Three-dimensional Numerical Code Research Articles

Dust growth and pebble formation in the initial stages of protoplanetary disk evolution

Aims. The initial stages of planet formation may start concurrently with the formation of a gas-dust protoplanetary disk. This makes the study of the earliest stages of protoplanetary disk formation crucially important. Here we focus on dust growth and pebble formation in a protoplanetary disk that is still accreting from a parental cloud core. Methods. We have developed an original three-dimensional numerical hydrodynamics code, which computes the collapse of rotating clouds and disk formation on nested meshes using a novel hybrid Coarray Fortran-OpenMP approach for distributed and shared memory parallelization. Dust dynamics and growth are also included in the simulations. Results. We found that the dust growth from ~1 µm to 1–10 mm already occurs in the initial few thousand years of disk evolution but the Stokes number hardly exceeds 0.1 because of higher disk densities and temperatures compared to the minimum mass Solar nebular. The ratio of the dust-to-gas vertical scale heights remains rather modest, 0.2–0.5, which may be explained by the perturbing action of spiral arms that develop in the disk soon after its formation. The dust-to-gas mass ratio in the disk midplane is highly nonhomogeneous throughout the disk extent and is in general enhanced by a factor of several compared to the fiducial 1:100 value. Low St hinders strong dust accumulation in the spiral arms compared to the rest of the disk and the nonsteady nature of the spirals is also an obstacle. The spatial distribution of pebbles in the disk midplane exhibits a highly nonhomogeneous and patchy character. The total mass of pebbles in the disk increases with time and reaches a few tens of Earth masses after a few tens of thousand years of disk evolution. Conclusions. We found that protoplanetary disks with an age ≤20 kyr can possess notable amounts of pebbles and feature dust-togas density enhancements in the disk midplane. Hence, these young disks can already be ripe for the planet formation process to start. Multidimensional numerical models of disk formation that consider the coevolution of gas and dust including dust growth are important to improve our understanding of planet formation.

Numerical Analysis of the Flow Structure around Inclined Solid Cylinder and Its Effect on Bed Shear Stress Distribution

The flow-inclined cylinder interaction is an application area in the industry (i.e., offshore wind turbines and pile-supported near-shore structures). Findings of recent studies have revealed the significance of eco-friendly coastal structures that needs the utilization of inclined cylinder. The primary purpose of this study was to better understand the influence of inclination on flow, turbulence, and bed shear stress character. To achieve this objective, a three-dimensional numerical code (the Reynolds-averaged Navier-Stokes model) was used. The numerical model was calibrated based on eleven velocity profiles obtained by point measurements data of the wake region of the inclined cylinder. The mean flow, turbulence, and secondary flow characteristics around the bodies were extensively investigated, particularly at points where experimental measurements are inapplicable with intrusive turbulence measurement devices. The findings of the study revealed that as the inclination of the cylinder increased, the coherent structures that largely control the flow dynamics in the wake zone became stable rather than cyclical. Specifically, it was determined that although vorticity couples underpinned the flow field behind the vertical cylinder, large-scale streamwise vortices replaced the visible coherent structures when the cylinders were inclined (LSCSVs). When the cylinder inclined 42 degrees, the reduction in amplification factor (τ0 / τ∞) over the bed was roughly fifty percent in terms of quantity. This finding shows that inclination is a streamlined form for a cylinder and may reduce the collapse risk due to scour.

Theoretical Study of Intermixing in Au/Si System under Swift Heavy Ion Irradiation

