Tim Gronarz

Influence of Index of Refraction and Particle Size Distribution on Radiative Heat Transfer in a Pulverized Coal Combustion Furnace

In this work, the influence of the radiative properties of coal and ash particles on radiative heat transfer in combustion environments is investigated. Emphasis is placed on the impact on the impact of the complex index of refraction and the particle size on particle absorption and scattering efficiencies. Different data of the complex index of refraction available in the literature are compared, and their influence on predictions of the radiative wall flux and radiative source term in conditions relevant for pulverized coal combustion is investigated. The heat transfer calculations are performed with detailed spectral models. Particle radiative properties are obtained from Mie theory, and a narrow band model is applied for the gas radiation. The results show that, for the calculation of particle efficiencies, particle size is a more important parameter than the complex index of refraction. The influence of reported differences in the complex index of refraction of coal particles on radiative heat transfer is small for particle sizes and conditions of interest for pulverized coal combustion. For ash, the influence of variations in the literature data on the complex index of refraction is larger, here, differences between 10% and 40% are seen in the radiative source term and radiative heat fluxes to the walls. It is also shown that approximating a particle size distribution with a surface area weighted mean diameter, D-32, for calculation of the particle efficiencies has a small influence on the radiative heat transfer.

The Influence of Subsurface Temperature Measurements on the Determination of Transient Wall-Side Boundary Conditions: An Analytical Tool

Abstract An analytical approximation for the two-dimensional heat conduction problem with temporally and spatially oscillating thermal boundary conditions is presented. In addition, simplified expressions for the damping and phase shift of the temperature signal between the surface and a “measurement” position inside the wall are derived and their validity in dependency on the inverse Fourier number is shown. The solution algorithm is implemented in a MATLAB program and made available for other researchers. In two case studies, the analytical solution is applied in order to evaluate the ability of experimental systems to measure instantaneous and local heat transfer coefficients as well as temperatures on a boundary.

Modeling of Anisotropic Scattering of Thermal Radiation in Pulverized Coal Combustion

In this work, the effect of applying different approximations for the scattering phase function on radiative heat transfer in pulverized coal combustion is investigated. Isotropic scattering, purely forward scattering, and a -Eddington approximation are compared with anisotropic scattering based on Mie theory calculations. To obtain suitable forward scattering factors for the -Eddington approximation, a calculation procedure based on Mie theory is introduced to obtain the forward scattering factors as a function of temperature, particle size, and size of the scattering angle. Also, an analytical expression for forward scattering factors is presented. The influence of the approximations on wall heat flux and radiative source term in a heat transfer calculation is compared for combustion chambers of varying size. Two numerical models are applied: A model based on the discrete transfer method (DTRM) representing the reference solution and a model based on the finite volume method (FVM) to also investigate the validity of the obtained results with a method often applied in commercial CFD programs. The results show that modeling scattering as purely forward or isotropic is not sufficient in coal combustion simulations. The influence of anisotropic scattering on heat transfer can be well described with a -Eddington approximation and properly calculated forward scattering factors. Results obtained with both numerical methods show good agreement and give the same tendencies for the applied scattering approximations.

Modeling of particle-radiation-interaction for the numerical simulation of coal combustion

In the present dissertation, scattering and absorption of thermal radiation by particles in coal combustion scenarios is investigated, modeling approaches are derived and a parametervariation is performed to quantify the influence of the parameters determining heat transfer. In the first section, scattering and absorption properties of coal particles are investigated, making use of the detailed Mie theory which serves as the reference solution throughout the present work. The complex index of refraction which is the material property that determines the interaction of matter with thermal radiation is introduced. Available data on the complex index of refraction for coal and ash particles in literature are compared, discussed investigated regarding their influence on the scattering and absorption properties. Then, modeling approaches are derived that allow to describe scattering and absorption by coal and ash particles in numerical simulations of coal combustion efficiently. This includes a novel approach to describe the variation of scattering and absorption properties of coal particles undergoing burnout based on a shell model. Also, new approximations for the scattering phase function are presented. A very promising approximation for the scattering phase function is provided by the modified Henyey-Greenstein scattering phase function and forward scattering factors calculated from precise Mie theory calculations. Finally, these models are implemented in a program to solve the radiative transport equation numerically. To be applied in a numerical scheme with an angular discretization, the scattering phase functions are integrated over discrete solid angles based on a customized integration procedure which is introduced in this work. The derived models are tested regarding their ability to describe scattering and absorption by particles. Besides the scattering and absorption properties of the particles, all remaining parameters determining radiative heat transfer in coal combustion scenarios are varied and their influence on heat transfer is investigated and the results are discussed. The most important finding for the present work is that with a good approximate scattering phase function, scattering by coal and ash particles can be described very reasonably. Finally, this thesis can be used as a guide on how to treat radiative heat transfer in coal combustion simulations.