Statistical Narrow-band Correlated-k Research Articles

Large-scale PANDA facility – radiation experiments and CFD calculations

Abstract CFD modelling of the thermo-hydraulic phenomena in the containment during the various phases of a severe accident necessarily requires consideration of radiative heat transfer – in the presence of steam. These radiative phenomena include (i) energy transfer within the gas mixture and (ii) between the gas and surrounding structures. Preliminary calculations carried out for these types of experiments within the OECD/NEA HYMERES-2 project with the CFD code containmentFOAM using a Monte Carlo solver for thermal radiation, demonstrated that the radiative heat transfer is significant even for very small amounts of vapour in the range of ≈0.1 % to ≈2 %. For this reason, the test matrix was tailored to the two opposite extremes: either gas compositions with a low vapour/steam content, where radiative heat transfer can be neglected, or gas mixtures with higher vapour contents, so that radiative heat transfer plays a dominant role. For the selected experiments of the H2P2 series and the corresponding CFD calculations, a vessel with a diameter of 4 m and a height of 8 m was preconditioned with different air-vapour mixtures (a) at room temperature and (b) elevated temperatures. A stable helium layer was then built-up in the upper part of the vessel. The gas was then compressed by injecting helium from above which resembles with best efforts a compression with a piston in a cylinder. This results in a height-dependent and transient increase of the gas temperature. These experiments and the associated CFD calculations were developed to isolate the phenomena of thermal radiation as good as possible from convective and diffusive effects – within the always present experimental limitations. For the reference experiment with ‘dry conditions’ corresponding to the lowest experimentally possible humidity of ≈0.1 %, we show that the use of a model without radiation provides the best agreement between the experimental and numerical results. For the much higher steam content of ≈60 %, the statistical narrow band correlated-k model (SNBCK), non-gray gas model, is the best candidate for future calculations – with computationally forgivable additional effort. We also provide with the Filtered Rayleigh Scattering technique (FRS) an outlook for a possible future instrumentation approach to better meet the requirements of the CFD community.

Effect of Particle Size Distribution and Complex Refraction Index of Alumina on Infrared Rocket Plume Signatures

ABSTRACT Although there are several studies existing in the literature modeling the infrared radiation signatures of solid motor rocket plumes, none of them investigate the effect of some simplifying assumptions such as using gray optical properties, Sauter-mean/mass-mean diameters, temperature-independent optical properties, etc., on thermal radiation characteristics of rocket plumes. These assumptions have the potential to improve the computational efficiency of the radiative transfer calculations by reducing the CPU time required by the solution of Mie theory. Therefore, the objective of this study is to investigate the influence of using (i) mean diameters instead of a particle size distribution (PSD), (ii) optical properties for different phases and crystal structures of Al2O3, (iii) temperature-independent optical properties of Al2O3, and (iv) gray optical properties of Al2O3 particles instead of spectral ones on the radiative heat transfer predictions under rocket plume conditions. For this purpose, a 3-D radiation model based on discrete ordinates method (DOM) coupled with statistical narrow band correlated-k (SNBCK) and Mie theory is utilized. Based on the outcomes of this study, it can be concluded that utilizing mean diameters, temperature-independent optical properties, and gray optical properties of Al2O3 for the calculation of particle radiative properties provides reasonably accurate radiative heat transfer predictions. Moreover, presence of different phases and crystal structures of Al2O3 in the rocket plume leads to significantly different infrared radiation signatures.

A Comparative Study of Entropy Generation Analysis Through Cartesian and Cylindrical Annulus Geometries

Abstract This research paper presents a comparative study dealing with entropy generation analysis in Cartesian and cylindrical annulus geometries. This numerical investigation involves heat and mass transfer coupled with forced convection and gas radiation in a semitransparent medium during the evaporation of a thin liquid film. The systems of equations are solved with interfacial and boundary conditions using an implicit finite volume method by the tridiagonal matrix algorithm method. The radiative transfer equation (RTE) was solved by the Ray tracing model. The statistical narrow band correlated-K model with the updated model parameters was applied to calculate the gas transmissivity. The main intent of this paper is to compare the entropy generation components in two different configurations. The result shows that the entropy generation related to heat and mass transfer in the channel is higher than that estimated for the cylindrical annulus. Regarding optimal design selection, the entropy generation analysis, detailed in this paper, suggests a preference for the cylindrical annulus geometry. Our results may guide designers to select from the studied configuration.

