基于激光吸收光谱技术的非均匀流场气体参数测量研究

为了探索激光吸收光谱技术在非均匀流场中的应用,提出了一种新的实现非均匀流场中气体参数定量测量的方法。预知被测流场中的温度变化范围后,选择在该温度范围内具有近似线性变化特性的谱线,线性拟合该温度范围内的谱线强度,结合实验测量的吸收光谱便可以实现非均匀流场中H₂O组分权重的温度积分平均值和H₂O组分积分平均值的定量测量。两温度分布和高斯温度分布模型的仿真研究证明了该方法的有效性和可靠性。两温度分布模型中的测量结果与理论值的偏差分别小于0.82%和1.10%,而高斯温度分布模型中不同光线中的测量值与理论值的最大偏差分别小于0.9%和3.6%。     

Voigt线型两翼拟合非均匀流场吸光度的方法研究

在吸收光谱领域特别是可调谐半导体激光直接吸收光谱(dTDLAS)技术中, 需要精确测量吸收光谱的积分吸光度值以精确反演出流场温度、组分浓度等参数。对于非均匀流场,单光路吸收光谱测量时,由于沿测量路径的谱线展宽随流场状态的变化而变化,见诸文献的研究主要采用Voigt或Lorentz线型对吸光度曲线拟合处理或直接对吸光度曲线数值积分获取积分吸光度值,针对方法可能引入的误差进行了模拟分析,并提出Voigt线型两翼拟合吸光度的方法来获取吸收光谱的积分吸光度值,以减小拟合误差。采用流场测量中常用的H₂O作为目标气体,选取了8条具有不同低态能级的吸收线,以实验室平焰炉为原型建立两种非均匀流场模型,并通过分段法对流场非均匀性进行等效处理。分别采用Voigt线型拟合法、数值积分法和Voigt线型两翼拟合法模拟计算两模型的积分吸光度值,通过与理论积分吸光度值对比得出各方法的误差大小,从而确定出在不同的非均匀流场情况下相适应的积分吸光度值获取方法。     

A New Numerical Solution of Fluid Flow in Stratigraphic Porous Media

A new numerical technique based on a lattice-Boltzmann method is presented for analyzing the fluid flow in stratigraphic porous media near the earth's surface. The results obtained for the relations between porosity, pressure, and velocity satisfy well the requirements of stratigraphic statistics and hence are helpful for a further study of the evolution of fluid flow in stratigraphic media.     

空间分数阶导数“反常”扩散方程数值算法的比较

分别采用显式差分格式、隐式差分格式以及Crank-Nicholson差分格式数值求解空间分数阶导数,并从局部截断误差、稳定性、计算量三个方面进行比较分析;通过数值算例验证分析结果.     

Numerical Study of Unsteady MHD Flow and Entropy Generation in a Rotating Permeable Channel with Slip and Hall Effects

This article investigates an unbiased analysis for the unsteady two-dimensional laminar flow of an incompressible, electrically and thermally conducting fluid across the space separated by two infinite rotating permeable walls.The influence of entropy generation, Hall and slip effects are considered within the flow analysis. The problem is modeled based on valid physical arguments and the unsteady system of dimensionless PDEs (partial differential equations) are solved with the help of Finite Difference Scheme. In the presence of pertinent parameters, the precise movement of the flow in terms of velocity, temperature, entropy generation rate, and Bejan numbers are presented graphically, which are parabolic in nature. Streamline profiles are also presented, which exemplify the accurate movement of the flow. The current study is one of the infrequent contributions to the existing literature as previous studies have not attempted to solve the system of high order non-linear PDEs for the unsteady flow with entropy generation and Hall effects in a permeable rotating channel. It is expected that the current analysis would provide a platform for solving the system of nonlinear PDEs of the other unexplored models that are associated to the two-dimensional unsteady flow in a rotating channel.     

A Remark on the Courant-Friedrichs-Lewy Condition in Finite Difference Approach to PDE's

The Courant-Friedrichs-Lewy condition (The CFL condition) is appeared in the analysis of the finite difference method applied to linear hyperbolic partial differential equations. We give a remark on the CFL condition from a view point of stability, and we give some numerical experiments which show instability of numerical solutions even under the CFL condition. We give a mathematical model for rounding errors in order to explain the instability.     

Peristaltic Flow of Couple Stress Fluid in a Non-Uniform Rectangular Duct Having Compliant Walls

The present study investigates the peristaltic flow of couple stress fluid in a non-uniform rectangular duct with compliant walls.Mathematical modeling is based upon the laws of mass and linear momentum.Analytic solutions are carried out by the eigen function expansion method under long-wavelength and low-Reynolds number approximations.The features of the flow characteristics are analyzed by plotting the graphs of various values of physical parameters of interest.Trapping bolus scheme is also presented through streamlines.     

