AN ADAPTIVE ALGORITHM OF PRECISE INTEGRATION FOR TRANSIENT ANALYSIS

This paper presents an improved precise integration algorithm fortransient analysis of heat transfer and some other problems. Theoriginal precise integration method is improved by means of the inve-rse accuracy analysis so that the parameter N, which has been takenas a constant and an independent pa- rameter without consideration ofthe problems in the original method, can be generated automaticallyby the algorithm itself.

Transient heat conduction analysis using the NURBS-enhanced scaled boundary finite element method and modified precise integration method

The Non-uniform rational B-spline （NURBS） enhanced scaled boundary finite element method in combination with the modified precise integration method is proposed for the transient heat conduction problems in this paper. The scaled boundary finite element method is a semi-analytical technique, which weakens the governing differential equations along the circumferential direction and solves those analytically in the radial direction. In this method, only the boundary is discretized in the finite element sense leading to a re- duction of the spatial dimension by one with no fundamental solution required. Neverthe- less, in case of the complex geometry, a huge number of elements are generally required to properly approximate the exact shape of the domain and distorted meshes are often un- avoidable in the conventional finite element approach, which leads to huge computational efforts and loss of accuracy. NURBS are the most popular mathematical tool in CAD industry due to its flexibility to fit any free-form shape. In the proposed methodology, the arbitrary curved boundary of problem domain is exactly represented with NURBS basis functions, while the straight part of the boundary is discretized by the conventional Lagrange shape functions. Both the concepts of isogeometric analysis and scaled boundary finite element method are combined to form the governing equations of transient heat conduction analy- sis and the solution is obtained using the modified precise integration method. The stiffness matrix is obtained from a standard quadratic eigenvalue problem and the mass matrix is determined from the low-frequency expansion. Finally the governing equations become a system of first-order ordinary differential equations and the time domain response is solved numerically by the modified precise integration method. The accuracy and stability of the proposed method to deal with the transient heat conduction problems are demonstrated by numerical examples.

Consideration of transient heat conduction in a semi-infinite medium using homotopy analysis method

In the current work, transient heat conduction in a semi-infinite medium is considered for its many applications in various heat fields. Here, the homotopy analysis method （HAM） is applied to solve this problem and analytical results are compared with those of the exact and integral methods results. The results show that the HAM can give much better approximations than the other approximate methods： Changes in heat fluxes and profiles of temperature are obtained at different times and positions for copper, iron and aluminum.

Bi-Fo time scaling method in the numerical simulation of transient conjugate heat transfer

Reliable transient thermal analysis plays a very important role in the engine safety analysis.Transient conjugate heat transfer simulation is an important way of temperature analysis.But there exists a great disparity in the time scales between solid conduction and fluid convection.The calculation cost of transient conjugate heat transfer analysis is very huge because of the tiny time step of computational fluid dynamics.The Bi-Fo time scaling method is proposed to improve the computational efficiency of transient conjugate heat transfer.On the one hand,this method carries out a similar transformation on solid heat conduction,scaling the calculation time with the product of density and specific heat capacity to maintain the consistency of Fourier number.On the other hand,it takes very short time for the fluid domain to recover stability after a boundary disturbance.Based on the above characteristic,the flow time is directly compressed to the same as that of the solid domain.It is verified by Mark II vane that increasing the solid thermal diffusivity can reduce the time scale of heat conduction.In the situation of rapidly stable flow field,scaling flow time does not affect the solid thermal boundary under corresponding dimensionless time.Within the application scope,the Bi-Fo time scaling method can greatly reduce the time cost of transient conjugate heat transfer simulation while maintaining the accuracy of transient temperature analysis.

考虑瞬态温度和应力约束的承载隔热多功能结构拓扑优化

一体化热防护结构通常处于严酷的非稳态热环境,热载荷作用的时间效应(即瞬态热效应)明显.为了避免瞬态热分析的巨大计算消耗,以往的一体化热防护结构优化设计研究通常将瞬态传热等效为相同热边界条件下的稳态传热,将稳态传热分析的温度场作为设计热载荷.然而,已有的研究表明稳态传热无法准确等效瞬态传热的作用效果,瞬态热效应对结构设计结果具有重要影响.文章研究了考虑瞬态热效应的一体化热防护结构优化设计问题,建立一种考虑瞬态温度和应力约束的一体化热防护结构拓扑优化方法.该方法以SIMP(solid isotropic material with penalization)法为基础,构建两种针对一体化热防护结构的热弹性结构拓扑优化模型:(1)考虑材料体积分数、最大应力和底面最大温度约束,以最小化结构应变能为目标的刚度设计模型;(2)考虑最大应力和底面最大温度约束,以最小化材料体积分数为目标的轻量化设计模型.通过求解瞬态热力耦合方程获得结构的热力耦合静力分析结果;通过响应量在空间和时间域的凝聚积分函数表征结构响应在时域内的最大值,并以此构建相应的约束和目标函数;采用伴随法推导约束和目标函数的灵敏度表达式.通过3个数值算例验证了本方法的有效性.数值算例结果表明,在瞬态传热条件下,本方法能够准确反映瞬态热效应对一体化热防护结构设计结果的影响;相比于基于稳态热分析的设计结果,考虑瞬态热效应的设计结果具有更优的性能.

