evaluation method have robust advantages and can be employed to evaluate pavement performance.

An overview of the null-field method. I: Formulation and basic results

In this paper we revisit the fundamentals of the null-field method with discrete sources. We prove the unique solvability of the null-field equations for the total field inside the particle and the internal field outside the particle, at all wavenumbers. For this purpose, we use the equivalence between the null-field and surface integral equations methods. Furthermore, we discuss the completeness property of different systems of discrete sources for a surface field approximation, and derive an infinite set of integral equations for the surface fields in a variety of discrete sources. Finally, we formulate the null-field scheme as an approach aiming to construct an approximate solution to the scattering problem. The way in which we introduce the T matrix of a particle is different from the standard approach relying on the assumption that the system of regular vector spherical wave functions for the interior problem is a basis.

Streamlined bodies drag force estimation using wake integration technique

In this paper, the drag force calculation around the SUBOFF submarine in axisymmetric configuration was investigated using the “Wake Integration Technique.” This method is usually used in wind tunnels as an auxiliary method instead of the common “surface integral technique” for flow around complex geometries or shock wave flows. The results of this method are dependent on data collection vertex space, distance, and section size, where practical suggestions were made for each parameter in this research. Furthermore, the contribution of the pressure, momentum, and fluctuation terms in the total drag force were also evaluated at different cross sections. These findings can be implemented in wind tunnels with small test section length and also to compare the results obtained by the common surface integral method. Simulations were carried out at different aspect ratios at zero angles of attack, and the capabilities of this method at inclined flows were also discussed. The obtained results were also compared against the common method, and the results show only 4% deviation at zero angle.

Design, synthesis and application of new iron-based cockscomb-like photocatalyst for high effectively degrading water contaminant under sunlight

Developing cheap and efficient photocatalyst is a vigorous pathway for gradually increasing rhodamine B (RhB) pollution problem. Herein, two novel iron-based photocatalysts g-C3N4/ZnO@Fe3O4 (Fe-heterojunction) and 2-amino-5-fluorobenzotrifluoride@Fe3O4 (Fe-organic ligand) were designed and synthesized which exhibit 100% photo-degradative ability with water contaminant RhB under sunlight in about 2 h. They were characterized by SEM, FT-IR, XRD, XPS and BET as well as the analysis of morphological structure and chemical composition. The ESR experiment was also carried out to explore the possible degradation mechanism. The UV-Vis spectrum and band gap energies were examined and calculated. Especially, the Fe-organic ligand photocatalyst shows a specific 3D cockscomb-like structure. This makes its degrading efficiency much improved. The recently developed robust field-only surface integral method was employed to explore the possible mechanism which confirmed with the experimental results. The optimum degradation conditions including ligand ratio, pH and concentration of RhB solution, were screened by orthogonal experiments. Also, the reusability and degradation kinetic equations of the two photocatalysts were built to give a typical reference for a large-scale industrial wastewater treatment as well as for the water sustainable utilization.

Non-Destructive Measurement of Three-Dimensional Plants Based on Point Cloud.

In agriculture, information about the spatial distribution of plant growth is valuable for applications. Quantitative study of the characteristics of plants plays an important role in the plants’ growth and development research, and non-destructive measurement of the height of plants based on machine vision technology is one of the difficulties. We propose a methodology for three-dimensional reconstruction under growing plants by Kinect v2.0 and explored the measure growth parameters based on three-dimensional (3D) point cloud in this paper. The strategy includes three steps—firstly, preprocessing 3D point cloud data, completing the 3D plant registration through point cloud outlier filtering and surface smooth method; secondly, using the locally convex connected patches method to segment the leaves and stem from the plant model; extracting the feature boundary points from the leaf point cloud, and using the contour extraction algorithm to get the feature boundary lines; finally, calculating the length, width of the leaf by Euclidean distance, and the area of the leaf by surface integral method, measuring the height of plant using the vertical distance technology. The results show that the automatic extraction scheme of plant information is effective and the measurement accuracy meets the need of measurement standard. The established 3D plant model is the key to study the whole plant information, which reduces the inaccuracy of occlusion to the description of leaf shape and conducive to the study of the real plant growth status.

