2D Axis-symmetry Research Articles

Discrete particle methods for granular bentonite material simulation

Bentonite clays are strategic materials to ensure the sealing capacity of engineered barrier systems (EBS) in deep geological repositories of high-level radioactive waste. Formerly installed in the form of compacted blocks, in recent years, there has been growing interest in EBS design using granular bentonite materials (GBM) due to improved construction processes [1]. GBM range from the powdered and granulated forms, both natural and obtained from crushed blocks, to compressed bentonite pellets, and the mixtures thereof. The effect of thermo-hydro-chemo-mechanical (THCM) conditions on the evolving gap-filling performance following installation has been investigated in full-scale experiments [2] and in laboratory-scale tests [3], with particular focus on bentonite pellet-powder mixtures [4, 5, 6].
 Numerical modelling of coupled THCM expansive soil behaviour is widespread using continuum methods, namely the finite element method [7, 8], applicable up to full-scale systems even though at the expense of resolution. At the laboratory scale, discrete particle-based methods accounting for the granular nature of bentonite materials in the early stages of hydration provide insight into pellet shape and local effects on the mechanical behaviour of dry pellet-powder systems as well as hydro-mechanical effects on the swelling capacity of GBM systems.
 The compressibility of dry pellet packings and pellet-powder mixture samples is modelled by the discrete element method (DEM). This method has been applied to study the swelling behaviour of pellets represented by spherical particles [9]. The DEM is a powerful tool for reproducing complex granular shapes by non-spherical particle surfaces [10] and also with clumps of spheres (Figure 1(a)), allowing to define mixed material and mechanical contact properties within the pellets. The deformation and fissuring of pellets under oedometer compression is tracked using a cohesive particle model [11], including damage for interparticle contacts in tension, which captures deformation associated phenomena such as surface spalling and pellet reorganisation occurring at stress levels below the diametral fracture. In addition, bentonite powder is represented by loose packings of upscaled spheres matching
 the experimental porosity of the fillings, interacting by a classical linear spring-dashpot contact model resulting in the reduced overall compressibility observed in pellet-powder mixtures [5].
 Flow through GBM systems is modelled by the new discrete particle-based XMm method [12]. In the XMm, the material is discretised into a set of bentonite units (BU) or particles acting as representative elementary volumes of a homogeneous continuum inside which the mass balance equations are solved at the megastructural (X), macrostructural (M), and microstructural (m) pore levels (Figure 1(b)). Moreover, the mechanical compatibility of the system is obtained from the coupling between strain increments and centroid displacements in each BU, where the contact stress and overlap between neighbouring particles are updated similarly to the DEM approach. The hydro-mechanical problem is posed as a set of ordinary differential equations (ODE) to be solved for each BU, and thus the efficiency of the XMm is a compromise between the typically reduced computational cost of ODE solvers and the number of BU considered. The XMm has been used to simulate the hydration of a powder sample with low heterogeneity [4], successfully capturing the evolution of the displacement field upon saturation in isochoric conditions. This method is applied to reproduce the confined hydration of a heterogeneous pellet-powder system [6]. Assuming 2D axisymmetry, the XMm allows defining different initial material properties in each BU introducing the heterogeneity of the sample. The evolving swelling pressure is reproduced as well as the hydration velocities at the different structural levels, showing the decreasing heterogeneity of the mixture.

중성 종의 열 유동 해석 및 플라스마 유체 시뮬레이션을 이용한 유도 결합 Ar/H2 플라스마의 특성 분석

Low temperature Ar/H2 plasma is widely used in various industries, including thin film synthesis and surface cleaning processes. In order to optimize the process conditions, it is important to analyze the characteristics of the Ar/H2 plasma regarding the behavior of electrons and ion species. However, the conventional method lacked information on the gas temperature distribution of neutral species, so it was insufficient to explain the correlation. So, a fluid model of 2D axis-symmetry based on inductively coupled plasma (ICP) source using Ar/H2 gas mixture has been developed. In order to investigate the characteristics of the Ar/H2 plasma in more detail, heat transfer equation was used to explain the effect of the neutral gas temperature. The changes in neutral gas temperature according to the pressure and mixture gas ratio were investigated. And the results of plasma parameters were compared with those obtained when the neutral gas temperature was fixed at 300K and 500K.

