Cartesian grids offer a valuable option to simulate aerodynamic flows around complex geometries such as multi-element airfoils, aircrafts, and rockets. Therefore, an adaptively-refined Cartesian grid generator and Euler solver are developed. For the mesh generation part of the algorithm, dynamic data structures are used to determine connectivity information between cells and uniform mesh is created in the domain. Marching squares and cubes algorithms are used to form interfaces of cut and split cells. Geometry-based cell adaptation is applied in the mesh generation. After obtaining appropriate mesh around input geometry, the solution is obtained using either flux vector splitting method or Roe&rsquo / s approximate Riemann solver with cell-centered approach. Least squares reconstruction of flow variables within the cell is used to determine high gradient regions of flow. Solution based adaptation method is then applied to current mesh in order to refine these regions and also coarsened regions where unnecessary small cells exist. Multistage time stepping is used with local time steps to increase the convergence rate. Also FAS multigrid technique is used in order to increase the convergence rate. It is obvious that implementation of geometry and solution based adaptations are easier for Cartesian meshes than other types of meshes. Besides, presented numerical results show the accuracy and efficiency of the algorithm by especially using geometry and solution based adaptation. Finally, Euler solutions of Cartesian grids around airfoils, projectiles and wings are compared with the experimental and numerical data available in the literature and accuracy and efficiency of the solver are verified.

Various error estimation and adaptive refinement techniques for the solution of electromagnetic integral equations were developed. Residual based error estimators and h-refinement implementations were done for the Method of Moments (MoM) solution of electromagnetic integral equations for a number of different problems. Due to high computational cost associated with the MoM, a cheaper solution technique known as the Locally-Corrected Nyström (LCN) method was explored. Several explicit and implicit techniques for error estimation in the LCN solution of electromagnetic integral equations were proposed and implemented for different geometries to successfully identify high-error regions. A simple p-refinement algorithm was developed and implemented for a number of prototype problems using the proposed estimators. Numerical error was found to significantly reduce in the high-error regions after the refinement. A simple computational cost analysis was also presented for the proposed error estimation schemes. Various cost-accuracy trade-offs and problem-specific limitations of different techniques for error estimation were discussed. Finally, a very important problem of slope-mismatch in the global error rates of the solution and the residual was identified. A few methods to compensate for that mismatch using scale factors based on matrix norms were developed.

In this thesis we describe the development of Reynolds- averaged Navier Stokes code for the flow past two- dimensional configuration. Particularly, emphasis has been laid on the study of low Reynolds number airfoil aerodynamics. The thesis consists of five chapters covering the back ground history, problem formulation, method of solution and discussion of the results and conclusion. Chapter I deals with a detailed background history of low Reynolds number aerodynamics, problem associated with it, state of the art, its importance in practical applications in aircraft industries. Chapter II describes the mathematical model of the flow physics and various levels of approximations. Also it gives an account of complexity of the equations at low Reynolds number regarding flow separation, transition and reattachment. Chapter III describes method of solution, numerical algorithm developed, description of various upwind schemes, grid system, finite volume discrieti-zation of the governing equations described in Chapter II. Chapter IV describes the application of the newly developed Navier Stokes code for the test cases from GAMM Workshop proceedings. Also it describes validation of the code for Euler solutions, Blasius solution for the flow past flat plate and compressible Navier Stokes solution for the flow past NACA 0012 Airfoil at low Reynolds number. Chapter V describes the application of the Navier Stokes code for the more test cases of current practical interest . In this chapter laminar separation bubble characteristics are investigated in detail regarding formation, growth and shedding in an unsteady environment. Finally the conclusion is drawn regarding the robustness of the newly developed code in predicting the airfoil aerodynamic characteristics at low Reynolds number both in steady and unsteady environment. Lastly, suggestion for future work has been highlighted.

