Publications

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Fluctuating boundary layer wall shear stress can be an important loading component for structures subjected to turbulent boundary layer flows. While normal force loading via wall pressure fluctuation is relatively well described analytically, there is a dearth of information for wall shear behavior. Starting with an approximate acoustic analogy we derive simple approximate expressions for both wall pressure and wall shear fluctuations behavior utilizing a Taylor hypothesis based analogy between streamwise and temporal fluctuations. Analytical results include longitudinal spatial correlation, autocorrelation, frequency spectrum, RMS intensity and longitudinal and lateral coherence expressions. While coefficients in these expressions usually require some empirical input they nonetheless provide useful predictions for functional behavior. Comparison of the models with available literature data sets suggests reasonable agreement. Dedicated high fidelity numerical computations (direct numerical simulations) for a supersonic boundary layer are used to further explore the efficacy of these models. The analytical models for wall pressure fluctuation and wall shear fluctuation spectral density compare well for low frequency with the simulations when Reynolds number effects are included in the pressure fluctuation intensity. The approximate analytical models developed here provide a physics-based connection between classical empirical expressions and more complete experimental and computational descriptions.

We investigate a novel application of deep neural networks to modeling of errors in prediction of surface pressure fluctuations beneath a compressible, turbulent flow. In this context, the truth solution is given by Direct Numerical Simulation (DNS) data, while the predictive model is a wall-modeled Large Eddy Simulation (LES). The neural network provides a means to map relevant statistical flow-features within the LES solution to errors in prediction of wall pressure spectra. We simulate a number of flat plate turbulent boundary layers using both DNS and wall-modeled LES to build up a database with which to train the neural network. We then apply machine learning techniques to develop an optimized neural network model for the error in terms of relevant flow features.

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Least-squares Petrov–Galerkin (LSPG) model-reduction techniques such as the Gauss–Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible flow problems where standard Galerkin techniques have failed. Furthermore, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform optimal projection associated with residual minimization at the time-continuous level, while LSPG techniques do so at the time-discrete level. This work provides a detailed theoretical and computational comparison of the two techniques for two common classes of time integrators: linear multistep schemes and Runge–Kutta schemes. We present a number of new findings, including conditions under which the LSPG ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and computationally that decreasing the time step does not necessarily decrease the error for the LSPG ROM; instead, the time step should be ‘matched’ to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible-flow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the LSPG reduced-order model by an order of magnitude.

Recent field experiments conducted in the near wake (up to 0.5 rotor diameters downwind of the rotor) of a Clipper Liberty C96 2.5 MW wind turbine using snow-based super-large-scale particle image velocimetry (SLPIV) (Hong et al., Nat. Commun., vol. 5, 2014, 4216) were successful in visualizing tip vortex cores as areas devoid of snowflakes. The so-visualized snow voids, however, suggested tip vortex cores of complex shape consisting of circular cores with distinct elongated comet-like tails. We employ large-eddy simulation (LES) to elucidate the structure and dynamics of the complex tip vortices identified experimentally. We show that the LES, with inflow conditions representing as closely as possible the state of the flow approaching the turbine when the SLPIV experiments were carried out, reproduce vortex cores in good qualitative agreement with the SLPIV results, essentially capturing all vortex core patterns observed in the field in the tip shear layer. The computed results show that the visualized vortex patterns are formed by the tip vortices and a second set of counter-rotating spiral vortices intertwined with the tip vortices. To probe the dependence of these newly uncovered coherent flow structures on turbine design, size and approach flow conditions, we carry out LES for three additional turbines: (i) the Scaled Wind Farm Technology (SWiFT) turbine developed by Sandia National Laboratories in Lubbock, TX, USA; (ii) the wind turbine developed for the European collaborative Mexico (Model Experiments in Controlled Conditions) project; and (iii) the model turbine presented in the paper by Lignarolo et al. (J. Fluid Mech., vol. 781, 2015, pp. 467-493), and the Clipper turbine under varying inflow turbulence conditions. We show that similar counter-rotating vortex structures as those observed for the Clipper turbine are also observed for the SWiFT, Mexico and model wind turbines. However, the strength of the counter-rotating vortices relative to that of the tip vortices from the model turbine is significantly weaker. We also show that incoming flows with low level turbulence attenuate the elongation of the tip and counter-rotating vortices. Sufficiently high turbulence levels in the incoming flow, on the other hand, tend to break up the coherence of spiral vortices in the near wake. To elucidate the physical mechanism that gives rise to such rich coherent dynamics we examine the stability of the turbine tip shear layer using the theory proposed by Leibovich & Stewartson (J. Fluid Mech., vol. 126, 1983, pp. 335-356). We show that for all simulated cases the theory consistently indicates the flow to be unstable exactly in the region where counter-rotating spirals emerge. We thus postulate that centrifugal instability of the rotating turbine tip shear layer is a possible mechanism for explaining the phenomena we have uncovered herein.

