Statistical Narrow Band 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.

Statistical Narrow Band model for vibrational nonequilibrium [formula omitted] radiation

This paper presents the development of a Statistical Narrow Band (SNB) model for CO2 in a nonequilibrium vibrational state. The population densities of the energy levels are modeled by a three-temperature approach (T,T12,T3) associated resp. to translation–rotation modes, symmetric-stretching and bending modes, and antisymmetric stretching mode, to compute nonequilibrium line by line (LBL) spectra. The nonequilibrium between vibrational temperatures induces spectral correlation issues between ησ/κσ and κσ, where ησ and κσ are the emission and absorption coefficients respectively. To overcome this issue, a vibrational splitting of the spectroscopic database is made to separate lines with completely different vibrational transitions. The SNB parameters are obtained by fitting the curves of growth from the LBL approach by a least squares error minimization using a Newton method for pure Lorentz and Doppler broadening regimes for each line class. The total SNB transmissivity is obtained by computing the product of each line class transmissivity, and the decorrelation between the spectra of the different classes is checked. Finally, the model is tested in Voigt broadening regime using a mixing rule by computing outlet radiative intensity of uniform and non-uniform columns and agrees well with the LBL approach. SNB parameters are available under request to the corresponding author.

Accurate evaluation on infrared spectral radiation for booster phase rocket exhaust plumes

Accurate modeling of rocket exhaust plumes’ infrared spectral radiation is of great significance in the field of aerospace. The existing classical statistical-narrow-band (SNB) model cannot adapt well to the highly heterogeneous plume temperature and concentration fields, with large radiation modeling errors at the spectral level. To overcome this limitation, this study presents an improved SNB model (I-SNB) for rocket plume infrared spectral radiation modeling, which categorizes the spectral lines within narrow band Δη into different groups according to their inconsistency in sensitivity to changes in both temperature and concentration along the plume integration path, ensuring that the spectral lines within the same group have similar behaviors with simultaneous changes in both temperature and concentration. The modeling accuracy of the present I-SNB model has been evaluated using FTIR spectral measurements and LBL benchmark solutions, demonstrating significantly better performance than the classical SNB model. Then, the I-SNB model has been used to investigate the rocket plume spectral radiation during the booster phase, the results of which have engagement guiding significance for the development of booster phase interception (BPI) of the space-based infrared early warning system.

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.

GPU-Accelerated infrared signature analysis model based on the Reverse Monte Carlo method

High-fidelity scene simulations are now possible thanks to advancements in computer technology. A fast analysis model for target infrared signature was developed by using the Graphics Processor Unit (GPU) device. The Malkmus statistical narrow band model is used to calculate the gas band-averaged transmittance. Mie scattering theory is used to calculate the particle scattering parameters, and based on the assumption that particles scatter light independently, the albedo and phase functions of the participating media are determined. The Reverse Monte Carlo method (RMCM) is used to complete the radiative transfer. Finally, a GPU device is used to accelerate the ray tracing process and achieve fast calculation of radiation. The calculation results show that the fast analysis model with high accuracy, and compared to Central Processing Unit (CPU) serial programs, the computational performance is greatly improved, with an acceleration ratio of more than 60. The thread block size has a significant impact on the occupancy and acceleration ratio, and the highest computational performance is obtained with the thread block size of 128. The scattering will reduce the acceleration ratio of the fast analysis model, and the performance will be reduced as the particle mass flow rate increases.

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.

Obstruction of infrared signature with cold gases

The idea of infrared signature reduction by injecting cold gas between the source and observer has been investigated. Statistical narrow band coefficients of ethylene have been generated from HITRAN spectroscopic database and proposed to attenuate radiation on the 8–14 μm spectral region whereas CO2 is employed for 3–5 μm wavelength band suppression. Dilution of ethylene with CO2 also suppresses the flammability and guarantees safe operation. Several 1-D test cases are solved to validate the developed solver, and the proposed method is tested on 1-D and 3-D problems. The results satisfactorily show that a significant and safe radiance reduction can be achieved with cold CO2 diluted ethylene injection between the exhaust and observer on the whole spectrum.

Study of Statistical Narrow-Band Models for Infrared Signature of an Aeroengine Exhaust Plume in Mid-wave Infrared and Short-Wave Infrared Band

Study of Statistical Narrow-Band Models for Infrared Signature of an Aeroengine Exhaust Plume in Mid-wave Infrared and Short-Wave Infrared Band

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).

