Two-dimensional Cylindrical Geometry Research Articles

Effect of Radial Neutron Reflector on the Characteristics of Nuclear Fuel Burn-Up Wave in a Fast Neutron Energy Spectrum Multiplying Medium: A Consistent Parametric Approach

Abstract The influence of radial neutron reflector on the build-up and propagation of a nuclear fuel burn-up wave in a fast multiplying medium is investigated using a consistent parametric approach. Coupled multigroup neutron diffusion equations with a burn-up evolution model are simulated on the two-dimensional cylindrical reactor geometry with azimuthal symmetry. Uranium–plutonium transmutation model is considered, and the simulation is performed by using the finite element multiphysics software package comsol. Transient characteristics of the burn-up wave are represented by two new parameters, namely, transient time (TT) and transient length (TL). TT and TL are defined as the time and distance required for the burn-up wave to attain its steady-state nature. Steady-state phases are characterized in terms of wave velocity, full width half maximum (FWHM), and full width 10% of maximum (FW10M). A sensitivity study of steady-state and transient parameters is conducted for the different values of radial reflector thickness. The potential relevance of these characterization parameters on the development of optimal geometrical configuration of radial neutron reflector in breed and burn (B&B)-based reactor design is addressed based on the sensitivity study.

Parallel Computing of Thermo-Fluid Modeling Related to the FSW Process

This paper is devoted to the numerical computation of a steady-state thermo-fluid modeling related to the Friction Stir Welding Process in a two-dimensional cylindrical geometry. It analyzes the efficiency of the implementation on parallel architectures of two finite-difference schemes on a structured grid. The first one applies the Newton-Raphson method to compute a numerical solution of this non-linear elliptic type equation, and uses an iterative sparse solver. The second one is based on a time-marching approach converging to the steady state solution thanks to a time-explicit computation. Their respective performance is presented and discussed. Some numerical simulation results are presented to validate the proposed approach.

Quantum Effects on Cylindrical Dust-ion Acoustic Waves in a Semiclassical Dense Dusty Plasma

The nonlinear cylindrical dust ion acoustic waves are studied in a collisional unmagnetized dense dusty plasma medium containing inertialess degenerated electrons and positrons, fluid ions, negatively charged dust fluid and neutrals in the background, including exchange-correlation effects of both electrons and positrons. Employing the reductive perturbation method, the damped Kadomstev–Petviashvili equation is derived in the framework of two-dimensional cylindrical geometry. An approximate analytical solution of this equation is also discussed. The quantum and geometrical effects on the dust ion acoustic waves have been investigated. It is found that the dust ion acoustic wave is modified by quantum diffraction, Fermi statistics and exchange-correlation potential. Moreover, it has been found that the nebulon structures of quantum dust ions acoustic wave are formed due to the Cartesian geometry and the transverse perturbation. It is also observed that the nebulon structure is significantly modified by the exchange-correlation effects.

Control of the Nanopore Architecture of Anodic Alumina via Stepwise Anodization with Voltage Modulation and Pore Widening.

Control of the morphology and hierarchy of the nanopore structures of anodic alumina is investigated by employing stepwise anodizing processes, alternating the two different anodizing modes, including mild anodization (MA) and hard anodization (HA), which are further mediated by a pore-widening (PW) step in between. For the experiment, the MA and HA are applied at the anodizing voltages of 40 and 100 V, respectively, in 0.3 M oxalic acid, at 1 °C, for fixed durations (30 min for MA and 0.5 min for HA), while the intermediate PW is applied in 0.1 M phosphoric acid at 30 °C for different durations. In particular, to examine the effects of the anodizing sequence and the PW time on the morphology and hierarchy of the nanopore structures formed, the stepwise anodization is conducted in two different ways: one with no PW step, such as MA→HA and HA→MA, and the other with the timed PW in between, such as MA→PW→MA, MA→PW→HA, HA→PW→HA, and HA→PW→MA. The results show that both the sequence of the voltage-modulated anodizing modes and the application of the intermediate PW step led to unique three-dimensional morphology and hierarchy of the nanopore structures of the anodic alumina beyond the conventional two-dimensional cylindrical pore geometry. It suggests that the stepwise anodizing process regulated by the sequence of the anodizing modes and the intermediate PW step can allow the design and fabrication of various types of nanopore structures, which can broaden the applications of the nanoporous anodic alumina with greater efficacy and versatility.

