An optimized and accurate Monte Carlo method to simulate 3D complex radiative enclosures

The modeling of radiative heat transfer in complex radiant enclosures is a particularly challenging subject. This simulation is often best treated by calculating distribution factors through the Monte Carlo method. In order to enhance performance of the Monte Carlo method, efficient algorithms to find location of emission and direction of emission in the original Monte Carlo method are implemented. Next, the best ray tracing algorithm is introduced by comparing timing results of the USD, the BSP, the Simplex and the VVA acceleration ray tracing algorithms to make it numerically efficient as possible. Also, the constrained maximum likelihood estimation is used to enhance accuracy of the Monte Carlo by smoothing inherent random errors in the estimated distribution factors to simultaneously satisfy both of the reciprocity and summation rules. Accuracy of the Monte Carlo method is tested for a classical problem, namely a 3D box, with diffuse gray walls. For efficiency study, the optimized Monte Carlo method is then tested for two real radiative enclosures with convex and concave geometries. All ray tracing algorithms are found to result in computational gains, with respect to direct calculations that do not employ any acceleration technique. In the considered test cases, the VVA and the USD algorithms are found to be clearly superior to the BSP and the Simplex algorithms, particularly for concave geometries that have some obstructions within the computational domain.     

A FAST MONTE CARLO SCHEME FOR THERMAL RADIATION IN SEMICONDUCTOR PROCESSING APPLICATIONS

Thermal radiation is the most effective way for rapid thermal processing (RTP) and rapid thermal chemical vapor deposition (RTCVD) of wafers. It is well known in the semiconductor equipment design community that the Monte Carlo method for radiation is the only method that can accurately model radiative transport in RTP and RTCVD reactors. However, it has often been argued that it is expensive and difficult to use as a commercial design tool. In this article, a fast Monte Carlo scheme is presented. The basic algorithm is the classical surface-to-surface ray-tracing algorithm. In addition, a modified form of the binary spatial partitioning (BSP) algorithm is implemented to speed up ray tracing by at least a factor of 3. The results demonstrate a high level of accuracy with fairly low computational cost.     

基于逆向Monte Carlo法的腔内小接受体红外辐射传递研究

针对MC方法在计算三维大辐射腔内小接受体所受到辐射时存在的耗时长难收敛等问题,采用三维逆向能束跟踪MonteCarlo方法(BMC),结合CFD数值模拟技术,分析了不同介质参数以及燃烧工况下,腔体内不同高度上红外辐射能传感器所接受的辐射能特性,并与正向MC方法进行了对比。模拟计算结果表明:BMC方法对于处理小接受体大发射源辐射传递问题具有明显的时间优越性,同时该方法可以用于基于辐射能的腔体内燃烧过程分析。     

Signal processing,Sobol sequences and hot sampling: Calculation of incident heat flux distributions surrounding diffusion flames

The calculation of the incident heat flux distribution external to a jet fire is a challenging task due to the ray effect. In this paper a new adaptive stochastic quadrature method called hot sampling is described. The new methodology is applied to the incident heat flux distribution surrounding a lifted natural gas jet fire. Hot sampling is demonstrated to be significantly more efficient than other reverse Monte Carlo methods. The new quadrature scheme is also shown to be more efficient than the discrete transfer method, a radiation methodology in common use for jet fire simulation. Hot sampling is particularly appealing for problems where the ray effect is significant as the bigger the ray effect the bigger the benefit of using an adaptive stochastic quadrature scheme.     

Monte Carlo radiative transfer simulation of a cavity solar reactor for the reduction of cerium oxide

Radiative heat transfer in a solar thermochemical reactor for the thermal reduction of cerium oxide is simulated with the Monte Carlo method. The directional characteristics and the power distribution of the concentrated solar radiation that enters the cavity is obtained by carrying out a Monte Carlo ray tracing of a paraboloidal concentrator. It is considered that the reactor contains a gas/particle suspension directly exposed to concentrated solar radiation. The suspension is treated as a non-isothermal, non-gray, absorbing, emitting, and anisotropically scattering medium. The transport coefficients of the particles are obtained from Mie-scattering theory by using the optical properties of cerium oxide. From the simulations, the aperture radius and the particle concentration were optimized to match the characteristics of the considered concentrator.     

