Two-dimensional Axisymmetric Simulations Research Articles

Infrared imaging diagnostics for intense pulsed electron beam.

Infrared imaging diagnostic method for two-dimensional calorimetric diagnostics has been developed for intense pulsed electron beam (IPEB). By using a 100-μm-thick tungsten film as the infrared heat sink for IPEB, the emitting uniformity of the electron source can be analyzed to evaluate the efficiency and stability of the diode system. Two-dimensional axisymmetric finite element method heat transfer simulation, combined with Monte Carlo calculation, was performed for error estimation and optimization of the method. The test of the method was finished with IPEB generated by explosive emission electron diode with pulse duration (FWHM) of 80 ns, electron energy up to 450 keV, and a total beam current of over 1 kA. The results showed that it is possible to measure the cross-sectional energy density distribution of IPEB with energy sensitivity of 0.1 J/cm(2) and spatial resolution of 1 mm. The technical details, such as irradiation protection of bremsstrahlung γ photons and the functional extensibility of the method were discussed in this work.

On the effects of a pressure induced amorphous silicon layer on consecutive spreading resistance microscopy scans of doped silicon

In this study, the evolution of the Scanning Spreading Resistance Microscopy (SSRM) signal, as a function of the doping level and of the bias voltage applied for consecutive scans, is carefully analyzed for an intimate high force contact between the tip and a silicon staircase test-structure. Within our experimental set-up, the SSRM technique, performed in ambient air, is used to collect the overall current flowing through the tip-sample Schottky nanocontact, taking into account the local spreading resistance contribution and the current flowing along the surface around the conductive tip. Whereas no significant bias voltage sign dependence is measured in n-type epitaxially doped silicon, a large increase of the overall resistance is demonstrated in lightly doped p-type silicon for a negatively biased sample. In this regime, the Schottky nanocontact blocks the spreading current, and a surface current of minority carriers can be observed. Moreover, micro-Raman analysis shows that the topside silicon layer, which remains after SSRM scanning is amorphous and therefore that SSRM scanning promotes silicon surface amorphization around the tip. Hence, the surface leakage current is suppressed, which impacts the total measured current, especially on lightly doped p-type silicon where it may play a significant role. By using Peak Force Tapping Quantitative Nano-Mechanical (PF-QNM) mode, the micro-structural, nano-mechanical properties are determined for n- and p-type epitaxially doped silicon, after successive SSRM scans. Finally, two-dimensional axisymmetric device simulations have been performed and confirm the impact of the minority carrier induced current on pristine samples. Thus, differential measurement between the first and the second SSRM scan allow the surface current to be probed.

FROM ENGINE TO AFTERGLOW: COLLAPSARS NATURALLY PRODUCE TOP-HEAVY JETS AND EARLY-TIME PLATEAUS IN GAMMA-RAY BURST AFTERGLOWS

We demonstrate that the steep decay and long plateau in the early phases of gamma-ray burst X-ray afterglows are naturally produced in the collapsar model, by a means ultimately related to the dynamics of relativistic jet propagation through a massive star. We present two-dimensional axisymmetric hydrodynamical simulations that start from a collapsar engine and evolve all the way through the late afterglow phase. The resultant outflow includes a jet core that is highly relativistic after breaking out of the star, but becomes baryon loaded after colliding with a massive outer shell, corresponding to mass from the stellar atmosphere of the progenitor star which became trapped in front of the jet core at breakout. The prompt emission produced before or during this collision would then have the signature of a high Lorentz factor jet, but the afterglow is produced by the amalgamated post-collision ejecta that has more inertia than the original highly relativistic jet core and thus has a delayed deceleration. This naturally explains the early light curve behavior discovered by Swift, including a steep decay and a long plateau, without invoking late-time energy injection from the central engine. The numerical simulation is performed continuously from engine to afterglow, covering a dynamic range of over 10 orders of magnitude in radius. Light curves calculated from the numerical output demonstrate that this mechanism reproduces basic features seen in early afterglow data. Initial steep decays are produced by internal shocks, and the plateau corresponds to the coasting phase of the outflow.

