Publications

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This report aims to unify several approaches for building stable projection-based reduced order models (ROMs). Attention is focused on linear time-invariant (LTI) systems. The model reduction procedure consists of two steps: the computation of a reduced basis, and the projection of the governing partial differential equations (PDEs) onto this reduced basis. Two kinds of reduced bases are considered: the proper orthogonal decomposition (POD) basis and the balanced truncation basis. The projection step of the model reduction can be done in two ways: via continuous projection or via discrete projection. First, an approach for building energy-stable Galerkin ROMs for linear hyperbolic or incompletely parabolic systems of PDEs using continuous projection is proposed. The idea is to apply to the set of PDEs a transformation induced by the Lyapunov function for the system, and to build the ROM in the transformed variables. The resulting ROM will be energy-stable for any choice of reduced basis. It is shown that, for many PDE systems, the desired transformation is induced by a special weighted L2 inner product, termed the %E2%80%9Csymmetry inner product%E2%80%9D. Attention is then turned to building energy-stable ROMs via discrete projection. A discrete counterpart of the continuous symmetry inner product, a weighted L2 inner product termed the %E2%80%9CLyapunov inner product%E2%80%9D, is derived. The weighting matrix that defines the Lyapunov inner product can be computed in a black-box fashion for a stable LTI system arising from the discretization of a system of PDEs in space. It is shown that a ROM constructed via discrete projection using the Lyapunov inner product will be energy-stable for any choice of reduced basis. Connections between the Lyapunov inner product and the inner product induced by the balanced truncation algorithm are made. Comparisons are also made between the symmetry inner product and the Lyapunov inner product. The performance of ROMs constructed using these inner products is evaluated on several benchmark test cases.

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A research project has recently begun to explore the viability of vertical axis wind turbines (VAWT) for future U.S. offshore installations, especially in resource-rich, deep-water locations. VAWTs may offer reductions in cost across multiple categories, including operations and maintenance (O&M), support structure, installation, and electrical infrastructure costs. The cost of energy (COE) reduction opportunities follow from three fundamental characteristics of the VAWT: lower turbine center of gravity, reduced machine complexity, and the opportunity for scaling the machine to very large sizes (10-20 MW). This paper discusses why VAWTs should be considered for offshore installation, describes the project that has been created to explore this prospect, and gives some early results from the project. These results indicate a potential for COE reduction of over 20%.

Marine hydrokinetic (MHK) devices are currently being considered for the generation of electrical power in marine tidal regions. Turbulence generated in the boundary layers of these channels interacts with a turbine to excite the blades into low-to mid-frequency vibration. Additionally, the self-generated turbulent boundary layer on the turbine blade excites its trailing edge into vibration. Both of these hydrodynamic sources generate radiated noise. Being installed in a marine ecosystem, the noise generated by these MHK devices may affect the fish and marine mammal well-being. Since this MHK technology is relatively new, much of the design practice follows that from conventional horizontal axis wind turbines. In contrast to other underwater turbomachines like conventional merchant ships that have solid blades, wind turbine blades are made of hollow fiberglass composites. This paper systematically investigates the contrast of this design detail on the blade vibration and radiated noise for a particular MHK turbine design. Copyright © 2012 by ASME.

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A high-performance computer was used to simulate ninety-six years of operation of a five megawatt wind turbine. Over five million aero-elastic simulations were performed, with each simulation consisting of wind turbine operation for a ten minute period in turbulent wind conditions. These simulations have produced a large database of wind turbine loads, including ten minute extreme loads as well as fatigue cycles on various turbine components. In this paper, the extreme load probability distributions are presented. The long total simulation time has enabled good estimation of the tails of the distributions down to probabilities associated with twenty-year (and longer) return events. The database can serve in the future as a truth model against which design-oriented load extrapolation techniques can be tested. The simulations also allow for detailed examination of the simulations leading to the largest loads, as demonstrated for two representative cases.

