Volume Integral Method Research Articles

Compensation of induction heating load edge‐effect by space control

PurposeThe purpose of this paper is to present a calculation optimization method that is able to achieve the best induced power profile (and subsequent temperature distribution) in a disk or billet workpiece processed by induction heating.Design/methodology/approachA volume integral method, also known as the mutually coupled circuits method, is implemented in MatLab® environment to solve axial‐symmetrical induction systems. It is completed with an optimization procedure based on Nelder‐Mead simplex algorithm, with the goal of obtaining a specified distribution of the induced power in the load. In this way, it is possible to predict current amplitudes for implementing the so‐called “zone controlled induction heating” (ZCIH) process.FindingsSome examples of calculation results are given, both for disc and billet loads. By the excitation of the inductor coils with a set of currents of appropriate amplitude and phase values, it is possible to achieve an optimized profile of induced power distributions.Originality/valueThis paper validates a method to predict currents and phases in a load‐inductor ZCIH system, confirming the possibility of obtaining specified induced power density distributions, according to the process requirements, e.g. for compensation of the load edge‐effect.

Analytical Model for the Extraction of Flaw-Induced Current Interactions for SQUID NDE

Incorporating an analytical approach to simulate the interaction of a series of long cracks and the induced current of a double-D excitation coil, we have developed a model-based method to do precise detection of the positions of the cracks in a metallic structure by using eddy-current superconducting quantum interference device (SQUID) nondestructive evaluation (NDE) measurements. Conventionally, the structure of the defects is found by iteratively solving a numerical forward problem, which is usually based on finite-element, boundary-element, or volume-integral method. This, however, incurs a heavy numerical burden, as every time the forward problem is to be solved, a rigorous numerical model should be inevitably employed to extract the complex distribution pattern of the induced current encountering defects of the structure. In this paper, an analytical approach is used for the modeling of the interaction of the induced current and a series of cracks in the sample. It duly considers the distribution of the induced current in the flawed samples, does not call for extremely high computational resource, and thus permits efficient NDE as the forward problem can be solved within a reasonable time. Here, a high- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Tc</i> first-order radio-frequency SQUID gradiometer is employed as the magnetic sensor of the NDE system to scan the samples with different cracks. The accuracy of the proposed algorithm is verified by having the extracted shape of the defects obtained by applying the proposed algorithm on the SQUID NDE measurements against the actual cracks.

Electron and Electrostatic Properties of Three Crystal Forms of Piracetam

The electron densities in three crystal forms of piracetam (triclinic form II, monoclinic form III, and triclinic piracetam monohydrate) were derived from high resolution X-ray diffraction experiments carried out at 100 K. For comparison, quantum mechanics calculations were also performed for the three compounds. The experimental electron density was refined using the Hansen–Coppens multipole model. The electron deformation density and the electrostatic potential were carefully analyzed in the three forms of piracetam. The atomic charges obtained by the flux of the electric field were found in excellent agreement with those obtained by the conventional volume integration method. The charge values compare qualitatively well with those obtained by theoretical calculations. The total electrostatic force exerted on each atom of the molecule has been investigated by using the Maxwell stress tensor as well as the interatomic forces. The experimental electrostatic interaction energies between dimers in the three...

Numerical Predictions of Air Temperature and Velocity Distribution to Assist in the Design of Natural Ventilation Piggery Buildings

Pigs are subjected to intensive environment control and management for higher productivity due to their sensitivity to climatic variation, which affects their growth and impacts greatly on the profitability of this industry. The appropriate temperature and air speed inside a piggery that meets the thermal comfort of the pigs depends on the age of the pigs; in this study grower pigs (32-52 kg) are considered. The aim of the current work is to model the air flow in a natural ventilation piggery numerically and hence predict the velocity and temperature of the air inside the piggery. The effect of some variation in the design of the piggery on the environment inside the piggery, and more specifically at the pigs’ level, has been also investigated. A steady two-dimensional numerical model including the effect of buoyancy, turbulence and heat generated by the pigs was solved using the computational fluid dynamics software Fluent, which is based on the integral volume method. Temperature and air speed inside the piggery and at the pigs’ level were predicted for a particular wind velocity and temperature to facilitate the comparison of the effect of the different variations in the design proposed in this study. These variations were reducing the height of the outer wall of the piggery to the same level as the pens and changing the type of fence used in the pens as well as adding louvers in the air opening, changing the shape of the roof and adding insulation to the roof. Air was assumed to enter the piggery at speed of 0.92 m/s to the southwest and at temperature of 34 °C. The results suggest that varying the type offence from a solid internal fence to ones made of separated bars (new fence) only did not have much impact on the environment inside the piggery. When this change was combined with the other variation such as lowering the outer walls it made some improvements. Combining the new fence, lowering the outer walls and changing the shape of the roof resulted in the highest increase in the air speed of about 0.2-0.4 m/s at the pigs’ level in comparison to the original design. Unfortunately this reduction was not large enough to bring temperature and air speed to the thermal comfort of these pigs at that climate; however this improvement would be sufficient in a milder climate. It was concluded that water sprayers are needed in this hot climate to meet the pigs’ thermal comfort limit. The addition of sprayers has been investigated and results show that a large portion of the piggery with the sprayers meets the thermal comfort of the pigs at this age. However, optimisation of the location of the sprayers and the amount of water to be used in the sprayers is recommended for future study so an economical watering system is obtained.

