A robust numerical model for premixed flames with high density ratios based on new pressure correction and IMEX schemes

In this study we present a model for the interaction of premixed flames with obstacles in a channel flow. Although the flow equations are solved with Direct Numerical Simulation using a low Mach number approximation, the resolution used in the computation is limited (∼1 mm) hence the inner structure of the flame and the chemical scales are not solved. The species equations are substituted with a source term in the energy equation that simulates a one-step global reaction. A level set method is applied to track the position of the flame and its zero level is used to activate the source term in the energy equation only at the flame front. An immersed boundary method reproduces the geometry of the obstacles. The main contribution of the paper is represented by the proposed numerical approach: an IMEX (implicit–explicit) Runge–Kutta scheme is used for the time integration of the energy equation and a new pressure correction algorithm is introduced for the time integration of the momentum equations. The approach presented here allows to calculate flames which produce high density ratios between burnt and unburnt regions. The model is verified by simulating first simple solutions for one- and two-dimensional flames. At last, the experiments performed by Masri and Ibrahim with square and rectangular bodies are calculated.     

Unsteady three-dimensional model of electric arc. Part 1. Mathematical model and testing results

A non-stationary three-dimensional mathematical model of the electric arc of constant current in the approximation of a partial local thermodynamic equilibrium of plasma is presented. For the purpose of testing the model and computer code a computation of the isothermal laminar viscous fluid flow past a circular cylinder (the testing of the dynamic part of the system of equations) and a computation of the axisymmetric electric arc with a reduced anode attachment have been done. A fair agreement of numerical results with experimental data points overall to the correctness of the mathematical model and the numerical solution technique.     

Theory of the free full-circle arc

A theoretical investigation of the full-circle arc located between two planes is presented. The circular arc shape is due to an applied magnetic field. The basic equations for conservations of mass, momentum, energy, and charge, as well as Maxwell's equations and the equation of state lead to a coupled set of partial differential equations. By means of Green's formula, this set is transformed into a set of integral equations. Using the analytically known Green's function, the system may be solved by an iteration procedure. For a simplified arc model, the quantities of interest are computed: The temperature distribution, the mass flow field, and the external magnetic field necessary to maintain this arc configuration.     

Measurement of the temperature and flow fields of the magnetically stabilized cross-flow N2 arc

A straight, steady-state cross-flow arc is burning in an N₂ wind tunnel. The arc is held in position by the balance of the Lorentz forces produced by an external magnetic field perpendicular to the arc axis and by the viscous forces of the gas flow acting on the arc column. The temperature field in the discharge is determined spectroscopically using the radiation of N I lines. Because of the lack of rotational symmetry an inversion method developed by Maldonado was used to determine the local emission coefficient from the measured integrated spectral intensity distributions across the arc in various directions. For known local temperature the mass flow field inside the arc may be evaluated from the convective term of the energy equation and the continuity equation. This is done by expanding the terms of these two equations around the point of the temperature maximum into Fourier-Taylor series and determining coefficients of the same order and power. The solution of the resulting set of algebraic equations yields the unknown coefficients of the mass flow. The flow field obtained by these calculations shows a relatively strong counterflow through the arc core. In the region for which the series expansion holds a partial structure pertaining to a closed double vortex can be recognized. The terms of the momentum equation are calculated on the basis of these results. In order to obtain a better understanding of the importance attributed to the individual local forces acting on the plasma, a simple model was devised which separates the momentum equation into gradient and curl terms. The discussion shows that the gradient part of the Lorentz force causes mainly the pressure gradient, while the much smaller rotational part of thej×B forces is responsible for propelling the mass flow. The momentum transport inside the arc as well as in its neighbourhood is due to the viscous forces and to the pressure gradient. By contrast, at larger distances from the arc it is essentially the inertial force that determines the momentum transport. It is shown that viscosity as a damping mechanism is necessary for the existence of stationary flow fields as investigated in this work.     

