Three-dimensional Formulation Research Articles

Influence of Latent Heat of Fusion on the Melt Pool Shape and Size in the Direct Laser Deposition Process

The melt pool calculating method is presented based on the solution of the heat conduction problem in a three-dimensional formulation, taking into account the latent heat of fusion and the change in thermophysical properties with temperature. In this case, the phase transitions of melting and crystallization are accounted for using the source method. Considering the latent heat of fusion in the heat transfer process leads to melt pool elongation, as well as to a slight decrease in its width and depth. Depending on the mode, the melt pool elongation can be up to 22%. The penetration depth is reduced by about 5%. The deposition width does not change practically. The presented model was validated by comparing the experimentally determined melt pool shape and its dimensions with the corresponding theoretically calculated results. Experimental data were obtained as a result of coaxial video recording and the melt pool crystallization. The calculated form of the crystallization isotherm changes from a U-shape to a V-shape with an increase in the power and speed of the process, which coincides with the experimental data.

LOCAL INDENTATION AS METHOD OF REDUCING FATIGUE CRACK GROWTH RATE

The possibility of a significant decrease in the growth rate of a fatigue crack is studied. The goal can be attained by creating a local field of residual stresses near the crack tip which arises due to the indentation of a spherical indenter. A methodology and program algorithm (in ANSYS) have been developed for numerical simulation of the problem in a three-dimensional formulation of the process of fatigue crack growth in the field of residual stresses. Considering the prospects of developing the technique with regard to the use of dynamic indentation, the ANSYS Explicit STR solver fully integrated into the calculation module was used in the macro. Proceeding from the solution of the elastoplastic problem the program provides determination of the fields of residual stresses (RS) at the first stage of the calculation and numerical simulation of the fatigue crack growth on the second stage. The effect of the indentation parameters (magnitude of the force applied to the indenter and the location of the indentation point, conditions of fixing) on the crack growth rate is considered. Methods for a significant reduction in the crack growth rate based on multiple preliminary indentation are substantiated. Using the developed program, we managed to solve a series of problems regarding the effect of different types of loading and fastenings on the growth rate of a fatigue crack in a plate with a through crack. The use of one-sided indentation of thin-walled objects with cracks, which are installed on the support surface, greatly simplifies the practical application of the technique for creating a residual stress field in the vicinity of the crack tip. It is shown that with multiple indentation along the crack propagation line, the fatigue crack growth rate is significantly lower than that when using a single indenter.

Formation of prestellar regions in collisions of molecular clouds simulations on heterogeneous computers

The processes occurring in near and far space have a significant impact on the safety of space flights. Processes such as explosions of supernovae and relativistic jets have a particularly great impact. They arise in quasars, black holes, protostars. Often such structures are observed during the formation of new stars. Such jets have a great impact on the safety of space flights. For example, there is currently no radiation shelter on the International Space Station, so astronauts are at serious risk of getting radiation sickness. In addition, the skin of the orbital station modules consists of aluminum, which accumulates secondary radiation. The formation process of new star systems is the result of complex processes that occur in interstellar gas. These processes include nonlinear interactions of turbulence, gravity, collisions of molecular clouds with each other, as well as rotation and several other factors. The evolution of the formation of superdense substance begins from the moment when it gathers in turbulent flows or is formed by supersonic collisions of molecular clouds with each other, or are formed during the intereaction of molecular clouds with supersonic waves, which are formed during the explosions of supernovae, until the moment when these superdense areas reach the prestellar density. Further, depending on several factors, these superdense formations either collapse or disintegrate and return to the interstellar medium. The analysis of observations allows to conclude that a significant part of the molecular clouds is not gravitationally bound. These conclusions are made based on the virial theorem, which expresses the connection between gravitational and kinetic energy. In this paper, a simulation of large molecular clouds collision in a three-dimensional formulation on ultra-high-resolution grids is carried out. Execution of such calculations requires a lot of computer capacity. The paper presents the results of computer modeling of large-scale processes of filament formation and superdense, gravitationally coupled structurally parallel computation clusters with hybrid architecture. Parallel simulation on supercomputers was conducted with author’s software, which uses a modified second-order Godunov method of accuracy of the Total Variation Diminishion type. Calculations were conducted on grids that contain more than one billion cells (1024 × 1024 × 1024). The gravitational potential is calculated on graphic processors. To refine the calculations, the method of adaptive refinement of the AMR grid is used. Simulation results are presented for cases of frontal collision of two molecular clouds, which density is distributed along the radius according to certain laws.