Unified Solution of Conjugate Fluid and Solid Heat Transfer-Part I.Solid Heat Conduction

A unified solution framework is proposed for efficiently solving conjugate fluid and solid heat transfer problems.The unified solution is solely governed by the compressible Navier-Stokes(N-S)equations in both fluid and solid domains.Such method not only provides the computational capability for solid heat transfer simulations with existing successful N-S flow solvers,but also can relax time-stepping restrictions often imposed by the interface conditions for conjugate fluid and solid heat transfer.This paper serves as Part I of the proposed unified solution framework and addresses the handling of solid heat conduction with the nondimensional N-S equations.Specially,a parallel,adaptive high-order discontinuous Galerkin unified solver has been developed and applied to solve solid heat transfer problems under various boundary conditions.

An optimized time-adaptive aerothermal coupling calculation method for aerothermal analysis of disc cavity system

In order to further achieve the balance between the calculation accuracy and efficiency of the transient analysis of the aero-engine disc cavity system,an Optimized Time-adaptive Aerother-mal Coupling calculation(OTAC)method has been proposed.It combines one-dimensional tran-sient calculation of air system,Conventional Sequence Staggered(CSS)method,Time-adaptive Aerothermal Coupling calculation(TAC)method and differential evolution optimization algorithm to obtain an efficient and high-precision aerothermal coupling calculation method of air system.Considering both the heat conduction in the solid domain and the flow in the fluid domain as unsteady states in the OTAC,the interaction of fluid-solid information within a single coupling time step size was implemented based on the CSS method.Furthermore,the coupling time step size was automatically adjusted with the number of iterations by using the Proportional-Integral-Deri vative(PID)controller.Results show that when compared with the traditional loosely coupling method with a fixed time step size,the computational accuracy and efficiency of the OTAC method are improved by 8.9%and 30%,respectively.Compared with the tight coupling calculation,the OTAC method can achieve a speedup of 1 to 2 orders of magnitude,while the calculation error is maintained within 6.1%.

非线性瞬态热传导的精细积分方法

采用精细积分法求解非线性瞬态热传导方程 .非线性因素包括热辐射边界条件和物性参数可变 .推导了瞬态非线性热传导方程中精细积分法的具体列式 .指出可利用指数矩阵的对称性和带宽特性提高算法的效率 ,并结合预测校正算法求解非线性方程 .

钻井全过程井筒-地层瞬态传热模型

井筒-地层温度是影响井筒压力控制、井壁稳定性预测、井下动力钻具与测量设备优选的关键因素之一。基于钻井液循环和停止循环期间井筒-地层各单元控制组件能量交换机理,建立了实际钻具组合与井身结构条件下循环和停止循环期间井筒-地层传热耦合数值模型。结合1口深井基础数据,分析了循环与停止循环期间井下温度分布规律。研究表明:套管下深长度对井筒温度影响较大,在套管段随着循环和停止循环时间增加,环空温度几乎不变,而在裸眼段随着循环时间增加环空温度降低,随着停止循环时间增加环空温度逐渐升高;循环期间钻井液对地层温度的扰动距离为2.8m,而停止循环期间扰动距离为4.6m。

瞬态温度场灵敏度分析的精细积分法

结合有限元法 ,提出了线性和非线性瞬态温度场灵敏度分析的精细积分方法。在精细积分法求解线性和非线性温度场的基础上 ,采用敏度分析的半解析法 ,推导了瞬态温度场灵敏度分析的精细积分列式。指出对于线性热传导问题 ,精细积分法求解敏度方程同样具有稳定、高精度的数值特性 ,而且能避免常规差分法的数值振荡现象。对于非线性热传导问题 ,提出了相应的求解办法。

连续梁瞬态振动离散时间精细传递矩阵法

针对连续梁振动问题,将通常诸如中心差分法、Hewmark-β法等结构动力学差分方法和矩阵指数精细积分法相结合,提出了一种高效求解连续梁瞬态振动的方法,离散时间精细传递矩阵法。该方法基于连续梁振动偏微分方程,将惯性项中加速度通过差分法线性化为位移的线性函数,于是原系统的连续偏微分方程就转化为线性非齐次常微分方程组。通过精细积分法求解该系统从一端到系统另一端的传递矩阵,非齐次项可选用梯形积分、高斯积分等方法得到,结合边界条件既可进行系统动力学分析。系统固有振动分析可视为读方法的特例。通过数值算例证明提出的方法精度高、有效。

基于Householder方法的子域精细积分

有限元法生成的矩阵通常具有尺度和带宽很大的特点,应用子域精细积分面临着选择子域的困难。本文采用Householder方法将矩阵三对角化,从而使子域精细积分可用于大型有限元系统。通过在子域精细积分中引入预估-校正格式,可以在不需要迭代的情况下得到比蛙跳格式更高的精度。

