Statistical Narrow-band Model Research Articles

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.

New coefficients of the weighted-sum-of-gray-gases model for gas radiation characteristics of hydrogen/natural gas blends combustion

To achieve carbon neutrality, hydrogen/natural gas blends are gaining momentum as a clean low-carbon fuel for the future. In order to accurately carry out the CFD numerical simulation of hydrogen/natural gas blends combustion, it is imperative to establish a precise model for gas radiation characteristics. The existing weighted-sum-of-gray-gases model (WSGGM) is not suitable for high hydrogen content fuels, such as hydrogen/natural gas blends. Hence, new coefficients of WSGGM is formulated specifically for the combustion of hydrogen/natural gas blends, drawing upon the groundwork established by the statistical narrow-band model (SNB model). This model is specifically designed to be applicable within the ambient pressures, encompassing the temperature regime of 400–2500 K, a path-length range of 0.001–60 m, and a hydrogen blending ratio of 20%–70%. The radiative heat transfer characteristics of the sum of the molar fraction of H2O and CO2 at 0.9, 0.6, and 0.3 were studied according to application conditions. The WSGGM is implemented to compute the radiative heat transfer in non-isothermal and non-homogeneous gas mixtures. When compared to the benchmark model, the deviation of the wall heat flux does not surpass 5.20%. The results demonstrate the excellent adaptability of the WSGG coefficients in simulating the radiative heat transfer during hydrogen/natural gas blends combustion.

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.

On the roles of humidification and radiation during the ignition of ammonia–hydrogen–air mixtures

It is well established that radiation plays an important role in the combustion process of premixed combustible mixtures, which significantly affects the flame temperature and chemical reaction rates during flame propagation. However, the impact of radiation, especially the radiation reabsorption effect, on minimum ignition energy (Emin) still lacks thorough research and understanding. In this study, the ignition processes of spherical NH3/H2/H2O/O2/N2 flames were simulated. Three different computational models, the adiabatic model (ADI), the optically thin model (OTM) and the statistical narrow-band model (SNB), were employed to determine the radiation effect (including both radiative heat loss and reabsorption) on Emin. Results indicated that the water content in the premixture suppressed ignition; characteristically, the addition of vol. 9.63% H2O in the premixture resulted in a nearly 40% increase of Emin under adiabatic condition. Both radiative heat loss and reabsorption effects increased Emin. The radiation effects on Emin, quantified as the relative differences between the OTM-/SNB- and ADI-obtained Emin, were up to 16.47% (for radiative heat loss) and 17.65% (for radiation reabsorption), respectively. It was further demonstrated that radiation increased Emin through the combination of three aspects: thermal effect, chemical effect and flame structure effect. The thermal effect, induced by the outward radiative emission, reduced the ignition kernel temperature significantly. The reduced temperature decelerated chemical reactions and then suppressed the chemical heat release, i.e., the chemical effect as reflected by the concentrations of H, O and OH radicals. Furthermore, the larger flame thickness obtained by the radiation models slowed down the diffusion of fuels, which weakened the chemical heat release and eventually increased the Emin. Moreover, the reaction-diffusion region simulated by SNB was enlarged due to the radiation reabsorption, and thus, Emin obtained by SNB was higher than that by OTM.

A new WSGG radiation model of CO/CO2 mixed gas for solar-driven coal/biomass fuel gasification

Gasification driven by solar energy with CO2 is an ideal way of low-carbon resource utilization. However, there is a lack of research on the radiation heat transfer process which is important in gasification simulation. In this study, we developed a new the weighted-sum-of-gray-gases (WSGG) model to calculate the radiation heat transfer properties of CO and CO2 mixtures in solar-driven coal/biomass fuel gasification. Benchmarked against the statistical narrow-band model (SNB) of the EM2C laboratory, the WSGG model is suitable for the temperature range of 400–2500 K and the path length range of 0.001–60 m. This study also explored the effect of the CO/CO2 molar ratio on the overall emissivity of the mixture. Furthermore, the model introduces a pressure term into the emissivity calculation process and broadens the pressure range (1 bar, 5 bar, 45 bar). For the first time, the WSGG model is applied to the case where the H/C element ratio is 0, and the fluctuating temperature distribution case (1000 – 2000 K) is analyzed, which is suitable for coal/biomass fuel gasification. In addition, this study calculated the one-dimensional radiation transfer equation. The results show that the average radiation source term difference between the new WSGG and the benchmark SNB model is within 5 % in common solar gasification engineering conditions (5 bar, 5 m). Meanwhile, this study also clarified the effect of pressure on the radiation heat transfer with different temperatures.

