Three-dimensional Phenomena Research Articles

3D Electromagnetic Field Analysis Applied to Evaluate the Accuracy of a Voltage Transformer under Distorted Voltage

Voltage transformers (VTs) are an important element of the measuring system that allows measuring the energy flow in medium and high voltage networks. Additional problems with the accuracy of the measurement introduced by the appearance of sources and nonlinear receivers cause deformation of the voltage shape in the energy system. Due to the high metrological requirements, the design of voltage transformers requires high accuracy (for class 0.2 ΔU ≤ 0.2, phase displacement ≤10 min), which is not possible with the use of analytical methods using approximate models. Therefore, only the application of numerical modeling by the finite element method, taking into account real three-dimensional phenomena, allows achieving high modeling accuracy. The article concerns the phenomenon of the influence of voltage higher harmonics of supply voltage on the accuracy (up to the 100th harmonic) of the measuring inductive voltage transformer (IVT). The applied modeling method takes into account the phenomena in the transformer core and the circuit equations resulting from the winding arrangement, which allows for the study of the deformation voltage transformation. Experimental tests on a real model to evaluate the method used were necessary. The article presents simulations for a model transformer, and results have been confirmed by experimental tests.

Inverse mechano-electrical reconstruction of cardiac excitation wave patterns from mechanical deformation using deep learning.

The inverse mechano-electrical problem in cardiac electrophysiology is the attempt to reconstruct electrical excitation or action potential wave patterns from the heart's mechanical deformation that occurs in response to electrical excitation. Because heart muscle cells contract upon electrical excitation due to the excitation-contraction coupling mechanism, the resulting deformation of the heart should reflect macroscopic action potential wave phenomena. However, whether the relationship between macroscopic electrical and mechanical phenomena is well-defined and unique enough to be utilized for an inverse imaging technique in which mechanical activation mapping is used as a surrogate for electrical mapping has yet to be determined. Here, we provide a numerical proof-of-principle that deep learning can be used to solve the inverse mechano-electrical problem in phenomenological two- and three-dimensional computer simulations of the contracting heart wall, or in elastic excitable media, with muscle fiber anisotropy. We trained a convolutional autoencoder neural network to learn the complex relationship between electrical excitation, active stress, and tissue deformation during both focal or reentrant chaotic wave activity and, consequently, used the network to successfully estimate or reconstruct electrical excitation wave patterns from mechanical deformation in sheets and bulk-shaped tissues, even in the presence of noise and at low spatial resolutions. We demonstrate that even complicated three-dimensional electrical excitation wave phenomena, such as scroll waves and their vortex filaments, can be computed with very high reconstruction accuracies of about 95% from mechanical deformation using autoencoder neural networks, and we provide a comparison with results that were obtained previously with a physics- or knowledge-based approach.

Rotating flows regarded as point-mechanical motions in the complex domain

It is shown that a large class of rotating disks flows described by an exact solution of the Navier–Stokes equations can be mapped on the mechanical motion of a point mass in the complex domain. The mathematical procedure, the physical features and the advantages of the point-mechanical approach are presented for von Kármán’s classical swirling flow and its magneto-hydrodynamic counterpart in detail. Further applications to axisymmetric flows are also addressed shortly. There turns out that the energy balance equation of the analogous particle motion, the corresponding Galilei formula and other familiar concepts of the point-mechanics, can serve as useful tools in the description of several viscous flows. It is achieved thus that mechanics of rotating flows can be interpreted from the mechanics of a point mass. At the same time the approach illustrates how three-dimensional phenomena can be connected to one-dimensional ones in the complex domain.

Coordinate transformation of three-dimensional image in integral imaging system illuminated by a point light source

The point light source is an important kind of directional light source. By using directional illumination, the performances of the integral imaging system will be enhanced. In this paper, the coordinate transformation characteristics of integral imaging systems illuminated by a point light source have been explored in detail. By using a dynamic point light source such as a moving light emitting diode to illuminate the imaging system, the position and size of the rendered three-dimensional image can be transformed in real time without updating the elemental images, and the depth of field of the imaging system is doubled. The coordinates of the three-dimensional image are changed with the distance between the point light source and the micro-lens array. The optical mechanism of the three-dimensional dynamic imaging phenomenon is analyzed. The coordinate transformation rules of the three-dimensional image are deduced and verified by experiments. The phenomenon may find potential applications in interactively three-dimensional display or augmented reality system.

