连续分层流体中内波传播的李群分析法

对于密度连续分层海洋流体中的内波传播,从绝热Boussinesq近似方程组出发,得出了考虑变密度的非线性控制方程。应用李群分析方法,推导出了系统偏微分方程组的多组允许无穷小对称性、守恒矢量以及群不变解,对不变解的有关性质进行了说明,给出了系统精确解析解表达式。本文的李群分析解析解与已有文献中内波传播过程密度和垂向速度随时间变化的数值模拟计算结果基本一致,密度和垂向速度随时间呈正弦振荡,并且李群分析解析解也可推导出内波色散关系具有各向异性特征。     

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研究了埋置于弹性地基内充液压力管道中非线性波的传播. 假设管壁是线弹 性的,地基反力采用Winkler线性地基模型,管中流体为不可压缩理想流体. 假定系统初始 处于内压为$P_0$的静力平衡状态,动态的位移场及内压和流速的变化是叠加在静 力平衡状态上的扰动. 基于质量守恒和动量定理,建立了管壁和流体耦合作用的非 线性运动方程组; 进而用约化摄动法, 在长波近似情况下得到了KdV方程,表征 着系统有孤立波解.     

KdV方程孤立子及其相互作用的Petrov-Galerkin有限元数值模拟

本文给出一种Petrov-Galerkin有限元方法,并用以求Kdv方程各种初值问题的数值解,包括孤立波进波解,多个孤立于的相互作用,孤立子与振荡尾波等,所得结果与分析解及其它数值结果作了比较,表明本方法精度高、稳定性好,几乎没有高频伪振荡,计算程序简洁、明瞭,经济实用。     

肾小管中液体流动特性的分析

本文分折了肾小管中液体的流动特性,假定穿过管壁流体的泸过现象服从一般的Starling定律,通过求解小Re数时的NaVjcr-Stokes方程,求得小管内流体压力,速度与流量的分析表达式,在此基础上,提出确定表征管壁渗透特性的参数的方法,所得结果与实验结果吻合得较好。     

基于水平集方法的毛管上升特征研究

毛管上升现象与许多行业密切相关,系统地对此现象进行研究具有重大意义。与传统理论研究方法不同,本文使用N-S方程耦合水平集方法模拟毛管气液上升行为。通过与简化条件的解析解对比,验证了模拟方法的可靠性。此外,详细地研究了毛管振荡现象,并分析了影响毛管振荡行为的主要因素。结果表明,水平集方法能够精确地表征毛管振荡现象,与数值解相比具有更高的精度。毛管长度的增加能够减弱液柱振荡,主要归结于非湿相气体的粘滞力作用;湿相密度和湿相粘度同样对毛管振荡现象影响显著。湿相密度越大,惯性力越大,促进了毛管振荡;而湿相粘度变大,会增大粘滞力作用,因此减弱了毛管振荡现象。毛管振荡是由多种影响因素共同控制的,流体的惯性力是造成毛管振荡的主要原因,而粘滞力是减弱毛管振荡行为的主要因素,使液柱振荡逐渐衰减,并稳定至平衡高度。     

基于水平集方法的毛管上升特征研究

毛管上升现象与许多行业密切相关，系统地对此现象进行研究具有重大意义。与传统理论研究方法不同，本文使用N-S方程耦合水平集方法模拟毛管气液上升行为。通过与简化条件的解析解对比，验证了模拟方法的可靠性。此外，详细地研究了毛管振荡现象，并分析了影响毛管振荡行为的主要因素。结果表明，水平集方法能够精确地表征毛管振荡现象，与数值解相比具有更高的精度。毛管长度的增加能够减弱液柱振荡，主要归结于非湿相气体的粘滞力作用；湿相密度和湿相粘度同样对毛管振荡现象影响显著。湿相密度越大，惯性力越大，促进了毛管振荡；而湿相粘度变大，会增大粘滞力作用，因此减弱了毛管振荡现象。毛管振荡是由多种影响因素共同控制的，流体的惯性力是造成毛管振荡的主要原因，而粘滞力是减弱毛管振荡行为的主要因素，使液柱振荡逐渐衰减，并稳定至平衡高度。     

流体黏性对输流管道运动方程及临界流速的影响

考虑实际流体黏性引起的管内流速非均匀分布,针对层流和两种不同的湍流流态,对理想流体情况下输流管道运动方程中的离心力项进行了修正,得到的修正系数分别为1.333(圆管层流)、1.020(光滑管壁圆管湍流)和1.037～1.055(粗糙管壁圆管湍流).根据修正后的运动方程得到的上述3种情况下的发散失稳临界流速比理想流体流动情况下依次分别低13.4%,1.0%和1.8%～2.6%.流体黏性对输流管道运动方程及临界流速的影响只与流态有关,雷诺数决定流态,而黏性系数通过雷诺数间接起作用.     

