“叶轮机械三元流动变分原理及有限元计算”项目获机械工业部重奖

机械土业部最近对1678年以来获得部科技成果一等奖及相当于该水平的四十个科研项目进行评选,选出十四项予以重奖。我院刘高联副研究员领导的“叶轮机械三无流动变分原理及有限元计算”项目入选并受到重奖。该项目完整地建立了叶轮机械气动力学各类命题的内容,建立了S_1流面、S_2流面的正命题、反革题、杂交命题的变分原理族、广义变分原理族、     

混流式水力机械S_2流面杂交命题的变分原理

本文从理论上研究水力机械转轮轴面流道的设计方法。首先用坐标旋转法和映象平面法分别解决混流式S_2流面杂交命题主方程的奇异性和求解域边界未定问题。然后对混流式S_2流面半反命题的变分原理进行反演变换得到混流式S_2流面不可压缩流动A,D和E类杂交命题的变分原理和广义变分原理。将原来求偏微分方程组的边值问题转化为求一等价泛函的驻值问题,从而可以应用各种变分直接解法如有限元法进行水力机械转轮轴面流道的设计、改型和三维流场分析。     

轴流式叶轮机S_2流面气动半反命题的变分原理与广义变分原理

本文建立了轴流式叶轮机S_2流面气动半反命题的一族变分原理与广义变分原理,并对复连通区的情况(例如包曼式透平级和涡轮风扇发动机中),提出了相应的处理办法。为了简化边界的处理,文中充分发挥了自然边界条件和人工分界面的有力作用,把全部边界条件(包括转轮区同静轮区的交接面条件)都化成了自然边界条件。本文结果为采用有限元法、变分一差分解法以及各种变分直接解法提供了一个较完密的理论基础。     

径流式S_1流面叶栅半反命题的变分原理

本文将径向动量方程作为主方程,用反推法建立了径流式S_1流面叶栅内不可压缩流动半反命题的变分原理与广义变分原理,将原偏微分方程组的边值问题转化为一等价泛函的驻值问题,从而可以用各种变分直接解法进行普遍的S_1流面叶栅的流场分析。     

流体机械中的三元流动理论——不可压缩流体的流线曲率法

随着高速电子计算机的出现,叶轮机械三元流动理论在可压缩流体的叶轮机械中得到广泛应用。其效果之显著,促使人们力图推广其应用范围,水力机械行业也不例外。 本文应用两类相对流面理论的基本思想和方法,推导出适合于水力机械设计的三元流动基本方程和计算方法。文中首先依据质量守恒原理及牛顿第二定律,推导出适合水力机械的三元流动理论的基本方程组;其次把基本方程组化为沿S_1和S_2相对流面上流体流动所必须遵循的方程组;最后给出S_1和S_2相对流面上相应的流线曲率法的基本公式和计算方法。     

流体机械中的三元流动理论——不可压缩流体的流线曲率法

四、流线曲率法解S_2流面问题 两类相对流面理论,把空间的三元问题简化为两个二元问题求解,使问题得到简化,但付出的代价是两个相对流面交替使用,相互迭代。而流线曲率法则把一个二元问题化为一个一元问题求解,使问题进一步简化,付出的代价是流线的迭代。 为简化计算,作如下限制:液体是无粘性的,叶轮内液体的相对运动是定常的,液体的相对运动是轴对称的。 1、沿计算站走向速度梯度方程的推导 推导速度梯度方程时所采用的符号:     

混流式水力机械S_2流面半反命题的变分原理

为了对混流(包括轴流和径流)式水力机械转轮内的三元流动进行分析,本文用分区组合法和坐标旋转法分别建立了混流式S_2流面不可压缩流动半反命题的组合式变分原理和统一的变分原理。     

