Two-dimensional Axisymmetric Geometry Research Articles

Mixing is easy: New insights for cosmochemical evolution from pre-stellar core collapse

Signposts of early planet formation are ubiquitous in substructured young discs. Dense, hot, and high-pressure regions that formed during the gravitational collapse process, integral to star formation, facilitate dynamical mixing of dust within the protostellar disc. This provides an incentive to constrain the role of gas and dust interaction and resolve potential zones of dust concentration during star and disc formation stages. We explore whether the thermal and dynamical conditions that developed during protostellar disc formation can generate gas flows that efficiently mix and transport the well-coupled gas and dust components. We simulated the collapse of dusty molecular cloud cores with the hydrodynamics code PLUTO augmented with radiation transport and self-gravity. We used a two-dimensional axisymmetric geometry and followed the azimuthal component of the velocity. The dust was treated as Lagrangian particles that are subject to drag from the gas, whose motion is computed on a Eulerian grid. We considered 1, 10, and 100 micron-sized neutral, spherical dust grains. Importantly, the equation of state accurately includes molecular hydrogen dissociation. We focus on molecular cloud core masses of 1 and 3 $M_ odot $ and explore the effects of different initial rotation rates and cloud core sizes. Our study underlines mechanisms for the early transport of dust from the inner hot disc regions via the occurrence of two transient gas motions, namely meridional flow and outflow. The vortical flow fosters dynamical mixing and retention of dust, while the thermal pressure driven outflow replenishes dust in the outer disc. Notably, these phenomena occur regardless of the initial cloud core mass, size, and rotation rate. Young dynamical precursors to planet-forming discs exhibit regions with complex hydrodynamical gas features and high-temperature structures. These can play a crucial role in concentrating dust for subsequent growth into protoplanets. Dust transport, especially, from sub-au scales surrounding the protostar to the outer relatively cooler parts, offers an efficient pathway for thermal reprocessing during pre-stellar core collapse.

Modeling the Anisotropic Transport Behavior for Axisymmetric 2D Electrode Particles Using a Modified Pseudo-2D Model Framework

This presentation extends widely used pseudo-2D (P2D) Li-ion battery models to include electrode particles that have strong crystal-scale anisotropies and possibly non-spherical shapes. Typical P2D models predict Li transport with representative spherical electrode particles by solving a one-dimensional diffusion equation in spherical coordinates. However, battery electrodes (graphite, NMC, etc.) may have strong crystalline anisotropies, leading to transport and mechanical properties that vary by orders of magnitude depending on crystallographic orientations. The anisotropic transport can cause large concentration gradients, possibly leading to particle fracture associated with concentration-induced stress. The remainder of the P2D model, such as Li-ion transport within the electrolyte solvent, remains essentially unchanged. The charge-transfer boundary conditions at the particle surfaces do need to accommodate the crystallographic anisotropy.The present model discretizes representative electrode particles in a two-dimensional finite-volume axisymmetric geometry, accounting for the anisotropic behaviors. The computational burden is greater than it is for the one-dimensional spherical solution. However, the P2D model with two-dimensional axisymmetric particle discretization still runs in only a few minutes on a typical personal computer.The model shows how electrode-particle anisotropy affects the battery performance, such as charge-discharge characteristics and electrochemical impedance spectroscopy. The model also predicts the concentration gradients and correlated stress for various axisymmetric, non-spherical particles.

Exploring ultra-high-intensity wakefields in carbon nanotube arrays: An effective plasma-density approach

Charged particle acceleration using solid-state nanostructures has attracted attention in recent years as a method of achieving ultra-high-gradient acceleration in the TV/m domain. More concretely, metallic hollow nanostructures could be suitable for particle acceleration through the excitation of wakefields by a laser or a high-intensity charged particle beam in a high-density solid-state plasma. For instance, due to their special channeling properties as well as optoelectronic and thermo-mechanical properties, carbon nanotubes could be an excellent medium for this purpose. This article investigates the feasibility of generating ultra-high-gradient acceleration using carbon nanotube arrays, modeled as solid-state plasmas in conventional particle-in-cell simulations performed in a two-dimensional axisymmetric (quasi-3D) geometry. The generation of beam-driven plasma wakefields depending on different parameters of the solid structure is discussed in detail. Furthermore, by adopting an effective plasma-density approach, existing analytical expressions, originally derived for homogeneous plasmas, can be used to describe wakefields driven in periodic non-uniform plasmas.