Analysis of the Essential Oils of Coriandrum sativum Using GC-MS Coupled with Chemometric Resolution Methods

The essential oils extracted from Coriandrum sativum L. were analyzed by GC-MS coupled with chemometric resolution methods. Through the chemometric resolution methods, peak clusters were uniquely resolved into the pure chromatographic profiles and mass spectra of each component. Qualitative analysis was performed by comparing the pure mass spectra with those in the NIST 05 mass spectral library. Quantitative analysis was performed using the total volume integration method. A total of 118 constituents were detected, of which 104 were identified, accounting for 97.27% of the total content. The results indicate that GC-MS combined with chemometric resolution methods can greatly enhance the capability of separation and the reliability of qualitative and quantitative results. The combined method is an economical and accurate approach for the rapid analysis of the complex essential oil samples in Coriandrum sativum L.

A Modified Formulation of the Volume Integral Equations Method for 3-D Magnetostatics

A magnetization-based formulation of the volume integral equations method for 3-D magnetostatics is discussed. The magnetization of each element is related, via the constitutive law of the material, to the average magnetic flux density within the element rather than to the value at the center as is usually done. This assumption leads to more accurate distribution of magnetization and allows a faster convergence of the solution. Moreover, it leads to more symmetric matrix of the coefficients and reduces the numerical instability due to looping patterns of magnetization, which is inherent to integral methods. The formulation is made effective by the use of a hybrid numerical and analytical approach, which allows for the fast and accurate calculation of the coefficients. The proposed model is validated and compared with the usual model both for saturable and linear material with high susceptibility.

Determination of Essential Oil Composition from Osmanthus fragrans Tea by GC-MS Combined with a Chemometric Resolution Method

The essential oils of the Osmanthus fragrans tea (OFT), Osmanthus fragrans (OF) and green tea (GT) had been extracted by steam distillation and analyzed by gas chromatography-mass spectrometry (GC-MS) with the help of heuristic evolving latent projections (HELP), an effective chemometric resolution method (CRM). The overlapping peak clusters were resolved into pure chromatograms and pure mass spectra with HELP. The qualitative analysis was performed by similarity searches in the National Institute of Standards and Technology (NIST) mass spectra database with the obtained pure mass spectrum of each component. Identification of some compounds was also assisted by comparison of temperature-programmed retention indices (PTRI) with authentic standards included in our own laboratory database under construction. The quantitative results were obtained by overall volume integration (OVI) method. A total of 67, 73 and 53 components in essential oils of the OFT, OF and GT were identified, accounting for 90.83%, 93.65% and 89.97% total contents of the essential oil of OFT, OF and GT, respectively.

Effect of Aerosol Generation Method on Measured Saturation Pressure and Enthalpy of Vaporization for Dicarboxylic Acid Aerosols