Image temperature calculation for gas and particle system by the mid-infrared spectrum using DRESOR and SNBCK model

The balance between spatial and spectral resolutions plays a key role in image temperature measurement using Imaging Fourier Transform Infrared Spectroscopy (IFTS). In this study, the performance of different combinations of spatial and spectral resolutions was investigated in a two-dimensional (2D) rectangular enclosure filled with gas and particle. The distributions of ratios of energy scattered or reflected (DRESOR) method combined with the statistical narrow band correlated-k (SNBCK) model was developed to obtain the radiative intensity image. Then the image temperature was calculated by the spectral thermometry. The accuracy of the DRESOR-SNBCK method was examined by comparison with the finite volume method (FVM)-line by line (LBL) method. The results showed that the average relative deviation of the image temperatures calculated by the spatial resolutions of 1 × 57 pixel and 1 × 140 pixel was <0.4%, indicating the accuracy of image temperatures was not improved by the increment of spatial resolution. However, the average relative error increased from 4.3% to 7.0% with the number of spectral bands increasing from 18 to 36. In addition, the large relative error of DRESOR-SNBCK method occurred in the low image temperature region due to the scattering effects. The average relative deviation of the homogeneous and inhomogeneous cases was <0.5%, indicating that the image temperatures were not affected by the gas homogeneity.

Monte Carlo method with SNBCK nongray gas model for thermal radiation in containment flows

During a postulated severe accident in light water reactors, containment flows are characterized by relatively low velocities and modest temperature differences after depressurization of the reactor cooling system. Owing to the low gas temperature level and small temperature differences, gas radiation heat transfer was neglected in CFD simulations of hydrogen transport and mixing in containment flows. During the natural mixing and dilution processes, thermal radiation can affect the fluid temperatures and thereby influence the buoyancy forces in the presence of large amounts of steam. In order to quantify the effect of thermal radiation, an efficient Monte Carlo method with statistical narrow band correlated-k (SNBCK) nongray gas model has been implemented to solve the radiative transfer equation within the framework of containmentFOAM. The tailored Monte Carlo solver is validated against the OECD/NEA SETH-2 PANDA ST1 experiments, and it is proven that gas radiation has a significant effect on the gas temperature field and the helium-steam mixing process. The results clearly indicate that gas radiation cannot be neglected in containment flows even at modest temperature differences (ΔT<50K).

Interaction of mixed convection with non-gray gas radiation in a partially heated horizontal pipe: entropy generation analysis

PurposeThis paper aims to numerically analyze the effect of non-gray gas radiation on mixed convection in a horizontal circular duct with isothermal partial heating from the sidewall. The influence of heater location on heat transfer, fluid flow and entropy generation is given and discussed in this study.Design/methodology/approachThe numerical computation of heat transfer and fluid flow has been developed by the commercial finite element software COMSOL Multiphysics. Radiation code is developed based on the T10 Ray-Tracing method, and the radiative properties of the medium are computed based on the statistical narrow band correlated-k model.FindingsThe obtained results depicted that the radiation considerably contributes to the temperature homogenization of the gas. The findings highlight the impact of the heater location on swirling flow. It is also shown that the laterally heating process provides better energy efficiency than heating from the top of the enclosure.Originality/valueThis study is performed to improve heat transfer and to minimize entropy generation. Therefore, it is conceivable to improve the model design of industrial applications.

Effect of combined natural convection and non-gray gas radiation on entropy generation through a cylindrical annulus

The present work is focused on the interaction between natural convection and thermal radiation in a participating medium through a cylindrical annulus. The Ray Tracing method through the quadrature T10 has been adopted in association with the Statistical Narrow Band correlated-k (SNBCK) model to solve the radiative part of the problem. Special attention is given to entropy generation and its dependency on the various governing parameters including the inner cylinder temperature, the outer cylinder radius, emissivities of the annulus walls, and the gas pressure. The results show that radiation remarkably affects the structure of the fluid flow and the temperature distribution, enhancing heat exchanges in the annulus. Moreover, it is found that the volumetric entropy generation due to radiative processes of medium should not be neglected and is comparable to the volumetric entropy generation due to heat conduction. It is also shown that increasing the emissivities of the cylinders intensifies entropy generation due to radiation through walls, but on the other hand doesn’t affect the volumetric entropy generation.

