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DOE OSTI2025

Leveraging interpolation models and error bounds for verifiable scientific machine learning

Effective verification and validation techniques for modern scientific machine learning workflows are challenging to devise. Statistical methods are abundant and easily deployed, but often rely on speculative assumptions about the data and methods involved. Error bounds for classical interpolation techniques can provide mathematically rigorous estimates of accuracy, but often are difficult or impractical to determine computationally. Here, in this work, we present a best-of-both-worlds approach to verifiable scientific machine learning by demonstrating that (1) multiple standard interpolation techniques have informative error bounds that can be computed or estimated efficiently; (2) comparative performance among distinct interpolants can aid in validation goals; (3) deploying interpolation methods on latent spaces generated by deep learning techniques enables some interpretability for black-box models. We present a detailed case study of our approach for predicting lift-drag ratios from airfoil images. Code developed for this work is available in a public Github repository.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Design of a Preliminary Family of Airfoils for High Reynolds Number Wind Turbine Applications

For the past 30 years, offshore wind turbines exhibited a continual pattern of growth that is expected to continue as the industry pushes for higher efficiency. Current designs for the next generation of wind turbines are so large that the chordwise Reynolds number of the blades is well beyond the design range of existing open-source airfoil families. This paper presents a preliminary family of new airfoils designed specifically for the needs of these next-generation offshore turbines, ranging from 21% thick to 30% thick with operating Reynolds numbers between 12 million and 18 million. These airfoils are intended to be alternative to the FFA airfoils that are commonly used on reference turbines such as the IEA 15MW and 22MW designs. In this work, airfoil performance metrics and design targets are developed, the design process is outlined, an optimization scheme is presented, and finally the airfoils and their simulated performance are compared to existing baselines. Lift to drag ratios in a clean condition were improved by up to 49.3% from the baseline FFA airfoil, and rough condition lift to drag ratio was improved by up to 9.3%. It is estimated that the cumulative improvements provided by this airfoil family would result in an approximately 1% increase of Annual Expected Power (AEP) for the 22 MW turbine compared to the current baseline.

airfoils↗

DOE OSTI2022

Effect of the J-Shaped Wind Turbine Airfoil Opening Ratio and Thickness on the Performance of Symmetrical Airfoils

Abstract In this work, the effect of the inner opening ratio on the J-shaped airfoils aerodynamic performance was studied and documented for symmetrical airfoils. Three different airfoil thicknesses were investigated: small (NACA0008), medium (NACA0015), and large (NACA0024). For each airfoil thickness, effects of three inner opening ratios were analyzed: one-third, one-half, and two-thirds. The performance of each opening ratio was compared with the performance of the solid airfoil “zero opening ratio” for different angles of attack between 5 deg and 20 deg. All designs were simulated using the computational fluid dynamics (CFD) technology against experimental results for solid NACA4412 airfoil in the University of Wisconsin-Milwaukee (UWM) wind tunnel facility and other published experimental data. It was found that large eddy simulation yields accurate solutions with a smaller number of mesh cells compared to the k–ω turbulence model but with much longer computational time. The lift-to-drag ratio for all studied airfoils has a maximum value for solid airfoils compared to those equipped with openings. For airfoils equipped with 00.00% opening ratio “solid,” NACA0015 airfoil has the maximum lift-to-drag ratio. Furthermore, it was found that NACA0008 equipped with a 33.33% opening ratio has the best performance of all studied J-shaped airfoils.

Energy & Fuels↗

DOE OSTI2022

Characterization of lift force and torque in prolate ellipsoid suspensions

The paper derives correlations for lift force and fluid torques acting on stationary prolate ellipsoid suspensions of aspect ratio (AR) 2.5, 5, and 10 subjected to uniform flow. Here, Particle Resolved Simulations (PRS) are conducted on a suspension of infinite extent in two directions for Reynolds number 10≤Re≤200 and solid fractions (φ) between 0.1≤φ≤0.3.The suspension-mean lift-to-drag ratio varies between 7% to 14% at Re=10 which increases to 14%~22% at Re=200. The torque-induced tip rotational acceleration can reach 38%~85% of drag-induced translational acceleration at Re=200. Single particle lift force and torque correlations of (Fröhlich et al., 2020) are modified and adapted to predict current angular-mean lift and torque data. The resulting lift correlation captures the PRS data within an average deviation below 7%. Torque exhibits a somewhat more complex dependency at AR=10 than the assumed sinθ ∙ cosθ variation but nevertheless the correlations predict angular-mean values with mean relative deviations of 16.6% at AR=10.