To date, most studies of the thermodynamic properties of organic aerosols have utilized test aerosols generated by spray atomization followed by a diffusion drying step. Some evidence points to possible biases in measured thermodynamic properties stemming from the presence of residual solvent (water or alcohol) in the dried aerosol. In the current study we compared measurements of thermodynamic properties of organic aerosols generated by atomization of aqueous solutions to those generated by homogeneous condensation using a modified Sinclair-La Mer generator. In particular, using the Integrated Volume Method (Saleh et al. 2008), we measured and compared the saturation pressure (P sat ) at 298 K and enthalpy of vaporization (ΔH) of C-6 (adipic) and C-9 (azelaic) dicarboxylic acid aerosol generated using these techniques. We found that P sat and ΔH exhibited no statistically significant difference across the tested aerosol generation methods, indicating that any residual solvent carried by the particles had no impact on the measurements. For adipic acid, we obtained P sat of 3.3 × 10−5 (±0.9 × 10−5) Pa and ΔH of 132 (±8) kJ/mol with atomization, and P sat of 4.2 × 10− 5 (±2.2 × 10−5) Pa and ΔH of 126 (±21) kJ/mol with homogeneous condensation; for azelaic acid, we obtained P sat of 1.4 × 10−5 (±0.5 × 10−5) Pa and ΔH of 145 (±15) kJ/mol with atomization, and P sat of 0.9 × 10− 5 (±0.3 × 10− 5) Pa and ΔH of 158 (±17) kJ/mol with homogeneous condensation. In addition, SEM images of the acids generated by the two methods showed no obvious difference in surface morphology.

Diffraction and external reflection by dielectric faceted particles

The scattering of light by dielectric particles much larger than the wavelength of incident light is attributed to diffraction, external reflection and outgoing refracted waves. This paper focuses on diffraction and external reflection by faceted particles, which can be calculated semi-analytically based on physical optics. Three approximate methods; the surface-integral method (SIM), the volume-integral method (VIM), and the diffraction plus reflection pattern from ray optics (DPR) are compared. Four elements of the amplitude scattering matrix in the SIM and the VIM are presented in an explicit form. Of interest is that diffraction and external reflection are separable in the SIM, whereas they are combined in the VIM. A feature of zero forward reflection is noticed in the SIM. The applicability of the DPR method is restricted to particles with random orientations. In the manner of van de Hulst, we develop a new technique to compute the reflection pattern of randomly oriented convex particles using spheres with the same refractive index, resulting in an improvement in the precision of the reflection calculation in near-forward and near-backward directions. The accuracy of the aforementioned three methods is investigated by comparing their results with those from the discrete-dipole-approximation (DDA) method for hexagonal particles at the refractive index of 1.3+i1.0. For particles with fixed orientations, it is found that the SIM and the VIM are comparable in accuracy and applicable when the size parameter is on the order of 20. The ray-spreading effect on the phase function is evident from the results of various size parameters. For randomly oriented particles, the DPR is more efficient than the SIM and the VIM.

A CELL-VERTEX FINITE VOLUME TIME DOMAIN METHOD FOR ELECTROMAGNETIC SCATTERING

A cell-vertex based flnite volume scheme is used to solve the time-dependent Maxwell's equations and predict electromagnetic scattering from perfectly conducting bodies. The scheme is based on the cell-vertex flnite volume integration method, originally proposed by Ni (1), for solution of the two dimensional unsteady Euler equations of gas dynamics. The resulting solution is second-order accurate in space and time, and requires cell based ∞uctuations to be appropriately distributed to the state vector stored at cell vertices at each time step. Results are presented for two-dimensional canonical shapes and complex three dimensional geometries. Unlike in gas dynamics, no user deflned numerical damping is required in this novel cell-vertex based flnite volume integration scheme when applied to the time-domain Maxwell's equations.

Optimization of the Ventilation System for a Forced Ventilation Piggery

Pigs are subjected to intensive environment control and management in order to achieve higher productivity. This is due to their sensitivity to climatic variation, which strongly affects their growth. This paper reports the design optimization of a forced ventilation piggery using computational fluid dynamics. This numerical investigation determined the effect of varying the number of ventilation openings and their location on the air flow pattern, speed, temperature, power needed, ability to remove heat and residence time. The effect of varying the ventilation rate in a range (0.05 – 0.8 m3/s), and ambient temperatures of 5°C and 32°C was also investigated. The modeled piggery has dimensions 40 m × 15 m × 2.6 m, with central walkway and gable roof with the apex at 3.9 m and is a common design in Australia. A steady-state two-dimensional numerical model based on the integral volume method, including the effects of buoyancy and heat generated by the pigs, was solved using the computational fluid dynamics software “Fluent.” Four designs were investigated and an optimum design, which facilitates better ventilation of the majority of the room, has been identified. In summer, an inlet velocity has been recommended which achieves optimum environment inside the piggery meeting the pigs' thermal comfort criteria with minimum power usage. During winter it became obvious that heating has to be used in all designs to be able to meet the pigs' thermal comfort criteria.

