Mathematical Modelling of the Dynamics of Granular Materials in a Rotating Cylinder

The current study is aimed at the development of a theoretical simulation tool based on Discrete Element Method (DEM) to 'interpret granular dynamics of solid bed in the cross section of the horizontal rotating cylinder at the microscopic level and subsequently apply this model to establish the transition behaviour, mixing and segregation.The simulation of the granular motion developed in this work is based on solving Newton's equation of motion for each particle in the granular bed subjected to the collisional forces, external forces and boundary forces. At every instant of time, the forces are tracked and the positions velocities and accelarations of each partcle is The software code for this simulation is written in VISUAL FORTRAN 90 After checking the validity of the code with special tests, it is used to investigate the transition behaviour of granular solids motion in the cross section of a rotating cylinder for various rotational speeds and fill fraction.This work is hence directed towards a theoretical investigation based on Discrete Element Method (DEM) of the motion of granular solids in the radial direction of the horizontal cylinder to elucidate the relationship between the operating parameters of the rotating cylinder geometry and physical properties ofthe granular solid.The operating parameters of the rotating cylinder include the various rotational velocities of the cylinder and volumetric fill. The physical properties of the granular solids include particle sizes, densities, stiffness coefficients, and coefficient of friction Further the work highlights the fundamental basis for the important phenomena of the system namely; (i) the different modes of solids motion observed in a transverse crosssection of the rotating cylinder for various rotational speeds, (ii) the radial mixing of the granular solid in terms of active layer depth (iii) rate coefficient of mixing as well as the transition behaviour in terms of the bed turnover time and rotational speed and (iv) the segregation mechanisms resulting from differences in the size and density of particles.The transition behaviour involving its six different modes of motion of the granular solid bed is quantified in terms of Froude number and the results obtained are validated with experimental and theoretical results reported in the literature The transition from slumping to rolling mode is quantified using the bed turnover time and a linear relationship is established between the bed turn over time and the inverse of the rotational speed of the cylinder as predicted by Davidson et al. [2000]. The effect of the rotational speed, fill fraction and coefficient of friction on the dynamic angle of repose are presented and discussed. The variation of active layer depth with respect to fill fraction and rotational speed have been investigated. The results obtained through simulation are compared with the experimental results reported by Van Puyvelde et. at. [2000] and Ding et at. [2002].The theoretical model has been further extended, to study the rmxmg and segregation in the transverse direction for different particle sizes and their size ratios. The effect of fill fraction and rotational speed on the transverse mixing behaviour is presented in the form of a mixing index and mixing kinetics curve. The segregation pattern obtained by the simulation of the granular solid bed with respect to the rotational speed of the cylinder is presented both in graphical and numerical forms. The segregation behaviour of the granular solid bed with respect to particle size, density and volume fraction of particle size has been investigated. Several important macro parameters characterising segregation such as mixing index, percolation index and segregation index have been derived from the simulation tool based on first principles developed in this work.

Assessment of Energy Conservation in Indian Cement Industry and Forecasting of Co2 Emissions

Cement industry ranks 2nd in energy consumption among the industries in India. It is one of the major emitter of CO2, due to combustion of fossil fuel and calcination process. As the huge amount of CO2 emissions cause severe environment problems, the efficient and effective utilization of energy is a major concern in Indian cement industry. The main objective of the research work is to assess the energy cosumption and energy conservation of the Indian cement industry and to predict future trends in cement production and reduction of CO2 emissions. In order to achieve this objective, a detailed energy and exergy analysis of a typical cement plant in Kerala was carried out. The data on fuel usage, electricity consumption, amount of clinker and cement production were also collected from a few selected cement industries in India for the period 2001 - 2010 and the CO2 emissions were estimated. A complete decomposition method was used for the analysis of change in CO2 emissions during the period 2001 - 2010 by categorising the cement industries according to the specific thermal energy consumption. A basic forecasting model for the cement production trend was developed by using the system dynamic approach and the model was validated with the data collected from the selected cement industries. The cement production and CO2 emissions from the industries were also predicted with the base year as 2010. The sensitivity analysis of the forecasting model was conducted and found satisfactory. The model was then modified for the total cement production in India to predict the cement production and CO2 emissions for the next 21 years under three different scenarios. The parmeters that influence CO2 emissions like population and GDP growth rate, demand of cement and its production, clinker consumption and energy utilization are incorporated in these scenarios. The existing growth rate of the population and cement production in the year 2010 were used in the baseline scenario. In the scenario-1 (S1) the growth rate of population was assumed to be gradually decreasing and finally reach zero by the year 2030, while in scenario-2 (S2) a faster decline in the growth rate was assumed such that zero growth rate is achieved in the year 2020. The mitigation strategiesfor the reduction of CO2 emissions from the cement production were identified and analyzed in the energy management scenarioThe energy and exergy analysis of the raw mill of the cement plant revealed that the exergy utilization was worse than energy utilization. The energy analysis of the kiln system showed that around 38% of heat energy is wasted through exhaust gases of the preheater and cooler of the kiln sysetm. This could be recovered by the waste heat recovery system. A secondary insulation shell was also recommended for the kiln in the plant in order to prevent heat loss and enhance the efficiency of the plant. The decomposition analysis of the change in CO2 emissions during 2001- 2010 showed that the activity effect was the main factor for CO2 emissions for the cement industries since it is directly dependent on economic growth of the country. The forecasting model showed that 15.22% and 29.44% of CO2 emissions reduction can be achieved by the year 2030 in scenario- (S1) and scenario-2 (S2) respectively. In analysing the energy management scenario, it was assumed that 25% of electrical energy supply to the cement plants is replaced by renewable energy. The analysis revealed that the recovery of waste heat and the use of renewable energy could lead to decline in CO2 emissions 7.1% for baseline scenario, 10.9 % in scenario-1 (S1) and 11.16% in scenario-2 (S2) in 2030. The combined scenario considering population stabilization by the year 2020, 25% of contribution from renewable energy sources of the cement industry and 38% thermal energy from the waste heat streams shows that CO2 emissions from Indian cement industry could be reduced by nearly 37% in the year 2030. This would reduce a substantial level of greenhouse gas load to the environment. The cement industry will remain one of the critical sectors for India to meet its CO2 emissions reduction target. India’s cement production will continue to grow in the near future due to its GDP growth. The control of population, improvement in plant efficiency and use of renewable energy are the important options for the mitigation of CO2 emissions from Indian cement industries