The Calculation Method Of Radiative Heat Transfer Based On The Full-Spectrum K-Distribution Model

Radiative heat transfer?RHT?is the most important mode of heat transfer and deeply coupled with turbulence and combustion in the process of high-temperature oxidizing reaction.Therefore,accurate RHT prediction is of great importance.Different from the other two heat transfer modes,radiation is a complex process including emission,absorption,scattering,transmission and reflection;moreover,RHT in high-temperature participating media displays very strong spectral behavior,making the problem great exacerbated to be solved.This has led to the development of different models for the simplification of RHT,among which the full-spectrum k-distribution?FSK?method has become the most promising one due to the excellent calculation performance.However,for the FSK method,there are still some applied problems remaining unsolved,such as,low accuracy of the FSK method in nonhomogeneous media,slow mixing process for k-distributions,etc.Hence,the FSK method becomes the core part of this dissertation and the RHT process in participating media is deeply investigated.The sake of the work is therefore to establish an accurate and efficient RHT calculation method.Started from the theory of the FSK method,the impacts of the quadrature scheme and the number of quadrature points on the accuracy of the FSK method were investigated.The radiative heat source in one-dimensional enclosure between two parallel plates filled with non-gray gases was calculated using the FSK method.Numerical calculations were conducted using three types of Gauss quadrature schemes and the results were compared with the line-by-line?LBL?calculations.Results indicated that the impacts of types of Gauss quadrature schemes on the accuracy of the FSK method can be neglected;and the acceptable accuracy can be obtained when the number of quadrature points was larger than or equal to 16 for all of the three types of Gauss quadrature schemes mentioned in this dissertation.Then,an FSK look-up table was constructed for gas mixtures within a certain range of thermodynamic states for three species,i.e.,CO₂,H₂O and CO.The k-distribution of a mixture was assembled directly from the summation of the linear absorption coefficients of the three species,avoiding the process of mixing and saving a large amount of computational time.The systematic approach to generate the table,including the generation of the pressure-based absorption coefficients and the generation of the k-distributions,was discussed.To efficiently obtain accurate k-values for arbitrary thermodynamic states from tabulated values,a 6-D linear interpolation method was employed.A large number of RHT calculations were carried out to test the accuracy of the FSK look-up table.Results showed that,excellent accuracy and efficiency,compared to the exact LBL results,can be reached with the FSK look-up table.During most combustion processes,strongly radiating soot particles are inevitably generated.However,the gas-only table cannot be used for gas-soot mixtures that are found in most combustion scenarios since it is impossible to assemble k-distributions for a gas mixed with soot particles from gas-only full-spectrum k-distributions.Consequently,a new FSK look-up table was required and constructed by optimizing the gas-only table and then adding one soot volume fraction to this optimized table.Two scaled flames were used to validate the new table.Results showed that the new table gives results of excellent accuracy for those benchmark results together with cheap computational cost for both gas mixtures and gas-soot mixtures.Besides,during the investigation,k-distributions were found always covering several orders of magnitude,making their accurate and efficient numerical integration quite difficult.Different quadrature schemes give different levels of accuracy as compared to exact values unless a large number of quadrature points are employed.Therefore,to improve efficient implementation of the FSK method,an integration method with quadrature transformation was investigated and presented in the work.With the quadrature transformation,the accuracy of the FSK method can be improved significantly for the same number of quadrature points.Based on this,the look-up table was also updated to include k-values corresponding to the new quadrature points with transformation.Finally,to resolve the disadvantages of the radiative solver which combines FSK model with photon Monte Carlo?PMC?method,i.e.,?1?the random-number database was required to be constructed depending on the reference state,?2?it may produce substantial errors in nonhomogeneous media,two random-number relationships were presented to determine the spectral variables and k-values used for ray tracing process.A random-number database was also constructed for the FSK/PMC method including species of CO₂,H2O,CO and soot.The RHT via two scaled flames was calculated to compare the FSK/PMC method with different random-number relationships.Results showed that,even though the eificiency got no improvements due to the mechanisms for all PMC solvers,the accuracy of FSK/PMC method with either one of the two new random-number relationships got significantly increased in nonhomogeneous media,which in turn,extends the application of FSK method.