Numerical modeling of imposed magnetohydrodynamic effects in hypersonic flows

Weakly ionized plasmas, formed in high enthalpy hypersonic flows, can be actively manipulated via imposed magnetic fields—a concept termed magnetohydrodynamic (MHD) flow control. Imposed MHD effects, within flows that exhibit multiple shock interactions, are consequential for emerging aerospace technologies, including the possibility of replacing mechanical control surfaces with magnetic actuation. However, numerical modeling of this flow type remains challenging due to the sensitivity of feature formation and the real gas modeling of weakly ionized, electrically conductive, air plasma. In this work, numerical simulation capabilities have been developed for the study of MHD affected, hypersonic flows, around two-dimensional axisymmetric non-simple geometries. The validated numerical methodology, combined with an advanced 19 species equation of state for air plasma, permits the realistic and efficient simulation of air plasmas in the equilibrium regime. Quantitative agreement is achieved between simulation and experiment for a Mach 5.6 double cone geometry with applied magnetic field. In the context of the magnetic actuation concept, numerical studies are conducted for varied conical surface angle and magnetic field configuration. For simple geometries with an elemental shock type, the MHD enhancement effect produces a self-similar shock structure. This paper demonstrates how, for hypersonic flows with complex shock interactions, the MHD affected flow is not only augmented in terms of shock position but may exhibit topological adaptations in the fundamental flow structure. A classification system is introduced for the emergent flow topologies identified in this work. Fluid-magnetic interactions are explored and explained in terms of the coupled mechanisms leading to (1) differences in magnitude of MHD enhancement effect and (2) structural adaptations of the flow topology. The applied numerical studies examine why increased conical surface angle does not amplify the MHD enhancement effect as expected from the base flow conditions, and the mechanisms by which the magnetic field configuration influences the MHD augmented shock structure. Most critically, classes of conditions are identified that produce topological equivalence between the magnetic interaction effects and a generalized mechanical control surface.

Colloidal exchange flow in ducts

Buoyancy-driven exchange flow, i.e. drainage of a heavy colloidal suspension by an immiscible light pure fluid in a vertical duct, is studied analytically. A lubrication model is developed for two-dimensional channel and axisymmetric pipe geometries. The outcome transport equations are solved numerically to capture the effect of important governing dimensionless parameters: Péclet number, precursor film thickness, Reynolds number, mixtures’ viscosity ratio, initial volume fraction of hard-sphere particles, particles concentration within the precursor film, and capillary number. Recent study of colloidal film flow over a flat surface reveals interface thinning over time due to diffusion impact on suspension viscosity. However, the current model suggests that there is no such thinning phenomenon observed for colloidal flows within confined geometry unless in the absence of surface tension. The extent of the mixed particle zone along the duct grows as the Péclet number is decreased. Precursor film thickness is found to decrease the capillary ridge height forming at heavy suspension front. Either an increase in the Reynolds number or a decrease in light-to-heavy-fluid viscosity ratio extends the interpenetration rate of mixtures. As the bulk volume fraction of particles is increased close to 50 %, interesting secondary fronts emerge within the flow that coincide with the range where the diffusion coefficient is minimized. The heavy suspension layer drains slightly faster when the gradient in particle concentration between the bulk and precursor film regions is maximum. Finally, the non-monotonic impact of surface tension on the extent of mixtures’ exchange zone is uncovered via simulations conducted at various capillary numbers.