含能材料密实床燃烧转爆轰的数值模拟

本文建立了含能材料密实床燃烧转爆轰的全粘性欧拉二维非定常两相反应流数学模型。将SIMPLE型的数值计算方法引入燃烧转爆轰的二维数值计算。对跨音速流动的处理和可压缩流体压力校正方程的建立提出了改进方法,并以无起爆药雷管作为算例。结果表明,本方法较好克服了二维两相流数值解的振荡现象。     

两相混合流体的非线性本构理论

本文从连续介质力学的基本原理出发,建立了微极流体与经典流体两相流动的非线性扩散理论。给出了混合流体本构方程的一般形式。对单相流体、单相微极流体及稀悬浮体三种特殊情形,得到了具体形式的二阶非线性本构方程,并同已有的理论进行了比较。     

水下爆炸气泡运动的理论研究

在适当深度的无黏、无旋的流体中对水下爆炸气泡运动特性进行理论研究。综合运用势流理论、能量方程以及拉格朗日方程建立气泡在不可压缩流体中的运动方程。并以此为基础,考虑重力、浮力以及阻力等多种因素对气泡运动特性的影响,通过引入新的边界积分方程,结合分析力学中完整非保守系统的Hamilton原理建立气泡在可压缩流体中的运动微分方程,并对微分方程进行求解。将方程的数值解与MSC.DYTRAN非线性有限元软件的计算结果以及经验公式进行对比,方程数值解与二者都具有较好的一致性。结果表明,基于非保守系统可压缩流体建立的气泡运动方程正确、可行,相关的理论研究和计算具有一定参考价值。     

Momentum and heat transfer of a special case of the unsteady stagnation-point flow

This paper investigates the unsteady stagnation-point flow and heat transfer over a moving plate with mass transfer,which is also an exact solution to the unsteady Navier-Stokes(NS)equations.The boundary layer energy equation is solved with the closed form solutions for prescribed wall temperature and prescribed wall heat flux conditions.The wall temperature and heat flux have power dependence on both time and spatial distance.The solution domain,the velocity distribution,the flow field,and the temperature distribution in the fluids are studied for different controlling parameters.These parameters include the Prandtl number,the mass transfer parameter at the wall,the wall moving parameter,the time power index,and the spatial power index.It is found that two solution branches exist for certain combinations of the controlling parameters for the flow and heat transfer problems.The heat transfer solutions are given by the confluent hypergeometric function of the first kind,which can be simplified into the incomplete gamma functions for special conditions.The wall heat flux and temperature profiles show very complicated variation behaviors.The wall heat flux can have multiple poles under certain given controlling parameters,and the temperature can have significant oscillations with overshoot and negative values in the boundary layers.The relationship between the number of poles in the wall heat flux and the number of zero-crossing points is identified.The difference in the results of the prescribed wall temperature case and the prescribed wall heat flux case is analyzed.Results given in this paper provide a rare closed form analytical solution to the entire unsteady NS equations,which can be used as a benchmark problem for numerical code validation.     

Turbulent forced convective heat transfer in two-phase evaporating droplet flow through a vertical pipe

A physical model was developed to study heat transfer in turbulent dispersed flow at very high vapor quality in a vertical pipe by numerically solving the coupling governing differential equations for both phases. Major heat transfer mechanisms included in the model were the thermal nonequilibrium effects, droplet vaporization, droplet deposition on the duct wall and thermal radiative transfer. The predicted results indicated that vapor superheating is dominant for the cases with high wall superheat, otherwise droplet vaporization dominates the energy transport processes. Heat transfer during the droplet-wall interaction only exists at low wall superheat but in small amounts.     

Heat transfer performance for batch oscillatory flow mixing

Experimental heat transfer data is presented for two batch operations of oscillatory flow mixing. In one case fluid is oscillated within a baffled tube and in the second case baffles are oscillated within a process fluid. For both situations the heat transfer coefficient depends on the intensity of oscillation, and the energy performance of each configuration corresponds to that of an equivalent net turbulent flow in a pipe or a batch stirred vessel. The results indicate that oscillatory flow batch mixing is as energy efficient as other conventional mixing configurations and the heat transfer performance indicates that each oscillatory flow mixing configuration could be satisfactorily used as a batch reactor system.     

An analytical theory of heated duct flows in supersonic combustors

One-dimensional analytical theory is developed for supersonic duct flow with variation of cross section, wall friction, heat addition, and relations between the inlet and outlet flow parameters are obtained. By introducing a selfsimilar parameter, effects of heat releasing, wall friction, and change in cross section area on the flow can be normalized and a self-similar solution of the flow equations can be found. Based on the result of self-similar solution, the sufficient and necessary condition for the occurrence of thermal choking is derived. A relation of the maximum heat addition leading to thermal choking of the duct flow is derived as functions of area ratio, wall friction, and mass addition, which is an extension of the classic Rayleigh flow theory, where the effects of wall friction and mass addition are not considered. The present work is expected to provide fundamentals for developing an integral analytical theory for ramjets and scramjets.     

