自适应网格方法在Stokes问题形状最优控制中的应用

为了求解流体力学中的形状最优控制问题,本文提出了一种与最优化准则方法相耦合的自适应网格方法.优化的目标是使得流体流动的能量耗散达到最小,状态方程是Stokes问题.本算法可以在减少计算量的情况下,保证流体的界面达到较高的分辨率.最优化算法采用的是非常稳定的经典最优化准则方法,自适应网格的指示函数是通过材料分布的信息得到的.虽然本文只是考虑了Stokes问题,但所得算法可以用来解决很广泛的一类流体动力学中的形状或拓扑最优化问题.     

方腔内Al2O3-H2O纳米流体热毛细对流的格子Boltzmann模拟

采用格子Boltzmann方法研究纳米颗粒形状影响下方腔内纳米流体热毛细对流的强化传热效果,主要分析了纳米粒子体积分数、颗粒形状以及Marangoni数Ma等相关参数对于纳米流体热毛细对流换热过程的影响。结果表明:长径比（长/半径）对纳米流体换热效果有影响,形状因子越大,平均Nu数Nu_ave越大。随着体积分数的增加,棒状、盘状和正方体状纳米颗粒均使热毛细对流的Nu_ave数减少,球状纳米颗粒条件下热毛细对流的Nu_ave数增加。Ma数越大,纳米流体热毛细对流的自由表面速度越大,对流换热效果也随之增强。      

形状梯度法求解不可压缩流的形状优化问题

流体中物体形状优化设计在实践中有重要的应用。对于区域内由Navier-Stokes方程描述的流体,本文研究以流体状态的泛涵为目标函数的优化问题。基于共轭方法与函数空间参数化方法,本文得到了问题的形状导数。在此基础上构造了一种共轭梯度算法。数值例子表明本文的方法是可行的和稳定的。     

封闭腔内MWCNT纳米流体自然对流传热的数值模拟

采用Fluent软件对封闭腔内纳米流体层流自然对流换热进行了数值模拟研究.重点分析了Ra数和纳米颗粒的体积分数对自然对流换热特性的影响.数值模拟结果表明:在机油中添加多壁碳纳米管(MWCNT)粒子并没有提高基液的自然对流传热特性;对于给定的Ra数下,随着纳米颗粒体积分数的增大,纳米流体的传热特性也随之减弱;对于给定的体积分数,随着Ra数的增大,纳米流体的传热特性显著增强,但纳米流体的传热性能比机油的要弱,且在同一体积分数下随着Ra数的增大,传热性能减弱的程度要减小.     

稳态径向传热模型管程流体温度测量方法

针对管程流体温度测量在没有预留测量窗口情况下存在测量困难的问题,提出一种管程流体温度间接测量方法,该方法基于管道外壁与空气热交换、管壁热传导、管道内壁与管程流体对流传热等公式,推出稳态径向传热模型.已知管道的材料、内外径尺寸等,通过测量管道外壁温度、环境温度、管程流体流速,即可间接测量管程流体温度.试验表明:该方法具有较高测量精度,误差＜0.31℃,具有较好应用前景.     

双重介质Stokes模型的改进变分时间步格式（英文）

在油藏模拟问题的应用中,研究流体相在复杂多孔介质耦合管道系统中的流动规律具有重要意义.最近一种名为双重介质Stokes的模型被研究开发,它用来模拟复杂双重介质管道系统,这种系统可以用在如页岩/致密油/气藏等真实问题中.新模型由双重介质模型和Stokes方程组成,双重介质模型用来控制多孔介质流,Stokes方程用来控制自由流,两者通过四个界面条件耦合在一起.这种耦合模型会生成巨大而复杂的系统,因此通常难于求解.本文我们提出一种改进的变分时间步格式,利用它有效且精确地求解由耦合的双重介质Stokes模型所导致的大型系统.     