The Use of the k-ω SST Turbulence Model for Mathematical Modeling of Jet Fire

Aim: The purpose of this study is to verify the usability of the k-ω SST turbulence model for the description of the combustion process during a vertical propane jet fire. Simulating a jet fire using computational fluid mechanics involves an appropriate selection of a mathematical model to describe the turbulent flow. It is important as the variables from this model also describe the rate of the combustion reaction. As a result, they have an impact on the size and shape of the flame. The selection of an appropriate model should be preceded by preliminary simulations. Project and methods: For this purpose, a vertical jet fire in no wind conditions was selected for simulation. Consequently, it was possible to develop a two-dimensional axisymmetric geometry. A good numerical mesh can be applied to such axisymmetric geometry. Selected process conditions allowed to create an axisymmetric numerical grid. Its values, proving the quality, are shown in a chart demonstrating the distribution of the parameter quality depending on the number of elements from which the numerical grid was built. In the work, a two-stage model of the combustion reaction was selected in order to verify whether the area in which the mole fraction of carbon monoxide will have significant values is so large that the selected kinetic reaction model will have an impact on the flame length. Results: Three simulations of jet fire taking place in the direction opposite to the force of gravity were performed. The simulations performed allowed for setting the basic L f parameter, which determines the flame length. Additionally, the length of the mixing path slift-off, needed to initiate the combustion reaction, was determined. The simulations performed allowed for comparing significant parameters characterizing the flame with the parameters calcu- lated using correlations included in the literature on the subject. Due to this comparison, it was possible to define an interesting scope of research work, because the length of the gas mixing path determined from the CFD simulation differed significantly from the values calculated from the correlation. Conclusions: Interestingly, such large differences between CFD results and correlations were not observed for the L f parameter. The correlations based on the Froude number give slightly higher values of the flame length than the results of the CFD simulation. On the other hand, the correlation based on the Reynolds number gives slightly lower values of the L f parameter than the values obtained from the CFD calculations. This may indicate that the effects related to the inertia forces (Re number) better describe the simulation process conditions than the correlations based on the influence of inertia forces and gravity forces (Fr number). Keywords: jet fire, mathematical modelling, computational fluid dynamics Type of article: short scientific report

Maximisation of installed net resulting force through multi-level optimisation of an ultra-high bypass ratio engine nacelle

Engine/wing interference in podded installations can introduce relevant changes to their isolated behaviour, especially for large turbofans with an ultra-high bypass ratio. With such coupled flow field, the interaction is best described by the integrated force acting on the whole aircraft. Rather than focusing on drag or thrust metrics separately, in this paper we maximise the net resulting force on the NASA CRM wing body with underwing-installed turbofans through a multi-level optimisation procedure of the engine nacelle. The first stage involves two-dimensional axisymmetric geometries for cowl and exhaust ducts shapes optimisation. The solutions are transformed into three-dimensional nacelles with pylon, featuring a non-axisymmetric inlet. The impact of the pylon on the exhaust flow is evaluated through a design of experiment and a successive surrogate-based optimisation. In the last step, nacelle/wing offset, intake angles, and engine orientation are assessed in the installed configuration at fixed lift. The final optimised design is compared with a baseline geometry initially defined, showing a significant improvement of the net vehicle thrust equal to 3% of the reference force. The result highlights a counteracting effect of individual force components, in a way that the installed resulting force can only be improved when considering them globally.

Formation of a Nanosecond Discharge in Argon at Atmospheric Pressure Under Gas Pre-Ionization Conditions

The results of modeling a nanosecond discharge in a uniform electric field in argon at atmospheric pressure based on two kinetic models are compared: with one and with six excited states, respectively. The analysis of the development of ionization waves in a centimeter gap in a two-dimensional axisymmetric geometry is performed. It is shown that the obtained result is influenced by the choice of the transport cross-section of electron scattering on the argon atom. The electric field strengths, charged particle concentrations, and velocities of cathode- and anode-directed ionization waves at different time points are compared.

