Detonation is a supersonic mode of combustion that is modeled by a system of conservation laws of compressible fluid mechanics coupled with the equations describing thermodynamic and chemical properties of the fluid. Mathematically, these governing equations admit steady-state travelling-wave solutions consisting of a leading shock wave followed by a reaction zone. However, such solutions are often unstable to perturbations and rarely observed in laboratory experiments. The goal of this work is to study the stability of travelling-wave solutions of detonation models by the following novel approach. We linearize the governing equations about a base travelling-wave solution and solve the resultant linearized problem using high-order numerical methods. The results of these computations are postprocessed using dynamic mode decomposition to extract growth rates and frequencies of the perturbations and predict stability of travelling-wave solutions to infinitesimal perturbations. We apply this approach to two models based on the reactive Euler equations for perfect gases. For the first model with a one-step reaction mechanism, we find agreement of our results with the results of normal-mode analysis. For the second model with a two-step mechanism, we find that both types of admissible travelling-wave solutions exhibit the same stability spectra. Then we investigate the Fickett’s detonation analogue coupled with a particular reaction-rate expression. In addition to the linear stability analysis of this model, we demonstrate that it exhibits rich nonlinear dynamics with multiple bifurcations and chaotic behavior.

<div>Vacuum is needed in many applications and, there are many types of pumps that can provide the vacuum level needed. One widely used pump is the liquid-ring vacuum pump, which does not involve any solid-solid contacts at interfaces where moving and stationary parts meet. Though liquid-ring vacuum pumps are efficient and robust, manufacturers have aggressive goals on improving efficiency, performance, and range of operations.</div><div> </div><div> In this research, time-accurate computational fluid dynamic (CFD) analyses were performed to study the flow mechanisms in a liquid-ring vacuum pump to understand how it works and how the design can be improved. Based on the understanding gained, a physics based reduced order model was developed for preliminary design of the liquid ring vacuum pumps.</div><div> </div><div> In the CFD analyses, the liquid (water) was modeled as incompressible, the gas (air) as an ideal gas, and turbulence by the shear-stress transport model. The gas-liquid interface was resolved by using the volume-of-fluid method, and rotation of the impeller was enabled by using a sliding mesh. Parameters examined include the suction pressure (75, 300, and 600 Torr) and the impeller's rotational speed (1150, 1450 and 1750 rpm) with the temperature of the gas at the inlet of the suction chamber kept at 300 K and the pressure at the outlet of the exhaust chamber kept at one atmosphere. The CFD solutions generated were verified via a grid sensitivity study and validated by comparing with experimental data. When compared with experiments, results obtained for the flow rate of the gas ingested by the pump had relative errors less than 6\% and results obtained for the power consumed by the pump had relative errors less than 13\%.</div><div> </div><div> Results obtained show the shape of the liquid ring to play a dominant role in creating the expansion ratio or the vacuum needed to draw air into the pump through the suction port and the compression ratio needed to expel the air through the discharge ports. Results were generated to show how centrifugal force from rotation and how acceleration/deceleration from the difference in pressure at the pump's inlet and outlet along with the eccentricity of the impeller relative to the pump's housing affect the shape of the liquid ring. Results were also generated to show how the rotational speed of the impeller and the pressure at the suction port affect the nature of the gas and liquid flow in the pump and the pump’s effectiveness in creating a vacuum. </div><div> </div><div> With the knowledge gained from the CFD study, a physics-based reduced-order model was developed to predict air ingested and power consumed by the pump as well as the liquid ring shape and pressure of the gas and liquid in the pump as a function of design and operating parameters. This model was developed by recognising and demonstrating that the amount of air ingested and power consumed by the pump is strongly dependent on the shape and location of the liquid ring surface. The flow rates of the gas ingested by the pump and the power consumed by the pump predicted by the model were compared with experimental data and relative errors were less than 12\% and 17\% respectively.</div>

The purpose of this study was to develop a robust fluid-structure-interaction (FSI) technology that can accurately model non-linear flutter responses for sub- and transonic fluid flow. The Euler equation set governs the fluid domain, which was spatially discretised by a vertex-centred edge-based finite volume method. A dual-timestepping method was employed for the purpose of temporal discretisation. Three upwind schemes were compared in terms of accuracy, efficiency and robustness, viz. Roe, HLLC (Harten-Lax-Van Leer with contact) and AUSM+-up Advection Up-stream Splitting Method). For this purpose, a second order unstructured MUSCL (Monotonic Upstream-centred Scheme for Conservation Laws) scheme, with van Albada limiter, was employed. The non-linear solid domain was resolved by a quadratic modal reduced order model (ROM), which was compared to a semi-analytical and linear modal ROM. The ROM equations were solved by a fourth order Runge-Kutta method. The fluid and solid were strongly coupled in a partitioned fashion with the information being passed at solver sub-iteration level. The developed FSI technology was verified and validated by applying it to test cases found in literature. It was demonstrated that accurate results may be obtained, with the HLLC upwind scheme offering the best balance between accuracy and robustness. Further, the quadratic ROM offered significantly improved accuracy when compared to the linear method. / Dissertation (MEng)--University of Pretoria, 2011. / Mechanical and Aeronautical Engineering / unrestricted

