PIV measurements for gas flow under gradient magnetic fields

Particle Image Velocimetry (PIV) techniques were developed to measure the convective N2-air flow under gradient magnetic fields. The velocity fields were calculated by the Minimum Quadratic Difference (MQD) algorithm and spurious vectors were eliminated by Delaunay Tessellation.The N2-air flow was measured as the magnetic flux density varying from 0～1.5T. A strengthened vortex flow of air was observed under the condition that the magnetic field was applied, and the velocity of N2 jet rose with the increase of the magnetic density. The experimental results show that the magnetic force will induce a vortex flow and cause a convection flow of the air mixture when both gradients of the O2 concentration and the magnetic field intensity exist.     

Transport phenomena in a knudsen molecular gas in a magnetic field

We consider the behavior of a strongly rarefied (Knudsen) polyatomic gas between two surfaces that have different temperatures in a magnetic field. We show that in the magnetic field H there can arise a flux of gas and a heat flux along the surfaces (odd functions in H), and also normal and tangential forces on the walls.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 124–130, January–February, 1979.     

A combined Chapman-Enskog and Grad method. III. Polyatomic gases in magnetic fields

A kinetic theory is developed for rarefied polyatomic gases of spherical and rough molecules with rotational energy in the presence of an external constant magnetic field. A method of solution of Boltzmann equation that combines features of the methods of Chapman-Enskog and Grad is used to determine transport coefficients that depend on the external magnetic field (Senftleben-Beenakker effect). Received August 4, 1997     

End effects in magnetohydrodynamic channels at finite magnetic reynolds numbers

The effects of the magnetic Reynolds number have been examined via the distribution of the magnetic fields induced by the motion of a medium in a rectangular channel with conducting walls in the presence of an inhomogeneous magnetic field; the effects of wall conductivity and geometry of the external field are also examined as regards the distribution of the induced currents, the Joule loss, and the electric and magnetic fields over the cross section. The problem has previously been considered for a channel with insulating walls [1].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 19–27, May–June, 1971.We are indebted to A. B. Vatazhin for his interest.     

THE BASIC SOLUTION OF A 3-D RECTANGULAR PERMEABLE CRACK IN A PIEZOELECTRIC/PIEZOMAGNETIC COMPOSITE MATERIAL

The solution of a 3-D rectangular permeable crack in a piezoelectric/piezomagnetic composite material was investigated by using the generalized Almansi’s theorem and the Schmidt method.The problem was formulated through Fourier transform into three pairs of dual integral equations,in which the unknown variables are the displacement jumps across the crack surfaces.To solve the dual integral equations,the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials.Finally,the relations between the electric filed,the magnetic flux field and the stress field near the crack edges were obtained and the efects of the shape of the rectangular crack on the stress,the electric displacement and magnetic flux intensity factors in a piezoelectric/piezomagnetic composite material were analyzed.     

FV/MC混合算法求解轴对称钝体后湍流流场

介绍一种有限容积／Monte Carlo结合求解湍流流场的相容的混合算法．有限容积法求解Reynolds平均的动量方程和能量方程，Monte Carlo方法求解模化的脉动速度—频率—标量联合的PDF方程．将该算法发展到无结构网格，探讨了在无结构网格中实现两种方法的耦合，包括颗粒定位，颗粒场和平均场之间数据交换等问题．并以二维轴对称钝体后湍流流场作为算例，比较了计算结果与实验结果．     

On the six-field model of fluids based on extended thermodynamics

We study the six-field model of fluids (ET6) derived from extended thermodynamics. The six fields are the mass density, the velocity, the temperature, and the dynamic pressure (nonequilibrium pressure). We present the basic system of field equations of ET6. And we elucidate its characteristic features through the studies of the singular limit from polyatomic to monatomic rarefied gases, of hydrodynamic fluctuation, and of a hard-sphere system. Open problems remained in ET6 at present are also pointed out.     

