Statistical Narrow-band Correlated-k Model 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.

Entropy generation analysis of a three-dimensional coal-fired furnace: A realistic study

An analysis of the entropy generation by radiative heat transfer in a three-dimensional virtual coal-fired furnace is performed. The gases, including CO2 and H2O, and particles, including soot, unburnt char and ash, are considered as a participating medium. The radiative transfer equation for a non-grey medium was solved by the discrete ordinate method, in which the radiative properties of the gases, soot, unburnt char and ash were obtained by using the statistical narrow-band correlated-k model, Rayleigh's theory, and Mie theory, respectively. The distributions of the local volumetric rate of entropy generation and the local rate of entropy generation at the wall are calculated. The contributions of various media in coal-burning furnaces to the radiative entropy generation rate (REGR) are evaluated, and the effects of several important factors, such as the oxidizer atmosphere, burnout rate, and the volume fraction of soot, unburnt char and ash on the REGR and dimensionless entropy generation were also investigated. The numerical results show that the irreversibility of the particle radiation contributes more than 80% of the volumetric radiative entropy generation. The concentration of particles also has an important effect on REGR, which decreases by 41% when the concentration of unburnt char and ash increases from 10 ppm to 50 ppm and decreases by 70% when the concentration of soot increases from 1 ppm to 6 ppm in a real-size furnace such as an optically thick furnace.

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.

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.

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.

Experimental and numerical study of the effects of the oxygen index on the radiation characteristics of laminar coflow diffusion flames

The oxygen concentration in the oxidizer stream (O2+N2) of laminar coflow ethylene diffusion flames is varied from 17% to 35% in order to study its influence on the flame height, the soot formation/oxidation processes, the smoke point characteristics, and the vertical distributions of radiative flux at a distance of 6.85cm from the flame axis. Measured values for all the investigated parameters are compared with the predictions provided by a numerical model based on a two-equation semiempirical acetylene-based soot model and on the statistical narrow-band correlated-k model to compute thermal radiation. Predictions are in overall reasonable agreement with the experiments for oxygen indices in the range 19–35%, whereas all the investigated parameters are significantly underestimated for an oxygen index of 17%. Measured flame heights based on CH∗ emission below, at, or slightly above the smoke point, as well as predicted stoichiometric flame heights, are found to be proportional to ζ=V˙f[D∞ln(1+1/S)]-1(T∞/Tad)0.67, where V˙f, D∞, S, and Tad are the volumetric flow rate of ethylene, the diffusion coefficient at ambient temperature, the stoichiometric molecular air-to-fuel ratio, and the adiabatic flame temperature. Soot formation processes are found to increase with the oxygen index, leading to higher values of the maximum soot volume fraction and the peak integrated soot volume fraction. In addition, the latter is reached at a nondimensional height (normalized by ζ of approximately 0.05, regardless of the oxygen index within the investigated range. Two regimes are evidenced: The first regime, occurring for oxygen indices lower than 25%, is dominated by soot oxidation and is characterized by an enhancement in both the maximum soot volume fraction and the fuel flow rate at the smoke point with the oxygen index. The second regime, occurring for oxygen indices higher than 25%, is dominated by soot formation; the rate of increase in the maximum soot volume fraction with the oxygen concentration is lower than in the first regime, whereas the fuel flow rate at the smoke point decreases. Finally, the peak of radiative flux increases with the oxygen index, but its rate of increase is also found to be considerably reduced for oxygen indices greater than 25%.

Influence of radiative property models on soot production in laminar coflow ethylene diffusion flames

Two axisymmetric laminar coflow non-smoking and smoking ethylene diffusion flames are studied numerically in order to assess the influence of different radiative property models on the soot formation and oxidation processes. Simulations are carried out by considering the Steady Laminar Flamelet (SLF) concept and a modified two-equation acetylene-based model to describe the soot nucleation, surface growth and oxidation processes. Several radiative property models are considered: the simple Optically Thin Approximation (OTA), the Weighted-Sum of Grey-Gases (WSGG), the Grey-Wide-Band model (GWB), the Statistical Narrow Band Correlated-k model (SNBCK) and the Full Spectrum Correlated-k model (FSCK). Comparisons between calculations carried out with the SNBCK model and experimental data show a reasonable agreement. Model results show that the choice of the radiative property models influence largely the soot prediction, especially in the upper part of the flame where oxidation occurs. Simulations show that the reabsorption of spectral gas and soot is an important feature and thus the commonly used OTA or grey models introduce large discrepancies. The GWB model leads to improved solutions, but it should be avoided if accurate predictions are desired. The FSCK provides equivalent results as compared to the SNBCK model with a substantial gain in CPU time.

Calculations of gas radiation heat transfer in a two-dimensional rectangular enclosure using the line-by-line approach and the statistical narrow-band correlated-k model

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.