Laser beam technology interventions in processing, packaging, and quality evaluation of foods

Laser emits light using an optical amplification process that is based on the stimulated emission of electromagnetic radiation. Thermal and non-thermal approaches are used in laser material processing. Some of the characteristics of lasers that make them beneficial for food processing are their ability to produce consistent heating, perfect control over the energy supply, the accuracy of spatial placement of the energy, and precise localized heating. Laser is a novel food processing method that can aid with precision cooking. In conjunction with the food layered manufacturing method, the laser cooking method can be used to print three-dimensional (3D) food formulations. In the food packaging sector, laser welding technology has been applied in the film joining process, such as in the flow pack packaging process or in hermetically sealed containers/cans. Soluble solid content and firmness of food products were determined using a laser light backscattering imaging technique. Laser-backscattering technology has also been discussed to model and quantify food attributes, as well as to help in the processing of solid and fluid food matrices. The practice of lasers in the processing of foods, packaging technology, microbial suppression, and food quality evaluation are discussed in this study.

Modeling curvature-resisting material surfaces with isogeometric analysis

Improved understanding of solid surface energy and its role in the overall mechanical properties is of great interest due to the emerging manufacturing techniques of nanostructures, coatings, and synthetic/biological bilayer–polymer hybrids. Continuum numerical modeling of surface stresses efficiently incorporates a zero-thickness membrane bonded to a bulk, intrinsically accounting for surface tension and surface elasticity. Compressive surface stresses are not possible in a purely membrane formulation, ignoring the surface flexural resistance. The extension of material surfaces to account for flexural resistance, i.e., the Steigmann–Ogden model, requires spatial derivatives of second order, posing significant challenges to standard discretization techniques. Hence, the effect of surface curvature resistance on the overall mechanical behavior of complex geometries remains elusive. Here, we develop a three-dimensional computational formulation of curvature-dependent surface energetics at finite strains using surface-enriched isogeometric analysis. Coupled with a hyperelastic bulk, bending-resistance of material surfaces furnishes a new physical length scale, i.e., the elastobending length. We quantify the effect of elastobending deformations for several numerical examples involving soft materials with thin coatings and liquid-shell surfaces, capturing budding-like behavior observed at cell membranes. Our results demonstrate a stiffer overall mechanical behavior when material surfaces resist bending deformations and illustrate how curvature effects lead to complex budding deformations at non-zero initial curvature states. The proposed methodology provides a robust computational foundation to help improve our understanding and mechanical characterization of soft solids, nanostructures, and biological membranes at small scales.

Three-dimensional simulation of full conduction-convection-radiation coupling with high Rayleigh numbers

The present research is focused on numerical analysis of heat transfer and fluid flow patterns when taking into account conduction, natural convection and surface thermal radiation under three-dimensional problem formulation. A hybrid mathematical model coupling the mesoscopic lattice Boltzmann equations with the macroscopic energy equation is built. The governing equations are solved in MATLAB. An in-house code developed in this work can be both run on central processing units and graphics processing units with almost no changes. Multiparameter analysis was performed when varying the Rayleigh number (Ra), surface emissivity, Biot number, conduction-radiation number, thermophysical properties and thickness of the solid walls. During numerical simulation, it was found that the vertical walls emissivity can be used as a tool to control thermal and flow behavior. In fact, three modes of heat transfer such as thermal stratification, thermal fluctuations and thermal plume were revealed when Ra = 108. With further increase of the Rayleigh number thermal and flow fluctuations were observed at the bottom half of the cavity. A significant discrepancy in results was observed between the 2D and 3D models when taking into account surface radiation. Finally, correlations for mean convective, radiative and effective Nusselt numbers were proposed.