Effects of oxygen concentration on the thermal and chemical structures of laminar coflow CO/H2 diffusion flames burning in O2/H2O atmosphere

The thermal and chemical structures of laminar coflow syngas diffusion flames burning in O2/H2O atmosphere were experimentally and numerically studied at 1 atm and initial temperature of 400 K. The O2/H2O molar ratio was varied from 20/80 to 100/0 to investigate the effects of oxygen concentration. An intensified CCD was used to capture the OH*-chemiluminescence based on which the measured flame heights were obtained. Numerical modelling was conducted using a detailed validated chemical mechanism including OH* formation, the discrete-ordinates method coupled with the statistical narrow-band correlated-K(SNBCK) model for the radiative properties of combustion products, and the conjugate heat transfer model to account for the heat transfer between the burner wall and the fuel and oxidizer streams. Results show that the measured flame heights agree well with the simulated values. The flame height and the maximum flame temperature decrease and increase respectively with increasing the O2 concentration. With increasing the O2 concentration, the maximum OH mole fraction first increases but finally decreases and peaks at the oxidizer composition of 90%O2-10%H2O. Increasing the O2 concentration has little influence on the flame attachment but significantly enhances the heat release rate of H + O2(+M) = HO2(+M) and this reaction is found to be the primary cause of the strong influence of the oxygen concentration on the burner tip temperature. As the oxygen concentration increases, syngas pyrolysis inside the fuel tube is promoted, mainly through the H consumption reactions due to the enhanced back diffusion of H from the flame front into the burner.

Heat and mass transfer of combined forced convection and thermal radiation within a channel: Entropy generation analysis

The present paper deals with a numerical modelling of thermal and mass transfer coupled by thermal radiation and forced convection in a semi-transparent medium during the evaporation of a thin water film used for wall protection within a channel. Particular attention is paid to the analysis of the entropy generation due to heat transfer and mass diffusion. The governing equations are solved numerically using the Finite Volume Method. Furthermore, the resolution of the Radiative Transfer Equation was carried out by the “Ray-Tracing” method according to a symmetric quadratic scheme of SN (S4) whereas the radiative properties of the non-grey gas were deduced by the application of the “Statistical Narrow Band Correlated-K” (SNB-CK) model. The effect of several parameters on entropy generation due to conduction, thermal radiation and mass diffusion are analysed in this paper. The results clearly demonstrate the major dominance of the wall radiative entropy generation in all the studied cases. The results also prove that for high values of drywall temperature and emissivity, the entropy generation due to mass diffusion augmented.

The effect of different HITRAN databases on the accuracy of the SNB and SNBCK calculations

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.

Measurements and modeling of PAH soot precursors in coflow ethylene/air laminar diffusion flames

New experimental and numerical results of a laminar ethylene-air co-flow non-premixed flame are compared, in terms of soot volume fraction and temperature, and of polycyclic aromatic hydrocarbons (PAH) distributions. Measurements involved UV-excited laser induced incandescence (properly calibrated), planar laser induced fluorescence (PLIF), and deconvoluted two-color pyrometry. In order to evidence soot and PAH, the comparison of prompt and delayed detection is carried out at four spectral detection wavelengths (340, 400, 450 and 550 nm). Numerical results are obtained using a detailed gas-phase chemical kinetics mechanism considering 94 species and 719 reactions, and a sectional soot model, together with a statistical narrow band correlated K (SNBCK) wide band model to account for radiation. Computed PAH, grouped by their number of rings, is found to exhibit a good correlation with experimental PLIF results at different spectral detection wavelengths. In particular, it is shown that 340 and 400 nm fluorescence signals indicate the presence of one up to four-ringed computed PAH, whereas the interpretation of measurements at larger wavelengths is found to be elusive, due to soot signal overlap. Furthermore, an interplay between temperature decrease, soot volume fraction increase and radiative heat transfer distribution with increasing fuel flow rate is also demonstrated.

Natural convection analysis through a radiatively participating media within a rectangular enclosure

A computational approach for the modelling of combined gas radiation and laminar natural convection heat transfer within a rectangular enclosure is presented. One wall among the others is maintained at a constant higher temperature (Th) while the others are of a constant lower temperature (Tc). The discrete-ordinate method (DOM) through S12 directions is applied to resolve the radiative transport equation (RTE) while the 'statistical narrow band correlated-k' (SNBCK) model is adopted to provide gas radiative properties. The effect of radiative contribution, the enclosure tilt angle, the boundary and geometry conditions are presented. Special attention is given to the effect scales of these parameters on the average Nusselt numbers. The results show that radiative effect remarkably contributes to the acceleration of the vortexes, improving heat exchanges at walls.

