One-dimensional Numerical Calculations Research Articles

Simulating the carbon distribution in zirconium alloy spent fuel cladding

The diffusivity values of C in pure Zr and in Zr containing dissolved O (Zr(O)) were determined in a temperature range of 623–1023 K for Zr and 923–1123 K for Zr(O) from depth profiles of C obtained by glow-discharge emission spectroscopy. The C diffusivity in Zr(O) decreased as the O concentration in Zr increased and that for Zr containing 15 at % O was two orders of magnitude smaller than that for pure Zr. One-dimensional numerical calculations of Fick’s diffusion equation with a Soret effect indicated various non-uniform distributions of C in a 5-mm-thick Zr matrix under a temperature gradient of 573 to 773 K for 3 years, assuming a heat of transport of − 1.5 to + 1.5 eV. Isothermal annealing at 773 K for 10 years could result in a uniform distribution, whereas dissolution of O in the interstitials of the Zr matrix would hinder C transport through the interstitials.Graphical As concentration of O increased in HIP Zr by 15 at%, the diffusivity of C decreased more than two orders of magnitude.For the positive {{Q}^{*}}_{c}, concentration of C slightly segregated at the surface of the cooler side but had maximum peaks at a middle to a higher temperature zone, and depleted at the surface of the hotter side.For the negative {{Q}^{*}}_{c}, concentration of C depleted at the surface of the cooler side and at the middle to the higher temperature zone, and highly segregated at the surface of the hotter side.

Numerical study on spark ignition of laminar lean premixed methane-air flames in counterflow configuration

ABSTRACT In the present work, the ignition of lean laminar premixed methane-air flames in a counterflow configuration is investigated using detailed numerical simulations. The dependence of the minimum energy necessary for a successful ignition on various parameters (spark geometry, spark duration, mixture composition, flow strain rates) is studied. A one-dimensional numerical calculation is performed using detailed chemical kinetics for the methane-air combustion system. Depending on various parameters, the system can be either successfully ignited (stable flame as stationary solution) or quenched (quenched flame as stationary solution). Furthermore, different detailed chemical mechanisms have been tested. A sensitivity analysis with respect to the Arrhenius parameters shows the key elementary reactions in the prediction of the minimal energy necessary for a successful ignition, which provides important information in the development of detailed chemical mechanisms.

NUMERICAL INVESTIGATION ON THE SPACE-TIME CORRELATION BETWEEN OBLIQUE DETONATION AND NORMAL DETONATION PROPAGATION

The propagation theory of one-dimensional detonation is complete and accurate, while prediction of two-dimensional oblique detonation propagation with large scale and high accuracy is still difficult primarily due to the treatment of wedge wall during the calculation and the modelling of viscosity. In this paper, the space-time correlation between two-dimensional steady oblique detonation induced by finite wedge and one-dimensional unsteady detonation supported by piston is investigated by numerical simulations of multi-species Euler equations with H2-Air detailed chemical kinetics. The initiation and propagation process of detonation wave, together with its interaction with rarefaction waves are numerically analyzed from the perspective of both space and time. The results show that under the same overdriven degree, the wave structure, wall parameters and profile variation calculated from one-dimensional case fit well both qualitatively and quantitatively with two-dimensional case after a certain space-time transformation, which validates the space-time correlation between one- and two-dimensional detonation waves. The difference mainly lies in the transition process between different stages of detonation development, such as the transition from over-driven oblique detonation wave to near Chapman-Jouguet (CJ) oblique detonation wave under the effect of rarefaction waves. Since most features of oblique detonation waves over finite wedge can be obtained efficiently by one-dimensional numerical calculation of piston-driven detonation and space-time transformation, the present work provides a feasible way to understand the spatial structure of oblique detonations waves, including detonation initiation, formation of over-driven oblique detonation and cellular structure downstream. Besides, this paper also provides a novel method to distinguish the effect of wall compression and boundary layer by comparing one- and two-dimensional numerical results. Moreover, the results imply that two-dimensional flow field over wedges of different shapes can be obtained with satisfying accuracy by altering the velocity of piston, which greatly reduces the time, cost and complexity of numerical simulation during the design of combustion chamber in an oblique detonation wave engine.