Les phases de conception et de validation de pièces mécaniques nécessitent des outils de calculs rapides et fiables, permettant de faire des choix technologiques en un temps court. Dans ce cadre, il n'est pas possible de calculer la réponse exacte pour l'ensemble des configurations envisageables. Les métamodèles sont alors couramment utilisés mais nécessitent un grand nombre de réponses, notamment dans le cas où celles-ci sont non-linéaires. Une solution est alors d'exploiter plusieurs sources de données de qualité diverses pour générer un métamodèle multi-fidélité plus rapide à calculer pour une précision équivalente. Ces données multi-fidélité peuvent être extraites de modèles réduits.Les travaux présentés proposent une méthode de génération de métamodèles multi-fidélité pour l'optimisation de structures mécaniques par la mise en place d'une stratégie d'enrichissement adaptatif des informations sur la réponse de la structure, par utilisation de données issues d'un solveur LATIN-PGD permettant de générer des données de qualités adaptées, et d'accélérer le calcul par la réutilisation des données précédemment calculées. Un grand nombre de données basse-fidélité sont calculées avant un enrichissement intelligent par des données haute-fidélité.Ce manuscrit présente les contributions aux métamodèles multi-fidélité et deux approches de la méthode LATIN-PGD avec la mise en place d'une stratégie multi-paramétrique pour le réemploi des données précédemment calculées. Une implémentation parallèle des méthodes a permis de tester la méthode sur trois cas-tests, pour des gains pouvant aller jusqu'à 37x. / Engineering simulation provides the best design products by allowing many design options to be quickly explored and tested, but fast-time-to-results requirement remains a critical factor to meet aggressive time-to-market requirements. In this context, using high-fidelity direct resolution solver is not suitable for (virtual) charts generation for engineering design and optimization.Metamodels are commonly considered to explore design options without computing every possibility, but if the behavior is nonlinear, a large amount of data is still required. A possibility is to use further data sources to generate a multi-fidelity surrogate model by using model reduction. Model reduction techniques constitute one of the tools to bypass the limited calculation budget by seeking a solution to a problem on a reduced order basis (ROB).The purpose of the present work is an online method for generating a multi-fidelity metamodel nourished by calculating the quantity of interest from the basis generated on-the-fly with the LATIN-PGD framework for elasto-viscoplastic problems. Low-fidelity fields are obtained by stopping the solver before convergence, and high-fidelity information is obtained with converged solution. In addition, the solver ability to reuse information from previously calculated PGD basis is exploited.This manuscript presents the contributions to multi-fidelity metamodels and the LATIN-PGD method with the implementation of a multi-parametric strategy. This coupling strategy was tested on three test cases for calculation time savings of more than 37x.

This work proposes a new method for using reduced order models in lieu of high fidelity analysis during the sensitivity analysis step of gradient based design optimization. The method offers a reduction in the computational cost of finite difference based sensitivity analysis in that context. The method relies on interpolating reduced order models which are based on proper orthogonal decomposition. The interpolation process is performed using radial basis functions and Grassmann manifold projection. It does not require additional high fidelity analyses to interpolate a reduced order model for new points in the design space. The interpolated models are used specifically for points in the finite difference stencil during sensitivity analysis. The proposed method is applied to an airfoil shape optimization (ASO) problem and a transport wing optimization (TWO) problem. The errors associated with the reduced order models themselves as well as the gradients calculated from them are evaluated. The effects of the method on the overall optimization path, computation times, and function counts are also examined. The ASO results indicate that the proposed scheme is a viable method for reducing the computational cost of these optimizations. They also indicate that the adaptive step is an effective method of improving interpolated gradient accuracy. The TWO results indicate that the interpolation accuracy can have a strong impact on optimization search direction.