3D thermal hydraulic characteristics analysis of pool-type upper plenum for lead-cooled fast reactor with multi-scale coupling program

The large space plenum of the lead-cooled reactor has complex three-dimensional thermal hydraulic phenomena such as thermal stratification and coolant mixing, which affects the safety performance of the reactor. In this paper, based on the multi-scale coupling program ATHLET-OpenFOAM, three-dimensional simulation of the hot pool for lead-cooled fast reactor M2LFR-1000 is carried out. Considering the axis symmetry of the hot pool model and reducing the amount of calculation, 1/8 model of the hot pool is selected to build the model by CFD, and the rest is simulated by system program ATHLET. The steady-state operation condition is first calculated by coupling program. Based on the calculation of steady-state condition, the main thermal parameters of M2LFR-1000 primary coolant system and the complex three-dimensional phenomena of the upper plenum under unprotected loss of flow accident (ULOF) are studied, and the results of multi-scale coupling calculation are compared with those of ATHLET alone. The results show that there is an obvious thermal stratification in the inner region and the outer region of the upper plenum in the early period of the accident, which slows down the speed of establishing natural circulation. During ULOF accident, there are obvious vortex flow changes in the inlet outer side and the outlet area of the upper plenum.

Three-dimensional Heisenberg critical phenomena in La0.6Bi0.1Sr0.3−xCaxMn0.9Cu0.1O3 manganites (x = 0 and 0.05)

In this paper, our main objective is to study the effect of Ca doping on the critical properties of La0.6Bi0.1Sr0.3−xCaxMn0.9Cu0.1O3 (x = 0 and 0.05). The X-ray diffraction analysis reveal that both specimens are indexed in the rhombohedral structure with R–3c space group. As for the magnetic studies, a second-order ferromagnetic–paramagnetic (FM–PM) phase transition takes place around the transition temperature (TC). Based on different methods such as extrapolation of the Arrott curve, Kouvel-Fisher procedure and critical isothermal analysis depending on the data from magnetic investigations, the examination of the critical behavior was performed. The values of the deduced critical exponent (β, γ, δ) for both compounds proved to be close to those predicted by Heisenberg's 3D model, revealing an inhomogeneous magnetic exchange coupling at short distances. These critical exponents show a good agreement with their corresponding values proven by Widom's law of scale, as well as the theory of scale. Additionally, a typical soft FM behavior with a low coercive field was observed at 10 K according to the hysteresis loops. These outcomes make our compounds good candidates for memory devices and magnetic recording.

Universal scaling laws rule explosive growth in human cancers.

Most physical and other natural systems are complex entities composed of a large number of interacting individual elements. It is a surprising fact that they often obey the so-called scaling laws relating an observable quantity with a measure of the size of the system. Here we describe the discovery of universal superlinear metabolic scaling laws in human cancers. This dependence underpins increasing tumour aggressiveness, due to evolutionary dynamics, which leads to an explosive growth as the disease progresses. We validated this dynamic using longitudinal volumetric data of different histologies from large cohorts of cancer patients. To explain our observations we put forward increasingly-complex biologically-inspired mathematical models that captured the key processes governing tumor growth. Our models predicted that the emergence of superlinear allometric scaling laws is an inherently three-dimensional phenomenon. Moreover, the scaling laws thereby identified allowed us to define a set of metabolic metrics with prognostic value, thus providing added clinical utility to the base findings.

Convective flow speed of particles in a vibrated powder bed

When a powder bed is vibrated, the particles may move like a fluid, and various flow patterns and surface shapes can exist, depending on the vibration conditions — particularly the frequency and amplitude. A two-dimensional (2D) bed is often used so that the flow pattern in a vibrated powder bed can be directly visualized. Because three-dimensional (3D) fluidization phenomena are complicated, 2D observation is not sufficient. However, it is difficult to observe the internal flow of a 3D fluidized bed. A unique method for doing this is positron emission particle tracking (PEPT), a technique derived from the same physical phenomena as in positron emission tomography (PET). In the most common version of the PEPT technique, the flow in a bed is analyzed by following the behavior of a single radioactively labeled particle. We adopted the PEPT technique to analyze flow patterns in a cylindrical vibrated powder bed. From the particle trajectory data obtained with PEPT, some characteristic internal flow structures that cannot be understood from observing surface particle motion were successfully obtained. However, it is difficult to clarify the detailed mechanisms driving such flow patterns from experimental data alone. Therefore, we also carried out numerical simulations based on the discrete element method (DEM). Because the DEM is a Lagrangian method, its computational time depends on the number of particles, so that simulations were restricted to 2D. In order to compare the simulated results to the experimental ones, the average speeds of particles were obtained. Consequently, it was found that the simulated average speed of particles depends only on the amplitude of the applied vibration. In general, good agreement between simulated and experimental results was obtained, but agreement became poorer under conditions of high frequency and low vibration strength.

