AN INPUT ESTIMATION APPROACH TO ON-LINE TWO-DIMENSIONAL INVERSE HEAT CONDUCTION PROBLEMS

Abstract

An on-line methodology to solve two-dimensional inverse heat conduction problems (IHCP) is presented. A new input estimation approach based on the Kalman filtering technique is developed to estimate the two separate unknown heat flux inputs on the two boundaries in real time. A recursive relation between the observed value of the residual sequence with unknown heat flux and the theoretical residual sequence of the Kalman filter that assumes known heat flux is formulated. A real-time least-squares algorithm is derived that uses the residual innovation sequence to compute the magnitude of heat flux. This recursive approach facilitates practical implementation, and its capabilities are demonstrated in several typical cases with discontinuous and time-varying heat flux inputs.     

SOLUTION TO INVERSE HEAT CONDUCTION PROBLEM IN NANOSCALE USING SEQUENTIAL METHOD

An inverse heat conduction problem for nanoscale structure is studied. The conduction phenomenon is modeled using the Boltzmann transport equation. Phonon-mediated heat conduction in one dimension is considered. One boundary is exposed to an unknown temperature and the other boundary, where temperature observation takes place, is subject to a known boundary condition. A sequential scheme with constant function specification is employed for inverse estimation of the unknown temperature. Sample results are presented and discussed.     

利用开路电压测量太阳电池外量子效率

首先利用太阳电池光照下的J-V特性,推导短路电流密度Jsc、开路电压Voc与光照面积和总面积的比值AΦ/AT之间的关系,分析利用短路电流密度测量外量子效率EQE(λ)SC的误差来源。并利用J-V特性将开路电压Voc表示的外量子效率EQE(λ)OC与常规利用短路电流密度Jsc表示的外量子效率EQE(λ)SC利用fEQE因子相关联。最后,测量不同面积晶体硅太阳电池的EQE(λ)OC、EQE(λ)SC并与PC1D模拟的EQE(λ)SCPC1D曲线进行对比,得到相应结论。该测试方法对提高太阳电池量子效率测试的准确性具有一定指导意义。     

恒温热源不可逆闭式中冷回热燃气轮机循环的功率和效率

用有限时间热力学方法首次研究了恒温热源条件下不可逆闭式中冷回热燃气轮机循环的功率、效率以及中间压比特性，导出了无因次功率及效率的解析式。通过数值计算方法，分析了中冷度、回热度对循环最优功率、最优效率及其对应的中间压比分配的影响。     

APPLICATION OF THE ADAPTIVE MATRIX FILTER TO INVERSE HEAT CONDUCTION PROBLEMS

A matrix filter has been developed to remove errors from temperature measurements in the field of heat conduction. It has been shown that the matrix filter substantially reduces the errors in measurements. The filter extended to a new adaptive matrix filter (AMF) enables identification of some thermal properties based on the temperature measurements of the system involved. The approach allows elimination of many problems associated with the solution of nonlinear equations. AMF can use data containing errors; this allows for a simultaneous estimation of unknown properties and removal of errors from measurements. It has been proved that the algorithm is very efficient.     

利用内光谱响应测量晶体硅太阳电池前表面复合速度

根据发射区电流密度的连续性方程,推导出了发射区杂质服从高斯函数和余误差函数分布情况下短波内光谱响应与前表面复合速度的模型,该模型短波波长的选择与扩散结深有关.并利用该模型对不同扩散条件下的晶体硅太阳电池前表面复合速度进行计算,结果与PC1D模拟结果符合较好.     

APPLICATION OF THE METHOD OF INTEGRAL RELATIONS TO TRANSIENT HEAT CONDUCTION

Abstract

This paper presents a general integral method of solving the one-dimensional transient heat conduction equation in a semi-infinite region with constant or variable thermal conductivity. The method is based upon the general framework of the orthonormal method of integral relations of Fletcher and Holt, with a modified procedure for obtaining the integral relations. In addition, a technique for obtaining the necessary initial conditions for the integral relations is proposed instead of the usual practice of using similarity solutions. The main advantages of the present method over most existing integral methods are its generality and controlled accuracy, as demonstrated by the numerical results obtained herein. Comparisons with available exact solutions are generally good.     