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 discrete spectral contributions based statistical narrow-band model for high-temperature combustion systems

In this work, we present a discrete spectral contribution based statistical narrow-band model (DSC-SNB) to solve the radiative transfer of high-temperature combustion systems, which employs a discrete spectral strategy to considerably improve the accuracy of the traditional SNB model. Based on the contribution of different gases to radiation, the DSC-SNB model divides the spectral lines into different groups within the spectral interval based on the low-level transition energies (E“). Treating the Line-by-Line (LBL) approach as the benchmark solution, several inhomogeneous high-temperature H2O-CO2-CO mixture columns are adopted to evaluate the DSC-SNB model. Results show that the DSC-SNB model performance is comparable with the traditional SNB model for isothermal gas mixture columns. The DSC-SNB model exhibits high accuracy under mid-high temperature or pure high temperature without low-temperature wrapping, outperforming the traditional SNB model. These findings could be used to reconstruct the multi-dimensional flame temperature field by building a highly accurate and efficient mathematical model for flame radiation prediction.

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.

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

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.

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.

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.

Temperature measurement of carbon dioxide using emission spectroscopy

This paper presents a relatively simple method for temperature measurement of hot carbon dioxide gas using an emission spectroscopy setup. The ν3 band emission at 4.3 µm is detected using an optical band-pass filter and a mercury cadmium telluride detector. A conversion methodology is introduced that calculates the detector voltage from the spectral radiance considering the spectral sensitivities of the optical components and the non-linear characteristics of the detector. Two radiation models, a line-by-line model and a random statistical narrow band model, are employed to calculate the spectral radiance at given flow conditions. Black body radiation is considered for radiance calculation for optically thick conditions. Temperatures under test conditions in a shock tube are determined using the proposed conversion methodology and are compared with the temperatures obtained from a computational fluid dynamics simulation. The accuracy and efficiency of the temperature measurement using the two radiation models and the black body curve are compared. It is confirmed that the proposed method is a reliable way to determine the temperature while using a relatively simple experimental setup. Detector voltages are presented for a wide range of temperature, pressure, and beam path length for applications under different test conditions.

A method based on ejector technology to suppress the infrared radiation of the special vehicle exhaust gas

In this study, a method based on ejector technology is proposed to effectively suppress the infrared radiation associated with the exhaust gas of special vehicles such as tanks, armored vehicles, and missile carriers. These vehicles emit exhaust gases at very high temperatures. First, a mathematical model of the exhaust pipe was established for the exhaust system of a certain type of special vehicle. Then, the 3-D flow field outside the exhaust pipe was numerically simulated using FLUENT 6.3 software. Thus, the temperature, pressure, and density of the exhaust-gas-flow field before and after adopting the proposed ejector technique were obtained. Second, the statistical narrowband model based on the Lorentzian profile was used to determine the average absorption coefficient of a narrow band. Then, the finite volume method was used to solve the radiation transfer equation in the gaseous medium. Finally, the spectral radiation brightness and mid-infrared radiation intensity distribution of the exhaust gas before and after adopting the ejector technique were obtained. Results show that the proposed method considerably decreased the infrared radiation intensity of the exhaust gas by approximately 70%. Thus, using the proposed ejector technology, the infrared radiation associated with the exhaust system of special vehicles can be effectively suppressed.

