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In the field of micro and mesoscale combustion, the feature of flame-wall thermal coupling is of great significance because of its small scale nature. Thus, this work provides a comprehensive heat transfer analysis in cylindrical combustors from the perspective of numerical simulation. The combustor has a fixed length-to-diameter aspect ratio of 10, and the channel diameter is scaling up from 1 mm to 11 mm to explore the influence of chamber dimension on heat transfer and flame structure. The distribution of convective and radiative heat flux on inner surface, contribution of thermal radiation are given. Moreover, the role of radiation in flame structure is analyzed, and the convective and radiative heat losses are quantitatively analyzed. We find that radiative heat flux is smaller compared to convective heat flux, and the proportion of radiative heat flux becomes larger with an increasing diameter. Thermal radiation does not change the flame structure when the diameter is less than 3 mm. When the diameter is greater than 5 mm, thermal radiation changes the location of flame front. The heat loss becomes larger at a smaller diameter, and heat loss ratio can reach approximately 73.6% in the combustor with diameter of 1 mm.

The statistical narrow band (SNB) and the statistical narrow band correlated-k (SNBCK) models were used with HITRAN2008, HITRAN2012, and HITRAN2016 databases, in order to demonstrate the effect that the different HITRAN database versions had on the accuracy of the SNB and SNBCK calculations. The line-by-line (LBL) calculation was based on the HITEMP data. Eight cases were calculated using the LBL, the SNB, and the SNBCK models in a one-dimensional enclosure between two parallel plates filled with CO2, H2O, or a mixture of both. The results demonstrated that the radiant flux and the source of the SNB and SNBCK models based on the HITRAN2012 and HITRAN2016 databases were in good agreement. This was not true in the 0.1 m short path. The improvement in accuracy from the HITRAN2016 to the HITRAN2012 database was not as accurate as the improvement from the HITRAN2012 database to the HITRAN2008 database. The results calculated using the same HITRAN database by the SNB model were more accurate than those obtained with the SNBCK model. And the lack of contribution of the hot lines in the three HITRAN databases leads to the relative error values of more than 20% on the radiant flux. This indicated that the HITRAN databases are not suitable for engineering calculations at a higher temperature.

The Distribution of Ratios of Energy Scattered by the medium Or Reflected by the boundary surface (DRESOR) method based on the Monte Carlo method is an important new approach to solve the radiative transfer equation accurately and efficiently. This method has been applied extensively for the detection and analysis of the furnace flame temperature. However, the discrete method, the number of direct incident radiation directions (DIRDs), and the number of scattered or reflected energy beams (SREBs) lack quantitative references. Therefore, in this paper, the effects of different discrete methods, the number of DIRDs, and the number of SREBs on the radiative heat flux, divergence error, and computational efficiency of three-dimensional homogeneous absorbing, emitting, and scattering media are analyzed. The results show that the random discrete method of the DIRD for the space element substantially reduces the divergence error of the radiation heat flux. The uniform discrete method of the DIRD should be used for the surface element to minimize the error of the radiation heat flux error. In addition, the relative error of the DRESOR method is reduced to 0.004, and the figure of merit reaches the maximum when the number of DIRDs is about 1000, the number of SREB is 500, and the scattering albedo is less than 0.8. The fitted equations describing the relationship between the calculation errors and the number of SREBs for the surface and space elements are obtained for different scattering albedos. An increase in the number of DIRDs and SREBs does not significantly reduce the calculation error. The results provide a quantitative reference for determining the parameters of the DRESOR method in radiant heat analysis.

The gas temperature fields of axisymmetric co-annular laminar diffusion ethylene flame jets in air and oxygen-enriched atmospheres were measured and visualized using large lateral shearing interferometry technique. Seven cases of reconstructed temperature fields were investigated using various compositions of fuel/oxidant with an average correction factor. The phase difference field were obtained using a fringe trace algorithm. A discrete Abel inversion process was adopted to resolve the refractive index distribution from the line-of-sight integrated data. The peak temperatures of the flame varied between 1980 K and 2050 K using air as the oxidant and increased to more than 2150 K when oxygen was added. Two separate high temperature zones, one located at the side edge of the flame, the other in the upper part of the flame around the centerline of the burner were observed in four of the seven instances of high mixture stoichiometry. The proposed methodology was verified to be suitable for the reconstruction of temperature distributions from the experimental measurement results.

