VTechWorks Repository :: Browsing by Author "Borggaard, Jeffrey T."

Browsing by Author "Borggaard, Jeffrey T."

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Active/Passive Controls and Energy Harvesting from Vortex-Induced Vibrations
Mehmood, Arshad (Virginia Tech, 2013-10-17)
Fluid-structure interactions occur in many engineering and industrial applications. Such interactions may result in undesirable forces acting on the structure that may cause fatigue and degradation of the structural components. The purpose of this research is to develop a solver that simulates the fluid-structure interaction, assess tools that can be used to control the resulting motions and analyze a system that can be used to convert the structure's motion to a useful form of energy. For this purpose, we develop a code which encompasses three-dimensional numerical simulations of a flow interacting with a freely-oscillating cylinder. The solver is based on the accelerated reference frame technique (ARF), in which the momentum equations are directly coupled with the cylinder motion by adding a reference frame acceleration term; the outer boundary conditions of the flow domain are updated using the response of the cylinder. We develop active linear and nonlinear velocity feedback controllers that suppress VIV by directly controlling the cylinder's motion. We assess their effectiveness and compare their performance and required power levels to suppress the motion of the cylinder. Particularly, we determine the most effective control law that requires minimum power to achieve a desired controlled amplitude. Furthermore, we investigate, in detail, the feasibility of using a nonlinear energy sink to control the vortex-induced vibrations of a freely oscillating circular cylinder. It has been postulated that such a system, which consists of a nonlinear spring, can be used to control the motion over a wide range of frequencies. However, introducing an essential nonlinearity of the cubic order to a coupled system could lead to multiple stable solutions depending on the initial conditions, system's characteristics and parameters. Our investigation aims at determining the effects of the sink parameters on the response of the coupled system. We also investigate the extent of drag reduction that can be attained through rotational oscillations of the circular cylinder. An optimization is performed by combining the CFD solver with a global deterministic optimization algorithm. The use of this optimization tool allows for a rapid determination of the rotational amplitude and frequency domains that yield minimum drag. We also perform three-dimensional numerical simulations of an inline-vibrating cylinder over a range of amplitudes and frequencies with the objective of suppressing the lift force. We compare the amplitude-frequency response curves, levels of lift suppression, and synchronization maps for two- and three-dimensional flows. Finally, we evaluate the possibility of converting vortex-induced vibrations into a usable form of electric power. Different transduction mechanisms can be employed for converting these vibrations to electric power, including electrostatic, electromagnetic, and piezoelectric transduction. We consider the piezoelectric option because it can be used to harvest energy over a wide range of frequencies and can be easily implemented. We particularly investigate the conversion of vortex-induced vibrations to electric power under different operating conditions including the Reynolds number and load resistance.
Adjoint-based space-time adaptive solution algorithms for sensitivity analysis and inverse problems
Alexe, Mihai (Virginia Tech, 2011-03-18)
Adaptivity in both space and time has become the norm for solving problems modeled by partial differential equations. The size of the discretized problem makes uniformly refined grids computationally prohibitive. Adaptive refinement of meshes and time steps allows to capture the phenomena of interest while keeping the cost of a simulation tractable on the current hardware. Many fields in science and engineering require the solution of inverse problems where parameters for a given model are estimated based on available measurement information. In contrast to forward (regular) simulations, inverse problems have not extensively benefited from the adaptive solver technology. Previous research in inverse problems has focused mainly on the continuous approach to calculate sensitivities, and has typically employed fixed time and space meshes in the solution process. Inverse problem solvers that make exclusive use of uniform or static meshes avoid complications such as the differentiation of mesh motion equations, or inconsistencies in the sensitivity equations between subdomains with different refinement levels. However, this comes at the cost of low computational efficiency. More efficient computations are possible through judicious use of adaptive mesh refinement, adaptive time steps, and the discrete adjoint method. This dissertation develops a complete framework for fully discrete adjoint sensitivity analysis and inverse problem solutions, in the context of time dependent, adaptive mesh, and adaptive step models. The discrete framework addresses all the necessary ingredients of a state–of–the–art adaptive inverse solution algorithm: adaptive mesh and time step refinement, solution grid transfer operators, a priori and a posteriori error analysis and estimation, and discrete adjoints for sensitivity analysis of flux–limited numerical algorithms.
