RTM充模分析控制体积法的求解方法

RTM充模分析在控制体积法对于某些单元会产生不对称的矩阵，为了充分利用现有的对称矩阵高效求解方法，本文提出了一种处理方法。由千方程矩阵的不对称性足比较弱且充模过程是一个渐变的过程，因此把不对称部分移到方程右边，在求解过程中只有在充满节点发生变化时更新方程的右边。采用预处理共轭梯度求解法计箅了两个实例，结果表明这样计算效果非常有效，尤其适于求解三维网格模型的充模分析。     

瞬态热传导方程的SPH法

光滑粒子流体动力学(Smooth Particle Hydrodynamics,SPH)作为一种无网格方法具有无网格、自适应性和拉格朗日性质。本文将SPH方法应用到瞬态热传导问题的求解,通过将二阶导瞬态热传导方程分解成两个一阶导的偏微分方程,同时对时间域进行离散,建立了基于SPH方法的瞬态热传导离散方程。通过镜像粒子法处理边界条件,提高了计算精度。对一维和二维瞬态热传导问题进行数值分析,采用lucy核函数和三次样条核函数进行求解,通过与精确解对比,验证了该方法的可行性和实用性。     

热辐射成像法测量大型炉膛内三维温度场的算法新进展

大型炉膛内三维燃烧场与炉内燃烧过程的安全性、经济性和污染物排放水平密切相关。相对于其他大型炉膛内三维温度场可视化监测技术(声学层析成像法和吸收光谱层析成像法),热辐射成像法具有系统紧凑、易于实施等特点,且时间分辨率和空间分辨率较高,具有较大的应用潜力。介绍了大型炉膛内热辐射成像原理;分析了辐射传递反问题的不适定性;综述了辐射传递反问题求解方法研究进展。构建大型炉膛内热辐射成像模型即利用热辐射成像矩阵,将炉膛边界传感器接收的辐射能量分布与炉内温度场、介质和壁面辐射特性联系起来;计算热辐射成像矩阵的关键在于获得介质和壁面单元散射或反射份额的分布,目前通常使用DRESOR法、逆向蒙特卡洛法等进行求解。通过热辐射成像矩阵的条件数判定可知,热辐射传递反问题是不适定性的,导致解的不唯一性甚至不存在性,以及微小测量误差会引起温度场重建的不稳定。目前求解该类不适定问题,主要有优化方法和正则化方法2类。优化方法可分为传统优化方法和智能优化方法。传统优化方法基于梯度计算,通过反复迭代计算减小目标函数,常见有最小二乘法、共轭梯度法等;但该类方法对初值依赖大,需要对目标函数求导数且无法获得全局最优解。智能优化...     

强电场下压电功能梯度板非线性动力分析的样条有限点法

针对强电场作用下基于线性压电本构方程求解压电功能梯度板固有频率存在误差的问题,本文考虑非线性压电效应,采用样条有限点法建立压电非线性动力分析模型,讨论强电场作用下压电非线性效应对固有频率的影响。研究表明,强电场作用下压电线性解与非线性解偏差较大,非线性效应不容忽视;由于功能梯度板的材料特性,相同电场强度下不同的施加方式,会得到不同的固有频率控制效果;基于样条有限点法建立的分析模型精确可靠,具有输入简单、处理边界条件简便等优点。     

热传导问题的SPH方法及其边界处理

本文将光滑粒子流体动力学（Smooth Particle Hydrodynamics,SPH）方法应用于热传导问题中,通过二阶导的SPH方法求解热传导离散方程。分别采用了镜像粒子法和固定边界粒子法处理SPH方法的边界条件,提高了计算精度;并对不同核函数和不规则边界的热传导问题进行数值模拟,结果表明,二阶导的SPH方法适用于求解热传导问题,并能达到较高的精度和稳定性。     

求解相变传热问题的等效热容法

采用等效热容法求解伴有相变过程的瞬态热传导问题.在整个区域建立统一的能量方程,将分区域求解问题化为整个区域的非线性问题处理.给出了解决相变温度为单一温度或者相变温度区间很小时产生的数值奇异问题的方法.用热焓判据判断单元是否发生相变,并考虑了固液两相材料物性参数的变化,相变界面位置按线性插值计算.算例表明,等效热容法求解相变传热问题,程序简单,计算效率高,相变界面位置计算准确.     