On Thursday, August 25, 2016, the ATDM L2 milestone review panel met with the milestone team to conduct a final assessment of the completeness and quality of the work performed. First and foremost, the panel would like to congratulate and commend the milestone team for a job well done. The team completed a significant body of high-quality work toward very ambitious goals. Additionally, their persistence in working through the technical challenges associated with evolving technology, the nontechnical challenges associated with integrating across multiple software development teams, and the many demands on their time speaks volumes about their commitment to delivering the best work possible to advance the ATDM program. The panel’s comments on the individual completion criteria appear in the last section of this memo.

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This report summarizes FY16 progress towards enabling uncertainty quantification for compressible cavity simulations using model order reduction (MOR). The targeted application is the quantification of the captive-carry environment for the design and qualification of nuclear weapons systems. To accurately simulate this scenario, Large Eddy Simulations (LES) require very fine meshes and long run times, which lead to week-long runs even on parallel state-of-the-art super- computers. MOR can reduce substantially the CPU-time requirement for these simulations. We describe two approaches for model order reduction for nonlinear systems, which can yield significant speed-ups when combined with hyper-reduction: the Proper Orthogonal Decomposition (POD)/Galerkin approach and the POD/Least-Squares Petrov Galerkin (LSPG) approach. The implementation of these methods within the in-house compressible flow solver SPARC is discussed. Next, a method for stabilizing and enhancing low-dimensional reduced bases that was developed as a part of this project is detailed. This approach is based on a premise termed "minimal subspace rotation", and has the advantage of yielding ROMs that are more stable and accurate for long-time compressible cavity simulations. Numerical results for some laminar cavity problems aimed at gauging the viability of the proposed model reduction methodologies are presented and discussed.

Simulations of the flow past a rectangular cavity containing a model captive store are performed using a hybrid Reynolds-averaged Navier–Stokes/large-eddy simulation model. Calculated pressure fluctuation spectra are validated using measurements made on the same configuration in a trisonic 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, along with correlations calculated for force/moment pairs, 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. The structure of identified cavity resonant tones is examined by visualization of filtered surface pressure fields.

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This report documents the combined work of the two meetings and serves as a key part of the foundation for the A2e/HFM effort for predictive modeling of whole wind plant physics.

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Discrete-optimal model-reduction techniques such as the Gauss{Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible ow problems where standard Galerkin techniques have failed. However, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform projection at the time-continuous level, while discrete-optimal techniques do so at the time-discrete level. This work provides a detailed theoretical and experimental comparison of the two techniques for two common classes of time integrators: linear multistep schemes and Runge{Kutta schemes. We present a number of new ndings, including conditions under which the discrete-optimal ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and experimentally that decreasing the time step does not necessarily decrease the error for the discrete-optimal ROM; instead, the time step should be `matched' to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible- ow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the discrete-optimal reduced-order model by an order of magnitude.

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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.

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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.

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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.

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Multi-megawatt Vertical Axis Wind Turbines (VAWTs) are experiencing an increased interest for floating offshore applications. However, VAWT development is hindered by the lack of fast, accurate and validated simulation models. This work compares six different numerical models for VAWTS: a multiple streamtube model, a double-multiple streamtube model, the actuator cylinder model, a 2D potential flow panel model, a 3D unsteady lifting line model, and a 2D conformal mapping unsteady vortex model. The comparison covers rotor configurations with two NACA0015 blades, for several tip speed ratios, rotor solidity and fixed pitch angle, included heavily loaded rotors, in inviscid flow. The results show that the streamtube models are inaccurate, and that correct predictions of rotor power and rotor thrust are an effect of error cancellation which only occurs at specific configurations. The other four models, which explicitly model the wake as a system of vorticity, show mostly differences due to the instantaneous or time averaged formulation of the loading and flow, for which further research is needed. © Published under licence by IOP Publishing Ltd.

The Wind Energy Technologies department at Sandia National Laboratories has developed and field tested a wind turbine rotor with integrated trailing-edge flaps designed for active control of the rotor aerodynamics. The SMART Rotor project was funded by the Wind and Water Power Technologies Office of the U.S. Department of Energy (DOE) and was conducted to demonstrate active rotor control and evaluate simulation tools available for active control research. 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.

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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.