Numerical simulation for the production of chemically active species in primary and secondary streamers in atmospheric-pressure dry air

Production of chemically active species in primary and secondary streamers is investigated using a two-dimensional axisymmetric numerical simulation model. The production processes of N2(v = 1), O(3P) and N(4S), which each have different threshold energies, are simulated using experimentally obtained pulsed voltages with peak values, Vpeak, of 18, 24 and 30 kV in dry air at atmospheric pressure. As Vpeak increases, the simulated length of the secondary streamer increases, although there is little change in the primary streamer characteristics. This means that the ratio of the secondary streamer phase to the primary streamer phase increases for increasing Vpeak. The simulated results show that as Vpeak increases, the energy efficiency of O(3P) production increases and that of N2(v = 1) production decreases. On the other hand, the energy efficiency of N(4S) production has reduced dependence on Vpeak. These characteristics can be explained by the spatiotemporal variations of the reduced electric field in the primary and secondary streamer.

Predictions of Heat Transfer and Flow Circulations in Differentially Heated Liquid Columns With Applications to Low-Pressure Evaporators

Numerical computations are presented for the temperature and velocity distributions of two differentially heated liquid columns with liquor depths of 0.1 m and 2.215 m, respectively. The temperatures in the liquid columns vary considerably with respect to position for pure conduction, free convection, and nucleate boiling cases using one-dimensional (1D) thermal resistance networks. In the thermal resistance networks the solutions are not sensitive to the type of condensing and boiling heat transfer coefficients used. However, these networks are limited and give no indication of velocity distributions occurring within the liquor. To alleviate this issue, two-dimensional (2D) axisymmetric and three-dimensional (3D) computational fluid dynamics (CFD) simulations of the test rigs have been performed. The axisymmetric conditions of the 2D simulations produce unphysical solutions; however, the full 3D simulations do not exhibit these behaviors. There is reasonable agreement for the predicted temperatures, heat fluxes, and heat transfer coefficients when comparing the boiling case of the 1D thermal resistance networks and the CFD simulations.

Investigating parametric effects on performance of a high-temperature URSOFC

Summary The aim of this paper is to investigate the effects of variable parameters on the performance of a unitized regenerative solid oxide fuel cell (URSOFC) using a two-dimensional axisymmetric simulation model. This model was validated using the performance curves of an in-house button-type URSOFC. The parameters studied include the operating temperature and the porosity, tortuosity, and grain diameter of the electrodes while the URSOFC is operated in the solid oxide fuel cell mode and the solid oxide electrolyzer cell (SOEC) mode. The predicted results show that the temperature and the electrode porosity have a beneficial effect on the performance of the URSOFC because of an enhancement of the electrochemical reactions and the species mass transfer, respectively. However, when the URSOFC is operated in the SOEC mode, the cell performance decreases as the electrode porosity increases. This indicates that the decreasing reaction active sites as a result of the higher porosity have a dominant effect on the performance in the SOEC mode. The cell performance also decreases as the tortuosity and grain diameter of the electrodes increase. In addition, the effect of the electrode grain diameter on the cell performance is predicted to be insignificant for the URSOFC operated in the SOEC mode. The results of investigations presented in this paper can assist in the optimal design and management of a URSOFC. Copyright © 2014 John Wiley & Sons, Ltd.

Numerical simulation of a 100-ton ANFO detonation

This work describes the results from a US government-owned hydrocode (SHAMRC, Second-Order Hydrodynamic Automatic Mesh Refinement Code) that simulated an explosive detonation experiment with 100,000 kg of Ammonium Nitrate–Fuel Oil (ANFO) and 2,080 kg of Composition B (CompB). The explosive surface charge was nearly hemispherical and detonated in desert terrain. Two-dimensional axisymmetric (2D) and three-dimensional (3D) simulations were conducted, with the 3D model providing a more accurate representation of the experimental setup geometry. Both 2D and 3D simulations yielded overpressure and impulse waveforms that agreed qualitatively with experiment, including the capture of the secondary shock observed in the experiment. The 2D simulation predicted the primary shock arrival time correctly but secondary shock arrival time was early. The 2D-predicted impulse waveforms agreed very well with the experiment, especially at later calculation times, and prediction of the early part of the impulse waveform (associated with the initial peak) was better quantitatively for 2D compared to 3D. The 3D simulation also predicted the primary shock arrival time correctly, and secondary shock arrival times in 3D were closer to the experiment than in the 2D results. The 3D-predicted impulse waveform had better quantitative agreement than 2D for the later part of the impulse waveform. The results of this numerical study show that SHAMRC may be used reliably to predict phenomena associated with the 100-ton detonation. The ultimate fidelity of the simulations was limited by both computer time and memory. The results obtained provide good accuracy and indicate that the code is well suited to predicting the outcomes of explosive detonations.