WELL-CONDITIONED NUMERICAL METHOD FOR THE NONLINEAR INVERSE HEAT CONDUCTION PROBLEM

A numerical procedure recently presented by the authors for linear inverse heat conduction problems is extended to nonlinear cases. The method is well conditioned in the sense that it always generates bounded solutions and never generates heat fluxes oscillating with increasing amplitude. The convergence of the algorithm is studied, and a set of examples shows convergence for a wide range of nonlinear problems. In the case of perfect data the accuracy of the estimated heat fluxes increases as the time step is decreased without need for additional stabilization or regularization. Filters allow perturbed data to be treated and facilitate attaining a balance between accuracy and resolving power.     

THE VALIDATION OF THE ROBUST INPUT ESTIMATION APPROACH TO TWO-DIMENSIONAL INVERSE HEAT CONDUCTION PROBLEMS

A novel adaptive and robust input estimation inverse methodology of estimating the time-varying unknown heat flux, named as the input, on the two active boundaries of a 2-D inverse heat conduction problem is presented. The algorithm includes using the Kalman filter to propose a regression model between the residual innovation and the two thermal unknown boundaries flux through given 2-D heat conduction state-space models and noisy measurement sequence. Based on this regression equation, a recursive least-square estimator (RLSE) weighted by the forgetting factor is proposed to on-line estimate these unknowns. The adaptive and robust weighting technique is essential since unknowns input are time-varied and have unpredictable changing status. In this article, we provide the bandwidth analysis together with bias and variance tests to construct an efficient and robust forgetting factor as the ratio between the standard deviation of measurement and observable bias innovation at each time step. Herein, the unknowns are robustly and adaptively estimated under the system involving measurement noise, process error, and unpredictable change status of time-varying unknowns. The capabilities of the proposed algorithm are demonstrated through the comparison with the conventional input estimation algorithm and validated by two benchmark performance tests in 2-D cases. Results show that the proposed algorithm not only exhibits superior robust capability but also enhances the estimation performance and highly facilitates practical implementation.     

AN ALTERNATIVE FORMULATION OF THE APPARENT HEAT CAPACITY METHOD FOR PHASE-CHANGE PROBLEMS

Abstract

In the apparent heat capacity method (AHCM) for heat transfer problems with phase change, the conventional time discretization is subject to severe restrictions on time steps in spite of the various approximation techniques that have been developed so far. To improve the conventional AHCM we propose an alternative formulation. By introducing a nominal heat capacity, the new time discretization can better approximate the time derivative of enthalpy while maintaining the same form as the conventional AHCM. The new formulation also establishes an equivalent relation between the full enthalpy formulation and the AHCM. A one-dimensional (I-D) Stefan problem is used as a test problem, and comparison is made between the solutions of the conventional and the new AHCM formulations. It is found that for implicit schemes with large time steps, the new formulation performs much better than the conventional AHCM     

余热利用有机物朗肯循环最佳热回收效率分析

首先通过分析余热回收动力循环的不可逆损失,得到循环的理想效率。其次,通过分析发现热回收效率随蒸发压力变化存在最佳值,并且最佳热回收效率与最小熵增率是等价的。然后,通过研究两种简化的余热利用动力模型,应用有限时间热力学的相关方法,指出最大热回收效率产生的原因。再次,研究了余热变化时系统最佳工况的变化。结果发现最佳蒸发压力随余热流量、入口温度增加而显著增加,而与余热组分关系不大。最后,研究了工质对系统最佳工况的影响,发现较高临界温度的工质,最佳蒸发压力较低。     

提高水源热泵机组效率的技术条件分析

以热力学完善度为评价指标,分析水源热泵在标准工况下各部件的不可逆损失程度,其中由压缩机和换热器引起的不可逆损失占总不可逆损失的80%以上。在此基础上,针对水源热泵的特点,对几种能提高其能效水平的技术进行定性和定量分析,结果表明均能有效提高机组的热力学完善度。对采用这些技术的水源热泵机组进行的测试中,制冷,45℃、55℃制热工况下,性能系数分别达到6.64、4.79和3.99。对市场上的部分水源热泵产品样本进行统计分析,结果表明制冷和制热工况的性能水平较低,热力学完善度平均值分别为0.270和0.423,绝大部分产品的性能提升空间超过20%。     

BOUNDARY ELEMENT METHOD APPLIED TO STEADY PERIODIC HEAT CONDUCTION

This paper describes implementation of the boundary element method to steady periodic heat-conduction problems. The use of a complex harmonic representation of the solution reduces the time-dependent parabolic partial differential equation to a time-independent Helmholtz equation. A simple numerical example is given, and excellent correlation with the analytical solution is achieved.     