Integrating 1D and 2D hydrodynamic,sediment transport model for dam-break flow using finite volume method

The purpose of this study is to set up a dynamically linked 1D and 2D hydrodynamic and sediment transport models for dam break flow.The 1D-2D coupling model solves the generalized shallow water equations,the non-equilibrium sediment transport and bed change equations in a coupled fashion using an explicit finite volume method.It considers interactions among transient flow,strong sediment transport and rapid bed change by including bed change and variable flow density in the flow continuity and momentum equations.An unstructured Quadtree rectangular grid with local refinement is used in the 2D model.The intercell flux is computed by the HLL approximate Riemann solver with shock captured capability for computing the dry-to-wet interface for all models.The effects of pressure and gravity are included in source term in this coupling model which can simplify the computation and eliminate numerical imbalance between source and flux terms.The developed model has been tested against experimental and real-life case of dam-break flow over fix bed and movable bed.The results are compared with analytical solution and measured data with good agreement.The simulation results demonstrate that the coupling model is capable of calculating the flow,erosion and deposition for dam break flows in complicated natural domains.     

VOF法模拟剪切流动下液滴的变形和断裂运动

本文对剪切作用下悬浮液滴在另一种不相融的液体中的变形和断裂过程进行了数值模拟.采用VOF(Volume ofFluid)法中的三维PLIC(Piecewise Linear Interface Calculation)算法实现界面的重构和输运,交错网格下投影法离散表面张力为源项的不可压缩Navier-Stokes方程....     

非结构网格上的B-B单方程模型湍流计算

研究如何在非结构网格上进行Navier Stokes(N-S)方程湍流计算.采用格心有限体积方法离散N-S方程.为了适应非结构网格,计算所用的湍流模型特别选用Baldwin Barth(B-B)单方程模型.此模型由一个单一的具有源项的对流扩散方程组成.为了能在非结构网格上求解B B单方程模型,提出一显式有限体积格式,并直接对带源项的格式进行稳定性分析,得到了相应的时间步长限制条件.最后以平板、RAE 2822翼型、多段翼型绕流等数值算例验证了计算方法的有效性.     

Self-Similar Gas Motion Near The Evaporating Electrode of An Electric Arc

Simple solutions of 1Dt gas-dynamical equations based on similarity analysis are possible for the gas surrounding a point source of mass and energy such as an electrode (cathode) arc spot. To obtain nontrivial (non-zero temperature) solutions throughout, two-scale formulation is used that permits an additional boundary condition near the source. Three generalised gas flow variables, R, Z and V, related to gas density, temperature and velocity are calculated and presented as functions of a single similarity parameter, λ, related to position and time. The computational results are compared with data from two gas discharge experiments: on gas disturbances due to an electric arc of micrometer length in atmospheric air and on expansion of a metal-vapour plasma cloud generated by a low-pressure cold-cathode arc.     

大气压下自由燃烧弧的温度场和速度场的数值模拟

采用标准SIMPLE算法，并作了一些修正，给出了具体的计算步骤和流程图，将其应用于磁流体动力学(MHD)方程进行数值求解．得到了轴对称情况下，自由燃烧弧的温度场和速度场的分布，并和实验结果进行了比较。分析了不同辐射模型对温度场的影响，发现辐射导致电弧温度降低，但不同的辐射模型对于电弧的温度影响不大。     

Determination of equivalent sound speed profiles for ray tracing in near-ground sound propagation

The determination of appropriate sound speed profiles in the modeling of near-ground propagation using a ray tracing method is investigated using a ray tracing model which is capable of performing axisymmetric calculations of the sound field around an isolated source. Eigenrays are traced using an iterative procedure which integrates the trajectory equations for each ray launched from the source at a specific direction. The calculation of sound energy losses is made by introducing appropriate coefficients to the equations representing the effect of ground and atmospheric absorption and the interaction with the atmospheric turbulence. The model is validated against analytical and numerical predictions of other methodologies for simple cases, as well as against measurements for nonrefractive atmospheric environments. A systematic investigation for near-ground propagation in downward and upward refractive atmosphere is made using experimental data. Guidelines for the suitable simulation of the wind velocity profile are derived by correlating predictions with measurements.     