边界层流动中湍斑的直接数值模拟

用Navier-Stokes方程直接数值模拟平板边界层流动中湍斑的形成和演化过程.发展了模拟湍斑的高精度、高分辨率的高效计算方法,包括推出四阶时间分裂法以提高精度;提出三维耦合差分方法,用于关于压力的泊松方程和关于速度的亥姆霍兹方程的空间离散,建立其四阶三维耦合中心差分格式;并采用四阶紧致迎风差分格式,避免了一般四阶中心差分格式不适用于边界邻域的困难和提高了分辨率;精心地处理各种边界条件,以保持精度和稳定.该方法适用于包含边界邻域的整个区域内的湍斑模拟.通过模拟平板边界层流动中湍斑的复杂演化过程,显示了湍斑的基本特征.     

A Numerical Study of Characteristic Slow-Transient Behavior of a Compressible 2D Gas-Liquid Two-Fluid Model

The purpose of this paper is to gain some insight into the characteristic behavior of a general compressible two-fluid gas-liquid model in 2D by using numerical computations. Main focus is on mass transport phenomena. Relatively few numerical results in higher dimensions can be found in the literature for this two-fluid model, in particular, for cases where mass transport dynamics are essential. We focus on natural extensions to 2D of known 1D benchmark test cases, like water faucet and gas-liquid separation, previously employed by many researchers for the purpose of testing various numerical schemes. For the numerical investigations, the WIMF discretization method introduced in [SIAM J. Sci. Comput. 26 (2005), 1449] is applied, in combination with a standard dimensional splitting approach. Highly complicated flow patterns are observed reflecting the balance between acceleration forces, gravity, interfacial forces, and pressure gradients. An essential ingredient in these results is the appearance of single-phase regions in combination with mixture regions (dispersed flow). Solutions are calculated and shown from early times until a steady state is reached. Grid refinement studies are included to demonstrate that the obtained solutions are not grid-sensitive.     

带通道插件管道流磁流体动力学效应的数值模拟

采用二维完全发展流模型对聚变反应堆包层带通道插件和压力平衡槽隙的矩形磁流体管流的MHD效应进行数值模拟,分析速度分布,MHD压降随哈德曼数以及通道插件的电导率的变化规律.与无插件磁流体管流相比,带绝缘通道插件管流MHD压降显著降低,MHD压降随哈德曼数的增加而减小,通道插件材料的电导率增加MHD压降系数减小.压力平衡槽隙处的回流与通道插件的电导率有关.在宏观上计算结果与实验结果和简化理论结果一致.     

Numerical Analysis of Unsteady Magneto-Biphase Williamson Fluid Flow with Time Dependent Magnetic Field

Numerical investigation of the dusty Williamson fluid with the dependency of time has been done in current disquisition. The flow of multiphase liquid/particle suspension saturating the medium is caused by stretching of porous surface. The influence of magnetic field and heat generation/absorption is observed. It is assumed that particle has a spherical shape and distributed uniformly in fluid matrix. The unsteady two-dimensional problems are modeled for both fluid and particle phase using conservation of mass, momentum and heat transfer. The finalized model generates the non-dimensioned parameters, namely Weissenberg number, unsteadiness parameter, magnetic parameter,heat generation/absorption parameter, Prandtl number, fluid particle interaction parameter, and mass concentration parameters. The numerical solution is obtained. Locality of skin friction and Nusselt number is deliberately focused to help of tables and graphs. While inferencing the current article it is clearly observed that increment of Williamson parameter, unsteadiness parameter, magnetic parameter, volume fraction parameter, and mass concentration parameter reduces the velocity profile of fluid and solid particles as well. And increment of Prandtl number, unsteadiness parameter,volume fraction parameter, and mass concentration parameter reduces the temperature profile of fluid and solid particles as well.     

垂直管内油水分散流的数值研究

建立封闭的双流体模型并对垂直管内油水分散流进行了数值模拟,采用κ-ε模型处理连续相的湍流结构。模型预测结果与实验数据的比较结果表明,该模型能较好地模拟垂直管湍流分散流的局部相含率分布和速度分布。     

周期性波纹通道内换热与流动的数值研究

采用曲线坐标系下压力与速度耦合的SIMPLER算法,数值研究了一种紧凑换热器中波纹通道内周期性充分发展的层流流动与换热情况,流动Re数的范围为100~1100,Pr数为0.7.计算考察了不同波纹高度、波纹间距对流动与换热的影响,并对模型参数进行了性能评价.计算结果表明,整体Nu数及fRe数随着流动Re数的增加而增加.随着波纹高度的增加或波纹间距的减小,换热增强,特别是在高Re数下波纹高度的增加更加强化换热.最佳波纹高度和间距分别为1.15 mm和13 mm.     

二维多相反应流的欧拉数值方法

本文研究二维多相反应流的数值模拟方法.对于非完全流体,考虑两种状态方程：刚性气体状态方程和JWL（Jones-Wilkins-Lee）型的状态方程.针对这些非完全流体,研究一种混合单元物理量重构法,它由单元内的已知物理量出发,应用单元内不同相的物理量之间的关系：混合密度与各自密度之间的关系、及混合内能与各物质内能之间的关系,再由温度与压强平衡条件,建立关于单变量的非线性方程,对所得方程通过"移动跟踪法"求解,得到单元内的压力、温度及声速等.再利用HLLC解法器,求解各个单元边界数值通量,从而构造一种高效的数值方法.数值结果表明：该算法能清晰地捕捉爆轰波的结构特征,胞格排列有序,三波点的特征明显.     

