【作者】 赵军明；

【导师】 刘林华；

【作者基本信息】 哈尔滨工业大学 ， 工程热物理， 2007， 博士

【摘要】 对于半透明参与性介质内辐射换热的求解已经发展了很多方法,综合来看,基于微分形式辐射传递方程离散的方法具有很好的适应性。对于均匀折射率介质内辐射传递的求解,离散坐标法和有限体积法具有可以方便经济地处理多维问题、灵活地处理复杂介质和边界特性、易于与其他换热方式进行耦合计算等优点,是目前应用最多的方法。对于梯度折射率介质内辐射传递的求解,其中有限体积法和有限元法避免了复杂耗时的弯曲光线轨迹的计算,表现了很好的适应性。但是目前已发展的这些方法都是低阶方法,一般仅具有一阶或二阶精度,同时只具有h收敛特性,为了得到需要的计算精度,只能通过繁杂的对网格加密或重新划分来实现。谱元法可以很好的克服低阶方法的不足,它兼具低阶有限元法和高阶谱方法的优点,将谱方法随着多项式阶数增加而收敛的p收敛特性与有限元法的易于适应复杂几何区域的优点及随着单元加密而收敛的h收敛特性充分结合。两种收敛方式使谱元法具有更优异的性能,其p收敛特性使谱元法可以在给定的网格划分情况下,仅通过增加单元近似多项式的阶数来达到收敛。本文结合均匀及梯度折射率介质内辐射传递方程的数值特性,发展并研究了基于不同离散方案的谱元法用于求解半透明介质内辐射传递、辐射与导热耦合换热及瞬态辐射传递问题的特性及性能。主要工作包括以下五个方面:1.发展了基于最小二乘稳定方案的谱元法用于求解均匀折射率介质内辐射传递方程,并给出了一种高效的数值实现算法。同时将该方法推广用于多维梯度折射率介质内辐射传递的求解。研究了该方法的数值稳定性及p收敛特性,其p收敛速率很快且满足指数规律。检验了该方法对于求解多维半透明均匀及梯度折介质内辐射传递的性能。给出了谱元法求解辐射传递方程的其他稳定方案及施加方式,研究并比较了基于其他稳定方案的谱元法求解半透明介质内辐射传递问题的性能。2.采用一种与辐射传递方程偶宇称分解不同的处理方式推导了一个基于原始变量的二阶辐射传递方程。该二阶方程具有辐射传递偶宇称公式的主要优点同时克服了其绝大部分缺点,可以方便的用于求解吸收、发射及各向异性散射介质内的辐射传递。对一阶和二阶方程的误差扰动特性进行了对比分析,数值分析结果表明二阶辐射传递方程具有更好的数值特性。给出了二阶辐射传递方程伽辽金法离散的一般公式,检验并研究了该二阶辐射传递方程对于求解多维辐射传递问题的性能。3.发展了基于间断伽辽金方案的谱元法用来求解多维半透明介质内的辐射传递。间断伽辽金方案不需要强加单元间的连续性,其离散得到的方程满足局部守恒性。该方法有效的消除了离散坐标方程对流特性造成的数值不稳定性。研究了该方法在结构及非结构网格时的p收敛特性。比较了单元边界数值通量的不同处理方式对该方法数值特性的影响。讨论了基于辐射传递方程离散的数值算法的两种射线效应,即边界热负荷不均及内部遮挡引起的射线效应。4.基于二阶辐射传递方程发展了一种谱元法用于求解多维半透明介质内辐射与导热的耦合问题。检验了其求解多维半透明介质内辐射与导热耦合问题的性能。研究了该谱元法求解辐射与导热耦合问题的h和p收敛特性。在不同普朗克数下p收敛速率很快且服从指数规律并显著优于h收敛速率。数值实验验证表明谱元法对于扭曲网格有着很好的适应性。5.基于间断谱元法具有局部守恒性、高阶精度及假扩散小等优点,将其推广用于瞬态辐射传递的求解。研究了平行光照射及瞬态漫射边界的特殊处理方法。给出了瞬态辐射传递方程间断谱元法离散和求解的实现过程。通过典型算例对提出的瞬态辐射传递求解的间断谱元法进行了验证,同时研究了其求解瞬态辐射传递问题的性能。更多还原

