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In this paper, the reliability analysis and residual life assessment model of gas pipelines with multiple corrosion pits are established. Aiming at the simulation evaluation of small failure probability of gas pipelines, a new method for reliability analysis and residual life assessment of gas pipelines with multiple internal corrosion pits is proposed, which is called the Hamiltonian Monte Carlo subset simulation (HMC-SS) method. Compared with the traditional MCS (Monte Carlo simulation) algorithm, the HMC-SS method has the advantages of less sampling, low cost, and high accuracy. And compared with the random walk SS method, the HMC-SS method can analyze the state space more efficiently and achieve faster convergence. In this paper, the HMC-SS method is applied to the reliability analysis and residual life assessment of gas pipeline engineering, and the sensitivity analysis of the random parameters affecting the failure probability of the pipeline is carried out. The results show that the corrosion rate, the depth of corrosion defects, and the wall thickness of the pipeline have great influence on the residual life of the pipeline, while the yield strength, working pressure, and the length of corrosion pits have no obvious influence on the failure probability and residual life of the pipeline. The analysis shows that the proposed HMC-SS method can be used as a reasonable tool for failure assessment of natural gas pipelines affected by corrosion to determine the remaining life of the pipeline system. This method provides a reliable theoretical basis for the integrity management of the gas pipeline.

Monte Carlo method (MCM) and finite volume method (FVM) are integrated to deal with combined conduction-radiation heat transfer problems in irregular geometries containing gray semitranspar...

A numerical model for evaporation along with internal radiation absorption of a non-spherical droplet is presented. In this model, the VOF method is utilized to trace the interface and the radiative transfer is taken into account by using the Monte Carlo method combined with a contour based interface reconstruction algorithm. Meanwhile, the dynamic mesh technique is applied to increase the computational efficiency. The validated model is used to investigate the radiation absorption inside prolate and oblate water droplets under infrared laser irradiation, and a parametric study for the effects of droplet’s shape and size is presented. The results reveal that the shape of droplet dominates the spectral absorptance when the droplet’s optical thickness is small, but for optically thick droplets, the radiation absorption turns to be dominated by the spectral reflectivity of the irradiated surface. For a deformable droplet under asymmetrically radiative heating, the incident radiation can significantly enhance the heat transfer and evaporation processes. In addition, the assumption of uniform radiation absorption is found to be valid to optical thin droplets, whereas this assumption will underestimate the average interface temperature and evaporation rate of droplets with large optical thickness.

This study aims to fully investigate the volumetric radiative properties of irregular open-cell foams made from semitransparent absorbing-scattering media such as ceramics. A Monte Carlo ray-tracing model was established in the limit of geometric optics to extract volumetric radiative properties of foams generated by a Voronoi tessellation technique. Three shape parameters for struts were proposed to mimic real struts. It was found that for extinction coefficient, the most influent parameters are porosity, mean cell diameter, and cross-sectional shape. For scattering albedo, it no longer depends on the surface reflectivity of solid struts but on the component radiative properties and strut shape parameters. Similarly, the scattering phase function no longer depends on the local reflection type but on an integrated contribution of the surface reflection, interface refraction, and volumetric radiation propagation inside the struts. The asymmetry factor is found closely related to the transparency of struts. Using the component radiative properties and structural parameters as input parameters, three analytical relations were established to respectively predict the extinction coefficients, scattering albedos, and asymmetry factors, which can be useful for the design and application of open-cell foams made from semitransparent media.

A novel integrated simulation of radiative transfer in metal foams is presented. It integrates the continuous-scale simulation with the direct discrete-scale simulation in a single computational domain. It relies on the coupling of the real discrete-scale foam geometry with the equivalent continuous-scale medium through a specially defined scale-coupled zone. This zone holds continuous but nonhomogeneous volumetric radiative properties. The scale-coupled approach is compared to the traditional continuous-scale approach using volumetric radiative properties in the equivalent participating medium and to the direct discrete-scale approach employing the real 3D foam geometry obtained by computed tomography. All the analyses are based on geometrical optics. The Monte Carlo ray-tracing procedure is used for computations of the absorbed radiative fluxes and the apparent radiative behaviors of metal foams. The results obtained by the three approaches are in tenable agreement. The scale-coupled approach is fully validated in calculating the apparent radiative behaviors of metal foams composed of very absorbing to very reflective struts and that composed of very rough to very smooth struts. This new approach leads to a reduction in computational time by approximately one order of magnitude compared to the direct discrete-scale approach. Meanwhile, it can offer information on the local geometry-dependent feature and at the same time the equivalent feature in an integrated simulation. This new approach is promising to combine the advantages of the continuous-scale approach (rapid calculations) and direct discrete-scale approach (accurate prediction of local radiative quantities).

