Axisymmetric Cylindrical Geometry Research Articles

Impact of temperature asymmetry and small fraction of static positive ions on the relaxed states of a relativistic hot pair plasma

Abstract The relaxed state of a magnetized relativistic hot plasma composed of inertial electrons and positrons having different relativistic temperatures and a fraction of static positive ions is studied. From the steady-state solutions of vortex dynamics equations and the relation for current density, a non-force-free triple Beltrami (TB) relaxed state equation is derived. The TB state is characterized by three scale parameters that consequently provide three different self-organized structures. The analysis of the relaxed state shows that for specific values of generalized helicities, the disparity in relativistic temperature and the existence of a small fraction of static positive ions in pair plasma can transform the nature of scale parameters. Moreover, an analytical solution of the TB state for an axisymmetric cylindrical geometry with an internal conductor configuration demonstrates that due to asymmetries of temperature and density of plasma species, diamagnetic structures can transform into paramagnetic ones and vice versa. The present study will improve our understanding of pair plasmas in trap-based plasma confinement experiments and astrophysical environments.

Experimental and numerical evaluation of phase-change material performance in a vertical cylindrical capsule for thermal energy storage

• Laboratory study of melting in a vertical cylinder heated from the bottom/side. • Directly visualized experimental results of convective and close-contact melting. • Original in-house numerical model encompassing all basic physical phenomena. • Melting patterns in a vertical cylindrical enclosure under realistic conditions. • Conclusions relevant for latent heat thermal energy storage units design. Thermal energy storage (TES) is considered vital for the advancement of renewable energy solutions. Latent heat thermal energy storage (LHTES) captures the thermal energy via a solid-liquid phase transition that occurs in phase-change materials (PCM). The PCM is usually encapsulated in some way. In this study, we consider PCM melting in a vertical cylindrical enclosure, that is a prototype of a capsule used in a future storage system. Moreover, we achieve the highly desirable close-contact melting (CCM), which speeds up the charging process significantly. First, different types of experiments are conducted to elucidate the melting behavior in an original experimental device that allows different types of melting in such configuration, demonstrating the prominent role of close-contact melting. The device main features are transparency of the melting chamber, separate heating methods for the periphery and the bottom of the chamber, and axisymmetric melting. To further investigate the heat transfer modes in the system, an in-house numerical model for combined convective and close-contact melting in an axisymmetric cylindrical geometry is validated with the experimental results. Then, this original model is used to simulate a vertical cylindrical shell in a practical configuration, namely, when an enclosure is exposed to fluid flow normal to its bottom. The results clearly illustrate the importance of close-contact melting for the overall melting process under practical conditions. The conclusions from this work would aid the design of LHTES installations which involve macro-encapsulated PCM.

Marangoni convection in shallow annular pools of silicone oil heated from above

A numerical study in a two-dimensional, axisymmetric cylindrical geometry is performed to evaluate the effect of Marangoni convection in shallow liquid layers of silicone oil. The study aims to understand Marangoni convection for a range of temperature gradients (9.0 K, 11.5 K, and 14.0 K), layer depths (4.0 mm, 4.5 mm, and 5.0 mm) under earth gravity (1.0 g), and microgravity (0.5 × 10 −3 g) conditions. The finite element method is used to solve the present problem using COMSOL V5.6 commercial tool. The microgravity studies ensure Marangoni convection dominates natural convection. In the present simulation, it is found that Marangoni convection is influenced more by temperature difference than layer depths as the change in temperature gradient gives a higher velocity deviation than a change in layer depths. In the presence of fluid meniscus, the thermo-capillary force is observed to be less significant in driving the flow as the peak velocity magnitude is observed to get reduced by 60%. From the microgravity study, it is clear that for velocity magnitude at z = 2.5 mm the Marangoni convection contributes to almost 90% of the total convection.

Distributed order fractional diffusion equation with fractional Laplacian in axisymmetric cylindrical configuration

In this paper, we consider the powers (fractional and natural) of the Laplacian operator in axisymmetric cylindrical geometry. We get the fundamental solution of the distributed order time-fractional diffusion equation with this type of fractional Laplacian and the fractional moment of solution is given. Our study is considered in the plane and half space cases and the roles of the Mittag-Leffler and Wright functions in the structures of solutions are also discussed.

