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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Multifidelity Approach to Sensitivity Estimation in Large-Eddy Simulation

A novel approach to compute affordable approximate sensitivities in a large-eddy simulation (LES) is proposed and assessed. The approach is based on solving a Reynolds-averaged Navier–Stokes (RANS) problem that has been linearized around the mean LES solution, with closure modeling required for the linearized changes in turbulent Reynolds stresses. In the present study, the closure modeling is based on a linearized algebraic turbulence model. The method is assessed for the flow over a NACA0012 airfoil at a fixed angle of attack, with the Reynolds number as the variable parameter. The results show that, provided an accurate linearized closure model, the method predicts the correct sensitivity of the skin friction coefficient and the mean velocity field at the cost of a linearized RANS, which provides an important proof-of-concept for this approach. Here, the linearized algebraic turbulence model with standard model coefficients produces a reasonably accurate sensitivity, but the results also suggest that accuracy could be gained from recalibrating the model coefficients for this new use of the model.

42 ENGINEERING↗
DOE OSTI2023

Deep learning closure models for large-eddy simulation of flows around bluff bodies

Near-wall flow simulation remains a central challenge in aerodynamics modelling: Reynolds-averaged Navier–Stokes predictions of separated flows are often inaccurate, and large-eddy simulation (LES) can require prohibitively small near-wall mesh sizes. A deep learning (DL) closure model for LES is developed by introducing untrained neural networks into the governing equations and training in situ for incompressible flows around rectangular prisms at moderate Reynolds numbers. The DL-LES models are trained using adjoint partial differential equation (PDE) optimization methods to match, as closely as possible, direct numerical simulation (DNS) data. They are then evaluated out-of-sample – for aspect ratios, Reynolds numbers and bluff-body geometries not included in the training data – and compared with standard LES models. The DL-LES models outperform these models and are able to achieve accurate LES predictions on a relatively coarse mesh (downsampled from the DNS mesh by factors of four or eight in each Cartesian direction). We study the accuracy of the DL-LES model for predicting the drag coefficient, near-wall and far-field mean flow, and resolved Reynolds stress. A crucial challenge is that the LES quantities of interest are the steady-state flow statistics; for example, a time-averaged velocity component $\langle {u}_i\rangle (x) = \lim _{t \rightarrow \infty } ({1}/{t}) \int _0^t u_i(s,x)\, {\rm d}s$ . Calculating the steady-state flow statistics therefore requires simulating the DL-LES equations over a large number of flow times through the domain. It is a non-trivial question whether an unsteady PDE model with a functional form defined by a deep neural network can remain stable and accurate on $t \in [0, \infty )$ , especially when trained over comparatively short time intervals. Our results demonstrate that the DL-LES models are accurate and stable over long time horizons, which enables the estimation of the steady-state mean velocity, fluctuations and drag coefficient of turbulent flows around bluff bodies relevant to aerodynamics applications.

Mechanics↗
DOE OSTI2023

Detailed Simulations of a Three-Stage Supercritical Carbon Dioxide Axial Compressor with a Focus on the Shrouded Stator Cavities Flow

This paper describes the findings of detailed simulations performed to investigate the impact of seal teeth cavity leakage flow on the aerodynamic and thermal performance of a three-stage supercritical CO 2 axial compressor. The study compares a shrouded stator configuration (with cavities) to a cantilevered stator configuration (without cavities) to highlight their differences. High-fidelity computational fluid dynamics simulations were performed using non-linear harmonic (NLH) and mixing plane assumptions, considering various possible rotor/stator interface configurations for mixing plane calculations. The key performance parameters for each case were compared, and the best-performing configuration selected for further analysis. The individual stage performance parameters are also examined and compared between the cantilevered and shrouded configurations. It was observed that in the shrouded case, the leakage flow enters the cavity downstream of the stator trailing edge and gets entrained into the primary flow upstream of the stator, leading to boundary layer changes at the hub and degradation of stator and downstream rotor performance. Vortical flow structures were also observed in the stator wells, which tended to change the flow angles around the region, thereby affecting mixing and velocity distribution, resulting in a slight deterioration of compressor performance. Additionally, the study examines windage heating due to shear work from rotating walls, including the seal teeth surface. The amount of shear work done on the leakage flow and the corresponding rise in fluid temperature were quantified, tabulated, and further compared with a simple analytical model, showing good agreement between them and, hence, validating the numerical approach used.