The apparent radiative behaviors of open cell nickel foams and their dependency on textural features and intrinsic optical properties are numerically investigated in the limit of geometrical optics. Five realistic nickel foams with high porosity from 0.87 to 0.97 and pore density from 10 to 40 PPI were used as samples. First, the representations of foams and their microstructures were obtained by using computed tomography and scanning electron microscope techniques. Second, a Backward Monte Carlo method that employed the realistic representations and their intrinsic optical properties facilitated the computation of the apparent directional spectral emissivity. The apparent emissivity and its dependency on textural features and intrinsic optical properties were subsequently investigated based on a specially defined Representative Elementary Volume. It was noted that at pore scale, the non-homogenized apparent emissivity fields can vary according to the local compositions near to the foam surface (solid strut and void space) and the void pore behaves somewhat like a “black cavity” for thermal radiation. For open cell foams composed of low emittance nickel struts, high-porosity cell network may increase the intrinsic emissivity by a maximum of nearly 4 times. A predictive relationship was established that links the homogenized apparent emissivity to the open porosity and the intrinsic emissivity of solid struts. These findings will provide a deeper understanding of both the non-homogenized and homogenized radiative behaviors of open cell foams.

Open-cell foams consisting of interconnected struts are widely used in thermal applications such as volumetric solar receivers. The thermal performance of foams strongly relies on their radiative behaviors which intrinsically depends on the radiative properties of struts. This study proposed a feasible approach to determine the radiative properties of solid struts by a pore scale identification from a macro scale measurement. First, the normal-hemispherical transmittance and reflectance spectra of two nickel foams were measured by an experimental system. Second, a pore scale forward calculation was conducted by a combination of Monte Carlo Ray-tracing method and real foam structures obtained from micro-computed tomography technique. Last, an Adaptive Particle Swarm Optimization algorithm was adopted to retrieve the spectral reflectivity and specularity of nickel struts from the measured spectra. The results show that it is unreasonable to assume the reflection behavior of strut surface simply as either specular or diffused, and also, it is unreliable to assign the reflectivity of strut surface directly by Fresnel's law. Within the investigated wavebands 0.4–2.2 μm, the average reflectivity of nickel struts is 12% lower than that of a nickel mirror. The proportion of specular reflection at nickel strut surface is between 37%–52%, almost increasing with wavelengths.

In this work, with all the characteristic morphologies considered, a numerical method for achieving the prediction of radiative properties of open-cell metal foam integrating different scales is presented. For the modeled micro-scaled rough ligament surface, the FDTD method is adopted for predicting the radiative properties of ligament surface elements. Meanwhile, at macro scale, the metal foam sheet is reconstructed by the CT technique, and the radiative properties of reconstructed foam sheet are numerically calculated with the Monte Carlo method. In the procedure of applying the introduced method, the radiative parameters of ligament surface elements, including the directional-hemispherical reflectivity and specularity parameter, are extracted from radiative properties of ligament surfaces. Then, these radiative properties are used for achieving the further numerical prediction of radiative behaviors of metal foams. The integrated-scale prediction of radiative properties of open-cell metal foam is accomplished by the introduced method, which integrates microscopic morphology of ligament surface and macroscopic solid ligament network. Furthermore, the presented method is applied for calculating the spectral radiative properties of nickel foams. The presented method is proven to be valid by comparing with experimental results. Additionally, the effects on the radiative properties caused by incident wavelength and angle are discussed.