Agronomic and Nitrate Leaching Impacts of Pelletized versus Granular Urea
Shah, Sanjay Bikram (Virginia Tech, 2000-08-02)
Agronomic and water quality impacts of urea particle size were evaluated through field and laboratory experiments and mathematical modeling. In a two-year field study, corn silage yield, corn nitrogen (N) removal, and nitrate-N (NO₃⁻-N) leaching from urea pellets (1.5 g each) and granules (0.01-0.02 g each) applied at 184 kg-N/ha were compared. A control treatment (no N) and two other N application rates (110 and 258 kg-N/ha) were also included. Urea particle size impact on dissolution rate, dissolved urea movement, mineralization, and N0³-N leaching were evaluated in the laboratory. A two-dimensional (2-D) mathematical model was developed to simulate the fate of subsurface-banded urea and its transformation products, ammonium (NH₄⁺)and NO₃⁻. With 184 kg-N/ha, corn silage yield was 15% higher (p = 0.02) and corn N removal was 19% higher (p = 0.07) with pellets than granules in the second year of the field study. In the absence of yield response at 110 kg-N/ha, reason for higher yield at 184 kg-N/ha with pellets was unclear. Greater N removal reduced NO₃⁻-N leaching potential from pellets compared to granules during the over-winter period. No urea form response to yield or corn N removal was observed in the first year. In 23 of 27 sampling events, granules had higher NO₃⁻-N concentration in the root zone than pellets, with average nitrate-N concentrations of 2.6 and 2.2 mg-N/L, respectively. However, statistically, NO₃⁻-N leaching from the root zone was unaffected by urea form, probably due to high variability within treatments masking the treatment effects. In October 1997, pellets retained 16% more (p = 0.04) inorganic-N in the top half of the root zone than granules, due to slower nitrification in pellets as was determined in the mineralization study. Slower NO₃⁻-N leaching allowed for greater N extraction by plants. Pellets had lower dissolution, urea hydrolysis, and nitrification rates than granules; however, nitrification inhibition was the dominant mechanism controlling N fate. The model took into account high substrate concentration effects on N transformations, important for simulating the fate of band-applied N. The model exhibited good mass conservative properties, robustness, and expected moisture and N distribution profiles. Differences in measured field data and model outputs were likely due to uncertainties and errors in measured data and input parameters. Model calibration results indicated that moisture-related parameters greatly affected N fate simulation. Sensitivity analyses indicated the importance of nitrification-related parameters in N simulation, particularly, their possible multiplicative effects. Need for extensive model testing and validation was recognized. The validated 2-D N model could be incorporated into a management model for better management of subsurface-banded granular N. However, the 2-D model is not appropriate for simulating the three dimensional N movement from pellets.
Analysis and Approximation of Viscoelastic and Thermoelastic Joint-Beam Systems
Fulton, Brian I. (Virginia Tech, 2006-07-21)
Rigidizable/Inflatable space structures have been the focus of renewed interest in recent years due to efficient packaging for transport. In this work, we examine new mathematical systems used to model small-scale joint dynamics for inflatable space truss structures. We investigate the regularity and asymptotic behavior of systems resulting from various damping models, including Kelvin-Voigt, Boltzmann, and thermoelastic damping. Approximation schemes will also be introduced. Finally, we look at optimal control for the Kelvin-Voigt model using a linear feedback regulator.
An Analysis of Stability Margins for Continuous Systems
Albanus, Julie C. (Virginia Tech, 1999-05-06)
When designing or reviewing control systems, it is important to understand the limitations of the system's design. Many systems today are designed using numerical methods. Although the numerical model may be controllable, stabilizable, or stable, small perturbations of the system parameters can result in the loss of these properties. In this thesis, we investigate these issues for finite element approximations of a thermal convection loop.