【Abstract】 Many numerical methods have been developed for solving radiative heat transfer in semitransparent participant media. By comprehensive comparison, the methods based on discretization of the differential form of radiative transfer equation possess very good adaptabities. As for solving radiative transfer in uniform index media, discrete ordinates method and finite volume method have many advantages, such as, they are convenient and efficient to deal with multidimensional problem, flexible to deal with problem with complex media and boundary properties, and easy to be adapted to coupled solution with other heat transfer processes, etc., as a result, they are the mostly often used methods until recently. As for solving radiative transfer in graded index media, the finite volume method and the finite element method avoid the time-consuming computation of curved ray trajectories, so they show very good adaptabities. However, these already developed methods are all low order methods, generally with only first or second order of accuracy, furthermore they provide only h-convergence property, as a result, in order to gain wanted accuracy, cumbersome mesh refining or remeshing is necessary.Spectral element method can effectively overcome the drawbacks of low order methods, which possesses both the advantages of low order finite element method and high order spectral method and best combines the p-convergence property of spectral methods, namely, convergence by increasing order of polynomial, and the advantage to be easy to applied to complex enclosures and the h-convergence property of finite element method, namely, convergence by mesh refining. Two convergence strategies make spectral element method are more effective, of which the p-convergence property make spectral element method can achieve convergence by just increasing the order of polynomial.By considering the numerical properties of radiative transfer equation for uniform and graded index media, this paper develops and studies the characteristics and performances of spectral element methods based on different discretization schemes to solve radiative transfer in semitransparent participant media, coupled radiative and conductive heat transfer and transient radiative transfer. The scope of present research contains five parts:1. A spectral element method based on least squares stabilization scheme is developed to solve radiative transfer in multidimensional uniform index media and an efficient implementation algorithm is presented. The proposed method is also extended to solve radiative transfer in graded index media. The stability and p-convergence characteristics of the method are studied and its p-convergence speed is very fast and follows exponential law. The performances of the method for solution of radiative transfer in multidimensional semitransparent uniform and graded index media are examined. Some other stabilization schemes of spectral element method and their imposing techniques are presented and the performances of spectral element method based on these stabilization schemes for solving radiative transfer in semitransparent media are studied and compared.2. A second order radiative transfer equation of primitive variable is derived by using a different way than the even parity formulation. This second order equation possesses major advantages of the even parity formulation of radiative transfer, but overcomes most of its drawbacks, and can be conveniently applied to solve radiative transfer in absorbing, emitting and anisotropically scattering media. Perturbation error analysis are made for both the first order and the second order equation, by comparison, the second order radiative transfer equation shows better numerical properties. A general formulation of Galerkin discretization of the second order radiative transfer equation is presented, and the performances of the second order equation are examined for solving multidimensional radiative transfer problems.3. A spectral element method based on discontinuous Galerkin scheme is developed to solve radiative transfer in multidimensional semitransparent media. The discontinuous Galerkin scheme need not to impose inter-elemental continuity and the resulting discretized equation own local conservativity. This method effectively eliminates the numerical instability caused by the convection property of discrete ordinates equation. The p-convergence characteristics of the proposed method are studied on both structured and unstructured meshes. Influences of different schemes for dealing with elemental boundary numerical flux on numerical properties of the proposed method are compared. Two kinds of ray effect are discussed for methods based on discretization of radiative transfer equation, namely, ray effect induced by boundary loading and ray effect induced by shielding of interior obstacle.4. Based on the second order radiative transfer equation, a spectral element method is developed to solve coupled radiative and conductive transfer in multidimensional semitransparent media. The performances of the proposed method are examined for solving coupled radiative and conductive heat transfer in multidimensional semitransparent media. The h- and p-convergence characteristics of the proposed method are studied. The p-convergence speeds are very fast and follow exponential law under different values of Plank number and are superior to the h-convergence speed. Numerical examinations show that spectral element method possesses very good adaptability to skewed meshes.5. Considering the discontinuous spectral element method has advantages, such as local conservativity, high order of accuracy and minimal artificial diffusion, it is extended to solve transient radiative transfer problems. Special treatment of the collimated irradiation and transient diffusive boundary are studied. The implementation of the discontinuous spectral element method for the discretization of transient radiative transfer equation is presented. The proposed discontinuous spectral element method for transient radiative transfer is examined by several classical examples, and its performances for solving transient radiative transfer are studied.更多还原