Combined close-contact and convective melting in a vertical cylindrical enclosure

The use of phase change materials (PCM) for latent heat thermal energy storage (LHTES) is receiving considerable amount of attention in recent years. Experimental findings have demonstrated that the so-called ‘close contact melting’ (CCM) enhances heat transfer during the melting process remarkably. Yet, the commercially-available numerical schemes are not suitable for the modeling of CCM. Therefore, in this study a new numerical model for combined convective and close-contact melting in an axisymmetric cylindrical geometry is devised. A full set of the governing conservation equations is solved using finite differencing framework, integrated with an advanced immersed boundary method for the fluid-solid interaction and enthalpy formulation for the phase change process into an original in-house code. First, the model is validated carefully for each physical phenomenon with known benchmarks. Then, a numerical study is conducted to elucidate the melting process in a vertical cylindrical enclosure heated isothermally from the bottom and side wall. Twelve study cases are considered in order to reveal the transient phase-change sequence dependence on the aspect ratio and the excess temperature. Detailed data on the flow and temperature fields are obtained. The overall results are generalized using a dimensional analysis, which includes the Fourier, Stefan and Archimedes numbers and the enclosure aspect ratio. A correlation for the melt fraction, suitable for all cases studied, is suggested.

The influence of Hall physics on power-flow along a coaxial transmission line

Extended-MHD simulations of a coaxial transmission line are performed in axisymmetric cylindrical geometry, in particular, in examining the influence of Hall physics on a plasma layer initialized against the anode versus the cathode, for which an MHD model is insensitive. The results indicate that Hall physics is required in order to model an electron E × B drift current in the electrode plasma, which is parallel to the anode current and opposite the cathode current. This results in confinement of the electrode plasma when initialized against the cathode and expansion of the plasma layer when initialized against the anode. The expansion in the anode-initialized case results in filaments of plasma bridging the gap, causing substantial power-flow losses. These results represent the first fluid simulations of power-flow, to our knowledge, that, by including Hall physics, recover fundamental aspects of anode and cathode dynamics predicted by kinetic theory while simulating over a dynamic range (nine orders of magnitude density variation from solid-density electrodes down to low-density electrode plasma) which is prohibitive for Particle-In-Cell (PIC) codes. This work demonstrates the need for further development of extended-MHD and two-fluid modeling of power-flow dynamics, which, possibly through hybridization with a PIC code, will eventually culminate in a code with reliable predictive capability for power-flow coupling and energy losses in pulsed-power systems.

Thermal wellbore strengthening through managed temperature drilling – Part I: Thermal model and simulation

This paper is the first part of a two-part series introducing a new and innovative managed temperature drilling technique for strengthening the wellbores of challenging oil and gas wells. This technique relies on heat generation within the borehole to increase the effective fracture gradient of near-wellbore zones in oil and gas wells. By releasing heat at exactly the right time and at the right location, the temperature in a near-wellbore zone can be raised, which in turn raises thermal stresses in this zone. This results in “thermal wellbore strengthening”, i.e. an increase in near-wellbore fracture initiation and propagation pressure that can be exploited to prevent or minimize induced mud losses during drilling, cementing and completion operations. As shown in Part II of this series, the heat-release is preferably achieved in a delayed fashion through the use of exothermic “heat-releasing” particles that are circulated to the zone(s) of interest in a dedicated carrier fluid.Part I describes a new computational thermal model for the proposed technique. Using finite volume techniques for an axisymmetric cylindrical geometry including a drillstring/workstring with internal and external fluid spaces, a casing string and a cementing layer (if present), and the rock formation, the model calculates the near-wellbore formation temperature as well as annulus and drill string temperature when a time-dependent and location-dependent heat generation source is acting. Model validation was conducted by comparing the simulation results from the model to analytical solutions as well as results obtained with a commercial software package for simplified cases (1D along the wellbore) with no heat source. Subsequently, near-wellbore temperature distributions were calculated for varying heat generation rates and fluid circulation times, and passed on to a geomechanical model to estimate the magnitude of the thermal strengthening effects on the fracture gradient. Results show that meaningful increases in near-wellbore stress can be obtained by the technique.The thermal wellbore strengthening technique, supported by the new thermal model described here, can be used to minimize lost circulation events and associated well trouble time and cost during drilling, cementing and completion operations, and may be particularly suited for wells with low drilling margins such as (ultra-)deepwater wells.