Assessment of radiative property models in non-gray sooting media

The radiative transfer equation (RTE) is solved by the Finite Volume Method (FVM) in 1D and 2D axisymmetric configurations containing mixtures of water vapor, carbon dioxide and soot. Several radiative property models, namely simple gray models, the Statistical Narrow Band Correlated- k (SNBCK) model, the Weighted-Sum-of-Gray-Gases (WSGG) model, the Full-Spectrum Correlated- k (FSCK) model, the Spectral-Line-Based Weighted-Sum-of-Gray-Gases (SLW) model, a Gray-Narrow-Band (GNB) model and a Gray-Wide-Band (GWB) model, are assessed by comparison with reference calculations based on the Ray Tracing (RT) method coupled with the Statistical Narrow Band (SNB) model. Different treatments of overlapping bands are implemented with the SNBCK model, namely the correlated approach, the uncorrelated approach, and the mixing schemes of Modest and Riazzi (J. Quant. Spectros. Rad. Trans. 90 (2005) 169–189) and of Solovjov and Webb (J. Quant. Spectros. Rad. Trans. 65 (2000) 655–672) (Superposition and Multiplication). The Full Spectrum (FS) k-distributions required to run both FSCK and SLW are assembled from the same narrow band (NB) database as for the SNB and the SNBCK models using either the mixing model of Modest and Riazzi or the Multiplication scheme. The correlated SNBCK is the most accurate model but is too time consuming for engineering applications. The computational efficiency of the SNBCK can be considerably improved without altering the quality of the solutions by using the gas mixing scheme of Modest and Riazzi. Numerical results show that, in this case, good accuracy for spectrally-integrated quantities is obtained by considering only a 2-point Gauss–Legendre quadrature scheme. The FSCK and the SLW, using FS k-distributions assembled with the Modest and Riazzi scheme, are found to be the best compromise in terms of accuracy and computational requirements. It is found that FSCK predictions remain satisfactory by reducing the number of quadrature points of the Gauss–Legendre scheme up to seven.

Effects of radiative heat transfer on the structure of turbulent supersonic channel flow

The interaction between turbulence in a minimal supersonic channel and radiative heat transfer is studied using large-eddy simulation. The working fluid is pure water vapour with temperature-dependent specific heats and molecular transport coefficients. Its line spectra properties are represented with a statistical narrow-band correlated-k model. A grey gas model is also tested. The parallel no-slip channel walls are treated as black surfaces concerning thermal radiation and are kept at a constant temperature of 1000 K. Simulations have been performed for different optical thicknesses (based on the Planck mean absorption coefficient) and different Mach numbers. Results for the mean flow variables, Reynolds stresses and certain terms of their transport equations indicate that thermal radiation effects counteract compressibility (Mach number) effects. An analysis of the total energy balance reveals the importance of radiative heat transfer, compared to the turbulent and mean molecular heat transport.

Effects of radiative heat transfer on the structure of turbulent supersonic channel flow

The interaction between turbulence in a minimal supersonic channel and radiative heat transfer is studied using large-eddy simulation. The working fluid is pure water vapour with temperature-dependent specific heats and molecular transport coefficients. Its line spectra properties are represented with a statistical narrow-band correlated-k model. A grey gas model is also tested. The parallel no-slip channel walls are treated as black surfaces concerning thermal radiation and are kept at a constant temperature of 1000 K. Simulations have been performed for different optical thicknesses (based on the Planck mean absorption coefficient) and different Mach numbers. Results for the mean flow variables, Reynolds stresses and certain terms of their transport equations indicate that thermal radiation effects counteract compressibility (Mach number) effects. An analysis of the total energy balance reveals the importance of radiative heat transfer, compared to the turbulent and mean molecular heat transport.

Application of the statistical narrow-band correlated-k model to entropy generation through non-grey gas radiation inside a spherical enclosure

In the present work, we proposed a numerical computation of entropy generation by radiative heat transfer through an absorbing-emitting non-grey gas, confined in a spherical enclosure. The 'Ray Tracing' method is associated to the statistical narrow band correlated-k SNBCK model, to solve the radiative transfer equation and to deduce the radiative properties of the gas. The effects of boundary conditions, enclosure dimensions and spectral correlation on the entropy generation are presented. The results show that the volumetric radiative entropy production is more developed in heating configuration while the wall radiative entropy production is more developed in case of cooling.

A numerical simulation on the infrared radiation of hot exhausting nozzles with a coupled flow and heat transfer model

A coupled model among flow field, solid temperature, species concentration and gas radiation, which was based on statistical narrow-band correlated-k model, was employed to predict the infrared radiations from hot exhausting nozzles. The parameters of narrow-band model were deduced from HITEMP line-by-line database. Several methods to increase computational efficiency and to save computational resources were employed, thus all the complicated computations could be operated on a personal computer. The predictions for three cases have been conducted to validate the accuracy of the methods mentioned above, including the temperature distribution of a water-cooling nozzle in rocket engines, the carbon dioxide absorptivity at the wavelength of 4.3 micron and the infrared radiation of a cylindrical furnace. Finally, the aerothermodynamic and infrared characteristics of two nozzles were predicted. It was shown that the infrared radiation intensity of chevron ejecting nozzle were obviously smaller than that of common axisymmetric convergent-divergent nozzle.

Effects of Gravity on Soot Formation in a Coflow Laminar Methane/Air Diffusion Flame

Simulations of a laminar coflow methane/air diffusion flame at atmospheric pressure are conducted to gain better understanding of the effects of gravity on soot formation by using detailed gas-phase chemistry, complex thermal and transport properties coupled with a semiempirical two-equation soot model and a nongray radiation model. Soot oxidation by O2, OH and O was considered. Thermal radiation was calculated using the discrete ordinate method coupled with a statistical narrow-band correlated-K model. The spectral absorption coefficient of soot was obtained by Rayleigh’s theory for small particles. The results show that the peak temperature decreases with the decrease of the gravity level. The peak soot volume fraction in microgravity is about twice of that in normal gravity under the present conditions. The numerical results agree very well with available experimental results. The predicted results also show that gravity affects the location and intensity for soot nucleation and surface growth.