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.

Qualitative Air Flow Modelling and Analysis of Data Centre Air Conditioning as Multiple Jet Array

Data centre is a centralized repository,either physical or virtual,for the storage,management and dissemination of data and information organized around a particular body and nerve centre of the present IT revolution.Data centre are expected to serve uniinterruptedly round the year enabling them to perform their functions,it consumes enormous energy in the present scenario.Tremendous growth in the demand from IT Industry made it customary to develop newer technologies for the better operation of data centre.Energy conservation activities in data centre mainly concentrate on the air conditioning system since it is the major mechanical sub-system which consumes considerable share of the total power consumption of the data centre.The data centre energy matrix is best represented by power utilization efficiency(PUE),which is defined as the ratio of the total facility power to the IT equipment power.Its value will be greater than one and a large value of PUE indicates that the sub-systems draw more power from the facility and the performance of the data will be poor from the stand point of energy conservation. PUE values of 1.4 to 1.6 are acievable by proper design and management techniques.Optimizing the air conditioning systems brings enormous opportunity in bringing down the PUE value.The air conditioning system can be optimized by two approaches namely,thermal management and air flow management.thermal management systems are now introduced by some companies but they are highly sophisticated and costly and do not catch much attention in the thumb rules.

Modelling of Ultraviolet and Vissible Emissions in Comets

Comets are the spectacular objects in the night sky since the dawn of mankind. Due to their giant apparitions and enigmatic behavior, followed by coincidental calamities, they were termed as notorious and called as `bad omens'. With a systematic study of these objects modern scienti c community understood that these objects are part of our solar system. Comets are believed to be remnant bodies of at the end of evolution of solar system and possess the material of solar nebula. Hence, these are considered as most pristine objects which can provide the information about the conditions of solar nebula. These are small bodies of our solar system, with a typical size of about a kilometer to a few tens of kilometers orbiting the Sun in highly elliptical orbits. The solid body of a comet is nucleus which is a conglomerated mixture of water ice, dust and some other gases. When the cometary nucleus advances towards the Sun in its orbit the ices sublimates and produces the gaseous envelope around the nucleus which is called coma. The gravity of cometary nucleus is very small and hence can not in uence the motion of gases in the cometary coma. Though the cometary nucleus is a few kilometers in size they can produce a transient, extensive, and expanding atmosphere with size several orders of magnitude larger in space. By ejecting gas and dust into space comets became the most active members of the solar system. The solar radiation and the solar wind in uences the motion of dust and ions and produces dust and ion tails, respectively. Comets have been observed in di erent spectral regions from rocket, ground and space borne optical instruments. The observed emission intensities are used to quantify the chemical abundances of di erent species in the comets. The study of various physical and chemical processes that govern these emissions is essential before estimating chemical abundances in the coma. Cameron band emission of CO molecule has been used to derive CO2 abundance in the comets based on the assumption that photodissociation of CO2 mainly produces these emissions. Similarly, the atomic oxygen visible emissions have been used to probe H2O in the cometary coma. The observed green ([OI] 5577 A) to red-doublet emission ([OI] 6300 and 6364 A) ratio has been used to con rm H2O as the parent species of these emissions. In this thesis a model is developed to understand the photochemistry of these emissions and applied to several comets. The model calculated emission intensities are compared with the observations done by space borne instruments like International Ultraviolet Explorer (IUE) and Hubble Space Telescope (HST) and also by various ground based telescopes.