Finite element analysis of temperature field with phase transformation and non-linear surface heat-transfer coefficient during quenching

I.IntroductionItiswell-knownthatthemechanicalpropertiescanbeimprovedbyquenchingtechnique.Thetemperaturefieldofworkpiecehasagreatinfluenceupontheresiduals'ressesandmicrostructureafterquenching.Thus,thecalculationoftemperaturefieldduringquenchinghasbeenthesubjectofmanyinvestigations.Inthepastresearches,thesurfaceheat-transfercoefficientshavebeenusuallytreatedasconstantitmayleadtotheerrorofcalculationintheanalysisoftemperature.Infact,thesurfaceheat-transfercoefficientsarethenonlinearfunctionofte…     

Analysis of transient temperature field in coke drums

One of the primary reasons leading to bulging and cracking in a coke drum is the severe temperature gradient due to cyclic temperature variation. Based on the twodimensional heat conduction theory, an analytical solution of the transient temperature field in the coke drum is obtained, which is different from the known FEM results. The length of the coke drum is considered finite. The dynamic boundary conditions caused by fluid uninterrupted rising in oiling and watering stages are simulated with the iteration method. Numerical results show that the present theoretical model can accurately describe basic features of the transient temperature field in the coke drum. Effects of the geometry of the coke drum and the rising velocity of quench water on the axial temperature gradient are also discussed.     

Calculation of coupled problem between temperature and phase transformation during gas quenching in high pressure

The gas quenching is a modern, effective processing technology. On the basis of nonlinear surface heat-transfer coefficient obtained by Cheng during the gas quenching, the coupled problem between temperature and phase transformation during gas quenching in high pressure was simulated by means of finite element method. In the numerical calculation, the thermal physical properties were treated as the functions of temperature and the volume fraction of phase constituents. In order to avoid effectual "oscillation" of the numerical solutions under smaller time step, the Norsette rational approximate method was used.     

THE TEMPERATURE ANALYSIS OF THE BILLET WITH PHASE CHANGE DURING CONTINUOUS CASTING

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Effects of dilatational phase transformation on target strength of ceramic materials

The effects of dilatational phase transformation on the target strength of ceramic materials are investigated based on Tate's model. The constitutive behavior of materials in different regions (elastic, cracked, plastic and phase transformation) are taken into account. It is found that, with a proper choice of material parameters, the dilatational phase transformation can increase effectively the target strengthR. This would be of importance in penetration-resistance design. This work is partially supported by the Excellent Youth Foundation of Harbin Institute of Technology     

TiNi合金冲击相变过程中温度变化规律的实验研究

针对初始SME(shape memory effect)和PE(pseudo-elastic)状态TiNi合金试样,采用带有红外测温系统的SHPB冲击压缩装置,实时测量了冲击相变过程中两种材料试样表面瞬态温度,并根据实验结果计算了相应的温度变化。实验结果表明,冲击加载相变过程中,温度随相变应变的增大而升高,当应变最大时,温度最高;卸载过程中,对初始PE状态试样,温度降低,对初始SME状态试样,温度保持最高温度不变或降低,这同加载最高温度有关;卸载完成后,两种试样温度均高于其初始温度。计算温度结果表明,相变耗散功对加、卸载相变过程中温度变化的作用不可忽略。     

爆炸场瞬态高温测试的实验研究

针对爆炸场瞬态高温测量需求,从辐射测温原理出发,建立红外比色测温系统。通过黑体炉实验标定出Si/Ge双通道比色测温仪的波长、带宽、光电转换系数等工作参数和测温范围,并将比色测温仪高温测温量程扩展至3 500℃。利用大能量电火花放电产生的爆炸场标定了测温仪的响应时间,结果显示测温仪响应时间不超过10μs。确定了标准测温仪和超限测温仪的温度计算公式,并将比色测温仪应用于TNT柱状炸药和云爆剂（FAE）爆炸场温度测试,可以为爆炸反应过程诊断和爆炸温度毁伤效应评估提供依据。     

Interface propagation and microstructure evolution in phase field models of stress-induced martensitic phase transformations