A systematic research on aeroacoustics conducted around the world for the last few decades has revealed various inherent characteristics of the jet noise radiation. However, a lot more needs to be done for the theoretical as well as experimental predictions of various jet noise features based on actual flow details. The work reported in the present thesis is an attempt in this direction. A critical study of existing literature on jet noise shows that none of the general wave equations lends itself easily for predictions of all the jet noise features. It is shown that while LighthilPs classical acoustic analogy approach, with some reasonable approximations, can be used to yield most of the information needed by the engineers, the convected wave equations of Phillips and Lilley are required to study the acoustic radiation in what has come to be known as "Refraction valley" or "Cone of relative silence". The characteristics of the sound field of underexpanded cold jet impingement flows were studied by measuring the noise emanating from two convergent nozzles of throat diameter 2.5 mm and 5 mm each and a convergent - divergent nozzle of exit diameter of 6.49 mm, when the jet impinges on a flat plate kept perpendicular to the direction of the jet. The measurements were conducted upstream of the nozzle over an extensive envelope of jet operating conditions such as chamber stagnation pressure, mass flow rate through the nozzle and diameter of the nozzle. The source strength at the jet boundary was obtained by measuring acoustic pressure amplitude close to the jet contour assuming it as locally cylindrical. Particular attention was focussed on backward projection of the sound field on to a cylindrical surface. This is the application of acoustic holography to study the sound radiation in the audio frequency region. With the help of FFT and software developed for this purpose, the theoretical predictions using data from several cylindrical surfaces were compared. A detailed analysis of noise radiation from a cold sonic and supersonic free jet was also carried out. The experimental work involved the measurement of noise field from a 2.5 mm, 5 mm convergent and a convergent - divergent nozzle of exit diameter of 6.49 mm and area ratio 1.687 for designed Mach number of two. The experimental setup consisted essentially of a pressure chamber made of mild steel, designed to withstand 50 bar pressure. This chamber is a cylinder with dia 0.421 m and length 0.85 m. The nozzles were made of mild steel. Compressed air approximately at room temperature is supplied to the nozzle via a control valve. The measuring and recording instruments consists of B & K Microphones, Preamplifiers, Conditioning amplifier and a Mediator, which measure a Sound Pressure Level at a point. The nozzles were operated at pressure ratio upto 25 bar. The noise signal was processed through 12 channel data acquisition system. Acoustic pressure and SPL were" calculated using theoretical relations and software developed. Using this software Fast Fourier Transformations of raw signal was obtained from 20 Hz to 20 kHz. Also constant SPL contour graphs were obtained. Source strength distribution at the jet boundary has been obtained by the principle of acoustic holography. Experimental values are closely matching with the results obtained by acoustic holography. The percentage error for acoustic pressure and SPL were less than 12%. The experimental results were used to obtain the source distribution in terms of gross jet parameters.

