3D Numerical Simulations Research Articles

3D hydrodynamic simulations of the Galactic supernova remnant CTB 109

Using detailed 3D hydrodynamic simulations we study the nature of the Galactic supernova remnant (SNR) CTB 109 (G109.1-1.0), which is well-known for its semicircular shape and a bright diffuse X-ray emission feature inside the SNR. Our model has been designed to explain the observed morphology, with a special emphasis on the bright emission feature inside the SNR. Moreover, we determine the age of the remnant and compare our findings with X-ray observations. With CTB 109 we test a new method of detailed numerical simulations of diffuse young objects, using realistic initial conditions derived directly from observations. We performed numerical 3D simulations with the RAMSES code. The initial density structure has been directly taken from $^{12}$CO emission data, adding an additional dense cloud, which, when it is shocked, causes the bright emission feature. From parameter studies we obtained the position $(\ell , b)=(109.1545^\circ , -1.0078^\circ)$ for an elliptical cloud with $n_\text{cloud}=25~\text{cm}^{-3}$ based on the preshock density from Chandra data and a maximum diameter of 4.54 pc, whose encounter with the supernova (SN) shock wave generates the bright X-ray emission inside the SNR. The calculated age of the remnant is about 11,000 yr according to our simulations. In addition, we can also determine the most probable site of the SN explosion. Hydrodynamic simulations can reproduce the morphology and the observed size of the SNR CTB 109 remarkably well. Moreover, the simulations show that it is very plausible that the bright X-ray emission inside the SNR is the result of an elliptical dense cloud shocked by the SN explosion wave. We show that numerical simulations using observational data for an initial model can produce meaningful results.

2D modeling of regeneration surface growth on a single-crystal sphere

This paper investigates the evolution of a sphere produced from a single crystal potassium alum in course of its regeneration, using numerical 2D-simulation in the kinematic model, which describes the growth of the regenerating surfaces.The modeling results demonstrate a qualitative agreement between the predictions of the kinematic model and real processes of sphere regeneration. It is shown that the face arising on the regenerating surface of a sphere may grow either more slowly or more rapidly than the surrounding surface. In the latter case, the face interacts with the regeneration surface and disappears from the sphere surface before intersecting in edges with neighboring faces. The influence of the input model parameters on the numerical modeling results is analyzed. It is established that the roughness parameters of the initial surface of a single-crystal sphere significantly affect the surface evolution during regeneration.

Numerical 2D And 3D Simulations of a Spherical Fabry–Pérot Resonator for Application as a Reference Cavity for Laser Frequency Stabilisation

Abstract We report on the results of a numerical study of deformations of a spherical Fabry-Pérot cavity that can be used for laser frequency stabilisation. It is demonstrated that for a precise simulation of the cavity deformations a 3D model has to be used instead of a simpler 2D model, which employs simulation on the symmetry plane of the cavity. To lower the sensitivity to environmental perturbations, it is suggested to use a material with a low density and a high Young’s modulus. We also show that the mechanical resonance frequencies of the cavity are mainly determined by the size of the cavity.

Numerical simulation of 3D sloshing flow in partially filled LNG tank using a coupled level-set and volume-of-fluid method

The motion induced 3D sloshing flow in partially filled LNG tank was investigated using a new coupled Level-Set and Volume-of-Fluid (CLSVOF) method incorporated into Finite-Analytic Navier–Stokes (FANS) method. In addition to accurately simulating the sloshing pattern inside LNG tank, impact pressures acting upon tank wall were also predicted by the CLSVOF method. Furthermore, the predicted impact pressures were compared with the corresponding experimental data and another numerical data by the pure level set method with global mass conservation scheme. The comparisons showed the CLSVOF method is capable of predicting the accurate sloshing induced impact and capturing the violent sloshing flow including wave breaking, jet formation, gas entrapping and liquid-gas interactions. The CLSVOF method also demonstrated the prominent feature in local and stable mass conservation.

