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DOE OSTI2022

Shock interacting with a random array of stationary particles underwater

Accurately predicting the force experienced by particles within a random bed during shock traversal is a challenging problem. In this paper, particle-resolved inviscid simulations of shock propagation over randomly distributed beds are performed, with the goal of quantifying the force on individual particles. Water was considered the continuum material, and then results were compared with previous research completed in air and the differences resulting from these different mediums were examined. Simulations were conducted for four different combinations of incident Mach number and bed volume fraction with the particles remaining stationary. Additionally, time-resolved streamwise and transverse force coefficients were calculated for each particle in the bed. It was observed that while the average force coefficient was similar to that of an isolated particle, the force on individual particles was substantially different. An important observation was that the inviscid drag force on some particles remained consistently positive, but others consistently negative even long after the passage of the shock. This persistent force on the particle was attributed to the potential flow fields that result from neighbors' specific locations upstream and downstream. Similar behavior was observed in the transverse force, with particles experiencing sustained force in the same lateral direction. These persistent forces are inviscid quasisteady contributions which with the viscous counterpart will play an essential role in the particle's long-term dispersion if allowed to move in response to the force.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Thermomagnetic responses of semimetals

Solid-state thermomagnetic modules operating based on the Nernst–Ettingshausen effects are an alternative to conventional solid-state thermoelectric modules. These modules are appropriate for low-temperature applications where the thermoelectric modules are not efficient. Here, we briefly discuss the application, performance, similarities, and differences of thermoelectric and thermomagnetic materials and modules. We review thermomagnetic module design, Nernst coefficient measurement techniques, and theoretical advances, emphasizing the Nernst effect and factors influencing its response in semimetals such as carrier compensation, Fermi surface, mobility, phonon drag, and Berry curvature. The main objective is to summarize the materials design criteria to achieve high thermomagnetic performance to accelerate thermomagnetic materials discovery.

42 ENGINEERING↗

DOE OSTI2026

Evaluating the Transport Mechanism for Lignocellulosic Inhibitors in Zymomonas mobilis

The conversion of lignocellulosic biomass to biofuels and bioproducts is limited by small inhibitory molecules generated during the pretreatment process. The diverse compounds within the cell wall hydrolysate including aldehydes, carboxylic acids, phenolics, and alcohols inhibit microbial growth by disrupting microbial membranes. Although Zymomonas mobilis combines high ethanol productivity with hopanoid-rich membranes that confer solvent tolerance, hydrolysate compounds still inhibit microbial growth. One proposed mitigation strategy is to pump these molecules out through active transport processes, reducing direct toxicity. However, if passive permeation rates are high, active transport would create a futile cycle where the exported molecules diffuse back in, creating a net drag on fitness. To investigate this hypothesis, we measure the passive permeation for thirty-three lignocellulose derived compounds using atomistic molecular dynamics simulations with enhanced sampling. Permeability coefficients determined spanned more than eight orders of magnitude driven largely by the balance between hydrophobicity and polarity. Hydrophobic inhibitors such as aromatic acids, aldehydes, and short chain alcohols readily partitioned into the membrane and showed high permeability consistent with rapid passive influx and strong toxicity. Most polar molecules have lower but still appreciable permeation rates, with only the most polar sugars having low permeabilities. By integrating these predictions together with hydrolysate composition information, we find that most of these molecules are so permeable that futile cycles where passive permeation overwhelms efflux is highly likely. These findings provide a predictive framework for strain engineering, highlighting that, for highly permeable inhibitors, reducing extracellular inhibitor concentrations through hydrolysate detoxification, pretreatment optimization, or dilution may be necessary to mitigate futile cycling and improve microbial productivity in industrial biorefineries.