The Dynamic Characteristics of a Small Hydraulic Poppet Safety Relief Valve

Hydraulic poppet pressure relief valve, which has the advantages of fast response and good sealing performance, is extensively used in the hydraulic industry. In this paper, a two-dimensional axisymmetric geometry model of the hydraulic poppet safety relief valve with a small size is established. Dynamic mesh, along with UDF in FLUENT software, is used in this study. The dynamic characteristics of a hydraulic poppet safety relief valve using CFD are investigated under different conditions. For incompressible hydraulic oil, a sharp force rise and collapse caused by a redirection of the fluid flow due to inertia forces is depicted, and the variation of the poppet motion under the influence of the back pressure is analyzed based on the flow information. The dynamic behavior of the hydraulic poppet relief valve under different set pressure is investigated. In the end, a numerical study on the instability of the poppet relief valve supplying a constant volumetric flow rate is performed, and the chatter frequency is obtained.

An extension of high-order shock-fitted detonation propagation in explosives

An update to the numerical shock-fitting scheme from [1] is proposed. The updated scheme locally lowers the order of the scheme in the region of secondary non-fitted waves that interact with the fitted front. In addition, it utilizes a non-uniform mapping from the physical space to the computational space along the streamline direction to offer computational savings over the use of an uniform spacing. The utility of the scheme is first demonstrated on planar ideal gas detonating flows. It is then applied to detonation propagation in a two-dimensional axisymmetric geometry while utilizing an Arrhenius Wescott-Stewart-Davis model for PBX 9502.

Analysis of the Ion-Optical Systems of Portable Neutron Generators

The results of numerical modeling of the ion-beam dynamics and the dynamics of secondary ions and electrons formed in the ion-optical system of a portable neutron generator are presented. The calculation was performed with the aid of the KARAT code in a two-dimensional flat geometry and axisymmetric geometry. To suppress back electrons, the magnetic field of permanent magnets was used in the flat geometry and a blocking electric field of an additional electrode was used in the axisymmetric geometry. The working configurations of both systems are shown.

Multiscale Model for Simulation of Large-Scale YBCO Solenoid Coils With <italic>J</italic> Infinite-Turn

Obtaining distributions of current density, magnetic field, and ac loss in coils is essential for practical applications. However, simulating large-scale 2-generation high-temperature-superconducting, YBCO coils is a challenging task. In this paper, we employ a multiscale model to successfully implement electromagnetic modeling of large-scale YBCO solenoid coils in two-dimensional axisymmetric geometry with the approximation of infinite turns (J infinite-turn). Based on the approximation, current penetration, magnetic field, and ac loss of coils can be obtained. The calculation results of multiscale models with J infinite-turn and uniform current density (J uniform) are compared with those from reference models which consider superconducting characteristics on each turn of coils with actual size based on H-formulation. Compared with J uniform, J infinite-turn improves the quality of current density and background magnetic field significantly and demonstrates good accuracy with errors less than 10% in terms of ac loss, whilst speeding up calculation by two orders of magnitudes than reference model. Also, the approximation shows more reliability if the coil is larger with more turns in pancakes.

Modeling the Air Pressure Increase Within a Powder Bed During Compression—A Step Toward Understanding Tablet Defects

The cause of tablet defects, such as cracking, bubbling, and capping, during compression is currently not fully understood. Prior experimental work suggests that an increase in internal air pressure on powder compression can directly contribute to the formation of cracks within a tablet. The present study examines the air pressure increase on compression in a fully two-dimensional axisymmetric tablet geometry while being coupled to a plasticity model describing the evolution of tablet relative density on consolidation. It is shown numerically that increasing compression speed results in a large air pressure increase on the order of 1-1.5 MPa which approaches the diametrical tensile strength of tablets. In addition, it is shown experimentally through X-ray microcomputed tomography scans of tablets made at various dwell times that increasing dwell times equivalent to that on a tablet press has no effect on the degree of cracking within the tablet. Only when dwell times reach a time scale of 10 to 100 s does the air pressure diminish to a point at which cracking is eliminated. The reduction in air pressure during these extended dwells is captured by the current model. The experimental and numerical work presented here couples for the first time an air pressure model and plasticity model on compression. In addition, it provides a foundation for understanding how realistic tableting aspects such as precompression and tablet size impact the air pressure increase on consolidation.