Study on the atmospheric pressure homogeneous discharge in air assisted with a floating carbon fibre microelectrode

Based on the consideration of increasing the number of initial electrons and providing an appropriate distribution of electric field strength for discharge space, a method of adopting the wire-cylindrical type electrode structure with a floating carbon fibre electrode to achieve atmospheric pressure homogeneous discharge (APHD) in air is proposed in this paper. Studies of the electrode characteristics show that this structure can make full use of the microdischarge process of the carbon fibre microelectrode and the good discharge effect of the helical electrode to provide plenty of initial electrons for the discharge space. Besides, the non-uniform electric field distribution with gradual change leads to the slow growth of electron avalanches in this structure. Thus, the initial discharge voltage can be reduced and the formation of filamentary discharge channels can be inhibited, which provides theoretical possibilities for the homogeneous discharge in atmospheric air. Experiments show that a three-dimensional uniform discharge phenomenon can be realized under a 6.0 kV applied voltage in a PFA tube of 6 mm inner diameter, displaying good uniformity and large scale.

Special-purpose computer for digital holographic high-speed three-dimensional imaging

Digital holography is attracting attention because it can record instantaneous three-dimensional (3D) information and record dynamic phenomena. However, when recording high-speed phenomena, the frame rate ranges from tens of thousands to hundreds of millions, and the calculation time of the reconstructed images is a problem. We have developed a special-purpose computer for high-speed 3D imaging using digital holography. The developed special-purpose computer has four calculation modules and has achieved a calculation time 68 times faster than that of a personal computer with 48 cores. With the developed computer, a total of 32 reconstructed images can be calculated in 0.69 ms from four holograms of 128 × 128 pixels with eight varying depths.

Physics-based model of wildfire propagation towards faster-than-real-time simulations

This paper presents the mathematical formulation, numerical solution, calibration and testing of a physics-based model of wildfire propagation aimed at faster-than-real-time simulations. Despite a number of simplifying assumptions, the model is comprehensive enough to capture the major phenomena that govern the behaviour of a real fire — namely the pyrolysation of wood; the combustion of a mono-phase medium composed of premixed gas of fuel and air; and the heat transferred by conduction, convection, radiation, mass diffusion and transport due to atmospheric wind. The model consists of a system of coupled partial differential equations, one ensuring the balance of enthalpy, and a set of equations representing the mass formation of each chemical species involved in the combustion. Dimensionality reduction is sought by modelling these three-dimensional phenomena in a two-dimensional space, which has been achieved by means of heat-sources and heat-sinks to account for the third dimension in the energy balance equation. Once calibrated with a widely used non-physics-based commercial wildfire simulator, the proposed FirePropagation Model for Fast simulations (FireProM-F) is tested, returning similar predictions in terms of the size and shape of the burnt area although similarity deteriorates for windy conditions. FireProM-F has the added benefit of being both physics-based and computationally inexpensive so that its interaction with fire suppressants may also be modelled in the future and simulated in real time.

Leading-Edge Vortex as a High-Lift Mechanism for Large-Aspect-Ratio Wings

Enabling a leading-edge vortex (LEV) is a possible mechanism to significantly increase the lift on wings. This is well known for slender delta wings, for which various analytical models were developed and show accurate predictions of the lift enhancement. This paper shows that, when suitably designing the wing planform, LEVs can also exist on high-aspect-ratio (high-AR) wings. In this study, a quasi-three-dimensional flow model is presented for solving the stationary LEV phenomenon over a high-AR swept back wing, with sweep increasing toward the wingtip. Our model captures the three-dimensional phenomenon by satisfying conservation of mass and vorticity within the LEV, and using a combination of strip theory and the lifting-line theory. Our model predictions are compared with flow visualization data on a parabolic swept back wing. Results confirm that suitable sweep wing geometry can fix an LEV steadily over the upper wing surface, resulting in significant lift enhancement of up to 70%.

