Two-dimensional Calculation Model Research Articles

Damage prediction and improvement method based on cutting mode of circular empty hole

Based on the theory of empty hole effect of cutting blasting, the Hopkinson effect and Saint–Venant principle are integrated to establish a two-dimensional calculation model of dynamic stress evolution of the holes wall, and then the dynamic fracture mechanism and damage distribution mode of the rock mass in the cutting area under the action of longitudinal waves are predicted. The results of the calculation and numerical simulation are verified by experiments, and the results show that: The time-varying stress function of the circular cavity wall conforms to the periodic dynamic evolution of the trigonometric function, and the theoretical calculation is consistent with the simulation results. Through the calculation of the round holes cut model and the square empty hole cut model, the change of the shape of the holes in the cut area changes the failure form of the surrounding rock mass. The circular empty hole wall is affected by the stress wave to produce "interval ring" destruction, and the effect of the reflected stretch wave is inhibited. The large range of rock mass in the square empty hole wall produces tensile and shear failure, and the rock mass collapses inward under the influence of the second stage stress. Among them, the empty space utilization rate of the square empty hole model is about 8.5 times that of the circular holes model. Vibration monitoring in the center of the cutting area shows that the vibration effect of the circular empty hole is larger than that of the square empty hole, and the proportion of rock breaking energy is lower.

Numerical Calculations for Curved Open Channel Flows with Advanced Depth-Integrated Models

This paper examines the effect of coupling several equations for vertical velocity profiles in a depth-integrated model to clarify the roles of three-dimensional flow structures minimizing the errors from the two-dimensional calculation model. In addition, this paper develops a numerical discretization method for the dispersion terms in the horizontal momentum equations. It is revealed that the use of the 2DC model underestimates the water surface elevation through the comparisons with the experimental datasets, advanced 2DC and 3DC results. The prediction of water surface elevation is considerably improved by taking into account of secondary flow effect with vorticity equations. It is clarified that the accuracy in predicting the water surface elevation is increased with increasing the degree of the function for vertical velocity profiles in advanced 2DC models or the number of vertical grids in 3DC model, while non-hydrostatic pressure and variation in vertical velocity have a second importance.

Modeling Corrosion Product Film Formation and Hydrogen Diffusion at the Crack Tip of Austenitic Stainless Steel.

Corrosion product films (CPFs) have significant effects on hydrogen permeation and the corrosion process at the crack tip. This paper established a two-dimensional calculation model to simulate the formation of CPFs at the crack tip and its effects on the crack tip stress status and hydrogen diffusion. The CPFs were simplified as a single-layer structure composed of Fe2O3, the effective CPFs boundary was modeled by the diffusion of oxygen, and the CPF-induced stress was modeled by hygroscopic expansion. The simulation was conducted with two stages; the first stage was to simulate the formation of CPFs formation and its effects on the crack tip stress status, while the second stage focused on the hydrogen diffusion with and without CPF formation under different external tensile loads. The results indicate that the highest compressive stress induced by the formation of CPFs is located at 50~60° of the crack contour and dramatically weakens the crack tip tensile stress at low-stress status. The CPFs can inhibit the hydrogen permeation into the crack tip, and the hydrostatic pressure effects on the redistribution of the permeated hydrogen are significant under larger external load conditions.

Two-dimensional calculation model for hazardous substances formation in combustion products of a spark-ignition engine

Introduction (problem statement and relevance). Improvement of environmental parameters of internal combustion engines is one of the most relevant tasks of the domestic transport engineering. Calculation support allows reducing the time and raising the efficiency of works for refining of the bench work process in order to meet the required parameters. The paper is devoted to development of a two-dimensional calculation model for hazardous substances formation in combustion products of spark-ignition engines based on the non-equilibrium kinetic models of formation of nitrogen oxides and carbon monoxide.Methodology and research methods. Computational methods for differential equations (ordinary and partial ones) are applied. Non-equilibrium kinetics of hazardous substances formation in combustion products is considered. The work process is calculated based on a combination of the mesh control-volume method and determination of the observable flame rate based on the experimental data (taking into account the development stage of the flame source).Scientific novelty and results. The new calculation method for flame propagation in the spark-ignition engine is suggested. The developed model combines such advantages as good predictability and short time of calculation.Practical significance. The model can be applied, in particular, to preliminary planning of three-dimensional calculations of the work process or their check in the absence of experimental data (at the stage of preliminary/concept design). The calculation results can be used as initial data for modeling of the exhaust gas aftertreatment (additional purification) system.