An analytical model of an urban heat island circulation in calm conditions

We obtain an analytical model solution to an idealization of an urban heat island (UHI) circulation—the steady shallow convective flow of a viscous stably stratified fluid over a differentially heated lower boundary without system rotation (no Coriolis force) or background wind. The coupled linearized equations of motion and thermal energy are solved for flows in two-dimensional Cartesian (slab-symmetric) and axisymmetric geometries forced by laterally varying surface buoyancies considered as Gaussian and parabolic arch functions. The scaled problem is free of governing parameters, and the solutions are universal. In all cases the flow is dominated by an in-up-out circulation. The updraft is stronger in the axisymmetric case than in the slab-symmetric case, while the surrounding downdraft, and the inflow and outflow branches of the circulation are stronger in the slab-symmetric case. These differences are explained in terms of the response of the perturbation pressure to the thermal forcing in the different geometries. The scalings themselves provide insight into observations that daytime UHI circulations can be stronger than nighttime circulations despite the relative weakness of urban–rural temperature contrasts during the daytime.

CFD simulation of single-phase heat transfer in a rotor-stator spinning disc reactor

A computational fluid dynamics (CFD) study on hydrodynamics and heat transfer in a rotor-stator spinning disc reactor (RSSDR), an inventive reactor technology engineered within the frame of process intensification, was performed with OpenFOAM®. This allows the investigation of locally resolved temperature profiles and heat transfer coefficients in the reactor gap, which is experimentally difficult for RSSDRs with small dimensions, while keeping computational costs low. The retrieved radial and tangential velocity and temperature profiles are in agreement with literature. Local stator-side heat transfer coefficients were determined, which increase with higher disc speeds and with increasing throughputs. Area-averaged heat transfer coefficients across the reactor gap were calculated and validated against experimental results performed on the setup simulated in this study; the numerical and experimental data are in qualitative agreement. This study presents the possibility to characterize an RSSDR in terms of hydrodynamics and heat transfer properties by means of a two-dimensional axisymmetric geometry and Reynolds-averaged Navier-Stokes (RANS) turbulence modeling in OpenFOAM®. Expensive measurements, which are difficult to perform particularly for RSSDRs with small dimensions, could thus be avoided, simulating industrial applications at the conditions of interest and designing the RSSDR setup accordingly.

Hollow Cathode Simulations with a First-Principles Model of Ion-Acoustic Anomalous Resistivity

A mathematical model of the ion–acoustic turbulence that is known to develop in the plume of hollow cathodes is presented. The model takes the form of a partial differential equation for the ion–acoustic wave energy density that can be solved concurrently with a set of the equations of motion that have been augmented with anomalous terms to account for the ion–acoustic turbulence-driven transport of momentum and heat for electrons and ions. Numerical simulations in two-dimensional axisymmetric geometry that solve the complete system of these equations show significantly better agreement with plasma measurements compared to a previous idealized model, which assumed complete saturation of the ion–acoustic turbulence and did not account for the growth stage of the waves. In particular, the model is able to predict accurately the location and magnitude of the maximum resistivity to the electron current along the cathode centerline.

A conservative MHD scheme on unstructured Lagrangian grids for Z-pinch hydrodynamic simulations

A new algorithm to model resistive magnetohydrodynamics (MHD) in Z-pinches has been developed. Two-dimensional axisymmetric geometry with azimuthal magnetic field Bθ is considered. Discretization is carried out using unstructured meshes made up of arbitrarily connected polygons. The algorithm is fully conservative for mass, momentum, and energy. Matter energy and magnetic energy are managed separately. The diffusion of magnetic field is solved using a derivative of the Symmetric-Semi-Implicit scheme, Livne et al. (1985) [23], where unconditional stability is obtained without needing to solve large sparse systems of equations. This MHD package has been integrated into the radiation-hydrodynamics code MULTI-2D, Ramis et al. (2009) [20], that includes hydrodynamics, laser energy deposition, heat conduction, and radiation transport. This setup allows to simulate Z-pinch configurations relevant for Inertial Confinement Fusion.

