叶轮机械三元流动函数的变域变分有限元解

根据流函数的变分原理，应用有限元方法对叶轮机械内部流场进行了求解，并应用变域变分的方法对叶栅下游周期性自由尾涡面进行了计算。理论计算与实验结果进行比较，结构表明理论计算和实验结果是相互吻合的。     

叶轮机械三元流动流函数的变域变分有限元解

根据流函数的变分原理 ,应用有限元方法对叶轮机械内部流场进行了求解 ,并应用变域变分的方法对叶栅下游周期性自由尾涡面进行了计算。理论计算与实验结果进行比较 ,结果表明理论计算和实验结果是相互吻合的。图 4参 3     

轴流式压气机级变几何叶栅的设计研究

先进的轴流式压气机在非设计状态下工作时,常利用某种变几何气流调节来适应速度图的需要。变几何调节可应用进口导叶、转子叶栅及单列和串列静子叶栅。通过典型的叶片基元性能曲线研究,说明现代设计中越来越愿采用变几何叶栅的理由;利用己发表的结果和简单分析指出绕固定轴旋转叶片作调节时出现的一些缺点。最后对应用气动与几何联合调节改变压气机特性提出建议。     

透平机械叶栅流场的有限元分析

本文采用文献[2]的变分原理,用有限元法求解透平机械叶栅的流场。求解域内的计算网格由计算机自动生成,采用八节点四边形等参数元素和半带宽的存贮方式,用直接法求解线性代数方程组。所求解的平面叶栅不可压缩流场的算例表明:当求解域的网格数目适合时.有限元法与Жуковский的积分方程法所得到的型面速度分布几乎重合在一起。     

船用燃气轮机变几何动力涡轮大攻角流动特性的三维数值模拟

采用三维数值模拟技术，研究了可调导叶转动导致变几何动力涡轮气动性能变化的流场机理。结果表明，在较小的转角范围内，采用大转折角设计的可调导叶使涡轮处于大攻角运行。在大正攻角或大负攻角下可调导叶级动叶栅流道内的三维分离流场结构及其产生机理有很大差异，而且大正攻角造成的吸力面分离流动更使整个涡轮的效率显著地下降。通过系统的机理分析，提出可调导叶宜采用较小转折角的后部加载叶型，而变几何动力涡轮可调导叶级动叶栅要采用较大负冲角的气动设计原则。     

变弯度叶栅的试验研究

对有缝隙的和无缝隙的变尾缘叶栅与变弯度叶栅进行了系统试验研究,取得了这种叶栅的气流转折角和损失以及落后角的变化规律。证实压气机变弯度叶栅可在较小的能量损失下实现较大的气流转折角,其工作特性比可转导叶明显优越。推荐的叶栅构型及其几何参数值可供设计直接使用,它是改善压气机调节性能,防止喘振,扩大稳定工作范围的行之有效的方法。     

单级轴流式变几何涡轮的计算模型及结果分析

为了研究涡轮静叶变几何后对整个涡轮级性能的影响，通过建立数学模型，对单级轴流式涡轮进行了一系列的热力计算，得到了在不同压比、不同转速下，涡轮静叶转角对涡轮流量、反力度，叶栅速度损失系数和轮周效率的影响。从计算结果中可看出，静叶的传动使得涡轮机的主要参数反力度发生变化，从而影响到整个级的运行；而对于损失系数来说，静叶的转动对静叶损失系数并无太大影响，在大部分转角范围内，使得动叶损失系数升高，减小了动叶损失。     

确定活塞环自由态外形的变分有限元法

把活塞环自由态形状的确定作为弹性力学反命题来求解。首先采用人工逆过程概念,把它转化为一个对偶的弹性力学正命题,即可建立它的变分原理,然后以变分原理为基础,按常规有限元法求数值解。这种方法精度较高,且计算程序通用化,实用方便,可以成为活塞环工程设计的基本计算工具之一。     

变几何平面叶栅数值模拟

使用CFD软件NUMECA对变几何平面叶栅三维流场进行了数值模拟。分析在不同叶片安装角下,叶片表面静压系数、出口总压损失系数和出口气流角的变化规律。结果表明：在叶栅转角范围内,随着安装角的增大,沿叶型表面气流的扩压段显著增加,叶栅出口气流角也会随之增大,而叶栅总损失不断减小,其中,叶型损失先减小后增大,叶顶间隙泄漏损失和端部二次流损失都是减小的。     

汽轮机变工况热力核算的逆顺序混合计算法

本文在分析汽轮机变工况热力核算的逆序法和顺序法的基础上,提出了逆顺序混合计算法。该法既便于计算汽轮机的超临界工况,又具有迭代嵚套层次少而易于收敛的优点。同时本文导出了由超音速叶栅的出口汽流参数,计算叶栅进口汽流参数的直接算式,而不必进行迭代计算.按本文所提出的逆顺序混合法所编制的程序,结构简单、计算速度快及精确度较高.     

On a direct variational method for nonlinear heat transfer

In this paper it is shown, that the partial nonlinear differential equation can be reduced to the variational problem. By means of the variational technique based on the Kantorovich method, a nonlinear boundary value problem can be reduced to the set of the ordinary differential equations. The accuracy of the method is estimated by comparing the solutions of problems solved using the variational method and the other method. In this paper the method for the construction of the trial functions is also presented. Three examples are included to illustrate the above method.     

SOME HAMILTONIAN-TYPE VARIATIONAL PRINCIPLES FOR MOTIONS OF A HYGROTHERMOELASTIC MEDIUM

In a mathematical modeling of the physical behavior of a hygrothermoelastic medium, a moisture field vector and a thermal field vector are introduced, Hamilton's principle is stated, and a three-field variational principle is derived. The differential variational principle is shown, as Euler - Lagrange equations, to generate the divergence equations and the associated natural boundary conditions of a hygrothermoelastic medium. This variational principle is augmented through an involutory transformation in order to incorporate the gradient equations and the constitutive relations of an anisotropic hygrothermoelastic medium; hence, a ten-field variational principle is formulated and some of its special versions recorded.     

