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Description
Modern day gas turbine designers face the problem of hot mainstream gas ingestion into rotor-stator disk cavities. To counter this ingestion, seals are installed on the rotor and stator disk rims and purge air, bled off from the compressor, is injected into the cavities. It is desirable to reduce the

Modern day gas turbine designers face the problem of hot mainstream gas ingestion into rotor-stator disk cavities. To counter this ingestion, seals are installed on the rotor and stator disk rims and purge air, bled off from the compressor, is injected into the cavities. It is desirable to reduce the supply of purge air as this decreases the net power output as well as efficiency of the gas turbine. Since the purge air influences the disk cavity flow field and effectively the amount of ingestion, the aim of this work was to study the cavity velocity field experimentally using Particle Image Velocimetry (PIV). Experiments were carried out in a model single-stage axial flow turbine set-up that featured blades as well as vanes, with purge air supplied at the hub of the rotor-stator disk cavity. Along with the rotor and stator rim seals, an inner labyrinth seal was provided which split the disk cavity into a rim cavity and an inner cavity. First, static gage pressure distribution was measured to ensure that nominally steady flow conditions had been achieved. The PIV experiments were then performed to map the velocity field on the radial-tangential plane within the rim cavity at four axial locations. Instantaneous velocity maps obtained by PIV were analyzed sector-by-sector to understand the rim cavity flow field. It was observed that the tangential velocity dominated the cavity flow at low purge air flow rate, its dominance decreasing with increase in the purge air flow rate. Radially inboard of the rim cavity, negative radial velocity near the stator surface and positive radial velocity near the rotor surface indicated the presence of a recirculation region in the cavity whose radial extent increased with increase in the purge air flow rate. Qualitative flow streamline patterns are plotted within the rim cavity for different experimental conditions by combining the PIV map information with ingestion measurements within the cavity as reported in Thiagarajan (2013).
ContributorsPathak, Parag (Author) / Roy, Ramendra P (Thesis advisor) / Calhoun, Ronald (Committee member) / Lee, Taewoo (Committee member) / Arizona State University (Publisher)
Created2013
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Description
Robotic swarms can potentially perform complicated tasks such as exploration and mapping at large space and time scales in a parallel and robust fashion. This thesis presents strategies for mapping environmental features of interest – specifically obstacles, collision-free paths, generating a metric map and estimating scalar density fields– in an

Robotic swarms can potentially perform complicated tasks such as exploration and mapping at large space and time scales in a parallel and robust fashion. This thesis presents strategies for mapping environmental features of interest – specifically obstacles, collision-free paths, generating a metric map and estimating scalar density fields– in an unknown domain using data obtained by a swarm of resource-constrained robots. First, an approach was developed for mapping a single obstacle using a swarm of point-mass robots with both directed and random motion. The swarm population dynamics are modeled by a set of advection-diffusion-reaction partial differential equations (PDEs) in which a spatially-dependent indicator function marks the presence or absence of the obstacle in the domain. The indicator function is estimated by solving an optimization problem with PDEs as constraints. Second, a methodology for constructing a topological map of an unknown environment was proposed, which indicates collision-free paths for navigation, from data collected by a swarm of finite-sized robots. As an initial step, the number of topological features in the domain was quantified by applying tools from algebraic topology, to a probability function over the explored region that indicates the presence of obstacles. A topological map of the domain is then generated using a graph-based wave propagation algorithm. This approach is further extended, enabling the technique to construct a metric map of an unknown domain with obstacles using uncertain position data collected by a swarm of resource-constrained robots, filtered using intensity measurements of an external signal. Next, a distributed method was developed to construct the occupancy grid map of an unknown environment using a swarm of inexpensive robots or mobile sensors with limited communication. In addition to this, an exploration strategy which combines information theoretic ideas with Levy walks was also proposed. Finally, the problem of reconstructing a two-dimensional scalar field using observations from a subset of a sensor network in which each node communicates its local measurements to its neighboring nodes was addressed. This problem reduces to estimating the initial condition of a large interconnected system with first-order linear dynamics, which can be solved as an optimization problem.
ContributorsRamachandran, Ragesh Kumar (Author) / Berman, Spring M (Thesis advisor) / Mignolet, Marc (Committee member) / Artemiadis, Panagiotis (Committee member) / Marvi, Hamid (Committee member) / Robinson, Michael (Committee member) / Arizona State University (Publisher)
Created2018
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Description
A major concern in the operation of present-day gas turbine engines is the ingestion of hot mainstream gas into rotor-stator disk cavities of the high-pressure turbine stages. Although the engines require high gas temperature at turbine entry for good performance efficiency, the ingested gas shortens the lives of the cavity