To improve the efficiency of full-spectrum correlated-k-distribution (FSCK), a new method FSCK-RSM has been proposed based on response surface methodology (RSM) in this paper. The k-distributions of FSCK was used to fit the response surface model based on radial basis function and the radiative calculation efficiency was improved by avoiding multiple computations and interpolation in the FSCK-RSM. The thermal radiation heat transfer of five combustion gases (H2O, CO2, CO, C2H2 and C2H4) in a one-dimensional layer was investigated and the radiative sources calculated by the LBL, SNB, FSCK and FSCK-RSM methods were given at different distributions of temperature and gas concentration. The results showed that the needed amount of input data was reduced by 677 times using FSCK-RSM comparing to the FSCK and the maximum of the average normalized deviation for FSCK-RSM was 2.46% in the non-isothermal homogeneous medium. The model was finally used for radiation reabsorption calculations in planar C2H4/O2/N2/CO2 flames with full coupling to heat transfer and multi-species chemistry. The computational time using the FSCK-RSM was found to be at most half of that using the FSCK method. This FSCK-RSM model was an effective method for addressing the radiation problems that occur in combustion systems.

In this paper, a distributed parameter model for tubular reactor in the ethylene cracking furnace based on 3-D temperature reconstruction is developed. The mathematical model was formulated to predict the distributions of the heat flux and the tube temperature while considering a non-uniform distribution of the surface heat transfer and the ethylene pyrolysis process. The results show that the heat flux distribution on the tubular reactor has four high heat flux zones, and the tube temperature reaches a maximum of 1088 °C. The value of the maximum tube temperature decreases compared with the value of the maximum heat flux due to the heat exchange coefficient of pyrolysis gas increasing slowly in the bend region. The tube temperature distribution was validated by using a spectrometer system and the errors between three major product yields at the tube outlet obtained by the proposed model and in-situ measured values were within 5%. This distributed parameter model can be used as a guide for ethylene cracking furnace operators and as a tool for design.

Most research on transient radiative transfer is coupled with blackbody, specular or diffuse surface, which may only provide limited or inefficient information to analyze transient radiation transfer problems under particular circumstances. This study aims to extend the DRESOR (Distribution of Ratios of Energy Scattered by the medium Or Reflected by the boundary surface) method to solve the transient radiative heat transfer in a one-dimensional, non-emitting, absorbing and isotropically scattering medium with a linear graded index coupled with the BRDF (Bidirectional Reflectance Distribution Function) surface, which is closer to a real surface and can offer more accurate information. Here, a Minnaert model for the BRDF surface is applied. Numerically computed results of the time-resolved reflectance and transmittance are compared with those obtained by DOM and DFEM with blackbody surfaces, which verifies the DRESOR method. Meanwhile, the comparison between BRDF surface and diffuse surface has also been carried out. With the increase of optical thickness, the time-resolved reflectance and transmittance profiles change from a single peak, to a double-peak, and finally to a single peak with a relatively large scattering albedo, especially under the graded index. The scattering albedo has a significant influence on the peak values of the reflectance and transmittance. With the increase of parameter k of Minnaert model, the difference between BRDF surface and diffuse surface enlarges significantly. Furthermore, compared with the corresponding diffuse surface, the relative time-resolved reflectance difference of the BRDF surface can reach 16.7% and the transmittance can reach 7.4% at some dimensionless time. The intensities with the change of time in some directions show an evident difference between BRDF and diffuse surface. These discrepancies imply that the BRDF surface has an important influence on the transient radiative transfer.

The traditional diffuse or specular surface assumption is insufficient to accurately characterize the reflection characteristics of a practical surface under some circumstances, which could cause distinct deviation in radiative heat transfer analysis and temperature measurements. The anisotropic reflection of a real surface can be well featured by the Bidirectional Reflectance Distribution Function (BRDF). This study aims to solve the radiative heat transfer in a two-dimensional non-uniform refractive index and anisotropic scattering medium coupled with the BRDF surface. The Distribution of Ratios of Energy Scattered by the medium Or Reflected by the boundary surface (DRESOR) method is extended to deal with this issue. The effect of BRDF surface on the radiative heat flux and radiative intensity is investigated varying with optical thickness and scattering albedo of medium by compared to the corresponding diffuse surface. It is found that the more deviation from the diffuse characteristics the BRDF surface has, the larger difference of the radiative heat flux and intensity between the BRDF and diffuse surface there exits. The increased optical thickness and scattering albedo both decrease the difference of radiative flux on the wall between the BRDF and corresponding diffuse surface. And the influence of the reflection of the BRDF boundaries can be alleviated with thick optical thickness or large scattering capacity in the medium. The results demonstrate that the BRDF surface can impose remarkable impact on the radiative heat transfer, and an appropriate BRDF model should be introduced to be coupled with radiative transfer procedure in the accurate analysis of multi-dimensional radiative transfer problem if the boundary possesses the anisotropic reflection properties.