The use of Volume of Fluid technique to analyze multiphase flows: Specific case of bubble rising in still liquids

A numerical study on rising bubbles in still liquids employing the Volume of Fluid (VOF) technique to track the interface is presented here. First, a combination of the correlation provided by Rastello et al. (2011) for the rectilinear motion of a bubble with that given by Clift et al. (1978) in the zig-zag ascension regime, conveniently made dimensionless, is proposed to determine the bubble terminal velocity for a wide range of bubble sizes and fluid properties. Furthermore, the crosspoint of both correlations gives the critical Weber number, Wec=ρlUT2D/σc, at which the transition from a rectilinear to a zig-zag bubble motion takes place in a liquid of a given Morton number, Mo=gμl4/σ3ρl. Concerning the numerical simulations, two different open source solvers have been evaluated, i.e. InterFoam and Gerris Flow Solver, to describe the motion of a stable bubble rising with a rectilinear path by performing two-dimensional axisymmetric simulations. The simulations show the presence of parasitic currents and variable results depending on the mesh resolution in the case of InterFoam, whereas no spurious results are observed in Gerris, which is therefore more suitable for these kinds of flows. Finally, the numerical results indicate that the gas properties hardly affect the bubble terminal velocity and shape, although they show that the flow field inside the bubble is highly affected by the gas density and viscosity. This result can be of relevance in heat and mass transfer processes where the mass diffusion or heat exchange can be enhanced by the convective motion induced inside the bubble.

Numerical Simulations of Flat Laminar Premixed Methane-Air Flames at Elevated Pressure

Two-dimensional axisymmetric simulation of stoichiometric methane-air flames stabilized on flat burners at elevated pressure is reported in the present work. Such flames, in practice, are experimentally obtained using the heat flux method for measurement of laminar burning velocity of fuel-oxidizer mixtures (Bosschaart and de Goey, 2004; Goswami et al., 2013). The method makes use of a burner with a perforated brass burner plate. The dimensions of such a plate play an important role in creating flat flames. The present investigation is focused on studying laminar premixed flame structure numerically at elevated pressure up to 15 bar using a one-step and a detailed chemical reaction mechanism. Three burner plate models (of varying hole diameter and porosity) are used in the simulations for pressures up to 7 bar with a one-step mechanism. The surface area increase of the flame was evaluated based on an isotherm at 900 K and the net reaction rate of methane compared to a flat flame. The comparison of these models shows that the surface area increase can significantly be reduced by choosing a smaller hole diameter and larger porosity. The results of the detailed simulations using an appropriate chemical reaction mechanism up to 15 bar using a burner plate model, which is similar to the ones used in experiments (mentioned above), show a nonlinear increase of the flame curvature with elevating pressure. A hole diameter of 0.25 mm and a pitch of 0.29 mm is suggested for a burner plate in such experiments. Flame structure at elevated pressure is also analyzed further based on species profiles obtained.

Models of the circumstellar medium of evolving, massive runaway stars moving through the Galactic plane

At least 5 per cent of the massive stars are moving supersonically through the interstellar medium (ISM) and are expected to produce a stellar wind bow shock. We explore how the mass loss and space velocity of massive runaway stars affect the morphology of their bow shocks. We run two-dimensional axisymmetric hydrodynamical simulations following the evolution of the circumstellar medium of these stars in the Galactic plane from the main sequence to the red supergiant phase. We find that thermal conduction is an important process governing the shape, size and structure of the bow shocks around hot stars, and that they have an optical luminosity mainly produced by forbidden lines, e.g. [OIII]. The Ha emission of the bow shocks around hot stars originates from near their contact discontinuity. The H$\alpha$ emission of bow shocks around cool stars originates from their forward shock, and is too faint to be observed for the bow shocks that we simulate. The emission of optically-thin radiation mainly comes from the shocked ISM material. All bow shock models are brighter in the infrared, i.e. the infrared is the most appropriate waveband to search for bow shocks. Our study suggests that the infrared emission comes from near the contact discontinuity for bow shocks of hot stars and from the inner region of shocked wind for bow shocks around cool stars. We predict that, in the Galactic plane, the brightest, i.e. the most easily detectable bow shocks are produced by high-mass stars moving with small space velocities.