Analytical solutions for diffuse interface propagation are found for two recently developed Landau potentials that account for the phenomenology of stress-induced martensitic phase transformations. The solutions include the interface profile and velocity as a function of temperature and stress tensor. An instability in the interface propagation near lattice instability conditions is studied numerically. The effect of material inertia is approximately included. Two methods for introducing an athermal interface friction in phase field models are discussed. In the first method an analytic expression defines the location of the diffuse interface, and the rate of change of the order parameters is required to vanish if the driving force is below a threshold. As an alternative and more physical approach, we demonstrate that the introduction of spatially oscillatory stress fields due to crystal defects and the Peierls barrier, or to a jump in chemical energy, reproduces the effect of an athermal threshold. Finite element simulations of microstructure evolution with and without an athermal threshold are performed. In the presence of spatially oscillatory fields the evolution self-arrests in realistic stationary microstructures, thus the system does not converge to an unphysical single-phase final state, and rate-independent temperature- and stress-induced phase transformation hysteresis are exhibited.     

LES of turbulent heat transfer: proper convection numerical schemes for temperature transport

Large eddy simulations of two basic configurations (decay of isotropic turbulence, and the academic plane channel flow) with heat transfer have been performed comparing several convection numerical schemes, in order to discuss their ability to evaluate temperature fluctuations properly. Results are compared with the available incompressible heat transfer direct numerical simulation data. It is shown that the use of regularizing schemes (such as high order upwind type schemes) for the temperature transport equation in combination with centered schemes for momentum transport equation gives better results than the use of centred schemes for both equations. Copyright © 2004 John Wiley & Sons, Ltd.     

The numerical solution of the transient two‐phase flow in rigid pipelines

Consideration is given in this paper to the numerical solution of the transient two‐phase flow in rigid pipelines. The governing equations for such flows are two coupled, non‐linear, hyperbolic, partial differential equations with pressure dependent coefficients. The fluid pressure and velocity are considered as two principle dependent variables. The fluid is a homogeneous gas–liquid mixture for which the density is defined by an expression averaging the two‐component densities where a polytropic process of the gaseous phase is admitted. Instead of the void fraction, which varies with the pressure, the gas–fluid mass ratio (or the quality) is assumed to be constant, and is used in the mathematical formulation. The problem has been solved by the method of non‐linear characteristics and the finite difference conservative scheme. To verify their validity, the computed results of the two numerical techniques are compared for different values of the quality, in the case where the liquid compressibility and the pipe wall elasticity are neglected. Copyright © 1999 John Wiley & Sons, Ltd.     

On the simulation of the transient temperature field or some viscoelasticity problems by structural analysis program

An idea is presented to solve the parabolic differential equation by the hyperbolic differential equation. We can simulate and compute the transient temperature field problems by a structural analysis program. Using only a single structural analysis program, the users can compute both temperature and thermal stress distributions on the same finite element mesh. The method thus extends the application of the structural analysis programs which have been implemented widely. As an example, the transient temperature field problem of a square plate is computed. The result is consistent with the theoretical result. A similar method for simulating some viscoelasticity problems of Kelvin model is also presented.     

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。     

超高速碰撞下相变效应的交错网格物质点法研究

超高速碰撞下的结构毁伤过程常伴随材料相变、断裂失效及碎片云的产生与演化,其所具有的压力强间断、材料非线性等几何大变形等问题给数值模拟带来了困难。交错网格物质点法SGMP通过背景网格格心积分消除了物质点法MPM跨网格误差,是模拟固体冲击爆炸等极端大变形与材料破坏问题的一种有效数值分析方法。本文将含金属相变的GRAY状态方程及含非线性内聚力断裂的Johnson-Cook修正金属模型引入SGMP中,模拟超高速碰撞单层、多层靶板问题。结果表明,SGMP和修正金属模型可以很好地模拟超高速碰撞问题中的碎片云形貌特征和相变效应。     

Investigation on the influence of nonuniform initial temperature on the transient heat transfer measurement of film cooling

Numerical and experimental investigations on the influence of nonuniform initial temperature on the transient heat transfer measurements are presented in this paper. The case of film cooling is investigated. When the initial wall temperature is nonuniform, the results of heat transfer coefficient and film cooling effectiveness, which are calculated by the equations derived with constant initial temperature, could deviate from the true values badly, especially in the condition of short test duration. Using initial wall temperature which is higher than the real values causes the results of heat transfer coefficient and film cooling effectiveness lower than the true values. And lower initial wall temperature produces higher results of heat transfer coefficient and film cooling effectiveness. However, when the initial temperature distribution in the region where conduction plays more influence on the wall surface temperature than the convection is well fitted by the cubic polynomial, accurate results can be obtained by the new equation which is derived from 1-D unsteady conduction model with nonuniform initial wall temperature. Some suggestions are also introduced to reduce the influence of nonuniform initial temperature when the initial temperature distribution is difficult to obtain and the equation derived from constant initial temperature has to be employed.     