多相多组元化学平衡相平衡计算(Ⅱ)——新算法GCG法

应用非线性规划的共轭梯度投影法,并结合化学平衡相平衡问题的特殊性,本文设计了一个新的多相多组元化学平衡相平衡通用计算方——GCG法.检验表明,它在大多数情况下(特别是对非理想体系)优于现存的RVCS、SVMP和M-SVMP三种通用算法.     

注塑流动与传热分析的自适应隐式控制体积法

在注塑流动与传热分析中采用自适应隐式控制体积法,利用自动控制的参数识别方法来自动调节时间步长,在每个时间步长流动将向前推进大约半个单元大小的距离,厚度方向的温度采用契比雪夫配点法进行计算,压力方程的求解方法是预条件共轭梯度法。计算结果表明,自适应隐式控制体积法的时间复杂度是结点数目的平方,而且1h之内可以求解10000结点规模的问题。     

非灰系统当量灰吸收系数的反演

提出了一种由气体温度场反向分析计算气体当量灰吸收系数的方法.采用段法（区域法）求解正问题,反演中采用求目标函数极小值的共轭梯度法.以直通式实验炉的测量数据为求解条件,用该计算得到了炉内气体介质当量灰吸收系数的分布.数值模拟结果表明,段法与共轭梯度法结合可以较好地反演非灰系统的当量灰吸收系数.与指数宽带段法模型结果的比较表明,反演得到的当量灰吸收系数具有与指数宽带模型相当的精度,但计算量小于宽带模型的1/10.     

注射充模过程的压力求解方法及其比较

提出了一个LU局部分解方法来求解注射充模过程的压力方程,并与其他迭代方法进行了比较。LU局部分解法是当矩阵在逐渐变大时,保留已经分解的部分,只对新增加的部分进行分解,因此相当于只对最后的稀疏矩阵进行了分解。计算表明,LU局部分解法比预条件共轭梯度法快大约1个量级,而预条件共轭梯度方法又比超松弛迭代法快大约1个量级。     

COMPARISON OF VARIOUS CONJUGATE GRADIENT METHODS FOR INVERSE HEAT TRANSFER PROBLEMS

Many inverse heat transfer problems can be solved efficiently through the minimization of a performance function utilizing the conjugate gradient method. The gradient of the performance function needed in the minimization procedure of the conjugate gradient method is obtained by employing either the adjoint variable method or the direct differentiation method. In the present study we consider an inverse problem of estimating time-varying strength of a heat source in a two-dimensional heat conduction system, and compare the adjoint variable method and the direct differentiation method in terms of accuracy and computational efficiency, and finally suggest a new method that exploits the advantageous aspects of both methods while avoiding the shortcomings of them.     

Inverse determination of boundary heat fluxes in a porous enclosure dynamically coupled with thermal transport

The inverse natural convection problem of estimating the heat source profiles in a porous enclosure is proposed in the present work. The physical model for the momentum conservation equation makes use of the Darcy-Brinkman equation, which allows the no-slip boundary condition on a solid wall to be satisfied. An iterative Fletcher-Reeves conjugate gradient method is applied such that the gradient of the cost function is introduced when the appropriate sensitivity and adjoint problems are defined. Particularly, the pressure-based SIMPLE algorithm is adopted to solve the continuum direct, sensitivity and adjoint problems in unification. Effects of thermal Rayleigh number, Darcy number, heat flux profiles, sensor locations and quantity on the accuracy of inverse solutions are investigated with or without the measurement errors. Additionally, the fluid and heat transport structures in the uniform porous layer are analyzed using the streamlines and heatlines, and the heat transfer potential is also explained by the variation of overall Nusselt number. Noise data solutions are regularized by stopping the iterations with the discrepancy principle of Alifanov, before the high frequency components of the random noises are reproduced. The present method solves inverse strong convection problem satisfactorily without any a priori information about the unknown heat flux to be estimated.     