Field-only surface integral equations: scattering from a dielectric body.

An efficient field-only nonsingular surface integral method to solve Maxwell's equations for the components of the electric field on the surface of a dielectric scatterer is introduced. In this method, both the vector wave equation and the divergence-free constraint are satisfied inside and outside the scatterer. The divergence-free condition is replaced by an equivalent boundary condition that relates the normal derivatives of the electric field across the surface of the scatterer. Also, the continuity and jump conditions on the electric and magnetic fields are expressed in terms of the electric field across the surface of the scatterer. Together with these boundary conditions, the scalar Helmholtz equation for the components of the electric field inside and outside the scatterer is solved by a fully desingularized surface integral method. Compared with the most popular surface integral methods based on the Stratton-Chu formulation or the Poggio-Miller-Chew-Harrington-Wu-Tsai (PMCHWT) formulation, our method is conceptually simpler and numerically straightforward because there is no need to introduce intermediate quantities such as surface currents, and the use of complicated vector basis functions can be avoided altogether. Also, our method is not affected by numerical issues such as the zero-frequency catastrophe and does not contain integrals with (strong) singularities. To illustrate the robustness and versatility of our method, we show examples in the Rayleigh, Mie, and geometrical optics scattering regimes. Given the symmetry between the electric field and the magnetic field, our theoretical framework can also be used to solve for the magnetic field.

Jet noise analysis using an efficient LES/high-Order acoustic coupling method

The use of a CFD/CAA method, where fluctuations are extracted on a surface and propagated analytically to the far-field, is becoming a practical approach for industrial jet noise prediction. However, the placement of the surface can be problematic and a source of error, so here an efficient LES/APE coupling method that relies on volumetric sources is utilised. This allows the use of an existing, well validated and robust finite volume LES code to compute the unsteady flow, from which the volumetric sources are extracted, to then compute the propagation of the acoustic waves to the far-field using a high-order finite element APE code with a grid more appropriate for this task. Furthermore, this coupled methodology allows the studying of noise propagation in complex configurations in which the use of surface integral methods could be challenging.In this work, a coupling strategy is used in which all the necessary data is exchanged directly via the high-speed communication network using an open-source library. The efficiency of the parallel-coupling strategy is demonstrated by applying it to a 2D canonical case and comparing it with an existing file-based approach. For the acoustic propagation, the APE solver used is called AcousticSolver, part of the high-order spectral/hp finite element open-source code Nektar++. The present LES/APE framework is fist validated for 3D jet applications by studying the noise propagation of a low-Reynolds number case. Then the method is applied to a more realistic high Reynolds number jet obtaining encouraging results in terms of flow and acoustic predictions.

Deep Learning Based Survey Region Estimation for Wake Integration Method

In the field of computational fluid dynamics, wake integration method has the advantage that can reduce non- physical drag effect by numerical viscosity. However, in order to define its appropriate integration region, visualization of physical quantities and quantitative evaluation are required. In this study, we propose CNN (Convolutional Neural Network) model to simplify the definition of the appropriate region. Data sets were created by computing 2D fluid analysis on 15 types of NACA airfoil and learning data were classified into three groups to compare the airfoil shapes contributing to generalization performance. The drag of the surface integral method was used as the training data and the entropy drag visualization image was used as input to learn and infer with the CNN model, and the drag distribution was predicted. As a result, the prediction error of the drag distribution was 1.19 (%) and it was clarified that the presence of a symmetric wing contributes to the generalization performance of the model.

SIE-DDM Based on a Hybrid Direct–Iterative Approach for Analysis of Multiscale Problems

In this article, surface integral equation domain decomposition method (SIE-DDM) based on a hybrid direct–iterative approach is proposed for multiscale electromagnetic simulation. The solution of SIE-DDM matrix system is typically built on the strategy of inner-outer loop. Therefore, the direct approach is preferred to the subsolver in each decomposed domain. Here, a fast direct approach based on an enhanced hierarchically off-diagonal low-rank (HODLR) format involving extended admissibility condition (EAC) is present as an alternative subsolver, in which a reconstructing and recompression technique (RRT) is proposed. The efficiency and accuracy can be further improved by using this technology. The inverse of each subdomain is obtained by Sherman–Morrison–Woodbury algorithm (SMWA), while the global system is still solved by the iterative method. This hybrid framework makes full use of strengths of terative and direct approaches. On the other hand, the fast direct solver provides a robust preconditioner for the matrix system, especially for ill-conditioned cases. Several numerical examples will demonstrate the proposed method.