Расчетное исследование эффективности системы подачи компонентов в модельном ракетном двигателе малой тяги на кислород-метане

The paper considers a model low-thrust rocket engine using the environmentally friendly gaseous oxygen–methane components as a scientific and technical lead obtained by the authors in the course of preliminary experimental studies. The engine design makes it possible to investigate the influence of the mixing unit configuration, namely position of the supply holes and presence or absence of the components swirling on the mixing process efficiency. Numerical simulation was carried out in a three-dimensional stationary formulation of “cold” mixing of gaseous oxygen and methane and was based on the Favre-averaged Navier — Stokes equations solution closed by the k–ω-SST turbulence model and the ideal gas state equation. Calculation results are provided for various configurations of the mixing unit. It is shown that the most efficient method for the considered model low-thrust rocket engine is the method of supplying gaseous components with swirling in a single direction.

Novel 3D coupled convection–diffusion model algorithm

The potential of a partial differential equations model is to anticipate its computational behavior. The simulation of a transient 3D coupled convection–diffusion system using a numerical model is described. The main objective of this article is to offer effective limited contrast compact finite difference techniques for use with nonlinear coupled partial differential systems that mimic overseeing differential frameworks. The three-dimensional compact finite difference formulation serves as the model’s foundation. An analytical model has been used to validate finite difference techniques that are numerically compact. By examining the consistency and union of the arrangement, which may be seen from figures and information tables, we can evaluate the model and the suggested numerical schemes. The schemes are unconditionally stable and accurate up to two orders in time and six orders in space, according to the results of the stability and accuracy tests. The implicit method used in the algorithm’s design was examined for stability criteria. Because mesh-independent solutions for non-linear differential systems are expensive, block tridiagonal matrix structures, measured in terms of L2 and L∞ norms, which are inherent characteristics of schemes and have excellent agreement with the investigation arrangement, are created.

ОЦІНКА СТІЙКОСТІ ДІЛЯНКИ СХИЛУ ОДЕСЬКОГО УЗБЕРЕЖЖЯ

Currently, there is a reduction in sites convenient for the construction of facilities. In this regard, the question of the development of new territories that were previously considered unsuitable or economically unprofitable for construction is increasingly being raised. Very often it is necessary to build buildings and structures on or near slopes. The development of landslide and landslide-prone slopes requires a comprehensive study, the results of which should be used in the selection of measures for the engineering protection of territories, as well as design and construction on slopes. The main task of engineers, when performing design and survey work in landslide-prone areas, is to assess the stability of the slope and the magnitude of the landslide pressure. The article calculates the stability of the landslide-prone slope of the Odessa coast for the purpose of further construction development. The slope in question is located on the Franzysky Boulevard, in the area of the Chkalov resort. The site features are in complex engineering and geological conditions (loess soils, collapsing properties of soils, several water-bearing layers). It has been established that deep block landslides of extrusion occurred earlier in this area. After landslide control measures consisting in construction of marine cost protection and drainage structures, an increase in slope stability was observed. Despite the measures taken, there is a beach erosion with partial destruction of coast protection structures, which can lead to increased abrasion and negatively affect the stability of the entire slope. Slope stability calculations are performed in two-dimensional and three-dimensional formulation. According to the flat schemes, calculations were performed in the Slide software package using Bishop and Janbu methods. The slope stability assessment in a three-dimensional formulation was performed by the finite element method using the Midas GTS NX calculation program and consists of determining the stress-strain state of the soil mass and the stability margin factor. Based on the calculation results obtained, the slope stability is assessed and options for landslide control (retaining) structures are proposed.

Density-based topology optimization of thin plate structure with geometric nonlinearity using a three-dimensional corotational triangle element formulation

Density-based topology optimization of thin plate structure with geometric nonlinearity using a three-dimensional corotational triangle element formulation

Modeling the use of an electrical heating system to actively protect asphalt pavements against low-temperature cracking

This paper addressed the case of an electrically heated asphalt pavement; it explored an unconventional application of such a system – not for combating snow and ice – but for mitigating low-temperature cracking. The investigation was done in silico, considering a stratified medium to represent the asphalt pavement system, a thin heat-generating layer to represent the heating system, and measured weather conditions from Greenland to emulate a cold region that can potentially produce thermal cracking. A thermomechanical model was outlined, consisting of a one-dimensional thermal formulation that accounts (also) for latent heat effects, and a three-dimensional mechanical formulation based on linear viscoelasticity that assumes thermo-rheological simplicity. A cold-weather event, leading to a thermal crack, was identified by the thermomechanical model. Additionally, a parametric investigation was carried out to quantify the effects of the heating system’s embedment depth and heating production on the activation timing needed to prevent cracking. It is found that mitigating low-temperature cracking with an embedded electric heating system is attainable and workable. Doing so is most effective when the heating system resides close to the ride surface. A procedure for automatic heating operation was proposed for practical implementation.

