Unified Numerical Model Research Articles

A Unified Numerical Approach to the Dynamics of Beams with Longitudinally Varying Cross-Sections, Materials, Foundations, and Loads Using Chebyshev Spectral Approximation

Structures with inhomogeneous materials, non-uniform cross-sections, non-uniform supports, and subject to non-uniform loads are increasingly common in aerospace applications. This paper presents a simple and unified numerical dynamics model for all beams with arbitrarily axially varying cross-sections, materials, foundations, loads, and general boundary conditions. These spatially varying properties are all approximated by high-order Chebyshev expansions, and discretized by Gauss–Lobatto sampling. The discrete governing equation of non-uniform axially functionally graded beams resting on variable Winkler–Pasternak foundations subjected to non-uniformly distributed loads is derived based on the Euler–Bernoulli beam theory. A projection matrix method is employed to simultaneously assemble spectral elements and impose general boundary conditions. Numerical experiments are performed to validate the proposed method, considering different inhomogeneous materials, boundary conditions, foundations, cross-sections, and loads. The results are compared with those reported in the literature and obtained by the finite element method, and excellent agreement is observed. The convergence, accuracy, and efficiency of the proposed method are demonstrated.

Unified numerical model for performance analysis of various cross-sections of concrete-filled stainless-steel tubular stub columns under axial loading

This research presents a unified numerical model for analyzing the performance of concrete-filled stainless-steel tubular (CFSST) stub columns with different cross-sectional shapes. The model converts the cross-sections of the CFSST columns with various shapes into an equivalent circular column, and a new concrete constitutive relation is proposed to estimate the compressive strength of confined concrete of CFSST columns with different cross-sections. To simulate the axial load–strain curves of CFSST columns, a computer program is used that converts the various cross-sections of CFSST columns into equivalent circular columns. To validate the model, 196 tested columns with various cross-sections gathered from previous literature are used. The unified model proposed is found to be accurately predicting the performance of CFSST columns. The model is then used to investigate the effects of concrete, steel yield stress, and the depth-to-thickness ratio on the different radius ratios and aspect ratios of CFSST columns. A unified design formula is also suggested to calculate the ultimate strength of CFSST columns with various shapes, and the proposed simplified model is shown to provide a more accurate estimation when compared to existing design codes.

A unified numerical model for simulating heat transfer in flows past porous bodies

AbstractA unified numerical model for simulating thermal flows past and through porous media whose thermal properties are identical with those of the surrounding fluid is proposed in this paper, which advances the work of the unified immersed boundary‐lattice Boltzmann flux solver (UIB‐LBFS). The proposed method greatly simplifies the conventional computation procedure for thermal flows past porous bodies by unifying the governing equations for the flow and temperature fields in both the porous and fluid domains. This is achieved by introducing a diffuse layer, across which the variation of the flow properties including its thermal features are expected to be smooth. Also, the developed method can be applied on either uniform or nonuniform grid since the numerical fluxes are locally reconstructed by LBFS at cell interfaces. In addition, the boundary conditions for both the flow and temperature fields at the porous‐fluid interface with complex shape can be implemented through IBM in a simple way. The proposed method is validated by several numerical examples over wide ranges of thermal parameters from forced convection to mixed convection. Excellent agreements are obtained for all simulations, including the one with severe temperature gradient in the thin temperature boundary layer at , which demonstrates the capabilities of the proposed method.

On the Melting Thresholds of Semiconductors under Nanosecond Pulse Laser Irradiation

In this work, a unified numerical model is used to determine the melting thresholds and to investigate the early stages of melting of several crystalline semiconductors (Si, Ge, GaAs, CdTe and InP) irradiated by nanosecond laser pulses. A molten fraction approach is used for continuous transition over the melting point. The results are compared with previously published theoretical and experimental data. A survey on the thermophysical and optical properties of the selected materials has been carried out to gather the most relevant data on temperature dependent properties for the solid and liquid states of these semiconductors where such data are available. A generalization of the obtained results is established that enables evaluation of the melting thresholds for different semiconductors based on their properties and irradiation conditions (laser wavelength, pulse duration).