QUICK格式在湍流旋流流动数值模拟中的应用

为研究不同精度的离散格式对湍流旋流流动数值模拟结果的影响,同时应用QUICK格式和混合格式对同轴射流旋流燃烧室内的湍流流动进行了数值模拟.在采用k-ε湍流模型的条件下,QUICK格式计算得到的燃烧室内气体轴向与切向速度及轴向脉动速度均方根值分布与实验数据符合较好,而混合格式给出的数值模拟结果则与实验有一定的偏差.     

Fully HOC Scheme for Mixed Convection Flow in a Lid-Driven Cavity Filled with a Nanofluid

A fully higher-order compact (HOC) finite difference scheme on the 9-point two-dimensional (2D) stencil is formulated for solving the steady-state laminar mixed convection flow in a lid-driven inclined square enclosure filled with water-$Al_2O_3$ nanofluid. Two cases are considered depending on the direction of temperature gradient imposed (Case I, top and bottom; Case II, left and right). The developed equations are given in terms of the stream function-vorticity formulation and are non-dimensionalized and then solved numerically by a fourth-order accurate compact finite difference method. Unlike other compact solution procedure in literature for this physical configuration, the present method is fully compact and fully higher-order accurate. The fluid flow, heat transfer and heat transport characteristics were illustrated by streamlines, isotherms and averaged Nusselt number. Comparisons with previously published work are performed and found to be in excellent agreement. A parametric study is conducted and a set of graphical results is presented and discussed to elucidate that significant heat transfer enhancement can be obtained due to the presence of nanoparticles and that this is accentuated by inclination of the enclosure at moderate and large Richardson numbers.     

Numerical Study of Mixed Convective Peristaltic Flow through Vertical Tube with Heat Generation for Moderate Reynolds and Wave Numbers

The current study focuses on the numerical investigation of the mixed convective peristaltic mechanism through a vertical tube for non-zero Reynolds and wave number. In the set of constitutional equations, energy equation contains the term representing heat generation parameter. The problem is formulated by dropping the assumption of lubrication theory that turns the model mathematically into a system of the nonlinear partial differential equations. The results of the long wavelength in a creeping flow are deduced from the present analysis. Thus, the current study explores the neglected features of peristaltic heat flow in the mixed convective model by considering moderate values of Reynolds and wave numbers. The finite element based on Galerkin's weighted residual scheme is applied to solve the governing equations. The computed solution is presented in the form of contours of streamlines and isothermal lines, velocity and temperature profiles for variation of different involved parameters. The investigation shows that the strength of circulation for stream function increases by increasing the wave number and Reynolds number. Symmetric isotherms are reported for small values of time-mean flow. Linear behavior of pressure is noticed by vanishing inertial forces while the increase in pressure is observed by amplifying the Reynolds number.     

有限雷诺数情况下微槽道可压缩流动滑移流模型稳定性的数值模似

通过对微槽道一阶滑移流模型稳定性的理论研究，发现在不可压缩流和雷诺数趋于零的情况下，当Knudsen数Kn大于1／9时，会出现不稳定现象．这一理论结论在可压缩流和有限雷诺数情况下是否成立，尚不清楚，采用成熟的计算方法，用数值计算来研究可压缩流和有限雷诺数情况下一阶滑移流模型的稳定性，发现随着雷诺数的减小，不稳定的临界Knudsen数也不断减小，逐渐趋近于在不可压缩流和雷诺数趋于零的情况下得到的理论分析结果。     

A High-Accuracy Finite Difference Scheme for Solving Reaction-Convection-Diffusion Problems with a Small Diffusivity

This paper is devoted to a new high-accuracy finite difference scheme for solving reaction-convection-diffusion problems with a small diffusivity $\varepsilon$. With a novel treatment for the reaction term, we first derive a difference scheme of accuracy $\mathcal{O}(\varepsilon^2 h + \varepsilon h^2 + h^3)$ for the 1-D case. Using the alternating direction technique, we then extend the scheme to the 2-D case on a nine-point stencil. We apply the high-accuracy finite difference scheme to solve the 2-D steady incompressible Navier-Stokes equations in the stream function-vorticity formulation. Numerical examples are given to illustrate the effectiveness of the proposed difference scheme. Comparisons made with some high-order compact difference schemes show that the newly proposed scheme can achieve good accuracy with better stability.     

三维有限差分波束传输法：用于Ti：LiNbO3方向耦合器的模拟

提出求解三维傍轴近似波动方程的交替方向隐式并分格式，并用它模拟Ｔｉ：ＬｉＮｂＯ３方向耦合器。