42 ENGINEERING↗

DOE OSTI2020

Water Energy Resource Innovation on the Cavitation Characteristics

The main purpose of this study is to numerically correlate the amount of generated vapor over a hydrofoil to the lift and drag coefficients acting on it. As such, cavitation characteristics were investigated of a hydrofoil in the cavitating, sub-cavitating, and non-cavitating flows for different angles of attacks (AoA) with the high upstream flow velocity. The hydrofoil was tested in a square water tunnel with water entering the tunnel at various velocities for each AoA ranges from 9.1 m/s to 12.2 m/s. It was found that lift and drag forces acting on the hydrofoil follow the trend of the experimental data quite closely. While the cavitation can be identified by a unique number (averaged vapor volume fraction), the work done created an inverse correlation between this number and the cavitation number at the same angle of attack. The lift force declines with the increase in the vapor content on the hydrofoil surface, meanwhile the drag force peaks at certain vapor volume fraction, and then, a huge reduction occurs with the considerable decrease in the corresponding cavitation number. A fourth-order correlation generated between the lift to drag (L/D) and the cavitation number (σ). It was found the lift-to-drag ratio decreases by the formation of the cavitation over the hydrofoil, thus causing a drop in the efficiency of the turbomachines.

42 ENGINEERING↗

DOE OSTI2022

Local correlation-based transition models for high-Reynolds-number wind-turbine airfoils

Abstract. Modern wind-turbine airfoil design requires robust performance predictions for varying thicknesses, shapes, and appropriate Reynolds numbers. The airfoils of current large offshore wind turbines operate with chord-based Reynolds numbers in the range of 3–15 million. Turbulence transition in the airfoil boundary layer is known to play an important role in the aerodynamics of these airfoils near the design operating point. While the lack of prediction of lift stall through Reynolds-averaged Navier–Stokes (RANS) computational fluid dynamics (CFD) is well known, airfoil design using CFD requires the accurate prediction of the glide ratio (L/D) in the linear portion of the lift polar. The prediction of the drag bucket and the glide ratio is greatly affected by the choice of the transition model in RANS CFD of airfoils. We present the performance of two existing local correlation-based transition models – one-equation model (γ− SA) and two-equation model (γ-Reθt‾- SA) coupled with the Spalart–Allmaras (SA) RANS turbulence model – for offshore wind-turbine airfoils operating at a high Reynolds number. We compare the predictions of the two transition models with available experimental and CFD data in the literature in the Reynolds number range of 3–15 million including the AVATAR project measurements of the DU00-W-212 airfoil. Both transition models predict a larger L/D compared to fully turbulent results at all Reynolds numbers. The two models exhibit similar behavior at Reynolds numbers around 3 million. However, at higher Reynolds numbers, the one-equation model fails to predict the natural transition behavior due to early transition onset. The two-equation transition model predicts the aerodynamic coefficients for airfoils of various thickness at higher Reynolds numbers up to 15 million more accurately compared to the one-equation model. As a result, the two-equation model predictions are more comparable to the predictions from eN transition model. However, a limitation of this model is observed at very high Reynolds numbers of around 12–15 million where the predictions are very sensitive to the inflow turbulent intensity. The combination of the two-equation transition model coupled with the Spalart–Allmaras (SA) RANS turbulence model is a good method for performance prediction of modern wind-turbine airfoils using CFD.