Monte Carlo simulations on the thermodynamic properties of high‐density gases

The thermodynamic properties of Ar, H₂ and CH₄ at high‐density conditions are studied using Monte Carlo simulations. The isotherms of Ar at 500K, H₂ at 1000K and CH₄ at 500K are obtained respectively. To validate the accuracy of the simulation results, the thermodynamic properties of these gases are also studied with van der Waals equation and compared with the reference data. The agreement with reference shows that Monte Carlo method can produce reliable thermodynamic properties of high‐density gases based on the accurate intermolecular potential model. Therefore, the accuracy of the simulations depends primarily on the accuracy of the potential model, and this dependence is also discussed. Copyright © 2012 John Wiley & Sons, Ltd.     

Heat transfer in subsonic high-temperature gas flow through three-dimensional curved channels

The heat transfer in subsonic high-temperature (T 2000°K) gas flow through a curved channel of rectangular cross section has been experimentally investigated. The local heat flow into the channel wall was measured by the modified gradient method, which consists in subdividing the walls by means of thin annular thermally-insulating partitions, measuring the temperature in the upper (gas) and lower (coolant) sections of the modules thus formed, and using these measurements to determine the local heat flux q_w on the assumption that the thermal field in the module is homogeneous. The soundness of this method has been demonstrated theoretically and experimentally and the expediency of using it in the intensive wall cooling regime has been confirmed. The method is employed to find the local heat flux fields over the- entire surface of the channel. The integrated fluxes q_w coincide to within 5% with the independently determined total increase in the enthalpy of the water in the cooling channels. A distinguishing feature of the investigation is the high relative curvature of the bend in the channel, which leads to the formation of a zone of intense separation on the convex (inner) wall. Three types of channel are examined. These differ with respect to the section beyond the bend which is either long or short or short with a contraction. A close correlation between the characteristics of the q_w fields and the hydrodynamic effects is detected and explained. These effects comprise: separation and reattachment of the flow, secondary effects in the bend, the formation of an unclosed separation zone in the short outlet section, the localization of this zone when the outlet section includes a contraction, and specific gas dynamic effects near the intersection of the surfaces.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 93–99, May–June, 1989.     

Stability of a melt/solid interface with reference to a plume channel

The structure of free-convection flow in a plume channel formed as a result of melting above a local heat source placed on the basement of a solid mass is experimentally investigated. The channel shape and the flow pattern in it are functions of the relative power Ka = N/N ₁, where N is the plume source power and N ₁ is the heat removed to the surrounding mass. When the heat is withdrawn from the plume channel by heat conduction, the channel represents a system of convective cells on whose boundaries there are channel constrictions. The temperature fields and the cell flow patterns are investigated. For mantle plumes, such as the Hawaiian, Iceland, and Bouvet plumes and extended igneous provinces, the basement diameter and the values of the criterion Ka are determined.     

Direct Statistical Simulation of a Supersonic Flow of a Binary Mixture of Rarefied Gases around a Transversely Positioned Cylinder

A supersonic flow of a binary mixture of gases in a wide range of rarefaction (from a flow with a Knudsen number K _n = 0.1 to a free-molecular flow) around a cylinder is studied by means of direct statistical Monte Carlo simulations (DSMC method). The influence of a small fraction of heavy particles in a light gas flow on the region of significant nonequilibrium near the cylinder and on the heat flux is considered.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 53–59, September–October, 2005.     

Calculation of magnetic fields and currents in axisymmetric systems of inductively coupled moving conductors

An algorithm for calculating magnetic fields and currents in axisymmetric systems of inductively coupled moving and stationary conductors is developed using a hybrid method which combines the finite and boundary element methods. The finite element method is used to approximate the unsteady diffusion equation for the θ-component of the magnetic vector potential in the conductors, and the boundary-element method is employed to eliminate the space around the conductors. The proposed method takes into account the connections of the conductors with each other or with external energy sources by means of ideal electrical circuits with lumped parameters R, L, and C. An effective method is developed to take into account the external circuits by an appropriate modification of the mass matrix and the source vector of the obtained system of ordinary differential equations. Examples of using the method to calculate the fields of single- and multi-turn solenoids, magnetic flux concentrators, and induction accelerators with various methods of delivering external electromagnetic energy are considered. The high computational efficiency of the method is shown, in particular, for the case of constant electrothermal properties and sizes of the conductors. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 22–29, January–February, 2009.     