Solutions of 2D and 3D non-homogeneous potential problems by using a boundary element-collocation method

This paper presents the boundary element method for the numerical simulation of 2D and 3D nonhomogeneous potential problems. A novel technique, called recursive composite multiple reciprocity method (RCMRM), is introduced to avoid the domain integral of the non-homogenous equation in the boundary element method (BEM). The proposed method has no requirement of domain discretization, and thus is a truly boundary-type numerical method. Numerical results illustrate that the present method is computationally efficient, accurate, and convergent with an increasing number of boundary elements and collocation points.

Coupled carbonation-rust formation-damage modeling and simulation of steel corrosion in 3D mesoscale reinforced concrete

This paper presents a modeling strategy to simulate the corrosion of steel reinforcement in atmospheric environment due to carbonation of concrete. Its principal objectives are to analyze the effects of the progressive formation of corrosion products at the steel/concrete interface on concrete cover cracking. The approach is based on modeling studies carried out independently on carbonation, corrosion and creep. These models are coupled and integrated into a numerical 3D simulation procedure for investigating the behavior of concrete mesostructures. A viscodamage model is used to reproduce both creep and damage behaviors of mortar, and the approach is applied to the simulation of a 3D reinforced concrete mesostructure including explicitly the coarse aggregates. The numerical results highlight the influence of aggregates and the effects of creep on crack initiation and propagation.

Software for numerical simulation of convection in spherical shells for hybrid CPU/GPU computing systems

This paper describes software developed by the authors for numerical 3D simulation of problems on hydrodynamics and heat transfer in spherical shells. The software was based on the OpenCL standard and intended for hybrid CPU/GPU computing systems with graphical processing units. The computations were implemented on a computing system with an Nvidia GTX Titan graphics accelerator. The presented results of the tests demonstrate the correctness of the obtained numerical solutions and the efficient use of GPUs for solving problems of computational fluid dynamics.

Simulation of magnetohydrodynamic effects during large-scale vortices generation in a liquid-metal coolant

This investigation is aimed at establishing the interrelation between the generation of a large-scale vortical motion and magnetohydrodynamic (MHD) effects in liquid-metal nuclear power plant coolants. The subjects of the study are three-dimensional liquid sodium flows in the presence of an external transverse magnetic field in bent and in rectilinear cylindrical channels with obstacles inside of them with different geometries that generate a large-scale vortical motion. To establish the governing dimensionless criteria and their influence on the distribution of the velocity and the magnetic fields, analytical solutions of the Hartmann problem were found to a 2D approximation. A numerical 3D simulation identified the regions of the most intensive induced magnetic field for the 3D Hartmann flow under consideration. The spatial distributions of the fields of the velocities, the vorticity, and the magnetic induction are obtained considering the position of the flow disturbance source. A correlation is found between the vortex formation effects in channels with a complex geometry and the fluctuations of the magnetic field induced in the area where the vortical structures are localized on imposition of a static magnetic field.

TYPE I PLANET MIGRATION IN A MAGNETIZED DISK. I. EFFECT OF LARGE-SCALE VERTICAL AND AZIMUTHAL FIELD COMPONENTS

We study the effects of a large-scale, ordered magnetic field in protoplanetary disks on Type I planet migration using a combination of numerical simulations in 2D and 3D and a linear perturbation analysis. Steady-state models of such disks require the inclusion of magnetic diffusivity. To make progress using ideal MHD, we focus on simplified field configurations, involving purely vertical ($B_z$) and azimuthal ($B_\varphi$) field components and a combination of the two. For each of the models we calculate the locations of the relevant resonances and of the turning points, which delineate the propagation regions of the MHD waves that transport angular momentum from the planet to the disk. We use both numerical and semianalytic methods to evaluate the cumulative back torque acting on the planet, and explore the effect of spatial gradients in the disk's physical variables on the results. We conclude that, under realistic (3D) circumstances, a large-scale magnetic field can slow down the inward migration that characterizes the underlying unmagnetized disk --- by up to a factor of $\sim 2$ when the magnetic pressure approaches the thermal pressure --- but it cannot reverse it. A previous inference that a pure-$B_\phi$ field whose amplitude decreases fast enough with radius leads to outward migration applies only in 2D. In fact, we find that, in 3D, a pure-$B_\phi$ disk undergoes a rapid transition to turbulence on account of a magnetorotational instability that is triggered by the planet-induced appearance of a weak $B_z$ component.