이중 안테나 제어에 따른 유도결합 N₂/NH₃/SiH₄ 플라스마의 전자 및 라디칼 밀도 분포

Low temperature N₂/NH₃/SiH₄ plasma is used to deposit hydrogenated silicon nitride(SiN<SUB>x</SUB>:H). In this process, the main factor influencing the quality of the deposited film is the active species, such as SiH<SUB>x</SUB> and NH<SUB>x</SUB> radicals. In the conventional methods, it was insufficient to explain the correlation between generation of active species and the process parameters. So, a fluid model of 2D axis-symmetry based on dual antenna inductively coupled plasma (ICP) source using N₂/NH₃/SiH₄ gas mixture has been developed for SiN<SUB>x</SUB>:H film deposition. The gas mixture model was comprised of 57 species, 195 chemical reactions and 16 surface reactions. The ratio of input power between independent antenna system affects the electron and SiH<SUB>x</SUB>, NH<SUB>x</SUB> radical generation. And it was observed that the spatial uniformity of electron and radical density increases when the independent input power of dual antenna system is set to 500:500W.

Numerical investigation of supercritical heat transfer of water flowing in vertical and horizontal tube with emphasis of gravity effect

Over a decade, coal-based thermal power plants are upgraded to operate at supercritical pressure conditions due to its high efficiency and low emissions. Water wall panels of a typical supercritical boiler are structured spirally in the lower furnace and vertically placed in the upper furnace. The spiral tubes are inclined at 19 to 22 degrees in which fluid behaves as in horizontal tubes. The design of water wall panels plays the key role in designing a supercritical boiler. The present work aims to numerically investigate the heat transfer behavior of both vertical and horizontal tubes at the supercritical conditions. Since the temperature distribution across the cross-section of vertical tube is uniform, a 2D axis symmetry tube has been considered for analyzing the vertical tube. Unlike vertical tube, the heat transfer characteristics is different for horizontal tubes. Therefore, a 3D tube has been modelled for the computation of horizontal tubes. In order to gain confidence, the present simulations are validated with experiments results available in the literature. Ansys-Fluent has been used in the present simulation. SST k-ω turbulence model is used in this analysis. In the present work, 10 mm diameter of 4m length of vertical tube has been chosen and simulated at low heat flux to mass flux ratio 0.27 and high heat flux to mass flux ratio 0.67 with pressure 241 bar. The effect of heat flux (q) to mass flux (G) ratio which is responsible for heat transfer enhancement and heat transfer deterioration has been studied for both vertical and horizontal tubes. The wall temperature has been plotted along the length of the tube for both top and bottom portion of horizontal tube and compared with wall temperature of vertical tube. The effect of buoyancy plays a vital role in the heat transfer behavior of horizontal tube compared to vertical tube. Heat transfer deterioration occurs due to buoyancy which has a direct linkage with gravity. Three cases were studied, one with full gravity (factor 1), half gravity (factor 0.5) and zero gravity (factor 0). It has been observed that, sudden rise in wall temperature occurs for the case gravity factor 1.0, i.e, considering the gravity effect. For the case of zero gravity, no sudden peak of local wall temperature is observed due to the absence of buoyancy term in the Navier-Stokes equations. Some of the thermo-physical properties like velocity, turbulent kinetic energy, density, wall temperature and turbulent viscosity are analyzed for three cases.

Turbulence Anisotropy Investigations in an Internal Combustion Engine

Abstract The assumption of isotropic turbulence is commonly incorporated into models of the internal combustion engine (ICE) in-cylinder flows. While preliminary analysis with two-dimensional (2D) velocity data indicates that the turbulence may tend to isotropy as the piston approaches top-dead-center (TDC), the validity of this assumption has not been fully investigated, partially due to the lack of three-component velocity data in ICEs. In this work, the velocity was measured using two-dimensional, three-component (2D-3C) particle image velocimetry in a single-cylinder, motored, research engine to investigate the evolution of turbulence anisotropy throughout the compression stroke. Invariants of the Reynolds stress anisotropy tensor were calculated and visualized, through the Lumley triangle, to investigate turbulence states. Results showed the turbulence to be mostly anisotropic, with preferential tendency toward 2D axisymmetry at the beginning of the compression stroke and approaching-isotropy near top-dead-center. Findings provide new insights into turbulence in dynamic, bounded flows to assist with the development of physics-based, quantitative models.

