Non-gray Walls Research Articles

An Improved nongray-wall emissivity-absorptivity model for the Full-Spectrum Correlated K-distribution method

In practical combustion chambers, the emissivity of wall materials in general varies spectrally and inappropriate treatments may lead to significant errors in modeling radiative heat transfer. To reduce the error of the Full-Spectrum Correlated K-distribution (FSCK) method in practical problems involving nongray walls, a nongray-wall model is proposed by reordering the wall emissivity and absorptivity separately, in which the Planck function at the wall temperature and an effective mean temperature is used as the weight function of wall emissivity and absorptivity, respectively. As a result, this new model preserves the wall emission and considers the spectral radiative property of the wall. Radiative heat transfer calculations in 1D and 3D configurations bounded by nongray walls are simulated to evaluate the accuracy of this new model. The results show that this new model is in general more accurate than the recently developed nongray-wall model (Liu et al., Int. J. Heat Mass Transf. 2021), especially in cases where the wall-to-wall radiative heat transfer plays an important role. It is also showed that this new model is less sensitive to the choice of the effective mean temperature and the medium blackbody emission-averaged temperature is recommended.

A nongray-wall emissivity model for the full-spectrum correlated k-distribution method based on uniform media assumption

The walls of high-temperature combustion devices are usually assumed to be black or gray in radiative heat transfer calculations to save computing resources; however, this simplification may introduce large errors. To improve the accuracy of the Full-Spectrum Correlated K-distribution (FSCK) method in calculations of nongray-wall radiative heat transfer problems without reducing the computational efficiency, a nongray-wall emissivity model for the FSCK method is proposed based on uniform-medium assumption. The accuracy of this nongray-wall emissivity model and the commonly used Planck-function-weighted gray-wall emissivity model is evaluated in 1D isothermal and homogeneous cases, 1D non-isothermal and inhomogeneous cases, and 3D flames bounded by walls coated with fly-ash deposit or soot deposit. The results show that the nongray-wall emissivity model for FSCK demonstrates much better accuracy than the gray-wall one, especially for cases of low wall temperatures. The nongray-wall emissivity model provides good accuracy over a wide range of optical depth, while the accuracy of the gray-wall emissivity model is highly dependent on the optical depth. The nongray-wall emissivity model based on the uniform-medium assumption can be applied to non-isothermal and inhomogeneous radiative heat transfer problems involving nongray walls.

Grouping the wall spectral bands for an effective computation of the radiative transfer in participating media bounded by non-gray walls

This study presents a methodology to solve the radiative transfer in participating media bounded by non-gray walls for direct use with global gas models. The method is based on grouping the wall emissivity/absorptivity spectral bands (GWB) to employ the total emissivity and absorptivity, instead of their spectral distributions, in the integration of the radiative transfer equation (RTE). The total emissivity is calculated from the wall surface temperature, whereas the concept of a reference medium temperature is introduced for determining the total absorptivity. Though the assumptions involved in the method are analyzed in the framework of the weighted-sum-of-gray-gases (WSGG) model, they can be readily extended to any global gas model. The performance of the GWB method is assessed for two test cases, consisting of a non-homogeneous, non-isothermal, one-dimension medium slab bounded by walls with different spectral emissivities and absorptivities. For these cases, choosing the medium-averaged temperature as the reference temperature to compute the wall total absorptivity led to an accurate prediction of the radiative heat transfer, with errors below 4% relative to a reference solution obtained by line-by-line integration.

Performance of banded SLW-1 in presence of non-gray walls and particles in fluidized bed combustors

In this study, banded one gas spectral line-based weighted sum of gray gases (banded SLW-1) model is coupled with a 3-D radiation code based on method of lines (MOL) solution of discrete ordinates method (DOM) for freeboard of METU 0.3 MWt atmospheric bubbling fluidized bed combustion (ABFBC) test rig containing non-gray gas, non-gray particle mixture bounded by non-gray walls. Spectral parameters of banded SLW-1 are estimated by the approach based on two emissivities calculated at two different path lengths L1 and L2. The predictive accuracy of banded SLW-1 model is tested by comparing its incident wall heat flux and source term predictions with measurements and predictions of banded SLW. The results indicate that band-wise selection of L1 and L2 based on spectrally averaged mean beam length provides the most accurate radiative heat transfer predictions. Furthermore, based on a sensitivity analysis on the test rig under consideration, utilization of path lengths L1 and L2 which are 0.10 and 1.10 times of the spectrally dependent mean beam length is found to yield the best radiative heat transfer predictions in terms of accuracy. Incident heat flux and source term predictions of banded SLW-1 are found to be in reasonable agreement with those of banded SLW under both air and oxy-fired conditions. Furthermore, CPU time requirement of banded SLW-1 is about 20–25 times lower than that of banded SLW. With the introduction of fly ash recycling, particle load increases an order of magnitude leading to further improvement in the accuracy of banded SLW-1. On the other hand, gray wall assumption leads to accurate radiative heat flux predictions whereas this assumption leads to considerable inaccuracies in the source term predictions in the upper region of freeboard. However, those inaccuracies become insignificant with the introduction of fly ash recycling. Application of the model to different wall conditions common in the industry indicates that discrepancies between the source term predictions of gray and non-gray cold water wall and those of gray and non-gray cold slag covered water wall are insignificant for the combustion test rig under consideration which is attributed to the combined effects of low wall temperatures and similar gray and non-gray wall emissivities.