Influence of grid resolution on the spectral characteristics of noise radiated from turbulent jets: Sound pressure fields and their decomposition

Jet noise remains a key target for aircraft noise reduction in the foreseeable future. While being extremely challenging, the requirement of predicting both low and high frequency noise spectra is increasingly important for design purposes. Novel approaches are needed to overcome the current numerical limitations in capturing the required broad noise spectra. Once sufficiently resolved, the energy contents of the numerically simulated near- and far-field sound pressure have intrinsic correlations among different levels of grid resolution. The present work explores the novel potential of such correlations to broaden the spectral prediction. The noise radiated from high subsonic turbulent jets is investigated using large-eddy simulation. The 3-D filtered compressible Navier-Stokes solutions are obtained for an axisymmetric and a serrated nozzle on successively refined multi-resolution grids, ranging from 5 to 80 million grid points. The radiated far-field sound is computed using the Ffowcs Williams – Hawkings (FW-H) surface integral method. Fourier decomposition for pressure near-field is applied to help identify the location of the sound source regions and the dominant directions of propagation, which provides a more thorough understanding of the effect of the grid resolution on the numerical cut-off frequencies of the far-field spectra. Further analysis of the far-field spectra and of their azimuthal modes confirms that a novel strategy to obtain a broadened overall sound spectrum is possible, at reduced computational cost, from a combination of multiple spectra from successively refined grids.

Wideband Models for the Electromagnetic Induction Signatures of Thin Conducting Shells

Wideband electromagnetic induction sensors have been shown to be more effective than traditional metal detectors at identifying metallic targets of interest when buried near abundant metallic clutter. A promising strategy for performing target identification using wideband data relies on characterizing the target response using a magnetic polarizability tensor (MPT) that is a function of frequency. In this paper, a surface integral method is presented for deriving the MPT in singularity expansion form using a modal decomposition. The method is verified by comparing the singularity expansion for a spherical shell to a derived analytical solution. The expansion coefficients for cylindrical tubes, of various aspect ratios, are compared to experimental results, showing good agreement. Finally, expansion coefficients are given for a disk and are compared to other numerical results.

Direct noise computation of a generic vehicle model using a finite volume method

This paper demonstrates the applicability of a finite volume method for the direct noise computation of road vehicles. For this purpose, a generic vehicle model consisting of major aeroacoustic components of a production car is considered. Such components are the A-pillar and the side mirror. The flow past the vehicle model is calculated using a compressible flow solver for low Mach number flows, accompanied with an approach based on detached eddy simulation for turbulence modelling. Two variants of the vehicle model are calculated, namely with and without side mirror. Validation of aerodynamic results is performed by comparing simulated surface pressure spectra on the side window to wind tunnel measurements. Thereafter, acoustic waves generation and propagation are examined. The propagation of acoustic waves from the sources to the windows surface is calculated directly using the compressible solver, as well as indirectly using a surface integral method. The results of both methods are then used as an input for a vibroacoustic model and surface acceleration spectra are compared between both approaches and wind tunnel measurements. A general assessment of both numerical approaches is given and the aeroacoustic impact of the A-pillar as well as the side mirror regarding their contribution to the overall acoustic level is presented.

A highly efficient porous rod-like Ce-doped ZnO photocatalyst for the degradation of dye contaminants in water.

