etd@IISc Collection:
http://hdl.handle.net/2005/27
2016-07-12T08:37:59ZA Residual Based h-Adaptive Strategy Employing A Zero Mean Polynomial Reconstruction
http://hdl.handle.net/2005/2515
Title: A Residual Based h-Adaptive Strategy Employing A Zero Mean Polynomial Reconstruction
Authors: Patel, Sumit Kumar
Abstract: This thesis deals with the development of a new adaptive algorithm for three-dimensional fluid flows based on a residual error estimator. The residual, known as the R –parameter has been successfully extended to three dimensions using a novel approach for arbitrary grid topologies. The computation of the residual error estimator in three dimensions is based on a least-squares based reconstruction and the order of accuracy of the latter is critical in obtaining a consistent estimate of the error. The R –parameter can become inconsistent on three–dimensional meshes depending on the grid quality. A Zero Mean Polynomial(ZMP) which is k–exact, and which preserves the mean has been used in this thesis to overcome the problem. It is demonstrated that the ZMP approach leads to a more accurate estimation of solution derivatives as opposed to the conventional polynomial based least-squares method. The ZMP approach is employed to compute the R –parameter which is the n used to derive the criteria for refinement and derefinement. Studies on three different complex test problems involving inviscid, laminar and turbulent flows demonstrate that the new adaptive algorithm is capable of detecting the sources of error efficiently and lead to accurate results independent of the grid topology.2016-04-17T18:30:00ZOptimal Guidance Of Aerospace Vehicles Using Generalized MPSP With Advanced Control Of Supersonic Air-Breathing Engines
http://hdl.handle.net/2005/2550
Title: Optimal Guidance Of Aerospace Vehicles Using Generalized MPSP With Advanced Control Of Supersonic Air-Breathing Engines
Authors: Maity, Arnab
Abstract: A new suboptimal guidance law design approach for aerospace vehicles is proposed in this thesis, followed by an advanced control design for supersonic air-breathing engines. The guidance law is designed using the newly developed Generalized Model Predictive Static Programming (G-MPSP), which is based on the continuous time nonlinear optimal control framework. The key feature of this technique is one-time backward propagation of a small-dimensional weighting matrix dynamics, which is used to update the entire control history. This key feature, as well as the fact that it leads to a static optimization problem, lead to its computational efficiency. It has also been shown that the existing model predictive static programming (MPSP), which is based on the discrete time framework, is a special case of G-MPSP. The G-MPSP technique is further extended to incorporate ‘input inequality constraints’ in a limited sense using the penalty function philosophy. Next, this technique has been developed also further in a ‘flexible final time’ framework to converge rapidly to meet very stringent final conditions with limited number of iterations.
Using the G-MPSP technique in a flexible final time and input inequality constrained formulation, a suboptimal guidance law for a solid motor propelled carrier launch vehicle is successfully designed for a hypersonic mission. This guidance law assures very stringent final conditions at the injection point at the end of the guidance phase for successful beginning of the hypersonic vehicle operation. It also ensures that the angle of attack and structural load bounds are not violated throughout the trajectory. A second-order autopilot has been incorporated in the simulation studies to mimic the effect of the inner-loops on the guidance performance. Simulation studies with perturbations in the thrust-time behaviour, drag coefficient and mass demonstrate that the proposed guidance can meet the stringent requirements of the hypersonic mission.
The G-MPSP technique in a fixed final time and input inequality constrained formulation has also been used for optimal guidance of an aerospace vehicle propelled by supersonic air-breathing engine, where the resulting thrust can be manipulated by managing the fuel flow and nozzle area (which is not possible in solid motors). However, operation of supersonic air-breathing engines is quite complex as the thrust produced by the engine is a result of very complex nonlinear combustion dynamics inside the engine. Hence, to generate the desired thrust, accounting for a fairly detailed engine model, a dynamic inversion based nonlinear state feedback control design has been carried out. The objective of this controller is to ensure that the engine dynamically produces the thrust that tracks the commanded value of thrust generated from the guidance loop as closely as possible by regulating the fuel flow rate. Simultaneously, by manipulating throat area of the nozzle, it also manages the shock wave location in the intake for maximum pressure recovery with sufficient margin for robustness. To filter out the sensor and process noises and to estimate the states for making the control design operate based on output feedback, an extended Kalman filter (EKF) based state estimation design has also been carried out and the controller has been made to operate based on estimated states. Moreover, independent control designs have also been carried out for the actuators so that their response can be faster. In addition, this control design becomes more challenging to satisfy the imposed practical constraints like fuel-air ratio and peak combustion temperature limits. Simulation results clearly indicate that the proposed design is quite successful in assuring the desired performance of the air-breathing engine throughout the flight trajectory, i.e., both during the climb and cruise phases, while assuring adequate pressure margin for shock wave management.2016-07-10T18:30:00ZClosed-form Solutions For Rotating And Non-rotating Beams : An Inverse Problem Approach
http://hdl.handle.net/2005/1832
Title: Closed-form Solutions For Rotating And Non-rotating Beams : An Inverse Problem Approach
Authors: Sarkar, Korak
Abstract: Rotating Euler-Bernoulli beams and non-homogeneous Timoshenko beams are widely used to model important engineering structures. Hence the vibration analyses of these beams are an important problem from a structural dynamics point of view. The governing differential equations of both these type of beams do not yield any simple closed form solutions, hence we look for the inverse problem approach in determining the beam property variations given certain solutions.