Entropy Generation due to Combined Natural Convection and Thermal Radiation within a Rectangular Enclosure

ABSTRACTThe present work investigates entropy production due to coupled natural convection/radiation heat transfer phenomenon in an inclined rectangular enclosure, isothermally heated from the bottom side and isothermally cooled from the other sides. The discrete-ordinate method is used in modeling the radiative transport equation while the statistical narrow band correlated-k model is adopted to deduce the radiative properties of the medium. The influence of pertinent parameters such as aspect ratio, inclination angle and walls emissivities on entropy generation is studied. It is found that the volumetric entropy generation is reduced when increasing the inclination angle of the enclosure. Moreover, it is shown that the minimum entropy production due to radiation heat transfer in participating media occurs at aspect ratio equal to unity.

Second law analysis of simultaneous heat and mass transfer through non-grey gas radiation within a cylindrical annulus

A numerical computation is performed to analyse entropy generation due to heat and mass transfer through non-gray gas radiation and forced convection within a cylindrical annulus. The inner cylinder, covered by a thin water film, is assumed to be adiabatic, while the outer one is considered to be isothermal and dry. The conservation equations are solved by applying the finite volume method. The radiative part of this study is solved by the 'Ray Tracing' method through S4 directions in association with the "statistical narrow band correlated-k" model. The results showed that entropy generation increases with dry wall temperature, annulus width and the outer wall emissivity. It is found that the radiative entropy generated at walls presents a clear dominance compared to entropy generated due to heat conduction, gas radiation and mass diffusion. It is justified that using a thin water film offers greater potential for protecting the inner wall against overheating.

Second law analysis of simultaneous heat and mass transfer through non-grey gas radiation within a cylindrical annulus

A numerical computation is performed to analyse entropy generation due to heat and mass transfer through non-gray gas radiation and forced convection within a cylindrical annulus. The inner cylinder, covered by a thin water film, is assumed to be adiabatic, while the outer one is considered to be isothermal and dry. The conservation equations are solved by applying the finite volume method. The radiative part of this study is solved by the 'Ray Tracing' method through S4 directions in association with the statistical narrow band correlated-k model. The results showed that entropy generation increases with dry wall temperature, annulus width and the outer wall emissivity. It is found that the radiative entropy generated at walls presents a clear dominance compared to entropy generated due to heat conduction, gas radiation and mass diffusion. It is justified that using a thin water film offers greater potential for protecting the inner wall against overheating.

Natural convection analysis through a radiatively participating media within a rectangular enclosure

A computational approach for the modelling of combined gas radiation and laminar natural convection heat transfer within a rectangular enclosure is presented. One wall among the others is maintained at a constant higher temperature (Th) while the others are of a constant lower temperature (Tc). The discrete-ordinate method (DOM) through S12 directions is applied to resolve the radiative transport equation (RTE) while the 'statistical narrow band correlated-k' (SNBCK) model is adopted to provide gas radiative properties. The effect of radiative contribution, the enclosure tilt angle, the boundary and geometry conditions are presented. Special attention is given to the effect scales of these parameters on the average Nusselt numbers. The results show that radiative effect remarkably contributes to the acceleration of the vortexes, improving heat exchanges at walls.

A comprehensive evaluation of different radiation models in a gas turbine combustor under conditions of oxy-fuel combustion with dry recycle

The oxy-fuel combustion is a promising CO2 capture technology from combustion systems. This process is characterized by much higher CO2 concentrations in the combustion system compared to that of the conventional air-fuel combustion. To accurately predict the enhanced thermal radiation in oxy-fuel combustion, it is essential to take into account the non-gray nature of gas radiation. In this study, radiation heat transfer in a 3D model gas turbine combustor under two test cases at 20atm total pressure was calculated by various non-gray gas radiation models, including the statistical narrow-band (SNB) model, the statistical narrow-band correlated-k (SNBCK) model, the wide-band correlated-k (WBCK) model, the full spectrum correlated-k (FSCK) model, and several weighted sum of gray gases (WSGG) models. Calculations of SNB, SNBCK, and FSCK were conducted using the updated EM2C SNB model parameters. Results of the SNB model are considered as the benchmark solution to evaluate the accuracy of the other models considered. Results of SNBCK and FSCK are in good agreement with the benchmark solution. The WBCK model is less accurate than SNBCK or FSCK. Considering the three formulations of the WBCK model, the multiple gases formulation is the best choice regarding the accuracy and computational cost. The WSGG model with the parameters of Bordbar et al. (2014) [20] is the most accurate of the three investigated WSGG models. Use of the gray WSSG formulation leads to significant deviations from the benchmark data and should not be applied to predict radiation heat transfer in oxy-fuel combustion systems. A best practice to incorporate the state-of-the-art gas radiation models for high accuracy of radiation heat transfer calculations at minimal increase in computational cost in CFD simulation of oxy-fuel combustion systems for pressure path lengths up to about 10barm is suggested.

