Browsing by Author "Pierre A. Gremaud, Committee Member"

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Acoustic Wave Dynamics in the Post-Bounce Phase of Core Collapse Supernovae
(2008-07-31) Heyward, Irvine Keith; Pierre A. Gremaud, Committee Member; John M. Blondin, Committee Chair; David Brown, Committee Member; Stephen P. Reynolds, Committee Member
Auxiliary Signal Design for Fault Detection for Nonlinear Systems: Direct Approach
(2008-05-06) Andjelkovic, Ivan V.; Negash Medhin, Committee Member; Pierre A. Gremaud, Committee Member; Stephen L. Campbell, Committee Chair; Ralph Smith, Committee Member
The main task of active fault detection is to design an auxiliary signal which acting on the system will reveal to the observer a potential fault of the system. There are numerous results that implement techniques of optimal control to calculate an auxiliary signal. However, the techniques and methods are almost exclusively designed for linear systems, while nonlinear systems are treated through linearization. In this thesis, we are providing a novel way of directly approaching nonlinear systems. We will start with a brief overview of the areas of the fault detection, optimal control, basic terminology and principles of active fault detection and previous research. Then we will present the novel p-norm approach enabling us to solve nonlinear problems directly using optimization. We will develop a direct optimization formulation for active fault detection for linear and nonlinear systems with additive uncertainty. We will present some test examples and point out the advantages and disadvantages of our new p-norm approach. Several illustrative examples will be presented and analyzed for a deeper understanding of underlying problems involved with nonlinear systems. We are hoping that this thesis will give guidelines for future users and researchers of how to approach active fault detection on nonlinear systems. Linear systems with model uncertainty have already been analyzed using the Riccati equations. Here we will develop a direct optimization formulation. After some test examples, we will solve several types of problems that cannot be solved using the Riccati approach, namely problems that contain additional constraints (soft or hard) on states of the system or on auxiliary signals. The quality of an auxiliary signal is usually measured by some cost function. We will examine the influence of several cost functions on our auxiliary signal design.
Granular Flow Models: Analysis and Numerical Simulations
(2003-09-15) Wieman, Robert E.; Hien T. Tran, Committee Member; Stephen Schecter, Committee Member; Michael Shearer, Committee Chair; Pierre A. Gremaud, Committee Member
We study elastoplastic transitions in solutions of the antiplane shear model of granular flow, and describe a time-periodic solution that arises when the antiplane shear model is discretized in space. The antiplane shear model is a simplification of the continuum equations representing the flow of granular materials. The modeling of granular flow has many applications, from agricultural silos to geomechanics: improved accuracy in modeling will lead to safer and more economical designs for silos and industrial hoppers, and make oil drilling a more efficient process. We construct approximate solutions to the antiplane shear model with piecewise linear initial data, which feature transitions between elastic and plastic states. These transitions travel with fixed speed. Numerical simulations demonstrate that the same elastoplastic transitions are the prominent features of the numerical solution. The periodic solution of discretized antiplane shear appears at a critical value of the elasticity parameter for antiplane shear. The bifurcation to a periodic solution appears to be a Hopf bifurcation. The periodic solution contains elastoplastic transitions, as well as a shear band that appears over part of the period. Away from the shear band, the periodic solution has four distinct regions, three elastic and one plastic. Refinement of the spatial discretization further resolves these states.