Effect of pressure broadening on the radiative heat transfer by CO and CH4 gases using line-by-line method with latest high-temperature database

As the development of current propulsion technology such as gas turbine and rocket chamber moving to higher working pressure, the radiative parameters of fuel, such as CH4 or CO, are required at elevated pressures, which in some cases are calculated without considering the pressure effect of line broadening. To investigate the pressure effect of line broadening on the radiative heat transfer, the radiative heat sources of a 1-D enclosure filled with CH4/CO and Planck mean absorption coefficients at elevated pressures were calculated using the statistical narrow band and line-by-line methods. The radiative parameters were conducted using high temperature molecular spectroscopic (HITEMP) 2019 (for CO) and HITEMP 2020 (for CH4) databases. The results showed that the pressure effect of line broadening on the calculations of radiative heat source of CH4 can be ignored when HITEMP 2020 database was used. For CO medium, the pressure effect of line broadening was over 40% at 30 atmosphere in all cases whichever methods and databases were used. The pressure broadening has a strong effect on the Planck mean absorption coefficient below 1000 K for CH4 and at the temperature of 500-900 K for CO at 30 atmosphere. The maximum pressure effects were 22% for CH4 and 18% for CO at 30 atmosphere, which illustrated the pressure effect of line broadening needed to be taken into account in the calculation of Planck mean absorption coefficient.

Effects of radiation reabsorption on the laminar burning velocity of methane/air and methane/hydrogen/air flames at elevated pressures

Due to the development of high-load and high-pressure combustion equipment, it is crucial to increase the accuracy of laminar burning velocity prediction under elevated pressures. However, the radiation ability of methane under high pressures is ignored, which may cause large discrepancies and fluctuations in the simulation of burning velocity. In this study, the HITRAN 2016 database was employed to build the Statistical Narrow-Band (SNB) model of methane at elevated pressures. The effects of radiation reabsorption on the laminar burning velocity were investigated in methane/air and methane/hydrogen/air flames using different radiation models. The simulation was conducted within a wide equivalence ratio (ϕ = 0.6–1.4) and the calculated pressures were up to 20 atm. Comparing the results of different radiation models revealed that the laminar burning velocity was promoted by radiation reabsorption. For varying equivalence ratios at P = 5 atm, in the case of ϕ = 0.6–1.2, the preheat-induced chemical effect by radiation reabsorption was the major factor affecting the burning velocity, controlled by R290 CH2 + O2<=greater than2H + CO2 and R86 2OH<=>O + H2O. And the direct radiation effect played the key role with the equivalence ratio between 1.2 and 1.4, enhanced by increasing concentration of methane. For methane/air flames under stoichiometric conditions, the effects of radiation reabsorption increased with pressure. The preheat-induced chemical effect, related to the consumption of H radical through R35 H + O2 + H2O<=>HO2 + H2O and R43 H + OH + M<=>H2O + M, was significant at P = 1–10 atm. And the direct radiation effect was the dominant factor above 10 atm by increasing optical thickness. Besides, the change of preheat-induced chemical effect by radiation reabsorption caused by H2 addition was examined. The results clarified that the dominant reactions remained the same, while the range of pressures where each reaction dominated changed as 20% H2 was added, owing to the higher sensitivity to H2 addition for R43 comparing to R35.

New WSGG model for gas mixtures of H2O, CO2, and CO in typical coal gasifier conditions

This study develops a new weighted-sum-of-gray-gases (WSGG) model for the radiative characteristics of CO, H2O, and CO2 mixtures in pulverized coal gasification plants under a typical high pressure (45 atm). This is significant for prediction of radiative heat transfer in computational fluid dynamic (CFD) calculation. The new high-pressure WSGG model and its parameters are based on the statistical narrow band (SNB) model of EM2C Laboratory. The new model applies to the temperature range of 500–3000 K and the path length range of 0.1–20 m. Moreover, the model can calculate the radiation characteristics of gas mixtures under different partial pressures of three gases. Therefore, the new model can be applied to the radiation transfer in pulverized coal gasification under specific high pressure. The results of one-dimensional cases show that the new model can well predict the radiative heat transfer process of gas mixtures. The error of radiation heat flux is less than 5.38%, and the radiation source term error is less than 0.67%, while the accuracy of the traditional WSGG model is very low under gasification conditions, and the error is more than 25% compared with the benchmark. When the new model is embedded into the CFD simulation of a high-pressure gasifier, the maximum temperature difference between the new and traditional models is up to 300 K, while the calculated absorption coefficient and radiation source term of gas mixtures are noticeably different. In conclusion, compared with the traditional model, the new WSGG model has higher accuracy for calculating gas radiation heat transfer under the condition of coal gasification. This paper also provides the parameters of the new model, which can be used in the CFD engineering simulation of coal gasification plants.

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.

