来流马赫数对叶栅吸力面可压边界层稳定性影响研究

针对叶栅高速流动稳定性预测及转捩问题，采用理论分析与实验测量相接合的方法。首先推导出正交曲线坐标系下三维扰动波的抛物化稳定性方程（PSE），在风洞实验中，采用叶栅表面压力测孔测量了设计叶栅表面静压分布。根据表面静压分布测量值，通过求解Falkner—Skan方程以获得不同来流马赫数下边界层内速度、压力、密度等参数的分布。将以上结果作为边界层平均流动值，结合数值离散化的正交曲线坐标系非线性抛物化稳定性方程（PSE）对流动的稳定性进行特征值分析。数值离散采用六阶精度差分格式，采用大步长隐格式法求解方程以保证求解的稳定性。计算结果表明本文所选用的实验叶栅由于加工量较小并采用后部加载叶型设计，边界层流动相对稳定。来流马赫数增加对边界层稳定性有微弱影响，会导致流动趋于不稳定。     

基于有限体积法的有压管道水锤计算

在水电站运行过程中,为了避免机组增减负荷产生的水锤威胁输水系统的安全,需要对有压管道中的水锤进行精确的模拟计算。基于有限体积法对有压管道水锤方程分别进行空间和时间尺度上的积分,并采用隐式的Crank-Nicolson格式对偏微分项进行处理,从而得到了具有二阶精度且无条件稳定的水锤方程离散格式。通过算例比较了该离散格式与特征线法的计算结果,结果表明,新推导的离散格式在计算有压管道水锤问题时具有较高的精度且稳定性较好。     

回融过程中土壤水热耦合迁移的数值模拟

针对冻土回融过程的不利影响,以沈阳市土壤为例,基于冻土水热耦合迁移的数学模型,采用中心差分格式线性化选代法求解,对现场土壤回融过程进行了数值模拟,并与试验结果进行了对比.结果表明,模拟中所采用的参数、数学模型及计算方法合理、有效.     

SCSD格式数值稳定性及计算精度的研究

概述对流项离散格式所引起的假扩散现象及选择不同的离散格式对数值计算过程的影响;在分析稳定性可控的对流项离散格式(stability controllable second-order difference scheme, SCSD)的基础上,提出求解二维对流扩散问题时,直接采用块修正技术和PDMA算法的强隐迭代算法,并对该格式在近边界节点的离散方程的处理上采用非均匀网格技术.通过典型算例验证,该方法不仅抑制了假扩散现象,保证了计算精度,同时也使稳定性得到增强.因此,采用SCSD格式离散对流项,应用非均匀网格处理近边界,并将TDMA算法和PDMA算法同时纳入求解离散方程的做法是合理的,整个程序的框架具有很强的通用性.     

热质渗透壁面饱和多孔介质通道流动与热质传递的数值模拟

利用数值模拟方法研究了多孔介质中存在温度梯度、浓度梯度并具有热质渗透壁面时的受迫对流对传热传质的影响。采用有限容积法在同位网格上离散控制多孔介质内流体流动与热质传递方程守恒方程(即N-S)，对流项采用二阶精度的QUICK格式，扩散项采用中心差分格式。利用SIMPLE算法求解压力和速度耦合问题。利用所发展的程序研究了在不同孔隙率，不同的温度、浓度边界条件下，流场、温度场和浓度场以及Nu和Sh的变化规律。     

差分算法在自由板温度应力场中的应用

针对有限元方法求解自由板温度应力存在计算模型复杂、工作量大等问题,以混凝土热传导方程为基础,推导出自由板温度场有限差分格式,并在温度场求解基础上,利用广义虎克定律和自由板特性,推导出自由板温度应力差分公式,并通过实例对自由板温度和应力进行求解。结果表明,差分算法求解自由板温度和应力场与有限元求解结果一致,且效率较高。     

燃气-蒸汽联合循环余热锅炉入口烟道结构优化数值模拟研究

应用通用软件FLUENT,对余热锅炉入口段的流场进行两维和三维数值模拟.采用标准k-ε两方程模型进行建模,方程的离散采用二阶迎风差分格式,并使用SIMPLE算法求解方程.将余热锅炉受热面管束处理为具有分布阻力和分布质量汇的多孔介质模型.得出了不同入口段结构对应的出口速度分布;根据出口速度的均匀性,确定了入口段最佳结构;并对两维和三维模型模拟结果的差异进行了分析.     