高温高压气井井筒温度场计算与分析

为确保高温高压气井的安全钻井,有必要对高温高压气井的井筒温度场进行研究。考虑井筒流体与地层传热,根据热力学定律和能量守恒定律,建立了钻井液循环期间钻柱内及环空流体瞬态温度模型,分析了钻井液排量和循环时间对环空温度的影响。研究结果表明:循环温度与静温剖面的偏离程度随循环排量和循环时间的增加而增大;小排量时环空钻井液温度比排量较大时更接近于静温剖面;随着排量的增加,井底循环温度逐渐降低;在相同排量下,随着循环时间的延长,环空瞬态温度场偏离静止温度场越多,环空温度逐渐趋于稳定。基于该瞬态温度模型,结合顺北鹰1井参数,计算得到的钻井液出口温度与现场实测值很接近,相对误差均在7%以内,验证了模型的可靠性。

短周期实验台涡轮机匣换热实时测量初探

本文简单介绍了采用铂膜单膜热流计和高速动态采集系统进行实时表面温度和热流率测量的原理和系统,并利用中国科学院工程热物理研究所的暂冲式短周期涡轮实验台进行了涡轮机匣换热的实时测量.测量所得的机匣表面实时温度与热流率呈现良好的周期性,并与涡轮转速相对应的高压动叶叶片通过频率相吻合.机匣表面实时温度的波动幅值极小,不超过0.4℃,而实时热流率的波动幅值达到几万瓦每平方米的量级.

中式烹饪用时间温度积分器的构建与验证

蛋白质变性能够较广泛地表征烹饪加热品质变化,因而寻找到一种z值为7.36℃的耐高温α-淀粉酶,与蛋白质热变性z值5~10℃相近。以该酶溶液为指示剂,在玻璃毛细管中封装后置入烹饪耐受性高的、特定形状的魔芋凝胶(g-KGM)载体,从而构建了烹饪研究用时间温度积分器(time temperature integrators,TTIs)装置。随后,在模拟烹饪过程而设定的对流传热条件下,通过传热学试验结合非稳态传热以及酶失活动力学数学模型计算得到剩余酶活,与TTIs装置指示剂酶活实测值比较,两者误差小于2.24%。进一步,应用该TTIs装置测定了实际烹饪爆炒过程的表面换热系数。所构建的TTIs装置,结合数值模拟,可以分析测量常规试验传热学方法无法应用的激烈烹饪中流体-颗粒的传热过程,也可应用于其他领域的移动颗粒传热学研究。

瞬态热传导问题的精细积分数值流形方法研究

数值流形方法(NMM)因其特有的双覆盖系统(数学覆盖和物理覆盖)在域离散方面具有独特的优势,而精细时间积分法则具有精度高、无条件稳定、无振荡以及计算结果不依赖于时间步长等特点。发展了用于研究二维瞬态热传导问题的精细积分NMM。结合待求问题的控制方程和边界条件,并基于修正变分原理导出了NMM的总体方程,给出了求解此类时间相依方程的精细时间积分及空间积分策略,选取了两个典型算例对方法的有效性进行了验证,结果表明本文方法可以高效高精度地求解瞬态热传导问题。

发射装药保温时间的模拟计算

为得到弹药及其相关部件保温时的准确保透时间,用热传导理论对发射装药保温过程中的传热特性进行分析,通过传热学计算和测试手段确定有关参数。利用三维实体建模软件Solidworks建立发射装药实体模型,通过ANSYS有限元模拟分析软件对发射装药内部温度的传递变化规律进行模拟,并进行了试验验证,得到发射装药温度场分布与保温时间的关系及发射装药保透所需时间。结果证明,现行军标规定的保温时间确有很大的压缩空间。

单层饱和多孔介质一维瞬态响应半解析解

基于Biot饱和多孔介质理论,以一类边界条件为例,提出一种单层饱和多孔介质一维瞬态响应问题的半解析求解方法。首先将基本方程和相应的初始条件、边界条件量纲一化,给出矩阵形式的位移控制方程。通过适当变换使边界条件齐次化,求解相应特征值问题,得到非齐次边界条件下的特征值和特征函数,并证明特征函数的正交性。利用该正交性,得到无限个仅阻尼项耦合的关于时间的常微分方程及相应的初始条件。截取有限项,采用精细时程积分法求解常微分方程组初值问题,并得到原问题的解,最后通过算例分析动力渗透系数对流固耦合作用的影响,验证方法的有效性。提出的方法不仅考虑孔隙流体、固体颗粒的压缩性及任意的惯性、黏滞和耦合作用,而且可以推广到任意非齐次边界条件的一维瞬态响应问题。

药头质量分布对电引火药头发火时间精度的影响

电引火药头发火时间是影响火工品延期精度的重要因素。制备药头药剂质量固定的电引火药头,统计质量分布;模拟药头发火环境,制备样品,测试不同质量水平药头的发火时间。结果表明:在现有生产工艺条件下,药头质量成正态分布,整体质量比工厂控制水平偏大,发火时间随质量变化在6.1 ms左右波动,在质量分布较为集中的15.74 mg区域附近,药头发火时间波动小,精度高。