Electric power has become a basic necessity of human life. The major share of electric power comes from fossil fuel which results in global warming and pollution. A share of generated power comes from nuclear power which is equally dangerous. Big hydro projects take away lots of fertile land. The continuous usage of fossil fuel also poses a threat of petroleum and coal getting over in the near future. The only way out of this energy scarcity is to depend more and more on renewable sources like solar, wind and micro-hydro. At present, instead of having preference over any particular source of renewable energy, effort should be made to extract power from every possible energy source available in whatever form it is and use it in an optimal way. Like any renewable energy sources, the wind power contains large potential for harnessing energy that has been well understood hundreds of years ago. The importance of wind power generation has come to focus recently both at installation and research level and lot of activities are being carried out for efficient use of wind energy. There are different types of wind turbine designs available in the literature. But the most commercially used model is the two or three blade horizontal axis propeller type wind turbine. Research has shown that variable speed operation of this type of turbine is advantageous over fixed speed operation in terms of total energy synthesis. The most commonly used machines for wind power conversion are synchronous machine, squirrel cage induction machine and slip ring induction machine (SRIM). Variable speed operation using synchronous machine or squirrel cage induction machine requires large ratings of the power converters. However, SRIM based variable speed wind generator is advantageous over other schemes due to its inherent advantages like lower power rating for the converters, higher energy capture and the flexibility of sharing reactive power between the stator and the rotor. SRIM is used for both grid connected and stand alone applications and have been reported in the literature. The grid connected applications have received major attention in the literature whereas there are only a very few instances of its stand alone counterparts. There are many places both within and outside India where utility grid has not yet reached or the available grid is very weak. Moreover, in many of the places, the transmission line is so long that the losses in the system are extremely high. Isolated wind power generation can be of great advantage in such places where the available wind power is harnessed and utilized locally. This has been the motivation to go for proposing an isolated wind power generation scheme in this thesis. The proposed scheme is designed to supply power to the load even when very low or no wind power is available. Therefore, a battery bank is also a part of the system. The power converter assembly of the proposed scheme has three major components. One is the rotor side converter which is connected to the rotor terminals of the SRIM. The second one is the stator side converter with output LC filter which is connected to the stator side. These two converters share a common DC link which is interfaced to the battery bank through a multi phase bi-directional fly-back DC-DC converter. Fig. 1. Overall block diagram of the proposed stand alone wind power generator Functionally, this thesis proposes a system as shown in Fig. 1, which has primarily two components with multiple energy ports viz. (i) the SRIM is one triple energy port component and (ii) the proposed power conditioner is another triple energy port component. The SRIM device consists of (i) a mechanical energy port that is interfaced with the windmill shaft (ii) an AC port through the stator windings that is interfaced with the micro-grid/load and (iii) a third port which is also an AC port through the rotor windings of the SRIM that interfaces with an AC port of the proposed power conditioner. The proposed power conditioner is another triple energy port device which consists of (i) a DC energy port that interfaces with a battery/accumulator, (ii) an AC port that interfaces with the rotor windings of the SRIM and (iii) another AC port that generates the micro-grid that is connected to the load and the stator port of the SRIM. The proposed power conditioner provides the frame work for managing the energy flow from the mechanical port of the SRIM to the rotor and accumulator as well as from the mechanical port to the stator/load and accumulator. Further, energy interaction can also take place between the stator and the rotor externally through the power conditioner. The power interfaces on all three energy ports of the proposed power conditioner poses several challenges that have been discussed in this thesis. This thesis focuses on developing schemes to solve these challenges as explained below. Speed sensorless control is a natural choice for slip ring induction machine because of the flexibility of sensing both stator and rotor currents. There are different methods proposed in the literature which deal with the speed sensorless control of slip ring induction machine. However, the elimination of the measurement noise in the flux position estimation is not sufficiently addressed. It is important to address this issue as this would lead to deterioration in rotor side control of SRIM if the measurement noise is not eliminated. Primarily, the schemes which use algebraic relation between the estimated rotor current in stator reference frame and the sensed rotor current, are prone to measurement noise. On the other hand, the schemes, which use rotor back-emf integration, are affected by DC drift problems, though they are not much affected by measurement noise. The proposed stator flux position estimation scheme incorporates the benefits obtained from both the above schemes while eliminating the disadvantages inherent to them. The rotor flux position is estimated by integrating the rotor back-electromotive force. The stator flux is then obtained from the rotor flux estimate. This integration mechanism leads to several problems like dc drift and lack of error decaying mechanism. This estimation scheme solves the above problems including reduction in the propagation of noise in the sensed current to the estimated rotor side unit vectors. On the implementation front, this scheme also eliminates the need for differentiating the unit vectors for estimating slip frequency. This makes the proposed flux estimator very robust. The proposed scheme is simulated and experimentally verified. There is an internal DC bus within the proposed power conditioner that manages the energy flow through the three energy ports. The internal DC bus is interfaced to an external accumulator or battery through a power interface called the multi phase bi-directional dc-dc converter. It is generally advantageous to have the motor rated for higher voltages in order to achieve better efficiencies for a given power rating as compared to low voltage motors. This implies higher DC bus voltage. On the other hand, it is advantageous to have the battery bank rated for low voltage in order to improve the volumetric efficiency which is better at lower battery bank voltages. Both these are contradictory requirements. The above problem is solved in this thesis by proposing a multi power port topology using a bidirectional fly-back converter that is capable of handling multiple power sources and still maintain simplicity and features like high gain, wide load variations and lower output current ripple. As a spin-off, the scheme can handle parallel energy transfer from even a eutectic combination of batteries without any additional control circuitry for parallel operation. Further, the scheme also incorporates a novel transformer winding technique which significantly reduces the leakage inductance of the coupled inductor. The proposed multi-port bidirectional converter is analyzed by including non-idealities like leakage inductance. The DC bus voltage regulation requirement is not very stringent because it is not directly fed to any load. Therefore, hysteresis voltage regulation with small proportional correction is used for DC bus voltage control. The proposed converter is built and experimentally verified in the proposed system as well as in a hybrid-electric vehicle prototype. The third port of the proposed power conditioner interfaces with the stator of the SRIM and the load. The stator/load needs to be connected to a stiff micro-grid. The control requirement of the micro-grid is very stringent because, even for a sudden variation in the wind speed or the load, the grid voltage magnitude and frequency should not change. The dynamic response of the grid voltage controller has to be very fast. Moreover, the grid voltage must be balanced in presence of unbalanced loading. This thesis proposes a converter called the stator side converter along with three phase L-C filter at its output to form the micro-grid. A generalized control scheme is proposed wherein the negative sequence components and the harmonics can be eliminated at the micro-grid by means of feed-forward compensators included in the fundamental positive synchronous reference frame alone. The theoretical foundation for this scheme is developed and discussed in the thesis. In isolated locations linear loads constitute a significant percentage of the total load. Therefore, on the implementation front, only the compensation of fundamental negative sequence is demonstrated. One more necessity for compensating the fundamental negative sequence is that, the SRIM offers only leakage impedance to the fundamental negative sequence components resulting in high fundamental negative sequence current even for a small fundamental negative sequence voltage present at the micro-grid. The proposed scheme ensures balanced three phase currents at the SRIM windings and the full unbalanced current is provided from the stator side converter. This scheme is validated both by simulation and experimentation. The proposed power conditioner is integrated and used in the implementation of the entire wind power generation scheme that is proposed in the thesis. The maximum power point tracking of the wind power unit is also incorporated in the proposed system. The simulation and experimental results are also presented. Finally, the engineering issues involved in the implementation of the proposed scheme are discussed in detail highlighting the hardware configuration and the equipments used. The wind turbine is emulated using a chopper controlled DC motor. The shaft torque of the DC motor is controlled to give the Cp−λ characteristic of a typical windmill. The control issues of the DC machine to behave as a wind turbine are also explained. Finally the thesis is concluded by a statement of potentials and possibilities for future work in this research area.