蒙特卡洛法模拟集热器入射面太阳辐射的算法研究

复杂几何形式的太阳集热器辐射分析一般采用射线跟踪法,模拟的太阳辐射仅考虑直射辐射的入射方向,不适用于精确的辐射分析。通过把集热器入射面作为太阳辐射的入射起始面,以蒙特卡洛法为基础模拟太阳辐射。通过考虑直射辐射、散射辐射、太阳辐射的光谱分布以及太阳辐射32/张角等影响因素,研究了模拟射线的辐射位置、辐射方向、波长分布及辐射能量的相关算法,并进行了数值计算验证。以上研究综合考虑了影响太阳辐射的因素,准确模拟了进入集热器入射面的太阳辐射,为太阳集热器精确的辐射分析提供了基础。     

基于模拟法下EENS值的系统可靠性裕度分析

随着电网向高压、远距离、大容量发展,对电网安全性要求日益显著,传统的N-1准则下可靠性计算已不能完全满足可靠性评估的要求.蒙特卡洛算法是一种概率随机抽样方法,利用该方法模拟系统状态,建立了参考状态序列,设计新的状态,并同参考状态比较,更加全面地反映系统压力和可靠性裕度,并利用期望缺供电量EENS作为可靠性指标来对系统的可靠性进行分析.     

附着液滴的玻璃层太阳辐射传递模型

针对液滴和玻璃层的太阳辐射传递特点,提出附着液滴玻璃层的太阳辐射传递模型。将入射的太阳辐射进行直散分离,基于蒙特卡洛射线追踪法对直射辐射光学性能进行计算,同时将入射角进行离散,分别在各角度范围内采用蒙特卡洛射线追踪法的直射辐射原理计算散射辐射光学性能。为了对模型进行验证,通过实验测试液滴覆盖率和太阳入射角对附着液滴玻璃层光学性能的影响,并与模型计算结果进行比较。结果表明：实验结果与计算结果差别较小,总透过率最大误差仅约为0.05,模型的准确性较高。附着液滴的玻璃层能有效降低太阳辐射透过率,且太阳辐射透过率随液滴覆盖率的增大而减小,随入射角的增大而减小。     

RADIATION ELEMENT METHOD FOR TRANSIENT HYPERBOLIC RADIATIVE TRANSFER IN PLANE-PARALLEL INHOMOGENEOUS MEDIA

In this study the radiation element method is formulated to solve transient radiative transfer with light radiation propagation effect in scattering, absorbing, and emitting media with inhomogeneous property. The accuracy of the method is verified by good agreement between the present calculations and Monte Carlo simulations. The sensitivity of the method against element size, ray emission number, and time increment size is examined. The transient effect of radiation propagation is essential in short-pulse laser radiation transport when the input pulse width is not considerably larger than the system radiation propagation time. The transient characteristics of radiative transfer are investigated in the media subject to collimated laser irradiation and/or diffuse irradiation withtemporal Gaussian and/or square profiles. The inhomogeneous profile of extinction coefficient of the medium affects strongly the transient radiative flux divergence inside the medium.     

Monte Carlo solution of anisotropic heat conduction

Based on the fixed-step random walk procedure a Monte Carlo algorithm for the solution of anisotropic heat conduction is presented. It is shown that the Monte Carlo solution is attainable only for a specified range of solid thermal conductivities. It is also illustrated that by following two simple clues considerable reduction in computation time may be achieved. Finally, steady-state temperature distribution, obtained by the Monte Carlo calculations, is presented for a two-dimensional anisotropic solid having simple geometry and boundary conditions.     