Numerical prediction of a single phase Pressurized Thermal Shock scenario for crack assessment in an Reactor Pressure Vessel wall

A pressurized thermal shock (PTS) in a reactor pressure vessel (RPV) wall of a Pressurized Water Reactor (PWR) could eventually lead to reduced integrity of the RPV. A PTS scenario may be initiated by a Loss-of-Coolant Accident (LOCA) in which the Emergency Core Cooling (ECC) injection causes a thermal shock in the vessel wall while the RPV is still partially pressurized. The traditional Thermal-Hydraulic system codes fail to reliably predict the complex three-dimensional thermal mixing phenomena in the downcomer occurring during the ECC injection. Therefore, a three-dimensional computational fluid dynamics (CFD) simulation of the transient is required to provide an accurate temperature distribution for reliable probabilistic analyses. The assessment of the failure probability due to a single phase PTS initiated by postulated defects in the vessel wall requires the computation of a long transient solution. Since the CFD calculation is computationally expensive, the symmetry of a four-leg PWR geometry is utilized to reduce the computational domain.In the present work, several Unsteady Reynolds Averaged Navier-Stokes (URANS) CFD simulations are performed to select an optimal computational domain that is representative for a typical PWR. The computed temperature distribution is provided as input for the structural analyses to calculate the Stress Intensity Factor (SIF) along several postulated defects. The SIF is then used to evaluate the potential of crack propagation initiation of the defects.

Modeling nonlinear site effects in physics-based ground motion simulations of the 2010–2011 Canterbury earthquake sequence

This study examines the performance of nonlinear total stress one-dimensional (1D) wave propagation site response analysis for modeling site effects in physics-based ground motion simulations of the 2010–2011 Canterbury, New Zealand earthquake sequence. This approach explicitly models three-dimensional (3D) ground motion phenomena at the regional scale, and detailed site effects at the local scale. The approach is compared with a more commonly used empirical VS30-based method of computing site amplification for simulated ground motions, as well as prediction via an empirical ground motion model. Site-specific ground response analysis is performed at 20 strong motion stations in Christchurch for 11 earthquakes with 4.7≤ MW≤7.1. When compared with the VS30-based approach, the wave propagation analysis reduces both overall model bias and uncertainty in site-to-site residuals at the fundamental period, and significantly reduces systematic residuals for soft or “atypical” sites that exhibit strong site amplification. The comparable performance in ground motion prediction between the physics-based simulation method and empirical ground motion models suggests the former is a viable approach for generating site-specific ground motions for geotechnical and structural response history analyses.

A Non-Tuned Machine Learning Technique for Abutment Scour Depth in Clear Water Condition

Abutment scour is a complex three-dimensional phenomenon, which is one of the leading causes of marine structure damage. Structural integrity is potentially attainable through the precise estimation of local scour depth. Due to the high complexity of scouring hydrodynamics, existing regression-based relations cannot make accurate predictions. Therefore, this study presented a novel expansion of extreme learning machines (ELM) to predict abutment scour depth (ds) in clear water conditions. The model was built using the relative flow depth (h/L), excess abutment Froude number (Fe), abutment shape factor (Ks), and relative sediment size (d50/L). A wide range of experimental samples was collected from the literature, and data was utilized to develop the ELM model. The ELM model reliability was evaluated based on the estimation results and several statistical indices. According to the results, the sigmoid activation function (correlation coefficient, R = 0.97; root mean square error, RMSE = 0.162; mean absolute percentage error, MAPE = 7.69; and scatter index, SI = 0.088) performed the best compared with the hard limit, triangular bias, radial basis, and sine activation functions. Eleven input combinations were considered to investigate the impact of each dimensionless variable on the abutment scour depth. It was found that ds/L = f (Fe, h/L, d50/L, Ks) was the best ELM model, indicating that the dimensional analysis of the original data properly reflected the underlying physics of the problem. Also, the absence of one variable from this input combination resulted in a significant accuracy reduction. The results also demonstrated that the proposed ELM model significantly outperformed the regression-based equations derived from the literature. The ELM model presented a fundamental equation for abutment scours depth prediction. Based on the simulation results, it appeared the ELM model could be used effectively in practical engineering applications of predicting abutment scour depth. The estimated uncertainty of the developed ELM model was calculated and compared with the conventional and artificial intelligence-based models. The lowest uncertainty with a value of ±0.026 was found in the proposed model in comparison with ±0.50 as the best uncertainty of the other models.