A pore scale model was established to investigate the high-temperature radiative properties of carbon foams with high porosity. Voronoi Tessellation for the random structure of carbon foams and Monte Carlo ray-tracing method was employed to simulate the apparent radiative behaviors and volumetric radiative properties. By compared with the measured data at room temperature in Ref. (Celzard et al., 2012), the numerical model was verified to possess a high precision, which the maximum deviation are 1.8% for normal absorptance, 0.3% for normal-hemispherical transmittance and 1.5% for normal-hemispherical reflectance, respectively. It is also acceptable for the simulated results of volumetric radiative properties. Based on the spectral radiative properties of carbon basic material found in Ref. (Touloukian and DeWitt, 1972), the spectral radiative properties of carbon foam sheets at high temperature between 1183 K and 2073 K were predicted. It was found that absorptance is dominant in the apparent radiative behaviors of carbon foams at high temperatures with a wavelength of 0.665 μm. Then, the bidirectional reflectance distribution function was numerically investigated. The results showed a backward scattering of the reflected energy at the foam sheet surface and reflected energy peaks are always located at around respective incident angles. For volumetric radiative properties at high temperatures, extinction coefficient ranged between 200 m−1 and 450 m−1, which had been verified with relation formula in an error of less than 1%. In addition, scattering albedo and scattering phase function were not only simulated but also compared with the empirical formulas, to some extent, agreed well with them.

Open-cell metallic foams are increasingly used in various thermal systems. The temperature distributions are significant for the comprehensive understanding of these foam-based engineering applications. This study aims to numerically investigate the modeling of the infrared surface temperature (IRST) of open-cell metallic foam measured by an infrared camera placed above the sample. Two typical approaches based on Backward Monte Carlo simulation are developed to estimate the IRSTs: the first one, discrete-scale approach (DSA), uses a realistic discrete representation of the foam structure obtained from a computed tomography reconstruction while the second one, continuous-scale approach (CSA), assumes that the foam sample behaves like a continuous homogeneous semi-transparent medium. The radiative properties employed in CSA are directly determined by a ray-tracing process inside the discrete foam representation. The IRSTs for different material properties (material emissivity, specularity parameter) are computed by the two approaches. The results show that local IRSTs can vary according to the local compositions of the foam surface (void and solid). The temperature difference between void and solid areas is gradually attenuated with increasing material emissivity. In addition, the annular void space near to the foam surface behaves like a black cavity for thermal radiation, which is ensued by copious neighboring skeletons. For most of the cases studied, the mean IRSTs computed by the DSA and CSA are close to each other, except when the material emissivity is highly weakened and the sample temperature is extremely high.

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 c...

Monte Carlo ray-tracing method has become a promising technique for solving radiative transfer. However, large memory footprint or long CPU time hampers its further utilization. In this work, a Monte Carlo ray-tracing method radiation solver called mcrtFOAM is developed in the framework of open source CFD toolbox OpenFOAM. The radiative source term is calculated based on the radiation distribution factor to avoid repeated ray tracing. In addition, a mesh-agglomeration technique is used to overcome the problem of memory catastrophe for storing a huge radiation distribution factor matrix caused by a large number of mesh elements. The key principle is to agglomerate the refined mesh elements to the coarse ones, and the calculation of radiation distribution factor as well as radiative source term is carried out in the coarse mesh, while the procedure of ray tracing as well as solving the heat conduction is performed in the refined mesh. After validation of the algorithm code within a cubic enclosure, a coupled conductive–radiative heat transfer problem within a cylindrical enclosure filled with gray semitransparent solids is also tested. To test the present solver in realistic industrial systems, a coupled conductive–radiative heat transfer within a tomographic porous structure with gray surfaces is further investigated. All results are compared with previous studies and the solutions by the Finite Volume Discrete Ordinate Method (FVDOM) in OpenFOAM, and they all show great satisfaction. When the mcrtFOAM solver is used for solving the radiative transfer equation, it is found that the CPU time and the memory footprint consumed by the present mcrtFOAM solver with mesh-agglomeration technique are far less than that without this technique. Convincing first implementation exercises indicate that both significant memory and CPU benefits can be expected for configurations of industrial interest These findings will contribute greatly to achieve the calculation of coupled heat transfer involving radiation within large number of mesh elements.