Determination of Activity Coefficients of Semi-Volatile Organic Aerosols Using the Integrated Volume Method

We demonstrate the use of the Integrated Volume Method (IVM) to estimate activity coefficients of semi-volatile organic compounds pertinent to ambient/atmospheric aerosols in binary mixtures. We generate binary solution aerosols with different mole fractions of individual components; for each mixture, we measure total change in aerosol volume upon heating from 25 ○ C to 35 ○ C, with the aerosols being at equilibrium in both states. The change in aerosol volume, or in other words, the partitioning between the particle phase and the gas phase, is used to determine activity coefficients of the compounds as a function of their mole fraction in the mixture. We demonstrate this method using the following four model systems. System 1: adipic acid–pimelic acid, which illustrates polar organic–polar organic interactions. Non-ideal behavior was observed with activity coefficients around three at infinite dilution. System 2: adipic acid–dioctyl sebacate, which illustrates polar organic–non-polar organic interactions...

Errors analysis in the evaluation of particle concentration by PDA on a turbulent two-phase jet: application for cross section and transit time methods

Phase-Doppler anemometry (PDA) is a powerful tool for two-phase flow measurements and testing. Particle concentration and mass flux can also be evaluated using the raw particle data supplied by this technique. The calculation starts from each particle velocity, diameter, transit time data, and the total measurement time. There are two main evaluation strategies. The first one uses the probe volume effective cross section, and it is usually simplified assuming that particles follow quasi one-directional trajectories. In the text, it will be called the cross section method. The second one includes a set of methods which will be denoted as “Generalized Integral Methods” (GIM). Concentration algorithms such as the transit time method (TTM) and the integral volume method (IVM) are particular cases of the GIM. In any case, a previous calibration of the measurement volume geometry is necessary to apply the referred concentration evaluation methods. In this study, concentrations and mass fluxes both evaluated by the cross-section method and the TTM are compared. Experimental data are obtained from a particle-laden jet generated by a convergent nozzle. Errors due to trajectory dispersion, burst splitting, and multi-particle signals are discussed.

Investigation of a Reflective Counter-Propagating Holographic Setup

A reflective counter-propagating holographic setup for optical data storage is presented. The system makes efficient use of the laser light by using the reference beam to generate the signal beam. After passing through the holographic medium, the reference beam is sent onto a spatial light modulator that directs the modified reference beam back into the holographic medium, where it interferes with the original reference beam. Thus 100% of the available laser power can be used for the reference beam. Furthermore, a special random phase mask and a corresponding data page format are introduced. The phase mask has an improved alignment tolerance of ±0.5 pixels in contrast to a conventional binary phase mask that has a tolerance of only ±0.1 pixels. Moreover, the mask still improves the shift-selectivity and eliminates the strong intensity peak in the Fourier plane. We investigate the shift selectivity and compare experimental and simulated results that were obtained with a two-dimensional fast-Fourier-transform (2D-FFT) volume integral method.

Prediction of acoustic radiation from axisymmetric surfaces with arbitrary boundary conditions using the boundary element method on a distributed computing system

This paper presents a computational technique using the boundary element method for prediction of radiated acoustic waves from axisymmetric surfaces with nonaxisymmetric boundary conditions. The aim is to predict the far-field behavior of underwater acoustic transducers based on their measured behavior in the near-field. The technique is valid for all wavenumbers and uses a volume integral method to calculate the singular integrals required by the boundary element formulation. The technique has been implemented on a distributed computing system to take advantage of its parallel nature, which has led to significant reductions in the time required to generate results. Measurement data generated by a pair of free-flooding underwater acoustic transducers encapsulated in a polyurethane polymer have been used to validate the technique against experiment. The dimensions of the outer surface of the transducers (including the polymer coating) were an outer diameter of 98 mm with an 18 mm wall thickness and a length of 92 mm. The transducers were mounted coaxially, giving an overall length of 185 mm. The cylinders had resonance frequencies at 13.9 and 27.5 kHz, and the data were gathered at these frequencies.

혼합 체적-경계 적분방정식법을 이용한, 함유체와 공동을 포함한 반무한 고체에서의 탄성해석

A mixed volume and boundary integral equation method (Mixed VIEM-BIEM) is used to calculate the plane elastostatic field in an isotropic elastic half-plane containing an isotropic or anisotropic inclusion and a void subject to remote loading parallel to the traction-free boundary. A detailed analysis of stress field at the interface between the isotropic matrix and the isotropic or orthotropic inclusion is carried out for different values of the distance between the center of the inclusion and the traction-free surface boundary in an isotropic elastic half-plane containing three different geometries of an isotropic or orthotropic inclusion and a void. The method is shown to be very accurate and effective for investigating the local stresses in an isotropic elastic half-plane containing multiple isotropic or anisotropic inclusions and multiple voids.