Discretized pressure Poisson algorithm for the steady incompressible flow on a nonstaggered grid

In the aspect of numerical methods for incompressible flow problems, there are two different algorithms: semi-implicit method for pressure-linked equations (SIMPLE) series algorithms and the pressure Poisson algorithm. This paper introduced a new discretized pressure Poisson algorithm for the steady incompressible flow based on a nonstaggered grid. Compared with the SIMPLE series algorithms, this paper did not introduce three correction variables. So, there is no need to implement the guess-and-correct procedure for the calculation of pressure and velocity. Compared with the pressure Poisson algorithm, there is no need to calculate unsteady Navier–Stokes equations for steady problems in the new discretized pressure Poisson algorithm. Meanwhile, as the finite volume method and cell-centered grid are used, the governing equation for pressure is obtained from the continuity equation and the boundary conditions for pressure are easily obtained. This new discretized pressure Poisson algorithm was tested at the lid-driven cavity flow problem on a nonstaggered grid and the results are also reliable.     

塔式太阳能腔体吸热器光热耦合模型与试验

基于蒙特卡洛方法建立光线追踪模型,利用CCD相机和朗伯板展开聚光实验,实验结果表明测量光斑与模拟光斑在大小、形状和能量分布上吻合良好。针对腔体吸热器提出光热耦合模型,考虑腔内不同吸热管之间的辐射换热,模拟结果与实验结果最大相对误差为8.6%。     

Combustion and heat transfer in model two-dimensional porous burners

A two-dimensional model of two simple porous burner geometries is developed to analyze the influence of multidimensionality on flames within pore scale structures. The first geometry simulates a honeycomb burner, in which a ceramic is penetrated by many small, straight, nonconnecting passages. The second geometry consists of many small parallel plates aligned with the flow direction. The Monte Carlo method is employed to calculate the viewfactors for radiation heat exchange in the second geometry. This model compares well with experiments on burning rates, operating ranges, and radiation output. Heat losses from the burner are found to reduce the burning rate. The flame is shown to be highly two-dimensional, and limitations of one-dimensional models are discussed. The effects of the material properties on the peak burning rate in these model porous media are examined. Variations in the flame on length scales smaller than the pore size are also present and are discussed and quantified.     

Simplex ray-object intersection algorithm as ray tracer for Monte Carlo simulations in radiative heat transfer analysis

In the thermal radiation analysis via Monte Carlo method, considerable computational resources are consumed to find the intersection point of an emitted energy bundle with radiant enclosure walls. Therefore, an efficient algorithm for ray-object intersection in complex geometries may cause saving time and computational effort. This paper presents a new ray-object intersection algorithm based on the well-known simplex method from linear programming. This algorithm works by searching a point in the feasible region which is defined by a set of plane equations of enclosure boundaries that maximize the line equation of the emitted energy bundle as the objective function. This algorithm is examined for two benchmark problems, namely two parallel plates with gray specular surfaces and a box with gray diffuse walls both in three-dimensional case. Although the computation time of the new proposed method is a bit higher than the conventional time, it is easy to implement because simplex algorithm is readily available as separate module in most programming languages. By using this algorithm number of objects which must be checked in complex geometries will be reduced considerably.     

Technical feasibility and economic viability of a small-scale grid connected solar thermal installation for electrical-energy saving

This paper reports on the techno-economic assessment of a grid-connected solar thermal system used for electrical-energy saving in the residential sector. The technical characteristics of the solar thermal system, based on a line-focus parabolic-trough concentrator, are given and its useful electrical and thermal-energy production is estimated using a simulation program based on a Monte Carlo method for reading solar radiation data. The economic assessment is performed using the Life-Cycle Savings (LCS) method and the payback period (PBP) of the investment's initial capital cost is determined.     