42 ENGINEERING↗
DOE OSTI2024

Three-Dimensional Aerodynamics and Vortex-Shedding Characteristics of Wind Turbine Airfoils over 360-Degree Angles of Attack

In this work, we present the first three-dimensional (3D) computational investigation of wind turbine airfoils over 360° angles of attack to predict unsteady aerodynamic loads and vortex-shedding characteristics. To this end, static–airfoil simulations are performed for the FFA-W3 airfoil family at a Reynolds number of 107 with the Improved Delayed Detached Eddy Simulation turbulence model. Aerodynamic forces reveal that the onset of boundary-layer instabilities and flow separation does not necessarily coincide with the onset of stall. In addition, a comparison with two-dimensional simulation data and flat plate theory extension of airfoil polars, suggest that, in the deep stall regime, 3D effects remain critical for predicting both the unsteady loads and the vortex-shedding dynamics. For all airfoils, the vortex-shedding frequencies are found to be inversely proportional to the wake width. In the case of slender airfoils, the frequencies are nearly independent of the airfoil thickness, and their corresponding Strouhal number St is approximately 0.15. Based on the calculated St, the potential for shedding frequencies to coincide with the natural frequencies of the International Energy Agency 15 MW reference wind turbine blades is investigated. The analysis shows that vortex-induced vibrations occur primarily at angles of attack of around ±90° for all airfoils.

17 WIND ENERGY↗
DOE OSTI2025

An airfoil-based synthetic actuator disk model for wind turbine aerodynamic and structural analysis

Here, this study introduces an airfoil-based refinement technique to enhance the Actuator Disk Model (ADM) for improved wind turbine aerodynamic load prediction and structural simulation in conjunction with Large Eddy Simulations of the wind flow. While ADM offers higher computational efficiency than the more detailed but resource-intensive Actuator Line Model (ALM), it traditionally lacks the resolution needed to capture the localized blade forces accurately. To address this limitation, we introduce a refinement technique that uses airfoil-specific data and employs interpolation-based grid point refinement, achieving ALM-comparable accuracy while preserving ADM's efficiency. Unlike conventional ADM that provides only rotor-disk averaged forces, our synthetic method tracks transient aerodynamic load variations over multiple blade revolutions, allowing us to calculate the distributions of maximum and minimum loads during typical cycles. Applied to the NREL 5 MW reference turbine, our enhanced ADM accurately predicts key aerodynamic parameters (angle of attack, axial velocity, lift, drag, axial and tangential forces along the blades) as well as structural responses (blade tip deflection, maximum stress, and stress concentration). Our results show that the tip deflection ranges from 2.33m (3.69 % of blade length) to 4.28m (6.79 %), with maximum stress concentration occurring near the blade root. This research demonstrates that a refined synthetic ADM approach can serve as a computationally efficient alternative for both aerodynamic analysis and structural simulation of wind turbine blades subjected to realistic wind fields.

17 WIND ENERGY↗
DOE OSTI2023

Expanded verification and validation studies of hypersonic aerodynamics with multiple physics-fidelity models

Hypersonic aerothermodynamics is an important domain of modern multiphysics simulation. The Multi-Fidelity Toolkit is a simulation tool being developed at Sandia National Laboratories to predict aerodynamic properties for compressible flows from a range of physics fidelities and computational speeds. These models include the Reynolds-averaged Navier–Stokes (RANS) equations, the Euler equations with momentum-energy integral technique (MEIT), and modified Newtonian aerodynamics with flat-plate boundary layer (MNA+FPBL) equations, and they can be invoked independently or coupled with hierarchical Kriging to interpolate between high-fidelity simulations using lower-fidelity data. However, as with any new simulation capability, verification and validation are necessary to gather credibility evidence. This work describes formal code- and solution-verification activities, as well as model validation with uncertainty considerations. Code verification activities on the MNA+FPBL model build on previous work by focusing on the viscous portion of the model. Viscous quantities of interest are compared against those from an analytical solution for flat-plate, inclined-plate, and cone geometries. The code verification methodology for the MEIT model is also presented. Test setup and results of code verification tests on the laminar and turbulent models within MEIT are shown. Solution-verification activities include grid-refinement studies on simulations that model the HIFiRE-1 wind tunnel experiments. These experiments are used for validation of all model fidelities. A thorough validation comparison with prediction error and uncertainty is also presented. Three additional HIFiRE-1 experimental runs are simulated in this study, and the solution verification and validation work examines the effects of the associated parameter changes on model performance. Finally, a study is presented that compares the computational costs and fidelities from each of the different models.