Application of Improved Truncation Error Estimation Techniques to Adjoint Based Error Estimation and Grid Adaptation
Derlaga, Joseph Michael (Virginia Tech, 2015-07-23)
Numerical solutions obtained through the use of Computational Fluid Dynamics (CFD) are subject to discretization error, which is locally generated by truncation error. The discretization error is extremely difficult to properly estimate and this in turn leads to uncertainty over the quality of the numerical solutions obtained via CFD methods and the engineering functionals computed using these solutions. Adjoint error estimation techniques specifically seek to estimate the error in functionals, but are dependent upon accurate truncation error estimates. This work examines the application of new, single-grid, truncation error estimation procedures to the problem of adjoint error estimation for both the quasi-1D and 2D Euler equations. The new truncation error estimation techniques are based on local reconstructions of the computed solutions and comparisons are made for the quasi-1D study in order to determine the most appropriate solution variables to reconstruct as well as the most appropriate reconstruction method. In addition, comparisons are made between the single-grid truncation error estimates and methods based on uniformally refining or coarsening the underlying numerical mesh on which the computed solutions are obtained. A method based on an refined grid error estimate is shown to work well for a non-isentropic flow for the quasi-1D Euler equations, but all truncation error estimations methods ultimately result in over prediction of functional discretization error in the presence of a shock in 2D. Alternatives to adjoint methods, which can only estimate the error in a single functional for each adjoint solution obtained, are examined for the 2D Euler equations. The defection correction method and error transport equations are capable of locally improving the entire computed solution, allowing for error estimates in multiple functionals. It is found that all three functional discretization error estimates perform similarly for the same truncation error estimate, although the defect correction method is the most costly from a computational viewpoint. Comparisons are made between truncation error and adjoint weighted truncation error based adaptive indicators. For the quasi-1D Euler equations it is found that both methods are competitive, however the truncation error based method is cheaper as a separate adjoint solve is avoided. For the 2D Euler equations, the truncation error estimates on the adapted meshes suffer due to a lack of smooth grid transformations which are used in reconstructing the computed solutions. In order to complete this work, a new CFD code incorporating a variety of best practices from the field of Computer Science is developed as well as a new method of performing code verification using the method of manufactured solutions which is significantly easier to implement than traditional manufactured solution techniques.
Application of r-Adaptation Techniques for Discretization Error Improvement in CFD
Tyson, William Conrad (Virginia Tech, 2015-12-08)
Computational fluid dynamics (CFD) has proven to be an invaluable tool for both engineering design and analysis. As the performance of engineering devices become more reliant upon the accuracy of CFD simulations, it is necessary to not only quantify and but also to reduce the numerical error present in a solution. Discretization error is often the primary source of numerical error. Discretization error is introduced locally into the solution by truncation error. Truncation error represents the higher order terms in an infinite series which are truncated during the discretization of the continuous governing equations of a model. Discretization error can be reduced through uniform grid refinement but is often impractical for typical engineering problems. Grid adaptation provides an efficient means for improving solution accuracy without the exponential increase in computational time associated with uniform grid refinement. Solution accuracy can be improved through local grid refinement, often referred to as h-adaptation, or by node relocation in the computational domain, often referred to as r-adaptation. The goal of this work is to examine the effectiveness of several r-adaptation techniques for reducing discretization error. A framework for geometry preservation is presented, and truncation error is used to drive adaptation. Sample problems include both subsonic and supersonic inviscid flows. Discretization error reductions of up to an order of magnitude are achieved on adapted grids.
Approximation and Control of the Boussinesq Equations with Application to Control of Energy Efficient Building Systems
Hu, Weiwei (Virginia Tech, 2012-05-21)
In this thesis we present theoretical and numerical results for a feedback control problem defined by a thermal fluid. The problem is motivated by recent interest in designing and controlling energy efficient building systems. In particular, we show that it is possible to locally exponentially stabilize the nonlinear Boussinesq Equations by applying Neumann/Robin type boundary control on a bounded and connected domain. The feedback controller is obtained by solving a Linear Quadratic Regulator problem for the linearized Boussinesq equations. Applying classical results for semilinear equations where the linear term generates an analytic semigroup, we establish that this Riccati-based optimal boundary feedback control provides a local stabilizing controller for the full nonlinear Boussinesq equations. In addition, we present a finite element Galerkin approximation. Finally, we provide numerical results based on standard Taylor-Hood elements to illustrate the theory.