Electromagnetic FEM studies of disruptions and engineering consequences for the power supply and coils design of planned upper divertor at ASDEX Upgrade

A new upper divertor is proposed for the ASDEX Upgrade (AUG) tokamak experiment. It is planned to be equipped with internal coils for investigation of alternative magnetic configurations like e.g. “snowflake” (Herrmann et al., 2017 [1]). Since the coils are close to the plasma, high induced and very stiff voltages are expected during disruption events. Because only very vague analytical estimates of voltages, forces and coupling factors were available, an improvement by the help of Finite Element Method (FEM) was envisaged. Therefore, recorded measurements of currents, plasma position, plasma profile and the geometry were integrated in an electromagnetic simulation as boundary conditions to calculate resulting field distributions during selected AUG disruptions. The time resolution can be better than 100 μs and the required computing resources are comparably small due to the assumption of 2D axis-symmetry. The results were compared with magnetic probe measurements integrated into the tokamak ultimately observing good agreement. After this, the FE model was modified including the new divertor to calculate all relevant parameters. The output of these calculations has strong implications for the coil and power supply design: i) The power supply will be protected by a new kind of crowbar to avoid damage of the power supply due to overvoltage and uncontrolled current and force rise of the coils. The concept of this so called “ripping crowbar” is introduced, which is now under development. ii) The coil cable should be coaxial shaped to monitor isolation faults and to become inherently safe against single-turn shortcuts, identified as destructive fault scenario.

Numerical Modelling on Modified Directional Solidification Process of Multi-crystalline Silicon Growth for Photovoltaic Applications

A transient global model was used to investigate the effect of bottom grooved furnace upon the directional solidification (DS) process of multi-crystalline silicon (mc-Si). The numerical simulation assumed geometry is perfect 2D axis-symmetry. The temperature distribution, crystal-melt (c-m) interface, thermal stress and dislocation density have been simulated. The modified heat exchanger block system was used for controlling the temperature gradient at the bottom of the crucible. The obtained result shows convex shape of the c-m interface. The von Mises stress and dislocation density were reduced while using the bottom grooved furnace. This work was carried out in the different grooves of radius 30 and 60 mm of the heat exchanger block of the DS furnace.

Modelling of fast jet formation under explosion collision of two-layer alumina/copper tubes

Under explosion collapse of two-layer tubes with an outer layer of high-modulus ceramics and an inner layer of copper, formation of a fast and dense copper jet is plausible. We have performed a numerical simulation of the explosion collapse of a two-layer alumina/copper tube using ANSYS AUTODYN software. The simulation was performed in a 2D-axis symmetry posting on an Eulerian mesh of 3900x1200 cells. The simulation results indicate two separate stages of the tube collapse process: the nonstationary and the stationary stage. At the initial stage, a non-stationary fragmented jet is moving with the velocity of leading elements up to 30 km/s. The collapse velocity of the tube to the symmetry axis is about 2 km/s, and the pressure in the contact zone exceeds 700 GPa. During the stationary stage, a dense jet is forming with the velocity of 20 km/s. Temperature of the dense jet is about 2000 K, jet failure occurs when the value of effective plastic deformation reaches 30.

N2/NH3/SiH4 유도 결합형 플라즈마의 압력과 혼합가스 비율에 따른 이온 및 중성기체 밀도 분포

A fluid model of 2D axis-symmetry based on inductively coupled plasma (ICP) reactor using N₂/NH₃/SiH₄ gas mixture has been developed for hydrogenated silicon nitride (SiNSUBx/SUB : H) deposition. The model was comprised of 62 species (electron, neutral, ions, and excitation species), 218 chemical reactions, and 45 surface reactions. The pressure (10~40 mTorr) and gas mixture ratio (N₂ 80~96 %, NH₃ 2~10 %, SiH₄ 2~10 %) were considered simulation variables and the input power fixed at 1000 W. Different distributions of electron, ions, and molecules density were observed with pressure. Although ionization rate of SiH₂⁺ is higher than SiH₃⁺ by electron direct reaction with SiH₄, the number density of SiH₃⁺ is higher than SiH₂⁺ in over 30 mTorr. Also, number density of NH+ and NH₄⁺ dramatically increased by pressure increase because these species are dominantly generated by gas phase reactions. The change of gas mixture ratio not affected electron density and temperature. With NH₃ and SiH₄ gases ratio increased, SiHx and NHx (except NH⁺ and NH₄⁺) ions and molecules are linearly increased. Number density of amino-silane molecules (SiHSUBx/SUB(NH₂)SUBy/SUB) were detected higher in conditions of high SiHSUBx/SUB and NHSUBx/SUB molecules density.