42 ENGINEERING↗
DOE OSTI2023

Coupling turbulent flow with blade aeroelastics and control modules in large-eddy simulation of utility-scale wind turbines

We present a large-eddy simulation framework capable of control co-design of large wind turbines, coupling the turbulent flow environment with blade aeroelastics and turbine controllers. The geometry and aerodynamics of the rotor blades and the turbine nacelle are parameterized using an actuator surface model. The baseline collective pitch control and individual pitch control (IPC) algorithms, consisting of a single-input, single-output proportional–integral controller and two integral controllers, respectively, are incorporated into the simulation framework. Furthermore, a second-order model based on the Euler–Bernoulli beam theory is implemented to describe the blade deformation. Simulations are carried out to investigate the impact of collective and individual pitch control strategies on the deflection of turbine blades. Our results show that the IPC reduces the blade tip deflection fluctuations in the out-of-plane direction, while the fluctuations of the blade tip deflection along the in-plane direction are barely affected by the IPC. Furthermore, the blade out-of-plane deformation fluctuation is underestimated by the one-way coupling approach compared to the two-way coupling approach. Furthermore, the findings of this study reveal the importance of advanced control systems in reducing the dynamic loads on wind turbine blades and underscore the potential of control co-design to reduce the levelized cost of wind energy.

42 ENGINEERING↗
DOE OSTI2025

Effect of artificial viscosity on shocked particle-laden flows for staggered grid Lagrangian methods

Abstract Shocked particle-laden flows are important to many natural and industrial processes. When simulating these systems, artificial viscosity is often required to prevent numerical artifacts, such as ringing, from arising in the pressure and density fields. The linear and quadratic coefficients of the artificial viscosity determine the amount of smoothing that occurs in these fields. For particle-laden flows, however, many of the fluid–particle interaction forces, for example, the pressure gradient force and unsteady forces, depend on gradients in the fluid fields. Furthermore, while the shock passes over a particle, these forces can be more dominant than drag. This means that the artificial viscosity coefficients affect how a particle and fluid interact when simulating shocked particle systems. Here this effect is investigated for isolated particles and for a particle curtain using a staggered grid Lagrangian approach. The artificial viscosity coefficients have a significant impact on the maximum force that a fluid imparts to a particle, which is important for determining whether a particle will break up in response to the shock. Furthermore, it is found that the density ratio between the particle and the fluid is important in determining whether the artificial viscosity coefficients have a significant impact on the particle’s motion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Aerodynamic Characterization of 3D Scanned Wind Turbine Blades Using Experimental and Computational Methods

This study presents an aerodynamic characterization of 3D scanned wind turbine blades using both experimental and computational methods. The research was conducted by Gulf Wind Technology and Sandia National Laboratories. The primary objective was to investigate the aerodynamic impacts of leading-edge manufacturing defects on wind turbine blades. The study utilized the Stratasys NEO 800 3D Printer for high-precision manufacturing and the GWT Accelerator Wind Tunnel for experimental testing. Computational simulations were performed using COMSOL Multiphysics to model the wind tunnel and analyze flow characteristics and OpenFOAM to study the aerodynamic impacts of leading-edge defects. OpenFAST was used to estimate how these defects can lead to revenue losses for wind farm operators as high as 6%. The results demonstrated significant aerodynamic performance variations due to defects, with detailed analysis provided through wind tunnel and CFD data. The findings contribute to the understanding of defect impacts on wind turbine blade performance and offer insights for future design improvements.

17 WIND ENERGY↗
DOE OSTI2024

Aerodynamic and production comparison of wind farms with downwind versus conventional upwind turbines

Ever-increasing turbine scales and their associated logistical challenges have reignited questions about the performance of downwind rotor configurations. A particular potential benefit of downwind rotor configurations is the farm-scale power increase that may be conferred by tilt-driven downward wake entrainment and associated wake recovery. In this work, a comprehensive aerodynamic analysis is carried out to understand the mechanisms for wake entrainment and recovery across a spectrum of velocity and inflow alignment conditions on a small, structured farm in order to understand the impact of downwind rotors on farm production. The results show that the benefits demonstrated previously in the literature for downwind-rotor farms in aligned flows are fragile, and, outside of strong farm/flow alignment conditions, power production benefits for small farms with downwind rotor configurations are significantly if not completely mitigated by misalignment effects. The work indicates that farm-scale benefits for downwind rotors must be realized either from large-scale entrainment benefits, with more exotic farm arrangements that can take advantage of the aerodynamic effects, or from beneficial fatigue impacts from entrainment of less turbulent outer boundary layer flows.