离心式压气机任意旋成面正命题变分有限元解

在文献[2]的基础上提出了离心式压气机任意旋成面正命题S_1流面的有限元解法。用八结点等参元对文献[1]中相应的变分原理Ⅱ进行有限元展开,采用了迭代法求解非线性方程,得出S_1流面流场中各点的速度势、速度、密度和压力值。本文结合具体叶轮造型,编制了考虑叶面有喷吸情况,能自动划分网格的有限元试算程序,进行了无分流叶片和有分流叶片的试算。本文还对满足后缘处K—J条件的处理方法作了尝试。     

用准正交面法分析叶轮机械三元流场的研究获国家科学技术进步奖

叶轮机械使用广泛,耗能很多,用数值分析方法研究叶轮通道中的流动状况,对改善叶轮的性能及提高效率极有意义. 我校应用力学系这一项目的研究人员,在两类流面理论的基础上提出的准正交面法是叶轮机械三元流动的一种三元数值解法,采用在每个准正交面上沿S_1,S_2流面交线两个方向上求解速度梯度方程,通过整个准正交面上的流量校核、反插等分流量点,在一次     

带长短叶片离心叶轮的三元流场

一、带长短叶片叶轮流场的解题思路有关流场计算公式作者在[1]已有详述,本文从略。1.解题关键(1)短叶片分流面S_2~*的确定要找到这个特殊的分流流面S_2~*(图1),它在短叶片前P点处自动一分为二,分解成     

Variational criterion for dissipative structures dominated by coupled mechanisms

By analyzing the similarity between the viscosity-inertia compromise for single fluid in turbulent pipe flow and the particle-fluid compromise in gas-solid fluidization, it is deduced that the variational criterion for dissipative structures dominated jointly by two sub-mechanisms (for instance, viscous effect and inertial effect in turbulent flow; particle movement and fluid movement in fluidization) could be physically expressed as mutually constrained extremum between the individual extremum tendencies of the sub-mechanisms, and could thus be mathematically formulated as a two-objective optimization problem.     

连续介质力学中的本构场能密度、余能密度和广义变分原理

该文对于弹性力学的和粘性流体力学的本构方程、粘性正压流体的物态方程等进行了统一的讨论,提出了本构场能密度和合能密度的概念,建立了统一的本构泛函变分原理和有关的广义变分原理。     

Evidence of power-law flow in the Mojave desert mantle

Studies of the Earth's response to large earthquakes can be viewed as large rock deformation experiments in which sudden stress changes induce viscous flow in the lower crust and upper mantle that lead to observable postseismic surface deformation. Laboratory experiments suggest that viscous flow of deforming hot lithospheric rocks is characterized by a power law in which strain rate is proportional to stress raised to a power, n (refs 2, 3). Most geodynamic models of flow in the lower crust and upper mantle, however, resort to newtonian (linear) stress-strain rate relations. Here we show that a power-law model of viscous flow in the mantle with n = 3.5 successfully explains the spatial and temporal evolution of transient surface deformation following the 1992 Landers and 1999 Hector Mine earthquakes in southern California. A power-law rheology implies that viscosity varies spatially with stress causing localization of strain, and varies temporally as stress evolves, rendering newtonian models untenable. Our findings are consistent with laboratory-derived flow law parameters for hot and wet olivine--the most abundant mineral in the upper mantle--and support the contention that, at least beneath the Mojave desert, the upper mantle is weaker than the lower crust.     

二维定常粘性气体不可压缩扩散流场半解析解

运用加法分离变量法，解析求解了二维定常粘性气体不可压缩扩散流场，得到了几组空气流场有源汇和无源汇情况下扩散流场的半解析解，并分析了其适用条件．所得结果具有重要理论意义，可以为数值计算提供标准解．拓展了加法分离变量法的适用领域，并对二维定常粘性气体不可压缩扩散流场这类复杂问题的解析求解进行了有益的尝试．     