Radiative transfer prediction in participating medium bounded with nongray walls using the SLW model

This study presents the application of the spectral line-based weighted-sum-of-gray-gases (SLW) model for the radiative transfer calculation in a participating medium bounded by two infinite, parallel and nongray walls. The proposed methodology presents a simplified approach to calculate the radiative transfer in the medium without the determination of the radiation intensity field at each wavenumber. The radiative transfer equation is modeled in a one-dimensional domain in which there is a non-isothermal homogeneous or non-homogeneous gaseous mixture of water vapor and carbon dioxide. The results are compared with the line-by-line (LBL) benchmark solution in order to quantify the magnitude of the error when using the SLW spectral model. The results show that the applied methodology provides satisfactory agreements with respect to LBL solution. In addition, it is shown that considering nongray walls leads to significant more accurate results in computation of the radiative heat transfer than the commonly applied gray wall assumption.

A wavenumber subinterval grouping strategy compatible with non-gray metal wall boundaries used in multi-scale multi-group full spectrum k-distribution gas radiation model

In the present work, strategies for the grouping of wavenumber subintervals were extended to deal with the compatibility of multi-scale multi-group full-spectrum k-distribution model with non-gray wall boundaries. The main idea is to enhance the correlated-k characteristics of absorption spectra of H2O-CO2 mixtures and emission spectra of non-gray wall within each divided group. The improvements in the calculation accuracies of radiative heat flux on the wall resulting from the new grouping strategy were evaluated using a series of 1D cases, in which combustion gases with strong inhomogeneities of temperature, pressure and molar ratio of water vapor to carbon dioxide were bounded by non-gray walls. The non-gray walls are assumed to be different metal materials with various surface states and temperatures. Finally, evaluation of the wavenumber subinterval grouping strategy was presented based on calculation of thermal imaging for directional radiation transfer from hot supersonic exhaust plume to a metal plate.

APPLICATION OF THE WEIGHTED-SUM-OF-GRAY-GASES MODEL TO NON-HOMOGENEOUS H2O/CO2 MIXTURES FOR MEDIA WITH NON-GRAY WALLS

The spectral modeling of the thermal radiation in participating media is a research area that has received constant attention due to its importance in a great number of engineering problems, especially because the highly irregular spectral dependence of the absorption coefficient of a gas with the wavenumber requires the adoption of alternative methods to determine the radiative properties. This work brings a numerical study of a one-dimensional system, bounded by perfectly diffuse and non-gray walls, filled by a non-homogeneous and non-isothermal mixture of water vapor and carbon dioxide. The main objective is to estimate the magnitude of the deviations in treating surfaces that should be considered non-gray as black or gray. The spectral modeling of the problem is performed by the weighted-sum-of-gray-gases (WSGG) model and the accuracy of the solution methodology developed is evaluated by means of comparisons against the results obtained by line-by-line (LBL) integration.

Improved banded method for spectral thermal radiation in participating media with spectrally dependent wall emittance

To develop an efficient and practical spectral radiation model for CFD simulations, a banded approach is proposed for a mixture of carbon dioxide and water vapor in varying thermodynamic states. Using a previously reported band dividing scheme, a statistical narrow band model is implemented to provide gray band absorption coefficient databases. The databases were then approximated by certain simple correlations, which can be readily used in CFD calculations of RTE solvers. The correlations were validated in several 1D and 3D benchmarks representing various combustion conditions. The accuracy and CPU cost of the proposed banded approach were studied and compared with those of other similar methods. The results demonstrated that the new approach is an efficient and accurate method that can be conveniently applied in a commercial CFD code for spectral radiation; moreover, it can handle non-gray walls. As a practical case study, the proposed approach was used to simulate radiative heat transfer within a back pass channel of a CFB boiler. The effect of combustion scenarios, i.e., air- and oxygen-fired, boiler load, inlet flow conditions, and wall material, was analyzed by the CFD model. The predictions of two different RTE solvers, i.e., P1 and DO, and the required CPU time were compared for gray and non-gray models.