An on-line three-dimensional temperature measurement experiment was carried out in a gas-fired pilot tubular furnace. Four flame image detectors were utilized to obtain two (red and green) monochromatic radiation intensity distributions, which can be calculated by the DRESOR method based on the radiation image processing technology. Then a revised Tikhonov regularization method was developed to reconstruct three-dimensional temperature distributions from the green monochromatic radiative intensity. Meanwhile, a Newton method combined with a least-squares method was used to simultaneously reconstruct radiative properties from the red one. The two calculation procedures were performed alternately, forming an iterative algorithm to a simultaneous reconstruction of temperature and radiative properties. The reconstructed temperatures agreed well with those measured by thermocouples for different cases with different calorific values and components of gas. The largest relative error was less than 3%, which vali...

Within a graded index medium, the radiative energy rays propagate in curved paths and with a varied speed of propagation, making the solution of the transient radiative transfer complex and difficult. The DRESOR method is extended to calculate the time-resolved reflectance and transmittance from a one-dimensional, non-emitting, absorbing, anisotropically scattering medium with a linear increasing graded index exposed to a collimated truncated Gaussian pulse. Comparisons are made with the results obtained by DOM and DFEM, which indicate that the DRESOR method is accurate and effective. Compared with uniform graded index, the increase in the gradient of the refractive index significantly reduces the peak value of the reflectance and transmittance, delays the occurrence time of the transmittance and increases the duration time. The double-peak phenomenon of the time-resolved transmittance is caused by the fact that the maximum values of intensity in different directions appear at different times, which occur much later as the polar angle increases. The double-peak phenomenon of the time-resolved transmittance becomes more obvious as the increase in the graded index, the scattering albedo and the optical thickness; and the decrease in the anisotropically scattering phase function coefficient.

Radiative intensity with high directional resolution at boundaries can provide abundant information about the medium properties and temperature, which is very useful for inverse analysis. Monte Carlo method is a widely used method due to its flexibility for complex radiative transfer problems. In this work Distributions of Ratios of Energy Scattered Or Reflected (DRESOR) method, which is based on Monte Carlo method, is developed for radiative intensity calculation in a three-dimensional rectangular enclosure which contains an emitting, absorbing, and isotropically scattering medium. The method is validated by comparing calculated radiative intensities with those of the reverse Monte Carlo method. Then, radiative intensity for different radiative problems is examined by DRESOR method. Comparing with reverse Monte Carlo method, DRESOR method shows much better time-efficiency. DRESOR method also shows an obvious advantage if radiative intensity with high directional resolution at many different boundary positions is required. To calculate radiative intensity with high directional resolution in a system where radiative source is confined to a small volume, both standard and reverse Monte Carlo method become inefficient, the results show that DRESOR method is still an efficient tool. The results given in this study demonstrate that DRESOR method is very advantageous in situations when high directional resolution is required.

Radiation heat transfer in a two-dimensional rectangular enclosure containing CO2/H2O/N2 mixtures was calculated using the line-by-line and the statistical narrow-band correlated-k models. The radiative transfer equation was solved using the discrete ordinates method along with the T7 quadrature scheme. The updated HITEMP spectroscopic database, HITEMP2010, was employed in line-by-line calculations to obtain the most accurate line-by-line results. The statistical narrow-band model parameters of Sourfiani and Taine [IJHMT 40, 987–991, 1997] were used to obtain the statistical narrow-band correlated-k model results. Calculations were carried out for five test cases involving isothermal/non-isothermal and homogeneous/inhomogeneous CO2/N2, H2O/N2, and CO2/H2O/N2 mixtures. The present line-by-line results can serve as benchmark results for the purpose of validating other approximate models in gas radiation heat transfer calculations in two-dimensional enclosures. Results of the statistical narrow-band correlated-k model are in good agreement with those of the line-by-line method in all the test cases. The statistical narrow-band correlated-k model was found sufficiently accurate to generate benchmark solutions in multi-dimensional gas radiation transfer problems where line-by-line calculations are infeasible due to excessively long computing time.