Zymomonas mobilis↗

DOE OSTI2022

Extremely Slow Diffusion of Gold Nanoparticles under Confinement in Mesoporous Silica

Here, we report an X-ray photon correlation spectroscopy (XPCS) study of the mobility of colloidal gold nanoparticles with a diameter of approximately 4 nm in glycerol under confinement within the channels of SBA-15 mesoporous silica with pore diameters of approximately 6 and 12 nm. The XPCS correlation functions result from an effective heterodyne signal due to the mixing of the coherent scattering from the nanoparticles and the mesoporous silica. Over the range of wave vectors and hence length scales probed, the nanoparticle dynamics are well described by one-dimensional diffusion. The nanoparticle diffusivity varies with temperature in a manner expected based on the temperature-dependent viscosity of glycerol; however, the magnitudes of the diffusion coefficients are several orders of magnitude smaller than those of the nanoparticles in bulk glycerol. We consider mechanisms that might contribute to this reduction in diffusivity including enhancement in hydrodynamic drag under confinement, effects of nanoparticle adsorption to the pore walls, and slowing structural dynamics in glycerol due to the combination of the nanometer-scale confinement and the presence of the nanoparticles.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Random Walks and Sticky Surfaces: Single-Molecule Measurements of Solute Diffusion in Ethanol/Water-Filled Anodic Alumina Nanopores

Nanoporous anodic aluminum oxide (AAO) membranes are now being explored for use in advanced chemical separations, including in the dehydration of biofuels such as ethanol. Optimization of membrane performance requires an in-depth understanding of how solvent mixtures and solutes behave under nanoconfinement. In this work, the diffusion of rhodamine B (RhB) dye through 10 nm and 20 nm AAO nanopores filled with a series of ethanol/water mixtures (0 - 33% water) is explored by fluorescence correlation spectroscopy (FCS). RhB was found to diffuse through the pores by two distinct mechanisms with mean diffusion coefficients, $D_f$ and $D_s$, reflecting fast and slow diffusive motions, respectively, with values that differ by nearly two orders of magnitude. Further, both $D_f$ and $D_s$ increased with pore size and were significantly smaller than $D_b$, the RhB diffusion coefficient in bulk liquid. Mean $D_f$ values follow a composition-dependent trend that closely mimics the viscosity dependence of $D_b$. Additional slowing of fast RhB diffusion is attributed to both hydrodynamic drag and electrostatic interactions with the nanopore surface. The mean $D_s$ values exhibit a different trend with increasing water content, revealing an increase in $D_s$ and a decrease in the contributions of slow diffusion to the observed dynamics. The fluorescence time transient data used in the analysis show that the slow diffusion process is strongly hindered and likely involves frequent adsorption of RhB to the pore surfaces. These results provide new insights into the detailed molecular-level mechanisms of mass transport in nanoporous AAO membranes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Emergent viscous hydrodynamics from a single quantum particle

We investigate an explicit example of how spatial decoherence can lead to hydrodynamic behavior in the late-time, long-wavelength regime of open quantum systems. We focus on the case of a single nonrelativistic quantum particle linearly coupled to a thermal bath of noninteracting harmonic oscillators at temperature T , a la Caldeira and Leggett. Taking advantage of decoherence in the position representation, we expand the reduced density matrix in powers of the off-diagonal spatial components, so that high-order terms are suppressed at late times. Truncating the resulting power series at second order leads to a set of dissipative transient hydrodynamic equations similar to the nonrelativistic limit of equations widely used in simulations of the quark-gluon plasma formed in ultrarelativistic heavy-ion collisions. Transport coefficients are directly determined by the damping constant γ , which quantifies the influence of the environment. The asymptotic limit of our hydrodynamic equations reduces to the celebrated Navier-Stokes equations for a compressible fluid in the presence of a drag force. Furthermore, our results shed new light on the onset of hydrodynamic behavior in open quantum systems where a system with few degrees of freedom is coupled to a large thermal environment.

Hydrodynamics↗

DOE OSTI2022

Correction to: Investigating the rheology of fluidized and non-fluidized gas-particle beds: implications for the dynamics of geophysical flows and substrate entrainment

We report natural geophysical mass flows are among the most complex granular systems and their dynamics are often modified by the presence of an interstitial fluid. Prediction of their runout requires the development of models estimating the solid stresses in these hazardous currents wherein excess pore-fluid pressure can develop. We use discrete element modelling (DEM-CFD) with a Coarse-Graining post-processing technique (CG) to investigate the rheology of unsteady gas-particle fluidized to non-fluidized granular beds placed on horizontal and inclined planes. Similar to fluidized beds immersed in viscous fluids, the effective friction coefficient of air-fluidized beds can be defined as a function of the classic μ(I)-rheology and the non-dimensional fluid or solid pressure to explain the failure and dynamics of granular flows with excess pore pressure on inclines. However, dilation imposed by fluid drag and particle collisions in gas-particle fluidized beds can drastically change its effective frictional properties. In contrast with the common assumption in water-particle flows that granular temperature is negligible, in our gas-particle simulations, the contribution of the velocity fluctuations to the stress tensor is significant. Hence, the shear stress is found to be non-zero even when the flow is fully fluidized in the inertial regime. These results suggest the need to better understand velocity fluctuations to predict the effective viscosity of sheared fluidized mixtures and are relevant for many applications. Notably, a unified approach is useful for many geophysical flows that encompass a range of fluidization conditions in a single flow such as pyroclastic density currents and snow avalanches.