“Magnetic-ribs” in fully developed laminar liquid–metal channel flow

This paper documents the numerical investigation of the effects of non-uniform magnetic fields, i.e. magnetic-ribs, on a liquid–metal flowing through a two-dimensional channel. The magnetic ribs are physically represented by electric currents flowing underneath the channel walls. The Lorentz forces generated by the magnetic ribs alter the flow field and, as consequence, the convective heat transfer and wall shear stress. The dimensionless numbers characterizing a liquid–metal flow through a magnetic field are the Reynolds (Re) and the Stuart (N) numbers. The latter provides the ratio of the Lorentz forces and the inertial forces. A liquid–metal flow in a laminar regime has been simulated in the absence of a magnetic field (Re_H = 1000, N = 0), and in two different magnetic ribs configurations for increasing values of the Stuart number (Re_H = 1000, N equal to 0.5, 2 and 5). The analysis of the resulting velocity, temperature and force fields has revealed the heat transport phenomena governing these magneto-hydro-dynamic flows. Moreover, it has been noticed that, by increasing the strength of the magnetic field, the convective heat transfer increases with local Nusselt numbers that are as much 27.0% larger if compared to those evaluated in the absence of the magnetic field. Such a convective heat transfer enhancement has been obtained at expenses of the pressure drop, which increases more than twice with respect to the non-magnetic case.     

不同形状微管道中的气体流动

不同形状微尺度管道(圆形、六边形、半圆形、不同宽高比的矩形)中的气体流动特性是微机电系统设计最为关心的问题之一.文中利用信息保存(IP)方法和直接模拟Monte Carlo(DSMC)方法进行研究,给出两种方法的计算结果相互符合,并与其它研究者的BGK模型方程计算结果进行了比较.对于微尺度管道中关心的低Mach数流动, IP方法的统计收敛效率明显优于DSMC方法.通过拟合IP和DSMC结果,给出了圆形、六边形、半圆形、不同宽高比的矩形截面情况下无量纲质量流率与等效Knudsen数的关系.     

Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials: A 3D study

In a recent publication (Yang et al., 2009. Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials. Int. J. Solids Struct. 46 (17) 3222–3234), we developed a finite element method capable of modelling complex two-dimensional (2D) crack propagation in quasi-brittle materials considering random heterogeneous fracture properties. The present study extends the method to model three-dimensional (3D) problems. First, 3D cohesive elements are inserted into the initial mesh of solid elements to model potential crack surfaces by a specially designed, flexible and efficient algorithm and corresponding computer program. The softening constitutive laws of the cohesive elements are modelled by spatially-varying 3D Weibull random fields. Monte Carlo simulations are then carried out to obtain statistical information of structural load-carrying capacity. A concrete cube under uniaxial tension was analysed as an example. It was found that as the 2D heterogeneous model, the 3D model predicted realistic, complicated fracture processes and load-carrying capacity of little mesh-dependence. Increasing heterogeneity in terms of the variance in the tensile strength random fields resulted in lower mean and higher standard deviation of peak loads. Due to constraint effects and larger areas of unsmooth, non-planar fracture surfaces, 3D modelling resulted in higher mean and lower standard deviation of peak loads than 2D modelling.     