MATTER MIXING IN ASPHERICAL CORE-COLLAPSE SUPERNOVAE: A SEARCH FOR POSSIBLE CONDITIONS FOR CONVEYING56Ni INTO HIGH VELOCITY REGIONS

We perform two-dimensional axisymmetric hydrodynamic simulations of matter mixing in aspherical core-collapse supernova explosions of a 16.3 $M_{\odot}$ star with a compact hydrogen envelope. Observations of SN 1987A have provided evidence that $^{56}$Ni synthesized by explosive nucleosynthesis is mixed into fast moving matter ($\gtrsim$ 3,500 km s$^{-1}$) in the exploding star. In order to clarify the key conditions for reproducing such high velocity of $^{56}$Ni, we revisit matter mixing in aspherical core-collapse supernova explosions. Explosions are initiated artificially by injecting thermal and kinetic energies around the interface between the iron core and the silicon-rich layer. Perturbations of 5% or 30% amplitude in the radial velocities are introduced at several points in time. We found that no high velocity $^{56}$Ni can be obtained if we consider bipolar explosions with perturbations (5% amplitude) of pre-supernova origins. If large perturbations (30% amplitude) are introduced or exist due to some unknown mechanism in a later phase just before the shock wave reaches the hydrogen envelope, $^{56}$Ni with a velocity of 3,000 km s$^{-1}$ can be obtained. Aspherical explosions that are asymmetric across the equatorial plane with clumpy structures in the initial shock waves are investigated. We found that the clump sizes affect the penetration of $^{56}$Ni. Finally, we report that an aspherical explosion model that is asymmetric across the equatorial plane with multiple perturbations of pre-supernova origins can cause the penetration of $^{56}$Ni clumps into fast moving matter of 3,000 km s$^{-1}$. We show that both aspherical explosion with clumpy structures and perturbations of pre-supernova origins may be necessary to reproduce the observed high velocity of $^{56}$Ni. To confirm this, more robust three-dimensional simulations are required.

Numerical analysis of vortex core phenomenon during draining from cylinder tank for various initial swirling speeds and various tank and drain port sizes

A dimple appears on a free surface while rotating a cylinder tank filled with liquid. The dimple starts to concentrically deeper to a drain port at the bottom center of the tank. Over time, the dimple penetrates the drain port, a free surface forms a long and slender string shape in the tank, and a so-called vortexing (air core) phenomenon occurs. The generation of a vortex core depends on the size of the tank and drain port, and on the properties of the liquid in the tank. In this study, the liquid level and the time at which the vortex core is initially generated are numerically investigated using different values of tank diameter, drain port diameter, and initial tank rotational speeds. Instead of a full three-dimensional analysis, a two-dimensional axisymmetric simulation is conducted. The momentum conservation equation in the circumferential direction is additionally solved in the two-dimensional mesh system. Several non-dimensional variables are created: the ratio of the air core generation distance and tank diameter, the diameter ratio of the tank and drain port, the rotational Reynolds number, the rotational Froude number, and the rotational Weber number. Finally, the nondimensional air core generation distance is correlated with the other non-dimensional parameters.

Applied magnetic field design for the field reversed configuration compression heating experiment

Detailed calculations of the formation, guide, and mirror applied magnetic fields in the FRC compression-heating experiment (FRCHX) were conducted using a commercially available generalized finite element solver, COMSOL Multiphysics(®). In FRCHX, an applied magnetic field forms, translates, and finally captures the FRC in the liner region sufficiently long to enable compression. Large single turn coils generate the fast magnetic fields necessary for FRC formation. Solenoidal coils produce the magnetic field for translation and capture of the FRC prior to liner implosion. Due to the limited FRC lifetime, liner implosion is initiated before the FRC is injected, and the magnetic flux that diffuses into the liner is compressed. Two-dimensional axisymmetric magnetohydrodynamic simulations using MACH2 were used to specify optimal magnetic field characteristics, and this paper describes the simulations conducted to design magnetic field coils and compression hardware for FRCHX. This paper presents the vacuum solution for the magnetic field.