Numerical simulations of transitional and turbulent natural convection in laterally heated cylindrical enclosures for crystal growth

ABSTRACTThe present numerical work, the first of its kind, aims at establishing the threshold parameters for dynamic similitude (based on the Rayleigh number (Ra)), for free convection in a cylindrical enclosure heated laterally. Ra considered in this study spanned a range between 750 and 8.8 × 108, where the characteristic length, L, used in its definition is represented by the ratio of cylindrical enclosure’s volume to its lateral surface area. The commercial code, ANSYS FLUENT, is used to model a 2-D axisymmetric cylindrical geometry. When comparatively analyzed, the results allowed conclusions associating values of the Ra with flow development from laminar to turbulent.

Particle diffusion and localized acceleration in inhomogeneous AGN jets – I. Steady-state spectra

We study the acceleration, transport, and emission of particles in relativistic jets. Localized stochastic particle acceleration, spatial diffusion, and synchrotron as well as synchrotron self-Compton emission are considered in a leptonic model. To account for inhomogeneity, we use a 2D axi-symmetric cylindrical geometry for both relativistic electrons and magnetic field. In this first phase of our work, we focus on steady-state spectra that develop from a time-dependent model. We demonstrate that small isolated acceleration region in a much larger emission volume are sufficient to accelerate particles to high energy. Diffusive escape from these small regions provides a natural explanation for the spectral form of the jet emission. The location of the acceleration regions within the jet is found to affect the cooling break of the spectrum in this diffusive model. Diffusion-caused energy-dependent inhomogeneity in the jets predicts that the SSC spectrum is harder than the synchrotron spectrum. There can also be a spectral hardening towards the high-energy section of the synchrotron spectrum, if particle escape is relatively slow. These two spectral hardening effects indicate that the jet inhomogeneity might be a natural explanation for the unexpected hard {\gamma}-ray spectra observed in some blazars.

Flame acceleration in channels with obstacles in the deflagration-to-detonation transition

It was demonstrated recently in Bychkov et al. [Bychkov et al., Phys. Rev. Lett. 101 (2008) 164501], that the physical mechanism of flame acceleration in channels with obstacles is qualitatively different from the classical Shelkin mechanism. The new mechanism is much stronger, and is independent of the Reynolds number. The present study provides details of the theory and numerical modeling of the flame acceleration. It is shown theoretically and computationally that flame acceleration progresses noticeably faster in the axisymmetric cylindrical geometry as compared to the planar one, and that the acceleration rate reduces with increasing Mach number and thereby the gas compressibility. Furthermore, the velocity of the accelerating flame saturates to a constant value that is supersonic with respect to the wall. The saturation state can be correlated to the Chapman–Jouguet deflagration as well as the fast flames observed in experiments. The possibility of transition from deflagration-to-detonation in the obstructed channels is demonstrated.

Numerical Simulation of Pure Argon Plasma Transport in a Linear Divertor Simulator

A two-dimensional numerical modeling is carried out to simulate argon plasma-neutral transport in a linear divertor simulator with an axisymmetric cylindrical geometry. A pure argon plasma flow is introduced from the source region into the transport region, and pumped out near the target plate. This numerical modeling is based on a time-dependent Braginskii’s fluid formulation for plasma transport and a simple diffusion model for neutral transport. The Bohm diffusion model is adopted for calculation of radial diffusion coefficients across the parallel magnetic field in the simulator. Using the design and operation parameters of the Multi-Purpose Plasma (MP2) facility at the National Fusion Research Institute (NFRI) in Korea, argon plasma properties such as density and temperature distributions are calculated, and the formation of ionization front is found in the transport region. Plasma equilibrium profiles along the near axis turn out to be actually unaffected by the pumping positions along the cylindrical wall. Moreover, a gas target divertor concept is numerically simulated to find out puffing effects as well as pumping roles. As increasing the puffing rate at the target plate, not only the ionization front in the plasma density profile is gradually moving toward the entrance region, but also plasma density and electron temperature at the target are dramatically reduced. Two relatively peaked poles in the neutral density profile are resulted from puffing and recycling neutrals, respectively.