Abstract: The behavior of the metallic multilayer Au100Å/Si100Å/Si under swift heavy ion irradiation has been studied within the inelastic thermal spike model. Gold has been chosen due to its insensitivity to irradiation. The heat transport in the electronic and lattice subsystem has been simulated using a three-dimensional numerical code that includes the energy transfer between the layers in a direction perpendicular to layer surfaces. The simulations have been done for four kinds of ions Pb, Xe, Kr, and Ar, at a specific energy of 3Mev/amu in order to study the influence of the electronic stopping power on the intermixing process. The results show that for Pb, Xe, and Kr, intermixing at the interface of Au/Si has been obtained. However, no mixing has been observed with Ar. Furthermore, the value of the interdiffusion coefficient for Au has been estimated to be approximately 11x10-4 cm2 s-1, which is characteristic of the liquid phase and, thus, supports the thermal spike model of mixing. For comparison, similar thermal spike simulations have been applied to Ti100Å/Si100Å/Si under the same irradiation conditions. We have found that Ti, which is a sensitive material, exhibits considerable intermixing with Si during Pb, Xe, and Kr irradiation. Whereas, a weak intermixing has been found after Ar irradiation; this is completely different from what has been observed in the Au/Si system. Keywords: Irradiation, Swift heavy ions, Thermal spike model, Ion beam mixing. PACS: 61.80.Az, 61.80.Jh, 61.80.LJ.

MATHEMATICAL MODELING OF UNSTATIONARY AIR POLLUTION PROCESS

Problem statement. The task of determining the dynamics of air pollution in the working room when air containing a chemically hazardous substance flows into it is considered. The peculiarity of this problem is that the formation of pollution areas in the room is influenced by many factors, especially the internal geometry (the presence of technological equipment in the room, furniture, etc.). Therefore, it is necessary to have specialized mathematical models that allow predicting the level of chemical air pollution in the room for a given type of pollution. The purpose of the article. Development of a three-dimensional numerical model for indoor air flow aerodynamics and mass transfer of a chemically hazardous substance entering the room through the ventilation system to predict the risk of toxic damage to workers. Methodology. A three-dimensional equation of convective-diffusion transport for a chemically hazardous substance is used to model the process of a chemically hazardous substance spread in the working room air. The air flow velocity field in the working room is calculated on the basis of the model for the incompressible fluid potential motion. For the numerical integration of the Laplace equation for the velocity potential, two finite-difference schemes are used. The splitting method and finite-difference schemes are used for the numerical integration of the three-dimensional mass transfer equation of the impurity. At each splitting step, the determination of the unknown concentration of the impurity is carried out according to an explicit formula. A computer code was created to conduct computational experiments based on the developed numerical model. Scientific novelty. A three-dimensional numerical model has been developed to analyse the dynamics of the formation of chemical air pollution areas in workplaces when impurities enter the premises through the ventilation system. A feature of the model is the consideration of the main physical factors affecting the formation of pollution areas and the calculation speed. Practical value. The numerical model and the computer code developed on its basis allow solving specific problems that arise when assessing the risk of toxic damage to workers at chemically hazardous facilities. Conclusions. An effective three-dimensional numerical model and computer code have been created, which allow predicting the level of chemical contamination of working premises when a toxic substance enters the premises through the ventilation system. The results of the computational experiment are presented.

Numerical and experimental study of natural convection heat transfer on flat and corrugated plates

PurposeThe purpose of this study is to numerically and experimentally investigate the natural convection heat transfer in flat plates and plates with square, trapezoidal and triangular corrugations.Design/methodology/approachThis work is an extension of the previous studies by Verderio et al. (2021a, 2021b, 2021c, 2021d, 2022a). An experimental apparatus was built to measure the plates’ temperatures during the natural convection cooling process. Several physical parameters were evaluated through the experimental methodology. Free and open-source computational tools were used to simulate the experimental conditions and to quantitatively and qualitatively evaluate the thermal plume characteristics over the plates.FindingsThe numerical results were experimentally validated with reasonable accuracy in the range of studied for the different plates. Empirical correlations of , and , with good accuracy and statistical representativeness, were obtained for the studied geometries. The convective thermal efficiency of corrugated plates (Δη), as a function of , was also experimentally studied quantitatively. In agreement with the findings of Oosthuizen and Garrett (2001), the experimental and numerical results proved that the increase in the heat exchange area of the corrugations has a greater influence on the convective exchange and the thermal efficiency than the disturbances caused in the flow (which reduce ). The plate with trapezoidal corrugations presented the highest convective thermal efficiency, followed by the plates with square and triangular corrugations. It was also proved that the thermal efficiency of corrugated plates increases with .Practical implicationsThe results demonstrate that corrugated surfaces have greater thermal efficiency than flat plates in heating and/or cooling systems by natural convection. This way, corrugated plates can reduce the dependence on auxiliary forced convection systems, with application in technological areas and Industry 4.0.Originality/valueThe empirical correlations obtained for the corrected Nusselt number and thermal efficiency for the corrugated plate geometries studied are original and unpublished, as well as the experimental validation of the developed three-dimensional numerical code.

