Monte Carlo simulation of radiative transfer in a refractive layered medium

In this work, we adapted the Monte Carlo method to simulate radiative transfer in a two-layer scattering slab with continuously varying refractive index in each of the two layers and a jump of refractive index at the interface between the two layers. The hemispherical reflectance (R _h ) and transmittance (T _h ) of the slab are obtained by tracing photon bundles propagating along curved trajectories. There is a very satisfying correspondence between the present results and those obtained by numerical solution of integral radiative transfer equation for the special cases with constant refractive index in each of the layers. The magnitude of numerical uncertainty decreases with the increase of bundles. The results show that the R _h decreases with the increase of the positive gradient of the refractive index considered. For the cases with constant total thickness, the R _h and the T _h increase with the increase of the ratio of upper-layer thickness to lower-layer thickness.     

Radiation equilibrium temperature field in a gradient index medium with specular surfaces

The radiation equilibrium temperature field in a gradient index semitransparent absorbing-emitting gray medium is analyzed. The medium is bounded by two semitransparent specular surfaces and possesses a refractive index varying spatially or dependent on temperature. By discretizing the medium into many sublayers and adopting a linear refractive index approximation for each sublayer, the curved ray tracing technique is developed to solve the radiation transfer in medium. The temperature field at radiation equilibrium is obtained based on the energy conservation. The influences of refractive index distribution and optical thickness on the temperature field as well as the coupled effect of temperature and refractive index are examined. The results display the significant influences of gradient index on radiation transfer and the temperature distribution.     

Numerical modelling of combined conductive and radiative heat transfer within square enclosure using discrete ordinate method

The current study addresses the mathematical modeling aspects of coupled conductive and radiative heat transfer in presence of absorbing, emitting and isotropic scattering gray medium within two-dimensional enclosure. The walls of the enclosure are considered to be opaque, diffuse and gray. The enclosure comprises isothermal vertical walls and insulated horizontal walls. The discrete ordinate method has been employed for modeling the radiative transport equation and the finite volume method has been adopted as the numerical technique. The effect of various parameters, i.e., radiation-conduction parameter, surface emissivity single scattering albedo and optical thickness has been illustrated.     

First-passage problem of a class of internally resonant quasi-integrable Hamiltonian system under wide-band stochastic excitations

In this paper, first-passage problem of a class of internally resonant quasi-integrable Hamiltonian system under wide-band stochastic excitations is studied theoretically. By using stochastic averaging method, the equations of motion of the original internally resonant Hamiltonian system are reduced to a set of averaged Itô stochastic differential equations. The backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the mean first-passage time are established under appropriate boundary and (or) initial conditions. An example is given to show the accuracy of the theoretical method. Numerical solutions of high-dimensional backward Kolmogorov and Pontryagin equation are obtained by finite difference. All theoretical results are verified by Monte Carlo simulation.     

Analysis of coupled conduction and radiation heat transfer in presence of participating medium- using a hybrid method

The current study addresses the mathematical modeling aspects of coupled conductive and radiative heat transfer in presence of absorbing, emitting and isotropic scattering gray medium within two-dimensional square enclosure. The walls of the enclosure are considered to be opaque, diffuse and gray. The enclosure comprised of isothermal vertical walls and insulated horizontal walls. A new hybrid method where the concepts of modified differential approximation employed by blending discrete ordinate method and spherical harmonics method, has been developed for modeling the radiative transport equation. The finite volume method has been adopted as the numerical technique. The effect of various influencing parameters i.e., radiation-conduction parameter, surface emissivity, single scattering albedo and optical thickness has been illustrated. The compatibility of the method with regard to solving coupled conduction and radiation has also been addressed.     

Transient two-dimensional radiative and conductive heat transfer in an axisymmetric medium

This work considers transient conductive and radiative heat transfer in a two-dimensional, cylindrical, scattering medium heated or cooled by internal heat source or boundary surface. A finite difference scheme is employed for handling the energy storage and the heat diffusion by conduction, while a discrete-ordinate method is used to analyze the radiative heat transfer. The effects of various parameters, including the conduction-radiation parameter, the scattering albedo and the emissivity of the boundary surfaces, are investigated. Received on 30 April 1997     

An iterative method for temperature gradient measurements in two-dimensional thermal boundary layer flows by speckle photography

An iterative method for measuring two-dimensional refractive index fields induced by convective heat transfer phenomena is presented. Starting from the so-called correction parabola, this reconstruction technique takes into account the local second derivative variation of the refractive index field. The efficiency of the method is analytically defined as a function of non-dimensional parameter and numerically investigated using a ray-tracing code for different classic index profiles and a thermal boundary layer case. Finally, as an implementation test, this algorithm is applied to an impinging jet heat transfer experiment using speckle photography measurement data set. The results show a relative dispersion of 20% compared to the parabola reconstruction when the refractive index gradient becomes more severe.     