基于变分不等式法的渗流有限元分析及程序设计

针对变分不等式法的渗流分析特点特别适用于边界强非线性渗流问题的数值模拟,采用统一建模语言(UML)分析了面向对象渗流有限元各类的关系,利用面向对象程序设计的封装、继承、多态三大机制,在UML类图的指导下对基于变分不等式法的渗流有限元分析进行了程序设计与开发.并通过两个算例验证了该程序的有效性和正确性.     

Application of a variational method to flow over a flat plate in the entrance region with variable physical properties

A variational method has been used to solve the flow over a flat plate in the entrance region at constant wall temperature. The physical properties, i.e. Thermal conductivity and viscosity, were assumed to be linear functions of temperature in the study. Two coupled equations were derived from the variational formulation and then solved by the analog/hybrid computer. Consequently, momentum boundary layer thickness,thermal boundary layer thickness local Nusselt number and local friction factor were found for the flow. For the constant properties case a comparison was made between the exact solution, and results obtained using the solution approach suggested in this paper.     

Approximate analyses of Fourier and non-Fourier heat conduction models by the variational principles based on Laplace transforms

Approximate analysis is a major application of variational principles for heat conduction. Recently, O’Toole’s variational principle for Fourier’s law has been extended to non-Fourier heat conduction models, which are applied to approximate analyses based on the Rayleigh–Ritz method. Suitable trial functions satisfying boundary conditions are sought, and then substituted into the variational principles to obtain the undetermined coefficients. From the inverse Laplace transforms, the approximate solutions are obtained. Examples are provided for 1D problems for different heat conduction models. The largest calculation errors are one or two orders of magnitude smaller than the equilibrium temperature, which will tend to be zero.     

COUPLED CONSISTENT THIRD-ORDER THEORY FOR HYBRID PIEZOELECTRIC BEAMS UNDER THERMAL LOAD

A new coupled consistent third-order theory is presented for thermal load on hybrid piezoelectric beams that satisfies exactly the shear traction-free conditions at the top and bottom of the beam for any electrical boundary conditions. The potential and thermal fields are discretized layer-wise as piecewise linear. The axial and transverse electric fields are considered. The deflection is approximated as uniform across the thickness and longitudinal displacement is approximated as a third-order variation. The equilibrium equations and the boundary conditions are derived from a variational principle. Analytical solutions are obtained for simply supported beams. The theory is assessed by comparison with the exact piezothermoelasticity solution and coupled first-order shear deformation theory solution for two thermal loads.     

Buckling under external pressure of cylinders with either torispherical or hemispherical end closures

In a number of applications, the actual boundary conditions at the ends of a cylinder are not taken into account properly when the structure is being designed against buckling. For example, in the design of submersibles the older theoretical treatments assume that bulkheads are present at the ends of the cylinders, whereas this form of construction is not always used.The purpose of the investigation described here is to study the effect of realistic boundary conditions on the elastic buckling pressure of unstiffened cylinders with torispherical or hemispherical end closures. In the present study only perfect, initially stress-free, structures are considered and their theoretical buckling pressures are obtained from a variational finite-difference program written for the digital computer.The numerical results presented were obtained from a limited parametric survey of the problem. In the main, linear buckling theory was used. However, as is shown, this can sometimes lead to unsafe predictions.The buckling pressures for the cylinders with hemispherical end closures, as predicted by the variational finite-difference technique, are also compared with a modified von Mises formula with corrections for the end closures. The agreement between the two sets of predictions was good within the range of the survey.     

Some theorems in Luikov''s theory of heat and mass transfer in capillary-porous bodies

The linear theory of heat and mass transfer is considered. Some general theorems are formulated, i.e. a reciprocity theorem and a variational theorem (no use is made of the Laplace transform). The functional derived herein gives all the governing equations, including the boundary and initial conditions, as Euler equations.     

NUMERICAL RESOLUTION OF A PHASE CHANGE PROBLEM WITH ZERO LATENT HEAT

Two numerical methods to simulate Ike behavior of a class offree-boundary thermal systems are presented and compared. The state of the system is governed by the conduction equation, where an isotherm defines the moving boundary for which a Neumann condition is considered. Unlike the classical Stefan problem, the moving boundary velocity does not appear explicitly in the heal balance

One method is based on the Friedman transformation and leads to a variational inequality defined on a fixed domain. Computation of the front velocity is not required

The other method uses the Landau transformation, leading to a new state equation of the convection-conduction type on a fixed domain. The convective part in the equation is due to the moving boundary. Estimation of the front velocity is obtained from the field temperature in the neighborhood of the boundary

The comparison between the two methods is performed on two examples—a freezing and a melting case—the exact solutions of which are known.     

Size dependent thermal buckling and postbuckling of functionally graded circular microplates based on modified couple stress theory

In this article, size-dependent thermal buckling and postbuckling behavior of a functionally graded circular microplate under uniform temperature rise field and clamped boundary conditions is investigated. Material properties are assumed to gradually vary through the thickness according to a simple power law. Equilibrium equations and associated boundary conditions are derived using variational method and based on modified couple stress theory, classical plate theory and von Kármán geometric nonlinearity. The differential quadrature method is used to discretize the governing equations. This technique is accompanied by an iterative method to determine the thermal postbuckling behavior of microplate. Finally, effects of length scale parameter, power law index and ratio of thickness to radius on the thermal buckling and postbuckling behavior of FG circular microplate are investigated.