Analysis of Self-Excited Combustion Instabilities Using Two- and Three-Dimensional Simulations

Three-dimensional simulations of combustion instability can provide extremely valuable insight into the problem physics, but they represent an enormous investment in time and, thus, may preclude parametric studies that are practical with two-dimensional simulations. Three numerical simulations of an unstable laboratory rocket combustor were performed to assess the effect of grid resolution and dimensionality on the ability to predict and model combustion instability. Computations show that two-dimensional axisymmetric simulations using both coarse and fine grids are able to capture the amplitude of the first longitudinal mode within an order of magnitude of what was measured in the experiment. Whereas the three-dimensional calculation based on the coarse grid resolution shows excellent agreement with the experimental level of instability two-dimensional simulations are valuable in parametric evaluations in developing diagnostic methods and in increasing the efficiency of expensive three-dimensional simulations.

LOCAL TWO-DIMENSIONAL PARTICLE-IN-CELL SIMULATIONS OF THE COLLISIONLESS MAGNETOROTATIONAL INSTABILITY

The magnetorotational instability (MRI) is a crucial mechanism of angular momentum transport in a variety of astrophysical accretion disks. In systems accreting at well below the Eddington rate, such as the central black hole in the Milky Way (Sgr A*), the rate of Coulomb collisions between particles is very small, making the disk evolve essentially as a collisionless plasma. We present a nonlinear study of the collisionless MRI using first-principles particle-in-cell (PIC) plasma simulations. In this initial study we focus on local two-dimensional (axisymmetric) simulations, deferring more realistic three-dimensional simulations to future work. For simulations with net vertical magnetic flux, the MRI continuously amplifies the magnetic field until the Alfv\'en velocity, v_A, is comparable to the speed of light, c (independent of the initial value of v_A/c). This is consistent with the lack of saturation of MRI channel modes in analogous axisymmetric MHD simulations. The amplification of the magnetic field by the MRI generates a significant pressure anisotropy in the plasma (with the perpendicular pressure being larger than the parallel pressure). We find that this pressure anisotropy in turn excites mirror modes and that the volume averaged pressure anisotropy remains near the threshold for mirror mode excitation. Particle energization is due to both reconnection and viscous heating associated with the pressure anisotropy. Reconnection produces a distinctive power-law component in the energy distribution function of the particles, indicating the likelihood of non-thermal ion and electron acceleration in collisionless accretion disks. This has important implications for interpreting the observed emission -- from the radio to the gamma-rays -- of systems such as Sgr A*.

MAGNETIC BRAKING FORMULATION FOR SUN-LIKE STARS: DEPENDENCE ON DIPOLE FIELD STRENGTH AND ROTATION RATE

We use two-dimensional axisymmetric magnetohydrodynamic simulations to compute steady-state solutions for solar-like stellar winds from rotating stars with dipolar magnetic fields. Our parameter study includes 50 simulations covering a wide range of relative magnetic field strengths and rotation rates, extending from the slow- and approaching the fast-magnetic-rotator regimes. Using the simulations to compute the angular momentum loss, we derive a semi-analytic formulation for the external torque on the star that fits all of the simulations to a precision of a few percents. This formula provides a simple method for computing the magnetic braking of sun-like stars due to magnetized stellar winds, which properly includes the dependence on the strength of the magnetic field, mass loss rate, stellar radius, suface gravity, and spin rate and which is valid for both slow and fast rotators.

Numerical investigation for pressure mitigation effects of dike on blast wave

The three-dimensional and two-dimensional axisymmetric fluid dynamics simulations were carried out to clarify the blast pressure mitigating effects of dike’s configuration in hemispherical explosion. The simulated peak overpressure on the ground under the hemispherical explosion was compared with the empirical formula by Kingery, and the simulated data were validated. In the analysis, the simplification techniques for the numerical simulation were employed under the following two assumptions. The pressure distribution behind the wide dike was estimated using the axisymmetric flowfield, and the back step model was applied under the small condition for θ, the angle formed by the ground and the line between the explosion core and the dike front corner. From the simulated results, it is clarified that the large θ provided the great reduction of the blast wave pressure at faraway position. In the small θ condition, the conditions of the dike end position and the dike height were significant parameters determining the magnitude of pressure reduction and mitigated area. The pressure reduction at the dike end and mitigated area were predicted numerically, and related to the dike conditions.