In this paper, the ES-DRESOR method, an equation-solving method to calculate the DRESOR values differently from the MCM used before, is proposed. In this method, a unit blackbody emission is supposed within a cell, while there is no emission from the remaining part of the system. This leads to the equations for the DRESOR values based on the incident radiation, and all the DRESOR values can be solved directly from the equations without the rays tracing used in the MCM. Numerical results show an excellent agreement of all DRESOR values found by ES-DRESOR method and MCM for 100 cells in 1D case with emitting, absorbing, and isotropic scattering medium and transparent boundaries. The average relative error for the intensity obtained by the ES-DRESOR method is only 3.372 × 10−5, lower by one order of magnitude than 4.022 × 10−4 obtained by the MCM under the same conditions. The CPU time for computing the DRESOR values using the MCM varies from a few hundred seconds to several thousand seconds. In contrast, it is less than 1 s using the ES-DRESOR method, showing an obvious improvement in the computational efficiency.

In this paper, a distributed parameter model for the evaporation system of a subcritical once-through, coal-fired, twin-furnace boiler based on 3-D temperature field reconstruction is developed. The imaginary wall surface was put forward to simplify the twin-furnace problem. The mathematical model was formulated for predicting the transient distributions of parameters, such as the heat flux, the metal-surface temperature and the steam quality; while considering the non-uniform distributions of the surface heat transfer coefficient and frictional resistance coefficient. The model was based on the 3-D temperature distribution got by a flame image processing technique. The model was validated by some measurable parameters of the evaporation system at three typical loads. The results show that the heat flux and the temperature which are located at the overlapping region of the two tangential flames are higher than those in other corners. This distributed parameter model on evaporation system reflects the in-situ operating status of the power plant boiler, which may lead to the subsequent research on a supercritical boiler.

A simulation investigation for simultaneous reconstruction of distributions of temperature and soot volume fraction from multi-wavelength emission in a sooting flame using the stochastic particle swarm optimizer (PSO) algorithm is presented. The self-absorption of the flame is considered. The selection of parameters of the stochastic PSO algorithm and detection wavelengths is analyzed. The effects of measurement errors and optical thickness of the flame on the accuracy of the reconstruction are investigated. It proved that the stochastic PSO algorithm is robust and can obtain accurate distributions of temperature and soot volume fraction from line-of-sight intensities in only several wavelengths, especially in the flame with large optical thickness, while other methods neglecting self-attenuation of the flame will take some errors.

Made available in DSpace on 2019-09-12T16:53:36Z (GMT). No. of bitstreams: 0 Previous issue date: 2011 National Natural Science Foundation of China Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) The paper reports experimental investigations on simultaneous measurement of temperature distribution and radiative properties in an oil-fired tunnel furnace by radiation analysis. Two color CCD cameras were used to obtain visible thermal radiation in the furnace. A radiation imaging model was established by the calculation of radiative transfer equation in the furnace. The temperature distribution and radiative properties can be obtained from the inversion of the radiative imaging model. The validity of radiative imaging model was verified by the numerical analysis of cavity radiation and isothermal system radiation, and the accuracy of reconstruction method was validated by simulation reconstruction. The experimental analysis was divided into two parts. Firstly, the temperatures of wall surface were calculated from the radiative image of refractory wall and compared with the measured temperature of a thermocouple. The difference between the two methods was only about 20 K. Secondly, the temperature distributions in the furnace, absorption coefficients of combustion medium, and emissivities of refractory wall were reconstructed. Because of a single burner in the tunnel furnace, the temperature distributions in the XY vertical sections in the furnace were with temperature higher in the center and lower near the refractory wall surface, and the temperatures decreased along the length of the tunnel furnace. The measured emissivity of refractory wall showed that the refractory material of RPA-MC30 is with high reflectivity in visible spectrum. (C) 2010 Elsevier Ltd. All rights reserved. [Lou, Chun; Li, Wen-Hao; Zhou, Huai-Chun] Huazhong Univ Sci & Technol, State Key Lab Coal Combust, Wuhan 430074, Hubei, Peoples R China [Salinas, Carlos T.] Universidade de Taubaté (Unitau), Dept Mech Engn, BR-12060440 Taubate, SP, Brazil