Increasing spin of a B-Star during the common envelope stage

Context. In its evolution, the MWC 656 binary system, consisting of a Be star and a black hole, has gone through the common envelope stage. The O and B stars of the early spectral subclasses can be characterised by lower rotational velocities and increased binary frequency. The B star in the MWC 656 system may have undergone rapid rotation during the common envelope stage. Aims. We study the change in the B star’s state of rotation due to an increase in its angular momentum during the common envelope stage and immediately afterwards. Methods. We performed one-dimensional numerical calculations of angular momentum transport in the interior of a slightly evolved star on the main sequence with a mass of 16 M⊙. Meridional circulation and shear turbulence are taken into account. Results. Due to the arrival of angular momentum through the star’s surface, the velocity of the meridional circulation increases by more than six orders of magnitude. Meridional circulation is the main mechanism for the transport of angular momentum into the star’s deep interior. The acquired angular momentum enters the convective core during the common envelope stage if the angular velocity of the accreted matter exceeds half the Kepler value. Conclusions. The star acquires a rotation typical of classical Be stars if the angular velocity of accreted matter rotation is close to the maximum possible value during the common envelope stage (∼80% of the Kepler value).

Seismic loading on cantilever retaining walls: Full-scale dynamic analysis

The assessment of realistic seismic loading on cantilever retaining wall requires modeling of actual seismic events to act on an integral cantilever wall. In this sense, an analysis is carried out to simulate eight candidate earthquake time histories. Scaling effect on seismic motions is taken into consideration through a one-dimensional numerical calculation using SHAKE2000 software. Two-dimensional PLAXIS finite element analysis is carried out through a full-scale seismic analysis of a typical cantilever retaining wall. Results of the analysis quantified seismic earth pressure in terms of magnitude and point of application. These results are presented in a non-dimensional chart to be compared with up-to-date seismic loading propositions. In conclusion, a relationship is proposed to relate the horizontal seismic inertial coefficient with a representative lateral seismic active earth pressure coefficient.

Study of the transient combustion of highly densified biomass briquette (Bio-coke) in an air flow

End-face combustion experiments were conducted on cylindrical bio-coke (BIC), i.e., a highly densified biomass briquette, to investigate whether quasi-one-dimensional steady combustion can be attained in 400-K air flow, as measured by a steady regression rate. In the experiment, it was found that the average regression rate in the first 0.01m of BIC was relatively small after ignition, whereas after the first 0.01m, the average regression rate became almost steady and much larger than that in the first 0.01m. This suggests that before the steady regression period is reached, a non-negligible unstable regression rate phase exists. To investigate this transient combustion phase, one-dimensional numerical calculations were conducted, and the time-dependent regression rate and temperature distribution were computed. The mechanisms controlling transient combustion and the effects of volatile and moisture contents on transient combustion behavior were examined. The results show that a transient combustion period exists before steady combustion is achieved. This transient combustion period decreases as volatile content increases, and moisture content has a similar effect on transient combustion as volatile content. The phenomenon can be explained by the different final steady temperature distribution and evolution rate from the initial temperature distribution to the final steady temperature distribution.

Investigation of fluid motion in valveless pulse detonation combustor with high-frequency operation

The motion of a fluid in a valveless pulse detonation combustor (PDC) at an operating frequency of 500Hz was investigated using a novel PDC, in which the inner diameter of the oxidizer feed line was equal to that of the combustor (inner diameter = 10mm). Gaseous oxygen was supplied to the PDC in a valveless mode. In contrast, supercritical ethylene was injected into the PDC in a direction perpendicular to its axis. The flame propagation speed and backflow of the burned gas were measured using 12 ion probes installed on the side wall. The measured flame propagation speeds in all the combustion tests were 107 ± 4% of the Chapman–Jouguet detonation speed. In addition, the experimental results were compared with those of a one-dimensional numerical calculation. Under the condition that the stop time of the fuel injection was equal to the spark time, the trajectory of the backflowing burned gas was identical to the experimental results, within 7%. Shortening the burned-gas backflow process was found to be essential to achieve a higher operating frequency.

A model of muscle contraction based on the Langevin equation with actomyosin potentials

We propose a muscle contraction model that is essentially a model of the motion of myosin motors as described by a Langevin equation. This model involves one-dimensional numerical calculations wherein the total force is the sum of a viscous force proportional to the myosin head velocity, a white Gaussian noise produced by random forces and other potential forces originating from the actomyosin structure and intra-molecular charges. We calculate the velocity of a single myosin on an actin filament to be 4.9–49 μm/s, depending on the viscosity between the actomyosin molecules. A myosin filament with a hundred myosin heads is used to simulate the contractions of a half-sarcomere within the skeletal muscle. The force response due to a quick release in the isometric contraction is simulated using a process wherein crossbridges are changed forcibly from one state to another. In contrast, the force response to a quick stretch is simulated using purely mechanical characteristics. We simulate the force–velocity relation and energy efficiency in the isotonic contraction and adenosine triphosphate consumption. The simulation results are in good agreement with the experimental results. We show that the Langevin equation for the actomyosin potentials can be modified statistically to become an existing muscle model that uses Maxwell elements.

