基于POD-Galerkin降维方法的热毛细对流分岔分析

作为流动与传热相互耦合的非线性过程, 热毛细对流有着复杂的转捩过程, 探究流场和温度场随参数变化而发生的分岔现象, 是热毛细对流研究的一个重要课题. 基于本征正交分解的POD-Galerkin降维方法可以通过提取特征模态, 构建低维模型, 实现流场的快速计算. 数值分岔方法可以通过求解含参数动力系统的分岔方程, 直接计算稳定解和分岔点. 探究了将直接数值模拟方法、POD-Galerkin降维方法、数值分岔方法的优势结合, 以提高热毛细对流转捩过程分析效率的可行性. 利用直接数值模拟得到的流场和温度场数据, 构建了不同体积比下, 二维有限长液层热毛细对流的POD-Galerkin低维模型, 在低维模型上采用数值积分及数值分岔方法计算了分岔点, 得到了低维方程的分岔图. 在一定参数范围内, 在低维模型上模拟热毛细对流, 对雷诺数和体积比进行参数外推, 通过与直接数值模拟的结果对比, 验证了低维模型的准确性与鲁棒性. 说明了低维方程可以定性反映原高维系统的流动特性, 而定量方面, 由低维模型和直接数值模拟计算得到的周期解频率的相对误差大约为5%. 验证了利用POD-Galerkin降维方法研究热毛细对流的可行性.      

封闭方腔内空气和水自然对流每一次分岔数值预报

采用二阶全展开ETG分裂步有限元方法,通过对流动拓扑的详细分析,在排除网格密度影响的基础上,结合二分法给出封闭方腔内空气和水两种典型流体自然对流发生第一次分岔时的临界Rayleigh数。计算结果表明,该方法可用于进行不同Prandtl数条件下方腔内自然对流流动第一次分岔的数值预报,可作为后续各阶分岔及转捩数值预报研究的基础。在相应的条件下,封闭方腔内空气比水更容易发生分岔,且空气的流动结构相对于水表现出一定的倾斜性。     

浮区热毛细对流

概述了浮区中平行于自由面的表面张力梯度驱动热毛细对流领域的研究. 研究兴趣集中于振荡热毛细对流的起振, 或者说从定常流动到振荡流动的转捩. 起振依赖于一系列的临界参数, 临界关系可以表示为这些临界参数的复杂函数. 实验结果表明, 振荡流中速度的变化和平均流动的速度有相同的量级, 而其它量的变化, 比如温度和自由面半径的波动, 相比于它们的平均量而言则要小得多. 因此, 起振应是流体中动力学过程的结果, 该问题是强非线性的. 在过去几十年中, 一些理论模型被引入来研究这个问题, 使用的方法包括理论分析方法、 线性不稳定性分析方法、 能量稳定性分析方法以及非定常的三维直接数值模拟. 其中直接数值模拟被认为是对强非线性过程进行深入分析的最适合方法, 通常能得到和实验较符合的结果. 从振荡热毛细对流向湍流的转捩提供了一个研究混沌行为的新系统, 开创了一个非线性科学的新前沿, 是一个集中了大量近期工作的研究热点. 该文对浮区热毛细对流作了一个回顾, 包括理论模型和分析, 以及实验研究.     

矩形液池热毛细对流转捩途径研究

主要研究矩形液池热毛细对流的分岔转捩. 通过测量流体内部温度振荡情况, 详细研究了热毛细对流的转捩过程和转捩途径. 实验发现, 矩形液池热毛细对流的转捩过程依次经历了定常、规则振荡、不规则振荡的阶段. 对于不同普朗特数的硅油在不同长高比情况下, 通向混沌的途径不同. 在转捩过程中, 随着温差的增加, 普朗特数在16 (1cSt) 以下和普朗特数为25 (1.5cSt)、长高比为26 的硅油热毛细对流主要以准周期分岔的转捩方式为主;而普朗特数为25 以上的则以倍周期分岔的转捩方式为主;两种分岔有时还会伴随有切分岔形式的出现.实验中还观察到了表面波动和对流涡胞振荡等现象.      