A mild and simple method was developed to synthesize a highly efficient photocatalyst comprised of Ce-doped ZnO rods and optimal synthesis conditions were determined by testing samples with different Ce/ZnO molar ratios calcined at 500 °C for 3 hours via a one-step pyrolysis method. The photocatalytic activity was assessed by the degradation of a common dye pollutant found in wastewater, rhodamine B (RhB), using a sunlight simulator. The results showed that ZnO doped with 3% Ce exhibits the highest RhB degradation rate. To understand the crystal structure, elemental state, surface morphology and chemical composition, the photocatalysts were characterized by X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), scanning electron microscope (SEM) and inductively coupled plasma emission spectroscopy (ICP), respectively. The newly developed, robust, field-only surface integral method was employed to explore the relationship between the remarkable catalytic effect and the catalyst shape and porous microstructure. The computational results showed that the dipole-like field covers the entire surface of the rod-like Ce-doped ZnO photocatalyst and is present over the entire range of wavelengths considered. The optimum degradation conditions were determined by orthogonal tests and range analysis, including the concentration of RhB and catalyst, pH value and temperature. The results indicate that the pH value is the main influential factor in the photocatalytic degradation process and the optimal experimental conditions to achieve the maximum degradation rate of 97.66% in 2 hours are as follows: concentration (RhB) = 10 mg/L, concentration (catalyst) = 0.7 g/L, pH 9.0 and T = 50 °C. These optimum conditions supply a helpful reference for large-scale wastewater degradation containing the common water contaminant RhB.

Frequency Optimization for Inductive Power Transfer Based on AC Resistance Evaluation in Litz-Wire Coil

A coil with a high quality factor $Q$ is desired to obtain a high efficiency for inductive power transfer (IPT). $Q$ is proportional to the coil inductance and operating frequency, while it is inversely proportional to the coil resistance, which increases with frequency. An optimized frequency exists to achieve the maximum efficiency. Eddy currents and resulting ac resistance in Litz-wire coils are attributed to magnetic field. Especially, the induction component of the ac resistance is approximately proportional to the squared magnetic field to which the coil is exposed to. FEA simulations are conducted and surface integral method is employed to determine the squared field. Additionally, the volume integral method is proposed to evaluate the overall effect of the field on the induction resistance. The optimized frequency for the maximum efficiency is obtained, using the squared field calculation and resulting ac resistance evaluation. Sample prototype coils are manufactured to verify the resistance analysis methods. An IPT system is built employing these coils. Experiments show that the IPT system achieves the highest efficiency at frequencies closed to the predicted optimized ones.

A Flexible SIE-DDM for EM Scattering by Large and Multiscale Problems

A flexible surface integral equation domain decomposition method (SIE-DDM) with reverse operation self-consistent evaluation (ROSE) is proposed to analyze the electromagnetic (EM) scattering by electrically large, multiscale, perfect electrically conducting objects. ROSE is developed for the robust implementation of the Robin transmission condition between adjacent subdomains in SIE-DDM. By interpolating a set of plane waves on the touching faces, small linear systems are constructed, and the entries of the transmission matrix can be solved algebraically. In doing this, direct numerical integration involving complicated geometrical operations over a nonconformal mesh can be avoided. Several numerical results will be presented to validate the effectiveness of the proposed method.

Comparison of surface and volume integral methods for transonic propeller acoustic predictions

A precise comparison of the surface and volume approaches of the Ffowcs Williams-Hawkings acoustic integral formulation is conducted for a propeller in transonic operating conditions. For both approaches, the calculations are carried out directly starting from CFD input data provided in the propeller rotating frame, i.e. with supersonically moving emission points. No approximation in the volume calculations, which could distort the comparison between both methods, is made. The principle and the calculation algorithm on which this particular integration technique is based are reviewed. Then calculations are carried out for four increasingly refined CFD meshes. They first confirm that both acoustic integral methods provide identical results when the numerical dissipation is negligible in the aerodynamic calculation. These calculations also show that the volume method is slightly less sensitive to the numerical dissipation than the surface method. However, the gain seems low compared to the computational cost of the volume integration. In addition, two techniques for determining the regions of the dominant acoustic sources are explored. With the first one, a rather conventional technique based on the local quadrupole term, the results show that specific terms, chosen according to the phenomenon concerned, may be better indicators of the real noise sources than the original shear and entropy terms. The second one, less known and consisting in calculating the elementary acoustic time signature radiated by each cell of the grid, seems more effective but may turn out to be costly in terms of data storage with the volume method.