The transport process of ultra-short light pulse propagation inside the nonemitting, absorbing, and scattering two-layer media is studied. Under the appropriate combination of the pulse width and scattering property of the probed medium, the temporal signal of the reflectance exhibits a direct correlation between the reflectance signal rise time and the location of the interface. The geometry under study is a two-layer structure. This study extends a prior work by authors, giving more extensive numerical simulations to rigorously test and revise the conditions of the optimal pulse width, which would reveal the dual-peak in the temporal reflectance signals.

The stability of Bickley jet with particle laden flow is investigated numerically. The stability characteristics are calculated for various Stokes numbers and particle concentrations. The results confirm the author's early calculations, which also shows that the numerical program is reliable. It is further shown that there is a critical value for the effect of Stokes number, which is about 2. The most damped mode occurs when Stokes number is of order of 10 for different particle concentrations and depends weakly on the wave number. The difference in the eigenfunctions and its derivatives between the particle-laden flow and the clean gas flow is insignificant for fine particles, while the difference for coarse particles is significant.

This article presents a simulation investigation for simultaneous determination of distributions of temperature and soot volume fraction in a nonoptically thin sooting flame using a decoupled reconstruction method. Flame temperature and emissivity images can be calculated from two monochromatic radiative intensity images in the visible spectrum range. Then, the distributions of temperature and soot volume fraction were reconstructed from flame temperature and emissivity images. Based on experimental data from a laminar ethylene diffusion flame available in the literature, the effects of measurement errors, detection wavelengths, and optical thickness on the accuracy of the reconstruction have been investigated.

Radiative intensity in 6,658 and 281 directions in the hemispheric space was provided by the distribution of ratios of energy scattered by the medium or reflected by the boundary surface method (DRESOR) at the boundary of a two-dimensional enclosure filled with isotropic and anisotropic scattering medium, respectively. The dimensionless radiative heat flux achieved by the DRESOR method agreed well with those by other methods in the literature. Besides the polar angle, the intensity at the boundary varies significantly with the azimuthal angle, especially for the points close to the emitting source. In the anisotropic scattering media, the largest boundary intensity occurs with the largest forward scattering capability.

Zhi-Feng Huang, Qiang Cheng, Cheng He, and Huai-Chun ZhouState Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, ChinaThe DRESOR method was applied to analyze the radiative transfer process inanisotropic scattering media with different boundary conditions in this paper. Themethod was validated by the integral formulation of the radiative transfer equation atfirst. Some variation regulations about the emissivity were obtained by extensivenumerical simulations. When the optical thickness of the media became very large,the emissivity converged to a constant value. The converged emissivity in the forwardscattering medium was the largest and that for the backward scattering medium wasthe smallest. Also the converged emissivity was associated with the scattering albedoof the media. The greater the scattering albedo was, the smaller the convergedemissivity was. When the scattering albedo decreased to zero the converged emissivityreached the blackbody emissivity at the same temperature. Furthermore, differentboundary conditions were considered. The results showed that if the temperature ofthe medium and the boundary was equal, the intensity at boundary was the same asthat for the blackbody emission at the same temperature, whether the boundaryreflectivity was 1.0 or not. When the temperature of the boundary was lower than thatof the medium, the boundary emissivity can reach 1.0 only if ρ = 1.0. Finally, theradiation flux was studied with different phase functions and different boundaryconditions. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(3): 138–152,2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI10.1002/htj.20198

In the decoupled reconstruction method, using an improved Tikhonov regularization method, the temperature distribution in a participating medium is reconstructed from the boundary temperature image, and the radiative properties (absorption and scattering coefficients) are updated from the measured radiative intensity image. These two steps are taken alternately until convergence is reached. The distributions of temperature and radiative properties for two one-dimensional cases are reconstructed by the method from the boundary temperature and intensity images disturbed by measuremental errors with standard deviations up to 0.05, and the method shows good accuracy and robustness.