A Numerically Efficient Damping Model for Acoustic Resonances in Microfluidic Cavities

Acoustofluidic damping is a crucial factor that limits the attainable acoustic amplitudes and therefore the effectiveness of acoustofluidic devices. It can be traced back to viscous and thermal dissipation in the bulk and in the boundary layers at cavity walls or suspended particles. However, numerical 3D simulations that include all relevant physics are prohibitively expensive since the acoustic boundary layers need to be resolved. We present a way to incorporate the dissipation effects into a synthetic acoustofluidic loss factor for the use in 3D device simulations. It comes at minimum numerical cost since boundary layers are resolved analytically. Our results and the validity of the physical assumptions we make in the derivation have been verified by analytical and numerical reference solutions. The acoustofluidic loss factor is easily incorporated in device models for a numerically feasible and quantitatively accurate prediction of acoustic amplitudes. In this sense, our work represents the missing link that allows to make not only qualitative but also quantitative predictions of acoustofluidic forces in realistic 3D devices.

Three-dimensional simulation of magneto-hydrodynamic implosion of multi-wire cylindrical liners by the FLUX-3D code

A three-dimensional magneto-hydrodynamic model of conductive radiating plasma, underlying the Euler (in the cylindrical coordinates r-φ-z) program code FLUX-3D, developed at the Russian Federal Nuclear Center VNIIEF, is presented. Finite-difference methods for solving the equations of the model on a stationary regular spatial grid are described. Results of numerical 3D simulation of a multi-wire Z-pinch in conditions of the Shot-51 experiment on electrophysical facility Z (USA) in the full (2π) azimuth angle are presented. The computation geometry has been approximated to the real experimental configuration, in which the electromagnetic energy was supplied to the chamber by a vacuum coaxial transmission line. In the numerical simulation, the dynamics of the acceleration of plasma ablated from tungsten wires as a function of the number of wires in the initial cylindrical assembly was studied. In addition, results of 3D calculations of the current implosion of multi-wire Z-pinch for two kinds of artificial perturbations on the plasma ablation intensity are presented. The reasons of the difference in the soft X-ray radiation pulses generated in these cases are discussed.

Diurnal tides on the Barents Sea continental slope

Measurements of diurnal tides over the continental slope between the Norwegian Sea and the Barents Sea shelf are presented. Numerical 3D simulations, in agreement with field data, show strong cross-slope velocities and large vertical displacements of the interface between Atlantic Water and intermediate water over the slope. The striking correspondence between the prominent observed and modeled diurnal oscillations gives confidence that this is well represented by the model. This variability, interpreted as tidally induced diurnal period topographic waves, is confined to the diverging topography of the continental slope west of Tromsøflaket. The model results reveal highly variable magnitudes of the oscillations and the cross shelf currents in time, related to variable strength of the background flow, the Norwegian Atlantic Current. We suggest that the diurnal topographic wave can be an effective mechanism for cross slope exchange between the Norwegian Sea and the Barents Sea shelf, and important for benthic and pelagic biological processes on the shelf and slope.