Aerodynamic Noise Prediction Using stochastic Turbulence Modeling

Amongst many approaches to determine the sound propagated from turbulent flows, hybrid methods, in which the turbulent noise source field is computed or modeled separately from the far field calculation, are frequently used. For basic estimation of sound propagation, less computationally intensive methods can be developed using stochastic models of the turbulent fluctuations (turbulent noise source field). A simple and easy to use stochastic model for generating turbulent velocity fluctuations called continuous filter white noise (CFWN) model was used. This method based on the use of classical Langevian-equation to model the details of fluctuating field superimposed on averaged computed quantities. The resulting sound field due to the generated unsteady flow field was evaluated using Lighthill's acoustic analogy. Volume integral method used for evaluating the acoustic analogy. This formulation presents an advantage, as it confers the possibility to determine separately the contribution of the different integral terms and also integration regions to the radiated acoustic pressure. Our results validated by comparing the directivity and the overall sound pressure level (OSPL) magnitudes with the available experimental results. Numerical results showed reasonable agreement with the experiments, both in maximum directivity and magnitude of the OSPL. This method presents a very suitable tool for the noise calculation of different engineering problems in early stages of the design process where rough estimates using cheaper methods are needed for different geometries.

Determination of saturation pressure and enthalpy of vaporization of semi-volatile aerosols: The integrated volume method

This study presents the integrated volume method for estimating saturation pressure and enthalpy of vaporization of a whole aerosol distribution. We measure the change of total volume of an aerosol distribution between a reference state and several heated states, with the heating performed in a thermodenuder. In both the reference and heated states, the aerosol should be at equilibrium: that is, the surrounding gas phase should be saturated with the vapor of the aerosol species. We derive an expression that correlates the volume change to the inverse of temperature from which the saturation pressure and enthalpy of vaporization can be estimated. Transport and aerosol dynamics computational models are developed to investigate the two conditions for this analysis to be valid: (1) the aerosol should be at equilibrium at the exit of the thermodenuder and (2) there should be no re-condensation or further evaporation downstream of the thermodenuder. The method is validated with lab generated adipic acid and pimelic acid aerosol. We obtained saturation pressure at 298 K and enthalpy of vaporization of 3.4 × 10 - 5 ( ± 1.2 × 10 - 5 ) Pa and 135 ( ± 13 ) kJ / mol for adipic acid, and 7.2 × 10 - 5 ( ± 1.7 × 10 - 5 ) Pa and 149 ( ± 10 ) kJ / mol for pimelic acid, which are in good agreement with the values reported in the literature.

New discretisation scheme based on splines for volume integral method

PurposeA numerical model dedicated to external eddy current inspection of tubes has been developed using the volume integral method (VIM). The purpose of this paper is to suggest new discretization schemes based on non‐uniform B‐splines for the solution of the state equation with the method of moments (MoM).Design/methodology/approachVIM is a semi‐analytical approach providing fast and accurate results for the simulation of eddy current testing (ECT) of pieces with canonical geometries. The state equation derived with this formalism is solved using the Galerkin variant of the well‐known MoM.FindingsThis paper shows that an accuracy improvement is achieved in MoM by using B‐splines with degree 1 or 2 as projection functions in MoM instead of pulse functions. Moreover, comparisons between simulation results show that, for all ECT configurations tested, the use of degree 1 B‐splines is sufficient to get this improvement.Originality/valueThe use of B‐splines functions has already been proposed for MoM in the literature, but not in the framework of the Galerkin variant of MoM. This paper also shows quantitative comparisons between experiment and simulation as well as a study of the minimal degree required to get an accuracy improvement in MoM.

Hybridization of volumetric and surface models for the computation of the T/R EC probe response due to a thin opening flaw

PurposeThe purpose of this paper is to describe the development of simulation tools dedicated to eddy current non destructive testing (ECNDT) on planar structures implying planar defects. Two integral approaches using the Green dyadic formalism are considered.Design/methodology/approachThe surface integral model (SIM) is dedicated to ideal cracks, whereas the volume integral method is adapted to general volumetric defects.FindingsThe authors observed that SIM provides satisfactory results, except in some critical transmitting/receiving (T/R) configurations. This led us to propose a hybrid method based on the combination of the two previous ones.Originality/valueThis method enables to simulate ECNDT on planar structures implying defects with a small opening using T/R probes.