Multi-frequency implicit semi-analog Monte-Carlo (ISMC) radiative transfer solver in two-dimensions (without teleportation)

We study the multi-dimensional radiative transfer phenomena using the ISMC scheme, in both gray and multi-frequency problems. Implicit Monte-Carlo (IMC) schemes have been in use for five decades. The basic algorithm yields teleportation errors, where photons propagate faster than the correct heat front velocity. Recently (Poëtte and Valentin, 2020 [22]), a new implicit scheme based on the semi-analog scheme was presented and tested in several one-dimensional gray problems. In this scheme, the material energy of the cell is carried by material-particles, and the photons are produced only from existing material particles. As a result, the teleportation errors vanish, due to the infinite discrete spatial accuracy of the scheme. We examine the validity of the new scheme in two-dimensional problems, both in Cartesian and Cylindrical geometries. Additionally, we introduce an expansion of the new scheme for multi-frequency problems. We show that the ISMC scheme presents excellent results without teleportation errors in a large number of benchmarks, especially against the slow classic IMC convergence.

Neutronic analysis of sodium‐cooled fast reactor design with different fuel types using modified CANDLE shuffling strategy in a radial direction

This study compares three fuel types using neutronic analysis for use in a sodium-cooled fast reactor (SFR) design with a modified CANDLE (Constant Axial shape of Neutron flux, nuclide densities, and power shape During Life of Energy production) radial shuffling strategy. SFR is one type of generation IV reactor that is currently under investigation for commercial implementation. In this study, the SFR design utilizes natural uranium as the fuel input. The designed reactor core has a two-dimensional cylindrical geometry for each fuel mixed oxide (MOX), uranium-plutonium nitride ([U-Pu]N), and uranium-plutonium zirconium ([U-Pu]Zr). A radial shuffling strategy, using natural uranium as the fuel input, is applied to the SFR to manage the nuclear fuel burn-up process of the long-life reactor. This strategy is called the modified CANDLE burn-up scheme. The reactor core is divided into 10 regions with equal volume to represent the 10 years that the reactor operates without refueling. Initially, the first (innermost) region of the reactor core is filled with natural uranium fuel. The result of the burn-up from the first region is then shuffled into the second region. The third region is the result of the burn-up that is shuffled from the second region, and so on. This mechanism only requires natural uranium as the input for each 10-year fuel cycle. In this study, the fuel movement scheme is examined for three fuels. Global neutronic parameters, such as the multiplication factors and burn-up analyses, are observed and optimized. Overall, for an output power of 500 MWth and an active core radius of 110 cm and height of 210 cm, the study indicates that (U-Pu)N is the optimal fuel to be applied in the SFR with a modified CANDLE burn-up scheme. (U-Pu)Zr reaches a critical condition at an output power of 500 MWth with an active core radius of 130 cm and a height of 210 cm; whereas criticality for MOX is achieved at an output power of 1500 MWth with an active core radius of 210 cm and a height of 210 cm.

Investigation of Numerical Evaluation Improvement for Three-Dimensional Infinite Cylindrical Heat Conduction Problems

Abstract To estimate the thermal properties from transient data, a model is needed to produce numerical values with sufficient precision. Iterative regression or other estimation procedures must be applied to evaluate the model again and again. From this perspective, infinite or semi-infinite heat conduction problems are a challenge. Since the analytical solution usually contains improper integrals that need to be computed numerically, computer-evaluation speed is a serious issue. To improve the computation speed with precision maintained, an analytical method has been applied to three-dimensional (3D) cylindrical geometries. In this method, the numerical evaluation time is improved by replacing the integral-containing solution by a suitable finite body series solution. The precision of the series solution may be controlled to a high level and the required computer time may be minimized by a suitable choice of the extent of the finite body. The practical applications for 3D geometries include the line-source method for obtaining thermal properties, the estimation of thermal properties by the laser-flash method, and the estimation of aquifer properties or petroleum-field properties from well-test measurements. This paper is an extension of earlier works on one-dimensional (1D) and two-dimensional (2D) cylindrical geometries. In this paper, the computer-evaluation time for the finite geometry 3D solutions is shown to be hundreds of times faster than the infinite or semi-infinite solution with the precision maintained.