17 WIND ENERGY↗
DOE OSTI2023

Turbulent entrainment in finite-length wind farms

In this article, we present an entrainment-based model for predicting the flow and power output of finite-length wind farms. The model is an extension of the three-layer approach of Luzzatto-Fegiz & Caulfield ( Phys. Rev. Fluids , vol. 3, 2018, 093802) for wind farms of infinite length, and assumes dependence of key flow quantities, such as the wind farm bulk velocity, on the streamwise distance from the farm entrance. To assist our analysis and validate the proposed model, we undertake a series of large-eddy simulations with different turbine spacing arrangements and layouts. Comparisons are also made with the top-down model with entrance effects of Meneveau ( J. Turbul. , vol. 13, 2012, N7) and data from the literature. The finite-length entrainment model is shown to be capable of capturing the power drop between contiguous rows of turbines as well as describing the advection and turbulent transport of kinetic energy in both the entrance and fully developed regions. The fully developed regime is approximated only deep in the wind farm, after approximately 15 rows of turbines. Our data suggest that for the cases considered in this study, the empirical coefficients that can be used to describe turbulent entrainment and transfers above the wind farm exhibit little dependence on the farm layout and may be considered constant for modelling purposes. However, the flow field within the wind farm layer can be strongly modulated by the turbine density (spacing) as well as the array layout, and to that extent it can be argued that they are both primary factors determining the wind farm power output.

17 WIND ENERGY↗
DOE OSTI2023

Aerodynamic characterization of two tandem wind turbines under yaw misalignment control using actuator line model

Yaw control has proven to be promising in alleviating the wake effects that plague the efficiency of wind farms. In this work, the actuator line modeling (ALM) method is adopted to simulate the flows over two tandem turbines distanced by 3–7 rotor diameters, with the yaw angle of the upstream rotor varying from γ 1 = 0° to 50°. The aim is to provide a comprehensive aerodynamic characterization of this simple wind farm under yaw misalignment control. With increasing yaw angle, the power generated by the downstream rotor increases, compensating the power loss in the upstream rotor, and resulting in significantly higher total power of the two turbines than that without yaw control. The maximum power output is achieved as the upstream wake of the yawed rotor is redirected away from the downstream rotor plane. Behind the downstream rotor, the secondary steering phenomenon is observed, where the wake is also redirected from the centerline. The use of the actuator line model also reveal unsteady aerodynamic characteristics that cannot be captured by lower-fidelity models. For the upstream rotor, the yaw misalignment results in time-varying change in the local angle of attack on the blade, giving rise to unsteady loading. The downstream rotor is partially submerged in the deflected wake incurred by the yawed upstream rotor. As the blade revolves into and out of the wake deficit, the blade experiences cyclic loading, leading to even stronger fluctuations in the aerodynamic loads than the upstream rotor. These analysis provides a comprehensive understanding of the yaw control effects on the two tandem rotors from the perspectives of aerodynamic performance, wake profiles, and unsteady characteristics. In conclusion, the insights gained from the present study can aid the design of collective yaw control strategies of wind farms, and lay the foundation for assessing the fatigue damage associated with yaw misalignment.