Two-Temperature Modeling of the Anode Contraction Region of High-Intensity Arcs

In this paper, an analytical model for a two-temperature plasma (Te > Tg) is established which is suitable for dealing with arcflow interactions induced by the arc itself. This model is applied to the anode contraction region of high-intensity argon arcs taking the interaction of anode and cathode jets close to the anode into account. The complete set of conservation equations describing the mass, charge, momentum, and energy transport of a two-temperature plasma with temperature-dependent transport properties is solved numerically by an interative finite-difference method using appropriate boundary conditions. Results for an atmospheric-pressure argon arc indicate that the temperature discrepancy between electrons and heavy particles is very pronounced in the arc fringes and in the regions close to the anode, while the departure from kinetic equilibrium becomes insignificant in regions in which the temperature exceeds 12 000 K (i.e., in the arc core). The computed temperature fields of the heavy particles in the anode contraction region resemble the observed arc appearance which clearly shows the interaction of anode and cathode jets in front of the anode.     

Cosmological constant: a lesson from Bose-Einstein condensates

The cosmological constant is one of the most pressing problems in modern physics. We address this issue from an emergent gravity standpoint, by using an analogue gravity model. Indeed, the dynamics of the emergent metric in a Bose-Einstein condensate can be described by a Poisson-like equation with a vacuum source term reminiscent of a cosmological constant. The direct computation of this term shows that in emergent gravity scenarios this constant may be naturally much smaller than the naive ground-state energy of the emergent effective field theory. This suggests that a proper computation of the cosmological constant would require a detailed understanding about how Einstein equations emerge from the full microscopic quantum theory. In this light, the cosmological constant appears as a decisive test bench for any quantum or emergent gravity scenario.     

Similarity Relations for the Electric Arc in Forced Axial Flow

The conservation equations of mass, momentum, and energy in differential form, Ohm's law, and the experimentally determined dependence of the interruption capability of the arc on current shape are employed to obtain similarity relations for high pressure electric arcs in forced axial flow around current zero. The similarity relations are then applied to assess the validity of laminar and turbulent flow models for the arc by comparing model predictions with experiment. It is found that the laminar flow model quite often predicts arc behavior contrary to experiment, while the turbulent flow model predictions are much more consistent with experiment. Moreover, the similarity relations should also be useful in exploring arc behavior under circumstances not discussed in this work.     

Der Einfluß einer radialen Masseneinströmung auf elektrische Lichtbögen

In this paper the influence of a radial instreaming gas on electric arcs is investigated. An axial or an azimuthal mass flow may be superimposed to the radial one. Using the basic equations of the single-fluid model of plasma physics the important properties and parameter dependences are numerically calculated and discussed. The results are compared with those of a corresponding arc without an instreaming radial mass flow. Using an arc heater with radial mass flow it is possible to reach much higher axis temperatures and enthalpy densities. Choosing a set of well selected working conditions nearly the whole electric input may be transformed into axial enthalpy flux of the gas to be heated. The paper illustrates the mutual interaction between the dynamic and thermic functions of an electric arc.     

考虑栅片烧蚀金属蒸气的栅片切割空气电弧仿真与实验研究

基于磁流体动力学理论(MHD)建立了考虑栅片烧蚀金属蒸气的三维空气电弧模型,对模型灭弧室内的的电弧跑动及切割过程进行了数值仿真与实验研究.在传统的质量,动量,能量守恒方程中引入了金属蒸气浓度方程耦合求解用于描述灭弧室内金属蒸气的对流与扩散.在计算中考虑了金属蒸气对于电弧等离子体热力学参数和输运参数的影响.通过计算获得了电弧运动及切割过程的电弧电压,温度分布,金属蒸气浓度分布,灭弧室内流场变化等,分析了由于金属蒸气存在引起的电弧等离子体电导率的变化在切割过程中对于电弧行为的影响.为了验证仿真模型的有效性,进 关键词： 金属蒸气 空气电弧 仿真分析 电弧切割     

Interacting dark energy with inhomogeneous equation of state

We have investigated the model of dark energy interacting with dark matter by choosing inhomogeneous equations of state for the dark energy and a nonlinear interaction term for the underlying interaction. The equations of state have dependencies either on the energy densities, the redshift, the Hubble parameter or the bulk viscosity. We have considered these possibilities and have derived the effective equations of state for the dark energy in each case.     