Perfectly Matched Layers for time-harmonic transverse electric wave propagation in cylindrical and toroidal gyrotropic media

In this paper we implement the stretched-coordinate Perfectly Matched Layer (PML) technique in [28] to emulate full power absorption outside the simulation domain for time-harmonic electromagnetic wave propagation in presence of gyrotropic dielectric tensor and curved geometry relevant for magnetized plasma devices. We recall the PML formulation as an artificial inhomogeneous lossy medium, following the stretching into the complex plane of a general system of three orthogonal curvilinear coordinates. We apply the general method in cylindrical and toroidal geometries. We then assess this technique in a simple case combining gyrotropy and coordinate curvature. Our test problem analytically quantifies the reflection of Transverse Electric (TE) cylindrical eigenmodes in a gyrotropic medium by a radial PML in cylindrical geometry. The obtained reflection coefficient involves wave, PML and geometric parameters at the PML location. The new coefficient generalizes the one obtained earlier with Cartesian coordinates, and becomes equivalent when the effects of the local cylindrical curvature at the PML (stretched) location can be neglected. These curvature effects are outlined and the limitations they impose on the properties of the PML are quantified as a function of the relevant parameters. Peculiarities related to the gyrotropy are also highlighted. Finite element calculations of the test problem in two-dimensional cylindrical geometry are exploited to verify these properties numerically. Indications are finally given on how to choose the PML parameters in order to obtain a minimal wave reflection at given numerical cost, taking into account errors associated with the numerical scheme.

Transition From Phasic to Tonic Contractility in Airway Smooth Muscle After Birth: An Experimental and Computational Modeling Study.

Fetal airway smooth muscle (ASM) exhibits phasic contractile behavior, which transitions to a more sustained "tonic" contraction after birth. The timing and underlying mechanisms of ASM transition from a phasic to a tonic contractile phenotype are yet to be established. We characterized phasic ASM contraction in preterm (128 day gestation), term (~150 day gestation), 1-4 month, 1 yr, and adult sheep (5yr). Spontaneous phasic activity was measured in bronchial segments as amplitude, frequency, and intensity. The mechanism of phasic ASM contraction was investigated further with a computational model of ASM force development and lumen narrowing. The computational model comprised a two-dimensional cylindrical geometry of a network of contractile units and the activation of neighboring cells was dependent on the strength of coupling between cells. As expected, phasic contractions were most prominent in fetal airways and decreased with advancing age, to a level similar to the level in the 1-4 month lambs. Computational predictions demonstrated phasic contraction through the generation of a wave of activation events, the magnitude of which is determined by the number of active cells and the strength of cell-cell interactions. Decreases in phasic contraction with advancing age were simulated by reducing cell-cell coupling. Results show that phasic activity is suppressed rapidly after birth, then sustained at a lower intensity from the preweaning phase until adulthood in an ovine developmental model. Cell-cell coupling is proposed as a key determinant of phasic ASM contraction and if reduced could explain the observed maturational changes.

PHYSICAL AND CHEMICAL FEATURES OF DYNAMIC OF POLYMERIC FLUID

In order to determine the nature of processes of the dynamic polymer flow with simple chemical reactions in two-dimensional cylindrical geometry, objects — a sugar melt and a high molecular weight fraction of glutenin of flour — were chosen in the hydrodynamic description, which were investigated on a rotational rheometer HAAKE RotoVisco 1 and the Moisture Analyzer OHAUS MB23. The nonlinear dynamics of a viscous flow of a compressible, homogeneous liquid with chemical reactions is considered. A nonstationary exact solution of the Poiseuille type is obtained. This solution is used to investigate the effect of viscosity and chemical reactions of the first order on the characteristics of the nonequilibrium dynamic states of the system. The present results of the joint research of the specialists of the All-Union Research Institute of the Confectionery Industry and the MEPhI are a continuation of the work on the formation of structures in food disperse systems and indicate that similar features can also be manifested in real flows of polymer liquids in various industrial installations.

Detailed Modeling of the Direct Reduction of Iron Ore in a Shaft Furnace.

This paper addresses the modeling of the iron ore direct reduction process, a process likely to reduce CO2 emissions from the steel industry. The shaft furnace is divided into three sections (reduction, transition, and cooling), and the model is two-dimensional (cylindrical geometry for the upper sections and conical geometry for the lower one), to correctly describe the lateral gas feed and cooling gas outlet. This model relies on a detailed description of the main physical–chemical and thermal phenomena, using a multi-scale approach. The moving bed is assumed to be comprised of pellets of grains and crystallites. We also take into account eight heterogeneous and two homogeneous chemical reactions. The local mass, energy, and momentum balances are numerically solved, using the finite volume method. This model was successfully validated by simulating the shaft furnaces of two direct reduction plants of different capacities. The calculated results reveal the detailed interior behavior of the shaft furnace operation. Eight different zones can be distinguished, according to their predominant thermal and reaction characteristics. An important finding is the presence of a central zone of lesser temperature and conversion.