The analysis of the calculation process related to labyrinth sealing with extraction

The work presents a calculation process enabling one-dimensional numerical calculations of labyrinth sealing. A DSV program determines the thermodynamic parameters of gas in the sealing chambers with extraction. The influence of the sealing length upon the stability of a matrix solution of the system of equations with the use of Cond(C) parameter is analysed. Next, the operation of the software extended with a module that enables determination of the initial pressure p0, to which the assumed mass flow for a set geometry and sealing length would correspond is discussed. The work analyzes Cond(C) and initial pressure values for various sealing lengths with an assumed leak value. The work also compares the values of static pressures on the extraction plane, as obtained from the measurements, to theoretically calculated values. The calculations and comparisons were made for various heights of incomplete sealing fissures

A113 微小重力場における電線被覆の過電流連続通電着火現象(OS-2:微小重力環境下における燃焼および熱工学的問題)

Ignition tests of overloaded electric wire were carried out in microgravity provided by airplane parabolic flight. Polyethylene insulated NiCr core wire (inner core diameter 0.5 and outer diameter 0.8 mm) was used as a test sample. The results showed that the ignition limit in terms of supplied electric power dramatically decreased with increase in microgravity time. It was suggested that the total electric energy supplied to the wire gave the primary criteria for ignition, which was consistent with experimental findings. Further, the importance of conductive heat loss to the surroundings was pointed out for very low electric current condition according to the simple one-dimensional numerical calculation.

The evaluation of two-sided orthant probabilities for a quadrivariate normal distribution

In this paper it is shown how a general two-sided orthant probability for a quadrivariate normal distribution can be evaluated by a one-dimensional numerical integral calculation. The quadrivariate normal distribution can have any covariance matrix and any mean vector. This affords a practical and efficient method for the calculation of these probabilities which is superior to simulation methods. The implementation of the algorithm is discussed, and some examples of its performance are provided.

Experimental studies into mixing of gases with different density in response to superposition of incident and reflected waves

Two qualitatively different types of mixing the oxygen-hydrogen mixture with argon at the stage of deceleration of the interface were obtained experimentally. One-dimensional numerical calculation and analysis of flow formation in a channel were carried out.

The evolution of stable magnetic fields in stars: an analytical approach

The absence of a rigorous proof of the existence of dynamically stable, large-scale magnetic fields in radiative stars has been for many years a missing element in the fossil field theory for the magnetic Ap/Bp stars. Recent numerical simulations, by Braithwaite & Spruit and Braithwaite & Nordlund, have largely filled this gap, demonstrating convincingly that coherent global scale fields can survive for times of the order of the main-sequence lifetimes of A stars. These dynamically stable configurations take the form of magnetic tori, with linked poloidal and toroidal fields, that slowly rise towards the stellar surface. This paper studies a simple analytical model of such a torus, designed to elucidate the physical processes that govern its evolution. It is found that one-dimensional numerical calculations reproduce some key features of the numerical simulations, with radiative heat transfer, Archimedes’ principle, Lorentz force and Ohmic decay all playing significant roles.

Photon-assisted tunneling in optical lattices: Ballistic transport of interacting boson pairs

In a recent experiment [Phys. Rev. Lett. 100, 040404 (2008)], an analog of photon-assisted tunneling was observed for a Bose-Einstein condensate in an optical lattice subject to a constant force plus a sinusoidal shaking. Contrary to previous theoretical predictions, the width of the condensate was measured to be proportional to the square of the effective tunneling matrix element, rather than a linear dependence. For a simple model of two interacting bosons in a one-dimensional optical lattice, both analytical and numerical calculations indicate that such a transition from a linear to a quadratic dependence can be interpreted through the ballistic transport and the corresponding exact dispersion relation of bound boson pairs.

Improvement of Structure of Traveling Wave Direct Energy Converter Simulator for Ion Flux with Wide Energy Spread

In D-3He fusion, most of fusion energy is carried by kinetic energy of created protons of 14.7 MeV. Concept of traveling wave direct energy converter (TWDEC) was proposed as an effective energy converter with less handling voltage. Although fundamental researches on TWDEC have been reported, the dependence on energy spread of flowing ions has not been investigated in spite of its significant effects against conversion efficiency. The paper treats this subject by an application of TWDEC simulator to GAMMA 10 tandem mirror whose end-loss flux has relatively wide energy spread. The energy distribution of the end-loss flux was measured, and a new structure of TWDEC simulator was designed according to the measured result. The conversion efficiency was estimated by one-dimensional numerical orbit calculations showing the designed structure had enough performance as TWDEC.

