Two-dimensional Axisymmetric Simulations Research Articles

Data Assimilation of Ideally Expanded Supersonic Jet Using RANS Simulation for High-Resolution PIV Data

Data assimilation using particle image velocimetry (PIV) and Reynolds-averaged Navier–Stokes (RANS) simulation was performed for an ideally expanded supersonic jet flying at a Mach number of 2.0. The present study aims to efficiently reconstruct all the physical quantities in the aeroacoustic fields that match well with a realistic, experimentally obtained flow field. The two-dimensional, two-component PIV measurement was applied to the jet axis plane, and the time-averaged velocity field was obtained using single-pixel ensemble correlation. Two-dimensional axisymmetric RANS simulation using the Menter shear stress transport (SST) model was also performed, and the parameters of the SST model were optimized via data assimilation using the ensemble Kalman filter. The standard deviation of the observation noise σ, which is a parameter of the ensemble Kalman filter, is estimated by the previously proposed method (Nakamura et al., Low-Grid-Resolution-RANS-Based Data Assimilation of Time-Averaged Separated Flow Obtained by LES. Int. J. Comp. Fluid. Dyn., 2022), and its effectiveness was investigated for the first time. This method effectively estimated the magnitude of σ at each generation without tuning the hyperparameters. The assimilated flow fields exhibited similar flow structures observed in PIV such as the potential core length or shear layer. Therefore, the present framework can be used to estimate time-averaged full flow fields that match well with experimentally observed flow fields, and has the potential to construct a database for the Navier-Stokes-based stability analysis that requires a full flow field.

Multi-physics field modeling and electrochemical performance analysis of medium-temperature methanol-fueled proton-conducting solid oxide fuel cell

ABSTRACT A two-dimensional axisymmetric multi-physics field simulation for a methanol-fueled proton-conducting solid oxide fuel cell (CH3OH-SOFC-H) was created in this work. The influence of structural and operating parameters on the performance of the cell was analyzed. Moreover, the cell performance was compared with that of a methanol-oxygen ion-conducting SOFC (CH3OH-SOFC-O) under the same operating conditions. It was found that the anode support enables CH3OH-SOFC-H to exhibit higher performance, with the highest power density being 1493.3 W‧m−2 at 973 K. As the anode flow rate rises, the current density rises and subsequently falls, with a peak of 7623.6 A‧m−2. Meanwhile, as the methanol content in the gas composition and the cathode flow rate increase, so does the current density. CH3OH-SOFC-H has better electrochemical performance at low and medium temperatures, reaching 562.64 W‧m−2 at 773K (66% higher than that of CH3OH-SOFC-O at the same operating conditions). Meanwhile, CH3OH-SOFC-O has better performance at high temperatures. This study provides a theoretical reference for the subsequent application and promotion of CH3OH-SOFC-H.

Numerical investigations of AC arcs’ thermal characteristics in the short gap of copper-cored wires

Excessive alternating current (AC) arcs generated in electric systems will accumulate heat and easily cause fire. This paper studies the thermal characteristics of different numbers of AC arc plasma generated in a short gap of copper-cored wires in the air. The number of AC arcs is controlled in the AC arc experiment and an infrared thermal imager measures the temperature change at the specified position. Based on magnetohydrodynamics (MHD), a two-dimensional axisymmetric AC arc discharge numerical simulation model is established. The volt-ampere characteristic of the AC arc is used to solve the MHD simulation model to obtain the same 'zero current' characteristics as the real AC arc in the experiment. A large amount of heat accumulates in the electrode gaps when the arc generation, and then the heat dissipates in the 'zero current' stage. The continuously generated arc makes the temperature higher. The volume of the space area with a temperature higher than 10,000 K increases with the arc current, but is unrelated to the number of arcs. The volume of the space area with a temperature higher than 524.15 K and the temperature on the electrode are both positively correlated with the number of AC arcs and arc current. The results of this study can provide a reference for the detection standard of AC arc faults and the prevention of electrical fire.