Phase-field approximations of the Willmore functional and flow

We discuss in this paper phase-field approximations of the Willmore functional and the associated \({\mathrm L}^{2}\)-flow. After recollecting known results on the approximation of the Willmore energy and its \({\mathrm L}^{1}\) relaxation, we derive the expression of the flows associated with various approximations, and we show their behavior by formal arguments based on matched asymptotic expansions. We introduce an accurate numerical scheme, whose local convergence is proved, to describe with more details the behavior of two flows, the classical and the flow associated with an approximation model due to Mugnai. We propose a series of numerical simulations in 2D and 3D to illustrate their behavior in both smooth and singular situations.

Numerical estimation of the thrust performance on a rotating detonation engine for a hydrogen–oxygen mixture

The numerical simulations of 2D and 3D rotating detonation engines for a hydrogen–oxygen mixture are performed using a detailed chemistry model. The comparison of 2D/3D flow fields for the same injection conditions indicates that the overall flow structures are in agreement for the two simulations and that both rotating velocities are approximately 96% of the CJ value. However, Isp for the 2D RDE is approximately 10s larger than Isp for the 3D RDE. The grid resolution study indicates that the higher grid resolution produces detonation cellular structure; however, its effects on Isp are approximately a few seconds. Although Isp in the 2D smallest scale for higher mass flow is approximately 10s larger than that of the other large scales, Isp for low mass flow is not affected by the scale. However, 3D scale effects are important because the radius of curvature along the circumferential direction changes, which affects the propagation of the rotating detonation. Because Isp and thrust are governed by the stagnation pressure and the micro-nozzle area ratio, the mass flow rate from the injector also depends on these parameters. Isp and thrust for RDE are found to be correlated with the mass flow rate, similar to the case of a conventional rocket engine. This result indicates that the two important parameters, A∗/A and p0, can be replaced by one parameter, i.e., the mass flow rate.

On the interfacial roughness scale in turbulent stratified two-phase flow: 3D lattice Boltzmann numerical simulations with forced turbulence and surfactant

Numerical 3D simulations of turbulent, stratified two-phase shear flow with a surfactant laden interface were used to test and develop a phenomenological interfacial roughness scale model where the energy required to deform the interface (buoyancy, interfacial tension, and viscous work) is proportional to the turbulent kinetic energy adjacent to the interface.The turbulence was forced in the upper and lower liquids in the simulations, to emulate the interfacial dynamics without requiring (prohibitively) large simulation domains and Reynolds numbers. The addition of surfactant lead to an increased roughness scale (for the same turbulent kinetic energy) due to the introduction of interfacial dilatational elasticity that suppressed horizontal motion parallel to the interface, and enhanced the vertical motion.The phenomenological roughness scale model was not fully developed for dilatational elasticity in this work, but we proposed a source term that represents surfactant induced pressure fluctuations near the interface. This source term should be developed further to account for the relation between surfactant density fluctuations and turbulence adjacent to the interface. We foresee that the roughness scale model can be used as a basis for more general interfacial closure relations in Reynolds averaged turbulence models, where also mobile surfactant is accounted for.

Experimental and numerical study of the compact heat exchanger with different microchannel shapes

Experimental and numerical analysis of heat transfer and fluid flow in the compact heat exchanger has been done in this paper. In an open circuit wind tunnel, developed on purpose for this investigation, the measurement of working media temperatures and mass flow rates for heat exchanger with microchannel coil has been accomplished. In accordance with the heat exchangers used for experiments, numerical 3D simulation of adequate geometry shapes has been done. With utilization of air/water side numerical simulation, more detailed results have been achieved in relation to the simulation that assumes constant temperature or constant heat flux on the pipe wall. Good agreement between experimentally measured and numerically calculated results has been accomplished. The influence of different microchannel shapes on heat transfer effectiveness and pressure drop has been studied numerically. Comparison of results has been made accompanied by the discussion and final conclusions.