Effects of total pressure on non-grey gas radiation transfer in oxy-fuel combustion using the LBL, SNB, SNBCK, WSGG, and FSCK methods

The effects of total pressure on gas radiation heat transfer are investigated in 1D parallel plate geometry containing isothermal and homogeneous media and an inhomogeneous and non-isothermal CO2–H2O mixture under conditions relevant to oxy-fuel combustion using the line-by-line (LBL), statistical narrow-band (SNB), statistical narrow-band correlated-k (SNBCK), weighted-sum-of-grey-gases (WSGG), and full-spectrum correlated-k (FSCK) models. The LBL calculations were conducted using the HITEMP2010 and CDSD-1000 databases and the LBL results serve as the benchmark solution to evaluate the accuracy of the other models. Calculations of the SNB, SNBCK, and FSCK were conducted using both the 1997 EM2C SNB parameters and their recently updated 2012 parameters to investigate how the SNB model parameters affect the results under oxy-fuel combustion conditions at high pressures. The WSGG model considered is the recently developed one by Bordbar et al. [19] for oxy-fuel combustion based on LBL calculations using HITEMP2010. The total pressure considered ranges from 1 up to 30atm. The total pressure significantly affects gas radiation transfer primarily through the increase in molecule number density and only slightly through spectral line broadening. Using the 1997 EM2C SNB model parameters the accuracy of SNB and SNBCK is very good and remains essentially independent of the total pressure. When using the 2012 EM2C SNB model parameters the SNB and SNBCK results are less accurate and their error increases with increasing the total pressure. The WSGG model has the lowest accuracy and the best computational efficiency among the models investigated. The errors of both WSGG and FSCK using the 2012 EM2C SNB model parameters increase when the total pressure is increased from 1 to 10atm, but remain nearly independent of the total pressure beyond 10atm. When using the 1997 EM2C SNB model parameters the accuracy of FSCK only slightly decreases with increasing the total pressure.

Sensitivity of Radiation Modeling to Property Estimation Techniques in the Freeboard of Lignite-Fired Bubbling Fluidized Bed Combustors (BFBCs)

Predictive accuracy and computationally efficiency of method of lines (MOL) solution of the discrete ordinate method (DOM) coupled with different radiative property estimation techniques (GG, SLW, SNBCK) are assessed by applying them to the prediction of incident radiative fluxes along the freeboard walls of a 0.3 MWt atmospheric bubbling fluidized bed combustor (ABFBC) and comparing their predictions with measurements generated previously from two runs one without and the other with recycle. Freeboard is treated as a three-dimensional rectangular enclosure containing a gray/non-gray, absorbing-emitting-isotropically scattering medium. Radiative properties of particles are evaluated by using geometric optics approximation. A comparative study is also provided between the source term distributions predicted by MOL solution of DOM with gray gas (GG), spectral line-based weighted sum of gray gases (SLW), and statistical narrow-band correlated-k (SNBCK) along the centerline of the freeboard for both runs. Comparisons reveal that the MOL solution of DOM with SLW model and geometric optics approximation provides accurate and computationally efficient solutions for wall fluxes and source term distributions in the freeboard of fluidized bed combustors containing particle laden combustion gases.

Effects of water vapor addition to the air stream on soot formation and flame properties in a laminar coflow ethylene/air diffusion flame

The effects of adding water vapor to the air stream on flame properties and soot volume fraction were investigated numerically in a laminar coflow ethylene/air diffusion flame at atmospheric pressure by solving the fully elliptic conservation equations and using a detailed C2 reaction mechanism including PAH up to pyrene and detailed thermal and transport properties. Thermal radiation was calculated using the discrete-ordinates method and a statistical narrow-band correlated-k based wide band model for the absorption coefficients of CO2 and H2O. Soot formation was modeled using a PAH based inception model and the HACA mechanism for surface growth and oxidation. Addition of water vapor significantly reduces radiation heat loss from the flame primarily through reduced soot loading and flame temperature. The added water vapor affects soot formation and flame properties through not only dilution and thermal effects, but also through chemical effect. The chemical effect is as significant as the dilution and thermal effects. The primary pathway for the chemical effect of water vapor is the reverse reaction of OH+H2↔H+H2O. Our numerical results confirm that the reduced H radical concentration leads to lower PAH concentrations and consequently lower soot inception rates. In contrast, the radiation effect due to the added water vapor was found to have a minor influence on both flame structure and soot formation in the laminar diffusion flame investigated.