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采用FLUENT软件分别对外加均匀横向磁场的等截面三维充分发展液态金属管流的层流模型和低雷诺数湍流Lam/Bremhost(LB)模型进行了数值模拟,分析了外加磁场对普通方管LB模型速度分布和压降的影响。比较在相同哈特曼数下,层流和湍流模型方管截面上速度分布和管道中MHD压降。其中,对电流的计算采用磁感应方程来求得。数值模拟结果证明了用低雷诺数LB湍流模型解决方管磁流体流动的可行性。通过层流模型和湍流模型的对比可知,层流模型有较短的入口长度,但管内流体的压降却很大;而湍流模型管内速度更加平均化,管内压降较小,但管内入口长度较长。     

MHD from a Microscopic Concept and Onset of Turbulence in Hartmann Flow

We derive higher order magneto-hydrodynamic （MHD） equations from a microscopic picture using pro-jection and perturbation formalism. In an application to Hartmann flow we find velocity profiles flattening towards the center at the onset of turbulence in hydrodynamic limit. Comparison with the system under the effect of a uniform magnetic field yields difference in the onset of turbulence consistent with observations, showing that the presence of magnetic field inhibits onset of instability or turbulence. The laminar-turbulent transition is demonstrated in a phase transition plot of the development in time of the relative average velocities vs. Reynolds number showing a sharp increase of the relative average velocity at the transition point as determined by the critical Reynolds number.     

The use of PDE centres in the local RBF Hermitian method for 3D convective-diffusion problems

In this work an extension is proposed to the Local Hermitian Interpolation (LHI) method; a meshless numerical method based on interpolation with small and heavily overlapping radial basis function (RBF) systems. This extension to the LHI method uses interpolation functions which themselves satisfy the partial differential equation (PDE) to be solved. In this way, a much improved reconstruction of partial derivatives can be obtained, resulting in significantly improved accuracy in many cases.     

相关分析法确定HL-1M装置磁流体的扰动模式

采用相关分析法模拟分析了HL-1M装置的磁扰动模式,模拟的结果同预期的结果一致。在具有磁流体不稳定性的典型放电中,探测到独立模m=2、3、4,耦合模m=2、3,以及同时出现的耦合模m=4、5和独立模m=5,给出了用扰动幅度的极向截面图分析磁扰动模式的结果,讨论了相关分析法在实验分析中的优点和局限性。     

Characterization of the three-dimensional supersonic flow for the MHD generator

A numerical procedure based on a five-wave MHD model associated with non-ideal, low magnetic Reynolds number MHD flows was developed in the present study for analyzing the flow fields in the MHD generator of a MHD bypass scramjet. The numerical procedure is composed of an entropy conditioned scheme for solving the non-homogeneous Navier-Stokes equations, in conjunction with an SOR method for solving the elliptic equation governing the electrical potential. It was found that a separation would take place near the downstream edge of the second electrode, where the local adverse pressure gradient is large, and the core of the flow field is characterized as a 2-D flow due to the Hartmann effects along the direction of the magnetic field. The electric current lines would be increasingly distorted as the magnetic interactive parameter increases, and even induce an eddy current. Induced eddy current was also found in the different cross-sections along the axial direction, all of these would definitely deteriorate the performance of the MHD generator. The cross-sectional M-shape velocity profile found along the axial direction between the insulating walls is responsible for the formation of the vortex flow at the corner of the insulator cross-section, which, in turn, induces the corner eddy current at the corner. A numerical parametric study was also performed, and the computed performance parameters for the MHD generator suggest that, in order to enhance the performance of MHD generator, the magnetic interaction parameter should be elevated.     

小尺度封闭空间声场的无网格数值算法

无网格法是一种新兴的数值计算方法,具有不需要网格支持的特点。本文将该方法引入室内声学建模,推导了无网格声场数值计算模型,并将其应用于典型小尺度封闭空间内部声场的数值分析。针对声传递函数,将本方法与理论解和SYSNOISE计算结果进行了比较,并将计算的混响时间与实验测量结果作了对比,表明本方法具有良好的精度。     

On the use of a meshless method for solving radiative transfer with the discrete ordinates formulations

A meshless method is presented for solving the radiative transfer equation in the discrete ordinates approach. It is shown that the primitive variables formulation is unstable for low values of the absorption coefficient while the even parity formulation is always stable and accurate.     