58 GEOSCIENCES↗

DOE OSTI2022

Improvement of two-phase closure models in CTF using Bayesian inference

Under the Consortium for Advanced Simulation of Light Water Reactors (CASL) program, extensive capabilities have been developed in CTF to analyze light-water reactors (LWRs) for normal operating conditions, departure from nucleate boiling (DNB), and system transients. However, further improvements are required in the modeling and simulation of boiling water reactors (BWRs), which is a focus of the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. In this work, CTF validation results were used to optimize selected modeling coefficients by calibrating to experimental data using a Bayesian inference approach. Here, calibration studies were conducted to improve (vapor) void fraction prediction without worsening the two-phase pressure drop prediction, as well as to improve the two-phase pressure drop prediction. Calibration was performed for interfacial drag and wall shear models. Surrogates were developed to alleviate the computational expense required for sampling the parameter space using Markov chain Monte Carlo (MCMC). An assessment performed with calibrated models demonstrated an improvement of CTF in its prediction of key parameters such as void fraction and two-phase pressure drop.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Influence of Heave Plate Topology on Reaction Force

In this study, we explore the role of heave plate topology on fluid reaction forces using three, representative shapes: a hexagonal flat plate, a hexagonal conic with an open top, and the same with a closed top that encloses a fluid mass. We force each test article sinusoidally in a quiescent tank and decompose the reaction force using forms of the Morison equation for phase-invariant and phase-dependent parameterizations. We find that a flat plate generates 5.3 % more fluid reaction force than the open conic topology, and 21.4% more than the enclosed conic. Asymmetric topologies generate asymmetric reaction forces, but the magnitude of asymmetry is limited by nearly symmetric fluid inertia forces, which dominate over drag for these test articles. Additionally, we observe asymmetric vortex dynamics for the flat plate when the Keulegan-Carpenter number is between 1 and 2, accompanied by a shift in the phase of the peak force by of the oscillation period. As a consequence of this shift, the hydrodynamic coefficients estimated from the phase-dependent Morison equation decomposition are asymmetric, suggesting that phase-dependent representations may not provide physical insight in some hydrodynamic regimes.

added mass↗

DOE OSTI2023

Aerodynamic Rotor Design for a 25 MW Offshore Downwind Turbine

Continuously increasing offshore wind turbine scales require rotor designs that maximize power and performance. Downwind rotors offer advantages in lower mass due to reduced potential for tower strike, and is especially true at large scales, e.g., for a 25 MW turbine. In this study, three 25 MW downwind rotors, each with different prescribed lift coefficient distributions were designed (chord, geometry, and twist) and compared to maximize power production at unprecedented scales and Reynolds numbers, including a new approach to optimize rotor tilt and coning based on aeroelastic effects. To achieve this objective the design process was focused on achieving high power coefficients, while maximizing swept area and minimizing blade mass. Maximizing swept area was achieved by prescribing pre-cone and shaft tilt angles to ensure the aeroelastic orientation when the blades point upwards was nearly vertical at nearly rated conditions. Maximizing the power coefficient was achieved by prescribing axial induction factor and lift coefficient distributions which were then used as inputs for an inverse rotor design tool. The resulting rotors were then simulated to compare performance and subsequently optimized for minimum rotor mass. To achieve these goals, a high Reynolds number design space was developed using computational predictions as well as new empirical correlations for flatback airfoil drag and maximum lift. Within this design space, three rotors of small, medium and large chords were considered for clean airfoil conditions (effects of premature transition were also considered but did not significantly modify the design space). The results indicated that the medium chord design provided the best performance, producing the highest power in Region 2 from simulations while resulting in the lowest rotor mass, both of which support minimum LCOE. The methodology developed herein can be used for the design of other extreme-scale (upwind and downwind) turbines.