Heat Transfer in Simultaneously Developing Turbulent Mixed Convection Flows in Vertical Tubes

This article investigates the simultaneously developing pure turbulent mixed convective regime and compares the hydrodynamic and thermal features of both buoyancy-assisted and opposed flows in a vertical tube. Two-dimensional (2D) axisymmetric steady-state simulations were carried out for Reynolds number, 5,000–20,000; Grashof number, 1.25 × 106 to 108; and Richardson number, 0.05–0.25 for a length-to-diameter ratio of 150 with uniform heat flux boundary condition and water as the working fluid. Three Reynolds-averaged-Navier–Stokes turbulence models were compared and then the most suitable model was used for the simulations. At a given Richardson number, the friction factor and Nusselt number are lower in the case of buoyancy-assisting flow compared to buoyancy-opposing flows. Similar friction factors and heat transfer trends were obtained at a given Grashof number. At varying Grashof numbers and Richardson numbers keeping the Reynolds number constant, no discernible variations were observed for both flows. The entry length was also examined, and it has been found that the hydrodynamic and thermal entry lengths are restricted to a length-to-diameter ratio of 25 and 20 for assisting and opposing flows, respectively. Correlations were developed for both flows to quantify the friction factor, Colburn factor, and Nusselt number in terms of the Reynolds number.

Effects of piezoelectric synthetic jet actuator parameters on synthetic jet formation process and actuator performance

Aiming at the problem that the non-linearity between the piezoelectric vibrator deflection and the excitation amplitude of the piezoelectric synthetic jet actuator (SJA) causes it difficult to obtain the variation laws of the synthetic jet (SJ) velocity accurately, a theoretical model of the whole flow field of the piezoelectric SJA is established and four important parameters (half period jet mean velocity, Reynolds number, effective jet length and energy) for evaluating the performance of the SJ are proposed. Then a two-dimensional axisymmetric numerical simulation is carried out with k-ω turbulence model to study the SJ formation process and the velocity characteristics of the SJ at the orifice. The results show that the fluid pressure in the cavity is the main reason causing the non-linearity between the piezoelectric vibrator deflection and the excitation amplitude, the influence of which decreases with the increase of the orifice diameter. The SJ velocity increases first and then decreases slowly with the increase of excitation frequency. The extreme point occurs at the first resonant frequency of the piezoelectric vibrator and the position of the maximum velocity occurs at 0.5 mm outside the orifice. Other conditions being constant, both the piezoelectric vibrator deflection and jet velocity have a maximum value when the radius ratio of the piezoelectric layer to the elastic layer is 0.75. Smaller piezoelectric layer thickness leads to larger lateral displacement of the piezoelectric vibrator, and the optimum thickness ratio is 0.25. The results of this study have important guiding significance for accurately obtaining the variation laws of the SJ velocity as well as rationally designing the piezoelectric SJA.

Comparing Early Evolution of Flames in X-Ray Bursts in Two and Three Dimensions

We explore the early evolution of flame ignition and spreading on the surface of a neutron star in three dimensions, in the context of X-ray bursts. We look at the nucleosynthesis and morphology of the burning front and compare to two-dimensional axisymmetric simulations to gauge how important a full three-dimensional treatment of the flame is for the early dynamics. Finally, we discuss the progress toward full-star resolved flame simulations.

Hydraulic modelling of a catalytic converter for pollutant reduction in atmosphere

Air pollution caused by cars is a major contributor to the greenhouse effect, making it an issue of widespread concern. End-of-combustion of an engine produces pollutants such carbon monoxide (CO), oxides of nitrogen (NOx), oxides of sulphur (SOx), particulate particles and unburned hydrocarbons (HC). The environment, air quality, and human health are all negatively affected by these contaminants. A catalytic converter is a pollution control device for every fuel-operated automobile exhaust system. Increasingly low emission standards and automobile space constraints necessitate optimizing the device geometry. The uniformity index parameter mainly judges a catalytic converter’s smooth working and operational life. In the present study, 16 catalytic converter geometry designs are investigated. Their effects on exhaust flow distribution, i.e., uniformity index, pressure drop, and peak pressure at monolith substrate entry, are identified and visualized through contour plots. A finite volume approach is used to study hydraulic diffusion inside the device with the help of the ANSYS Fluent CFD package. Two-dimensional axisymmetric CFD simulations identify optimum design parameters among the considered geometries. The design of diffuser geometry is crucial in maintaining a uniform flow across monolith honeycomb structures.