Approximation of Parametric Dynamical Systems
Carracedo Rodriguez, Andrea (Virginia Tech, 2020-09-02)
Dynamical systems are widely used to model physical phenomena and, in many cases, these physical phenomena are parameter dependent. In this thesis we investigate three prominent problems related to the simulation of parametric dynamical systems and develop the analysis and computational framework to solve each of them. In many cases we have access to data resulting from simulations of a parametric dynamical system for which an explicit description may not be available. We introduce the parametric AAA (p-AAA) algorithm that builds a rational approximation of the underlying parametric dynamical system from its input/output measurements, in the form of transfer function evaluations. Our algorithm generalizes the AAA algorithm, a popular method for the rational approximation of nonparametric systems, to the parametric case. We develop p-AAA for both scalar and matrix-valued data and study the impact of parameter scaling. Even though we present p-AAA with parametric dynamical systems in mind, the ideas can be applied to parametric stationary problems as well, and we include such examples. The solution of a dynamical system can often be expressed in terms of an eigenvalue problem (EVP). In many cases, the resulting EVP is nonlinear and depends on a parameter. A common approach to solving (nonparametric) nonlinear EVPs is to approximate them with a rational EVP and then to linearize this approximation. An existing algorithm can then be applied to find the eigenvalues of this linearization. The AAA algorithm has been successfully applied to this scheme for the nonparametric case. We generalize this approach by using our p-AAA algorithm to find a rational approximation of parametric nonlinear EVPs. We define a corresponding linearization that fits the format of the compact rational Krylov (CORK) algorithm for the approximation of eigenvalues. The simulation of dynamical systems may be costly, since the need for accuracy may yield a system of very large dimension. This cost is magnified in the case of parametric dynamical systems, since one may be interested in simulations for many parameter values. Interpolatory model order reduction (MOR) tackles this problem by creating a surrogate model that interpolates the original, is of much smaller dimension, and captures the dynamics of the quantities of interest well. We generalize interpolatory projection MOR methods from parametric linear to parametric bilinear systems. We provide necessary subspace conditions to guarantee interpolation of the subsystems and their first and second derivatives, including the parameter gradients and Hessians. Throughout the dissertation, the analysis is illustrated via various benchmark numerical examples.
Approximations and Object-Oriented Implementation for a Parabolic Partial Differential Equation
Camphouse, Russell C. (Virginia Tech, 1999-01-27)
This work is a numerical study of the 2-D heat equation with Dirichlet boundary conditions over a polygonal domain. The motivation for this study is a chemical vapor deposition (CVD) reactor in which a substrate is heated while being exposed to a gas containing precursor molecules. The interaction between the gas and the substrate results in the deposition of a compound thin film on the substrate. Two different numerical approximations are implemented to produce numerical solutions describing the conduction of thermal energy in the reactor. The first method used is a Crank-Nicholson finite difference technique which tranforms the 2-D heat equation into an algebraic system of equations. For the second method, a semi-discrete method is used which transforms the partial differential equation into a system of ordinary differential equations. The goal of this work is to investigate the influence of boundary conditions, domain geometry, and initial condition on thermal conduction throughout the reactor. Once insight is gained with respect to the aforementioned conditions, optimal design and control can be investigated. This work represents a first step in our long term goal of developing optimal design and control of such CVD systems. This work has been funded through Partnerships in Research Excellence and Transition (PRET) grant number F49620-96-1-0329.
Approximations for Singular Integral Equations
Herdman, Darwin T. (Virginia Tech, 1999-05-12)
This work is a numerical study of a class of weakly singular neutral equations. The motivation for this study is an aeroelastic system. Numerical techniques are developed to approximate the singular integral equation component appearing in the complete dynamical model for the elastic motions of a three degree of freedom structure, an airfoil with trailing edge flap, in a two dimensional unsteady flow. The flap can be viewed as an active control surface to dampen vibrations that contribute to flutter. The goal of this work is to provide accurate approximations for weakly singular neutral equations using finite elements as basis functions for the initial function space. Several examples are presented in order to validate the numerical scheme.