A Shielding System Proposal for the Cabling of Electric Glass Melters

This paper analysesthe impact on workers of the electromagnetic field produced by large furnaces for glass production. The paper also propose a solution for the reduction and the containment of magnetic induction levels below the limits imposed by national and international directives. Using a three-dimensional numerical calculation code based on the hypothesis of filiform conductors in the air (Biot-savart law). The choice of the solution is based on the technique named highly coupled magnetically passive loop technique (HMCPL). The solution was then implemented and a comparison between the magnetic induction values before and after the installation of the shielding solution is presented.

Mean wind flow reconstruction of a high-rise building based on variational data assimilation using sparse pressure measurements

The paper investigates the applicability of the variational data assimilation approach to reconstruct three-dimensional wind flows around a high-rise building model, and provides guidelines towards an efficient reconstruction. The objective is to determine the best distributed control parameters based on the Reynolds-averaged-Navier–Stokes (RANS) model coupled with pressure data. The strategy considers a distributed additive forcing control parameter, acting on the momentum equation and/or the transport equation of turbulent dissipations, where the closure is performed. To avoid unphysical solutions and accelerate the optimization convergence a Sobolev gradient descent regularization is proposed and compared with penalty techniques. The proposed data assimilation framework is applied to a realistic wind engineering estimation problem combining sparse wall pressure measurements with a routinely used industrial three-dimensional RANS numerical code. Results demonstrate that wall-pressure data is a meaningful enough piece of information to recover accurately the wake flow extension. A hybrid control parameter on the transport of the dissipation and the momentum equations leads to very precise results, whereas the Sobolev gradient descent direction gives efficient regularization and a fast convergence. These findings can be useful for future application of such a data assimilation technique to wind engineering problems.

Implementation of the Non-Associated Elastoplastic MSDPu Model in FLAC3D and Application for Stress Analysis of Backfilled Stopes

The multiaxial Mises-Schleicher and Drucker-Prager unified (MSDPu) criterion has been shown to exhibit several specific features compared to other yield and failure criteria, including a nonlinear mean stress dependency, influence of the Lode angle, use of independent uniaxial compressive and tensile strength values and absence of an apex (singularity) on the envelope surface in the negative stress quadrant. However, MSDPu has been seldom used in practice to solve geotechnical and geomechanical engineering problems mainly because it had not yet been fully implemented into three-dimensional (3D) numerical codes. To fill this gap, a 3D elastoplastic MSDPu formulation is developed and implemented into FLAC3D. The proposed MSDPu elastic-perfectly plastic (EPP) constitutive model is then validated against existing analytical solutions developed for calculating the stress and displacement distributions around cylindrical openings. The FLAC3D MSDPu-EPP model is then applied to evaluate the vertical and horizontal stress distributions in a three-dimensional vertical backfilled stope. The numerical results obtained with the MSDPu-EPP model are compared with those obtained with the Mohr-Coulomb EPP model, to highlight key features of the new formulation.

Numerical modeling of even harmonic generation in XFELs with planar and helical undulators

The article presents a numerical study of even harmonic generation in X-ray free-electron lasers (XFELs) with planar and helical undulators. The second harmonic in FELs has been recorded in APS, LCLS and VISA experiments. It is important to take into account the second harmonic in experiments, for example, with crystals, since it can make a significant contribution to the generation of harmonics in FELs, both in X- and Y-polarizations, thereby affecting the results of research. In this paper, we present expressions for coupling coefficients and a three-dimensional time-dependent numerical code that models harmonic generation in XFELs with single-frequency planar and helical undulators. In the second part of the paper we consider production of the sub-terawatt radiation in the ångstrom range in a FEL with a helical undulator using the electron beam from the European XFEL (EuXFEL). The X- and Y-polarizations of the second harmonic are also discussed.