Numerical Analysis of Droplet Impacting on an Immiscible Liquid via Three-Phase Field Method.

In this work, we establish a two-dimensional axisymmetric simulation model to numerically study the impacting behaviors between oil droplets and an immiscible aqueous solution based on the three-phase field method. The numerical model is established by using the commercial software of COMSOL Multiphysics first and then validated by comparing the numerical results with the previous experimental study. The simulation results show that under the impact of oil droplets, a crater will form on the surface of the aqueous solution, which firstly expands and then collapses with the transfer and dissipation of kinetic energy of this three-phase system. As for the droplet, it flattens, spreads, stretches, or immerses on the crater surface and finally achieves an equilibrium state at the gas-liquid interface after experiencing several sinking-bouncing circles. The impacting velocity, fluid density, viscosity, interfacial tension, droplet size, and the property of non-Newtonian fluids all play important roles in the impact between oil droplets and aqueous solution. The conclusions can help to cognize the mechanism of droplet impact on an immiscible fluid and provide useful guidelines for those applications concerning droplet impact.

Late-time post-merger modeling of a compact binary: effects of relativity, r-process heating, and treatment of transport

Detectable electromagnetic counterparts to gravitational waves from compact binary mergers can be produced by outflows from the black hole-accretion disk remnant during the first 10 s after the merger. Two-dimensional axisymmetric simulations with effective viscosity remain an efficient and informative way to model this late-time post-merger evolution. In addition to the inherent approximations of axisymmetry and modeling turbulent angular momentum transport by a viscosity, previous simulations often make other simplifications related to the treatment of the equation of state and turbulent transport effects. In this paper, we test the effect of these modeling choices. By evolving with the same viscosity the exact post-merger initial configuration previously evolved in Newtonian viscous hydrodynamics, we find that the Newtonian treatment provides a good estimate of the disk ejecta mass but underestimates the outflow velocity. We find that the inclusion of heavy nuclei causes a notable increase in ejecta mass. An approximate inclusion of r-process effects has a comparatively smaller effect, except for its designed effect on the composition. Diffusion of composition and entropy, modeling turbulent transport effects, has the overall effect of reducing ejecta mass and giving it a speed with lower average and more tightly-peaked distribution. Also, we find significant acceleration of outflow even at distances beyond 10 000 km, so that thermal wind velocities only asymptote beyond this radius and at higher values than often reported.

Can we observe the ion-neutral drift velocity in prestellar cores?

ABSTRACT Given the low-ionization fraction of molecular clouds, ambipolar diffusion is thought to be an integral process in star formation. However, chemical and radiative-transfer effects, observational challenges, and the fact that the ion-neutral drift velocity is inherently very small render a definite detection of ambipolar diffusion extremely non-trivial. Here, we study the ion-neutral drift velocity in a suite of chemodynamical, non-ideal magnetohydrodynamic (MHD), two-dimensional axisymmetric simulations of prestellar cores where we alter the temperature, cosmic-ray ionization rate, visual extinction, mass-to-flux ratio, and chemical evolution. Subsequently, we perform a number of non-local thermodynamic equilibrium (non-LTE) radiative-transfer calculations considering various idealized and non-idealized scenarios in order to assess which factor (chemistry, radiative transfer, and/or observational difficulties) is the most challenging to overcome in our efforts to detect the ion-neutral drift velocity. We find that temperature has a significant effect in the amplitude of the drift velocity with the coldest modelled cores (T = 6 K) exhibiting drift velocities comparable to the sound speed. Against expectations, we find that in idealized scenarios (where two species are perfectly chemically co-evolving) the drift velocity ‘survives’ radiative-transfer effects and can in principle be observed. However, we find that observational challenges and chemical effects can significantly hinder our view of the ion-neutral drift velocity. Finally, we propose that $\rm {HCN}$ and $\rm {HCNH^+}$, being chemically co-evolving, could be used in future observational studies aiming to measure the ion-neutral drift velocity.

