| Particulate media are widely used in nature and industrial processes such as energy,power and chemical industries,many of which are applied in high-temperature environments and radiative heat transfer becomes the main heat transfer process.Traditionally,the particulate medium is used as a typical participating medium,where the analysis of radiative heat transfer is based on the classical radiative transfer equation as the fundamental theoretical framework.However,the derivation of the classical radiative transfer equation makes many assumptions about the properties of the medium,such as the requirement that the particles are randomly distributed,the absorption and scattering of particles are independent,any two particles are sufficiently far apart from each other and the attenuation of light in the medium satisfies Beer’s law.These assumptions make the classical radiative transfer equations generally only applicable to the analysis of radiative heat transfer in sparse particle systems,while for dense particle media,which often exist in engineering applications,Beer’s law may not hold due to particle position correlation and intense shadowing effect,resulting in the classical radiative transfer theory not applicable to the analysis of radiative heat transfer in dense particle systems.At present,the conditions for the applicability of Beer’s law in dense particle systems are not clear,and there is an urgent need to develop an effective continuum theoretical model for the analysis of radiative heat transfer in dense particle systems where Beer’s law does not hold.This thesis focuses on the conditions for quantitatively determining the applicability of Beer’s law in dense particle systems and the effective continuum theoretical model of radiative heat transfer in dense non-Beerian particle systems,and through a combination of theoretical derivation and numerical simulation,quantifies the conditions for the applicability of Beer’s law and establishes an effective continuum theoretical model of radiative heat transfer in dense non-Beerian particle systems,the main contents are as follows:Beer’s law is the basis of classical radiative transfer theory,an analytical method to quantitatively measure the applicability of Beer’s law in the particulate system is proposed and the condition for determining the applicability of Beer’s law in a particle system is obtained.A particle motion method is proposed for generating particle systems with different randomness,and a checking-box method is proposed for quantitatively characterizing the structural randomness of the particle system,and a structural randomness indicator(SRI)is defined based on the standard deviation of the particle volume in the checking boxs,and Beer’s law valid indicator(BVI)is also defined based on the concept of coefficient of determination in statistics.The results show that the nonBeerian phenomenon also exists in an isotropic and homogeneous particle system,and the structural randomness of a system is an important factor influencing the validity of Beer’s law in the particle system.For a general granular system,when the structural randomness indicator SRI > 0.6,the Beer’s law valid indicator BVI > 0.99,Beer’s law is considered to be valid.To address the problem that the classical radiative transfer equation is not applicable in the dense non-Beerian particle system,an effective continuum theoretical model for radiative heat transfer in the dense non-Beerian particle systems is established from the particle-scale heat balance equation by rigorous derivation.Based on the particle-scale heat balance equation,an integral form of the continuum medium-scale control equation applicable to dense non-Beerian particle systems is derived by extending the radiation distribution factor to the continuous scale and introducing the concept of radiation distribution function,and it takes the radiation distribution function and volume emissivity as the basic input radiation property parameters.The numerical discretization method of this integral form of the control equation is given,as well as different treatment strategies for obtaining the radiation distribution function from the radiation distribution factor.The accuracy of the developed effective continuum medium theoretical model is verified by comparing the results of the particle-scale temperature field simulation.The radiation distribution function defined based on the extension of the radiation distribution factor to the continuum scale is the basic radiative property parameter of the theoretical model of the effective continuum theoretical model for the radiative heat transfer of the particle system,and its spatial distribution law is not yet clear.To address this problem,on the basis of the distribution law of radiation distribution function composed of inverse square law term and exponential decay term,further considering the effect of multiple scattering between particles in the system and the effect of randomness of the particle system,an improved analytical relation for the radiation distribution function between particles is given.It is extended to the radiative heat transfer between particle and wall,and then the analytical relation for the radiation distribution function between particles and walls is obtained.Compared with the direct simulation results,it shows that the given inter-particle and particle-wall radiation distribution function relations can describe the spatial distribution characteristics of the corresponding radiation distribution function well.The method based on the radiative effective thermal conductivity is an empirical method for the effective continuum treatment of radiative heat transfer in a dense particle system,and the radiative thermal conductivity of the particle system is its basic radiative physical parameter,and the calculation method of the radiative effective thermal conductivity of the particle system under the consideration of particle non-isothermality is not enough.To address this problem,a theoretical model based on the radiation distribution factor is proposed to obtain the radiative effective thermal conductivity of the particle system under particle non-isothermal conditions.The radiation distribution factor is divided into a zero-order component,which corresponds to the conventional radiative distribution factor,and a first-order component,which takes into account the effect of non-isothermal properties of the particles.Two ideal conditions of extremely high and low thermal conductivity of solids are analyzed,corresponding to isothermal particles(radiative Biot number << 1)and non-isothermal particles(radiative Biot number >> 1)system,and it is found that the effective radiative thermal conductivity of the particle system differs significantly between isothermal and non-isothermal conditions of particles with high particle filling ratio and surface emissivity.When the particle spacing in a dense particle system is reduced to a wavelength comparable to or smaller than the thermal characteristic wavelength,the effects of nearfield photon tunneling and many-body interaction on heat transfer are obvious,and it is doubtful whether the effective continuum theoretical model established before can be extended to the near-field system.In order to deepen the understanding of the near-field radiative heat transfer properties of dense micro-nano-particle systems,the effect of many-body interaction on the near-field radiative heat transfer between nanoparticles is analyzed based on the coupled electromagnetic dipole near-field radiative heat transfer theory.Further,the total near-field radiative energy of the central particle is given based on the near-field radiative heat transfer theory,and the concept of radiation distribution function is extended to be used for the characterization of near-field radiative heat transfer in the micro-nano particle system,thus extending the effective continuum theoretical model of radiative heat transfer in the dense particle system based on the radiation distribution function to the near-field,and verifying the results by comparing with the particle-scale temperature field simulation and other literature results. |