17 WIND ENERGY↗
DOE OSTI2023

Progress in the validation of rotor aerodynamic codes using field data

Within the framework of the fourth phase of the International Energy Agency (IEA) Wind Task 29, a large comparison exercise between measurements and aeroelastic simulations has been carried out featuring three simulation cases in axial, sheared and yawed inflow conditions. Results were obtained from more than 19 simulation tools originating from 12 institutes, ranging in fidelity from blade element momentum (BEM) to computational fluid dynamics (CFDs) and compared to state-of-the-art field measurements from the 2 MW DanAero turbine. More than 15 different variable types ranging from lifting-line variables to blade surface pressures, loads and velocities have been compared for the different conditions, resulting in over 250 comparison plots. The result is a unique insight into the current status and accuracy of rotor aerodynamic modeling. For axial flow conditions, a good agreement was found between the various code types, where a dedicated grid sensitivity study was necessary for the CFD simulations. However, compared to wind tunnel experiments on rotors featuring controlled conditions, it remains a challenge to achieve good agreement of absolute levels between simulations and measurements in the field. For sheared inflow conditions, uncertainties due to rotational and unsteady effects on airfoil data result in the CFD predictions standing out above the codes that need input of sectional airfoil data. However, it was demonstrated that using CFD-synthesized airfoil data is an effective means to bypass this shortcoming. For yawed flow conditions, it was observed that modeling of the skewed wake effect is still problematic for BEM codes where CFD and free vortex wake codes inherently model the underlying physics correctly. The next step is a comparison in turbulent inflow conditions, which is featured in IEA Wind Task 47. Doing this analysis in cooperation under the auspices of the IEA Wind Technology Collaboration Program (TCP) has led to many mutual benefits for the participants. The large size of the consortium brought ample manpower for the analysis where the learning process by combining several complementary experiences and modeling techniques gave valuable insights that could not be found when the analysis is carried out individually.

17 WIND ENERGY↗
DOE OSTI2025

JHTDB-wind: a web-accessible large-eddy simulation database of a wind farm with virtual sensor querying

This paper introduces JHTDB-wind (https://turbulence.idies.jhu.edu/datasets/windfarms, last access: 11 November 2025), a publicly accessible database containing large-eddy simulation (LES) data from wind farms. Building on the framework of the Johns Hopkins Turbulence Database (JHTDB), which hosts direct numerical simulation (DNS) and some LES datasets of canonical turbulent flows, JHTDB-wind stores the 4D space–time history of the flow and provides users the ability to access and query the data via a web-based virtual sensor interface. The initial dataset comprises LES results from a large wind farm with 10×6 turbines, modeled using a filtered actuator line method, under conventionally neutral atmospheric conditions. These data comprise 1 h (hour) of flow field data (velocity, pressure, potential temperature deviation, subgrid-scale (SGS) eddy viscosity, and turbine forces, approximately 15 TB (terabytes) and wind turbine data – including both turbine-level operational quantities and blade-level aerodynamic quantities (approximately 1.3 TB) – stored in Zarr and Parquet formats, respectively. Data retrieval is facilitated by the giverny Python package, allowing remote users to query the database in Python or MATLAB (C and Fortran support are available for flow field data). This paper details the simulation setup and demonstrates data access through examples that analyze wind farm flow structures and turbine performance. The framework is extensible to future datasets, including the JHTDB-wind diurnal cycle simulation analyzed in Xiao et al. (2025).

17 WIND ENERGY↗
DOE OSTI2025

Freestream turbulence effects on unsteady wind turbine loads and wakes: An IDDES study

We investigate numerically the effects of freestream turbulence on the unsteady aerodynamics and wakes of the National Renewable Energy Laboratory Phase VI wind turbine rotor for increasing wind speed. Turbulence is modeled using the Improved Delayed Detached-Eddy Simulation (IDDES) method. As a first step, a detailed mesh resolution study is conducted with the decaying freestream turbulence model at turbulence intensity of 0.5%. Our blade-resolved IDDES simulations show that grid-independent average torque and thrust results can be achieved with relatively coarse meshes, whereas dramatically higher mesh resolution is required for grid-independent results for power spectral densities of thrust force, especially in the deep-stall regime. Comparing the loads with the Shear-Stress Transport model demonstrates the superiority of IDDES in predicting massively separated flows. The aerodynamic performance and wake predictions with the decaying freestream turbulence model are compared with the synthetic freestream turbulence model. Both models predict nearly the same loads, spectral energy content, and wake characteristics. The properties of both the near- and far-wake regions are then examined. Furthermore, we show that separated boundary layers accelerate turbulent mixing and entrainment of the external flow, which results in faster wake recovery. The effect of increasing turbulence intensity to 6% is investigated using the synthetic freestream turbulence model. In contrast with the fully attached boundary layer, higher freestream turbulence in deep stall does not significantly affect the loads and vortex-shedding characteristics. However, the turbulent mixing in the wake is enhanced, which further hastens the recovery of the self-similar velocity profile. In general, increasing the wind speed at high turbulence intensity shifts the recovery farther upstream and increases the wake width.