Determination of Secondary Cooling Zone Heat Transfer Coefficient with Different Alloy Types and Roughness in DC Casting by Inverse Heat Conduction Method

The cooling characteristic curves in a heated ingot with a diameter of 100 mm quenched by a water jet were measured under different conditions. A two-dimensional calculation model was established to calculate the HTC of magnesium alloy ingot with water spray cooling. Data from cast-in thermocouples trail were input into the model and the HTCs were back-calculated for the water quench region. The HTCs were calculated under different alloy types and roughness conditions, and the relationship between the ingot surface temperature, roughness, and the HTC was established accordingly. The results show that the greater the thermal conductivity of the alloy, the greater the heat transfer coefficient (HTC). The HTCs of AZ80, AZ31, and ZK60 alloys increase successively. With the decrease in the surface temperature, the HTC in both the impingement zone and the free−falling zone shows a trend of a rapid increase at first, then slowly increasing to the maximum value, and finally, a rapid decrease, with the peak value appearing at about 400 K. Considering the influence of the ingot surface temperature and the surface roughness on the HTC, the mathematical relationships between them are established.

Simulation study of the effect of electrode embedded with magnesia-carbon material on the breakdown process in micro-gap and electric field in arc

The breakdown plays an important role in the process of arc striking, which can form an early conductive channel between electrode and molten pool. In this paper, a two-dimensional transient micro-gap breakdown model of argon gas under atmospheric pressure and a two-dimensional calculation model of electric field in arc were established, and the effect of the electrode embedded with magnesia-carbon material on the breakdown process and electric field in arc are studied. It is found that the breakdown process between the electrode and the molten pool develops in the form of positive streamer, whether using ordinary electrode or electrode embedded with magnesia-carbon material. The electrode embedded with magnesia-carbon material can accelerate the development of head of electron avalanche in the process of breakdown in micro-gap, increase the electron density of head of electron avalanche and shorten the time consumed in the process of breakdown. Under the external voltage in AC arc, the maximum value of electric field strength changes periodically, the region of the maximum value and maximum value increases with the increase of the radius of the magnesia-carbon material, resulting in serious distortion in the distribution of electric field, which can effectively reduce the breakdown voltage threshold.

Application of immersed boundary-lattice boltzmann method in failure of automobile door sealing strip

Immersed boundary-lattice Boltzmann method was used to study the failure of automobile door sealing strip considering fluid-structure interaction under pressure difference. Based on the actual vehicle model, a two-dimensional calculation model of simplified automobile door sealing strip was established by using immersed boundary method, and practical problems such as the equivalent sealing strip wall thickness correction, wall friction, and pressure balance holes were solved. The accuracy of the model was verified by finite element method. The unsteady pressure outside the vehicle was obtained by CFD and verified by wind tunnel experiment, which could be used as references for setting boundary conditions. In the process of studying the seal failure, by setting the average value, the fluctuation amplitude and the frequency of pressure difference, an automatic iterative program was compiled to obtain the failure situations of the seal under critical pressure difference conditions. The results show that the constant value of the unsteady pressure outside vehicle is the dominant factor, then the coupling between the unsteady pressure frequency and the sealing strip natural frequency, or the increase of the fluctuation range will aggravate seal failure.