干燥转轮除湿器的新数学模型与RDCS程序

发展了干燥转轮除湿器的数学模型。控制方程中除考虑周向对流项｛平和上士及非定常项上Ｌ和运二外，还增加了吸附剂中的热扩散项＼共和外关及质量扩散项于共和才知。新编ＲＤＣＳ程序，采用松驰迭代法求解离散方程组。空间差分涉及对流和扩散两种不同的传热、传质形式，对流项采用一阶迎风差分格式，扩散项采用中心差分格式。时间差分可根据需要采用显格式、全隐格式或其它半隐格式。将ＲＤＣＳ与国外除湿器的数值计算结果和为数不多的实验数据作了比较。结果表明，ＲＤＣＳ的精度更高，适用范围更广。新建立的数学模型能更全面地反映干燥转轮中经历的传热、传质过程的物理本质。     

平面自由射流中燃料扩散的大涡模拟

对甲烷－空气预混气体的平面自由射流进行了大涡模拟,采用分步投影法求解动量方程,亚格子项采用标准Smagorinsky亚格子模式模拟,压力泊松方程采用修正的循环消去法快速求解,空间方向采用二阶精度的差分格式,在时间方向上采用二阶精度的显式差分格式。模拟结果给出了预混气体射流中拟序结构对燃料扩散的影响,表明促使燃料扩散的主要因素是射流中的拟序结构,由浓度梯度导致的组分扩散较弱。     

基于Matlab的混凝土平面温度自应力差分解法

针对传统的混凝土温度应力计算方法存在的不足,采用基于Matlab的混凝土平面温度自应力的差分解法,对大体积混凝土平面温度自应力进行仿真计算,即依据混凝土热传导方程及其边界控制条件,在构建混凝土平面温度场求解模型的基础上,考虑温度自应力的计算模型,建立温度自应力的差分计算格式,利用Matlab的编程与可视化功能,对工程实例中的大体积混凝土温度自应力进行仿真计算,并与有限元计算结果进行比较。结果表明,该算法计算结果与有限元计算结果一致,精度可满足工程需要,且可对温度场及温度自应力进行可视化的实时输出,为大体积混凝土施工与仿真计算提供了参考。     

Second order fully discrete and divergence free conserving scheme for time-dependent conduction–convection equations

This work presents a Crank–Nicolson extrapolation scheme for the two-dimensional time-dependent conduction–convection equations. Mixed finite element method is applied for the spatial approximation of the velocity, pressure and temperature. The time discretization is based on the Crank–Nicolson scheme for the linear term and semi-implicit scheme for the nonlinear term. Moreover, the stability analysis and error estimations are derived. Finally, numerical tests confirm the theoretical results of the presented method and show the efficient method conserves the property of divergence free of the original equations to some extent.     

Effect of thermal radiation on an unsteady MHD flow over an impulse vertical infinite plate with variant temperature in existence of Hall current

In this paper, the effects of thermal radiation on unsteady MHD flow viscous incompressible electrically conducting fluid past an impulsively started oscillating vertical plate with variable temperature and constant mass diffusion in the presence of Hall current have been presented. The dimensionless governing partial differential equations of the flow have been solved numerically by using the Galerkin finite element method. The numerical solutions for fluid velocity, angular velocity, temperature, and concentration are represented graphically whereas the numerical results of primary skin friction, rate of heat and mass transfer are presented in tabular form for various parameters involved. The current results were compared to the existing analytical solution based on the Crank–Nicolson implicit finite difference technique. The current study's findings have been shown to be extremely consistent with earlier findings.     

Chemical reaction effects on magnetohydrodynamic convective flow past a vertical absorbent plate with ramped wall temperature and concentration

The numerical analysis is conducted to evaluate the heat generating as well as Soret–Dufour influences on magnetohydrodynamic unsteady chemically reacting fluid. It is owing to an exponentially stimulating perpendicular porous plate entrenched in the absorbent medium by considering ramped surface temperatures and concentrations in the endurance of thermal radiating. The fundamental governing set of equations of the fluid dynamics in the flow is converted into dimensionless form by inserting suitable dimensionless parameters and variables, and the resulting equations are numerically solved by the efficient Crank–Nicolson implicit finite difference method. The influence of several important substantial parameters into the model on the velocity, temperature, and concentration of the fluid, in addition to the skin-frictions coefficient, Nusselt's number along with Sherwood's number for both thermal conditions has been studied and explored intensely by making use of graphs and tables. It is discovered that, with mounting values of Dufour, heat generating as well as thermal radiating parameters, the fluid temperatures, and velocity enhanced. Likewise, it is noticed that increasing the Soret parameter causes escalated fluid velocity and concentration, whereas the reverse result is noted with the chemical reaction parameter.     