Coupled radiation-convection heat transfer inside a unit metal foam layer with high-flux irradiation is studied using improved scale-integrated simulation. It integrates the discrete-scale CFD simulation with that of continuum-scale via the multi-domain concept with thermal radiation effect considered. Conservations of mass flux and energy are satisfied on these specified subdomain interfaces, and a special defined transition zone with geometry-dependent functional quantities is introduced within the continuum-scale subdomain. This zone is adjacent to the discrete-scale subdomain which ensures a reasonable transition. Absorbed radiative fluxes and radiative heat transfer within the whole domain are calculated with Monte Carlo method and treated as heat sources. The problem under consideration has been investigated via the discrete-scale simulation, the continuum-scale simulation, and the scale-integrated simulation. The accurateness of scale-integrated simulation has been fully validated for predicting both flow field and heat transfer characteristics in comparison with the outcomes of discrete-scale simulation and other investigations. Deviations between the outcomes of continuum-scale simulation and discrete-scale simulation are found to be mainly caused by inconsistent local absorbed radiative heat fluxes distribution and impinging effect around the entry region. Up to 70% and 60% reduction of computation time and memory footprints are achieved when scale-integrated strategy is employed for the CFD simulation compared with the discrete-scale simulation. Meanwhile, the detailed fluctuated characteristics of the local concerned region and overall heat transfer performance can be precisely reflected. It may break up the computation limitations of the discrete-scale simulation in studying the energy transport process in foam based solar receiver applications.

To investigate the transmission performances of solar windows subjected to concentrated sunlight, an integrated sunlight transferring model was built, which was formed by a dish and a curved surface window. Considering the dish performances and the window materials, the transmissivity of the windows was predicted by the Monte Carlo ray-tracing method (MCRTM). The results show that the transmissivity of the quartz glass window is about 12.0% higher than that of the sapphire window because the refractive index and the absorption coefficient of the quartz glass is lower than that of the sapphire. For a combined dish and window system, the influences of the window geometries on the transmissivity are negligible. However, decreasing the slope errors and tracking errors of the dish is able to improve the transmission performances of the windows.

A Modified Monte-Carlo Method (MMCM) in which phonon bundles take non-energy is developed to model the steady state phonon radiative transfer in nanoscale materials. Heat transfer in silicon thin films is analyzed to examine the validity of the developed method. The temperature distributions and cross-plane thermal conductivity are determined by using the developed method for the silicon thin films and compared with the results in reference. The results indicate that the developed method has a good accuracy in solving the phonon radiative transfer in nanoscale materials. In addition, numerical accuracy can be improved by the increase of the number of samples in the simulations.

An energy transfer and conversion model for high-temperature solar cavity receivers has been developed using the transport behaviour of solar radiation as described by the spectral radiative exchange factors. A Monte-Carlo ray-tracing method coupled with optical properties was adopted, to predict radiation characteristics of the solar collector system by calculating radiative exchange factors. A cavity receiver with a plano-convexo quartz window was proposed, based upon the directional characteristics of the focal flux and the redistribution effect of the quartz window. Parametric studies on the windowed receiver provided a more uniform flux distribution, higher efficiency and lower loss than the windowless receivers. The predicted results serve as a design reference for the solar receivers or reactors in high-temperature applications.

The Monte Carlo ray-tracing method is applied and coupled with optical properties to predict the radiation performance of solar concentrator/cavity receiver systems. Several different cavity geometries are compared on the radiation performance. A flux density distribution measurement system for dish parabolic concentrators is developed. The contours of the flux distribution for target placements at different distances from the dish vertex of a solar concentrator are taken by using an indirect method with a Lambert and a charge coupled device (CCD) camera. Further, the measured flux distributions are compared with a Monte Carlo-predicted distribution. The results can be a valuable reference for the design and assemblage of the solar collector system.