Study on numerical calculation of flow structures in a curved open channel with advanced depth-integrated models

A better understanding of flow structures distribution in rivers is crucial to determine the safety degree of rivers. A practical and reliable model is required to overcome the issue of the long computational time of a three-dimensional calculation model and the lack of computation detail of a two-dimensional calculation model for flow structures distribution simulation in rivers. This paper presented an advanced depth-integrated numerical calculation method called the bottom velocity calculation (BVC) to reproduce the flow structures in a curved open channel. BVC method is an integrated multiscale simulation of flows in rivers that can evaluate vertical distributions of velocities and bottom velocity distributions by introducing depth-averaged horizontal vorticity and horizontal momentum equations on a water surface. It has several models, such as simplified bottom velocity calculation (SBVC) with shallow water assumption and general bottom velocity calculation (GBVC) method without the assumptions. The advantages of the BVC method, including SBVC and GBVC models, are validated in this paper using experimental datasets of a curved open channel and compared to two-dimensional and three-dimensional models. The results show that the BVC method has good reproducibility to simulate the flow structures distribution in the channel.

Two-Dimensional Model for Calculation of the Working Process of a Spark-Ignited Engine

Two-Dimensional Model for Calculation of the Working Process of a Spark-Ignited Engine

An improved approach to evaluate the compaction compensation grouting efficiency in sandy soils

This study focuses on a prediction approach of compaction compensation grouting efficiency in sandy soil. Based on Darcy\'s law, assuming that the grouting volume is equal to the volume of the compressed soil, a two-dimensional calculation model of the compaction compensation grouting efficiency was improved to three-dimensional, which established a dynamic relationship between the radius of the grout body and the grouting time. The effectiveness of this approach was verified by finite element analysis. The calculation results show that the grouting efficiency decreases with time and tends to be stable. Meanwhile, it also indicates that the decrease of grouting efficiency mainly occurs in the process of grouting and will continue to decline in a short time after the completion of grouting. The prediction three-dimensional model proposed in this paper effectively complements the dynamic relationship between grouting compaction radius and grouting time, which can more accurately evaluate the grouting efficiency. It is practically significant to ensure construction safety, control grouting process, and reduce the settlement induced by tunnel excavation.

Removal of paint layer by layer using a 20 kHz 140 ns quasi-continuous wave laser

In this paper, an investigation of laser cleaning of the paint on aluminum substrates using a 20 kHz 140 ns quasi-continuous wave laser was presented both theoretically and experimentally. The temperature distribution and its relationship with the average overlapping rate of adjacent laser spots, which affects the cleaning efficiency, were analyzed and simulated in a two-dimensional calculation model, and the temperature elevation and ablation depth of the paint under the action of quasi-continuous wave laser pulses were obtained. The removal of paint layer by layer is conducted experimentally and compared with the calculation. The quantitative removal of 3 layers of paint with a surface paint of 80 μm, an intermediate paint of 50 μm, and a primer paint of 50 μm was realized. The laser removal of paint involves the heating of the paint to a critical temperature by absorbing certain number of laser pulses and the vaporization of the heated paint. The experimental results show that the experimental results agree well with the simulated results when the paint is relatively thick. In the case that the thickness of paint becomes thinner, the simulation results does not agree well with the experimental results, a more comprehensive model considering heat conduction effect of the substrate is needed.

Multi-objective genetic optimization of the heat transfer for tube inserted with porous media

This work is aimed at determining the best configurations of porous media inserted in a tube to achieve the excellent performance of fluid flow and heat transfer. Both geometry parameters and property parameters are the variables to be optimized. In order to evaluate the performance of tube, two conflicting objectives, Nusselt number Nu and friction factor f, are simultaneously considered. In the optimization process, computational fluid dynamics (CFD) and multi-objective genetic algorithm are coupled to obtain the numerical solutions of two-dimensional calculation model and Pareto front composed of non-inferior solutions. Besides, an attempt of utilizing limited resources is made by applying the penalty function instead of adding or modifying governing equations to restrain the flow resistance. Subsequently, technique for order preference by similarity to an ideal solution (TOPSIS) is employed to help decision makers determine the best alternative from the Pareto front. The results selected by TOPSIS are compared with the alternative which has the maximum Nusselt number. It is found that TOPSIS is effective to balance deferent objectives and determine compromise parameters.