Non-gray gas and soot radiation heat transfer to a spherical fuel particle in combustion scenarios

Thermal radiation is an important heat transfer mode in flames and combustion systems. Non-gray gas and soot radiation is one of the most important heat feedback mechanisms to the preheating of fuel particles. The Discrete Ordinates Method (DOM) is used to solve the radiative transfer equation and the statistical Narrow Band k-distribution (SNBCK) method is used to model the non-gray radiation to investigate the radiative heat flux imposed on a spherical fuel particle immersed in high-temperature media. A range of gas temperature, pressure, gas volume size, mole fraction of radiating gas species and soot volume fraction are considered. Based on the datasets from the DOM-SNBCK model, two predictive models are developed by function fitting and neural networks. The function fitting model explicitly accounts for the dependence of radiative heat flux on the fitting parameters, but suffers from noticeable errors. The neural network results are in great agreement with the DOM-SNBCK results and can be used to estimate the non-gray gas and soot radiation heat transfer to spherical fuel particles.

Effects of radiation reabsorption on laminar NH3/H2/air flames

Ammonia combustion, owing to its zero greenhouse gas CO2 emission, is attracting attention for energy utilization. However, the thermal radiation of NH3 has not been reported and involved in the numerical simulations of ammonia flames, which may cause serious errors in estimating the laminar flame speeds. In this study, the effects of radiation reabsorption on the laminar flame speed at different equivalence ratios and elevated pressures were numerically investigated using planar NH3/H2/air flames. The Statistical Narrow-Band (SNB) model parameters for NH3 were generated and used for simulations of NH3/H2/Air flames, considering the radiation reabsorption. It was found that the radiation reabsorption exhibited a non-monotonic behavior at ϕ = 0.65–1.6, with the maximum enhancement of flame speed up to 15.6%. The effects of radiation reabsorption were controlled by both radiation and chemistry. The preheat-induced chemical effect dominated at ϕ = 0.65–1.25 and the enhancement of flame speed was mainly influenced by H, OH and NH2 radicals, which were primarily controlled by the reactions R36, R257 and R246, respectively. In contrast, the direct radiation effect dominated at ϕ = 1.25–1.6 and the enhancement of flame speed was mainly affected by the increasing mole fraction of NH3. With increasing pressures, the preheat-induced chemical effect dominated at P = 1–10 atm and the enhancement of flame speed were mainly impacted by H and NNH radicals, which were controlled by the reactions R44 and R257, respectively. At higher pressures above 10 atm, direct radiation effect was dominating and the enhancement of flame speed was mainly controlled by the increasing optical thickness.

Simulation and analysis of hot plume infrared signature based on SNB model

Abstract Numerical calculation of infrared emission from hot plume is of great significance for flight monitoring and detections. In this paper, the SNB (statistical narrow band) model established with parameters derived from the high-resolution spectral database HITEMP 2010 is used to perform the hot plume infrared signature simulations. Accuracy of the model is examined by the exact LBL (line by line) method, which proves the model’s reliability to predict radiative properties of combustion gases. In the application part, the SNB model is used to analyze infrared signatures of aircraft plumes cruising at different flight altitudes. The results show that cruising at a higher-altitude will obviously reduce the plume infrared emission. Besides, the plume infrared emissive energy mainly concentrates in a special wavenumber interval and can be strongly absorbed by atmosphere.

Simulation and analysis of hot plume infrared signature based on SNB model

Abstract Numerical calculation of infrared emission from hot plume is of great significance for flight monitoring and detections. In this paper, the SNB (statistical narrow band) model established with parameters derived from the high-resolution spectral database HITEMP 2010 is used to perform the hot plume infrared signature simulations. Accuracy of the model is examined by the exact LBL (line by line) method, which proves the model’s reliability to predict radiative properties of combustion gases. In the application part, the SNB model is used to analyze infrared signatures of aircraft plumes cruising at different flight altitudes. The results show that cruising at a higher-altitude will obviously reduce the plume infrared emission. Besides, the plume infrared emissive energy mainly concentrates in a special wavenumber interval and can be strongly absorbed by atmosphere.

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.

Improved global model for predicting gas radiative properties over a wide range of conditions

Calculating radiative transfer in gas mixtures, especially those containing CO2 and H2O, is important for high temperature applications, such as boilers and furnaces. Of all the models that can perform such calculations, the weighted-sum-of-gray-gas (WSGG) model is currently the most widely used one for solving engineering problems, due to its excellent computational efficiency. However, the validity range of a WSGG model is usually limited because its accuracy strongly depends on the conditions at which the model coefficients are generated. In this work, a general model is developed for predicting the total emissivities of gas mixtures containing CO2, H2O, and any non-absorbing gases. The model can be used for a wide range of conditions: temperatures 300–2900 K, pressures 1–60 bar and path lengths 0.01–100 m for any mixture compositions. The model is developed based on artificial neural networks (ANN) trained using around 4.5 million samples generated by a statistical narrow band model. Two ANNs were selected—considering both accuracy and computational speed—and were compared against existing WSGG models. The first ANN model has more than an order of magnitude smaller mean error than those of existing WSGG models, and its computational speed is comparable to the WSGG model. The second ANN model has even higher accuracy than the first model, but with slightly lower computational speed.