Comprehension of shock wave modulation phenomena due to electromagnetic energy by using three-dimensional numerical simulation

Recently, the development of the supersonic transportation system is desired. For the development, the reduction of the wave drag and sonic boom is crucial problem. For the solution of the problem, the shock wave modulation technique by using the electro-magnetic power is one of the promising methods. This technique makes use of the baroclinic effect. For the application of this method to the other method of vortex generation method in the supersonic flow field, such as the scram jet engine inlet, the comprehension of the baroclinic effect is inevitable. In this study, for the comprehension of the baroclinic effect due to the electro-magnetic power, the three-dimensional numerical analysis code to simulate the interaction between the shock wave and the temperature modulated field was developed. The results were verified by comparing with the experimental visualization data.

Application of time-domain methods for marine hydrodynamic and hydroelasticity analyses of floating systems

ABSTRACT The application of transient three-dimensional numerical code ITU-WAVE is presented for the prediction of hydrodynamic characteristics of floating bodies. The time histories of unsteady motions are directly presented with respect to Impulse Response Functions (IRFs). First-order steady forces of wave-resistance, sinkage force and trim moment are solved as the steady-state limit of surge radiation IRF. The numerical prediction of second-order mean force is presented using near-field method based on the direct pressure integration. The hydrodynamic and structural parts are fully coupled through modal analysis for the solution of hydroelastic analysis. A stiff structure is then studied assuming that contributions of rigid body modes are much bigger than elastic modes. A discrete control of latching is used to increase the bandwidth of the efficiency of Wave Energy Converters (WEC). ITU-WAVE numerical results for different floating bodies show satisfactory agreements compared to analytical, other numerical and experimental results.

Simulating the postfailure behavior of the seismically- triggered Chiu-fen-erh-shan landslide using 3DEC

The dip-slope Chiu-fen-erh-shan landslide, estimated to have a volume of 36 × 106 m3, was triggered by the Mw 7.6 Chi-Chi earthquake. The debris covered an area of 1.95 km2 and claimed 36 lives. Although different discrete element methods have been applied to simulate the postfailure behavior of the Chiu-fen-erh-shan landslide in the last two decades, the lateral and dip-slope rock movements, the impact of the sliding debris against the hill in front of the slope toe and its final deposition have not been fully simulated. The major objective of this study was to investigate the possibility of applying three-dimensional (3D) numerical modeling code 3DEC to numerically model the debris movement and deposition of the Chiu-fen-erh-shan landslide under the impact of the Chi-Chi earthquake. By incorporating the spacing and orientation information of the joints and bedding planes, the slope was modeled as an assemblage of polyhedrons. Seismic ground motions were simultaneously applied in three dimensions. The shoveling effect was considered to erode the hill in front of the slope toe so as to extend the impact area and match more closely actual depositional topography. This study showed that the 3DEC simulations captured essential 3D characteristics of the landslide and resulted in a postfailure configuration similar to that observed in the field.

Numerical study of the second harmonic generation in FELs

A numerical study of the effect of betatron oscillations on the second harmonic generation in free-electron lasers (FELs) is presented. Analytical expressions for the effective coupling strength factors are derived that clearly distinguish all contributions in subharmonics and each polarization of the radiation. A three-dimensional time-dependent numerical FEL code that takes into account the main FEL effects and the individual contribution of each electron to the second harmonic generation is presented. Also, the X- and Y-polarizations of the second harmonic are analyzed. The second harmonic was detected in experiments at the Advanced Photon Source (APS) Low Energy Undulator Test Line (LEUTL) and Linac Coherent Light Source (LCLS) in the soft X-ray regime. The approach presented in the article can be useful for a comprehensive study and diagnostics of XFELs. In the paper, the LCLS and Pohang Accelerator Laboratory X-ray Free-Electron Laser (PAL-XFEL) experiments are modeled. The simulation results are in a good agreement with the experimental data.