The Art of Modeling and Simulation of Multiscale Biochemical Systems
Pu, Yang (Virginia Tech, 2015-05-14)
In this thesis we study modeling and simulation approaches for multiscale biochemical systems. The thesis addresses both modeling methods and simulation strategies. In the first part, we propose modeling methods to study the behavior of the insulin secretion pathway. We first expand the single cell model proposed by Bertram et. al. to model multiple cells. Synchronization among multiple cells is observed. Then an unhealthy cell model is proposed to study the insulin secretion failure caused by weakening of mitochondria function. By studying the interaction between the healthy and unhealthy cells, we find that the insulin secretion can be reinstated by increasing the glucokinase level. This new discovery sheds light on antidiabetic medication. In order to study the stochastic dynamics of the insulin secretion pathway, we first apply the hybrid method to model the discrete events in the insulin secretion pathway. Based on the hybrid model, a probability based measurement is proposed and applied to test the new antidiabetic remedy. In the second part, we focus on different simulation schemes for multiscale biochemical systems. We first propose a partitioning strategy for the hybrid method which leads to an efficient way of building stochastic cell cycle models. Then different implementation methods for the hybrid method are studied. A root finding method based on inverse interpolation is introduced to implement the hybrid method with three different ODE solvers. A detailed discussion of the performance of these three ODE solvers is presented. Last, we propose a new strategy to automatically detect stiffness and identify species that cause stiffness for the Tau-Leaping method, as well as two stiffness reduction methods. The efficiency is demonstrated by applying this new strategy on a stiff decaying dimerization model and a heat shock protein regulation model.
A Bayesian Approach to Estimating Background Flows from a Passive Scalar
Krometis, Justin (Virginia Tech, 2018-06-26)
We consider the statistical inverse problem of estimating a background flow field (e.g., of air or water) from the partial and noisy observation of a passive scalar (e.g., the concentration of a pollutant). Here the unknown is a vector field that is specified by large or infinite number of degrees of freedom. We show that the inverse problem is ill-posed, i.e., there may be many or no background flows that match a given set of observations. We therefore adopt a Bayesian approach, incorporating prior knowledge of background flows and models of the observation error to develop probabilistic estimates of the fluid flow. In doing so, we leverage frameworks developed in recent years for infinite-dimensional Bayesian inference. We provide conditions under which the inference is consistent, i.e., the posterior measure converges to a Dirac measure on the true background flow as the number of observations of the solute concentration grows large. We also define several computationally-efficient algorithms adapted to the problem. One is an adjoint method for computation of the gradient of the log likelihood, a key ingredient in many numerical methods. A second is a particle method that allows direct computation of point observations of the solute concentration, leveraging the structure of the inverse problem to avoid approximation of the full infinite-dimensional scalar field. Finally, we identify two interesting example problems with very different posterior structures, which we use to conduct a large-scale benchmark of the convergence of several Markov Chain Monte Carlo methods that have been developed in recent years for infinite-dimensional settings.
Bayesian Parameter Estimation on Three Models of Influenza
Torrence, Robert Billington (Virginia Tech, 2017-05-11)
Mathematical models of viral infections have been informing virology research for years. Estimating parameter values for these models can lead to understanding of biological values. This has been successful in HIV modeling for the estimation of values such as the lifetime of infected CD8 T-Cells. However, estimating these values is notoriously difficult, especially for highly complex models. We use Bayesian inference and Monte Carlo Markov Chain methods to estimate the underlying densities of the parameters (assumed to be continuous random variables) for three models of influenza. We discuss the advantages and limitations of parameter estimation using these methods. The data and influenza models used for this project are from the lab of Dr. Amber Smith in Memphis, Tennessee.
A Class of Immersed Finite Element Spaces and Their Application to Forward and Inverse Interface Problems
Camp, Brian David (Virginia Tech, 2003-11-19)
A class of immersed finite element (IFE) spaces is developed for solving elliptic boundary value problems that have interfaces. IFE spaces are finite element approximation spaces which are based upon meshes that can be independent of interfaces in the domain. Three different quadratic IFE spaces and their related biquadratic IFE spaces are introduced here for the purposes of solving both forward and inverse elliptic interface problems in 1D and 2D. These different spaces are constructed by (i) using a hierarchical approach, (ii) imposing extra continuity requirements or (iii) using a local refinement technique. The interpolation properties of each space are tested against appropriate testing functions in 1D and 2D. The IFE spaces are also used to approximate the solution of a forward elliptic interface problem using the Galerkin finite element method and the mixed least squares finite element method. Finally, one appropriate space is selected to solve an inverse interface problem using either an output least squares approach or the least squares with mixed equation error method.