FDF-based combustion instability analysis for evolution of mode shapes and eigenfrequency in the multiple flame burner

In this work, the FDF (flame describing function)-based combustion instability analysis together with the Helmholtz solver has been made for the wide range of velocity perturbation and plenum length in the multiple premixed burner. The Helmholtz solver is based on the commercial software COMSOL and the present numerical analysis is made for the two-dimensional axisymmetric geometry. This study has been mainly motivated to systematically analyze the effects of the velocity perturbation on the detailed evolution of eigenfrequency and mode transformation characteristics versus the variation of the plenum length. Due to the realistic treatment for the acoustic boundary conditions as well as the pressure jump condition across the perforated plate, the present study is able to predict the continuous transformation of the mode shapes according to the variation of the plenum length. To precisely analyze the nonlinear combustion instability phenomena in the multiple flame combustor, computations are made for the wide range of velocity perturbation and plenum length. In terms of stable and unstable ranges of frequency, numerical results yield the comparable results with measurements. Moreover, the present numerical results for the higher velocity perturbation ratios clearly reveal the frequency locking phenomenon which does not change the eigenfrequency even for the condition transforming the acoustic modes several times. Based on numerical results, the detailed discussions are made for effects of the velocity perturbation on the evolution of eigenfrequency and mode transformation characteristics versus the variation of the plenum length.

Analytical, numerical and experimental analysis of induction heating of graphite crucible for melting of non‐magnetic materials

This study presents analytical formulation used for design of helical coil for induction heating of solid and hollow cylindrical non-magnetic workpiece (graphite crucible). This formulation is applied for estimation of the active power in graphite crucibles and reactive power drawn by the induction coil in presence of different wall thickness (30, 20, 10 and 5 mm) of graphite crucibles at different frequency (1-50 kHz). Magnetic field produced by induction coil is estimated by using empirical factors suggested by kNagaoka et al. Induction heating processes, i.e. electromagnetism and heat transfer physics are mathematically modelled by Maxwell and Fourier equations, respectively. Finite-element method is used to solve the electromagnetic field in frequency domain and heat transfer in transient domain. Numerical analysis is carried out by using two-dimensional axisymmetric geometry. Analytical results and numerical results are compared and are found to be in good agreement with each other. Experimentally obtained coil voltage and graphite crucible temperature were compared with numerical results and the authors found that they also match very well confirming the validity of their assumptions in analytical/numerical approach.

Direct simulations of outdoor blast wave propagation from source to receiver

Outdoor blast waves generated by impulsive sources are deeply affected by numerous physical conditions such as source shape or height of burst in the near field, as well as topography, ground nature, or atmospheric conditions at larger distances. Application of classical linear acoustic methods may result in poor estimates of peak overpressures at intermediate ranges in the presence of these conditions. Here, we show, for the first time, that converged direct fully nonlinear simulations can be produced at a reasonable CPU cost in two-dimensional axisymmetric geometry from source location to more than \(500\,\hbox {m/kg}^{1/3}\). The numerical procedure is based on a high-order finite-volume method with adaptive mesh refinement for solving the nonlinear Euler equations with a detonation model. It is applied to a real outdoor pyrotechnic site. A digital terrain model is built, micro-meteorological conditions are included through an effective sound speed, and a ground roughness model is proposed in order to account for the effects of vegetation and unresolved scales. Two-dimensional axisymmetric simulations are performed for several azimuths, and a comparison is made with experimental pressure signals recorded at scaled distances from 36 to \(504\,\hbox {m/kg}^{1/3}\). The relative importance of the main physical effects is discussed.