A Current-Zero Arc Model Based on Forced Convection

A simplified arc model based on the integral method is used to study the arc behavior in a supersonic nozzle. Emphasis is placed on the energy balance of the overall arc, which extends to the arc thennal boundary. Similarity rules for aerodynamic and electrical quantities are established, and a quantitative definition of current zero period is given. Computations have been done for two nozzle geometries. The nozzle geometry plays the role of shaping the arc, thereby affecting the axial electric field distribution. Performance curves in terms of the critical rate of rise of recovery voltage (rrrv)c and di/dt at current zero are established. It has been found that (rrrv)c can be seriously affected by the distortion of the current waveform near current zero due to arc-circuit interaction. When experimentally measured current waveform is used as an input, a good quantitative agreement is obtained for the Liverpool orifice arc [1] between theory and experimental results. A satisfactory agreement has also been achieved for the axial electric field distribution without adding a turbulence term into the energy equation. The limitations of the present arc model is also discussed in detail.     

Heat transfer and cold cathode erosion in electric arc heaters

A simple thermophysical model is proposed for cold electrode erosion in electric arc heaters. The model regards erosion as characterized by an effective enthalpy of electrode material ablation, resulting in heat unbalance between heat supply and heat removal by conduction. Replacing the arc spot by a moving surface heat source, the space-time evolution of the electrode surface temperature is studied in coordinates coupled to the source. Applying heat diffusion equations, we show that the erosion problem can be represented by a system of three simple equations. An experimental coaxial setup, with a magnetically driven arc, has been used for the erosion measurements in copper electrodes. Special thermal experiments were carried out for measuring needed arc spot parameters. A comparison of the model with our own and other experimental data demonstrates a reasonable agreement. The present model reveals the relative significance of the different parameters in the erosion process, and permits us to predict the erosion behavior in cold electrode electric arc heaters in a wide range of parameters     

超声速后台阶流动/射流相互作用的数值模拟

采用高精度格式求解二维Navier-Stokes方程研究超声速射流与同向超声速后台阶流动相互作用的流场基本结构及规律,分别应用5阶WENO格式、6阶中心差分格式离散对流项和黏性项,时间推进采用3阶Runge-Kutta格式,并应用消息传递接口（message passing interface,MPI）非阻塞式通信实现并行化.分别研究了超声速后台阶流动、超声速射流的基本结构特征,以此讨论和分析超声速后台阶流动/射流相互作用的特征,以及不同来流条件对波系结构、涡结构、剪切层、膨胀扇等的影响,尤其是来流剪切层和射流剪切层的相互作用,形成复杂的波系结构及相互干扰的流动现象.      

An iterative algorithm for computing aeroacoustic integrals with application to the analysis of free shear flow noise

An iterative algorithm is developed for the computation of aeroacoustic integrals in the time domain. It is specially designed for the generation of acoustic images, thus giving access to the wavefront pattern radiated by an unsteady flow when large size source fields are considered. It is based on an iterative selection of source-observer pairs involved in the radiation process at a given time-step. It is written as an advanced-time approach, allowing easy connection with flow simulation tools. Its efficiency is related to the fraction of an observer grid step that a sound-wave covers during one time step. Test computations were performed, showing the CPU-time to be 30 to 50 times smaller than with a classical non-iterative procedure. The algorithm is applied to compute the sound radiated by a spatially evolving mixing-layer flow: it is used to compute and visualize contributions to the acoustic field from the different terms obtained by a decomposition of the Lighthill source term.