Extremely selective modal oscillation of random lasing induced by strong multiple scattering

We report on a new physical aspect of random lasing, an extremely selective modal oscillation by using a two-dimensional calculation model. The developed model consists of two theoretical subsystems, two-dimensional scattering model for describing multiple scattering process and rate equation model for describing lasing process. Using this model, we show how emission spectrum behaves as the scattering state of photons inside the system changes. It is shown that specific and strong modal oscillation takes place in a closed loop path of emitted photons, efficiently supported by the background multiple scattering. With the increase of multiple scattering events around the closed loop path, the system starts to oscillate with an extremely strong mode without any ASE (amplified spontaneous emission) noise.

SoilFlex: A model for prediction of soil stresses and soil compaction due to agricultural field traffic including a synthesis of analytical approaches

Soil compaction is one of the most important factors responsible for soil physical degradation. Soil compaction models are important tools for controlling traffic-induced soil compaction in agriculture. A two-dimensional model for calculation of soil stresses and soil compaction due to agricultural field traffic is presented. It is written as a spreadsheet that is easy to use and therefore intended for use not only by experts in soil mechanics, but also by e.g. agricultural advisers. The model allows for a realistic prediction of the contact area and the stress distribution in the contact area from readily available tyre parameters. It is possible to simulate the passage of several machines, including e.g. tractors with dual wheels and trailers with tandem wheels. The model is based on analytical equations for stress propagation in soil. The load is applied incrementally, thus keeping the strains small for each increment. Several stress–strain relationships describing the compressive behaviour of agricultural soils are incorporated. Mechanical properties of soil can be estimated by means of pedo-transfer functions. The model includes two options for calculation of vertical displacement and rut depth, either from volumetric strains only or from both volumetric and shear strains. We show in examples that the model provides satisfactory predictions of stress propagation and changes in bulk density. However, computation results of soil deformation strongly depend on soil mechanical properties that are labour-intensive to measure and difficult to estimate and thus not readily available. Therefore, prediction of deformation might not be easily handled in practice. The model presented is called SoilFlex, because it is a soil compaction model that is flexible in terms of the model inputs, the constitutive equations describing the stress–strain relationships and the model outputs.

Numerical simulation for the Piston effect and thermal diffusion observed in supercritical nitrogen

Heat transport mechanism in supercritical nitrogen near the pseudo-critical line is investigated using a two-dimensional calculation model that is a rectangular cavity with a horizontal heated wall located at the top. The thermo-fluid dynamics equations are solved directly using the finite difference method. The calculation results qualitatively agree with the experimental results, which were obtained using a laser holography interferometer. It is verified that thermal energy is propagated by the Piston effect around the pseudo-critical line.

Quench analysis of an ITER 13T-40kA Nb 3Sn coil (CS insert)

In order to analyze the quench characteristic of a cable-in-conduit (CIC) conductor that has a sub-cooling channel at the center of conductor cross section, an axisymmetric two-dimensional calculation model was developed. The tests and calculation results of the central solenoid (CS) insert were compared regarding the pressure drop and the behavior of the total voltage, temperature and normal zone propagation in the quench. They show good agreement. Therefore, the effectiveness of the calculation model is verified. It was also found that there is coolant convection between the central channel and bundle region even in a steady state. This makes the pressure drop in the central channel larger than that in a cylindrical pipe which has a smooth surface. In addition, it was found that the higher temperature of the coolant flowing through the central channel heats the coolant and the cable in the bundle region. It can be said that the hot coolant flowing through the central channel accelerates normal zone propagation.

Characteristics of a dye laser amplifier transversely pumped by copper vapor lasers with a two-dimensional calculation model

A two-dimensional rate equation model, taking into consideration the transverse absorption loss of pump laser power, is proposed to evaluate the characteristics of a dye laser amplifier with a large input laser beam diameter pumped by high average power copper vapor lasers. The calculations are in good agreement with the measurements taken with a Rhodamine 6G dye, and the model can be used for evaluation of the dye concentration at any wavelength.