A three-dimensional (3-D) Monte Carlo model is developed for predicting electrical conductivity of polymer matrix composites filled with conductive curved fibers. The conductive fillers are modeled as a 3-D network of finite sites that are randomly positioned. The percolation behavior of the network is studied using the Monte Carlo method, which leads to the determination of the critical fiber volume fraction (or the percolation threshold). The effect of fiber curliness on the percolation behavior is incorporated in the current model by using 3-D arm-shaped fibers, each of which needs five independent geometrical parameters (i.e., three coordinates for its vertex and two orientation angles) for its identification. There are three controlling parameters for such fibers, namely the fiber arm length, the fiber aspect ratio, and the fiber arm angle. The new model also considers the sample size and scaling effects. The simulation results reveal an exponential relationship between the fiber aspect ratio and the percolation threshold: the higher the aspect ratio, the lower the threshold. It is also found that the curliness largely influences the percolation threshold: the more curved the fiber, the higher the threshold. However, the effect of curliness diminishes with the increase of the fiber aspect ratio. With the percolation threshold obtained from the Monte Carlo model, the effective electrical conductivity of the composite is then determined by applying the theory of percolation. The numerical results indicate that the composite conductivity decreases as the fibers become more curved and as the fiber aspect ratio decreases. These predicted trends of the percolation threshold and composite conductivity are in good agreement with existing experimental and simulation results.

By discretizing the medium into many sublayers and employing a linear refractive index approximation for each sublayer, a curve Monte Carlo method is developed to solve the radiative heat transfer in an absorbing and scattering gradient-index medium. The probability models for emission point and radiation transfer path samplings are derived. For an absorbing and isotropic scattering medium with a sinusoidal refractive index distribution, the effects of optical thickness, boundary characteristics, and isotropic scattering on radiative equilibrium temperature and radiative heat flux in the medium are investigated by the method. From the analysis, some valuable information is obtained.

The surface infrared radiation is an important part that contributes to the infrared image of the airplane. The Monte Carlo method for the infrared image calculation is suitable for the complex geometry of targets like airplanes. The backward Monte Carlo method is prior to the forward Monte Carlo method for the usually long distance between targets and the detector. Similar to the non-gray absorbing media, the random number relation is developed for the radiation of the spectral surface. In the backward Monte Carlo method, one random number that reverses the wave length (or wave number) may result deferent wave numbers for targets’ surface elements on the track of a photon bundle. Through the manipulation of the densities of a photon bundles in arbitrary small intervals near wave numbers, all the wave lengths corresponding to one random number on the targets’ surface elements on the track of the photon bundle are kept the same to keep the balance of the energy of the photon bundle. The model developed together with the energy partition model is incorporated into the backward Monte Carlo method to form the spectral backward Monte Carlo method. The developed backward Monte Carlo method is used to calculate the infrared images of a simple configuration with two gray spectral bands, and the efficiency of it is validated by compared the results of it to that of the non-spectral backward Monte Carlo method . Then the validated spectral backward Monte Carlo method is used to simulate the infrared image of the SDM airplane model with spectral surface, and the distribution of received infrared radiation flux of pixels in the detector is analyzed.

Some calculation techniques with the Monte Carlo method in stray radiation evaluation such as imaginary covers, domain decomposition, coordinate conversion, principle of weight-equivalent sampling, randomness of radiant characteristic of heat insulating coat are described. Employing these techniques, the stray radiation calculation for a large optical system can be achieved in a personal computer. Taking a satellite-borne optical system, for example, the stray radiation flux and stray radiation environment of the system is obtained. The calculation results present a reference for the design of the optical system.

In an infrared optical system, the thermal radiation of high temperature components is the major noise as stray radiation that degrades the system performance. Backward Monte Carlo method based on radiation distribution factor is proposed to perform the stray radiation calculation. Theoretical deduction and some techniques are presented, considering the semitransparent element like IR window as radiation emitter. The radiation distribution factors are calculated with ray tracing from the detector to radiation sources. Propagation of stray radiation and its distribution on the detector are obtained simultaneously. It is unnecessary to implement ray tracing again to study the effect of different temperatures for a given system, expect that the geometry or radiative property is changed. An infrared system is simulated using this method. Two different situations are discussed and the analysis shows that stray radiation is mainly created by IR window and lens tube.

An algorithm of ray tracing Monte Carlo method was developed to simulate concentrating characteristics of solar radiation transfer to solar array with an ideal shape solar concentrator (ISSC). The effects of the solar angle, slope error and tracing error on the concentrated solar flux were investigated, and a uniformity factor is defined to evaluate the concentrating solar beam. The results of calculation show that the non-uniform factors lie in the range from 0.6 to 0.8 under these influencing effects.