可压缩自由剪切流混合转捩大涡模拟

针对湍流气动光学效应与冲压发动机气体混合机理问题,开展了可压缩混合层流动空间模式大涡模拟和时间模式直接数值模拟研究.通过对流场(包含亚/亚混合、超/亚混合两种情况)失稳、转捩直至完全湍流的空间发展过程的研究表明,对流Mach数0.4状态下流场失稳以二维最不稳定扰动为主;非线性发展中,基频涡对并及展向涡撕裂主控流动转捩,流场发生混合转捩;转捩后脉动流场基本达到局部各向同性,此时,湍流Mach数低于0.3,流动压缩性可近似忽略.     

NUMERICAL INVESTIGATION ON FLOW STABILITY OF RAYLEIGH-B?NARD CONVECTION OF COLD WATER IN A RECTANGULAR CAVITY COOLED AND HEATED SYMMETRICALLY RELATIVE TO THE TEMPERATURE OF DENSITY MAXIMUM

为了解具有密度极值流体瑞利-贝纳德对流特有现象和规律,利用有限容积法对长方体腔内关于密度极值温度对称加热-冷却时冷水瑞利-贝纳德对流的分岔特性进行了三维数值模拟,得到了不同条件下的对流结构型态及其分岔序列,分析了密度极值特性、瑞利数、热边界条件以及宽深比对瑞利-贝纳德对流的影响. 结果表明:具有密度极值冷水瑞利-贝纳德对流系统较常规流体更加稳定,且流动型态及其分岔序列更加复杂;相同瑞利数下多种流型可以稳定共存,各流型在相互转变中存在滞后现象;随着宽深比的增加,流动更易失稳,对流传热能力增强;系统在导热侧壁时比绝热侧壁更加稳定,对流传热能力有所减弱;基于计算结果,采用线性回归方法,得到了热壁传热关联式.     

有水平流时双流体混合物对流的时空演变

在水平流动作用下混合流体(比如水和酒精)的Rayleigh-Benard对流,由于外部强制力和内在行波传播的耦合,构成了研究开流系统中斑图选择和非线性耗散波的理想模型系统,本文介绍对该系统初步的研究成果.首先简述了线性稳定性分析以及水平流对行波非线性分岔特性的影响,然后主要给出我们对这一系统在有限空间非周期边界条件下一维行波对流的研究成果,包括存在的时空形态及其特性对Rayleigh数和槽道长度的依赖关系,最后给出了进一步工作的展望.      

大尺寸液桥热毛细对流失稳性地面实验研究

开展大尺寸液桥浮力-热毛细对流地面实验, 探究流场转捩的临界条件及临界状态附近的流动情况. 通过粒子图像测速方法(PIV) 获得流体速度场, 研究液桥内部定常和转捩后的流场结构以及流体运动规律;并用红外热像仪测量液桥自由面温度分布, 研究流体流动的时空演化和温度振荡. 实验发现大尺寸半浮区液桥浮力-热毛细对流临界值与几何参数有关, 在大普朗特(Prandtl) 数情况下, 流场存在由稳定态向不稳定态再到混沌的转捩过程, 在临界马兰哥尼(Marangoni) 数附近, 流场内会出现行波现象, 流动模式也会随高径比的变化而发生变化;当继续增大马兰哥尼数, 流动会进入混沌状态.      

