Computation of direct intensity and medium intensity by using the discrete ordinates method

On the basis of the discrete ordinate scheme with (an) infinitely small weight(s), an easy-to-use and comprehensive method, named multi-rays method, is developed to calculate total, direct and medium intensities in arbitrarily specified directions. In doing this, for each of the specified directions, three identical discrete directions with infinitely small weights are employed to represent the three intensities. The new method is verified with two standard test problems, and is used to compute the intensities in two anisotropically scattering problems.     

On the use of a meshless method for solving radiative transfer with the discrete ordinates formulations

A meshless method is presented for solving the radiative transfer equation in the discrete ordinates approach. It is shown that the primitive variables formulation is unstable for low values of the absorption coefficient while the even parity formulation is always stable and accurate.     

Heat transfer characteristics of a porous radiant burner under the influence of a 2-D radiation field

This paper deals with the heat transfer analysis of a 2-D rectangular porous radiant burner. Combustion in the porous medium is modelled as a spatially dependent heat generation zone. The gas and the solid phases are considered in non-local thermal equilibrium, and separate energy equations are used for the two phases. The solid phase is assumed to be absorbing, emitting and scattering, while the gas phase is considered transparent to radiation. The radiative part of the energy equation is solved using the collapsed dimension method. The alternating direction implicit scheme is used to solve the transient 2-D energy equations. Effects of various parameters on the performance of the burner are studied.     

The method of lines solution of discrete ordinates method for radiative heat transfer in cylindrical enclosures

A radiation code based on method of lines solution of discrete ordinates method for radiative heat transfer in axisymmetric cylindrical enclosures containing absorbing-emitting medium was developed and tested for predictive accuracy by applying it to (i) test problems with black and grey walls (ii) a gas turbine combustor simulator enclosing a non-homogeneous absorbing-emitting medium and benchmarking its steady-state predictions against exact solutions and measurements. Comparisons show that it provides accurate solutions for radiative heat fluxes and can be used with confidence in conjunction with CFD codes based on the same approach.     

The discrete ordinates method for anisotropic scattering in the neutron transport theory: The critical sphere problem

The spherical harmonics method for anisotropic scattering in the neutron transport theory related to the critical sphere problem was investigated by Yildiz [The spherical harmonics method for anisotropic scattering in neutron transport theory: the critical sphere problem. JQSRT 2001;71:25-37]. Some numerical results and figures that they provided are incorrect. The correct numerical results for the critical radius are obtained and tabulated for different scattering parameters by using the discrete ordinates method.     

高效偶阶离散纵标法研究及初步验证

采用TAKEDA基准题验证高效偶阶离散纵标法(HEPSN)的临界计算功能,数值结果表明：有效增殖因数和各区域平均中子通量密度值与基准值吻合良好,堆芯区域的平均中子通量密度误差在0.7%以内,其他区域较扩散理论误差显著减小。相较于传统离散纵标法,HEPSN计算效率更高,需要的存储更小;相较于扩散理论,HEPSN的计算精度更高。因而,高效偶阶离散纵标法在大规模输运计算中具有很好的应用前景。     

The method of lines solution of discrete ordinates method for non-grey media

A radiation code based on method of lines (MOL) solution of discrete ordinates method (DOM) for radiative heat transfer in non-grey absorbing-emitting media was developed by incorporation of a gas spectral radiative property model, namely wide band correlated-k (WBCK) model, which is compatible with MOL solution of DOM. Predictive accuracy of the code was evaluated by applying it to 1-D parallel plate and 2-D axisymmetric cylindrical enclosure problems containing absorbing-emitting medium and benchmarking its predictions against line-by-line solutions available in the literature. Comparisons reveal that MOL solution of DOM with WBCK model produces accurate results for radiative heat fluxes and source terms and can be used with confidence in conjunction with computational fluid dynamics codes based on the same approach.     

A theoretical study of radiation between two concentric spheres using a modified discrete ordinates method associated with Legendre transform

A modified discrete ordinates method (DOM) is used in spherical participating media. The radiative intensity is broken up into two components. One component is traced back to the enclosure's source. It is called direct intensity. The other component is rather traced back to the contribution of the medium itself. It is called diffuse intensity. Thus, the radiative transfer equation (RTE) is transformed into two simultaneous equations: a direct RTE and a diffuse RTE. The direct RTE is solved analytically. The diffuse RTE is solved numerically using the DOM. The streaming angular derivative term appearing in spherical geometry is modeled by making use of the Finite Legendre Transform. We study a pure radiation transfer problem between two concentric spheres. The medium is assumed to be gray and isotropically scattering. The limiting spheres are considered to be opaque, gray, diffusely emitting and diffusely reflecting with uniform emissivity over each surface. The obtained results are compared with available cases reported in the literature. In particular, relative importance of the direct radiation in optically thin media is studied.     