A unified numerical model for two-phase porous, mush and suspension flow dynamics in magmatic systems

SUMMARYMagmatic systems in the Earth’s mantle and crust contain multiple phases including solid crystals, liquid melt and low viscosity fluids. Depending on depth, tectonic setting and chemical composition, magmatic systems can range from partially molten rock at low melt fraction to magma mushes at intermediate melt fraction to magmatic suspensions at high melt fraction. However, the theories underpinning most process-based models of magmatic systems describe magma as a single-phase fluid, or as a two-phase mixture either in the porous flow regime at low melt fractions or in the suspension flow regime at high melt fractions. Connections between the two-phase end-member theories are poorly established and hinder investigations into the dynamics of mush flows at intermediate phase fractions, leaving a significant gap in bridging trans-crustal magma processing from source to surface. To address this knowledge gap and unify two-phase magma flow models, we develop a 2-D system-scale numerical model of the fluid mechanics of an n-phase system at all phase proportions, based on a recent theoretical model for multiphase flows in igneous systems. We apply the model to two-phase, solid-liquid mixtures by calibrating transport coefficients to theory and experiments on mixtures with olivine-rich rock and basaltic melt using a Bayesian parameter estimation approach. We verify the model using the method of manufactured solutions and test the scalability for high resolution modelling. We then demonstrate 1-D and 2-D numerical experiments across the porous, mush and suspension flow regimes. The experiments replicate known phenomena from end-member regimes, including rank-ordered porosity wave trains in 1-D and porosity wave breakup in 2-D in the porous flow regime, as well as particle concentration waves in 1-D and mixture convection in 2-D in the suspension flow regime. By extending self-consistently into the mush regime, the numerical experiments show that the weakening solid matrix facilitates liquid localization into liquid-rich shear bands with their orientation controlled by the solid stress distribution. Although the present model can already be used to investigate three-phase mixtures using conceptually derived transport coefficients, more rigorous calibration to experiments and end-member theories is needed to ensure accurate timescales and mechanics. With a self-consistent way to examine multiphase mixtures at any phase proportion, this new model transcends theoretical limitations of existing multiphase numerical models to enable new investigations into two-phase or higher magma mush dynamics.

Cathode-arc-anode behavior in cooling-induced cathode-focusing GTA system: A unified numerical model

A gas tungsten arc (GTA) is an important heat source for manufacturing, cooling to the tungsten electrode has a critical influence on the cathode-arc-anode behavior because cooling-induced cathode-focusing (CICF) effect forms. In this research, a unified arc-electrode model is established to predict the influence of tungsten electrode cooling degree on heat transfer behavior in the cathode-arc-anode system. The results show that enhancing the cooling degree of the tungsten electrode can: (1) increase the arc voltage and arc power; (2) increase the arc pressure and the heat transferred to the anode and improve the arc penetration ability; (3) but slightly increase the heat transfer to the cathode tungsten rod at a given arc current. The developed model is validated by available experimental data. The research results deepen the understanding to the CICF effect and provide guidance for increasing optimizing the GTA torch structure to improve the arc penetration ability.

Numerical reproduction and prediction of rock failure behavior: From short term to long term

Rock is a natural geological material; its time-dependent failure presents complex nonlinear and random characteristics under the interaction effects of various mechanisms. Previous research focuses on either short-term or long-term failure behavior. Here, we develop a new unified numerical model to address short-term and long-term rock failures in one framework. Viscoelastic, viscoplastic, and damage mechanisms are considered and integrated under thermodynamic consistency. The corresponding parameters feature definite physical meanings. Mean-field homogeneous (HO) analysis and mesoscale-based heterogeneous (HE) analysis are proposed. Numerical schemes are validated via several representative examples. In both short-term and long-term situations, the proposed model can reproduce and predict time-dependent failure behaviors (such as the failure mode, strength, and failure time). Rock failure is controlled by various energy dissipation components and exhibits prominent time-dependent characteristics at different time scales. The effect of mesoscopic details sustainably enlarges as time prolongs. Furthermore, the fluctuation in material properties at the mesoscale profoundly affects the macroscopic nonlinear, stochastic, and discrete behavior. Our research provides insights into time-dependent rock failure and catastrophe forecast.

