Matthew F. Barone

Measures of agreement between computation and experiment: validation metrics

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.

Stable Galerkin reduced order models for linearized compressible flow

The Galerkin projection procedure for construction of reduced order models of compressible flow is examined as an alternative discretization of the governing differential equations. The numerical stability of Galerkin models is shown to depend on the choice of inner product for the projection. For the linearized Euler equations, a symmetry transformation leads to a stable formulation for the inner product. Boundary conditions for compressible flow that preserve stability of the reduced order model are constructed. Preservation of stability for the discrete implementation of the Galerkin projection is made possible using a piecewise-smooth finite element basis. Stability of the reduced order model using this approach is demonstrated on several model problems, where a suitable approximation basis is generated using proper orthogonal decomposition of a transient computational fluid dynamics simulation.

Joint Experimental/Computational Investigation Into the Effects of Finite Width on Transonic Cavity Flow.

Recently acquired experimental data on pressure fluctuations in cavities of equal length (L) to depth (D) ratio but varying length to width (L/W) ratio have shown substantial variations in the dominant modes in the cavity. These observations have been carried out at subsonic and transonic Mach numbers at cavity L/D=5, which puts the cavity flow in the “open” category. This paper presents results from a joint computational and experimental investigation undertaken at Sandia to explain these observations. To this end, simulations of L/D=5.0 cavity at L/W=1.0,1.67 and 5.0 have been carried out and analyzed. The results show strong differences in the mean flow structure between the three widths. The widest cavity shows significantly higher turbulence intensities across the cavity. The unsteady wall pressures reveal that in this case, significant tunnel wall interactions are present, intensifying the pressure fluctuations and the shear layer oscillations. The differences in the wall pressures and turbulent flow field are smaller for the L/W=1.0 and 1.67 cavities. The L/W=1.67 cavity is strongly influenced by the streamwise vortices at the spanwise edges of the cavity, resulting in strong three dimensional variations in mean flow across the width of the cavity. In the case of the narrowest cavity, this effect is minimal, with the resultant flow field showing predominantly two-dimensional character.

A Design of a Hydrofoil Family for Current-Driven Marine-Hydrokinetic Turbines

The natural kinetic motion of oceans, rivers, and other bodies of water is a promising resource for sustainable power production. Rotor-based marine and hydrokinetic (MHK) turbines generate electricity from river, tidal, and other water currents, operating analogously to wind turbines in air. An MHK rotor designer can draw upon a vast body of general purpose and wind power specific airfoils, but application specific hydrofoils can more optimally meet the needs of MHK power. We present the MHKF1 family of hydrofoils, designed upon experience drawn from wind turbine airfoils and incorporating hydro-specific considerations. The MHKF1 hydrofoils were developed to balance the following design objectives: (1) basic hydrodynamic performance with lift to drag ratio (l/d) as a key metric, (2) limited sensitivity to soiling because of biofouling concerns and the high cost of maintenance in the marine environment, (3) sufficient thickness for structural efficiency, (4) good stall characteristics, (5) hydrodynamic and geometric compatibility such that the different hydrofoils of the family can be applied on the same rotor blade, (6) low susceptibility to cavitation, and (7) low susceptibility to singing. While the first five criteria are common to wind turbine airfoil design, the last two are specific to operation in water. Cavitation, the formation of bubbles within a fluid, can have numerous detrimental effects including erosion of impinged surfaces, degraded performance, vibration, and noise. The minimum surface pressure of the MHKF1 hydrofoils were managed to reduce the likelihood of cavitation. Singing, a hydroacoustic/hydroelastic phenomenon of the trailing edge of hydrofoils, results in noise and vibration. To suppress singing, trailing edge thicknesses were increased and hydrofoil variants were designed with “anti-singing” profiles. The MHKF1 hydrofoils were developed with a combination of inverse and direct design methods using XFOIL and various routines for parameterizing hydrofoil geometries and surface velocity distributions. Performance was further evaluated with OVERFLOW, a Reynolds averaged Navier Stokes computational fluid dynamics code.Copyright

Low-dimensional model of spatial shear layers

The aim of this work is to develop nonlinear low-dimensional models to describe vortex dynamics in spatially developing shear layers with periodicity in time. By allowing a free variable g(x) to dynamically describe downstream thickness spreading, we are able to obtain basis functions in a scaled reference frame and construct effective models with only a few modes in the new space. To apply this modified version of proper orthogonal decomposition (POD)/Galerkin projection, we first scale the flow along y dynamically to match a template function as it is developing downstream. In the scaled space, the first POD mode can capture more than 80% energy for each frequency. However, to construct a Galerkin model, the second POD mode plays a critical role and needs to be included. Finally, a reconstruction equation for the scaling variable g is derived to relate the scaled space to physical space, where downstream spreading of shear thickness occurs. Using only two POD modes at each frequency, our models capture ...