一种基于几何重构的Youngs-VOF耦合水平集追踪方法

针对界面追踪方法中拉格朗日方法和欧拉--拉格朗日方法计算效率低、不适用大变形、不能应用于三维数值计算模型等问题,研究了一种效率高、界面清晰、适用于三维模型的计算气液两相界面迁移特性的欧拉运动界面追踪方法,该方法将"米"状相邻单元Youngs方法用于运动界面重构,将Youngs-VOF和水平集通过几何方法耦合,提高运动界面精度,克服了VOF和水平集方法存在的缺陷,避免了利用高阶导数本身的稳定性去求解水平集对流方程和距离函数方程."米"状相邻单元Youngs方法避免了数值耗散、数值色散性以及非线性效应引起的捕捉界面模糊的情况.Youngs-VOF耦合水平集方法既保证了计算界面时的稳定性,与拉格朗日方法相比又提高了计算效率.利用Youngs-VOF耦合水平集方法与VOF方法对单个气泡在水中上升过程数值计算与实验对比并对经典剪切流场中圆形运动界面模型的数值计算,验证了Youngs-VOF耦合水平集方法的有效性并比VOF方法捕捉界面更清晰、锐利;通过对溃坝--自由表面流动过程数值计算并与实验进行对比,验证了Youngs-VOF耦合水平集方法的稳定性以及对三维数值模型的适用性.      

一种基于几何重构的Youngs-VOF耦合水平集追踪方法

针对界面追踪方法中拉格朗日方法和欧拉–拉格朗日方法计算效率低、不适用大变形、不能应用于三维数值计算模型等问题,研究了一种效率高、界面清晰、适用于三维模型的计算气液两相界面迁移特性的欧拉运动界面追踪方法,该方法将"米"状相邻单元Youngs方法用于运动界面重构,将Youngs-VOF和水平集通过几何方法耦合,提高运动界面精度,克服了VOF和水平集方法存在的缺陷,避免了利用高阶导数本身的稳定性去求解水平集对流方程和距离函数方程."米"状相邻单元Youngs方法避免了数值耗散、数值色散性以及非线性效应引起的捕捉界面模糊的情况. Youngs-VOF耦合水平集方法既保证了计算界面时的稳定性,与拉格朗日方法相比又提高了计算效率.利用Youngs-VOF耦合水平集方法与VOF方法对单个气泡在水中上升过程数值计算与实验对比并对经典剪切流场中圆形运动界面模型的数值计算,验证了Youngs-VOF耦合水平集方法的有效性并比VOF方法捕捉界面更清晰、锐利;通过对溃坝–自由表面流动过程数值计算并与实验进行对比,验证了Youngs-VOF耦合水平集方法的稳定性以及对三维数值模型的适用性.     

Thermal instability induced by buoyancy and surface tension with radiative transfer

The onset of steady, cellular convection in a horizontal fluid layer heated from below is considered taking into account the possibility of radiative heat transfer in addition to conduction and convection. The radiation is found to have a stabilizing effect even in the presence of surface tension. The effect of surface viscosity and surface deflexion are also discussed. The coupling between the surface tension and buoyancy becomes weaker as the radiative heat transfer rate is increased.     

Conjugate heat transfer in square enclosures

Building elements represented by square vertical enclosures encircled with finite walls or with centered solid body, could maintain the equivalent fluid volumes through the volume ratio scale. Present work aims to investigate the fluid flow and heat transfer in these two building elements. Complete two-dimensional numerical simulation of the conjugate heat conduction and natural convection occurring in both enclosures is carried out. An analytical expression for the minimum size of the inserted body at which the body begins to suppress the natural convection flow is proposed and validated by the numerical results. The fluid flow and heat transfer characteristics are analyzed through the streamlines, heatlines, and total heat transfer rates across both enclosures. Results reveal that heat transfer rates across both enclosures are complex functions of the volume ratio scale, Rayleigh number, and the relative thermal conductivity.     

A high-accuracy temporal–spatial pseudospectral method for time-periodic unsteady fluid flow and heat transfer problems

A temporal–spatial pseudospectral (TSP) method is proposed for the high-accuracy solutions of time-periodic unsteady fluid flow and heat transfer problems. In this method, both the spatial and temporal derivative terms in the governing equations are computed by pseudospectral method. The spatial derivatives are computed through Chebyshev and Lagrange polynomials while the time derivatives are computed by Fourier series. The TSP method is capable of directly finding out the periodic state solutions without the necessity to resolve the initial transient state solutions, hence holds high computational efficiency and high numerical accuracy properties for the time-periodic problems. This method is validated by three 2D benchmark problems: the time-periodic incompressible flow with exact solutions; the natural convection in enclosure with time-periodic temperature on one sidewall, and on both sidewalls. The TSP results fit well the exact solutions or the benchmark solutions and the TSP accuracy is much higher than the time marching spatial pseudospectral accuracy. Some time-dependent fluid flow and heat transfer characteristic parameters are analysed. The proposed TSP method could be further extended to more complex time-periodic unsteady fluid flow and heat transfer problems where high-accuracy results are required.     