downwind rotors↗

DOE OSTI2026

A buoyancy–shear–drag–scalar-based turbulence model for power-law acceleration-driven Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing

A previously developed phenomenological turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing based on a general buoyancy–shear–drag model [O. Schilling, “A buoyancy–shear–drag-based turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing,” Physica D 402, 132238 (2020)] is extended to include active or passive scalar mixing and power-law acceleration-driven Rayleigh–Taylor mixing. The buoyancy–shear–drag equations are coupled to a scalar variance equation that is used to define the molecular mixing parameter θ m , and when the scalar is active, modifies the Rayleigh–Taylor and Kelvin–Helmholtz mixing layer growth parameters to depend on the asymptotic value of this parameter, θ mol . Here, the scalar variance equation is closed by algebraically or differentially modeling the scalar variance dissipation rate. Nonlinear analytical solutions of the model are obtained in the total and separate bubble and spike mixing layer width formulations with the algebraic scalar variance dissipation rate for each instability, which are then used to calibrate the mechanical and scalar equation coefficients to predict specific values of physical observables and molecular mixing parameters. Surrogate mechanical and scalar turbulent fields can be constructed by multiplying a presumed self-similar spatial profile by appropriate functions of the width and its time derivative, and of the scalar obtained by solving the ordinary differential model equations. The explicit modeling and solution of turbulent transport equations are not required. The bubble and spike mixing layer width and scalar variance equations are then solved numerically for constant-acceleration Rayleigh–Taylor, impulsively reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing, confirming that the prescribed level of molecular mixing is correctly predicted and illustrating the spatiotemporal evolution of the scalar fields.

Buoyancy–drag↗

DOE OSTI2022

OC6 phase I: Improvements to the OpenFAST predictions of nonlinear, low-frequency responses of a floating offshore wind turbine platform

We report in the OC5 and OC6 projects, the authors observed a persistent underprediction of the nonlinear, low-frequency responses of an offshore wind semisubmersible with many mid-fidelity engineering models, including the OpenFAST tool developed by the National Renewable Energy Laboratory. Both the low-frequency wave excitation in surge and pitch and the resulting resonance motions were severely underpredicted. In response, we developed several modifications to the OpenFAST model from the OC5/6 projects to improve the predictions of the low-frequency wave loads and responses. All modifications are in the modeling of the viscous drag forces. Efforts were made to provide physical justifications to the changes and to limit the number of additional parameters requiring tuning, so that the modified model can be applied to other floating wind systems. With the proposed modifications, the predictions of the low-frequency surge and pitch wave loads on a fixed floater and the resonance responses of a floating structure are both significantly improved with a single set of model coefficients, which leads to good agreement with the measurements from the OC6 wave-basin experimental campaign.

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↗

DOE OSTI2020

Improvements to CTF Closure Models for Modelling of Two-Phase Flow

This report documents the efforts to improve the CTF prediction of void fraction and two-phase pressure drop by improving two-phase closure models. Previous validation activities have revealed that CTF tends to overpredict void fraction and two-phase pressure drop. In response to this, two approaches were taken to improve CTF’s predictive capabilities. Based on findings that the interfacial drag and subcooled boiling models significantly impact void prediction, alternative closure models for these physical effects were found and implemented into the code. An extensive assessment was performed by using the existing and newly added two-phase experimental data, which showed that void prediction, wall temperature, and two-phase pressure-drop results are improved by using the newly implemented models. A second approach for improving CTF modeling accuracy involved the use of a Bayesian calibration process that uses CTF validation data to optimize selected modeling coefficients and closure model multipliers to achieve a more accurate prediction of experimental results. A similar assessment was performed with calibrated models that improved the void and pressure-drop prediction for test cases that were both included and not included in the calibration dataset. Results of this study will be used to change the models used in CTF to achieve more accurate BWR analyses moving forward. This study also identified opportunities for improving additional closure models and other opportunities to use calibration techniques to improve CTF.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Improving the modeling of near-wall interphase heat transfer in porous media models of Pebble Bed Reactors