水平变化波导中声传播问题的高效稳定耦合简正波解

提出了一种高效、精确而且数值稳定的耦合简正波方法,用于求解水平变化波导中的声传播问题。与现有的数值模型相比,本方法采用合理的归一化距离解,极大地提高了数值稳定性;通过结合一个前向传播过程和一个后向传播过程,该方法极大地提高了计算精度,可用于精确求解水平变化波导中的声传播问题,尤其适用于大角度斜坡以及海底与海水声阻抗差别较大的问题;此外,通过采用单次散射近似,该方法极大地提高了计算效率,而且对计算条件要求较低。从数值结果可以看出,本方法是一种高效、精确而且数值稳定的求解水平变化波导声传播问题的耦合简正波方法。     

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给出了通道插件管道MHD效应的初步实验结果,结果表明：中心区流速分布与数值预测的差别较大,且不同位置的管道截面流速分布不同,在压力平衡孔之间呈周期性变化;宏观的中心区与边缘区流量分配、MHD压降与简化理论预测结果相接近。这些数据将给FCI管道数值分析模型的完善和液态包层设计提供参考。     

An accurate and efficient method for treating aerodynamic interactions of cloud droplets

Motivated by a need to improve the representation of short-range interaction forces in hybrid direct numerical simulation of interacting cloud droplets, an efficient method for treating the aerodynamic interaction of two spherical particles settling under gravity is developed. An effort is made to ensure the accuracy of our method for any inter-particle separation by considering three separation ranges. The first is the long-range interaction where a multipole method is applied. After a decomposition into six simple configurations, explicit formulae for drag forces and torques are derived from an approximate Force–Torque–Stresslet (FTS) formulation. The FTS formulation is found to be accurate when the separation distance normalized by the average radius is larger than 5. The second range concerns the short-range interaction where the interaction force could be very large. Leading-order lubrication expansions are employed for this range and are found to be accurate when the normalized separation is less than about 0.01. Finally, for the intermediate range where no simple method is available, a third-order polynomial fitting is proposed to bridge the treatments for long-range and short-range interactions. After optimizing the precise form of polynomial fitting and matching locations, the force representation is found to be highly accurate when compared with the exact solution for Stokes flows. Using this method, collision efficiencies of cloud droplets sedimenting under gravity have been calculated. It is shown that the results of collision efficiency are in excellent agreement with results based on the exact Stokes flow solution. Collision efficiency results are also compared to previous results to further illustrate the accuracy of our calculations. The effects of particle rotation and the attractive van der Waals force on the collision efficiency are also studied. The efficient force representation developed here is more general than the usual lubrication expansion and thus can serve as a better approach to correct unresolved short-range interactions in particle-resolved simulations.     

An accurate and stable method of array element tiling for high-power laser facilities

Due to laser-induced damage, the aperture of optics is one of the main factors limiting the output capability of highpower laser facilities. Because of the general difficulty in achieving large-aperture optics, an alternative solution is to tile some small-aperture ones together. We propose an accurate, stable, and automatic method of array element tiling and verify it on a double-pass 1 × 2 tiled-grating compressor in the XG-III laser facility. The test results show the accuracy and stability of the method. This research provides an efficient way to obtain large-aperture optics for high-power laser facilities.     

An Hermitian method for the solution of radiative transfer problems

A new method for the solution of the radiative transfer equation is developed. The resulting system, like the ordinary difference equations is tridiagonal in form and easy to use. Numerical examples are given which show the superiority of the new technique to previous differential and integral equation methods.     

Different nano-particles volume fraction and Hartmann number effects on flow and heat transfer of water-silver nanofluid under the variable heat flux

Nanofluid flow and heat transfer composed of water-silver nanoparticles is investigated numerically inside a microchannel. Finite volume approach (FVM) is applied and the effects of gravity are ignored. The whole length of Microchannel is considered in three sections as l₁=l₃=0.151 and l₂=0.71. The linear variable heat flux affects the microchannel wall in the length of l₂ while a magnetic field with strength of B₀ is considered over the whole domain of it. The influences of different values of Hartmann number (Ha=0, 10, 20), volume fraction of the nanoparticles (ɸ=0, 0.02, 0.04) and Reynolds number (Re=10, 50, 200) on the hydrodynamic and thermal properties of flow are reported. The investigation of slip velocity variations under the effects of a magnetic field are presented for the first time (to the best knowledge of author) while the non-dimensional slip coefficient are selected as B=0.01, 0.05, 0.1 at different states.     

赤道面磁层顶位形的磁流体力学模拟研究

磁层顶位置和形状的动态特征描绘是地球物理和空间物理研究的难点之一.文章基于太阳风-磁层-电离层耦合的全球磁流体力学（MHD）数值模拟,运用电流密度极大法确定磁层顶位形,并具体研究两种典型太阳风动压（D_p）和几种不同行星际磁场的z分量（B_z）条件下,地球赤道面上方磁层顶动态特征.模拟结果显示,磁层顶日下点高度r₀主要由D_p控制.随着D_p增加,磁层顶被压缩,r₀显著减小.相同D_p条件下,在B_z由南向（B_z<0）逐渐减小,并转为北向（B_z>0）逐渐增大的过程中,r₀缓慢增大.不同条件下,磁层项张角φ变化较小,反映了赤道面磁层顶结构的相似性.与Shue98低纬磁层顶经验模型比较,MHD模拟能再现磁层顶日下点位置r₀对D_p的响应,而r₀随B_z变化的饱和性仅出现在低速太阳风条件下.MHD模拟和经验模型的磁层项张角φ差别小于2.5°,但模拟显示φ随B_z的变化趋势并非简单线性关系.     

