This work examines simulation requirements for ensuring accurate predictions of compressible cavity flows. Lessons learned from this study will be used in the future to study the effects of complex geometric features, representative of those found on real weapons bays, on compressible flow past open cavities. A hybrid RANS/LES simulation method is applied to a rectangular cavity with length-to-depth ratio of 7, in order to first validate the model for this class of flows. Detailed studies of mesh resolution, absorbing boundary condition formulation, and boundary zone extent are included and guidelines are developed for ensuring accurate prediction of cavity pressure fluctuations.
This work examines simulation requirements for ensuring accurate predictions of compressible cavity flows. Lessons learned from this study will be used in the future to study the effects of complex geometric features, representative of those found on real weapons bays, on compressible flow past open cavities. A hybrid RANS/LES simulation method is applied to a rectangular cavity with length-to-depth ratio of 7, in order to first validate the model for this class of flows. Detailed studies of mesh resolution, absorbing boundary condition formulation, and boundary zone extent are included and guidelines are developed for ensuring accurate prediction of cavity pressure fluctuations.
An approach for building energy-stable Galerkin reduced order models (ROMs) for linear hyperbolic or incompletely parabolic systems of partial differential equations (PDEs) using continuous projection is developed. This method is an extension of earlier work by the authors specific to the equations of linearized compressible inviscid flow. The key idea is to apply to the PDEs a transformation induced by the Lyapunov function for the system, and to build the ROM in the transformed variables. For linear problems, the desired transformation is induced by a special inner product, termed the "symmetry inner product", which is derived herein for several systems of physical interest. Connections are established between the proposed approach and other stability-preserving model reduction methods, giving the paper a review flavor. More specifically, it is shown that a discrete counterpart of this inner product is a weighted L2 inner product obtained by solving a Lyapunov equation, first proposed by Rowley et al. and termed herein the "Lyapunov inner product". Comparisons between the symmetry inner product and the Lyapunov inner product are made, and the performance of ROMs constructed using these inner products is evaluated on several benchmark test cases.
This report describes work performed from June 2012 through May 2014 as a part of a Sandia Early Career Laboratory Directed Research and Development (LDRD) project led by the first author. The objective of the project is to investigate methods for building stable and efficient proper orthogonal decomposition (POD)/Galerkin reduced order models (ROMs): models derived from a sequence of high-fidelity simulations but having a much lower computational cost. Since they are, by construction, small and fast, ROMs can enable real-time simulations of complex systems for onthe- spot analysis, control and decision-making in the presence of uncertainty. Of particular interest to Sandia is the use of ROMs for the quantification of the compressible captive-carry environment, simulated for the design and qualification of nuclear weapons systems. It is an unfortunate reality that many ROM techniques are computationally intractable or lack an a priori stability guarantee for compressible flows. For this reason, this LDRD project focuses on the development of techniques for building provably stable projection-based ROMs. Model reduction approaches based on continuous as well as discrete projection are considered. In the first part of this report, an approach for building energy-stable Galerkin ROMs for linear hyperbolic or incompletely parabolic systems of partial differential equations (PDEs) using continuous projection is developed. The key idea is to apply a transformation induced by the Lyapunov function for the system, and to build the ROM in the transformed variables. It is shown that, for many PDE systems including the linearized compressible Euler and linearized compressible Navier-Stokes equations, the desired transformation is induced by a special inner product, termed the “symmetry inner product”. Attention is then turned to nonlinear conservation laws. A new transformation and corresponding energy-based inner product for the full nonlinear compressible Navier-Stokes equations is derived, and it is demonstrated that if a Galerkin ROM is constructed in this inner product, the ROM system energy will be bounded in a way that is consistent with the behavior of the exact solution to these PDEs, i.e., the ROM will be energy-stable. The viability of the linear as well as nonlinear continuous projection model reduction approaches developed as a part of this project is evaluated on several test cases, including the cavity configuration of interest in the targeted application area. In the second part of this report, some POD/Galerkin approaches for building stable ROMs using discrete projection are explored. It is shown that, for generic linear time-invariant (LTI) systems, a discrete counterpart of the continuous symmetry inner product is a weighted L2 inner product obtained by solving a Lyapunov equation. This inner product was first proposed by Rowley et al., and is termed herein the “Lyapunov inner product“. Comparisons between the symmetry inner product and the Lyapunov inner product are made, and the performance of ROMs constructed using these inner products is evaluated on several benchmark test cases. Also in the second part of this report, a new ROM stabilization approach, termed “ROM stabilization via optimization-based eigenvalue reassignment“, is developed for generic LTI systems. At the heart of this method is a constrained nonlinear least-squares optimization problem that is formulated and solved numerically to ensure accuracy of the stabilized ROM. Numerical studies reveal that the optimization problem is computationally inexpensive to solve, and that the new stabilization approach delivers ROMs that are stable as well as accurate. Summaries of “lessons learned“ and perspectives for future work motivated by this LDRD project are provided at the end of each of the two main chapters.