基于热传导逆问题方法预测材料热物性参数

建立了一种应用Levenberg-Marquardt迭代过程求解非线性热传导逆问题用于预测材料热物性的方法.以平板内的一维非稳态热传导为研究对象,在准确的数值计算结果上施加非均匀随机误差来模拟瞬态温度实验数据,应用该方法分别对热传导系数为常数、热传导系数和容积比热容为常数以及热传导系数和容积比热容为温度的函数3种情况进行了预测.参数预测结果表明,方法对基于瞬态实验方法进行热物性预测具有良好的适应性,并适用于分析多类热传导逆问题,该方法还能为优化实验提供有效信息.     

基于红外测温的对流换热系数反识别算法研究

The heat transfer coefficient in a multidimensional heat conduction problem is obtained from the solution of the inverse heat conduction problem based on the thermographic temperature measurement. The modified one-dimensional correction method （MODCM）, along with the finite volume method, is employed for both two- and three-dimensional inverse problems. A series of numerical experiments are conducted in order to verify the effectiveness of the method. In addition, the effect of the temperature measurement error, the ending criterion of the iteration, etc. on the result of the inverse problem is investigated. It is proved that the method is a simple, stable and accurate one that can solve successfully the inverse heat conduction problem.     

An inverse radiation problem of estimating heat-transfer coefficient in participating media

In the radiant cooler, where the hot gas from the pulverized coal gasifier or combustor is cooled to generate steam, the wall heat-transfer coefficient varies due to ash deposition. In the present work, we investigate an inverse radiation problem of estimating the heat-transfer coefficient from temperature measurement in the radiant cooler. The inverse radiation problem is solved through the minimization of a performance function, which is expressed by the sum of square residuals between calculated and observed temperature, utilizing the conjugate gradient method. The gradient of the performance function is evaluated by means of the improved adjoint variable method, which resolves the difficulty associated with the singularity of the adjoint equation through its inherent regularization property. The effects of the number of measurement points and measurement noise on the accuracy of estimation are also investigated.     

基于有限元离散的不规则管道几何边界红外瞬态检测识别

建立了带有不规则腐蚀内边界的管道二维瞬态传热模型,基于有限元法和共轭梯度法的导热反问题求解方法对管道内边界识别问题进行了研究,比较分析了管道外表面稳瞬态温度对内边界变化敏感程度的差异性,指出内边界瞬态检测识别比稳态检测识别更具优越性并利用数值试验进行了验证。同时,考察了测温误差、初始假设等因素对管道内边界瞬态检测识别结果的影响。在较大测温误差的情况下,采用瞬态检测条件从不同初始假设值出发都能准确地反演识别出管道内边界腐蚀后的几何形状,从而证明了算法的有效性和稳定性,表明了红外瞬态检测定量识别管道内边界的可行性。     

精确计算不同温度下液体导热系数的新方法

根据液体微观结构的特点和热传导机理，发展了一种计算液体导热系数的新方法。对２７３种物质６２７１个数据点的计算结果表明，该方法在很宽的温度范围（熔点到沸点以上温度）内具有很高的准确度，平均误差仅０．２９２％，计算精度优于文献方法。     

基于最小二乘法预测的导热反问题求解

根据体表红外热像图获得体内异常热源信息可抽象为一个含有未知内热源的导热反问题,其求解过程需要对计算区域内温度场进行反复计算,对于复杂的三维物理模型反演过程耗时较长。采用粒子群算法用以反演未知参数,并结合最小二乘法对部分粒子位置对应的目标函数值进行预测。在反演过程中,对远离群体的粒子进行位置的重新分配,避免计算资源的浪费。分析不同预测系数对粒子搜索过程的影响,采用了线性递减的预测系数。数值验证结果表明：基于最小二乘法预测的粒子群算法能在保证反演精度的前提下减少导热问题计算次数,缩短反演所需时间。     

Solving an Inverse Problem of Erosive Burning Rate Reconstruction

A new method for an experimental study of burning processes in condensed substances is suggested, based on the statement and solution of inverse problems. An inverse problem of reconstructing the erosive burning rate of solid propellants from experimental data is formulated. The choice of an approach to solving the problem by the joint application of well-known methods for inverse problem solution and specific features of experimental studies of burning processes, in particular, erosive burning, has been justified. The problem solution is illustrated by a numerical example. The testing involves a comparative analysis of two optimization methods: although both methods are characterized by an identical accuracy, the steepest descent method has a higher rate of convergence for this class of problems than the conjugate gradient method.