Transformational-zone method of calculation of complex heat exchange during flow of optically active medium inside tube of diffuse grey surface

The paper presents analytical and experimental investigations of influence of radiative heat transfer on complex heat exchange during flow of optically active gas inside a pipe of diffusegrey properties. It was assumed that the pipe is heated from the outside by a constant heat flux and gas flowing inside is both absorbing and emitting and of small optical density. The influence of length and radiative properties of the pipe surface and of the gas temperature distribution on the wall and in the gas were analysed. The influence of radiative energy transfer on overall heat transfer coefficient was estimated. Mathematical model of radiative convective heat exchange in a system of one-dimensional temperature field, based on zone division method of Hottel and surface transformation, was verified numerically and experimentally. The results of numerical calculations were compared with experimental results obtained during carbone dioxide (CO₂) flow inside electrically heated ceramic tube. The set of nonlinear differential equations was solved by Runge-Kutta method with Hamming modification and with the use of separable-kernel method.     

An analytical treatment for combined heat transfer by radiation,convection and conduction within a heat insulating wall structure

An analytical procedure has been proposed to attack a highly conjugate thermal problem associated with radiation, convection and conduction within a heat insulating wall structure. Firstly, an analytical solution is derived for fully-developed mixed convective flow through parallel plates. Secondly, the resulting expressions for convection are coupled with radiation and conduction equations to form a set of heat balance equations for each heat transfer surface. Illustrative calculations are conducted to estimate heat transfer rates through a heat insulating roof structure with an aluminum partition with high reflectivity, subject to solar radiation in summer. The effect of an aluminum partition on the heat insulation is elucidated.     

Exact solutions for the incompressible viscous fluid of a porous rotating disk flow

The present paper is concerned with a class of exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous fluid flow motion due to a porous disk rotating with a constant angular speed. The three-dimensional equations of motion are treated analytically yielding derivation of exact solutions with suction and injection through the surface included. The well-known thinning/thickening flow field effect of the suction/injection is better understood from the exact velocity equations obtained. Making use of this solution, analytical formulas corresponding to the permeable wall shear stresses are extracted.Interaction of the resolved flow field with the surrounding temperature is further analyzed via the energy equation. As a result, exact formulas are obtained for the temperature field which take different forms depending on whether suction or injection is imposed on the wall. The impacts of several quantities are investigated on the resulting temperature field. In accordance with the Fourier‘s heat law, a constant heat transfer from the porous disk to the fluid takes place. Although the influence of dissipation varies, suction enhances the heat transfer rate as opposed to the injection.     

Convective heat transfer for viscoelastic fluid in a curved pipe

In this paper, fully developed convective heat transfer of viscoelastic flow in a curved pipe under the constant heat flux at the wall is investigated analytically using a perturbation method. Here, the curvature ratio is used as the perturbation parameter and the Oldroyd-B model is applied as the constitutive equation. In the previous studies, the Dirichlet boundary condition for the temperature at the wall has been used to simplify the solution, but here exactly the non-homogenous Neumann boundary condition is considered to solve the problem. Based on this solution, the non-axisymmetric temperature distribution of Dean flow is obtained analytically and the effect of flow parameters on the flow field is investigated in detail. The current analytical results indicate that increasing the Weissenberg number, viscosity ratio, curvature ratio, and Prandtl number lead to the increase of the heat transfer in the Oldroyd-B fluid flow.     

Heat transfer measurements and correlations for air–water flow of different flow patterns in a horizontal pipe

Heat transfer coefficients were measured and new correlations were developed for two-phase, two-component (air and water) heat transfer in a horizontal pipe for different flow patterns. Flow patterns were observed in a transparent circular pipe using an air–water mixture. Visual identification of the flow patterns was supplemented with photographic data, and the results were plotted on the flow regime map proposed by Taitel and Dukler and agreed quite well with each other. A two-phase heat transfer experimental setup was built for this study and a total of 150 two-phase heat transfer data with different flow patterns were obtained under a uniform wall heat flux boundary condition. For these data, the superficial Reynolds number ranged from 640 to 35,500 for the liquid and from 540 to 21,200 for the gas. Our previously developed robust two-phase heat transfer correlation for a vertical pipe with modified constants predicted the horizontal pipe air–water heat transfer experimental data with very good accuracy. Overall the proposed correlations predicted the data with a mean deviation of 1.0% and an rms deviation of 12%.