Numerical investigation of the effects of axial temperature gradient and cooling rate on InGaSb crystal growth under micro-gravity

In order to investigate the transport phenomena, growth mechanism of InGaSb crystal growth under microgravity, and also to optimize future space experiments, two-dimensional axisymmetric numerical simulations were carried out with different axial temperature gradients and cooling rates. Results showed that under microgravity condition both crystal growth process and grown crystal qualities were significantly affected by its axial temperature gradients and cooling rates. Simulation suggested that an axial temperature gradient around 0.6 K/mm with cooling rate of 0.048 K/h can accelerate and optimize the whole dissolution and growth process of InGaSb crystal growth in space, preventing complete dissolution of feed crystals, improving growth rates and grown crystal compositional uniformity.

Comprehensive Study of Mass Ejection and Nucleosynthesis in Binary Neutron Star Mergers Leaving Short-lived Massive Neutron Stars

By performing general relativistic hydrodynamics simulations with an approximate neutrino radiation transfer, the properties of ejecta in the dynamical and post-merger phases are investigated in the cases in which the remnant massive neutron star collapses into a black hole in ≲20 ms after the onset of the merger. The dynamical mass ejection is investigated in three-dimensional simulations. The post-merger mass ejection is investigated in two-dimensional axisymmetric simulations with viscosity using the three-dimensional post-merger systems as the initial conditions. We show that the typical neutron richness of the dynamical ejecta is higher for the merger of more asymmetric binaries; hence, heavier r-process nuclei are dominantly synthesized. The post-merger ejecta are shown to have only mild neutron richness, which results in the production of lighter r-process nuclei, irrespective of the binary mass ratios. Because of the larger disk mass, the post-merger ejecta mass is larger for more asymmetric binary mergers. Thus, the post-merger ejecta can compensate for the underproduced lighter r-process nuclei for asymmetric merger cases. As a result, by summing up both ejecta components, the solar residual r-process pattern is reproduced within the average deviation of a factor of three, irrespective of the binary mass ratio. Our result also indicates that the (about a factor of a few) light-to-heavy abundance scatter observed in r-process-enhanced stars can be attributed to variation in the binary mass ratio and total mass. Implications of our results associated with the mass distribution of compact neutron star binaries and the magnetar scenario of short gamma-ray bursts are discussed.

Numerical investigation of two-dimensional axisymmetric and three-dimensional flow simulations over a benchmark underwater vehicle

Two-dimensional (2D) axisymmetric simulation is an efficient and time-saving computational fluid dynamics (CFD) technique when the body is axisymmetric, and the flow is along the length of the body. In the present paper, this technique is used to investigate turbulent flow around the bare hull configuration of the Defense Advanced Research Project Agency submarine model. Verification and validation of the results are done at three levels. The values of the total resistance, the distribution of the wall shear stress and the pressure on the surface, and the velocity profiles at various distances from the nose are compared with results obtained by using three-dimensional (3D) simulations and experimental results from the literature. The uncertainty in CFD results due to meshing is reported using Richardson Extrapolation. It is shown that the errors are minor, and the savings in computer memory and computation time are tremendous using 2D axisymmetric simulations. Good CFD practices essential for 2D axisymmetric simulations are also presented in this article, which will be helpful for the CFD community to conduct numerical investigations on any other axisymmetric bare hull bodies, such as torpedoes, missiles, submarines, and autonomous underwater vehicles in the future. Finally, the components of drag, coefficient of pressure, and wall shear stress at the highest speed (9.26 m/s) are also obtained using 2D axisymmetric simulation, which has not been previously reported in any other literature. The level of rigor in the 2D axisymmetric simulation reported here is rarely seen in recent literature.