A volume integral implementation of the Goldstein generalised acoustic analogy for unsteady flow simulations

A new volume integral method based on the Goldstein generalised acoustic analogy is developed and directly applied with large-eddy simulation (LES). In comparison with the existing Goldstein generalised acoustic analogy implementations, the current method does not require the computation and recording of the expensive fluctuating stress autocovariance function in the seven-dimensional space–time. Until now, the multidimensional complexity of the generalised acoustic analogy source term has been the main barrier to using it in routine engineering calculations. The new method only requires local pointwise stresses as an input that can be routinely computed during the flow simulation. On the other hand, the new method is mathematically equivalent to the original Goldstein acoustic analogy formulation, and, thus, allows for a direct correspondence between different effective noise sources in the jet and the far-field noise spectra. The implementation is performed for conditions of a high-speed subsonic isothermal jet corresponding to the Rolls-Royce SILOET experiment and uses the LES solution based on the CABARET solver. The flow and noise solutions are validated by comparison with experiment. The accuracy and robustness of the integral volume implementation of the generalised acoustic analogy are compared with those based on the standard Ffowcs Williams–Hawkings surface integral method and the conventional Lighthill acoustic analogy. As a demonstration of its capabilities to investigate jet noise mechanisms, the new integral volume method is applied to analyse the relative importance of various noise generation and propagation components within the Goldstein generalised acoustic analogy model.

Impedance Analysis of a Meander Coil with Rectangular Cross Section Above a Planar Conductor Using Vertex Description

Meander coils are widely used in eddy-current testing (ECT) and many other fields. Since the coil impedance is a key parameter that affects device performance, many scholars have studied impedance modeling. However, the modeling process of existing methods is cumbersome and complicated due to the complex structure of a meander coil. In this paper, a new method for the impedance calculation of a meander coil is proposed. First, a single rectangular coil is taken as an example, and its impedance expressions are deduced with the surface integral method. Then, a vertex description method for impedance calculation regarding meander coils is put forward by defining the position factor and angle factor. Finally, impedance calculations and verification experiments on a series of meander coils with different geometric dimensions are presented. The experimental results are in good agreement with the calculated ones. Therefore, the proposed method effectively calculates the impedance of meander coils and also simplifies the impedance calculation of coils with complex structures. Consequently, it is greatly significant for the coil design in terms of cost and design cycle reduction.

Effective and Practical Methods to Calculate the Second-Order Buoyancy in Magnetic Fluid Acceleration Sensor

This paper concerns the nature of the peculiar second-order buoyancy experienced by a magnet in magnetic fluid acceleration sensor. The equilibrium differential equation of magnetic fluid under the action of magnetic field and gravity field is established and the expression for calculating the second-order buoyancy is derived. Three practical and effective methods to calculate the second-order buoyancy called surface integral method, magnetic force method, and equivalent magnetic force method are proposed. Besides, the second-order buoyancy is calculated by the three methods mentioned above and measured experimentally. The calculation results are in very good agreement with the experimental results, for all the three methods, the calculation error is less than 7% compared with the numerical range of second-order buoyancy. Both calculation and experimental results show that the second-order buoyancy increases rapidly with the decrease of the axial distance between the bottom of the magnet and the container, and the trend can be fitted well by an exponential function.

Spatial Signature Analysis of Submarine Magnetic Anomaly at Low Altitude

To study the magnetic signature of submarines and improve the performance of magnetic anomaly detectors in the antisubmarine warfare, the generation mechanism of the submarine magnetic field (SMF) is first introduced. Magnetic fields produced by submarines are classified into five major types by the cause and state of submarines. Besides, the prediction model of the SMF at low altitude is proposed. Based on the surface integral method, the continuation formula of the magnetic field is derived from the vector potential. According to the magnetic field of a real mockup, the distribution of the SMF is obtained by the continuation formula, and the data of the magnetic anomaly caused by submarines are produced at different heights. Then, the spatial signature of the magnetic anomaly is analyzed. The result of analysis shows that the magnetic anomaly of ferromagnetic submarines has evident characteristics. The distribution of the magnetic anomaly is spatially symmetrical, and the peak values of its components and total field occur in special positions. Furthermore, the signal strength of the magnetic anomaly is sufficiently large to be detected. So the identification of underwater magnetic target can be realized by the special magnetic signature.