Optimal control problems are often characterized by discontinuities or switchings in the control variables. One way of accurately capturing the irregularities in the solution is to use a high resolution (dense) uniform grid. This requires a large amount of computational resources both in terms of CPU time and memory. Hence, in order to accurately capture any irregularities in the solution using a few computational resources, one can refine the mesh locally in the region close to an irregularity instead of refining the mesh uniformly over the whole domain. Therefore, a novel multiresolution scheme for data compression has been designed which is shown to outperform similar data compression schemes. Specifically, we have shown that the proposed approach results in fewer grid points in the grid compared to a common multiresolution data compression scheme. The validity of the proposed mesh refinement algorithm has been verified by solving several challenging initial-boundary value problems for evolution equations in 1D. The examples have demonstrated the stability and robustness of the proposed algorithm. Next, a direct multiresolution-based approach for solving trajectory optimization problems is developed. The original optimal control problem is transcribed into a nonlinear programming (NLP) problem that is solved using standard NLP codes. The novelty of the proposed approach hinges on the automatic calculation of a suitable, nonuniform grid over which the NLP problem is solved, which tends to increase numerical efficiency and robustness. Control and/or state constraints are handled with ease, and without any additional computational complexity. The proposed algorithm is based on a simple and intuitive method to balance several conflicting objectives, such as accuracy of the solution, convergence, and speed of the computations. The benefits of the proposed algorithm over uniform grid implementations are demonstrated with the help of several nontrivial examples. Furthermore, two sequential multiresolution trajectory optimization algorithms for solving problems with moving targets and/or dynamically changing environments have been developed.

Thesis (Ph.D.)--McMaster University (Canada), 1995. / Source: Dissertation Abstracts International, Volume: 57-03, Section: B, page: 2118. Adviser: G. F. Round.

Thesis (M.S.)--Florida State University, 2006. / Advisor: Piyush Kumar, Florida State University, College of Arts and Sciences, Dept. of Computer Science. Title and description from dissertation home page (viewed June 7, 2006). Document formatted into pages; contains viii, 45 pages. Includes bibliographical references.

In this paper we present two hierarchically preconditioned methods for the fast solution of mesh equations that approximate 2D-elliptic boundary value problems on unstructured quasi uniform triangulations. Based on the fictitious space approach the original problem can be embedded into an auxiliary one, where both the hierarchical grid information and the preconditioner by decomposing functions on it are well defined. We implemented the corresponding Yserentant preconditioned conjugate gradient method as well as the BPX-preconditioned cg-iteration having optimal computational costs. Several numerical examples demonstrate the efficiency of the artificially constructed hierarchical methods which can be of importance in the industrial engineering, where often only the nodal coordinates and the element connectivity of the underlying (fine) discretization are available.

No description available.