Oscillations of highly magnetized non-rotating neutron stars

Highly magnetized neutron stars are promising candidates to explain some of the most peculiar astronomical phenomena, for instance, fast radio bursts, gamma-ray bursts, and superluminous supernovae. Pulsations of these highly magnetized neutron stars are also speculated to produce detectable gravitational waves. In addition, pulsations are important probes of the structure and equation of state of the neutron stars. The major challenge in studying the pulsations of highly magnetized neutron stars is the demanding numerical cost of consistently solving the nonlinear Einstein and Maxwell equations under minimum assumptions. With the recent breakthroughs in numerical solvers, we investigate pulsation modes of non-rotating neutron stars which harbour strong purely toroidal magnetic fields of 1015−17 G through two-dimensional axisymmetric general-relativistic magnetohydrodynamics simulations. We show that stellar oscillations are insensitive to magnetization effects until the magnetic to binding energy ratio goes beyond 10%, where the pulsation mode frequencies are strongly suppressed. We further show that this is the direct consequence of the decrease in stellar compactness when the extreme magnetic fields introduce strong deformations of the neutron stars.

Thermal Characteristics of Gaseous-Helium-Cooled HTS Cables With Practical Operating Conditions

High temperature superconducting (HTS) cables have the advantages of low loss and large capacity transmission. The cryogen used for HTS cable cooling is mainly liquid nitrogen. In some applications, using gaseous helium (GHe) as a cryogen has advantages. For example, it can reduce the weight of the system, remove the risk of frostbite of surrounding equipment and people caused by leakage of liquid nitrogen, and avoid suffocation due to evaporation of liquid nitrogen in confined spaces. Temperature is closely related to the performance of superconducting tapes. Therefore, it is of great significance to study the thermal characteristics of cables using GHe as cryogen under several important operating conditions. These conditions include cooling, carrying rated current, cryocooler fails, both cryocooler and cryogenic gas circulation pump fail, and local hot spot. In this article, a two-dimensional axisymmetric simulation model of a 50-m 4 kA HTS cable was built in COMSOL to study the thermal characteristics of GHe-cooled HTS cables. The range of mass flow rates of GHe suitable for operation of this cable was calculated considering different operating conditions.

Heat Transfer in Rocket Combustion Chambers Firing Plates: Role of Injector Confinement

In this work the effect of the injector lateral confinement on flowfields and thermal loads in the injection region of a rocket combustion chamber is investigated. The reference test case consists of a gaseous-methane/gaseous-oxygen turbulent, non-premixed flame emanating from a single shear coaxial injector. Two baseline configurations are defined in order to model different situations encountered within a hypothetical multi-injector plate: a wall-bounded configuration is chosen to investigate the injector–wall interaction, while a symmetric condition is used to mimic the mutual interaction between injectors located in the inner part of the injection plate. The effect of the lateral confinement length is assessed by means of a parametric analysis, varying this feature in a range of interest for both configurations. The analysis is performed using two-dimensional axisymmetric simulations, carried out by means of a low-Mach number, unsteady Reynolds-averaged Navier–Stokes framework employing a non-adiabatic flamelet-based turbulent combustion model. It is found that the confinement length mainly affects the recirculation region, causing wider and warmer recirculation with increasing confinement lengths and therefore increasing thermal loads in the injection plate region.

Inversion of thermal properties of lunar soil from penetration heat of projectile using a 2D axisymmetric model and optimized PSO algorithm

The thermophysical parameters of lunar soil can be inferred from the temperature field during the invasion process of reconnaissance projectile. This paper adopts a two-dimensional axisymmetric model to reconstruct the projectile invasion process. An optimized particle swarm optimization method is then used to retrieve the thermophysical parameters of lunar soil. When the reconnaissance projectile penetrates the lunar interior, it rubs against the lunar soil and generates heat, which diffuses between the projectile body and the lunar soil. The sensors inside the reconnaissance projectile measure the temperature variation of the projectile body to inverse the thermophysical parameters. This paper carried out physical modeling of the penetration process of reconnaissance projectile. A two-dimensional axisymmetric simulation model is constructed for the physical process, and the adaptive inertial weight particle swarm algorithm is adopted. The inversion experiment of lunar soil thermophysical parameters based on the simulation model shows that the inversion error is less than 10%, which verifies the feasibility of this method.