Monte Carlo Simulation of Contaminant Transport: I. Long-range Correlations in Fracture Conductivity

We develop a network model of fractures, and use the model to study transport of contaminants by groundwater through natural geological media. The fractures are narrow rectangular channels between large flat parallel plates, which are embedded in the surrounding rock matrix. The fracture-permeabilities and the fracture-widths are obtained from both uniform and fBm distributions. The pressure distribution in the network, and subsequently the velocity of groundwater in each channel, is obtained. The transport problem in an individual fracture is solved in Laplace space using the realized groundwater velocities and network mass conservation. The transform space solutions are then inverted to real time using a fast and efficient inversion algorithm. Monte Carlo simulations are then carried out by repeating the above procedure for a large number of realizations. The main focus of this study is to explore the effects correlated fracture-permeabilities and fracture-widths have on the transport of contaminants. While the primary transport mechanism is convection, we also study such processes as adsorption onto the fracture surface, and radioactive decay. We show how these phenomena, individually and in combination with one another, affect the overall transport process. In addition, we investigate the nature of the mixing zone, and discuss how these results can be helpful in developing remediation techniques for a contaminated site.     

Accuracy of the Modified Eucken Correction to the Thermal Conductivity of Molecular Gases

The results of calculating the thermal conductivities of nine low-density molecular gases N₂, O₂, NO, CO, CO₂, N₂O, CH₄, CF₄, and SF₆ obtained using the modified Eucken correction are compared with the standard results.     

Experimental study on rise velocities of single bubbles in liquid metal under the influence of strong horizontal magnetic fields in a flat vessel

The ascent of single argon bubbles with equivalent diameters (d_eq) between 3.43 and 6.28 mm is investigated at room temperature in a flat, rectangular vessel by means of ultrasound Doppler velocimetry (UDV). GaInSn is used as a working liquid and magnetic flux intensities up to B ≈ 0.918 T are applied. A decelerating effect on the rise velocity is observed at lower, an accelerating effect at medium and a reduction at higher field strengths. Maximum velocities are achieved when the ratio of N/C_D ≈ 1, bubble paths are substantially rectilinear at N/C_D > 2. The mean ascent velocities are compared with literature and data of this work as well as other publications is provided in tables.     

Heat transfer correlation for boiling flows in small rectangular horizontal channels with low aspect ratios

In the present experimental study, a correlation is proposed to represent the heat transfer coefficients of the boiling flows through horizontal rectangular channels with low aspect ratios. The gap between the upper and the lower plates of each channel ranges from 0.4 to 2 mm while the channel width being fixed to 20 mm. Refrigerant 113 was used as the test fluid. The mass flux ranges from 50 to 200 kg/m² s and the channel walls were uniformly heated up to 15 kW/m². The quality range covers from 0.15 to 0.75 and the flow pattern appeared to be annular. The modified Lockhart–Martinelli correlation for the frictional pressure drop was confirmed to be within an accuracy of ±20%. The heat transfer coefficients increase with the mass flux and the local quality; however the effect of the heat flux appears to be minor. At the low mass flux condition, which is more likely to be with the smaller gap size, the heat transfer rate is primarily controlled by the liquid film thickness. A modified form of the enhancement factor F for the heat transfer coefficient in the range of Re_LF200 well correlates the experimental data within the deviation of ±20%. The Kandlikar's flow boiling correlation covers the higher mass flux range (Re_LF>200) with 10.7% mean deviation.     

Numerical investigation of static flow instability in a low-pressure subcooled boiling channel

A three-dimensional two-fluid model to predict subcooled boiling flow at low pressure is presented. The model is adopted to investigate the two-phase flow and heat transfer characteristics in a heated channel. The presence of bubbles as a consequence of heating flow through a vertical rectangular channel has a significant effect on the overall pressure drop along the channel. Numerical results were compared against a series experimental data performed at various conditions – mass flux, heat flux, inlet temperature and exit pressure. Good agreement on the overall pressure drop was achieved. The onset of flow instability velocity was also accurately determined when compared against measurements. Predicted results of void fraction provided useful information towards a more fundamental understanding of the occurrence of onset of nucleate boiling, onset of significant voiding and onset of flow instability. The phenomenon of boiling onset oscillations was also predicted through the use of the two-fluid model.