Investigation of Classification and Anomalies Based on Machine Learning Methods Applied to Large Scale Building Information Modeling

Building Information Models (BIM) capable of collecting and synchronizing all the data related to a construction project into a unified numerical model consisting of a 3D representation and additional metadata (e.g., materials, physical properties, cost) have become commonplace in the building sector. Their extensive use today, alongside the increase in experience with BIM models, offers new perspectives and potentials for design and planning. However, large-scale complex data collection leads to two main challenges: the first is related to the automatic classification of BIM elements, namely windows, walls, beams, columns, etc., and the second to detecting abnormal elements without manual intervention, particularly in the case of misclassification. In this work, we propose machine learning for the automated classification of elements, and for the detection of anomalies based on geometric inputs and additional metadata properties that are extracted from the building model. More precisely, a Python program is used to decipher the BIM models (available as IFC files) for a series of complex buildings, and three types of machine learning methods are then tested to classify and detect objects from a large set of BIM data. The approach is tested on a variety of practical test cases.

Effect of pumping gas on temperature field and pressure in hollow tungsten arc

A hollow tungsten negative pressure arc (HTNA) is a heat source that controls the gas flow inside a tungsten electrode and optimizes the arc output. However, to ensure the widespread applicability of HTNAs, the factors affecting the temperature and pressure distribution of an HTNA should be studied. In this study, the effect of pumping gas on the temperature and pressure distribution of an HTNA is elucidated through experiments and numerical simulations. A double spectral line acquisition system with nine optical transmission fibers was used to obtain the arc light intensity for the temperature calculation and spatial reconstruction. Consequently, a unified numerical model was developed to quantitatively study the physical field distribution under the effect of pumping gas. It was observed that the maximum temperature of the traditional gas tungsten arc (GTA) and hollow tungsten arc (HTA) decreased more than that of the HTNA owing to the effects of pumping gas. By analyzing the current density and flow field, it was concluded that convective heat transfer owing to pumping gas is the primary cause of the temperature difference between the arcs rather than Joule heat. Compared with the effect of the Lorenz force, the arc flow had a more significant effect on the pressure difference between the inner and outer tungsten electrodes. The gas in the arc region flowing into tungsten also affected the arc pressure on the base metal surface. The results of this study are expected to provide guidance for controlling the energy output of the welding arcs.

Computer Intelligent Numerical Simulation of TIG Welding Using Platy Tungsten Electrode

In order to reveal the law of arc plasma flow and heat transfer in the process of flat tungsten electrode TIG welding as auxiliary heat source for hardfacing of cast iron surface. According to the free burning TIG arc using platy tungsten electrode, A three dimensional (3D) model for tungsten inert gas welding using platy tungsten electrode has been developed. The whole region of platy tungsten TIG arc, namely, platy tungsten cathode, arc plasma and anode surface is treated in a unified numerical model. By using fluent software to do the second development of equations source and solve these equations, the distribution of temperature, velocity and current density are obtained. The simulation results show that the current of flat tungsten electrode is more dispersed, and the heat generation of arc is more dispersed, which leads to the decrease of arc temperature; The current density on the cathode is much higher than that on the anode.

Simulation Study on the Development Process and Phase Interface Structure of Gas-Liquid Slug Flow in a Horizontal Pipe

Here, a unified 3D numerical model of gas-liquid two-phase flow in a horizontal pipe was established using the interface capture method based on the open source software package OpenFOAM. Through numerical simulation of the natural slugging and development process of slug flow under different working conditions, the motion, phase interface structure, pressure and velocity field distributions of the liquid slug were fully developed and analyzed. The simulation results are consistent with the experiment. The results showed that during the movement of the slug head, there is a throwing phenomenon and a wave-like motion of the liquid slug. In addition, the slug tail and body area have very similar velocity profiles, and the overall velocity field distribution becomes more uniform with the development of liquid slug. Moreover, there are sudden pressure fluctuations at the head and tail of the liquid slug.