Flow Dynamics Around Permeable Spur Dike in a Rectangular Channel

In this study, numerical simulations were performed to investigate the flow and turbulence characteristics of rectangular spur dikes with varying permeability using the Reynolds stress turbulence model developed by three-dimensional (3-D) numerical code FLUENT (ANSYS). In this research, both permeable and impermeable spur dikes were investigated with varying permeability (25%, 37%, 49%, 62%, and 74%) to show its effect on the flow structure. At zh=3.5 cm (where z is the maximum flow depth, and zh is mid of flow depth), 3-D flow velocities and depth-averaged velocities were measured in the horizontal plane. Different velocity profiles and contours, turbulent intensities (T.I), and turbulent kinetic energy (TKE) were analyzed at various selected positions. The findings indicate that an increase in the permeability of the spur dikes up to 74% had a reciprocal effect on the mean stream-wise velocity. Moreover, the recirculation regions created within the impermeable spur dike field decreased with increased permeability of spur dikes. The permeable spur dike head showed a significant decrease in T.I, and TKE compared to the impermeable spur dike. Therefore, to protect the spur dike head from severe turbulent flow during floods and reduce the spur dike field’s recirculation region, a permeable spur dike is preferred.

Mesoscopic Damage and Fracturing of Heterogeneous Brittle Rocks Based on Three-dimensional Polycrystalline Discrete Element Method

Rock heterogeneities often control microcracking on the grain scale and therefore the mechanical behavior of the rock on the macroscale. We therefore studied the fracture patterns, mechanical behavior and strength of granular rocks using the three-dimensional numerical modeling code 3DEC. The numerical rock specimens, built using software package Neper, comprised an assemblage of Voronoi polyhedra designed to resemble grains. Different grains, representing different rock-forming minerals, and the contacts between the grains were assigned different mechanical and physical properties, accounting for the grain scale heterogeneity observed in natural granular rocks. The model accurately captured the evolution of damage on the grain scale (tensile and shear microcracks) and the macroscopic mechanical behavior, strength, and failure patterns observed in laboratory experiments performed on sandstone. Based on this validation, we explored the influence of grain size and shape distribution on the mechanical behavior of granular rock. We show that rock specimens characterized by a wide grain size distribution were weaker than those with a narrow grain size distribution, but that grain sphericity distributions does not significantly influence strength. We also found that increasing the initial porosity reduced specimen strength, due to the concentration of stress around the voids, and that intergranular cracking was the dominant contact damage mechanism during uniaxial compression. Due to the ease of flexibility in varying grain scale parameters, we conclude that the model used herein is a powerful tool that can be used to study the mechanical behavior, strength, and failure patterns of rock.

Experimental Evaluation of Rapid Flat Jack Testing with Various Shaped Saw-Cut Slots

The flat jack test is one of the oldest and simplest in situ stress measurement techniques that has generally fallen out of favour in current rock engineering practice. Although there are a number of limitations with the test, the direct pressure measurement obtained from the test, without need of stiffness parameters, and significant volume of rock involved in the test, compared to other tests, is an asset. The proliferation of relatively easy to use three-dimensional numerical modelling software codes can help to overcome some of the theoretical and practical limitations of the test. In addition, modelling also presents opportunities to utilize various shaped bladders within simple saw-cut slots, as opposed to the conventional lined-drilled slot cut with grouting of the flat jack in place. The use of a simple rock saw to cut a narrow slot for simple insertion of an ungrouted bladder allows for more rapid and economical testing. In this study, the use of rapid, saw-cut slots in combination with various bladder shapes (e.g., semi-circular or rectangular) was investigated experimentally in the laboratory. An experimental program was developed to conduct flat jack testing on large concrete blocks in the laboratory under known, controlled stress conditions. The findings were used to develop correction factors to account for various shapes of saw-cut slots in combination with various shapes of bladders. Three-dimensional finite element modelling was used to further verify and examine the experimental findings.