An efficient solution method for evaluating radiative transport in a foam layer is a valuable tool for predicting the properties of the layer. Two different solution methods have been investigated. First, a reverse Monte Carlo (RMC) simulation has been developed. In the RMC simulation photon bundles are traced backwards from a detector to the source where they were emitted. The RMC method takes advantage of time reflection symmetry, allowing the photons to be traced backwards in the same manner they are tracked in a standard forward Monte Carlo scheme. Second, a reduced order model based on the singular value decomposition (ROM) has been developed. ROM uses solutions of the reflectance-time profiles found for specific values of the governing parameters to form a solution basis that can be used to generate the profile for any arbitrary values of the parameter set. The governing parameters that were used in this study include the foam layer thickness, the asymmetry parameter, and the scattering coefficient. Layer thicknesses between 4 cm and 20 cm were considered. Values of the asymmetry parameter varied between 0.2 and .08, while the scattering coefficient ranged from 2800 m-1 to 14000 m-1. Ten blind test cases with parameters chosen randomly from these ranges were run and compared to an established forward Monte Carlo (FMC) solution to determine the accuracy and efficiency of both methods. For both RMC and ROM methods the agreement with FMC is good. The average difference in areas under the curves relative to the FMC curve for the ten cases of RMC is 7.1% and for ROM is 7.6%. One of the ten cases causes ROM to extrapolate outside of its data set. If this case is excluded the average error for the remaining nine cases is 5.3%. While the efficiency of RMC for this case is not much greater than that of FMC, it is advantageous in that a solution over a specified time range can be found, as opposed to the FMC where the entire profile must be found. ROM is a very efficient solution method. After a library of solutions is developed, a separated solution with different parameters can be found essentially in real-time. Because of the efficiency of this ROM it is a very promising solution technique for property analysis using inverse methods.

We investigate the implementation of nontraditional open-loop and closed-loop control techniques to systems at the micro and macro scales. At the macro level, we consider a quay-side container crane. It is known that the United States relies on ocean transportation for 95% of cargo tonnage that moves in and out of the country. Each year over six million loaded marine containers enter U.S. ports. Current growth predictions indicate that container cargo will quadruple in the next twenty years. To cope with this rapid growth, we develop a novel open-loop input-shaping control technique to mitigate payload oscillations on quay-side container cranes. The proposed approach is suitable for automated crane operations, does not require any alterations to the existing crane structure, uses the maximum crane capabilities, and is based on an accurate two-dimensional four-bar-mechanism model of a container crane. The shaped commands are based on a nonlinear approximation of the two-dimensional model frequency and, unlike traditional input-shaping techniques, our approach can account for large hoisting operations. For operator-in-the-loop crane operations, we develop a closed-loop nonlinear delayed-position feedback controller. Key features of this controller are that it: does not require major modifications to the existing crane structure, accounts for motion inversion delays, rejects external disturbances, and is superimposed on the crane operator commands. To validate the controllers, we construct a 1:10 scale model of a 65-ton quay-side container crane. The facility consists of a 7-meter track, 3.5-meter hoisting cables, a trolley, a traverse motor, two hoisting motors, and a 50-pound payload. Using this setup, we demonstrated the effectiveness of the controllers in mitigating payload oscillations in both of the open-loop and closed-loop modes of operation. At the micro level, we consider a micro optical device known as the torsional micromirror. This device has a tremendous number of industrial and consumer market applications including optical switching, light scanning, digital displays, etc. To analyze this device, we develop a comprehensive model of an electrically actuated torsional mirror. Using a Galerkin expansion, we develop a reduced-order model of the mirror and verify it against experimental data. We investigate the accuracy of representing the mirror using a two-degrees-of-freedom lumped-mass model. We conclude that, under normal operating conditions, the statics and dynamics of the mirror can be accurately represented by the simplified lumped-mass system. We utilize the lumped-mass model to study and analyze the nonlinear dynamics of torsional micromirrors subjected to combined DC and resonant AC excitations. The analysis is aimed at enhancing the performance of micromirrors used for scanning applications by providing better insight into the effects of system parameters on the microscanner's optimal design and performance. Examining the characteristics of the mirror response, we found that, for a certain DC voltage range, a two-to-one internal resonance might be activated between the first two modes. Due to this internal resonance, the mirror exhibits complex dynamic behavior. This behavior results in undesirable vibrations that can be detrimental to the scanner performance. Torsional micromirrors are currently being implemented to provide all-optical switching in fiber optic networks. Traditional switching techniques are based on converting the optical signal into electrical signal and back into optical signal before it can be switched into another fiber. This reduces the rate of data transfer substantially. To realize fast all-optical switching, we enhance the transient dynamic characteristics and performance of torsional micromirrors by developing a novel technique for preshaping the voltage commands applied to activate the mirror. This new approach is the first to effectively account for inherent nonlinearities, damping effects, and the energy of the significant higher modes. Using this technique, we are able to realize very fast switching operations with minimal settling time and almost zero overshoot. / Ph. D.

