A Study On Vortex Knots

In this thesis an attempt is made to study vortex knots based on the work of Keener . It is seen that certain mistakes have been crept in to the details of this paper. We have chosen this study for an investigation as it is the first attempt to study vortex knots. Other works had given attention to this. In chapter 2 we have considered these corrections in detail. In chapter 3 we have tried a simple extension by introducing vorticity in the evolution of vortex knots. In chapter 4 we have introduced a stress tensor related to vorticity. Chapter 5 is the general conclusion.Knot theory is a branch of topology and has been developed as an independent branch of study. It has wide applications and vortex knot is one of them. As pointed out earlier, most of the studies in fluid dynamics exploits the analogy between vorticity and magnetic induction in the case of MHD. But vorticity is more general than magnetic induction and so it is essential to discuss the special properties of vortex knots, independent of MHD flows. This is what is being done in this thesis.

Techniques for Enhancing Wind Energy Generation - A CFD Based Multibody Dynamics Approach in Horizontal Axis Wind Turbines

Wind energy has emerged as a major sustainable source of energy.The efficiency of wind power generation by wind mills has improved a lot during the last three decades.There is still further scope for maximising the conversion of wind energy into mechanical energy.In this context,the wind turbine rotor dynamics has great significance.The present work aims at a comprehensive study of the Horizontal Axis Wind Turbine (HAWT) aerodynamics by numerically solving the fluid dynamic equations with the help of a finite-volume Navier-Stokes CFD solver.As a more general goal,the study aims at providing the capabilities of modern numerical techniques for the complex fluid dynamic problems of HAWT.The main purpose is hence to maximize the physics of power extraction by wind turbines.This research demonstrates the potential of an incompressible Navier-Stokes CFD method for the aerodynamic power performance analysis of horizontal axis wind turbine.The National Renewable Energy Laboratory USA-NREL (Technical Report NREL/Cp-500-28589) had carried out an experimental work aimed at the real time performance prediction of horizontal axis wind turbine.In addition to a comparison between the results reported by NREL made and CFD simulations,comparisons are made for the local flow angle at several stations ahead of the wind turbine blades.The comparison has shown that fairly good predictions can be made for pressure distribution and torque.Subsequently, the wind-field effects on the blade aerodynamics,as well as the blade/tower interaction,were investigated.The selected case corresponded to a 12.5 m/s up-wind HAWT at zero degree of yaw angle and a rotational speed of 25 rpm.The results obtained suggest that the present can cope well with the flows encountered around wind turbines.The areodynamic performance of the turbine and the flow details near and off the turbine blades and tower can be analysed using theses results.The aerodynamic performance of airfoils differs from one another.The performance mainly depends on co-efficient of performnace,co-efficient of lift,co-efficient of drag, velocity of fluid and angle of attack.This study shows that the velocity is not constant for all angles of attack of different airfoils.The performance parameters are calculated analytically and are compared with the standardized performance tests.For different angles of ,the velocity stall is determined for the better performance of a system with respect to velocity.The research addresses the effect of surface roughness factor on the blade surface at various sections.The numerical results were found to be in agreement with the experimental data.A relative advantage of the theoretical aerofoil design method is that it allows many different concepts to be explored economically.Such efforts are generally impractical in wind tunnels because of time and money constraints.Thus, the need for a theoretical aerofoil design method is threefold:first for the design of aerofoil that fall outside the range of applicability of existing calalogs:second,for the design of aerofoil that more exactly match the requirements of the intended application:and third,for the economic exploration of many aerofoil concepts.From the results obtained for the different aerofoils,the velocity is not constant for all angles of attack.The results obtained for the aerofoil mainly depend on angle of attack and velocity.The vortex generator technique was meticulously studies with the formulation of the specification for the right angle shaped vortex generators-VG.The results were validated in accordance with the primary analysis phase.The results were found to be in good agreement with the power curve.The introduction of correct size VGs at appropriate locations over the blades of the selected HAWT was found to increase the power generation by about 4%