UBC Theses and Dissertations
UBC Theses and Dissertations
Mathematical modelling of lime kilns Georgallis, Mike
Rotary kilns have wide use in industry from the calcination of limestone to cement manufacturing to calcining of petroleum coke etc. These machines have survived and have been continuously improved (fuel efficiency, automation) for over a century. Modelling has aided the design and operation of rotary kilns over the years. In the present study, a three-dimensional steady-state model to predict the flow and heat transfer in a rotary lime kiln is presented. All important phenomena are included for the pre-heat and calcination zones. The model is based on a global solution of three submodels for the hot flow, the bed and the rotating wall/refractories. Information exchange between the models results in a fully coupled 3-D solution of a rotary lime kiln. The hot flow model uses block-structured body-fitted coordinates with domain segmentation. This results in a capability of simulating flows in complex three-dimensional geometries with local refinement that capture details of the burner geometry and hood/kiln interactions. The CFD solver was developed by Nowak within the Department of Mechanical Engineering at the University of British Columbia. The method is based on the finite volume method. The model includes buoyancy effects, turbulence (using the standard κ-ε model), evolution and combustion of gaseous species (through Magnussen's model), and radiation through the ray-tracing technique (Discrete Ordinate Method). Combustion of natural gas or oil may be modelled. The bed model solves for a three-dimensional energy and species transport balance in the non-Newtonian flow field. The field is modelled as two distinct Newtonian regions: an active layer adjacent to the hot flow and a plug flow region below. The bed model is based on the finite element method and was developed as part of this thesis. The calcium carbonate reaction is modelled and assumed to be dominated by heat transfer. Reaction proceeds as a function of temperature and a bulk particle size diameter. An effective thermal conductivity (modified by a mass diffusion factor) is used for the granular bed heat transfer in the active layer. The bed flow field is supplied via a vorticity-stream function formulation and satisfies continuity equation. A 3-D temperature field results along with distributions for CaCO3 and CaO. Carbon dioxide is released to the hot flow. A three-dimensional wall model, also developed as part of this thesis and based on the finite element method, includes varying conductivity within the metal and refractories. Rotation is included through a convective plug flow term in the energy equation (V = ΩxR). Heat is lost to the ambient through free convection and radiation. The overall model is validated using UBC's pilot kiln trials (5m laboratory kiln). The solutions indicate that the present model may be used to identify problems of kiln operation or design. Prediction of a wealth of information is possible for various (primary air/fuel) input conditions, kiln geometries and burner designs. When the flow field, temperature distributions and species concentrations are visualized and understood for a given kiln operating condition, optimization and diagnosis of operational problems can be greatly enhanced through the use of the present computational tool. Analyzing complex aerodynamic flows (secondary flows) of hood/kiln interactions through flame visualization (and possible impingement) also has the potential of increasing refractory life.
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