Analysis on high-temperature oxidation and growth stress of iron-based alloy using phase field method

High-temperature oxidation is an important property to evaluate thermal protection materials. However, since oxidation is a complex process involving microstructure evolution, its quantitative analysis has always been a challenge. In this work, a phase field method (PFM) based on the thermodynamics theory is developed to simulate the oxidation behavior and oxidation induced growth stress. It involves microstructure evolution and solves the problem of quantitatively computational analysis for the oxidation behavior and growth stress. Employing this method, the diffusion process, oxidation performance, and stress evolution are predicted for Fe-Cr-Al-Y alloys. The numerical results agree well with the experimental data. The linear relationship between the maximum growth stress and the environment oxygen concentration is found. PFM provides a powerful tool to investigate high-temperature oxidation in complex environments.     

半无限介质瞬态热传导的同伦分析法

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.     

Stiffness and strength of phase transformation ceramics containing misoriented microcracks

Microcracks exert a large influence on the behavior of phase transformation ceramics. In this paper, the cause of microcracking is interpreted and the interaction between transformation particles and microcracks is described to estimate the stiffness and strength through the modified equivalent inclusion method by the authors. Three point bend experiments on Al₂O₃/ZrO₂ ceramics are performed and a comparison between the theoretical and measured results confirms the rationality of the analytical model proposed in this paper and the important role of microcracks.     

Interval finite difference method for steady-state temperature field prediction with interval parameters

A new numerical technique named interval finite difference method is proposed for the steady-state temperature field prediction with uncertainties in both physical parameters and boundary conditions. Interval variables are used to quantitatively describe the uncertain parameters with limited information. Based on different Taylor and Neumann series, two kinds of parameter perturbation methods are presented to approximately yield the ranges of the uncertain temperature field. By comparing the results with traditional Monte Carlo simulation, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed method for solving steady-state heat conduction problem with uncertain-but-bounded parameters.     

高维线性插值方法及其在3维温度场计算中的应用

通过分析1维和2维线性插值可以推导出任意斜角直线坐标系下n维线性插值的一般计算公式以及有唯一解的条件,这一结论能够应用于三维温度场计算。可以将n维插值问题归结如下:已知n 1维空间中的n 1个点的坐标以及第n 2个点的n个坐标分量xn 2,1,x n 2,2,,xn 2,n,求解该点的第n 1个坐标分量xn 2,n 1。根据线性插值定义,第n 2个点位于前n 1个点所确定的n维超平面上。根据这一条件列写方程、求解方程可得到插值xn 2,n 1。n维插值问题有唯一解的条件是已知的n 1个点在n维空间中构成的多面体的体积不为0。推导过程在斜角直线坐标系中完成,因而结论具有较大普适性。     

A new numerical method for determining heat transfer and packing distribution in particle heat exchangers for concentrated solar power

The complex nature of the physics of solid-gas interactions in concentrated solar particle heat exchangers signifies the need to develop new and cutting-edge numerical models to understand these interactions with the overarching goal of optimizing industrial solar thermal processes. To this end, a coupled computational fluid dynamics and discrete element method is developed to unravel near-wall particle flow physics of solar industrial heat exchangers. In addition, advanced post-processing functions are developed to provide a high-end data visualization and quantitative assessment of the packing distribution of solar particle heat exchangers. The validated numerical model shows that the particle temperature varies considerably throughout the entire fluid filled packed particle bed and it is shown that thermal radiation contribution becomes more profound at higher operating temperatures, namely 1073–1173 K. Also, the temperatures and solid volume fractions of the near-wall particles differ greatly compared to the bulk particles. The methods presented herein can be implemented by engineers and scientists to evaluate near-wall packing distributions and thermal characteristics, which would be useful for optimizing the geometric morphology of solar industrial heat exchangers.