Calculations of radiative intensity in one-dimensional gaseous media with black boundaries using the statistical narrow band model

Directional radiative intensity over specific spectral region provides fruitful information inside gas fired systems, and is very useful for inverse analysis, such as temperature and species concentration reconstruction. The statistical narrow band (SNB) model has acceptable time efficiency for practical applications and has been shown to have good accuracy to calculate integral radiative quantities, such as radiative heat flux and radiative source term. No previous work provides its accuracy information for solving spectral radiative intensity in combustion systems, which is to be investigated in this work. The SNB model is applied to solve radiative transfer in one-dimensional gaseous media with black boundaries. Gaseous media of CO2 and H2O with uniform and non-uniform distributions of temperature and mole fraction are considered. The line-by-line (LBL) method is considered as the benchmark solution. Results show that the accuracy of spectral radiative intensity for CO2 media is very good (with errors less than 2%) in most bands. The errors of spectral radiative intensity for H2O media are larger than 5% in many spectral bands and the maximum error is larger than 10%. Accordingly, a strategy to improve the accuracy of the SNB model by generating a new set of narrow band parameters is proposed in this work. Results show that errors in most bands reduce to less than 2% using the new set of parameters. While spectral radiative intensity shows different magnitudes of errors for different gaseous media and different sets of narrow band parameters, radiative heat flux always has good accuracy with largest error less than 3.5%. This work provides comprehensive accuracy information of the SNB model to calculate radiative intensity and radiative heat flux in gaseous media, and the proposed strategy to generate narrow band parameters improves the accuracy of the SNB model significantly.

Numerical analysis of point-source infrared radiation phenomena of rocket exhaust plumes at low and middle altitudes

Rocket exhaust plume treated as a significant radiation source has been widely used in space-based detection. In this paper, infrared radiation signatures of plumes were studied in the view of the phenomenon. The reacting plume flows were calculated by an axisymmetric computational fluid dynamics (CFD) solver. Radiative properties of gases were evaluated with the statistical narrow-band (SNB) model by relying on the NASA-3080 database. The line-of-sight (LOS) based on the single-line-group (SLG) approximation was employed for radiative transfer computations. The numerical model was validated against reference data. Based on this model, radiation characteristics of Atlas-II liquid rocket plumes were computed and analyzed in aspects of afterburning, atmospheric attenuation, spectral bands and observation angle. Results show that afterburning has a significant improvement in the wavelengths of 1.5–6.0 μm. Also, the atmospheric attenuation greatly decreases the plume radiance at low altitudes but it can be ignored above 40 km. Radiance is strongly dependent on the spectral bands. The altitude-varying spectral dependency can contribute to the rocket altitude estimation. The effect of the observation angle on the radiance distributions is varying with the spectra band and the flight altitude. These results are helpful for the design of the rocket motors and the application of the infrared detecting system.

Effect of hot water vapor on strand surface temperature measurement in steel continuous casting

The surface temperature of continuous casting slab in water spraying zone is a key parameter of production control. However, the accuracy of radiation temperature measurement is greatly affected by water vapor at high temperature. In this paper, a mathematical radiative heat transfer model combined with an analytical radiation thermometry model was developed. The hot water vapor absorption coefficient at a spectral resolution of 25 cm−1 as an input parameter to the radiative heat transfer model is obtained by employing the statistical narrow-band model along with gray-band approximation on the basis of the updated database HITEMP 2010. The proposed model was applied to quantitatively calculate the surface temperature, obtained by ratio and single waveband thermometer for infrared waveband from 50 cm−1 to 11250 cm−1, of assumed gray strand covered by hot water vapor. Detailed simulation studies were performed considering the following parameters: concentration of the hot water vapor, reflectivity of the target surface, background temperature of the surrounding surfaces and distance between target and thermometer. A sensitivity analysis was put forward trying to ascertain how the proposed model depends on those parameters. As the results indicate, both hot water vapor and reflected ambient radiation greatly affect the measurement accuracy of the radiation thermometry. The temperature errors caused by hot water vapor are spectrally selective. The most suitable spectral regions for ratio and single waveband thermometer operating and a criterion for choosing the optimal wavelength pairs for ratio thermometry were put forward. The analyses in the paper may provide necessary theoretical supports for the design and application of a radiation thermometer in the presence of hot water vapor.