An efficient, stability-preserving model reduction technique for non-linear initial boundary value problems whose solutions exhibit inherently non-linear dynamics such as metastability and periodic regimes (limit cycles) is developed. The approach is based on the 'continuous' Galerkin projection approach in which the continuous governing equations are projected onto the reduced basis modes in a continuous inner product. The reduced order model (ROM) basis is constructed via a proper orthogonal decomposition (POD). In general, POD basis modes will not satisfy the boundary conditions of the problem. A weak implementation of the boundary conditions in the ROM based on the penalty method is developed. Asymptotic stability of the ROM with penalty-enforced boundary conditions is examined using the energy method, following linearization and localization of the governing equations in the vicinity of a stable steady solution. This analysis, enabled by the fact that a continuous representation of the reduced basis is employed, leads to a model reduction method with an a priori stability guarantee. The approach is applied to two non-linear problems: the Allen-Cahn (or 'bistable') equation and a convection-diffusion-reaction system representing a tubular reactor. For each of these problems, bounds on the penalty parameters that ensure asymptotic stability of the ROM solutions are derived. The non-linear terms in the equations are handled efficiently using the 'best points' interpolation method proposed recently by Peraire, Nguyen et al. Numerical experiments reveal that the POD/Galerkin ROMs with stability-preserving penalty boundary treatment for the two problems considered, both without as well as with interpolation, remain stable in a way that is consistent with the solutions to the governing continuous equations and capture the correct non-linear dynamics exhibited by the exact solutions to these problems. Published 2012. This article is a US Government work and is in the public domain in the USA. © 2012 John Wiley & Sons, Ltd.

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The preliminary design for a three-bladed cross-flow rotor for a reference marine hydrokinetic turbine is presented. A rotor performance design code is described, along with modifications to the code to allow prediction of blade support strut drag as well as interference between two counter-rotating rotors. The rotor is designed to operate in a reference site corresponding to a riverine environment. Basic rotor performance and rigid-body loads calculations are performed to size the rotor elements and select the operating speed range. The preliminary design is verified with a simple finite element model that provides estimates of bending stresses during operation. A concept for joining the blades and support struts is developed and analyzed with a separate finite element analysis. Rotor mass, production costs, and annual energy capture are estimated in order to allow calculations of system cost-of-energy. Evaluation Only. Created with Aspose.Pdf.Kit. Copyright 2002-2011 Aspose Pty Ltd Evaluation Only. Created with Aspose.Pdf.Kit. Copyright 2002-2011 Aspose Pty Ltd

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The proposed DOE/Sandia Scaled Wind Farm Technology Facility (SWiFT) hosted by Texas Tech University at Reese Technology Center in Lubbock, TX, will provide a facility for experimental study of turbine-turbine interaction and complex wind farm aerodynamics. This document surveys the current status of wind turbine wake and turbine-turbine interaction research, identifying knowledge and data gaps that the proposed test site can potentially fill. A number of turbine layouts is proposed, allowing for up to ten turbines at the site.

Aerodynamic noise from wind turbine rotors leads to constraints in both rotor design and turbine siting. The primary source of aerodynamic noise on wind turbine rotors is the interaction of turbulent boundary layers on the blades with the blade trailing edges. This report surveys concepts that have been proposed for trailing edge noise reduction, with emphasis on concepts that have been tested at either sub-scale or full-scale. These concepts include trailing edge serrations, low-noise airfoil designs, trailing edge brushes, and porous trailing edges. The demonstrated noise reductions of these concepts are cited, along with their impacts on aerodynamic performance. An assessment is made of future research opportunities in trailing edge noise reduction for wind turbine rotors.

