Quantitative Evaluation And Numerical Experiment Study On The Computational Accuracy For Monte Carlo Method Of Radiative Heat Transfer

Radiative heat transfer is a fundamental problem in the fields of energy power and aerospace.As the main research method of radiatve heat transfer,the numerical calculation method of thermal radiation plays an important role.Monte Carlo Method(MCM)can accurately deal with complex radiative heat transfer problems,such as spectral characteristics,heterogeneous media,anisotropic scattering,and complex geometric shapes,which has become one of the major choices to solve radiative heat transfer problems.With the expansion of the application of Monte Carlo Method in the numerical simulation of thermal radiation,how to analyze the uncertainty of the calculation results has become the focus of attention.One of the most powerful advantages of Monte Carlo Method over other traditional numerical methods of thermal radiation is that it is a statistical simulation technique,and the errors in the results can be estimated by statistical uncertainty.The mechanism of Monte Carlo statistical errors is revealed,and the effections of various factors on calculation errors and accuracy are accurately grasped.The computational accuracy for Monte Carlo calculation of radiative heat transfer under radiation equilibrium condition is evaluated and analyzed quantitatively.Setting the encloure to isothermal and radiation equilibrium state,that is,energy is only transmitted through the radiation inside and on the surface of the medium,and the wall and medium have uniform and equal temperature distribution.Under the condition of radiation equilibrium,the exact values of surface heat flux and/or spatial heat flux divergence(heat source or heat sink)are all zero,so the absolute and relative calculation errors of Monte Carlo Method calculation results of surface heat flux and/or spatial heat flux divergence can be accurately calculated.For fixed and uniform distribution of medium surface and space radiation properties,the effects of the number of energy bundles per unit(NEB),the mesh density level(MDL)and the mean optical thickness per element(MOTE)on the computational accuracy and efficiency for Monte Carlo Method of radiative heat transfer.The results show that MOTE is the key scale parameter of the calculation error of surface element by Monte Carlo Method;if MOTE changes little,then the error will not change significantly with the same NEB with different mesh density level and optical thickness.When MOTE is less than 0.1 or so,even if discrete elements become more finer,the computational time will increase greatly,but the computational accuracy will not be improved significantly.The proportional relation between the minimum calculation error of surface and space elements and NEB is established.If the desired error level of radiative heat transfer calculation is set at an acceptable cost of 1.0%,the minimum NEB of surface element is 3000 and the minimum NEB of space element is 750.By evaluating the errors introduced by the changes of physical conditions such as surface emissivity and the scattering albedo of the media participating in radiation,the accuracy can be quantitatively evaluated under various radiation properties.When MOTE is less than 0.1,bilinear fitting method is used to respectively establish the bilinear relationship between the minimum error of surface and space element and two independent influencing factors(the number of energy bundles and the surface emissivity),so as to select appropriate spatial discrete mesh density and the number of energy bundles according to the requirements of calculation error level.The monte carlo calculation accuracy of two special non-equilibrium radiative heat transfer is evaluated.The radiation non-equilibrium state is caused by the uneven distribution of temperature inside the cube encloure.The convergence value of radiative heat flux and/or divergence of radiative heat flux under the condition of the limit thin or thick optical thickness of the medium can be obtained,which can be used as the accurate value of radiative heat flux under the limit condition.The accuracy of Monte Carlo Method in non-equilibrium state is obtained by estimating the deviation of the limit convergence and the results.When the optical thickness of the medium is lower than 0.001 or so,the calculation errors of the surface and space elements remain basically unchanged at the minimum error level.The number of energy bundles directly affects the level of minimum calculation error.When the number of energy bundles increases by two orders of magnitude,the calculation error decreases by one order of magnitude.When the number of energy beams reaches 10,000,the minimum calculation error of surface radiative heat flux reaches 1.0%,and the calculation precision reaches the expected precision value.For the calculation of the space divergence of radiative heat flux,the minimum number of energy beams needed to achieve the desired accuracy is about 3000.The performance and quality of monte carlo method are quantitatively analyzed.Every order of magnitude increase of energy bundles number will lead to an order of magnitude increase of computational time at the same time,which is conducive to improving accuracy.For every doubling of mesh density,the computational time increases by about 10 times.When the mesh density and the number of energy bundles are fixed,the computational time is related to surface emissivity,scattering albedo and optical thickness.When MOTE is less than 0.1,the computational time is only related to the surface emissivity,which decreases with the increase of the surface emissivity.When the MOTE is greater than 0.1,the computational time is affected by the scattering albedo of the medium and the optical thickness.The calculation time increases with the increase of the scattering albedo of the medium,while the increase of the optical thickness will lead to the overall decrease of the computational time.At this time,the surface emissivity has little effect on the computational time.In order to achieve the desired accuracy based on the optimal performance,the Monte Carlo simulation is not to increase the number of energy bundles without limit to reduce the calculation error,but to obtain near the minimum number of energy bundles,so as to achieve the optimal balance between the calculation cost and the computational accuracy.