An assessment of thermo-mechanically induced fatigue damage of a steam turbine shaft

The increasing demands on the flexibility of steam turbines due to the use of renewable energy sources substantially alters the fatigue strength requirements of components of these facilities. The work summarized hereafter was initiated by the effort to develop the methodology of prediction of thermo-mechanical fatigue of steam turbine rotors. A significant effort was put into local thermo-mechanical stress-strain response modelling in the shaft material. An FE model of the structure assuming 2D axisymmetry idealisation was developed and verified. In-house codes based on a variety of approaches to assess critical location and fatigue damage, including the Manson-McKnight and the Nagode methods, were created. The experimental programme aimed to investigate the material fatigue behaviour under the thermo-mechanical conditions was initiated in order to provide data for calibrating and verifying the fatigue prediction procedures. A preliminary study on thermo-mechanical fatigue behaviour was conducted and the results are summarized in the paper.

유체 시뮬레이션을 이용한 선형 마이크로웨이브 플라즈마의 특성 분석

Discharge characteristics of linear microwave plasma were investigated by using fluid simulation of 2D axis-symmetry based on finite elements method. The microwave power was 2.45 GHz TEM mode and transmitted through linear antenna. Resistive power and pressure were considered simulation variables and argon was used for working gas. A decrease of electron density along the quartz tube was observed in low power condition but relatively uniform plasmas were generated in chamber by increasing the resistive power. The electron temperature was highly detected near the surface of quartz tube because the electron was heated only dielectric surface. The power transmission efficiency decreased and characteristics of surface plasma were observed in high electron density condition.

Parallel blast simulation of nonlinear dynamics for concrete retrofitted with steel plate using multi-solver coupling

The blast damage behaviors for concrete panels retrofitted with steel plates exposed to blast loading are investigated. In order to enhance the reliability of the simulation results, the equation of state, strength, and failure model of materials are implemented in an explicit analysis program, AUTODYN. In particular, the implemented formulation includes the rate-dependent plasticity and damage softening; the non-linear strain and strain-rate hardening and non-linear strain softening. Furthermore, simplified and idealized 2D axis-symmetry, 3D, and parallel 3D simulations are compared in order to achieve accurate and efficient computation running times using multi-solver coupling method. Comparing the 2D axis-symmetry and 3D models, 2D model is stiffer and has a smaller deflection than the 3D models by geometries of retrofit material. The result of 3D numerical simulation becomes mesh size dependent, because of the explosive characteristics and mechanical properties of concrete. The parallel 3D simulation shows good scalability up to 15 processors and can be simulated at very high speed-up, while still consuming a reasonable amount of run times. Also, the retrofitted concrete panels are compared to the non-retrofitted concrete panel; maximum deflection and maximum deflection ratio are reduced by 1 mm, 3 mm, and 5 mm thick steel plates, scabbing can be prevented by retrofitted with steel plates. The simulation result shows good agreement with the experimental result. Finally, discussion on the numerical results with respect to code criteria and damage localization in retrofitted concrete panels is presented.

MAGNETOSPHERIC ACCRETION AND EJECTION OF MATTER IN RESISTIVE MAGNETOHYDRODYNAMIC SIMULATIONS

The ejection of matter in the close vicinity of a young stellar object is investigated, treating the accretion disk as a gravitationally bound reservoir of matter. By solving the resistive MHD equations in 2D axisymmetry using our version of the Zeus-3D code with newly implemented resistivity, we study the effect of magnetic diffusivity in the magnetospheric accretion-ejection mechanism. Physical resistivity was included in the whole computational domain so that reconnection is enabled by the physical as well as the numerical resistivity. We show, for the first time, that quasi-stationary fast ejecta of matter, which we call {\em micro-ejections}, of small mass and angular momentum fluxes, can be launched from a purely resistive magnetosphere. They are produced by a combination of pressure gradient and magnetic forces, in presence of ongoing magnetic reconnection along the boundary layer between the star and the disk, where a current sheet is formed. Mass flux of micro-ejection increases with increasing magnetic field strength and stellar rotation rate, and is not dependent on the disk to corona density ratio and amount of resistivity.