Violation of the incompressibility of liquid by simple shear flow

In standard fluid dynamics, the density change associated with flow is often assumed to be negligible, implying that the fluid is incompressible. For example, this has been established for simple shear flows, where no pressure change is associated with flow: there is no volume deformation due to viscous stress and inertial effects can be neglected. Accordingly, any flow-induced instabilities (such as cavitation) are unexpected for simple shear flows. Here we demonstrate that the incompressibility condition can be violated even for simple shear flows, by taking into account the coupling between the flow and density fluctuations, which arises owing to the density dependence of the viscosity. We show that a liquid can become mechanically unstable above a critical shear rate that is given by the inverse of the derivative of viscosity with respect to pressure. Our model predicts that, for very viscous liquids, this shear-induced instability should occur at moderate shear rates that are experimentally accessible. Our results explain the unusual shear-induced instability observed in viscous lubricants, and may illuminate other poorly understood phenomena associated with mechanical instability of liquids at low Reynolds number; for example, shear-induced cavitation and bubble growth, and shear-banding of very viscous liquids such as metallic glasses and the Earth's mantle.     

一种对船桨干扰问题的黏势流耦合求解方法

基于黏性流计算流体力学(CFD)及势流理论,建立了一种黏流雷诺平均方程/面元法耦合迭代求解方法,对船桨相互作用问题进行了数值模拟.自由面的船体绕流场模拟应用CFD黏流方法,螺旋桨水动力载荷计算采用势流面元法.在黏性流场模拟中得到桨盘面处的总速度分布,减去螺旋桨诱导速度得到实效伴流速度并作为势流计算速度进口条件,螺旋桨效应以体积力的形式在黏性流场中体现.计算值与试验值的对比结果表明,黏势流耦合迭代求解方法能较好地预报船桨干扰问题,且较全域船桨离散化网格CFD求解船桨干扰的方法,计算量大为减少.该方法充分融合了黏势流方法的优点,既能计及黏性效应又能发挥势流快速准确的优势,能够拓展应用于船体及螺旋桨性能预报及设计优化的研究.     

Effects of MgO and TiO<Subscript>2</Subscript> on the viscous behaviors and phase compositions of titanium-bearing slag

The effects of MgO and TiO₂ on the viscosity, activation energy for viscous flow, and break-point temperature of titanium-bearing slag were studied. The correlation between viscosity and slag structure was analyzed by Fourier transform infrared (FTIR) spectroscopy. Subsequently, main phases in the slag and their content changes were investigated by X-ray diffraction and Factsage 6.4 software package. The results show that the viscosity decreases when the MgO content increases from 10.00wt% to 14.00wt%. Moreover, the break-point temperature increases, and the activation energy for viscous flow initially increases and subsequently decreases. In addition, with increasing TiO₂ content from 5.00wt% to 9.00wt%, the viscosity decreases, and the break-point temperature and activation energy for viscous flow initially decrease and subsequently increase. FTIR analyses reveal that the polymerization degree of complex viscous units in titanium-bearing slag decreases with increasing MgO and TiO₂ contents. The mechanism of viscosity variation was elucidated. The basic phase in experimental slags is melilite. Besides, as the MgO content increases, the amount of magnesia–alumina spinel in the slag increases. Similarly, the sum of pyroxene and perovskite phases in the slag increases with increasing TiO₂ content.     

气泡粘性对上升运动特性影响的FTM模拟

为了研究气泡粘性对其上升过程的速度、形态以及阻力系数的影响,基于FTM(Front- Tracking Method)模拟了气泡在粘性流体中的运动,通过改变气泡粘性来改变气液粘度比,研究了气泡内的速度分布以及气泡周围粘性剪切应力的分布和变化特点。研究表明：气液粘度比较小时,流场中的粘性耗散很强,气泡的粘度主要影响其平衡速度和形态,气液粘度比较大时,粘性耗散减弱,其平衡速度和形态基本无变化,气泡粘性主要影响气泡内的速度分布;气泡上升过程中的阻力系数随粘度比增大而减小,粘性剪切应力则呈现相反的变化趋势。气泡上升过程中,周围的粘性剪切应力关于中心轴线对称分布,出现最大粘性切应力的区域由气泡两侧逐渐向气泡底部边缘过渡;气泡尾部边缘的形变引起气泡尾部的表面张力不平衡,使得气泡的形态发生改变。