USING INVERSE MODELING TO ESTIMATE THE INCIDENT HEAT FLUX REQUIRED TO ACHIEVE TEMPERATURE UNIFORMITY ACROSS A CIRCULAR DISK

This article presents a systematic inverse modeling analysis for estimating the incident heat flux required to achieve temperature uniformity across a circular disk during thermal processing. A one-dimensional thermal model, temperature-dependent thermal properties of silicon, and a future-time algorithm of inverse heat transfer method are used. Vertical and lateral edge-heat compensations on the perimeter are discussed. The required edge-heat compensations for maintaining uniform temperature across 100-mm-diameter (0.6-mm-thick), 150-mm-diameter (0.675-mm-thick), 200-mm-diameter (0.725-mm-thick), and 300-mm-diameter (0.775-mm-thick) silicon disks are evaluated intuitively using inverse modeling. Our numerical results show that temperature uniformity can be efficiently achieved using inverse modeling. The resulting maximum temperature differences in our present study were only 0.279, 0.583, 0.989, and 0.178 ° C across 100-, 150-, 200-, and 300-mm-diameter disks, respectively.     

我国热泵热水机能效水平分析

对我国热泵热水机的能效现状进行调研,结果显示有约1/3的空气源普通型热泵热水机及超过1/2的水源热泵热水机产品的COPh不能达到GB/T 21362—2008中相应要求。提出采用热力学完善度(η)分析的方法,并参照我国现有房间空调器、单元式空调机及冷水机组的能效等级标准,分析热泵热水机的能效等级标准。建议该标准分为3级,其中水源式1～3级COPh/ηh依次为5.1/0.407、4.8/0.382、4.5/0.359,空气源普通式相应值依次为4.3/0.296、4.0/0.276、3.7/0.255。     

RADIATIVE HEAT TRANSFER IN AXISYMMETRIC GEOMETRIES USING AN UNSTRUCTURED FINITE-VOLUME METHOD

The finite-volume method is extended to compute radiation in axisymmetric geometries using unstructured polyhedral meshes. Control angle overhangs, resulting from the nonalignment of the angular discretization with cell faces, are accounted for in the differencing. Conservative discretization of the angular redistribution term is proposed, and allows the solution of axisymmetric problems on the same two-dimensional mesh as the fluid flow. The method is shown to be equivalent to the mapping procedure of Chui and Railhby. The scheme is applied to a number of benchmark problems and is shown to perform satisfactorily.     

APPLICATION OF AN ALTERNATING METHOD TO THE THERMOELASTIC PROBLEMS WITH MULTIPLE CIRCULAR HOLES IN AN INFINITE DOMAIN

This paper presents a new efficient procedure to analyze the thermoelastic problems with multiple circular holes in two-dimensional infinite domain using an alternating method. To achieve this purpose, the analytical solutions including the temperature and associated thermal stress for the arbitrary heat flux across the single circular hole boundary in an infinite domain are first derived. Both the temperature and thermal stress fields in the thermal problems are simultaneously solved by these analytical solutions with the successive iterative superposition process. Compared with the solution of the conventional finite-element technique, the present method has been more accurate and has more advantages. Effects of the distributions and sizes of the holes on the stress concentration in the thermal problems also are evaluated in detail herein.     

SOLUTION OF THE INVERSE PROBLEMS IN HEAT TRANSFER AND THERMAL STRESS ANALYSIS

The stable method of soloing inverse problems in heat transfer and inverse problems concerning thermal stress control in elements of complex shapes is presented. Based on the discrete form of Duhamel's integral and on so-called future time steps, a simple and accurate method of solving one- and multi-dimensional inverse problems is developed. Two examples illustrating the application of the described method are presented.