Investigation Of Predicted Helicopter Rotorhub Drag and Wake Flow with Reduced Order Modeling

The rotor hub is one of the most important components of the modern helicopter. This complex collection of linkages and plates has numerous responsibilities, including the translation of pilot input to system response, anchoring the blades to the rotor mast, and sustaining the various forces transmitted by the blades. Due its intricate design and relatively small sized components the rotor hub interacts with the incoming flow to create a highly chaotic, turbulent wake which impinges on the fuselage and empennage. This assembly has also been found to be one of the primary contributors to the total vehicle parasite drag. Unfortunately studying the rotor hub and its wake more closely is made difficult by the limitation of both modern experimental and computational methods. From an experimental standpoint tests are expensive to run, difficult to gather large amounts of data from, and can require full or high scale Reynolds numbers. Computational Fluid Dynamics (CFD) predictions of hub flows are limited by high grid resolution requirements, and lengthy grid generation and simulation times. Modal decompositions provide robust options for reduced order modeling of fluid flows. Several modal decomposition methods are tested for the validity of their application to the complex flow fields that form around rotor hubs. Four variations of two rotor hub designs, a baseline and low drag, are simulated in forward flight. This selection of hubs was chose to examine the effects of both hub geometry and aerodynamic optimization on the rotor hub surface forces and wake. Flow solutions were found using the OVERFLOW2.2n overset, structured, RANS solver created and maintained by NASA. Simulations were conducted using a fully turbulent model and the grid generation and computational equations specifics are discussed in further detail. Each of the four hub variants was subjected to the same flow conditions. Several variants of modal decomposition and other post processing techniques were used on the resultant surface force and wake data in order to Characterize the hub flow field

The Price of Synchrony: Resistive Losses due to Phase Synchronization in Power Networks

We investigate the total resistive losses incurred in returning a power network of identical generators to a synchronous state following a transient stability event or in maintaining this state in the presence of persistent stochastic disturbances. We formulate this cost as the input-output $H^2$ norm of a linear dynamical system with distributed disturbances. We derive an expression for the total resistive losses that scales with the size of the network as well as properties of the generators and power lines, but is independent of the network topology. This topologically invariant scaling of what we term the price of synchrony is in contrast to typical power system stability notions like rate of convergence or the region of attraction for rotor-angle stability. Our result indicates that highly connected power networks, whilst desirable for higher phase synchrony, do not offer an advantage in terms of the total resistive power losses needed to achieve this synchrony. Furthermore, if power flow is the mechanism used to achieve synchrony in highly-distributed-generation networks, the cost increases unboundedly with the number of generators.Comment: 7 pages; 2 figure

Optimal reduced oder modeling of power systems based on synchronic modal equivalencing

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1996.Includes bibliographical references (leaves 73-76).by Julio E. Castrillón Candás.M.S

Multi-objective design optimization framework for structural health monitoring

The purpose of this dissertation is to demonstrate the ability to design health monitoring systems from a systematic perspective and how, with proper sensor and actuator placement, damage occurring in a structure can be detected and tracked. To this end, a design optimization was performed to determine the best locations to excite the structure and to collect data while using the minimum number of sensors. The type of sensors used in this design optimization was uni-axis accelerometers. It should be noted that the design techniques presented here are not limited to accelerometers. Instead, they allow for any type of sensor (thermal, strain, electromagnetic, etc.) and will find the optimal locations with respect to defined objective functions (sensitivity, cost, etc.). The use of model-based optimization techniques for the design of the monitoring system is driven by the desire to obtain the best performance possible from the system given what is known about the system prior to implementation. The use of a model is more systematic than human judgment and is able to take far more into account by using information about the dynamical response of a system than even an experienced structural engineer. It is understood in the context of structural modeling that no model is 100\% accurate and that any designs produced using model-based techniques should be tolerant to modeling errors. Demonstrations performed in the past have shown that poorly placed sensors can be very insensitive to damage development. To perform the optimization, a multi-objective genetic algorithm (GA) was employed. The objectives of the optimization were to be highly sensitive to damage occurring in potential “hot spots” while also maintaining the ability to detect damage occurring elsewhere in the structure and maintaining robustness to modeling errors. Two other objectives were to minimize the number of sensors and actuators used. The optimization only considered placing accelerometers, but it could have considered different type of sensors (i.e. strain, magneto-restrictive) or any combination thereof

A homotopy algorithm for digital optimal projection control GASD-HADOC

The linear-quadratic-gaussian (LQG) compensator was developed to facilitate the design of control laws for multi-input, multi-output (MIMO) systems. The compensator is computed by solving two algebraic equations for which standard closed-loop solutions exist. Unfortunately, the minimal dimension of an LQG compensator is almost always equal to the dimension of the plant and can thus often violate practical implementation constraints on controller order. This deficiency is especially highlighted when considering control-design for high-order systems such as flexible space structures. This deficiency motivated the development of techniques that enable the design of optimal controllers whose dimension is less than that of the design plant. A homotopy approach based on the optimal projection equations that characterize the necessary conditions for optimal reduced-order control. Homotopy algorithms have global convergence properties and hence do not require that the initializing reduced-order controller be close to the optimal reduced-order controller to guarantee convergence. However, the homotopy algorithm previously developed for solving the optimal projection equations has sublinear convergence properties and the convergence slows at higher authority levels and may fail. A new homotopy algorithm for synthesizing optimal reduced-order controllers for discrete-time systems is described. Unlike the previous homotopy approach, the new algorithm is a gradient-based, parameter optimization formulation and was implemented in MATLAB. The results reported may offer the foundation for a reliable approach to optimal, reduced-order controller design

Comparison of POD reduced order strategies for the nonlinear 2D Shallow Water Equations

This paper introduces tensorial calculus techniques in the framework of Proper Orthogonal Decomposition (POD) to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied to polynomial nonlinearities of any degree $p$. Such nonlinear terms have an on-line complexity of $\mathcal{O}(k^{p+1})$, where $k$ is the dimension of POD basis, and therefore is independent of full space dimension. However it is efficient only for quadratic nonlinear terms since for higher nonlinearities standard POD proves to be less time consuming once the POD basis dimension $k$ is increased. Numerical experiments are carried out with a two dimensional shallow water equation (SWE) test problem to compare the performance of tensorial POD, standard POD, and POD/Discrete Empirical Interpolation Method (DEIM). Numerical results show that tensorial POD decreases by $76\times$ times the computational cost of the on-line stage of standard POD for configurations using more than $300,000$ model variables. The tensorial POD SWE model was only $2-8\times$ slower than the POD/DEIM SWE model but the implementation effort is considerably increased. Tensorial calculus was again employed to construct a new algorithm allowing POD/DEIM shallow water equation model to compute its off-line stage faster than the standard and tensorial POD approaches.Comment: 23 pages, 8 figures, 5 table