The objective of this dissertation is to present a modeling and simulation methodology for MEMS devices and identify and understand the associated nonlinearities due to large deflections, electric actuation, impacts, and friction. In the first part of the dissertation, we introduce a reduced-order model of flexible microplates under electric excitation. The model utilizes the von Karman plate equations to account for geometric nonlinearities due to large plate deflections. The Galerkin approach is employed to reduce the partial-differential equations of motion and associated boundary conditions into a finite dimensional system of nonlinearly coupled ordinary-differential equations. We use the reduced-order model to analyze the mechanical behavior of a simply supported microplate and a fully clamped microplate. Effect of various design parameters on both the static and dynamic characteristics of microplates is studied. The second part of the dissertation presents comprehensive modeling and simulation tools for impact microactuators. Nonsmooth dynamics due to impacts and friction are studied, combining various approaches, including direct numerical integration, root-finding technique for periodic motions, continuation of grazing periodic orbits, and local analysis of the near grazing dynamics. The transition between nonimpacting and impacting long term motions, referred to as grazing bifurcations, indicates the transition between on and off states of an impact microactuator. Three different on-off switching mechanisms are identified for the Mita microactuator. These mechanisms also generalize to arbitrary impacting systems with a similar nonlinearity. A local map based on the concept of discontinuity mapping provides an effcient and accurate tool for the grazing bifurcation analysis. Nonlinear impacting dynamics of the microactuator are studied in detail to identify various bifurcations and parameter ranges corresponding to chaotic motions. We find that the frequency-response curves of the impacting dynamics are significantly different from those of the nonimpacting dynamics. / Ph. D.

In most of the engineering and industrial flow applications, one encounters fluid-structure interaction. This interaction can lead to some undesirable forces acting on the structure, causing its damage or fatigue. The phenomenon, being complex in nature, requires thorough understanding of the flow physics. Analyzing canonical flows, such as the flow past a cylinder, provides fundamental concepts governing the fluid behavior. Despite a simpler geometry, studying such flows are a building block in an effort to comprehend, model, and control complicated flows. For the flow past a circular cylinder, we examine the phenomenon of vortex shedding observed in many bluff body wakes. We develop a parallel computational fluid dynamics (CFD) code to solve the incompressible Navier-Stokes equations on curvilinear coordinates to analyze vortex shedding. The algorithm is implemented on a distributed-memory, message-passing parallel computer, and a domain decomposition technique is employed to partition the grid into various processors. We validate and verify the numerical results with existing experimental and numerical studies. We analyse the performance of the parallel CFD solver by computing the speed-up and efficiency of the solver. We also show that the algorithm is scalable and can be efficiently employed to study other engineering problems requiring larger grid sizes and computational domains. Various other features of the solver, such as the turbulence model, moving boundary techniques, shear, and other canonical flows are also presented. Direct numerical simulations (DNS) are performed to simulate the flow past a circular cylinder to compute the velocity and pressure fields. Based on the flow realizations of the DNS data, we use the proper orthogonal decomposition (POD) tool to determine the minimum degrees of freedom (or modes) required to represent the flow field. For the current nonlinear problem, the dominant POD modes are used in a Galerkin procedure to project the Navier-Stokes equations onto a low-dimensional space, thereby reducing the distributed-parameter problem into a finite-dimensional nonlinear dynamical system in time. We use long-time integration of the reduced-order model to calculate periodic solutions and alternatively use a shooting technique to home on the system limit cycles. We obtain the pressure-Poisson equation by taking the divergence of the Navier-Stokes equation and then project it onto the pressure POD modes. Then, we decompose the pressure into lift and drag components and compare the results with the CFD results. To reduce the fluctuating forces on the structure, we implement full-state feedback control on the low-dimensional model with suction applied aft of the separation point. The control algorithm is successfully simulated using the CFD code and suppression of vortex-shedding is achieved. / Ph. D.

Yes / This paper presents a novel closed-form covariance model using covariance matrix decomposition for both continuous-time and discrete-time stochastic systems which are subjected to Gaussian noises. Different from the existing covariance models, it has been shown that the order of the presented model can be reduced to the order of original systems and the parameters of the model can be obtained by Kronecker product and Hadamard product which imply a uniform expression. Furthermore, the associated controller design can be simplified due to the use of the reduced-order structure of the model. Based on this model, the state and output covariance assignment algorithms have been developed with parametric state and output feedback, where the computational complexity is reduced and the extended free parameters of parametric feedback supply flexibility to the optimization. As an extension, the reduced-order closed-form covariance model for stochastic systems with parameter uncertainties is also presented in this paper. A simulated example is included to show the effectiveness of the proposed control algorithm, where encouraging results have been obtained. / National Natural Science Foundation of China [grant number 61573022], [grant number 61290323] and [grant number 61333007]