An extensive database of simulated loads representing almost 100 years of operation of a utility-scale wind turbine has been developed using high-performance computing resources. Such a large amount of data makes it possible to evaluate several proposals being considered in planned revisions of industry guidelines such as the International Electrotechnical Commission's 61400-1 wind turbine design standard. Current design provisions, especially those dependent on large amounts of data, can be critically examined and validated or alternative proposals can be made based on studies using this loads database. We discuss one design load case in particular that requires nominal 50-year loads, often difficult to establish with limited simulations followed by statistical extrapolation, to which a load factor (1.25) is applied. Alternatives that use other load statistics easier to establish from simulations are systematically evaluated. Such robust load statistics are associated with lower levels of uncertainty. Load factors to be applied to such alternative nominal loads are higher than those for the 50-year load. We discuss how the loads database developed enabled systematic study of a proposal that can serve as an alternative to use of a factored 50-year load. Calibration of this proposal accounts for the uncertainty in estimation of loads from simulation and the large database allows assessment against 50-year loads with quantifiable (and low) uncertainty.
This report documents the data post-processing and analysis performed to date on the field test data. Results include the control capability of the trailing edge flaps, the combined structural and aerodynamic damping observed through application of step actuation with ensemble averaging, direct observation of time delays associated with aerodynamic response, and techniques for characterizing an operating turbine with active rotor control.
Simulations of a rectangular cavity containing a model captive store are performed using a Hybrid Reynolds-averaged Navier-Stokes/Large Eddy Simulation (RANS/LES) model. The fluid flow simulations are coupled to a structural dynamics finite element model using a one-way pressure transfer procedure. Simulation results for pressure fluctuation spectra and store acceleration are compared to measurements made on the same configuration in a tri-sonic wind tunnel at Mach numbers of 0.60, 0.80, and 1.47. The simulation results are used to calculate unsteady integrated forces and moments acting on the store. Spectra of the forces and moments reveal that a complex relationship exists between the unsteady integrated forces and the measured resonant cavity modes as indicated in the cavity wall pressure measurements. Predictions of the store accelerations from the coupled model show some success in predicting both forced and natural modal responses of the store within the cavity environment, while also highlighting some challenges in obtaining statistically converged results for this class of problems.
A newly-developed computational fluid-structure interaction framework for simulation of stores in captive carriage environments is validated. The computational method involves one-way coupling, with pressure loads calculated by a hybrid RANS-LES CFD model transferred to a structural dynamics solver. Validation is performed at several levels. First, the ability of the CFD model to accurately predict the flow-field and resulting aerodynamic loads in an empty cavity is assessed against wind tunnel data. In parallel, the structural dynamics model for a simulated store is calibrated and then validated against a shaker table experiment. Finally, predictions of aerodynamic loads and store vibrations from the coupled simulation model are compared to new wind tunnel experimental data for a model captive carriage configuration.