SENSMG: First-Order Sensitivities of Neutron Reaction Rates, Reaction-Rate Ratios, Leakage, keff, and α Using PARTISN

SENSMG is a tool for calculating the first-order sensitivities of reaction-rate ratios, keff, and α in critical problems and reaction-rate ratios, reaction rates, and leakage in fixed-source problems to multigroup cross sections, isotope densities, material mass densities, and interface locations using the PARTISN multigroup discrete-ordinates code by implementing Generalized Perturbation Theory. SENSMG can be used for one-dimensional spherical and slab (r) and two-dimensional cylindrical (r-z) geometries. For fixed-source (leakage) problems, SENSMG relies on the MISC and/or SOURCES4C codes to compute neutron source rate densities from spontaneous fission and (α,n) sources. SENSMG is a combination of Python and Fortran and was developed under Linux. This computer code abstract describes all user inputs, the input file, and output files. This computer code abstract describes how SENSMG can be modified to support different computer platforms, PARTISN versions, or cross-section availability. Several verification problems are presented in which SENSMG results are compared with MCNP6, SCALE6.2, and direct perturbations (central differences). SENSMG is available at https://github.com/jafavorite/SENSMG. SENSMG can be modified to accommodate other deterministic transport codes that have an adjoint capability.

Heat transport and coupling modes in Rayleigh–Bénard convection occurring between two layers with largely different viscosities

A high-resolution numerical simulation model in two-dimensional cylindrical geometry was used to discuss the heat transport and coupling modes in two-layer Rayleigh-Bénard convection with a high Rayleigh number (up to the order of 109), an infinite Prandtl number, and large viscosity contrasts (up to 10−3) between an outer, highly viscous layer (HVL) and an inner, low-viscosity layer (LVL). In addition to mechanical and thermal interaction across the HVL-LVL interface, which has been investigated by Yoshida and Hamano [“Numerical studies on the dynamics of two-layer Rayleigh-Bénard convection with an infinite Prandtl number and large viscosity contrasts,” Phys. Fluids 28(11), 116601 (2016)], the spatiotemporal analysis in this study provides new insights into (1) heat transport over the entire system between the bottom of the LVL and the top of the HVL, in particular that associated with thermal plumes, and (2) the convection regime and coupling mode of the two layers, including the transition mechanism between the mechanical coupling mode at relatively low viscosity contrasts and the thermal coupling mode at higher viscosity contrasts. Although flow in the LVL is highly time-dependent, it shares the spatially opposite/same flow pattern synchronized to the nearly stationary upwelling and downwelling plumes in the HVL, corresponding to the mechanical/thermal coupling mode. In the transitional regime between the mechanical and thermal coupling modes, the LVL exhibits periodical switching between the two phases (i.e., the mechanical and thermal coupling phases) with a stagnant period. A detailed inspection revealed that the switching was initiated by the instability in the uppermost boundary layer of the LVL. These results suggest that convection in the highly viscous mantle of the Earth controls that of the extremely low-viscosity outer core in a top-down manner under the thermal coupling mode, which may support a scenario of top-down hemispherical dynamics proposed by the recent geochemical study.

Effect of Cellular Instability on the Initiation of Cylindrical Detonations**Supported by the National Natural Science Foundation of China under Grant Nos 91541206 and 91441131.

The direct initiation of detonations in one-dimensional (1D) and two-dimensional (2D) cylindrical geometries is investigated through numerical simulations. In comparison of 1D and 2D simulations, it is found that cellular instability has a negative effect on the 2D initiation and makes it more difficult to initiate a sustaining 2D cylindrical detonation. This effect associates closely with the activation energy. For the lower activation energy, the 2D initiation of cylindrical detonations can be achieved through a subcritical initiation way. With increasing the activation energy, the 2D cylindrical detonation has increased difficulty in its initiation due to the presence of unreacted pockets behind the detonation front and usually requires rather larger source energy.