Commutation Error in Reduced Order Modeling
Koc, Birgul (Virginia Tech, 2018-10-01)
We investigate the effect of spatial filtering on the recently proposed data-driven correction reduced order model (DDC-ROM). We compare two filters: the ROM projection, which was originally used to develop the DDC-ROM, and the ROM differential filter, which uses a Helmholtz operator to attenuate the small scales in the input signal. We focus on the following questions: ``Do filtering and differentiation with respect to space variable commute, when filtering is applied to the diffusion term?'' or in other words ``Do we have commutation error (CE) in the diffusion term?" and ``If so, is the commutation error data-driven correction ROM (CE-DDC-ROM) more accurate than the original DDC-ROM?'' If the CE exists, the DDC-ROM has two different correction terms: one comes from the diffusion term and the other from the nonlinear convection term. We investigate the DDC-ROM and the CE-DDC-ROM equipped with the two ROM spatial filters in the numerical simulation of the Burgers equation with different diffusion coefficients and two different initial conditions (smooth and non-smooth).
Computational Advancements for Solving Large-scale Inverse Problems
Cho, Taewon (Virginia Tech, 2021-06-10)
For many scientific applications, inverse problems have played a key role in solving important problems by enabling researchers to estimate desired parameters of a system from observed measurements. For example, large-scale inverse problems arise in many global problems and medical imaging problems such as greenhouse gas tracking and computational tomography reconstruction. This dissertation describes advancements in computational tools for solving large-scale inverse problems and for uncertainty quantification. Oftentimes, inverse problems are ill-posed and large-scale. Iterative projection methods have dramatically reduced the computational costs of solving large-scale inverse problems, and regularization methods have been critical in obtaining stable estimations by applying prior information of unknowns via Bayesian inference. However, by combining iterative projection methods and variational regularization methods, hybrid projection approaches, in particular generalized hybrid methods, create a powerful framework that can maximize the benefits of each method. In this dissertation, we describe various advancements and extensions of hybrid projection methods that we developed to address three recent open problems. First, we develop hybrid projection methods that incorporate mixed Gaussian priors, where we seek more sophisticated estimations where the unknowns can be treated as random variables from a mixture of distributions. Second, we describe hybrid projection methods for mean estimation in a hierarchical Bayesian approach. By including more than one prior covariance matrix (e.g., mixed Gaussian priors) or estimating unknowns and hyper-parameters simultaneously (e.g., hierarchical Gaussian priors), we show that better estimations can be obtained. Third, we develop computational tools for a respirometry system that incorporate various regularization methods for both linear and nonlinear respirometry inversions. For the nonlinear systems, blind deconvolution methods are developed and prior knowledge of nonlinear parameters are used to reduce the dimension of the nonlinear systems. Simulated and real-data experiments of the respirometry problems are provided. This dissertation provides advanced tools for computational inversion and uncertainty quantification.
Computational Algorithms for Face Alignment and Recognition
Bellino, Kathleen Ann (Virginia Tech, 2002-04-27)
Real-time face recognition has recently become available for the government and industry due to developments in face recognition algorithms, human head detection algorithms, and faster/low cost computers. Despite these advances, however, there are still some critical issues that affect the performance of real-time face recognition software. This paper addresses the problem of off-centered and out-of-pose faces in pictures, particularly in regard to the eigenface method for face recognition. We first demonstrate how the representation of faces by the eigenface method, and ultimately the performance of the software depend on the location of the eyes in the pictures. The eigenface method for face recognition is described: specifically, the creation of a face basis using the singular value decomposition, the reduction of dimension, and the unique representation of faces in the basis. Two different approaches for aligning the eyes in images are presented. The first considers the rotation of images using the orthogonal Procrustes Problem. The second approach looks at locating features in images using energy-minimizing active contours. We then conclude with a simple and fast algorithm for locating faces in images. Future research is also discussed.