Numerical simulation of arc, metal transfer and its impingement on weld pool in variable polarity gas metal arc welding

• A unified numerical model involving arc, droplet and molten weld pool for VP-GMAW process is presented. • The heat transfer behavior and driving forces of metal formation and falling on the weld pool is quantitatively discussed. • At the same welding current during pulse cycle, the arc temperature in EN current phase is greater than EP current phase. • The arc plasma generated at EN current phase shows a constricted arc shape at the electrode tip. • The phenomenon of finger-like shape penetration observed during experiment is simulated and explained. A unified numerical model of the variable polarity gas metal arc welding process is developed based on the solution of magnetohydrodynamic equations within the framework of the phase-field algorithm. The droplet formation, necking, detachment, transfer through the arc plasma, and impingement onto the weld pool are investigated at different electrode positive (EP) and electrode negative (EN) regions of the current pulse regime under the condition of one droplet per pulse. The current density, electromagnetic force, surface tension, transient melt-flow velocity, and Joule heating effects are calculated. The numerical results indicate that the arc plasma generated in the EN current phase has a constricted arc shape at the electrode tip compared with the typical bell shape arc in the EP current phase. At the same welding current during the pulse cycle, the arc plasma temperature in the EN current phase is greater than that in the EP current phase. The model shows that before the droplet detaches, the surface tension forces are dominant, whereas during the EP current phase, the electromagnetic forces strongly intensify along the liquid bridge, thereby causing droplet detachment. In addition, the phenomenon of finger-like shape penetration due to the momentum transferred by a falling droplet to the bottom of the weld pool is simulated. The predicted results well agree with the high-speed images and weld pool parameters, accordingly validating the formulated model.

Single variable-based unified numerical model for plane elastic problems of stress analysis in Cartesian and polar coordinate systems

A unified numerical model for stress analysis of plane problems of structural mechanics in Cartesian and polar coordinate systems is presented. The traditional two-variable problem of stress analys...

Single variable-based unified numerical model for plane elastic problems of stress analysis in Cartesian and polar coordinate systems

Single variable-based unified numerical model for plane elastic problems of stress analysis in Cartesian and polar coordinate systems

A unified numerical model for wetting of soft substrates

AbstractThe wetting of deformable elastic structures has been recently shown to comprise a rich variety of new physical phenomena (stick‐slip motion, durotaxis, Shuttleworth effect, etc.) whose fundamental understanding demands for numerical simulation tools. In this article, we develop a novel unified model and numerical method for this problem. As special features, the method includes exact incompressibility and a linear monolithic assembly of the Navier‐Stokes and Cahn‐Hilliard equations which stabilizes dominant surface tension at small interface lengths. Also, solid viscosity is included which offers the opportunity to simulate the surfing behavior of droplets on viscoelastic substrates for the first time. We show that the method is highly accurate and more robust than most previous approaches and illustrate its potential by numerical simulation examples.

Quantitative investigation of laser-induced damage fatigue in HfO2 and ZrO2 single layer coatings.

The decrease of laser-induced damage threshold (LIDT) of optical materials when irradiated with multiple laser pulses is an important phenomenon commonly known as the optical fatigue effect. In case of pulsed femtosecond irradiation fatigue is usually attributed to incubation of laser-induced lattice defects. In this study, standard S-on-1 LIDT test was complimented with in situ time-resolved digital holographic microscopy (TRDHM) to quantitatively investigate fatigue of catastrophic damage for HfO2 and ZrO2 single layer ion-beam-sputtered optical coatings. It was identified that ablation (critical damage) was preceded by exponential increase in optical path length visible as positive phase shift (subcritical damage). Atomic force microscopy was used to show that physical damage originates as localized 100 nm wide nanogrooves perpendicular to laser polarization. A novel link was established between LIDT fatigue and mechanical fatigue crack growth from cyclic loads which allowed construction of a unified numerical fatigue model that reproduced both S-on-1 and TRDHM experimental data.