OpenMP parallel computing of 2D TiC combustion synthesis process using an explicit finite-volume scheme

This paper analyzes from a numerical point of view the ignition and propagation of the combustion front during the exothermic TiC combustion synthesis of a material made of pressed titanium and carbide particles when thermophysical properties are either assumed constant or temperature and conversion rate dependent. A two-dimensional cylindrical geometry is considered. The heat supply is prescribed on one, two or three sides of the physical domain. A one-step kinetics is used to describe the reaction Ti+C→TiC in a solid phase and leads to the computation of the conversion rate. A coupling with a non-linear heat equation which takes into account the heat generated by the exothermic kinetics and the two allotropic phase-changes is considered. An explicit finite-volume discretization of the coupled system is constructed and analyzed. Time-step’s stability condition is given for a general expression of the thermo-physical characteristics. A discrete maximum principle is reported. Open MP API was used to parallelize the numerical software written in C. An average speedup of three was obtained on an intel quad-core processor i7-2600. The ignition time and the fraction of unreacted material are systematically computed and compared for several heat supply scenario.

Discrete Ordinates Method for the Transport Equation Preserving One-Dimensional Spherical Symmetry in Two-Dimensional Cylindrical Geometry

To calculate instability flows where radiative transport plays a role, it is mandatory to have one-dimensional (1-D) spherical symmetry. To obtain this 1-D symmetry, a new approach for solving the transport equation in the context of the discrete ordinates method is proposed in two-dimensional cylindrical geometry. Based on a new formulation of the spatial transport term, this method allows us to derive a scheme preserving the 1-D symmetry on an equal-angle zoning mesh. We prove this property at both discrete angle and spatial levels. Numerical results show that the scheme based on our method preserves constant solutions and the 1-D symmetry, and it is consistent of order 1.

Lasing properties from dye-doped holographic polymer dispersed liquid crystal confined in two-dimensional cylindrical geometry

In this paper, we investigate the lasing behavior of holographic polymer dispersed liquid crystals (H-PDLCs) filled in capillary tubes (CTs). The emission properties from CTs with various core diameters are explored experimentally. The experimental results show that the smallest threshold is 19.4 μJ/pulse in CTs III (300 μm) corresponding to the largest FWHM 0.42 nm. The minimum FWHM is 0.29 nm in CTs I (75 μm) corresponding to largest threshold 31.5 μJ/pulse. According to experimental results and theoretical analysis, the different lasing behaviors from various core diameters of CTs are mainly due to the effect of phase separation between LC-rich and polymer-rich area during exposure. The temperature effects on lasing properties of H-PDLC in CTs were also investigated. Our work verifies the possibility to achieve miniature laser devices in cylindrical confinement structures, such as CT, hollow-fiber or photonic crystal fiber, and extends the applicable scope of H-PDLC.

Peculiarities of isolated acoustic pulses generated for exerting influence on a treated material in liquid media

It is shown that isolated acoustic waves can arise and propagate in liquids with inhomogeneous spatial distribution of the pressure and density perturbations; the necessary condition of their appearance is significant inhomogeneity of the pulse front structure. The main properties of these wave formations are analyzed within two-dimensional cylindrical geometry, giving substantial grounds to assume the existence of great prospects for their effective practical utilization.

Numerical Modelling Point-to-Plane of Negative Corona Discharge in N2 Under Non-Uniform Electric Field

The paper presents a simulation model of the negative corona discharge in N2 under various pressures. The simulated discharge is of a negative point-to-plane mass type, with an inter-electrode separation distance of 20 mm and a symmetry about the axis of discharge. This simulation investigates the behavior of the neutral density and temperature for different pressures in the range of 0.1–10.0 bar. The spatial and temporal evolution of the neutral gas is analyzed based upon the equations of continuity, momentum and energy in a two-dimensional cylindrical geometry model. For that geometry of the system, the FCT (Flux Corrected Transport) technique was adopted. The results show that the pressure plays a significant role of the neutrals dynamics.

Two-Dimensional Hybrid Model for High-Current Electron Beam Transport in a Dense Plasma

A two-dimensional hybrid code is developed to model the transport of a high-current electron beam in a dense plasma target. The beam electrons are treated as particles and described by particle-in-cell simulation including collisions with the target plasma particles. The background target plasma is assumed to be a stationary fluid with temperature variations. The return current and the self-generated electric and magnetic fields are obtained by combining Ampère's law without the displacement current, the resistive Ohm's law and Faraday's law. The equations are solved in two-dimensional cylindrical geometry with rotational symmetry on a regular grid, with centered spatial differencing and first-order implicit time differencing. The algorithms implemented in the code are described, and a numerical experiment is performed for an electron beam with Maxwellian distribution ejected into a uniform deuterium-tritium plasma target.