Forward and backward Monte Carlo methods may become inefficient when the radiant source is collimated and radiation onto a small, arbitrary spot and onto a small, arbitrary direction cone is desired. In this paper, the DRESOR method was formulated to study the radiative heat transfer process in an isotropically scattering layer exposed to collimated radiation. As the whole spherical solid angle space was uniformly divided into 13,316 discrete solid angles, the intensity at some point in up to such discrete directions was given. The radiation fluxes incident on a detector inside the layer for varying acceptance angles by a step of 2deg were also measured, which agreed well with those in literature. The radiation flux across the top and the bottom boundaries were also provided.

For a 2-D furnace system filled with a gray medium, surrounded by gray emitting/absorpting and diffusely reflecting wall surfaces, the temperature distribution is reconstructed using an improved Tikhonov regularization method with radiative energy images detected from the boundary of the furnace, uniform absorptivity of both the wall surfaces and the medium being updated from the temperature images grasped from the boundary too. These steps are taken alternately till a convergence is reached. The measurement errors with normal distribution of standard square deviation of 0.01 are taken into consideration for the radiative energy image and temperature image data. The reconstruction errors for radiative properties vary from 1.45% to 10.75%, and for the highest temperature are within 2%. Comparatively, the reconstruction result for the sharper temperature distribution is not as good as that for the smoother temperature distribution. The applicability of the proposed method may be practically valuable.

Since it is difficult to calibrate the absolute radiative energy information from any digital image data, a new model is proposed by which the temperature distributions in furnaces are no longer related with the absolute radiative energy images, but with a sort of temperature image. The temperature images are obtained through using the so-called monochromatic-reference method, described in detail. It is shown that the new model has its objectivity in reflecting the temperature distributions in furnaces, and does not change significantly with the aperture or shutter speed of the camera used. The easier calibration for the temperature than for absolute radiative energy makes this treatment more applicable.

Distributions of ratios of energy scattered or reflected (DRESOR) method is a very efficient tool used to calculate radiative intensity with high directional resolution, which is very useful for inverse analysis. The method is based on the Monte Carlo (MC) method and it can solve radiative problems of great complexity. Unfortunately, it suffers from the drawbacks of the Monte Carlo method, which are large computation time and unavoidable statistical errors. In this work, an equation solving method is applied to calculate DRESOR values instead of using the Monte Carlo sampling in the DRESOR method. The equation solving method obtains very accurate results in much shorter computation time than when using the Monte Carlo method. Radiative intensity with high directional resolution calculated by these two kinds of DRESOR method is compared with that of the reverse Monte Carlo (RMC) method. The equation solving DRESOR (ES-DRESOR) method has better accuracy and much better time efficiency than the Monte Carlo based DRESOR (original DRESOR) method. The ES-DRESOR method shows a distinct advantage for calculating radiative intensity with high directional resolution compared with the reverse Monte Carlo method and the discrete ordinates method (DOM). Heat flux comparisons are also given and the ES-DRESOR method shows very good accuracy. [DOI: 10.1115/1.4025133]

In the fast algorithm, the total energy received by pinhole image-formation elements is divided into two parts: the direct part and indirect part. The indirect energy was related to the direct part, and the latter was calculated through a concept of effective angle factor for image formation. For 2-D systems filled with emitting, absorbing, isotropically scattering medium and surrounded by diffusely reflecting wall surfaces, the results through using the fast algorithm approached the statistical average values of those calculated using the Monte Carlo method, and the computation time can be nearly 50 times faster.

Boiler prediction of the hydraulic resistance is helpful for the safe operation of a water wall in a supercritical boiler. In this paper, the density distribution for the resistance calculation of a water wall at the supercritical pressure is numerically analyzed, and a distributed parameter model of the hydraulic resistance is developed in a down-fired 600 MWe supercritical boiler using a three-dimensional temperature distribution. The results show that the difference in the density along the radial direction is small and that the hydraulic resistance of the water wall tubes at the supercritical pressure is affected by the critical phenomenon of the working fluid and the allocation of heat flux of the boiler. The simulation cases and in situ operation data demonstrate the model. The model provides a new analysis method for the hydraulic resistance characteristics of a water wall in this thermodynamic system, and the derived model builds a foundation for developing flow monitoring and a thermal-hydraulic design. [DOI: 10.1115/1.4024875]