Influence of Electrode Energy Balance on Gas Convective Pattern of a High-Pressure Xenon Short Arc Lamp

The transport of tungsten vapour evaporated from the electrode surfaces of a high-pressure xenon short-arc lamp, which is dominated by the gas convection in the lamp, determines the location and extent of the blackened area on the inner bulb wall. We have investigated factors affecting the vapour transport and other important phenomena related to the gas convection using a unified numerical model. The influence of the lamp operating parameters and also the thermodynamic and transport properties of the gas is discussed. The predicted lamp characteristics and phenomena agree well with experimental results. The gas velocity in the lamp is strongly affected by the Lorentz force and the gas density, which respectively depend on the current and the filling pressure. The viscosity and density of the gas adjacent to the anode surface were found to depend on the anode energy balance and to affect the resistance of the gas flow, which in turn affects the separation point of the gas flow from the anode surface. This indicates that the anode surface temperature, which is determined by the energy balance between the gas and the anode, also affects the blackening location.

The effect of electrode energy balance on variable polarity plasma arc pressure

The plasma arc evolution and the physical mechanism associated with variable polarity plasma arc (VPPA) remain unclear, slowing down its process development and optimization. In this work, we revealed its increasing phenomenon in the initial segment of electrode negative (EN) phase through the experimental measurement of VPPA pressure. The current increasing enlarged the pressure difference between EN and electrode positive (EP) phase. A unified numerical simulation model was developed coupling tungsten electrode, constricting nozzle, plasma arc and workpiece for clarifying the mechanism of pressure evolution. In this model, the electrical conductivity of gas adjacent to melting region in tungsten electrode is considered to be superior than that of gas adjacent to solid region. Through the evolution of temperature field and energy transfer, the electrode was gradually cooled mainly by thermionic electron emission at the initial segment of EN phase, because of which the current attachment shrank to the electrode tip. Thus, the electromagnetic force depending on the current density increased in EN phase, leading to an increase in the plasma arc pressure. Our results clarified aspects of energy balance physics behind VPPA, which is critical for its development.

Numerical Simulation of Jumping Droplet Condensation.

Jumping droplet condensation has been shown to enhance heat transfer performance (≈100%) when compared to dropwise condensation by reducing the time-averaged droplet size (≈10 μm) on the condensing surface. Here, we develop a rigorous, three-dimensional numerical simulation of jumping droplet condensation to compute the steady-state time-averaged droplet size distribution. To characterize the criteria for achieving steady state, we use maximum radii (Rmax) tracking on the surface, showing that Rmax settles to an average in time once steady state is reached. The effects of the minimum jumping radius (0.1-10 μm), maximum jumping radius, apparent advancing contact angle (150-175°), and droplet growth rate were investigated. We provide a numerical fit for the droplet size distribution with an overall correlation coefficient greater than 0.995. The heat transfer performance was evaluated as a function of apparent contact angle and hydrophobic coating thickness, showing excellent agreement with prior experimentally measured values. Our simulations uncovered that droplet size mismatch during coalescence has the potential to impede the achievement of steady state and describe a new flooding mechanism for jumping droplet condensation. Our work not only develops a unified numerical model for jumping droplet condensation that is extendable to a plethora of other conditions but also demonstrates design criteria for nonwetting surface manufacture for enhanced jumping droplet condensation heat transfer.

Modeling of a xenon short arc lamp considering the behavior of tungsten vapour evaporated from electrodes

The tungsten vapour produced from the electrodes during short arc lamp operation is transported by gas convection and then deposited on the inner quartz bulb wall to form a tungsten thin film, causing the wall to blacken. We have been able to consider important phenomena for the first time by developing a unified numerical simulation model incorporating relevant sub-models. These include the absorption of the radiant energy due to blackening of the lamp and the temporal variation in the lamp parameters. The validity of the numerical simulation model is first evaluated by comparison with experimental results. The basic characteristics of the lamp obtained using the model is found to be in good agreement with the experimental results and other research results. The influence of the bulb wall blackening is then examined. The temperature of the bulb is shown strongly affected by convective heat transfer from the hot gas, and the temperature rise of the bulb after blackening is found to be primarily governed by the absorption of the radiant energy by the tungsten thin film. Through the increase in the bulb temperature, the gas temperature in the bulb is also increased. This raises the operating pressure, which increases the stress on the bulb wall. Consequently, it is demonstrated that the probability of breakage gradually increases with time due to the blackening by tungsten vapour deposition.