Firstly, we look for a rotating beam, with pinned-free boundary conditions, whose eigenpair (frequency and mode-shape) is same as that of a uniform non-rotating beam for a particular mode. It is seen that for any given mode, there exists a flexural stiffness function (FSF) for which the ith mode eigenpair of a rotating beam with uniform mass distribution, is identical to that of a corresponding non-rotating beam with same length and mass distribution. Inserting these derived FSF's in a finite element code for a rotating pinned-free beam, the frequencies and mode shapes of a non-rotating pinned-free beam are obtained. For the first mode, a physically realistic equivalent rotating beam is possible, but for higher modes, the FSF has internal singularities. Strategies for addressing these singularities in the FSF for finite element analysis are provided. The proposed functions can be used as test functions for rotating beam codes and also for targeted destiffening of rotating beams.
Secondly, we study the free vibration of rotating Euler-Bernoulli beams, under cantilever boundary condition. For certain polynomial variations of the mass per unit length and the flexural stiffness, there exists a fundamental closed form solution to the fourth order governing differential equation. It is found that there are an infinite number of rotating beams, with various mass per unit length variations and flexural stiffness distributions, which share the same fundamental frequency and mode shape. The derived flexural stiffness polynomial functions are used as test functions for rotating beam numerical codes. They are also used to design rotating cantilever beams which may be required to vibrate with a particular frequency.
Thirdly, we study the free vibration of non-homogeneous Timoshenko beams, under fixed-fixed and fixed-hinged boundary conditions. For certain polynomial variations of the material mass density, elastic modulus and shear modulus, there exists a fundamental closed form solution to the coupled second order governing differential equations. It is found that there are an infinite number of non-homogeneous Timoshenko beams, with various material mass density, elastic modulus and shear modulus distributions, which share the same fundamental frequency and mode shape. They can be used to design non-homogeneous Timoshenko beams which may be required for certain engineering applications.2012-12-03T18:30:00ZParametric Analysis Of A Free Piston Stirling Engine For Spacecraft Power Applications With A Radioisotope Heat Source
http://hdl.handle.net/2005/2339
Title: Parametric Analysis Of A Free Piston Stirling Engine For Spacecraft Power Applications With A Radioisotope Heat Source
Authors: Bhaskaran, Ramprasad
Abstract: Stirling engines are promising candidates for applications where air breathing engines cannot be used. Self contained engines capable of operating independently of the environment are required to convert thermal energy into electric power, or to perform other necessary functions. These are ideally suited for power generation onboard spacecrafts with radioisotope heat source. These engines can power interplanetary missions to Mars and beyond.
The problem of parametric analysis, sensitivity and numerical optimization of Stirling cycle engine is discussed and applied to a specific example of a 2kWe free piston Stirling engine. Stirling cycle simulation programs are generated with emphasis and adaptations peculiar to free piston design for space use. Design algorithms are generated in MatLab and optimization toolbox is used for the parametric analysis adopted in this thesis.
A free piston beta Stirling engine with a linear alternator configuration has been studied for the interdependency and performance effects of various important operational parameters. The analysis has been carried out in order to optimize the primary parameters, weight vis a vis envelope (length and diameter) and stroke of the engine, to make it suitable for space use. The major cycle parameters considered are operating pressure, linear speed, dead space ratio and swept volume ratio, classified as secondary parameters. The whole analysis has been carried out at a cycle temperature ratio of 0.4 for a heat source temperature of 873 K, typical of a radioisotope heat source.
The optimization is carried out for the defined design requirements viz. envelope of 50 × 50 cm , stroke of less than 10 cm, and heat source temperature of 873 K. The process of parametric optimization of the primary parameters viz engine envelope and stroke are carried out with respect to the secondary parameters. Iterations are carried out on the design programs in MatLab. The results indicate that the three primary parameters have a different set each, of the secondary parameter values when optimized to the design requirement.
The fmincon solver of MatLab in the optimization tool box is selected in order to validate the optimization results. The solver is used to find a minimum of a constrained nonlinear multivariable function defining the primary parameters. The results obtained concur with the optimization results generated by the design algorithm. Further, the interdependency amongst the primary and secondary parameters is studied by generating MatLab plots for all possible combinations among the various parameters.
The effect of variations in the pressure and linear speed on the system envelope and stroke are more pronounced at lower range values of the pressure and speed and the variations of the primary parameter values are constant at higher ranges. The effect of dead space ratio and swept volume ratio (>1.0) is not pronounced.
The requirements in the environment of space place a number of constraints upon a Stirling engine/alternator design that are not present in terrestrial applications. High specific power is achieved by designing the engine for higher pressure and frequency operation than a terrestrial Stirling engine, and by using light weight materials where appropriate. Cylinder is the heart of the engine and it forms a major proportion of the total system mass. Mass and heat loss estimates and analysis have been carried out on the cylinder for various materials of construction. Based on the analysis feasibility exists for a Cu-Ni combination. The system would have a mass of 7kg with a specific power estimate of 0.28kW/kg and a conduction heat loss to mass ratio of 159W/kg.
The system obtained by numerical analysis is modeled in system simulation software SIMULATIONX. The simulation of the system is studied and a sensitivity analysis performed in order to assess the parametric interdependency of the whole free piston Stirling engine system. The system sensitivity to piston and displacer mass is studied using the simulation model.
Sensitivity results indicate that there is a range of mass values within which the system is operational, mass values outside the range makes the system non-functional. Also the range is a function of various parameters and detailed analysis is required in this direction in order to further optimize all the functional parameters. Engineering approximation is carried out using the curve fitting toolbox in MatLab to generate design equations in order to provide preliminary design data for the designer, further a scaling study is carried out at various power levels in order to assess the sensitivity of system geometry at various power levels.2014-07-10T18:30:00Z