Line by line based band identification for non-gray gas modeling with a banded approach

The banded approach or box model is a method to include the non-grayness of combustion gases in radiation heat transfer calculations. However, the determination of the correct limits for the bands and the effective band absorption coefficients is still something of a black art. In this study, the line by line (LBL) spectral absorption coefficient profile has been implemented to obtain the effective number of bands, and bands’ limits for pure H2O, pure CO2 and a H2O-CO2 gas mixture. A mathematical technique has been used to smooth the LBL profiles of pure gases in atmospheric pressure in order to be used for identifying the gray bands. The optimization for selecting the bands is done by analyzing the radiative heat transfer in several one-dimensional benchmarks. After obtaining the optimal band dividing scheme, a set of correlations for the pressure based gray band absorption coefficient of pure gases is found by integrating the line by line spectral absorption coefficient weighted by the corresponding black body intensity along the bands. In contrary to the previous similar works, by using the LBL data for pressure based gray absorption coefficient of the bands, the current correlations are independent of gas concentration and path length. The present approach could successfully support the non-gray walls. The method has been validated using several benchmarks and exhibited comparable accuracy with other available models.

Efficient cumulative wavenumber model of radiative transfer in gaseous media bounded by non-gray walls

The cumulative wavenumber method for solution of the spectral radiative transfer problems in high temperature gases is extended to account for non-gray walls. The proposed efficient CW-1 method with optimized step-wise constant representation of the wall spectral properties is an attempt to minimize the number of equations requiring solution while preserving reasonable accuracy. The influence of spectral modeling of the non-gray walls on predicted total net radiative flux divergence in the medium and on the wall net radiative fluxes is demonstrated.

Assembly of full-spectrum k-distributions from a narrow-band database; effects of mixing gases, gases and nongray absorbing particles, and mixtures with nongray scatterers in nongray enclosures

Full-spectrum k-distributions provide great accuracy combined with outstanding numerical efficiency for the evaluation of radiative transfer in absorbing-emitting molecular gases, but they do have several shortcomings: (1) It is difficult to assemble k-distributions for gas mixtures from precalculated full-spectrum k-distributions of individual gas species (i.e., without calculating the mixture k-distribution directly from the HITRAN/HITEMP database), (2) it is impossible to assemble k-distributions for a gas mixed with nongray absorbing particles (such as soot) from gas-only full-spectrum k-distributions, and (3) like all global models, full-spectrum k-distributions cannot accommodate nongray scattering behavior and/or nongray wall reflectances. In the present paper we show how these restrictions can be relaxed by (1) assembling full-spectrum k-distributions for a gas mixture from a narrow-band k-distribution database created for individual gas species, (2) by assembling gas and nongray absorbing particle mixture full-spectrum k-distributions from the same narrow-band database, and finally (3) by showing how a group of part-spectrum k-distributions can be generated from the same database to accommodate nongray scattering and nongray walls.

Assembly of full-spectrum k-distributions from a narrow-band database; effects of mixing gases, gases and nongray absorbing particles, and mixtures with nongray scatterers in nongray enclosures

Full-spectrum k-distributions provide great accuracy combined with outstanding numerical efficiency for the evaluation of radiative transfer in absorbing-emitting molecular gases, but they do have several shortcomings: (1) It is difficult to assemble k-distributions for gas mixtures from precalculated full-spectrum k-distributions of individual gas species (i.e., without calculating the mixture k-distribution directly from the HITRAN/HITEMP database), (2) it is impossible to assemble k-distributions for a gas mixed with nongray absorbing particles (such as soot) from gas-only full-spectrum k-distributions, and (3) like all global models, full-spectrum k-distributions cannot accommodate nongray scattering behavior and/or nongray wall reflectances. In the present paper we show how these restrictions can be relaxed by (1) assembling full-spectrum k-distributions for a gas mixture from a narrow-band k-distribution database created for individual gas species, (2) by assembling gas and nongray absorbing particle mixture full-spectrum k-distributions from the same narrow-band database, and finally (3) by showing how a group of part-spectrum k-distributions can be generated from the same database to accommodate nongray scattering and nongray walls.

Rapid Calculation of Radiant Energy Transfer Between Nongray Walls and Isothermal H2O or CO2 Gas

Calculation of band absorption and, consequently, radiant transfer to nongray walls can be made by use of the fractional band absorption obtained from recent band absorption measurements. The fractional band absorption and other quantities needed for calculation of radiation heat transfer to isothermal H2O or CO2 gas are presented graphically for convenient use.