随机响应面法最优概率配点数目分析

系统地研究随机响应面法采用线性无关原则选取概率配点的优越性,给出了基于线性无关原则选取概率配点的流程图,比较了基于回归方法和基于线性无关原则选取概率配点的优缺点。算例结果表明,基于回归方法选取概率配点时,配点数目应保证Hermite系数矩阵达到满秩,此时随机响应面法的计算精度才能得到保证,计算效率也远远高于传统的蒙特卡洛模拟方法。基于线性无关原则选取概率配点的随机响应面法在保证计算精度的同时,其计算效率远远高于基于回归方法选取概率配点的随机响应面法,它是结构可靠度分析一种有效的方法,尤其适用于极限状态方程不能用显式函数表达的复杂结构可靠度问题。研究成果为随机响应面法最优概率配点数目的确定奠定了一定的基础。     

离散系统通用动力学方程求解算法的研究进展

离散系统中的颗粒物在凝并、破碎、冷凝/蒸发、成核、沉积等事件作用下颗粒尺度分布的时间演变由通用动力学方程所描述.该方程为一典型的部分积分微分方程,普通数值方法难以求解.本文详细介绍了求解通用动力学方程的矩方法、分区法、离散法、离散-分区法、MonteCarlo方法等几种算法的原理、优缺点和最新的研究进展,并着重介绍了MonteCarlo算法,包括基于时间驱动Monte Carlo方法、基于事件驱动MonteCarlo方法、常数目法、常体积法以及多重Monte Carlo算法.      

Wave scattering method for dynamic response analysis of structures with stochastic parameters

The wave scattering method is presented to analyze dynamic response of frameworks with stochastic parameters. First, with the uncertain physical, geometric, and loading properties in consideration, the stochastic waveguide equations containing the axial, torsional and flexural wave modes are established. Second, the stochastic wave scattering equation and wave translation matrix are derived to obtain the wave modes. Third, the methodology to extract the generalized displacements and forces from stochastic wave modes is proposed. Finally, a cantilever beam, a planar framework, and a space framework have been presented as numerical examples to illustrate the e?ciency of the proposed method. It is found that the results obtained by the proposed method with higher computational e?ciency show an excellent agreement with those by Monte Carlo simulation method. Furthermore, the influences of stochastic parameters on dynamic response are revealed.     

Effect of Radiation Scattering on the Dynamics of the Transitional Zone During Solidification of a Semitransparent Material

The effect of isotropic scattering in a two-phase zone on the velocity of boundaries, thickness of the transitional zone, and distribution of the solid phase over the two-phase zone thickness in the course of solidification of a semitransparent material is considered. A generalized model of phase transition in a semitransparent medium is used. The results of numerical calculations show that radiation scattering can exert a significant effect on the structure and size of the two-phase zone and also on heat transfer (temperature gradient) in the crystal being formed.     

Combined radiative and convective heat transfer in a three-dimensional rectangular channel at different wall temperatures

 This paper deals with a numerical study of combined convective and radiative heat transfer in a three-dimensional rectangular duct with hydrodynamically and thermally developing laminar flow. The gas is assumed to be an incompressible, absorbing, emitting, isotropically scattering, gray medium. Isothermal, gray, diffuse boundary walls at different temperatures are assumed. The finite-volume method (FVM) is adopted to describe both convective and radiative heat transfer. The coupled continuity and momentum equations are solved by means of SIMPLER algorithm. Numerical results for the radiative flux show very good agreement with the available data. The effects of aspect ratio, optical thickness, scattering albedo and wall emissivity on the mean bulk temperature are also investigated. By splitting the heat flux into convective and radiative contributions, the relative importance of these components is assessed for a typical range of values of the parameters. Received on 9 February 1999     

Radiation and laminar forced convection of non-Newtonian fluid in a circular tube

Interaction of radiation with thermally developing laminar forced convection of power-law, non-Newtonian, absorbing, emitting, isotropically scattering, gray fluid through an isothermal circular tube with a black boundary is investigated. The energy equation is solved by an implicit finite-difference scheme, while the radiation part of the problem is solved by the collocation method. Results are presented for the effects of conduction-to-radiation parameter, single scattering albedo, optical thickness and the inlet temperature on the local Nusselt number along the tube for the case of power-law index n=1/3, 1 and 3, where the case n=1 corresponds to the Newtonian fluid.     