Large-scale simulation of gasification reaction with mass transfer for metallurgical coke: Model development

Large-scale simulation of gasification for a highly resolved coke model with hundreds of millions of voxels was carried out. Three-dimensional phenomena could be evaluated by the numerical simulation, while our previous study was limited to one-dimensional distribution due to the high computational load. The coke model was developed from micro X-ray CT images of a cylindrical coke sample with a radius of 20 mm, and the screen resolution was 20.6 µm/pixel. In the resolved pores, the mass transfer with CO2 gasification was analyzed, whereas voxels of the coke matrix adjacent to the pore vanished due to the reaction. Coke was found to degrade non-uniformly as the reaction progressed, and the areas with highly concentrated carbon matrix voxels remained unchanged. These characteristic areas were derived from the X-ray CT images. Focusing on the concentration distribution of CO2, it was found that the rate-controlling step changed from pore diffusion to chemical reaction with structural change at 1573 K.

Simulation of three-dimensional chemical dissolution of limestone

The development of prediction techniques for the evolution of karstic caves is essential for geohazard prevention because limestone collapse commonly accompanies their complex dissolution process. Previous studies to understand the dissolution mechanisms focus on field-based and/or small-scale experimental approaches. Although several large-scale numerical simulations have been conducted due to improved computing capabilities, mathematical modelling and numerical simulation for the three-dimensional dissolution of limestone remains unavailable. In this study, we examine the three-dimensional dissolution phenomenon of calcium carbonate in limestone and propose mathematical and numerical models based on an advection, reaction, and diffusion system involving Darcy’s law. Additionally, we implement the models using a finite difference method involving the constrained interpolation profile with conservative semi-Lagrangian scheme, and dissolution patterns of the calcium carbonates obtained by the proposed model are presented. The simulation demonstrates that the dissolution of calcium carbonate is strongly related to the groundwater flow, with increasing pores and cavities toward the groundwater flow direction, and the dissolution rate depends on the contact area between the groundwater and limestone.

THREE-DIMENSIONAL NATURAL CONVECTION PHENOMENA AROUND A UNIFORMLY HEATED CUBICAL BODY LOCATED AT THE CENTER OF A SPHERICAL ENCLOSURE

THREE-DIMENSIONAL NATURAL CONVECTION PHENOMENA AROUND A UNIFORMLY HEATED CUBICAL BODY LOCATED AT THE CENTER OF A SPHERICAL ENCLOSURE

Using Pixel-Based Microscope Images to Generate 3D Reconstructions of Frozen and Thawed Plant Tissue.

Histological analysis of frozen and thawed plants has been conducted for many years but the observation of individual sections only provides a two-dimensional representation of a three-dimensional phenomenon. Currently available optical sectioning techniques for viewing internal structures in three dimensions are either low in resolution or the instrument cannot penetrate deep enough into the tissue to visualize the whole plant. Methods using higher resolution equipment are expensive and often require time-consuming training. In addition, conventional stains cannot be used for optical sectioning techniques. We present a relatively simple and less expensive technique using pixel-based (JPEG) images of conventionally stained histological sections of an Arabidopsis thaliana plant. The technique uses commercially available software to generate a 3D representation of internal structures.

Characterization of temperature-dependent fluid properties in compressible viscous fluid flow induced by oscillation of disk

Abstract Time-dependent compressible flow of viscous fluid with temperature dependent density, thermal conductivity and viscosity is considered. The motion in fluid is generated due to periodic oscillations of rotating disk. The normalized system of partial differential equations is achieved by adopting similarity transformations. The obtained system is then solved numerically using Successive over Relaxation (SOR) method and finite difference schemes. The local similar solutions are presented. One-dimensional graphs, two-dimensional contours and three-dimensional flow phenomenon are drawn graphically. Tabular description of various physical parameters is also presented.