Thermal and optical engineering applications of electromagnetic wave scattering from rough surfaces include temperature measurement, radiation heating process, etc. Most of the surfaces have random roughness and are often with coating material different from the substrate. However, the understanding of radiative properties of coated rough surfaces is not well addressed at this point. This paper presented a novel hybrid partial coherence and geometry optics (HPCGO) model to improve the generic geometry optics (GO) prediction by incorporating a previously developed partial coherence reflectance equation. In this way, HPCGO expands the applicable region of GO model and largely reduces the computation time of integrating different wavelength results in the regular hybrid model that considers coherence effect only. In this study, the HPCGO model is first compared with the more rigorous Maxwell equations solvers, the finite-difference time-domain (FDTD) method, and integral equation (IE) method. Then, the HPCGO model is applied to study the coherent effect of directional-hemispherical reflectance from coated rough surfaces. It is found the roughness of coated rough surface can cause partially coherent or noncoherent scattered light even if the incident light source is coherent. It also shows the reflected electromagnetic wave’s coherence effect reduces with increased coating thickness and surface roughness, besides the previously recognized incident wave-number bandwidth. The effect of reduce coherence in scattered wave is quantified. Finally a regime map, even limited in the roughness and coating thickness dimensionless parameter ranges, provides the region of validity of the HPCGO model. [DOI: 10.1115/1.4024466]

Thermal radiation transfer in one-dimensional enclosure between two parallel plates filled with real gases, namely CO2, H2O, or their mixtures, was calculated using the line-by-line approach and the statistical narrow-band model. Line-by-line calculations were carried out using the HITEMP1995, HITRAN2004, HITRAN2008, HITEMP2010, and updated CDSD-1000 databases. This study demonstrates the importance of spectral database to the accuracy of line-by-line calculations through a systematic comparison of line-by-line results using different databases. Calculations of the statistical narrow-band model were conducted using the EM2C narrow-band database. The strong dependence of line-by-line results on the spectral database was demonstrated through several gas radiation transfer problems in planar-plate enclosure containing real gases of both isothermal or non-isothermal and uniform or non-uniform concentrations at 1 atm. Fairly significant differences were found between the line-by-line results using the HITEMP2010 database and those using older databases. Very good agreement in both the wall heat flux and the radiative source term was observed between the line-by-line results using the HITEMP2010 database and the results of the statistical narrow-band model in all the cases tested, confirming the EM2C narrow-band parameters for both H2O and CO2 are accurate. For cases involving CO2 the line-by-line results using the HITEMP2010 database are in excellent agreement with those using the updated CDSD-1000 databases. The line-by-line results based on the HITEMP2010 database should be used as benchmark solutions to evaluate the accuracy of other approximate models.

A new and improved method based on the concept of discrete ordinates scheme with infinitely small weights (DOS+ISW) is developed for modeling radiative heat transfer in three-dimensional participating media. To demonstrate the effectiveness of the method in mitigating ray effects, the ray effects caused by (1) abrupt step changes in the boundary conditions and (2) the stepwise variation of the medium emissive power are considered. In this work, angular quadrature sets with large number of discrete ordinate directions are chosen to mitigate ray effects while at the same time keeping the computational time increase to a minimum. Comparing with the conventional discrete ordinates method, the difference is that intensities in these directions are calculated by DOS+ISW method. Intensity with fine directional resolution calculated by this method is validated by comparing with that of reverse Monte Carlo method. The large number of discrete ordinate directions used in the new method becomes computationally prohibitive in the conventional discrete ordinates method due to the increased computer memory and computation time requirements.

A time-dependent distribution of ratios of energy scattered by the medium or reflected by the boundary surfaces (DRESOR) method was proposed to solve the transient radiative transfer in a one-dimensional slab. This slab is filled with an absorbing, scattering, and nonemitting medium and exposed to a collimated, incident serial pulse with different pulse shapes and pulse widths. The time-dependent DRESOR values, representing the temporal response of an instantaneous, incident pulse with unit energy and the same incident direction as that for the serial pulse, were proposed and calculated by the Monte Carlo method. The temporal radiative intensity inside the medium with high directional resolution can be obtained from the time-dependent DRESOR values. The transient incident radiation results obtained by the DRESOR method were compared to those obtained with the Monte Carlo method, and good agreements were achieved. Influences of the pulse shape and width, reflectivity of the boundary, scattering albedo, optical thickness, and anisotropic scattering on the transient radiative transfer, especially the temporal response along different directions, were investigated.