Modelling wave-ice interactions in three dimensions in the marginal ice zone.

This study concerns wave-ice interactions in the marginal ice zone (MIZ). We compare idealized simulations using two recent three-dimensional formulations for wave-ice interactions for flexible ice floes, with selected parametrizations for the scattering of ocean surface waves due to individual ice floes. These parametrizations are implemented in a modern version of the wave model WAVEWATCH III® (hereafter, WW3) as source terms in the action balance equation. The comparisons consist of simple hypothetical experiments to identify characteristics of the wave-ice parametrizations. Comparisons show that the two new wave-ice formulations give attenuation of wave heights that can be less intense in the direction of propagation than those of other considered formulations. Within the wave energy spectrum, the one-dimensional attenuation extends over the entire frequency domain to the high-frequency limit. Within the MIZ beyond the ice edge, there is evidence for a 'roll-over' effect in the simulations of attenuation. These new formulations can potentially improve previous parametrizations in simulations of wave scattering and attenuation within the MIZ. This article is part of the theme issue 'Theory, modelling and observations of marginal ice zone dynamics: multidisciplinary perspectives and outlooks'.

The Methods of Three-Dimensional Modeling of the Hydrogenerator Thrust Bearing

In the presented scientific work, the basic design versions of the thrust bearings of Hydrogenerators are considered. The main causes of emergencies in the thrust bearing unit of a high-power Hydrogenerator are considered. The main requirements for the operation of thrust bearings are submitted. Cause-and-effect relationships of emerging and development of defects are established. Existing methods for calculating the stressed state of a thrust bearing in the classical formulation for a stationary mode of operation are considered. The main features of the operation of the thrust bearing unit are investigated in relation to the features of the sliding bearings. The calculation of the elastic chambers of the hydraulic thrust bearing in a three-dimensional formulation is carried out, taking into account the physical properties of the oil, the material of the chambers and distribution of the acting loads. It is shown that the applied designs of Join Stock Company “Ukrainian Energy Machines” can be used in high-power Hydrogenerators.

Computer and physical modeling of multiple isothermal forging of EK61 superalloy

Studies on the process of multiple isothermal forging of high-temperature nickel-based EK61 superalloy using computer simulation in the DEFORM-3D software package in a three-dimensional formulation and a comparison with experimental data were carried out. Based on the simulation results, it is shown that with each subsequent stage of forging, the maximum strain values become higher, and the strain differences in the central and peripheral regions become smaller. Such a strain distribution leads to the formation of a homogeneous ultrafine-grained (UFG) microstructure. The initial coarse-grained microstructure is gradually transformed into a fine-grained microduplex type microstructure at 0.77Tmelt and with a further decrease in the processing temperature to 0.73Tmelt, it is transformed into a submicroduplex type (γ + δ) UFG microstructure.

CALCULATION OF GAS EMISSION FLOWS FROM THE SURFACES OF THE FLOW PART MOLECULAR STAGE OF A VACUUM PUMP

An algorithm and an example of calculation of gas emission flows from the urfaces of a molecular stage with helical channels made on the stator of a hybrid turbo molecular vacuum pump are considered. The Monte Carlo method in a three-dimensional formulation was used in calculations of the molecular regime of gas flow.