CPS construction for laser coating with a general-purpose three-dimensional thermohydraulics numerical simulation code SPLICE

CPS construction for laser coating with a general-purpose three-dimensional thermohydraulics numerical simulation code SPLICE

Influence of Stope Excavation on Drift Convergence and Support Behavior: Insights from 3D Continuum and Discontinuum Models

Numerical modeling is an important tool in rock engineering. The choice for a particular numerical method is based on its capacity to represent the problem boundary conditions, the material behavior, and the pertinent rock mass failure mechanisms. It follows that there could be more than one numerical method suitable for a particular problem. In this respect, the selection of a particular method will be dictated by a series of technical and practical trade-offs. This paper addresses issues associated with the simulation of jointed rock masses and ground support by employing both continuum and discontinuum numerical methods. The focus is on the explicit simulation of a jointed rock mass and the implementation of ground support using a three-dimensional numerical code based on the distinct element method. 3DEC was used to generate continuum and discontinuum rock mass models, which were calibrated based on field instrumentation data from the George Fisher mine, in Australia. In particular, the investigation focused on the response of the ground support system, consisting of both reinforcement and surface support elements, to stress changes associated with the excavation of nearby stopes. The main difference between the constructed continuum and discontinuum 3DEC models was the representation of the rock mass at the location of the instrumented drift. In the continuum model, an equivalent continuum rock mass model, with the ubiquitous-joint (UJ) constitutive model, was used, whereas in the discontinuum model, joints were simulated explicitly. In this case study, it was observed that the adopted discontinuum modeling approach provided more realistic results than the continuum model with the UJ constitutive model, in terms of the drift convergence, support behavior, and depth of yielded zone due to the excavation of stopes near the instrumented section of the drift.

Reynolds stress modeling of flow characteristics in a vegetated rectangular open channel

A computational technique to simulate turbulent and vegetated flow in a rectangular open channel was investigated. Reynolds stress model was implemented to the circular vegetation patch flow configuration for the investigation of flow properties and turbulence characteristics. A finite volume-based model was developed using a three-dimensional (3-D) numerical code FLUENT and the pre-processor Geometry and Mesh Building Intelligent Toolkit. The model was first validated and then used for simulation purpose. Vertical distribution of mean stream-wise velocities was computed at typical locations. A deceleration in the magnitude of stream-wise velocities was observed within the vegetation patch zone. Minimum values of velocity magnitude were observed directly behind the vegetation structures. Turbulence characteristics in the form of Reynolds stresses and turbulent kinetic energies investigated by this model showed that turbulence was greater in the regions of vegetation patch. This Reynolds stress modeling formulation has shown to be capable of capturing important mean flow and turbulence characteristics in the configuration considered.

A fully coupled hydro-mechanical material point method for saturated dense granular materials

The stability of a dense granular assembly can be greatly reduced by a pore pressure of the interstitial fluid, and the body may fail and transit from a solid-like state to a fluid-like state. This process involves two major problems: large deformation and hydro-mechanical coupling. In this work, a three-dimensional fully coupled hydro-mechanical model using material point method (MPM) is developed. Darcy's law, considering the inertial effect, is adopted to govern the motion of interstitial water, and the conservation of momentum of the mixture is used to govern the motion of the solid, i.e., granular materials. The spatial discretization schemes for these equations are derived using the generalized integration material point method (GIMP), and the proposed coupled MPM formulation is implemented in a three-dimensional numerical code. The developed model is first quantitatively validated by comparing the simulation results of temporal evolution of spatial distribution of hydraulic pressure in a one-dimensional oedometer test with the analytical results. An experiment is designed to observe the failure of a saturated sand pile, in which the partial-saturated region is avoided by increasing the hydraulic head at the input boundary, and the kinetic energy of water is dissipated by a filtering cloth. The failure process is simulated with the MPM code. It is found that the location of the shear band in the simulation agrees with the location of the sliding surface in the experiment. The temporal evolutions of the spatial distributions of hydraulic pressure and the solid velocity distribution at a specific time are given to provide insight into the mechanism of the failure process. This work would be helpful in understanding the initiation mechanism of debris flows induced by rainfall, and sand production in gas hydrate-bearing sediments due to increasing fluid content associated with hydrate dissociation.