Backscatter phase-Doppler anemometry for transparent non-absorbing spheres

The application of phase-Doppler anemometer for scattering angles between the main rainbow and direct backscatter, was examined by calculating the spatial intensity distribution and the phase of the light scattered by a particle crossing the measuring volume. Geometrical optics was assumed and contributions to the scattered light due to reflection on the external surface of the particle and first internal reflection were considered. The response curve of the technique was calculated for different particle refractive indices, beam intersection angles, collection angles and spacings between the collection apertures. Linear response curves were obtained after integration of the intensity of the scattered light over sufficiently large rectangular collection apertures, but they became non-monotonic after a critical value of phase shift, which varied with the optical arrangement between around 220° and 360°, did not scale with common scaling parameters used for forward scatter light, and limited the possible size range of the instrument for one optical arrangement. The particle refractive index determined the collection angle and limited sizing to particles with little uncertainty in refractive index, since a 5% change in refractive index led to uncertainties in size of the order of 100%. An alternative sizing technique is suggested for the backscatter region.     

Solution of Fixed Final State Optimal Control Problems via Simple Cell Mapping

A strategy is proposed to solve the fixed final state optimalcontrol problem using the simple cell mapping method. A non-uniform timestep simple cell mapping is developed to create a general database fromwhich solutions of various optimal control problems can be obtained. Atwo-stage backward search algorithm is proposed to eliminate degeneratedpaths often associated with the simple cell mapping. The proposed methodcan accurately delineate the switching curves and eliminate false limitcycles in the solution. The method is applied to two optimal controlproblems with bang-bang control. The well-known minimum time controlproblem of moving a point mass from any initial condition to the originof the phase plane is studied first. This example has exact solutionsavailable which provide a yardstick to examine the accuracy of themethod. The cell size dependence of the solution accuracy is studiednumerically. The second example is a variable stiffness feedback controlproblem with tuning range saturation. The strategy proposed is able toprovide the switching curves in the phase plane. This result has notbeen obtained before.     

Stochastic averaging method for estimating first-passage statistics of stochastically excited Duffing–Rayleigh–Mathieu system

The first-passage statistics of Duffing-Rayleigh- Mathieu system under wide-band colored noise excitations is studied by using stochastic averaging method. The motion equation of the original system is transformed into two time homogeneous diffusion Markovian processes of amplitude and phase after stochastic averaging. The diffusion process method for first-passage problem is used and the corresponding backward Kolmogorov equation and Pontryagin equation are constructed and solved to yield the conditional reliability function and mean first-passage time with suitable initial and boundary conditions. The analytical results are confirmed by Monte Carlo simulation.     

动力学平衡方程的辛两步求解算法

基于线性多步方法的构造格式和辛变换,给出了动力学方程的两种辛两步法求解格式,它们分别具有四阶精度和二阶精度,但都只有二阶格式的计算量,因此四阶辛两步法具有较大的应用价值。对两种辛两步法和解析解进行了数值比较,证明了二阶精度辛两步格式在一定条件下就是欧拉中点保辛算法,或δ=0.5和α=0.25的Newmark辛格式。     

First passage failure of quasi-partial integrable generalized Hamiltonian systems

The first passage failure of quasi-partial integrable generalized Hamiltonian systems is studied by using the stochastic averaging method. First, the stochastic averaging method for quasi-partial integrable generalized Hamiltonian systems is introduced briefly. Then, the backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the conditional mean of first passage time are derived from the averaged Itô equations. The conditional reliability function, the conditional probability density and mean of the first passage time are obtained from solving these equations together with suitable initial condition and boundary conditions, respectively. Finally, one example is given to illustrate the proposed procedure in detail and the solutions are confirmed by using the results from Monte Carlo simulation of the original system.     

结构随机分析的Monte Carlo加权残值法

本文提出一种结构随机分析的Monte Carlo加权残值法。文中建立了这种方法的基本列式,并通过静力挠度、固有频率和屈曲荷载等算例,表明本文方法理论简捷,计算工程量少,精度较高,是随机结构数值分析的有效方法。     

基于Novozhilov理论带隔板连续弯箱位移参数的动态Bayes估计

推导了基于Novozhilov理论的简支弯箱有限曲条控制方程,并结合柔度法解决了带隔板连续弯箱的求解问题。首次建立了带隔板连续弯箱位移参数的动态Bayes误差函数,推导了相应的动态Bayes均值和方差表达式,提出步长的一维自动寻优方案后,结合共轭梯度法研究了带隔板连续弯箱位移参数的动态Bayes估计方法,同时给出了带隔板连续弯箱位移参数具体估计步骤。通过典型算例分析,总结了带隔板连续弯箱位移参数先验信息准确性判定方法及位移参数动态Bayes随机估计的其它重要结论。