17 WIND ENERGY↗

DOE OSTI2022

Accurate hydrodynamic force and torque correlations for prolate spheroids from Stokes regime to high Reynolds numbers

Detailed simulations of flow around various prolate spheroids are performed using multi-relaxation time lattice Boltzmann method (LBM). The simulations are performed in the Reynolds numbers range 0.1 ≤ Re ≤ 2000 at different incident angles 0°≤ φ ≤ 90° for various prolate spheroids of aspect ratios 1 ≤ λ ≤ 8. The Re is based on the volume equivalent sphere diameter. From the simulations, accurate correlations for average drag, lift and torque coefficients (C D , C L , and C T respectively) are proposed. The mean deviations between the correlations and the simulation data for C D , C L , and C T are 2%, 6.5%, and 4.7% respectively. Furthermore, the correlations are fitted with the physics in mind such that they can be extrapolated beyond the regimes simulated. The fits are designed such that correlations reduce to analytical (C D and C L ) solutions available for prolate spheroids in the limit Re ≈ 0. At high Re, the correlations mimic the asymptotic flattening of C D as for spheres and therefore, we expect the correlations to be valid until the critical Re (≈ 10 5 ). Furthermore, extensive comparison of our correlations with other high-fidelity simulations from literature demonstrate the accuracy of our work compared to other correlations from literature. This work enables researchers to perform accurate unresolved Euler-Lagrangian simulations for a wide range of elongated particles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

The nonlinear behavior of generic tail fins for small wind turbines

This paper describes analysis and measurements of the yaw response of tail fins for small wind turbines. It is based on an extension of unsteady slender body theory (USBT) to cover non-slender fins and high angles of incidence, both of which make the theory nonlinear. We provide three main additions to the substantial literature on linearized USBT for tail fins. First, USBT is extended to high angles by modeling the nonlinear vortex dynamics. Second, the restriction to slender bodies is removed by modeling the chordwise load variation. Third, we consider the effect of time-varying wind speed. Further, the extended theory is compared to wind tunnel measurements of the yaw behavior of delta, elliptical, and rectangular tail fins without a rotor and nacelle. The fins were released from initial yaw angles of -40° and -80°; the latter is of sufficient magnitude to show the importance of the nonlinear yaw dynamics. Generally good agreement was found between the theory and measurements, and the theory was shown to be more accurate than a “polar” or quasi-steady model which uses only the lift and drag of a delta planform. Of the three planforms, the rectangular one showed the lowest accuracy in terms of frequency but the damping was accurately predicted. Overall, the results demonstrate the importance of nonlinearity in the response of a yawing tail fin, particularly for the higher aspect ratio fins at large yaw angles.

17 WIND ENERGY↗

DOE OSTI2020

Performance and Wake Characterization of a Model Hydrokinetic Turbine: The Reference Model 1 (RM1) Dual Rotor Tidal Energy Converter

The mechanical power and wake flow field of a 1:40 scale model of the US Department of Energy’s Reference Model 1 (RM1) dual rotor tidal energy converter are characterized in an open-channel flume to evaluate power performance and wake flow recovery. The NACA-63(4)-24 hydrofoil profile in the original RM1 design is replaced with a NACA-4415 profile to minimize the Reynolds dependency of lift and drag characteristics at the test chord Reynolds number. Precise blade angular position and torque measurements were synchronized with three acoustic Doppler velocimeters (ADV) aligned with each rotor centerline and the midpoint between the rotor axes. Flow conditions for each case were controlled to maintain a hub height velocity, uhub= 1.04 ms−1, a flow Reynolds number, ReD= 4.4 × 105, and a blade chord length Reynolds number, Rec= 3.1 × 105. Performance was measured for a range of tip-speed ratios by varying rotor angular velocity. Peak power coefficients, CP= 0.48 (right rotor) and CP= 0.43 (left rotor), were observed at a tip speed ratio, λ= 5.1. Vertical velocity profiles collected in the wake of each rotor between 1 and 10 rotor diameters are used to estimate the turbulent flow recovery in the wake, as well as the interaction of the counter-rotating rotor wakes. The observed performance characteristics of the dual rotor configuration in the present study are found to be similar to those for single rotor investigations in other studies. Similarities between dual and single rotor far-wake characteristics are also observed.

30 DIRECT ENERGY CONVERSION↗