桁架动力学形状优化的统一设计变量方法

研究了具有多种约束 ,特别是动力学约束 (频率约束 )作用下的平面桁架形状优化问题。提出一种将两类不同性质的设计变量 (尺寸变量、节点几何坐标变量 )变换为统一形式的无量纲设计变量的方法 ,解决了不同性质变量耦合引起的收敛困难问题 ,并拓展了设计空间。联合运用内点罚函数法、DFP法 (即变尺度法 )和一维搜索技术 (二次插值法 ) ,将约束优化问题转化为无约束序列优化问题 ,得到了满意的优化结果。算例表明本文方法对桁架形状优化的有效性 ,并显示了算法的简洁性和工程设计实用性     

柴油机流固耦合传热仿真研究

为解决发动机活塞组-缸套-冷却水-机体之间传热边界条件难以确定的问题,尤其是冷却水和缸套、机体之间的流固边界的温度和换热系数,将这几个部件作为一个耦合系统进行传热研究.该系统既包括了流体和固体之间的流动与传热的耦合,也包括了固体与固体之间的耦合传热.利用有限元分析软件的流固耦合计算功能,以所建立的某增压柴油机的流固耦合系统为例进行了仿真计算,得到了耦合系统的温度场和流场.这样把单个零件的传热外边界条件变成内边界,使得传热仿真更合理更简单.和实验测量值的对比结果表明:仿真结果与实测数据吻合较好,用流固耦合方法模拟柴油机活塞组-缸套-冷却水-机体之间的稳态传热是可行的.     

基于Fluent的钛合金激光氮化机理及数值模拟

基于非等温产生的表面张力梯度导致熔池区域内的马兰戈尼对流对激光氮化传热和传质过程有重大的影响。本文采用计算流体软件Fluent对钛的激光氮化过程进行探究和重现,结合传热过程中材料温升引起的相变模型及流体体积函数(VOF)模型分析气—液降膜传质机理,通过建立瞬态激光氮化温度场和浓度场的耦合模型,对激光氮化过程的传热,熔池流动和传质机理进行数值模拟。分析结果给出了钛工件的熔池形成、内部流动、氮化层的氮含量及其分布与激光参数之间的关系,为激光氮化工艺参数优化提供了理论依据。     

基于不同截面形状的螺旋弹性管束换热器传热特性分析EI北大核心CSCD

为探究截面形状对螺旋弹性管束(spiral elastic tube bundle,SETB)换热器传热性能的影响,基于四种截面形状(四边形、六边形、椭圆形和圆形),采用双向流固耦合计算方法,对单层四螺旋弹性管束在不同入口速度条件下的振动和传热特性进行了研究。结果表明:不同截面形状的螺旋弹性管束在换热器内不同安装位置的振动响应有明显的不同。截面为椭圆形的螺旋弹性管束在振动和不振动条件下的传热系数最高,管束圆周上的局部传热系数最大,说明管束截面形状为椭圆时的传热性能最佳。振动能够实现强化传热,但振动剧烈的螺旋弹性管束其传热性能并不一定最佳,在进行螺旋弹性管束换热器设计时,并不是要一味追求高强度的振动,还要综合考虑螺旋弹性管束的安装位置和截面形状。     

Primal-dual sensitivity analysis of active sets for mixed boundary-value contact problems

The constrained minimization problem of contact mechanics is investigated as a mixed boundary-value problem determined on the active (contact) set of the solution. Using primal-dual methods of the shape sensitivity analysis, asymptotic expansions of the primal and dual state variables and the cost functional of energy are obtained with respect to a perturbation of the active set in the direction of an arbitrary velocity vector field.     

Arterial cannula shape optimization by means of the rotational firefly algorithm

This article presents global optimization results of arterial cannula shapes by means of the newly modified firefly algorithm. The search for the optimal arterial cannula shape is necessary in order to minimize losses and prepare the flow that leaves the circulatory support system of a ventricle (i.e. blood pump) before it reaches the heart. A modification of the standard firefly algorithm, the so-called rotational firefly algorithm, is introduced. It is shown that the rotational firefly algorithm allows for better exploration of search spaces which results in faster convergence and better solutions in comparison with its standard version. This is particularly pronounced for smaller population sizes. Furthermore, it maintains greater diversity of populations for a longer time. A small population size and a low number of iterations are necessary to keep to a minimum the computational cost of the objective function of the problem, which comes from numerical solution of the nonlinear partial differential equations. Moreover, both versions of the firefly algorithm are compared to the state of the art, namely the differential evolution and covariance matrix adaptation evolution strategies.     