Numerical simulation of 2D sloshing waves using SPH with diffusive terms

A numerical model based on the Smoothed Particle Hydrodynamics (SPH) method is developed which can appropriately simulate two-dimensional (2D) sloshing waves starting from smooth harmonic to violent breaking waves in a partially filled rectangular water container. This is achieved by employing a single set of numerical tools for solving the fluid flow problem under given boundary conditions. Recently, δ-SPH model has been proven to be superior to standard SPH for solving fluid flow problems covering a broad range of Reynolds (Re) numbers including violent fluid motion involving free surface fragmentation. Present work extends this further by applying δ-SPH to non-violent sloshing waves with specific focus in capturing higher order harmonics as generally predicted by an analytical or potential flow based model. An in depth analysis has been carried out to identify major factors affecting the present δ-SPH model from predicting higher order harmonics. The role of XSPH factor as used in SPH in smoothening of velocity has further been revisited to investigate its’ effect on pressure, particularly in violent sloshing flows. Inter-comparison has been performed with few other SPH versions (namely, fully incompressible SPH (ISPH) and f-SPH, apart from standard weakly compressible SPH (WCSPH)) for selected cases. The model prediction for different physical quantities of sloshing has been found to be in good agreement with results from other experimental, numerical and analytical based studies. Based on the present study, suitable scales for the tuning factors have been proposed for the development of robust SPH models which is expected to simulate sloshing waves defined by relatively broader d/L (ratio of initial water depth to tank length) ranges.

Numerical time-dependent 3D simulation of flow pattern and heat distribution in an ammonothermal system with various baffle shapes

A numerical analysis of an ammonothermal synthesis process for the bulk growth of nitride crystals was performed. The analysis includes the development of a thermal model for a lab-scale ammonothermal autoclave, which was validated by in situ temperature measurements and applied to tailor the temperature field inside the autoclave. Based on the results of the global thermal 2D simulations, a local 3D model was used to include convective phenomena in the analysis. Moreover, the influence of the baffle and different baffle shapes on the flow velocity was investigated. Fluctuations of the temperature as well as the flow velocities occur, indicating that 3D considerations are essential to accurately investigate the heat and mass transport in ammonothermal systems.

Statistical Estimation of Mechanical Parameters of Clarinet Reeds Using Experimental and Numerical Approaches

A set of 55 clarinet reeds is observed by holography, collecting 2 series of measurements made under 2 different moisture contents, from which the resonance frequencies of the 15 first modes are deduced. A statistical analysis of the results reveals good correlations, but also significant differences between both series. Within a given series, flexural modes are not strongly correlated. A Principal Component Analysis (PCA) shows that the measurements of each series can be described with 3 factors capturing more than $90\%$ of the variance: the first is linked with transverse modes, the second with flexural modes of high order and the third with the first flexural mode. A forth factor is necessary to take into account the individual sensitivity to moisture content. Numerical 3D simulations are conducted by Finite Element Method, based on a given reed shape and an orthotropic model. A sensitivity analysis revels that, besides the density, the theoretical frequencies depend mainly on 2 parameters: $E_L$ and $G_{LT}$. An approximate analytical formula is proposed to calculate the resonance frequencies as a function of these 2 parameters. The discrepancy between the observed frequencies and those calculated with the analytical formula suggests that the elastic moduli of the measured reeds are frequency dependent. A viscoelastic model is then developed, whose parameters are computed as a linear combination from 4 orthogonal components, using a standard least squares fitting procedure and leading to an objective characterization of the material properties of the cane \textit{Arundo donax}.

Thermoelectric magnetic flows in melt during directional solidification

Thermoelectric magnetic (TEM) flows in melts, which are generated by TEM forces in liquids, were uncovered by the shape evolution of the planar solid/liquid interface during directional solidification. The solid/liquid interface developing from an initially tilted shape to a nearly flat one has been in situ and real-time observed by means of synchrotron X-ray radiography. The corresponding numerical 3D simulations and velocity measurements of flows in the melt confirm that TEM flows exist and respond to this interface shape change. This observation provides visible evidence for TEM flows in melt and their influence on the solid/liquid interface dynamics when directional solidification is conducted in a magnetic field.