The early evolution of magnetar rotation – I. Slowly rotating ‘normal’ magnetars

ABSTRACT In the seconds following their formation in core-collapse supernovae, ‘proto’-magnetars drive neutrino-heated magnetocentrifugal winds. Using a suite of two-dimensional axisymmetric magnetohydrodynamic simulations, we show that relatively slowly rotating magnetars with initial spin periods of P⋆0 = 50–500 ms spin down rapidly during the neutrino Kelvin–Helmholtz cooling epoch. These initial spin periods are representative of those inferred for normal Galactic pulsars, and much slower than those invoked for gamma-ray bursts and superluminous supernovae. Since the flow is non-relativistic at early times, and because the Alfvén radius is much larger than the proto-magnetar radius, spin-down is millions of times more efficient than the typically used dipole formula. Quasi-periodic plasmoid ejections from the closed zone enhance spin-down. For polar magnetic field strengths B0 ≳ 5 × 1014 G, the spin-down time-scale can be shorter than the Kelvin–Helmholtz time-scale. For B0 ≳ 1015 G, it is of the order of seconds in early phases. We compute the spin evolution for cooling proto-magnetars as a function of B0, P⋆0, and mass (M). Proto-magnetars born with B0 greater than $\simeq 1.3\times 10^{15}\, {\rm \, G}\, (P_{\star 0}/{400\, \rm \, ms})^{-1.4}(M/1.4\, {\rm M}_\odot)^{2.2}$ spin down to periods >1 s in just the first few seconds of evolution, well before the end of the cooling epoch and the onset of classic dipole spin-down. Spin-down is more efficient for lower M and for larger P⋆0. We discuss the implications for observed magnetars, including the discrepancy between their characteristic ages and supernova remnant ages. Finally, we speculate on the origin of 1E 161348−5055 in the remnant RCW 103, and the potential for other ultra-slowly rotating magnetars.

Simulation of the Axial-Flow Centrifugal Bubble Separator for Liquid-Fueled Molten Salt Reactors Using Eulerian Two-Fluid Model

The axial-flow centrifugal bubble separator designed for the gaseous fission product removal system in liquid-fueled molten salt reactors is simulated using the Eulerian two-fluid model coupled with the Adaptive Multiple Size Group method to account for the significant coalescence and breakup in the bubble separator. The behavior of the gas core in the bubble separator is mimicked by the symmetric interfacial area concentration model. The separator efficiency, local velocity, and pressure profiles at various conditions are compared with experimental data. Good agreement is found between the experiment and the simulation for the separator efficiency. With the coalescence and breakup being accounted for, the effect of the inlet void fraction on the separator efficiency is correctly captured. For the local pressure and velocity profiles, the agreement is only quantitative due to the simplifications on the geometry and potential limitations of the current computational fluid dynamics models. As good agreement is found for the separator efficiency, the sensitivity study is performed for various operational and design parameters with further simplified two-dimensional axisymmetric simulation.

Transport simulations of pre-thermal quench shattered pellet injection in ITER: code verification and assessment of key trends

The material assimilation of the shattered pellet injection (SPI) in the pre-thermal quench phase in ITER is studied numerically by means of one-dimensional (1D) transport simulations. Such a simplified 1D approach is useful to perform extensive and systematic studies of key engineering parameters to optimize the ITER Disruption Mitigation System. The simulation results are compared with two-dimensional (2D) axisymmetric simulations by the nonlinear magnetohydrodynamic code JOREK for 5 neon/95 hydrogen SPI in the 15 MA hydrogen L-mode discharge to clarify the characteristics of SPI assimilation that can be analyzed within the range of the 1D model. Reasonable agreement between the 1D SPI simulation by the INDEX code and the 2D simulations by the JOREK code is found for total ablation rates, the radiation power, and the density and temperature profile evolution. The key process that was studied with the transport code is the onset of the radiative cold front that destabilizes the plasma current profiles. The injection parameters for the neon mixed hydrogen SPI are widely scanned to identify the timescale for the radiative cold front to form. Depending on the relative velocity of the cold front and the SPI fragments, the plasma cooling process can differ significantly. SPI with high injection velocities and large shard sizes results even in an inside-out plasma cooling that leads to hollow temperature profiles in the simulations reported here.