Modeling of the Dish Receiver With the Effect of Inhomogeneous Radiation Flux Distribution

In this work, a new modeling coupling the inhomogeneous radiation flux distribution for the dish receiver is proposed and developed. The radiation transmission and absorbing process of the dish concentrating system is achieved by using the Monte Carlo ray tracing method (MCRT method), which reveals the high-order nonuniformity of the irradiance flux distribution on the inner wall of the dish receiver. The implementation of the three-dimensional numerical simulation coupling the heat loss of the dish receiver is by combining the microscopic MCRT method and the macroscopic SIMPLE method. In addition, a coupled photon statistic method is established to ensure the accuracy of heat flux distribution computation. The modeling result reveals that the temperature distributions of the inner receiver surface are significantly influenced by the inhomogeneous radiation flux. The temperature of the high local heat flux density area that lies in the middle part of the inner surface reaches 1374.8 K, which is even higher than the top area. In addition, the combined heat losses from natural convection and surface radiation are analyzed and compared respectively. It is found that the surface radiation heat loss is the predominant heat loss pattern of the combined heat transfer, and the natural convection loss is sensitive to solar intensity and the orientation of dish cavity receiver but changes little with the emissivity of the inner surface.     

Bidirectionally weighted Monte Carlo method for radiation transfer in the participating media

A bidirectionally weighted Monte Carlo method has been developed for radiation transfer in participating media. For every two elementary cells, the radiation exchange is expressed as the weighted combination of those obtained from the forward and reverse Monte Carlo methods. And the weight is derived, so that the standard deviation of the radiation exchange is minimized, in contrast to the forward and reverse methods for the same computing cost. Moreover, this method can be applied to complex systems such as that containing highly spectral media. In benchmark solutions, the method was validated and results in less statistical errors than other types of Monte Carlo methods.     

High‐throughput computation and the applicability of Monte Carlo integration in fatigue load estimation of floating offshore wind turbines

Long‐term fatigue loads for floating offshore wind turbines are hard to estimate because they require the evaluation of the integral of a highly nonlinear function over a wide variety of wind and wave conditions. Current design standards involve scanning over a uniform rectangular grid of metocean inputs (e.g., wind speed and direction and wave height and period), which becomes intractable in high dimensions as the number of required evaluations grows exponentially with dimension. Monte Carlo integration offers a potentially efficient alternative because it has theoretical convergence proportional to the inverse of the square root of the number of samples, which is independent of dimension. In this paper, we first report on the integration of the aeroelastic code FAST into NREL's systems engineering tool, WISDEM, and the development of a high‐throughput pipeline capable of sampling from arbitrary distributions, running FAST on a large scale, and postprocessing the results into estimates of fatigue loads. Second, we use this tool to run a variety of studies aimed at comparing grid‐based and Monte Carlo‐based approaches with calculating long‐term fatigue loads. We observe that for more than a few dimensions, the Monte Carlo approach can represent a large improvement in computational efficiency, but that as nonlinearity increases, the effectiveness of Monte Carlo is correspondingly reduced. The present work sets the stage for future research focusing on using advanced statistical methods for analysis of wind turbine fatigue as well as extreme loads. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical Calculation of the Effective Thermal Conductivity of Nanocomposites

The effective thermal conductivity (K _eff) of carbon nanotube (CNT) composites is affected by the thermal boundary resistance (TBR), the dispersion pattern, and geometry distribution of the CNTs. Traditional effective medium theories assume that CNTs are perfectly dispersed without considering TBR. In this work, we report the development of a new algorithm using CNTs with 3-D worm-like geometry and different persistence lengths. We describe how to obtain K _eff using simulations of these realistic CNT configurations with off-lattice Monte Carlo simulation. The results are compared with straight cylinder models without effects of persistence length.     

Multi-stage power source and grid coordination planning method considering grid uniformity

Given the increasing uncertainties in power supply and load, this paper proposes the concept of power source and grid coordination uniformity planning. In this approach, the standard deviation of the transmission line load rate is considered as the uniformity evaluation index for power source and grid planning. A multi-stage and multi-objective optimization model of the power source and grid expansion planning is established to minimize the comprehensive cost of the entire planning cycle. In this study, the improved particle swarm optimization algorithm and genetic algorithm are combined to solve the model, thus improving the efficiency and accuracy of the solution. The analysis of a simple IEEE Garver’s 6-node system shows that the model and solution method are effective and feasible. Moreover, they are suitable for the coordinated planning of the power source and grid under a diversified nature of power supply and load.