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The aerodynamic and acoustic performance of a Kevlar-walled anechoic wind tunnel test section has been analyzed. Aerodynamic measurements and panel method calculations were performed on a series of airfoils to reveal the influence of the test section walls, including their porosity and flexibility. A lift interference correction method was developed from first principles which shows consistently high accuracy when measurements are compared to viscous free-flight calculations. Interference corrections are an order of magnitude smaller than those associated with an open jet test section. Blockage corrections are found to be a fraction of those which would be associated with a hard-wall test section of the same size, and are negligible in most cases. New measurements showing the acoustic transparency of the Kevlar and the quality of the anechoic environment in the chambers are presented, along with benchmark trailing edge noise measurements. © 2010 by William J. Devenport, Ricardo A. Burdisso, Aurelien Borgoltz, Patricio Ravetta and Matthew F Barone.

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CACTUS (Code for Axial and Cross-flow TUrbine Simulation) is a turbine performance simulation code, based on a free wake vortex method, under development at Sandia National Laboratories (SNL) as part of a Department of Energy program to study marine hydrokinetic (MHK) devices. The current effort builds upon work previously done at SNL in the area of vertical axis wind turbine simulation, and aims to add models to handle generic device geometry and physical models specific to the marine environment. An overview of the current state of the project and validation effort is provided.

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The aerodynamic performance and aeroacoustic noise sources of a rotor employing flatback airfoils have been studied in field test campaign and companion modeling effort. The field test measurements of a sub-scale rotor employing nine meter blades include both performance measurements and acoustic measurements. The acoustic measurements are obtained using a 45 microphone beamforming array, enabling identification of both noise source amplitude and position. Semi-empirical models of flatback airfoil blunt trailing edge noise are developed and calibrated using available aeroacoustic wind tunnel test data. The model results and measurements indicate that flatback airfoil noise is less than drive train noise for the current test turbine. It is also demonstrated that the commonly used Brooks, Pope, and Marcolini model for blunt trailing edge noise may be over-conservative in predicting flatback airfoil noise for wind turbine applications.

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This report describes work performed from October 2007 through September 2009 under the Sandia Laboratory Directed Research and Development project titled 'Reduced Order Modeling of Fluid/Structure Interaction.' This project addresses fundamental aspects of techniques for construction of predictive Reduced Order Models (ROMs). A ROM is defined as a model, derived from a sequence of high-fidelity simulations, that preserves the essential physics and predictive capability of the original simulations but at a much lower computational cost. Techniques are developed for construction of provably stable linear Galerkin projection ROMs for compressible fluid flow, including a method for enforcing boundary conditions that preserves numerical stability. A convergence proof and error estimates are given for this class of ROM, and the method is demonstrated on a series of model problems. A reduced order method, based on the method of quadratic components, for solving the von Karman nonlinear plate equations is developed and tested. This method is applied to the problem of nonlinear limit cycle oscillations encountered when the plate interacts with an adjacent supersonic flow. A stability-preserving method for coupling the linear fluid ROM with the structural dynamics model for the elastic plate is constructed and tested. Methods for constructing efficient ROMs for nonlinear fluid equations are developed and tested on a one-dimensional convection-diffusion-reaction equation. These methods are combined with a symmetrization approach to construct a ROM technique for application to the compressible Navier-Stokes equations.

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With the increasing role of computational modeling in engineering design, performance estimation, and safety assessment, improved methods are needed for comparing computational results and experimental measurements. Traditional methods of graphically comparing computational and experimental results, though valuable, are essentially qualitative. Computable measures are needed that can quantitatively compare computational and experimental results over a range of input, or control, variables to sharpen assessment of computational accuracy. This type of measure has been recently referred to as a validation metric. We discuss various features that we believe should be incorporated in a validation metric, as well as features that we believe should be excluded. We develop a new validation metric that is based on the statistical concept of confidence intervals. Using this fundamental concept, we construct two specific metrics: one that requires interpolation of experimental data and one that requires regression (curve fitting) of experimental data. We apply the metrics to three example problems: thermal decomposition of a polyurethane foam, a turbulent buoyant plume of helium, and compressibility effects on the growth rate of a turbulent free-shear layer. We discuss how the present metrics are easily interpretable for assessing computational model accuracy, as well as the impact of experimental measurement uncertainty on the accuracy assessment.