Phase-field model for multicomponent alloy solidification

A phase-field model is presented for studying the solidification of multicomponent alloys, which can consider the different diffusion mechanisms between the substitutional and the interstitial solutes appropriately. By defining the interfacial region as a mixture of solid and liquid with the same inter-diffusion potential and determining and matching the phase-field parameters to the alloy properties at a thin-interface limit condition, the limit of interface thickness due to the contribution of the chemical free energy density in the interfacial region is remarkably relieved and a large-scale calculation domain is permitted. One-dimensional numerical calculations for the solidification of an dilute Fe–Mn–C alloy system demonstrate that the model could provide a good description for the equilibrium and kinetic properties for isothermal solidification of multicomponent alloys. Two-dimensional computations for the evolution of large-scale dendritic microstructures is performed and solute distributions in both the solid and liquid phase and the dendritic shapes are compared at different temperatures.

The Field Condition: A New Constraint on Spatial Resolution in Simulations of the Nonlinear Development of Thermal Instability

We present the dynamics of a thermally bistable medium using one-dimensional numerical calculations, including cooling, heating, thermal conduction, and physical viscosity.We set up a two-phase medium from a thermally unstable one-phase medium and follow its long-term evolution. To clarify the role of thermal conduction, we compare the results of the two models, with and without thermal conduction. The calculations show that the thermal conduction helps to generate the kinetic energy of translational motions of the clouds. Next, we focus on spatial resolution because we have to resolve the Field length $\lambda_{\rm F}$, which is the characteristic length scale of the thermal conduction. The results show convergence only when thermal conduction is included and a large enough cell number is used. We find it necessary to maintain a cell size of less than $\lambda_{\rm F}/3$ to achieve a converged motion in the two-phase medium. We refer to the constraint that $\lambda_{\rm F}/3$ be resolved as the ``Field condition''. The inclusion of thermal conduction to satisfy the Field condition is crucial to numerical studies of thermal instability (TI) and may be important for studies of the turbulent interstellar two-phase medium: the calculations of TI without thermal conduction may be susceptible to contamination by artificial phenomena that do not converge with increasing resolutions.

The influence of the state of a compressed thermonuclear substance on the combustion of inertial fusion targets under direct ignition by a short radiation pulse

One-dimensional numerical calculations were performed to study the dependence of conditions for initiating thermonuclear combustion and of the target gain of direct-ignition inertial fusion targets ignited by a short radiation pulse on the initial temperature of a preliminarily compressed fuel and the initial heat energy distribution between plasma electrons and ions in the ignition region (igniter). The igniter parameters at which an effective thermonuclear target explosion with a G ∼ 103 target gain occurred were shown to substantially depend on the initial temperature of the major fuel fraction and the initial heat energy distribution between igniter electrons and ions. The heat energy of the igniter passed a minimum as the size of the igniter decreased. The dependences of these minimum energies on the temperature of the major fuel fraction at various initial energy distributions between igniter electrons and ions were determined. An increase in the temperature of the major fuel fraction was shown to decrease the target gain.

Plume expansion of a laser-induced plasma studied with the particle-in-cell method

The initial stage of laser-induced plasma plume expansion from a solid in vacuum and the effect of the Coulomb field have been studied. We have performed a one-dimensional numerical calculation by mapping the charge on a computational grid according to the particle-in-cell (PIC) method of Birdsall et al. It is assumed that the particle ablation from a surface with a fixed temperature takes place as a pulse, i.e. within a finite period of time. A number of characteristic quantities for the plasma plume are compared with similar data for expansion of neutrals as well as fluid models: Density profiles n( x, t), velocity distributions of ions u( x, t), distribution functions for velocities F( v x ) of ions or electrons as well as the time dependence of kinetic energy E kin( t) for both type of particles. We found a significant increase in the velocities of the ions at the expense of field potential energy as well as electron energy. We have estimated the time constant for energy transfer between the electrons and the ions. The scaling of these processes is given by a single parameter determined by the Debye length obtained from the electron density in the plasma outside the surface.

STUDY OF SEDIMENT DISCHARGE IN A RESEVOIR BY AN OPERATION OF WATER SURFACE ELEVATION

Sediment accumulation in reservoirs is one of the serious problems in the dam management works in Japan. In this paper, two series of experiments are conducted to simulate the sediment release from the dam reservoir with an operation of water surface elevation of the reservoir. Onedimensional numerical calculation is tested using the experimental condition. It is found that the one-dimensional model can predict the behavior of the sediment movement. However, it is suggested that two-dimensional model is required to predict more accurate sediment movement.