HT-7装置MHD的实时检测与控制

在HT-7装置实验研究中,利用主动反馈调制低杂波(LHW)实时有效地抑制了MHD不稳定性。介绍了用DAQ2010高速采集卡为硬件的系统对HT-7装置实验中MHD的实时检测和控制。     

几种液体金属自由表面的MHD不稳定性实验研究

介绍了在核工业西南物理研究院的液态金属实验回路(LMEL)上获得的几种可供液态偏滤器-限制器系统选用的液体自由表面的磁流体动力学(MHD)效应不稳定性的实验结果。实验发现：自由表面射流在穿越梯度横磁场时射程变短、截面变扁平,但MHD效应稳定,调节射流与磁场的夹角可以控制射流的流动特性;自由表面膜流MHD效应存在三种现象,即层流、溪状流和湍流。层流是由多束射流打到固体表面产生的(简称“射-膜流”),从MHD效应角度考虑,“射-膜流”将是四种可选液态偏滤器-限制器系统的液体自由表面形式中最佳的选择。同时,探讨了从物理的角度来理解四种自由表面形式的MHD效应的现象。     

An efficient method for the solution of Riccati equation in structural control implementation

An efficient method for the solution of the Riccati equation in structural control implementation is presented in this paper. Through order reduction and appropriate selection of weighting functions, the solution time for the Riccati equation is dramatically reduced as no iteration is involved in the solution process. This achievement is very useful and sometimes critical in the structural control as the solution process of the Riccati equation is the most time-consuming part of any optimal control problem. It requires an inordinate amount of processing time when applied to large optimal control problems. As is well known, any time delay in structural control will cause unsynchronized application of the control forces and this can not only reduce the effectiveness of a structural active control system, but may also cause instability in the control system. The proposed method is easy to implement and high in efficiency and can significantly reduce the time delay in structural control implementation.     

An efficient and stable spectral method for electromagnetic scattering from a layered periodic structure

The scattering of acoustic and electromagnetic waves by periodic structures plays an important role in a wide range of problems of scientific and technological interest. This contribution focuses upon the stable and high-order numerical simulation of the interaction of time-harmonic electromagnetic waves incident upon a periodic doubly layered dielectric media with sharp, irregular interface. We describe a boundary perturbation method for this problem which avoids not only the need for specialized quadrature rules but also the dense linear systems characteristic of boundary integral/element methods. Additionally, it is a provably stable algorithm as opposed to other boundary perturbation approaches such as Bruno and Reitich’s “method of field expansions” or Milder’s “method of operator expansions”. Our spectrally accurate approach is a natural extension of the “method of transformed field expansions” originally described by Nicholls and Reitich (and later refined to other geometries by the authors) in the single-layer case.     

An efficient and accurate reconstruction algorithm for the formulation of cell-centered diffusion schemes

A new reconstruction algorithm is proposed for constructing cell-centered diffusion schemes on distorted meshes. Its main feature is that edge unknowns are defined at certain balance points, the locations of which depend on the diffusion coefficient and the skewness of grid cells, so as to obtain a two-point reconstruction stencil. Implementing the new algorithm for the approximation of gradients, we extend the IDC (improved deferred correction) scheme, which was proposed by Traoré et al. [P. Traoré, Y. Ahipo, C. Louste, A robust and efficient finite volume scheme for the discretization of diffusive flux on extremely skewed meshes in complex geometries, J. Comput. Phys. 228 (2009) 5148–5159], to handle diffusion problems with discontinuous coefficients. Numerical results demonstrate the accuracy and efficiency of the extended scheme.     

Multiscale modeling of nanoindentation in copper thin films via the concurrent coupling of the meshless Hermite-Cloud method with molecular dynamics

This paper investigates the 2D nanoindentation of a copper thin film using a concurrent multiscale method. The method uses molecular dynamics (MD) simulation in the atomistic region, the strong-form meshless Hermite-Cloud method in the continuum region and a handshaking algorithm to concurrently couple them. A fully atomistic simulation is also carried out to validate the multiscale method. The results, namely the load versus indentation depth graph obtained from the multiscale method shows only slight quantitative variation from that of the full atomistic model. More importantly, the graphs from both simulations show a similar trend thus validating the 2D multiscale method. The displacement profile without discontinuities further supports the efficiency of the multiscale method in ensuring smooth exchange of information between the atomistic and continuum domains. The material properties extracted from the simulation include the force/unit length values obtained by dividing the maximum load on the indenter by its contact perimeter, instead of the hardness value obtained in 3D simulations. By restricting the atomic scale detail to the critical regions beneath the indenter, the multiscale method effectively saves computational resources to more than one order (close to 13 times less for this problem), thus making it feasible to simulate problems of larger dimensions that are not amenable to complete atomistic simulations.