Aerodynamic and Aeroacoustic Properties of a Flatback Airfoil: An Update

Results from an experimental study of the aerodynamic and aeroacoustic properties of a atback version of the TU Delft DU97-W-300 airfoil are presented for a chord Reynolds number of 3 10 6 . The data were gathered in the Virginia Tech Stability Wind Tunnel, which uses a special aeroacoustic test section to enable measurements of airfoil self-noise. Corrected wind tunnel aerodynamic measurements for the DU97-W-300 are compared to previous solid wall wind tunnel data and are shown to give good agreement. Aeroacoustic data are presented for the atback airfoil, with a focus on the amplitude and frequency of noise associated with the vortex-shedding tone from the blunt trailing edge wake. The effect of a splitter plate attachment on both drag and noise is also presented. Computational Fluid Dynamics predictions of the aerodynamic properties of both the unmodied DU97-W-300 and the atback version are compared to the experimental data. Technical risks associated with the use of atback airfoils for the inboard region of wind turbine blades include increased aerodynamic noise and increased aerodynamic drag. Both of these penalties are the result of the blunt trailing edge shape and the wake that is produced by this shape. The relatively low pressure at the blunt base results in a much larger drag force than for a conventional airfoil shape. The effect of this drag penalty on rotor thrust and torque coefcient for typical inboard twist angles is not severe, and in fact can be offset by the additional lift that a atback airfoil generates. 3 Consideration of drag reducing devices such as splitter plates or trailing edge serrations may be desireable to further boost performance, however. The increased noise from the atback is due primarily to the vortex shedding phenomenon associated with bluff- body wakes. The vortex shedding often leads to tonal noise, similar to the Aeolian tones of o w past circular cylinders. The intensity of bluff-body vortex shedding tones at low Mach number scales with the sixth power of the relative o w velocity. Broadband aeroacoustic noise sources associated with turbulent boundary layer-trailing edge interaction scale with the fth power of the relative o w velocity. Since outboard o w velocities are much higher than those encoun- tered inboard, the overall aerodynamic noise levels of a rotor incorporating inboard atback shapes will likely continue to be dominated by outboard trailing edge noise. However, two aspects of the atback noise source may be cause for concern. First, the vortex-shedding noise from atbacks is likely to be contained in a relatively low-frequency band (50-200 Hz). Some community noise regulations have separate low-frequency noise standards apart from considera- tion of A-weighted sound, which emphasize higher frequencies to which the human ear is more sensitive. Second, the

Galerkin reduced order models for compressible flow with structural interaction

The Galerkin projection procedure for construction of reduced order models of compressible flow is examined as an alternative discretization of the governing differential equations. The numerical stability of Galerkin models is shown to depend on the choice of inner product for the projection. For the linearized Euler equations, a symmetry transform leads to a stable formulation for the inner product. Boundary conditions for compressible flow that preserve stability of the reduced order model are constructed. Coupling with a linearized structural dynamics model is made possible through the solid wall boundary condition. Preservation of stability for the discrete implementation of the Galerkin projection is made possible using piecewise-smooth finite element bases. Stability of the coupled fluid/structure system is examined for the case of uniform flow past a thin plate. Stability of the reduced order model for the fluid is demonstrated on several model problems, where a suitable approximation basis is generated using proper orthogonal decomposition of a transient computational fluid dynamics simulation.

Aeroelastic Modeling of Large Offshore Vertical-axis Wind Turbines: Development of the Offshore Wind Energy Simulation Toolkit.

The availability of offshore wind resources in coastal regions makes offshore wind energy an attractive opportunity. There are, however, significant challenges in realizing offshore wind energy with an acceptable cost of energy due to increased infrastructure, logistics, and operations and maintenance costs. Vertical-axis wind turbines (VAWTs) are potentially ideal candidates for offshore applications, with many apparent advantages over the horizontal-axis wind turbine configuration in the offshore arena. VAWTs, however, will need to undergo much development in the coming years. Thus, the Offshore Wind ENergy Simulation (OWENS) toolkit is being developed as a design tool for assessing innovative floating VAWT configurations. This paper presents an overview of the OWENS toolkit and provides an update on the development of the tool. Verification and validation exercises are discussed, and comparisons to experimental data for the Sandia National Laboratories 34meter VAWT test bed are presented. A discussion and demonstration of a “loose” coupling approach to external loading modules, which allows a greater degree of modularity, is given. Results for a realistic VAWT structure on a floating platform under aerodynamic loads are shown and coupling between platform and turbine motions is demonstrated. Finally, future plans for development and use of the OWENS toolkit are discussed.

Decades of Wind Turbine Load Simulation.

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, wit h 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.

Multi-Fidelity Uncertainty Quantification: Application to a Vertical Axis Wind Turbine Under an Extreme Gust.

Designing better vertical axis wind turbines (VAWTs) requires considering the uncertainwind conditions they operate in and quantifying the e ect of such uncertainties. We studythe e ect of an uncertain extreme gust on the maximum forces on the blades of the VAWT.The gust is parametrized by three random variables that control its location, length andamplitude. We propose a multi- delity approach to uncertainty quanti cation that usespolynomial chaos to create an approximation to the high- delity statistics via a correctionfunction based on the di erence between high and low- delity simulations. The multi- delity method provides accurate statistics on the maximum forces for a small numberof simulations and the multi- delity statistics are consistent with the high- delity (CFD)statistics. We developed a practical method to simulate a gust, that changes its magnitudein the ow direction, in a CFD solver by combining the eld velocity method (FVM) andthe geometric conservation law (GCL). The ability to study the e ect of the gust with thehigh- delity (CFD) solver is crucial as the low- delity (blade element/vortex lattice) solverunderestimates the e ect of the gust on the maximum forces.