Computational Approaches to Improving Room Heating and Cooling for Energy Efficiency in Buildings
McBee, Brian K. (Virginia Tech, 2011-08-25)
With a nation-wide aim toward reducing operational energy costs in buildings, it is important to understand the dynamics of controlled heating, cooling, and air circulation of an individual room, the "One-Room Model Problem." By understanding how one most efficiently regulates a room's climate, one can use this knowledge to help develop overall best-practice power reduction strategies. A key toward effectively analyzing the "One-Room Model Problem" is to understand the capabilities and limitations of existing commercial tools designed for similar problems. In this thesis we develop methodology to link commercial Computational Fluid Dynamics (CFD) software COMSOL with standard computational mathematics software MATLAB, and design controllers that apply inlet airflow and heating or cooling to a room and investigate their effects. First, an appropriate continuum model, the Boussinesq System, is described within the framework of this problem. Next, abstract and weak formulations of the problem are described and tied to a Finite Element Method (FEM) approximation as implemented in the interface between COMSOL and MATLAB. A methodology is developed to design Linear Quadratic Regulator (LQR) controllers and associated functional gains in MATLAB which can be implemented in COMSOL. These "closed-loop" methods are then tested numerically in COMSOL and compared against "open-loop" and average state closed-loop controllers.
Computational Investigations of Boundary Condition Effects on Simulations of Thermoacoustic Instabilities
Wang, Qingzhao (Virginia Tech, 2016-02-17)
This dissertation presents a formulation of the Continuous Sensitivity Equation Method (CSEM) applied to the Computational Fluid Dynamics (CFD) simulation of thermoacoustic instability problems. The proposed sensitivity analysis approach only requires a single run of the CFD simulation. Moreover, the sensitivities of field variables, pressure, velocity and temperature to boundary-condition parameters are directly obtained from the solution to sensitivity equations. Thermoacoustic instability is predicted by the Rayleigh criterion. The sensitivity of the Rayleigh index is computed utilizing the sensitivities of field variables. The application of the CSEM to thermoacoustic instability problems is demonstrated by two classic examples. The first example explores the effects of the heated wall temperature on the one-dimensional thermoacoustic convection. The sensitivity of the Rayleigh index, which is the indicator of thermoacoustic instabilities, is computed by the sensitivity of field variables. As the heat wall temperature increases, the sensitivity of the Rayleigh index decreases. The evolution from positive to negative sensitivity values suggests the transition from a destabilizing trend to stabilizing trend of the thermoacoustic system. Thermoacoustic instabilities in a self-excited Rijke tube are investigated following the relatively simple thermoacoustic convection problem. The complexity of simulating the Rijke tube increases in both dimensions and mechanisms which incorporate the species transport process and chemical reactions. As a representative model of the large lean premixed combustor, Rijke tube has been extensively studied. Quantitative sensitivity analysis sets the present work apart from previous research on the prediction and control of thermoacoustic instabilities. The effects of two boundary-condition parameters, i.e. the inlet mass flow rate and the equivalence ratio, are tested respectively. Small variations in both parameters predict a rapid change in sensitivities of field variables in the early stage of the total time length of 1.2s. The sensitivity of the Rayleigh index "blows up" at a specific time point of the early stage. In addition, variations in the inlet mass flow rate and the equivalence ratio lead to opposite effects on the sensitivity of the Rayleigh index. There exist some common findings on the application of the CSEM. For both thermoacoustic problems, the sensitivities of field variables and the Rayleigh index exhibit oscillatory nature, confirming that thermoacoustic instability is an overall effect of the coupling process between fluctuations of pressure and heat release rate. All the sensitivities of the Rayleigh index show rapid changes and "blow up" in the early stage. Although the numerical errors could influence the fidelity of computational results, it is believed that the rapid changes reflect the susceptibility to thermoacoustic instabilities in the studied systems. It should also be noted that the sensitivities are obtained for small variations in influential parameters. Therefore, the resulting sensitivities do not predict the occurrence of thermoacoustic instabilities under a condition that is far from the reference state determined by either CFD simulation results (employed in this dissertation) or experimental data. The sensitivity solver developed for the present research has the feature of flexibility. Additional mechanisms and more complicated instability criteria could be easily incorporated into the solver. Moreover, the sensitivity equations formulated in this dissertation are derived from the full set of nonlinear governing equations. Therefore, it is possible to extend the use of the sensitivity solver to other CFD problems. The developed sensitivity solver needs to be optimized to gain better performance, which is considered to be the primary future work of this research.

Browsing by Author "Borggaard, Jeffrey T."

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