The effect of maximum open height on operating characteristics of polymer injected pump poppet valve

Reciprocating polymer injected pump is the key injection equipment of tertiary oil recovery, the poppet valve in it exists the problem of large vibration noise, low efficiency and short life when transportation high viscosity medium. So the CFD technique is adopted to simulate and analyze the inner flow fields of fluid end poppet valve. According to the practical structure of the poppet valve, a simplified 2D axis-symmetry geometry model of the flow field is established. Combined with pump speed, plunger stroke and plunger diameter, given the boundary condition of the inlet valve, then the numerical simulation of flow field under six different maximum open heights is done depending on software Fluent. The relationship between open height to valve gap flow velocity, hydraulic loss and lag angle is obtained. The results indicate that, with the increase of open height, the valve gap flow velocity decreases, inlet outlet pressure differential decreases and hydraulic loss decreases. But the lag angle is continuously increasing with the increase of maximum open height, the valve has a good work performance when the open height is 1, 1.5, 2, 2.5, 3mm, but when it reaches 3.5mm, the valve performance becomes poor. The study can offer certain reference to understand operating characteristics of poppet valve, help to reduce the hydraulic losses and raise volume efficiency of the pump.

Quantification of the distribution of blood flow pressure with postures

At a different angle, this study analyzed the contour chart of blood flow pressure, extreme pressure and its position to quantify DBFP in thirteen different postures with gravity considered or not (G ≠ 0 or G = 0). The aim was to determine the suitable body positions, in which the postural model of a single vessel could be simplified to two-dimensional (2D) symmetrical one while only considering such factors as posture and gravity. Computational fluid dynamic simulations were performed. Numerical results demonstrated that the DBFP showed 2D axisymmetry at ±90° and three-dimensional (3D) asymmetry at any other posture with G ≠ 0, and 2D axisymmetrical one at any posture with G = 0. Therefore, modeling a vessel as a 2D model is feasible in space and at ±90° posture on earth. In addition, the maximum pressure occurred between the inlet and the middle of the vessel, and its position variation mainly happened in the range of 0° - 15°. For a single vessel, this study provides the first theoretical evidence for cardiovascular modeling in microgravity and may help guide the researchers in designing defense devices for astronauts or patients clinically.

Approximate analytical models of temperature and thermal stresses for 2D axis-symmetry object with temperature-dependent properties

This paper presents the approximate analytical models of temperature and thermal stress in a two-dimensional axis-symmetry object. The models can be used to deal with some non-linear factors caused by temperature-dependent properties using multiple parameter perturbation method. Two cases have been used to test the models proposed in this paper. The first case study is the comparison of analysis of the rotor with our models and FEM (finite element method) and it is shown that our models have a satisfactory accuracy. The second case is the application of our models to sensitivity studies. The models proposed reduce computational time significantly compared with FEM method and hence can be used for online analyzing of thermal state of a two-dimensional axis-symmetry object and inverse heat conduction problems.

초고속기용 열박음 로터 제작을 위한 로터의 치수에 따른 가열온도의 해석적 예측

This paper deals with shrink fit analysis of rotor by 2D cross-section, 2D axis-symmetry, and 3D FEM model. And this paper presents 2nd order approximation function of thermal expansion displacement by design variables (shape dimension, heating temperature, sleeve length, interference etc.), table of orthogonal array and RSM(response surface methodology). The possibility of the rotor with shrink fit is evaluated by thermal expansion displacement. If thermal expansion displacement is larger than interference, shrink fit enable to make the rotor. 2D axis-symmetry model and 3D model are more reasonable than 2D cross-section model, because stress and strain is different along length of shaft.

Three-Dimensional Pavement Analysis with Nonlinear Subgrade Materials

The nonlinear models of pavement base and subgrade were briefly reviewed. Subroutines of the three-dimensional finite-element analysis in the ABAQUS package were developed for nonlinear behavior of a coarse-grained base and subgrade. The programs were validated by comparing them with the theoretical-solution-based program BISAR and the 2D finite-element program ILLI-PAVE. Significant discrepancy was found between the 3D analysis and the 2D axisymmetric analysis, especially for the deformation results. It was also found that the stiffness matrices of the nonlinear materials were not symmetrical, which causes accuracy problems in those programs based on 2D axisymmetry formulations. The results of nonlinear analysis and linear analysis were also compared. It was concluded that the determinations of the resilient modulus for the linear models is critical to interpret the behaviors of nonlinear materials.