Mixed convective heat transfer characteristics and mechanisms in structured packed beds

The structured packed bed is considered a promising reactor owing to its low pressure drop and good heat transfer performance. In the heat transfer process of thermal storage in packed beds, natural convection plays an important role. To obtain the mixed convective heat transfer characteristics and mechanisms in packed beds, numerical simulations and coupling analyses were carried out in this study on the unsteady process of fluid flow and heat transfer. A three-dimensional model of the flow channel in the packed bed was established, and the Navier–Stokes equations and Laminar model were adopted for the computations. The effects of the driving force on fluid flow around a particle were studied in detail. The differences in velocity and density distributions under different flow directions due to effect of the aiding flow or opposing flow were intuitively demonstrated and quantitatively analyzed. It was found that the driving force strengthens the fluid flow near the particle surface when aiding flow occurs and inhibits the fluid flow when opposing flow occurs. The boundary layer structure was changed by the natural convection, which in turn influences the field synergy angle. For the aiding flow, the coordination between the velocity and density fields is higher than that for the opposing flow. By analysis the effects of physical parameters on mixed convective heat transfer, it is indicated that with an increase in the fluid-solid temperature difference or the particle diameter, or a decrease in the fluid temperature, the strengthening or inhibiting effect of natural convection on the heat transfer became more significant.     

Analytical investigation of Bénard-Marangoni convection heat transfer in a shallow cavity filled with two immiscible fluids

The mechanism of natural and Marangoni convection in a system with two stratified fluid layers without mass transfer at the interface is investigated. The basis of the analytical solution is an assumption of parallel flow over a large portion of the system. The two cases of heat fluxes through horizontal or vertical opposite walls are considered. It is demonstrated that four different patterns of convection can be observed in the present system. The zone of occurrence of these flow patterns are specified in terms of non-dimensional parameters. Velocity and temperature distributions, stream function and Nusselt number are presented over a wide range of the governing parameters. The results obtained are explained in terms of the basic physical mechanisms that govern these flows showing many interesting aspects of the complex interaction between the buoyant and surface tension mechanisms.     

Experimental and numerical study on unsteady natural convection heat transfer in helically coiled tube heat exchangers

Both of experimental and numerical investigations were performed to understand unsteady natural convection from outer surface of helical coils. Four helical coils with two different curvature ratios were used. Each coil was mounted in the shell both vertically and horizontally. The cold water was entered the coil and the hot water in the shell was cooling by unsteady natural convection. A CFD code was developed to simulate natural convection heat transfer. Equations of tube and shell are solved simultaneously. Statistical analyses have been done on data points of temperature and natural convection Nusselt number. It was revealed that shell-side fluid temperature and the Nusselt number of the outer surface of coils are functions of in-tube fluid mass flow rate, specific heat of fluids and geometrical parameters including length, inner diameter of the tube and the volume of the shell, and time.     

Similarity solution of free convective boundary-layer behavior at a stretching surface

In the present study, free convection and heat transfer behavior of electrically conducting fluid in the boundary layer over a vertical continuously stretching surface is investigated. The effects of free convection, magnetic field, suction/blowing at the surface and the stretching speed of the surface on the flow and heat transfer characteristics are considered. By applying one-parametric group theory to analysis of the problem, a similarity solution is found. The governing equations of continuity, momentum and energy are solved numerically by a fourth-order Runge-Kutta scheme. The numerical results, which are obtained for the flow and heat transfer characteristics, reveal the influences of the parameters. Received on 9 September 1998