Here, this work aims to improve capabilities for modeling localized effects in porous media models of Pebble Bed Reactors. The wall-channeling effect is the primary local phenomenon of interest in a PBR, where the presence of the reflector wall disrupts the pebble packing, causing the pebbles near the wall to pack less efficiently and creating large void regions. Accurate modeling of the near-wall region is important as it will affect core bypass flow and temperature predictions. Porous media models are commonly used for design scoping and plant-level simulations of PBRs. Although these models have some capabilities to model the near-wall region, the correlations that are available in porous media codes are often inaccurate when a multi-region model is used to discretize the near-wall region. This work employs a high-to-low analysis to study the accuracy of available interphase heat transfer closures. NekRS, a spectral element computational fluid dynamics code, is used to perform Large Eddy Simulations. These LES simulation results are compared to porous media model results from the Pronghorn porous media code. The friction term of the KTA drag closure is first improved, reducing the error in the prediction of the near-wall velocity from over 50% to less than 5%. This is combined with improvements to the form term from previous works to produce a drag closure that is capable of accurately modeling the wall-channeling effect across a variety of flow conditions. The Nusselt number predictions of several heat transfer correlations are compared to the high-fidelity results where it is found that the KTA heat transfer correlation is capable of accurately predicting the local Nusselt numbers that were determined in the high-fidelity simulation. Comparison of the radial solid temperature profiles, however, reveal discrepancies between NekRS and Pronghorn. It is discovered that the implementation of the interphase heat transfer coefficient that exists in many current porous media codes is not valid when local porosities are modeled. Instead, it is suggested that the interphase heat transfer coefficient should be dependent on the local porosity, the Nusselt number, and the local solid surface-to-volume ratio. Implementation of this change produces improvement in the agreement between the results obtained by NekRS and Pronghorn while using the KTA heat transfer correlation.

interphase heat transfer↗

DOE OSTI2022

Role of Three-Dimensional Swirl in Forced Convection Heat Transfer Enhancement in Wavy-Plate-Fin Channels

The influence of wall-corrugation-induced swirl flow on enhanced forced convection in wavy-plate-fin cores has been investigated. Three-dimensional computational simulations were carried out for steady-state periodically developed air flow (Pr ~ 0.71; 50 ≤ Re ≤ 4000) with channel walls subject to constant-uniform temperature conditions. The recirculation that develops in the wall troughs and grows to have an axially helical character is scaled by the Swirl number Sw. As Sw increases with higher flowrate and/or corrugation severity, tornado-shaped vortices appear in the wave trough region midway of the interfin channel height, then extend longitudinally to encompass majority of the flow channel. The local wall-shear and heat transfer coefficient variations indicate that boundary-layer thinning upstream of the wave peak aids in intensifying momentum and heat transfer. However, the flow recirculation in wall trough impedes heat transfer at low Sw due to flow stagnation but promotes it at high Sw because of the vortices-induced augmented fluid mixing. The effects of this secondary flow are quantified by Φf(or j), which is seen to increase log-linearly as fin corrugation aspect ratio γ and/or fin spacing ratio ζ increases; the influence of cross section aspect ratio α is marginal. Moreover, the pressure drag penalty due to swirl critically affects overall pressure loss, and its proportion remains nearly constant when α varies, but grows as Sw, γ, and/or ζ increases and can be as much as 80% of the total pressure drop.

Engineering↗

DOE OSTI2021

Local wave-number model for inhomogeneous two-fluid mixing

We analyze the local wave-number (LWN) model, a two-point spectral closure model for turbulence, as applied to the Rayleigh-Taylor (RT) instability, the flow induced by the relaxation of a statically-unstable density stratification. Model outcomes are validated against data from 3D simulations of the RT instability. In the first part of the study we consider the minimal model terms required to capture inhomogeneous mixing and show that this version, with suitable model coefficients, is sufficient to capture the evolution of important mean global quantities including mix-width, turbulent mass flux velocity, and Reynolds stress, if the start time is chosen such that the earliest transitions are avoided. However, this simple model does not permit the expected finite asymptote of the density-specific-volume covariance b. In the second part of the study, we investigate two forms for a source term for the evolution of the spectrum of density-specific-volume covariance for the LWN model. The first includes an empirically motivated calibration of the source to achieve the final asymptotic state of constant b. Here, the second form does not require calibration but, in conjunction with enhanced diffusion and drag captures the full evolution of all the dynamical quantities, namely, the mix-layer growth, turbulent mass-flux velocity, Reynolds stress, as well as the desired behavior of b.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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↗