Shape design sensitivity analysis for non-linear anisotropic heat conducting solids and shape optimization by the BEM

Shape design sensitivity analysis (SDSA) expressions have been derived for non-linear anisotropic heat conducting solid bodies by following the material derivative concept and adjoint variable method of optimal shape design given in the literature. The variation of a general integral functional has been described in terms of primary and adjoint quantities evaluated at the varying boundaries. As an example problem in shape optimization, optimal outer boundary profiles of an orthotropic solid body are obtained by the boundary element method (BEM), after reformulating the SDSA equations in a form which is most suitable for the BEM.     

OPTIMAL DESIGN FOR NON-STEADY-STATE METAL FORMING PROCESSES—I. SHAPE OPTIMIZATION METHOD

We suggest a shape optimization method for a non-linear and non-steady-state metal forming problem. It consists in optimizing the initial shape of the part as well as the shape of the preform tool during a two-step forging operation, for which the shape of the second operation is known. Shapes are described using spline functions and optimal parameter values of the splines are searched in order to produce, at the end of the forging sequence, a part with a prescribed geometric accuracy, optimal metallurgical properties and for a minimal production cost. The finite element method, including numerous remeshing operations, is used for the simulation of the process. We suggest using a least-squares-type algorithm for the unconstrained optimization method (based on external penalty) for which we describe the calculation of the derivatives of the objective function. We show that it can reduce to calculations which are equivalent to the derivative calculations of steady-state processes and to evolution equations. Therefore, the computational cost of such an optimization is quite reasonable, even for complex forging processes. Lastly, in order to reduce the errors due to the numerous remeshings during the simulation, we introduce error estimation and adaptive remeshing methods with respect to the calculation of derivatives.     

Shape optimal design of elastic planar frames with non-linear response

This paper describes an approach to shape optimal design of elastic planar frames with non-linear response. The foundation of the proposed approach forms an appropriate strategy of shape representation of the structure, based on the design element technique. A frame structure is treated as to be assembled from several frame design elements, which in turn may consist of several appropriately joined beam finite elements. The shape of each frame design element is defined by convenient functions involving Bezier blending polynomials. The original formulation of the beam finite element, proposed by Saje, is modified in order to fit nicely into the context of the frame design element technique. The formulation of the shape optimal design problem in a form of a problem of non-linear mathematical programming and its solution by employing gradient-based methods of mathematical programming are discussed briefly. The theory is illustrated with two numerical examples.     

Die shape optimal design in three-dimensional shape metal extrusion by the finite element method

A new approach to die shape optimal design in shape extrusion is presented. In this approach, the design problem is formulated as an optimization problem incorporating the three-dimensional finite element analysis model, and optimization of the die shape is conducted on the basis of the design sensitivities. The approach is applied to the determination of the die shapes for extrusion of parts with various cross sections including polygons and T sections. © 1998 John Wiley & Sons, Ltd.     

Shape optimization using time evolution equations

In this study, we deal with a numerical solution based on time evolution equations to solve the optimization problem for finding the shape that minimizes the objective function under given constraints. The design variables of the shape optimization problem are defined on a given original domain on which the boundary value problems of partial differential equations are defined. The variations of the domain are obtained by the time integration of the solution to derive the time evolution equations defined in the original domain. The shape gradient with respect to the domain variations are given as the Neumann boundary condition defined on the original domain boundary. When the constraints are satisfied, the decreasing property of the objective function is guaranteed by the proposed method. Furthermore, the proposed method is used to minimize the heat resistance under a total volume constraint and to solve the minimization problem of mean compliance under a total volume constraint.     

Sensitivity Analysis Methods to Design Optimal Ship Hulls

Automatic procedures for the design of ship hull geometries yielding minimal wave resistance and wave breaking are an attractive opportunity from both the economical and practical standpoints. Estimating the cost function gradient according to the Sensitivity Equation and Adjoint Methods (SEM, AM) instead of using the standard finite difference approximations has the potential of reducing the computational cost of the overall optimization procedure. Aim of this paper is to assess the actual extent of the cost reduction. Speed-up factors of up to 3.3 have been obtained in the evaluation of the cost function gradient and of about 1.6 in the overall optimization procedure applied to an optimal shape design problem of an existing tanker ship. The SEM and AM methods perform better than finite differences mainly because of (i) the smaller number of flow solutions needed to compute the cost function gradient and (ii) the opportunity of using the same LU factored matrix for both the flow solver and the SEM or AM equations, a circumstance arising as a consequence of having chosen a linearized potential flow model of the 3D free-surface problem.