Shear-Driven Particle Size Segregation: Models, Analysis, Numerical Solutions, and Experiments
(2009-12-04) May, Lindsay Bard Hilbert; Michael Shearer, Committee Chair; Karen E. Daniels, Committee Co-Chair; Pierre A. Gremaud, Committee Member; Mansoor A. Haider, Committee Member
Granular materials segregate by particle size when subject to shear, as in avalanches. Particles roll and slide across one another, and other particles fall into the voids that form, with smaller particles more likely to fit than larger particles. Small particles segregate to the bottom of the sample, and larger particles are levered upward. These processes are known as kinetic sieving and squeeze expulsion. The evolution of the volume fraction of small particles (ratio of the volume of small particles to the total volume of the system) corresponds to the evolution of segregation in a binary mixture of particles and can be modeled by a nonlinear first order partial differential equation, provided the velocity or shear is a known function of position. In an avalanche, shear is approximately uniform in depth, however, in boundary driven shear, the velocity is nonlinear and a shear band forms adjacent to the boundary. We explore size segregation with a laboratory experiment and by analyzing a model. We classify solutions to a fundamental initial boundary value problem for avalanche flow in two space dimensions akin to a two dimensional Riemann problem. We describe three solution types; the initial condition determines which solution occurs. We also modify the partial differential equation to model segregation in a system that experiencing nonuniform shear. We measure a velocity profile from the experimental data from a Couette experiment, which provides parameters used to visualize the solution to the initial boundary value problem. We experimentally investigate size segregation using an annular Couette cell, which is constructed of concentric cylinders and has a moving lower boundary that imparts shear to the system and an upper confining boundary that is free to move vertically to accommodate changes in the volume of the system. Initially, the Couette cell contains a layer of large particles below a layer of small particles. The system dilates as shear begins, then contracts as the sample mixes, and again expands as the sample resegregates; the height of the system is correlated to the amount of mixing or segregation. At the end of the experiment, we find a layer of small particles below a layer of large particles. The initial condition for the partial differential equation corresponds to the one dimensional initial configuration of the experiment. We solve two initial boundary value problems, one with a piecewise linear shear rate and one with an exponential shear rate, where the parameters for both cases are derived from the experimental data. In each case, we use the method of characteristics to solve the initial boundary value problem. In both cases, almost all pieces of the solution can be explicitly calculated, and those that cannot are calculated numerically. In the piecewise linear case, there is a material interface across which the characteristic speed jumps; in the exponential case, the characteristics are curved. We compare the model with the exponential shear rate to the experimental data. The model solution is the volume fraction of small particles at time t and location z. We cannot measure the volume fraction locally in the experiment; instead the height of the sample is an indirect measurement of the amount of mixing or segregation. We map the volume fraction to a theoretical height which we compare to the experimental height data. We conclude that the model captures qualitative features of the experimental data, but there are features of the experiment that we cannot capture with the model.
A Variable Turbulent Prandtl and Schmidt Number Model Study for Scramjet Applications.
(2009-03-23) Keistler, Patrick G.; Fred R. DeJarnette, Committee Member; Jack R. Edwards, Committee Member; Hassan A. Hassan, Committee Chair; Pierre A. Gremaud, Committee Member
A turbulence model that allows for the calculation of the variable turbulent Prandtl (Prt) and Schmidt (Sct) numbers as part of the solution is presented. The model also accounts for the interactions between turbulence and chemistry by modeling the corresponding terms. Four equations are added to the baseline k-ÃŽÂ¶ turbulence model: two equations for enthalpy variance and its dissipation rate to calculate the turbulent diffusivity, and two equations for the concentrations variance and its dissipation rate to calculate the turbulent diffusion coefficient. The underlying turbulence model already accounts for compressibility effects. The variable Prt/Sct turbulence model is validated and tuned by simulating a wide variety of experiments. Included in the experiments are two-dimensional, axisymmetric, and three-dimensional mixing and combustion cases. The combustion cases involved either hydrogen and air, or hydrogen, ethylene, and air. Two chemical kinetic models are employed for each of these situations. For the hydrogen and air cases, a seven species/seven reaction model where the reaction rates are temperature dependent and a nine species/nineteen reaction model where the reaction rates are dependent on both pressure and temperature are used. For the cases involving ethylene, a 15 species/44 reaction reduced model that is both pressure and temperature dependent is used, along with a 22 species/18 global reaction reduced model that makes use of the quasi-steady-state approximation. In general, fair to good agreement is indicated for all simulated experiments. The turbulence/chemistry interaction terms are found to have a significant impact on flame location for the two-dimensional combustion case, with excellent experimental agreement when the terms are included. In most cases, the hydrogen chemical mechanisms behave nearly identically, but for one case, the pressure dependent model would not auto-ignite at the same conditions as the experiment and the other chemical model. The model was artificially ignited in that case. For the cases involving ethylene combustion, the chemical model has a profound impact on the flame size, shape, and ignition location. However, without quantitative experimental data, it is difficult to determine which one is more suitable for this particular application.