Publications

Abstract not provided.

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.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

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.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

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.

Abstract not provided.