Thermo‐mechanical adjustment after impacts during planetary growth

The thermal evolution of planets during their growth is strongly influenced by impact heating. The temperature increase after a collision is mostly located next to the shock. For Moon to Mars size planets where impact melting is limited, the long term thermo‐mechanical readjustment is driven by spreading and cooling of the heated zone. To determine the time and length scales of the adjustment, we developed a numerical model in axisymmetric cylindrical geometry with variable viscosity. We show that if the impactor is larger than a critical size, the spherical heated zone isothermally flattens until its thickness reaches a value for which motionless thermal diffusion becomes more effective. The thickness at the end of advection depends only on the physical properties of the impacted body. The obtained timescales for the adjustment are comparable to the duration of planetary accretion and depend mostly on the physical properties of the impacted body.

Effects of Radiative Transfer Modeling on Transient Temperature Distribution in Semitransparent Glass Rod

This paper presents a method of modeling the radiative energy transfer that takes place during the transient of joining two concentric, semitransparent glass cylinders. Specifically, we predict the two-dimensional transient temperature and heat flux distributions to a ramp input which advances the cylinders into a furnace at high temperature. In this paper, we discretize the fully conservative form of two-dimensional Radiative Transfer Equation (RTE) in both curvilinear and cylindrical coordinate systems so that it can be used for arbitrary axisymmetric cylindrical geometry. We compute the transient temperature field using both the Discrete Ordinate Method (DOM) and the widely used Rosseland’s approximation. The comparison shows that Rosseland’s approximation fails badly near the gap inside the glass media and when the radiative heat flux is dominant at short wavelengths where the spectral absorption coefficient is relatively small. Most prior studies of optical fiber drawing processes at the melting point (generally used Myers’ two-step band model at room temperature) neglect the effects of the spectral absorption coefficient at short wavelengths λ<3μm. In this study, we suggest a modified band model that includes the glass absorption coefficient in the short-wavelength band. Our results show that although the spectral absorption coefficient at short wavelengths is relatively small, its effects on the temperature and heat flux are considerable.

Transient cooling of a cylindrical glass gob

Transient cooling of a hot glass gob by internal combined conduction and radiation is analyzed. The spectral dependence of the absorption coefficient on wavelength and temperature is appropriately accounted for by solving the radiative transfer equation for the axisymmetric cylindrical geometry. Specularly reflecting boundaries are considered and Fresnel's equations are used to predict the spectral directional reflection and transmission characteristics of the interfaces. The finite volume method is used to solve numerically the thermal energy equation, and discrete ordinates method (DOM, S–N method) is employed to solve the radiative transfer equation. Dynamic cooling calculations have been performed and transient temperature distributions, temperature gradients, convective and combined convective plus radiation results are presented and discussed. The results show that for the initial and thermal conditions of interest, the interior of the glass cools primarily by radiation and only in the surface layers (0.8< r/ R<1.0) is conduction of the same order of magnitude as radiation.

Transient conductive-radiative cooling of an optical quality glass disk

Transient combined conductive-radiative heat transfer is analyzed in an optical quality glass disk. Typically semitransparent materials such as a glass have spectrally selective absorption and emission characteristics. In the present analysis the spectral dependence of the absorption coefficient on wavelength is appropriately accounted for, and discrete ordinates method is used to solve the radiative transfer equation for the axisymmetric cylindrical geometry. Specularly reflecting boundaries are considered, and Fresnel's equations are used to predict the spectral radiation characteristics at the interfaces. The numerical analysis is validated by comparing predictions to the experimental results for soda-lime glass. As an example, BK7 optical quality glass is considered as a semitransparent medium.