GPU accelerated simulations of 3D deterministic particle transport using discrete ordinates method

Graphics Processing Unit (GPU), originally developed for real-time, high-definition 3D graphics in computer games, now provides great faculty in solving scientific applications. The basis of particle transport simulation is the time-dependent, multi-group, inhomogeneous Boltzmann transport equation. The numerical solution to the Boltzmann equation involves the discrete ordinates (S_n) method and the procedure of source iteration. In this paper, we present a GPU accelerated simulation of one energy group time-independent deterministic discrete ordinates particle transport in 3D Cartesian geometry (Sweep3D). The performance of the GPU simulations are reported with the simulations of vacuum boundary condition. The discussion of the relative advantages and disadvantages of the GPU implementation, the simulation on multi GPUs, the programming effort and code portability are also reported. The results show that the overall performance speedup of one NVIDIA Tesla M2050 GPU ranges from 2.56 compared with one Intel Xeon X5670 chip to 8.14 compared with one Intel Core Q6600 chip for no flux fixup. The simulation with flux fixup on one M2050 is 1.23 times faster than on one X5670.     

Finite element formulation of the first- and second-order discrete ordinates equations for radiative heat transfer calculation in three-dimensional participating media

Two finite element methods (FEMs), FEDOM1 and FEDOM2 (standing for the first and the second finite element discrete ordinates methods, respectively), are formulated and numerically tested. The reference second-order discrete equation is modified in its scattering terms and is applied to the problems of absorbing/emitting and anisotropically scattering media by using the FEM. Numerical features of the developed FEMs are compared with one of the discrete ordinates interpolation method (DOIM), which uses a finite difference scheme. Prediction results of radiative heat transfer by these two FEMs are compared with reference solutions and verified in three-dimensional enclosures containing participating media. The results of FEDOM1 and FEDOM2 agree well with exact solutions for the problem of absorbing/emitting medium with various range of optical thickness. Generally, the two FEMs show more accurate results than DOIM. And FEDOM1 shows more accurate results than FEDOM2 in most of the test problems. Both of the developed FEMs show reasonable results compared with published Monte Carlo solutions for the tested absorbing/emitting and anisotropically scattering media. Although the FEDOM2 is not as accurate as the FEDOM1, it shows its own advantages that it reduces CPU time and memory space of dependent variable to half.     

Analysis of collimated radiation in participating media using the discrete transfer method

A general formulation of the discrete transfer method is provided to analyze radiative heat transfer problems in a participating medium subjected to collimated radiation. The formulation is validated by considering 1-D planar absorbing, emitting and anisotropically scattering gray medium in radiative equilibrium. Anisotropy of the medium is approximated by linear anisotropic phase function. For the purpose of comparison, the problem is also solved analytically. Results are obtained for different angles of incidence of the collimated radiation. At a given angle of incidence, results are obtained for forward, isotropic and backward scattering situations. Heat flux results are compared over a wide range of values of the extinction coefficient. Emissive power distributions in the medium are also obtained for some cases. The discrete transfer method results are found to compare very well with the analytic results.     

Application of multidimensional scheme and the discrete ordinate method to radiative heat transfer in a two-dimensional enclosure with diffusely emitting and reflecting boundary walls

Radiative heat transfer is the dominant mode of heat transfer in many engineering problems, including combustion chambers, space, greenhouses, rocket plume sensing, among others. The aim of this study is to develop an efficient method capable of eliminating ray effects in complex 2D situations and to use the developed code for other problems including combined conduction and convection in connection with CFD codes. A complete genuinely multidimensional discretization in two-dimensional discrete ordinates method is formulated to solve radiative heat transfer in a rectangular enclosure composed of diffusely emitting and reflecting boundaries and containing homogeneous media that absorbs, emits and scatters radiation. A new genuinely multidimensional differencing scheme is used to solve the radiative transfer equation with S₄, S₆, S₈, T₆, T₇, T₈ and T₉ angular quadrature schemes. Different cases are analyzed and the results are compared when possible with those obtained by others researchers.     