Methods for analysis of fluid-structure interaction using high fidelity simulations are critically reviewed. First, a literature review of modern numerical techniques for simulation of aeroelastic phenomena is presented. The review focuses on methods contained within the arbitrary Lagrangian-Eulerian (ALE) framework for coupling computational fluid dynamics codes to computational structural mechanics codes. The review treats mesh movement algorithms, the role of the geometric conservation law, time advancement schemes, wetted surface interface strategies, and some representative applications. The complexity and computational expense of coupled Navier-Stokes/structural dynamics simulations points to the need for reduced order modeling to facilitate parametric analysis. The proper orthogonal decomposition (POD)/Galerkin projection approach for building a reduced order model (ROM) is presented, along with ideas for extension of the methodology to allow construction of ROMs based on data generated from ALE simulations.

With the increasing role of computational modeling in engineering design, performance estimation, and safety assessment, improved methods are needed for comparing computational results and experimental measurements. Traditional methods of graphically comparing computational and experimental results, though valuable, are essentially qualitative. Computable measures are needed that can quantitatively compare computational and experimental results over a range of input, or control, variables and sharpen assessment of computational accuracy. This type of measure has been recently referred to as a validation metric. We discuss various features that we believe should be incorporated in a validation metric and also features that should be excluded. We develop a new validation metric that is based on the statistical concept of confidence intervals. Using this fundamental concept, we construct two specific metrics: one that requires interpolation of experimental data and one that requires regression (curve fitting) of experimental data. We apply the metrics to three example problems: thermal decomposition of a polyurethane foam, a turbulent buoyant plume of helium, and compressibility effects on the growth rate of a turbulent free-shear layer. We discuss how the present metrics are easily interpretable for assessing computational model accuracy, as well as the impact of experimental measurement uncertainty on the accuracy assessment.

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In this study, we describe the extension of the 2-d preliminary design bluff body drag estimation tool developed by De Chant1 to apply for 3-d flows. As with the 2-d method, the 3-d extension uses a combined approximate Green's function/Gram-Charlier series approach to retain the body geometry information. Whereas, the 2-d methodology relied solely upon the use of small disturbance theory for the inviscid flow field associated with the body of interest to estimate the near-field initial conditions, e.g. velocity defect, the 3-d methodology uses both analytical (where available) and numerical inviscid solutions. The defect solution is then used as an initial condition in an approximate 3-d Green's function solution. Finally, the Green's function solution is matched to the 3-d analog of the classical 2-d Gram-Charlier series and then integrated to yield the net form drag on the bluff body. Preliminary results indicate that drag estimates computed are of accuracy equivalent to the 2-d method for flows with large separation, i.e. less than 20% relative error. As was the lower dimensional method, the 3-d concept is intended to be a supplement to turbulent Navier-Stokes and experimental solution for estimating drag coefficients over blunt bodies.

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Receptivity of compressible mixing layers to general source distributions is examined by a combined theoretical/computational approach. The properties of solutions to the adjoint Navier-Stokes equations are exploited to derive expressions for receptivity in terms of the local value of the adjoint solution. The result is a description of receptivity for arbitrary small-amplitude mass, momentum, and heat sources in the vicinity of a mixing-layer flow, including the edge-scattering effects due to the presence of a splitter plate of finite width. The adjoint solutions are examined in detail for a Mach 1.2 mixing-layer flow. The near field of the adjoint solution reveals regions of relatively high receptivity to direct forcing within the mixing layer, with receptivity to nearby acoustic sources depending on the source type and position. Receptivity 'nodes' are present at certain locations near the splitter plate edge where the flow is not sensitive to forcing. The presence of the nodes is explained by interpretation of the adjoint solution as the superposition of incident and scattered fields. The adjoint solution within the boundary layer upstream of the splitter-plate trailing edge reveals a mechanism for transfer of energy from boundary-layer stability modes to Kelvin-Helmholtz modes. Extension of the adjoint solution to the far field using a Kirchhoff surface gives the receptivity of the mixing layer to incident sound from distant sources.