Three-dimensional contact formulation for assessment of dynamic interaction of pantograph and overhead conductor rail system

Overhead conductor rail (OCR) is an important power supply device in tunnel railway lines. The penalty method is widely adopted to model the dynamic interaction behaviour of the pantograph-OCR system (POCRs), while it is difficult to determine a proper contact stiffness value. This paper proposes a three-dimensional contact formulation for the POCRs based on the Lagrange multiplier method. Accurate contact forces can be obtained easily by this contact formulation without the trouble of determining the contact stiffness. Contact force is defined in the global coordinate system as a three-dimensional vector. Coulomb law of friction is adopted in this paper to describe the tangential contact force, and the train speed is included in the contact formulation. The central finite difference approximation method is utilised, and an iteration procedure is elaborated to calculate the accurate contact force vector. The proposed contact formulation is verified by comparing simulation results with in-line measured data. The maximum statistical relative error of the contact force is only 2.63%. The advantages of the proposed contact formulation are also demonstrated by comparing it with the penalty method.

Geometrically nonlinear analysis of friction pendulum systems under tri-directional excitation

A three-dimensional formulation for a mass sliding with friction on a concave spherical surface is presented and used to describe the behavior of friction pendulum systems under extreme tri-directional excitation. The proposed approach accounts for large deformations and includes a procedure for handling the characteristic stop-and-go, or stick-slip, motion of friction-based systems. A set of numerical examples are carried out comparing the results of the proposed formulation with available analytical solutions. Where these are not available, such as in the case of earthquake excitation, the convergence rate of Newton’s method and energy balance plots illustrate the accuracy of the computed solutions. Tri-directional earthquake simulations demonstrate the vulnerability of friction pendulum systems to nearly-periodic, and near-fault, long-period ground motions.

From two- to three-dimensional continuum-kinematics-inspired peridynamics: More than just another dimension

Continuum-kinematics-inspired Peridynamics (CPD) has been recently proposed as a geometrically exact formulation of peridynamics that is also thermodynamically and variationally consistent. Unlike the original formulation of peridynamics (PD), CPD can accurately capture the Poisson effect. For a three-dimensional analysis, CPD builds upon one-, two- and three-neighbor interactions. The isotropic three-dimensional CPD formulation of non-local elasticity therefore involves three material constants associated with length, area and volume. This manuscript aims to establish the relationships between the material parameters of CPD and isotropic linear elasticity for three-dimensional problems. In addition to addressing significant technical difficulties that arise when advancing from two- to three-dimensional problems, this contribution unravels several key features that are entirely absent in a two-dimensional analysis (Ekiz et al., 2022). It is shown that the three material parameters of CPD reduce to two independent parameters in the linearized framework, and can be expressed in terms of any pairs of isotropic linear elasticity constants, such as Lamé parameters. The analysis here provides a physical interpretation for the first Lamé constant, for the first time. Finally, we establish the admissible ranges for CPD material parameters.

Vulnerability Analysis of Structural Systems under Extreme Flood Events

Vulnerability analyses of coastal or inland bridges in terms of flood actions and structural and fluid flow characteristics are carried out. In particular, a numerical model based on a two-phase fluid flow is implemented for the multiphase fluid system, whereas a three-dimensional formulation based on shell/volume finite elements is adopted for the structure. The governing equations can simulate the interaction between fluids and the structures, by using the Arbitrary Lagrangian–Eulerian (ALE) strategy. The results of the hydrodynamic forces, bridge displacements and dynamic amplification factors (DAFs) show that the existing formulas, available in the literature or in structural design codes, do not accurately predict the maximum design effects. For the investigated cases, the DAFs may vary from 1 to 4.5. The worst scenarios are observed for the upload vertical direction. Finally, the performance of the protection fairing system is investigated. The results show that such devices are able to efficiently reduce the effects of the wave load in terms of the applied hydraulic forces on the structure and bridge deformability, in particular, with 40% more accuracy than the unprotected configuration.

Численное исследование влияния температурных изменений на грунт в условиях многолетней мерзлоты

The article is devoted to the numerical solution of the Stefan problem for studying the process of soil thawing in permafrost conditions. An enthalpy solution method was constructed, and the applicability of this method was considered. The numerical solution was found using the Pismen-Rekford scheme in 2D and 3D cases. The developed computational algorithms are parallelized for use on modern high performance computational systems. An approach has been implemented for modeling thermal processes in the thickness of an arbitrary array of substances, taking into account arbitrary initial conditions and environmental conditions. Mathematical modeling of the process of thawing of the upper layer of permafrost was carried out in two-dimensional and three-dimensional formulations, including the formulation with a gas reservoir located in the ground.