Entrance region flow of a power-law fluid in concentric annuli with rotating inner wall

The laminar flow of a power-law non-Newtonian fluid in the entrance region of a concentric annulus is investigated numerically. The inner cylinder rotates with a constant angular velocity while the outer cylinder is stationary. Using the Prandtl boundary layer assumptions, the continuity and momentum equations are solved iteratively using a finite difference method. A Crank Nicolson method is used to obtain the velocity components and the pressure at each step of the axial direction. The development of the axial velocity profile, transverse (radial and tangential) velocity profiles, pressure drop have been studied. Computations are obtained for various axial positions and various flow indices.     

Computational unsteady flow analysis for third‐grade fluid from an isothermal vertical cylinder through a Darcian porous medium

The present study describes a mathematical model for free‐convective laminar incompressible boundary layer flow of a third‐grade fluid of the Reiner‐Rivlin differential type, external to an evenly heated semi‐infinite vertical cylinder through a two‐dimensional porous medium. Assuming a homogenous‐isotropic porous medium, simulation of bulk drag effects at low Reynolds number is conducted with the Darcy model. The resulting partial differential equation boundary value problem is normalized using suitable transformation variables. The highly nonlinear time‐dependent coupled conservation equations along with boundary conditions are resolved computationally with an optimized Crank‐Nicolson finite difference code. Validation with previous studies is included. The heat transport and skin‐friction coefficients are computed for different values of emerging nondimensional parameters. Furthermore, steady‐state and transient fluid flow variables are shown graphically. An enhanced fluid velocity is observed for increased Darcy number and the reverse trend is computed for higher values of third‐grade viscoelastic parameter. Also, the rate of heat transfer is observed to increase with greater Darcy number and a reduction in third‐grade viscoelastic parameter. A key observation which is drawn from the present study is that for third‐grade fluid the flow variables deviate significantly from a hot cylindrical wall as compared with a Newtonian fluid. The study is relevant to thermal polymer coating applications in aerospace materials processing.     

An iterative stabilized CNBS–CG scheme for incompressible non-isothermal non-Newtonian fluid flow

An iterative stabilized fractional step scheme abbreviated as I-CNBS–CG is developed, in which the Crank–Nicolson method based split (CNBS) scheme and the characteristic-Galerkin (CG) method are, respectively, used to discretize and solve the non-Newtonian momentum–mass conservation equations and the energy conservation equation in consideration of their convective character. Owing to introduction of an iterative procedure into the scheme the stability of the proposed scheme in time domain is greatly enhanced and much larger time step sizes are allowed to be used than those limited in existing explicit and semi-implicit ones. The proposed I-CNBS–CG scheme particularly suits to numerically model the non-isothermal non-Newtonian fluid flows with moderate or high viscosity and low thermal conductivity, such as molten polymer flow process in a mould cavity. Numerical experiments with the power-law fluid model demonstrate the improved performances of the proposed scheme.     

A Crank–Nicolson Scheme with ADI to Compute Heat Conduction in Laser Surface Hardening

In this article, a two‐dimensional (2D) numerical model of a Crank–Nicolson scheme with alternating‐direction implicit (ADI) is developed for a heat conduction model in the laser surface hardening process. A numerical solution is compared to the analytical solution and shows a better suitability. Numerical experiment of the repetitive heating is carried out using the present model in order to investigate influences of processing parameters on temperature profiles. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(6): 522–541, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21085     

Hall and ion-slip effects on MHD natural convective flow past an unbounded vertical porous channel with thermodiffusion

The consequences of Soret in addition to Dufour of natural convection heat and mass transfer for the unsteady three-dimensional boundary layer flow through a perpendicular condition of the existence of viscous dissipation, invariable suction, Hall as well as ion slip consequences into relation. The prevailing partial differential equation is dissolved digitally utilizing the implicit Crank–Nicolson finite difference method. The velocity, temperature, as well as concentration dispensations, is addressed computationally and demonstrated by the graphs. Numerical values of the Nusselt number, skin friction as well as Sherwoods numbers nearby the plate are discussed for a choice of values of substantial parameters and are displayed in a tabular manner. It is noticed that the temperature of the fluid diminishes with higher Prandtl numbers. The resulting velocity diminishes with the growing Hartmann number. Rotation, Soret, and Dufour parameters strengthen the velocity and momentum boundary layer thickness. The velocity intensifies through growing Hall and ion-slip parameters and the revoke trend is acquired with enhancement in suction parameter.