Discrete ordinates interpolation method incorporated into a flow and energy solver for solution of combined heat transfer problems

Combined conduction-radiation and natural convection-radiation in two-dimensional enclosures containing gray absorbing/emitting medium are numerically investigated. The discrete ordinates interpolation method (DOIM) is used to solve the radiative transfer equation (RTE). It is incorporated into a commercial software (FLUENT^®) by using user-defined function (UDF) to be used in a finite volume-based code for fluid flow computation. Two issues are critically examined: accuracy and versatility. Cases of combined conduction-radiation are considered first and the results are compared with other benchmark solutions to validate the accuracy. Additional problems are also tested to verify the capability of handling unstructured grid system and irregular geometry. Combined natural convection-radiation problem is then examined varying the optical thickness. The radiation effect is investigated through the profiles of velocity, temperature distributions and streamlines. The results are compared with discrete ordinates (DO) solutions, Rosseland solutions and P1 solutions which are offered by FLUENT^® package. The accuracy and other numerical characteristics of DOIM are scrutinized. The DOIM shows very successful results from the viewpoint of accuracy and grid compatibility. It is proved to be a reliable future numerical tool for combined heat transfer problems in engineering applications.     

Modeling of nanoshells spectra in evanescent wave field via discrete sources method

Simple, fast and flexible computer model to analyze optical spectra of individual nanoshells deposited on a prism surface has been developed. It is based on rigorous theory of discrete sources method and enables to account for complete interaction between scatterer and prism surface analytically. Model is implemented to examine local biosensor operation in a field of evanescent waves.     

颜色失真二维彩色条形码的自适应阈值机读法

采用紫外辐照加速老化方法研究纸基彩色条形码的褪色规律。基于CIELAB模型分析紫外辐照累计时间与二维条形码色差的关系，对4色打印标签的检测结果表明：品红色褪变速率较大，青色、黄色和黑色的褪变速率逐次减小。基于RGB三基色直方图和概率统计原理，提出能有效校正颜色失真、正确机读二维条形码的“自适应阈值法”。实验表明：对于紫外25h加速老化后的褪色条形码，“自适应阈值法”的机读误码率≤0.05%。该研究结果为褪色彩色条形码标签进入实用阶段提供了实验依据。     

Observation of molecular migration in porous media using 2D exchange spectroscopy in the inhomogeneous magnetic field

We present a new method for observing fluid diffusion in a porous medium. The method employs 2D exchange spectroscopy for molecules diffusing in the presence of local magnetic field inhomogeneities, in our case distilled water in various sized glass bead packs. Our experiment involves an acquisition and evolution time domain with the two Fourier domains corresponding to the spectral distribution of local fields. We show that exchange in the internal magnetic field can be seen in a 2D spectrum with a characteristic time on the order of that required to diffuse 0.15 sphere diameters with similar behavior found for computer simulations. The method is potentially useful for studying the internal migrations in more complicated systems such as sandstones or other porous media.     

Modeling a sensitive pressure and temperature sensor using rectangular PCF by 2-D FDTD technique

We propose a sensitive pressure and temperature sensor depends on hollow core rectangular photonic crystal fiber. The proposed modeling is carried out by implementing 2-D finite difference time domain (FDTD) method. The two parameters like pressure and temperature plays a vital role in reservoir engineering to increase the production rates of oil well and our sensor technique is depend on the transmission peak wavelength shift which is caused by temperature/pressure change, and geometrical parameter of the structure of rectangular PCF. Here we have done simulation for various work using 2-D FDTD method application to sensing. We have shown the proposed design which provides the sensitivity with linear dependence of the resonance wavelength over refractive index of PCF holes at a operating wavelength of 1.55 μm.     

物体内部三维位移场分析的数字图像相关方法

提出了物体内部三维位移场的数字图像相关分析方法，对物体变形前后，或连续变形的两个相邻状态的内部三维结构的数字图像，通过相关运算获得三维位移场.文中给出了三维相关法的体搜索窗口、相关函数及亚像素运算的相关系数拟合函数.数字模拟结果证明了三维相关法的正确性及可靠性.位移计算精度为0.02像素. 关键词： 数字图像相关 三维相关 亚像素     

Real-time analysis of 3-D axisymmetric refractive index field by photorefractive holographic interferometry

A real-time test method for determining the refractive index distributions of 3-D axisymmetric temperature field around a flame with the use of a photorefractive holographic interferometer is proposed. Some techniques in data processing for improving the quality of resultant interferogram are developed. Experimental results, which show the effectiveness of this method and agree with theoretical expectations, are also given.     

电磁发射复合型结构拦截弹的3维电磁场有限元建模与仿真

为了达到拦截弹的连续发射、提高拦截效果和加固驱动线圈的目的,提出了一种复合型结构的拦截弹.在建立数学模型时,基于麦克斯韦方程组,对非铁磁材料区域、铁磁材料区域、空间区域等求解区采用矢量磁位和标量磁位来描述3维电磁场,并采用Ansoft有限元分析软件中的MAXWELL3D模块对新型结构拦截弹的电磁场和涡流场分布情况进行了...