The solar array which provides most of energy for the satellite plays a very important role. And the conversion coefficient of solar cell used in the solar array is directly influenced by the array temperature, which is also responsibility for the stability and safety of satellite, especially for the solar array. This paper discusses the solar array temperature fields under different situations, including the periods of the satellite operating in spring, summer and winter. Obtaining the incidence angle of the solar array in the three periods, the radiative heat flux is computed by Monte Carlo method (MCM) and the finite volume method (FVM) is employed to win the temperature field, with the harmonic mean value being used for the heat transfer at interface between different materials. The results show that, the temperature fields of the solar array are quite different for various seasons, and the highest temperature of the array is 308 K in spring, the lowest temperature is 225 K in summer, which is caused by the shadow of the earth.

This paper aims at predicting radiation characteristics of the solar collector system by the Monte Carlo method with respect to the corresponding optical properties. Several probability models were introduced to analyze the effects of sunshape and surface roughness. Directional characteristics of radiative flux in the focal region and flux distribution of the cavity receiver were considered. An equivalent radiation flux method is presented for designing the shape of the cavity receiver. Based on the relative numerical simulation results, a new shape cavity receiver called “upside-down tear drop” is proposed to meet an almost uniform radiation flux field. Radiation effects due to multiple reflections and thermal emission in the cavity are parametrized by using the radiative exchange factor. The calculation results can be a valuable reference for the design and assemblage of the dish solar collector system. DOI: 10.1115/1.2840570

[Abstract] A microstructure-based model for predicting the effective electrical conductivity of nickel nanostrand reinforced polymer composites is developed by using the Voronoi tessellation technique and the resistor network theory. Voronoi diagrams with different degrees of cell shape irregularity (amplitude a) are generated by perturbing a regular packing of seeds to model the microstructures of nanostrand networks. Ten resistor networks are constructed for each type of nanostrand network samples (with the same value of a) to obtain the mean value and standard deviation of the effective electrical conductivity. Kallmes and Corte’s statistical model is employed to relate the utilized nanostrand volume fraction and the initial nanostrand volume fraction. The simulation results indicate that the effective electrical conductivity, on average, decreases as cell shapes become more irregular. The use of a regular hexagonal lattice can lead to a moderate improvement in the conductivity over that of a completely random network. The values of conductivity predicted by the current model are found to agree fairly well with existing experimental data and predictions based on the Monte Carlo technique. In addition, it is revealed that the polymer nanocomposites behave isotropically in terms of its electrical conductivity.

Transient electron dynamics in quantum well (QW) structure is very important for designing terahertz (THz) lasers based on subband transitions. In this paper, four three-level (indexed by 0, 1 and 2) asymmetric stepped GaAs/AlxGa1−xAs QW structures with different doping conditions are designed, and an ensemble Monte Carlo method is adopted to comparatively analyze the corresponding electron dynamics. We find that transient population reversion between upper two subbands is strongly dependent on a low doping density and doping position far away from electron ensemble to reduce electron–electron (EE) scattering and impurity scattering. The results also show that three types of EE scattering, E21E00, E22E01 and E21E22, subscripts representing the initial and final levels of an electron, dominate the EE scattering contribution to the transient population reversion. The ground state is found to have the highest average energy among the three levels, which may seriously weaken the optical pumping efficiency.

A three-dimensional (3D) Monte Carlo model is developed to study the fiber curliness effect on the percolation threshold of a composite filled with electrically conductive curved fibers. These fibers are simulated as zigzag-shaped fibers that are randomly positioned in the composite, forming a 3D random network. The simulation results show that the fiber curliness can significantly affect the percolation threshold: the more curved the fibers, the higher the threshold. The results also reveal an exponential relationship between the threshold and the fiber aspect ratio: the higher the aspect ratio, the lower the threshold. These predicted trends agree well with existing experimental and simulation results based on straight fibers or curved fibers with simpler shapes.

An ensemble Monte Carlo method is employed to study the carrier dynamics of optically pumped 3-subband quantum-well lasers under sub-picosecond pulse excitation. The influences in time and energy domains of electron?electron scatterings (EES) toward the electron distributions on each subband, both critically important for inter-subband THz lasers, are carefully analyzed. We find that, out of three subbands, EES would affect the occupancy on the ground subband most seriously, and the upper laser subband may be influenced more easily by EES than the lower laser subband.