A major concern in the operation of present-day gas turbine engines is the ingestion of hot mainstream gas into rotor-stator disk cavities of the high-pressure turbine stages. Although the engines require high gas temperature at turbine entry for good performance efficiency, the ingested gas shortens the lives of the cavity internals, particularly that of the rotor disks. Steps such as installing seals at the disk rims and injecting purge (secondary) air bled from the compressor discharge into the cavities are implemented to reduce the gas ingestion. Although there are advantages to the above-mentioned steps, the performance of a gas turbine engine is diminished by the purge air bleed-off. This then requires that the cavity sealing function be achieved with as low a purge air supply rate as possible. This, in turn, renders imperative an in-depth understanding of the pressure and velocity fields in the main gas path and within the disk cavities. In this work, experiments were carried out in a model 1.5-stage (stator-rotor-stator) axial air turbine to study the ingestion of main air into the aft, rotor-stator, disk cavity. The cavity featured rotor and stator rim seals with radial clearance and axial overlap and an inner labyrinth seal. First, time-average static pressure distribution was measured in the main gas path upstream and downstream of the rotor as well as in the cavity to ensure that a nominally steady run condition had been achieved. Main gas ingestion was determined by measuring the concentration distribution of tracer gas (CO2) in the cavity. To map the cavity fluid velocity field, particle image velocimetry was employed. Results are reported for two main air flow rates, two rotor speeds, and four purge air flow rates.
ContributorsJunnarkar, Nihal (Author) / Roy, Ramendra P (Thesis advisor) / Mignolet, Marc (Committee member) / Lee, Taewoo (Committee member) / Arizona State University (Publisher)
Created2010
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Description
Numerous works have addressed the control of multi-robot systems for coverage, mapping, navigation, and task allocation problems. In addition to classical microscopic approaches to multi-robot problems, which model the actions and decisions of individual robots, lately, there has been a focus on macroscopic or Eulerian approaches. In these approaches, the

Numerous works have addressed the control of multi-robot systems for coverage, mapping, navigation, and task allocation problems. In addition to classical microscopic approaches to multi-robot problems, which model the actions and decisions of individual robots, lately, there has been a focus on macroscopic or Eulerian approaches. In these approaches, the population of robots is represented as a continuum that evolves according to a mean-field model, which is directly designed such that the corresponding robot control policies produce target collective behaviours.



This dissertation presents a control-theoretic analysis of three types of mean-field models proposed in the literature for modelling and control of large-scale multi-agent systems, including robotic swarms. These mean-field models are Kolmogorov forward equations of stochastic processes, and their analysis is motivated by the fact that as the number of agents tends to infinity, the empirical measure associated with the agents converges to the solution of these models. Hence, the problem of transporting a swarm of agents from one distribution to another can be posed as a control problem for the forward equation of the process that determines the time evolution of the swarm density.



First, this thesis considers the case in which the agents' states evolve on a finite state space according to a continuous-time Markov chain (CTMC), and the forward equation is an ordinary differential equation (ODE). Defining the agents' task transition rates as the control parameters, the finite-time controllability, asymptotic controllability, and stabilization of the forward equation are investigated. Second, the controllability and stabilization problem for systems of advection-diffusion-reaction partial differential equations (PDEs) is studied in the case where the control parameters include the agents' velocity as well as transition rates. Third, this thesis considers a controllability and optimal control problem for the forward equation in the more general case where the agent dynamics are given by a nonlinear discrete-time control system. Beyond these theoretical results, this thesis also considers numerical optimal transport for control-affine systems. It is shown that finite-volume approximations of the associated PDEs lead to well-posed transport problems on graphs as long as the control system is controllable everywhere.
ContributorsElamvazhuthi, Karthik (Author) / Berman, Spring Melody (Thesis advisor) / Kawski, Matthias (Committee member) / Kuiper, Hendrik (Committee member) / Mignolet, Marc (Committee member) / Peet, Matthew (Committee member) / Arizona State University (Publisher)
Created2019
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Description
The problem of modeling and controlling the distribution of a multi-agent system has recently evolved into an interdisciplinary effort. When the agent population is very large, i.e., at least on the order of hundreds of agents, it is important that techniques for analyzing and controlling the system scale well with

The problem of modeling and controlling the distribution of a multi-agent system has recently evolved into an interdisciplinary effort. When the agent population is very large, i.e., at least on the order of hundreds of agents, it is important that techniques for analyzing and controlling the system scale well with the number of agents. One scalable approach to characterizing the behavior of a multi-agent system is possible when the agents' states evolve over time according to a Markov process. In this case, the density of agents over space and time is governed by a set of difference or differential equations known as a {\it mean-field model}, whose parameters determine the stochastic control policies of the individual agents. These models often have the advantage of being easier to analyze than the individual agent dynamics. Mean-field models have been used to describe the behavior of chemical reaction networks, biological collectives such as social insect colonies, and more recently, swarms of robots that, like natural swarms, consist of hundreds or thousands of agents that are individually limited in capability but can coordinate to achieve a particular collective goal.

This dissertation presents a control-theoretic analysis of mean-field models for which the agent dynamics are governed by either a continuous-time Markov chain on an arbitrary state space, or a discrete-time Markov chain on a continuous state space. Three main problems are investigated. First, the problem of stabilization is addressed, that is, the design of transition probabilities/rates of the Markov process (the agent control parameters) that make a target distribution, satisfying certain conditions, invariant. Such a control approach could be used to achieve desired multi-agent distributions for spatial coverage and task allocation. However, the convergence of the multi-agent distribution to the designed equilibrium does not imply the convergence of the individual agents to fixed states. To prevent the agents from continuing to transition between states once the target distribution is reached, and thus potentially waste energy, the second problem addressed within this dissertation is the construction of feedback control laws that prevent agents from transitioning once the equilibrium distribution is reached. The third problem addressed is the computation of optimized transition probabilities/rates that maximize the speed at which the system converges to the target distribution.
ContributorsBiswal, Shiba (Author) / Berman, Spring (Thesis advisor) / Fainekos, Georgios (Committee member) / Lanchier, Nicolas (Committee member) / Mignolet, Marc (Committee member) / Peet, Matthew (Committee member) / Arizona State University (Publisher)
Created2020