Numerical Simulation for Mechanical Behavior of Carbon Black Filler Particle Reinforced Rubber Matrix Composites

In this paper, the micromechanical finite element method based on Representative Volume Element has been applied to study and analyze the macro mechanical properties of the carbon black filled rubber composites by using two-dimensional plane stress simulations and three-dimensional axisymmetric simulations under uniaxial compression respectively. The dependence of the macroscopic stress-strain behavior and the effective elastic modulus of the composites, on particle shape, particle area/volume fraction and particle stiffness has been investigated and discussed. Additionally, the simulation results of the two-dimensional plane stress model and the three-dimensional axisymmetric model are evaluated and compared with the experimental data, which shows that the two-dimensional plane stress simulations generate poor predictions on the mechanical behavior of the carbon black particle reinforced rubber composites, while the three-dimensional axisymmetric simulations appear to give a better prediction.

The effect of friction on indenter force and pile-up in numerical simulations of bone nanoindentation

Nanoindentation is a useful technique for probing the mechanical properties of bone, and finite element (FE) modeling of the indentation allows inverse determination of elastoplastic constitutive properties. However, all but one FE study to date have assumed frictionless contact between indenter and bone. The aim of this study was to explore the effect of friction in simulations of bone nanoindentation. Two-dimensional axisymmetric FE simulations were performed using a spheroconical indenter of tip radius 0.6 μm and angle 90°. The coefficient of friction between indenter and bone was varied between 0.0 (frictionless) and 0.3. Isotropic linear elasticity was used in all simulations, with bone elastic modulus E = 13.56 GPa and Poisson’s ratio of 0.3. Plasticity was incorporated using both Drucker–Prager and von Mises yield surfaces. Friction had a modest effect on the predicted force–indentation curve for both von Mises and Drucker–Prager plasticity, reducing maximum indenter displacement by 10% and 20% respectively as friction coefficient was increased from zero to 0.3 (at a maximum indenter force of 5 mN). However, friction has a much greater effect on predicted pile-up after indentation, reducing predicted pile-up from 0.27 to 0.11 μm with a von Mises model, and from 0.09 to 0.02 μm with Drucker–Prager plasticity. We conclude that it is potentially important to include friction in nanoindentation simulations of bone if pile-up is used to compare simulation results with experiment.

JET PROPAGATIONS, BREAKOUTS, AND PHOTOSPHERIC EMISSIONS IN COLLAPSING MASSIVE PROGENITORS OF LONG-DURATION GAMMA-RAY BURSTS

We investigate by two-dimensional axisymmetric relativistic hydrodynamical simulations (1) jet propagations through an envelope of a rapidly rotating and collapsing massive star, which is supposed to be a progenitor of long duration gamma ray bursts (GRBs), (2) breakouts and subsequent expansions into stellar winds and (3) accompanying photospheric emissions. We find that if the envelope rotates uniformly almost at the mass shedding limit, its outer part stops contracting eventually when the centrifugal force becomes large enough. Then another shock wave is formed, propagates outwards and breaks out of the envelope into the stellar wind. Which breaks out earlier, the jet or the centrifugal bounce-induced shock, depends on the timing of jet injection. If the shock breakout occurs earlier owing to a later injection, the jet propagation and subsequent photospheric emissions are affected substantially. We pay particular attention to observational consequences of the difference in the timing of jet injection. We calculate optical depths to find the location of photospheres, extracting densities and temperatures at appropriate retarded times from the hydrodynamical data. We show that the luminosity and observed temperature of the photospheric emissions are both much lower than those reported in previous studies. Although luminosities are still high enough for GRBs, the observed temperature are lower than the energy at the spectral peak expected by the Yonetoku-relation. This may imply that energy exchanges between photons and matter are terminated deeper inside or some non-thermal processes are operating to boost photon energies.