QUENCHING OF FLAT GLASS BY IMPINGING AIR JETS

Quenching of hot glass by impinging round air jets is analyzed. Understanding of the temperature distribution in glass is required for thermal tempering operations. In the analysis the spectral dependence of the absorption coefficient on wavelength is appropriately accounted for by solving the radiative transfer equation for the axisymmetric cylindrical geometry. Specularly reflecting boundaries are considered, and Fresnel's equations are used to predict the spectral directional reflection and transmission characteristics of the interfaces. The finite volume method is used to solve numerically the thermal energy equation. The numerical calculations have been carried out for combined forced convection and radiation cooling from the surfaces. Transient temperature distributions for parametric calculations are presented and discussed. Determination of the resulting stresses under given impingement and thermal conditions is also discussed.

Spherical harmonics — Finite element treatment of neutron transport in cylindrical geometry

A variational spherical harmonics (DP N ) method is used in conjunction with the finite element method to solve the transport of neutron beams. The method is developed for finite axisymmetric cylindrical geometry. In this model, the angular distribution along the path of neutron travel is separated into two sub-ranges of the forward and the backward moving particles. The system of the model equations is cast in terms of an even and an odd vector analogue to the even-parity transport technique. The finite element method is applied in space to solve the resulting coupled system of equations. A source-free cylinder with specified incident flux on the z = 0 surface is considered in this study. The model is based on the DP 1 and DP 3 orders of expansion. The study demonstrates the advantages of the DP N method in accounting for the discontinuity of the angular flux in the direction of particles with no approximation. Results for the scalar flux are presented in isodose curve (contour) form for homogeneous and non-homogeneous media with different absorbing and purely scattering media. Numerical results compared favorably with those obtained by the exact solutions.

An analytic benchmark solution to the linear, time-dependent isothermal laminar flow fission-product plateout problem

The time-dependent convective-diffusion equation with radioactive decay is solved analytically in axisymmetric cylindrical geometry for laminar and slug velocity profiles under isothermal conditions. Concentration-dependent diffusion is neglected. The laminar flow solution is derived using the method of separation of variables and Frobenius' technique for constructing a series expansion about a regular singular point. These solutions, which describe the transport of fission products in a flowing stream, are then used to determine the pointwise and integrated concentrations of radioactive material deposited on a conduit wall using a standard mass-transfer model. Extensive parametric investigations have been conducted by varying the wall mass-transfer coefficient, diffusion coefficient, flow velocity, pipe radius and species half-life in the deposition models. The computational results indicate that the plateout estimates for the slug flow model are typically 5–100% greater than for the laminar model. The effect of axial diffusion is necessarily negligible for Péclet numbers greater than 100. Little increased plateout is observed for Péclet numbers less than 100; an additional 8% is predicted for a Péclet number of 20 if axial diffusion is included. Characteristic stream, wall and integrated deposition profiles are shown. Representative results from the analysis of fission-product deposition measurements for diffusion tubes in the Fort St Vrain high-temperature gas-cooled reactor plateout probe are presented. Using single-region slug and laminar models, the wall mass-transfer coefficients, diffusion coefficients and inlet concentrations are determined using least-squares analysis. The diffusion coefficients and inlet concentrations are consistent between tubes. The computed diffusion coefficients and wall mass-transfer coefficients are in agreement with known literature values. The analysis indicates that little difference can be discerned between computed laminar and slub flow-model parameters unless accurate data is obtained under strictly regulated conditions.

The dynamic effect of flux ropes on Rayleigh-Bénard convection

The interaction between magnetic fields and convection in a fluid heated from below is investigated in an axisymmetric cylindrical geometry. When Rm, the magnetic Reynolds number, is large the field is concentrated into a thin rope on the axis of the cylinder. For weak magnetic fields a larger Rayleigh number is necessary to produce a flux rope than that needed for infinitesimal convection. For larger total fluxes, however, the opposite is true and the system is subcritically unstable to steady motions. The results are contrasted with those found by Busse (1975) for the corresponding two-dimensional roll problem.