17 WIND ENERGY↗
DOE OSTI2023

Large Eddy Simulation of Gasoline Sprays in a Lagrangian–Eulerian Framework Using the High-Order Spectral Element Method

Predicting the spray evolution using simulations requires accurate modeling of the turbulent gas-phase flow field. Here, in this study, the high-order spectral-element method (SEM), implemented in the code Nek5000, was used to provide highly resolved solutions to the turbulent flow field. Spray modeling capabilities were implemented into the Nek5000 code. The spray is modeled in a Lagrangian–Eulerian (LE) framework, where the liquid is represented by discrete parcels of droplets. The method for coupling liquid and gas in the context of SEM is described, which allows for very fine meshes to be used without affecting the stability of the solution. Large-eddy simulations (LES) of the eight-hole ECN Spray G gasoline injector were conducted. Numerical results are compared against experimental data for liquid penetration, droplet size and gas velocity. The morphology of the multiplume spray is compared against experimental data. The effect of different spray injection inputs is analyzed. It was found that using a plume direction of 33 deg and an injection cone angle of 30 deg produced the best results overall. This work shows the applicability of SEM for spray modeling applications, where use of a high-order flow solver can help us understand the multiplume spray aerodynamics and how it leads to plume collapse under certain conditions. Results also highlight the need for tuning spray input parameters in the LE framework, even when high-fidelity gas flow solutions are possible.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2025

Modeling and Analysis of Wind Turbine Wake Vortex Evolution Due to Time-Constant Spatial Variations in Atmospheric Flow

Modern utility-scale wind turbines are evolving toward larger, lighter, and more flexible designs to meet the growing demand for renewable energy while minimizing logistical costs. However, these advancements in lightweight design result in heightened aeroelastic sensitivity, leading to complex interactions which affect the rotor’s capacity to withstand aerodynamic loading and the cascading effects that manifest in the wake’s vortex-structure evolution under variable atmospheric conditions. In this paper, we analyze the influence of stream-wise fluctuating atmospheric flow conditions on wind turbines with large, flexible rotors through simulations of the National Rotor Testbed (NRT) turbine, located at Sandia National Labs’ Scaled Wind Farm Technology (SWiFT) facility in Lubbock, Texas. The Common Ordinary Differential Equation Framework (CODEF) modeling suite is used to simulate wind turbine aeroelastic oscillatory behavior and wind farm vortex–wake interactions for a range of conditions with spatially variant atmospheric flow. CODEF solutions for turbine operation in wind conditions featuring only one parameter fluctuation are compared to wind conditions with several wind parameter variations in combination. By isolating individual inflow variations and comparing them to multi-parameter scenarios, we determine the contributions of each atmospheric factor to rotor dynamics, wake evolution, and downstream wind farm interactions. The purpose of this paper is to analyze the effects of spatial variations in atmospheric flow on the topological evolution of wind turbine vortex wakes, which constitutes a gap in the current understanding of wind turbine wake dynamics. The insights gained from this study are particularly valuable for the development of wind farm control strategies aimed at mitigating the adverse effects of wake interactions, enhancing energy capture, and improving the overall stability of wind farm operations. With these insights, we aim to contribute to the development of modeling and simulation tools to optimize utility-scale wind power plants operating in diverse atmospheric environments.

Farrell, Alayna (ORCID:000000023555720X)↗
DOE OSTI2025

Effect of Surface Roughness on Dynamic Stall in Pitching Motion

Dynamic stall plays a critical role in determining the performance and stability of a wide range of fluid-dynamics systems in various engineering applications. This unsteady aerodynamic phenomenon is particularly significant for maneuvering aircraft wings, jet aircraft subjected to gust encounters, helicopter rotor blades, and wind turbine blades [1–3]. The prediction of the dynamic stall vortex (DSV) is challenging due to factors such as unsteady aerodynamics, three-dimensional (3-D) effects, turbulence and flow separation, incoming gust, and surface impact effects [4–6]. Hence, advanced computational techniques and modeling approaches in computational fluid dynamics (CFD) would be required to enhance the accuracy and reliability of DSV predictions in dynamic stall scenarios. In the past, Batther and Lee [7] employed delayed detached eddy simulations (DDES) to understand the flow physics associated with the onset of dynamic stall. Their approach demonstrated that DDES achieves results comparable to those obtained from large-eddy simulations at a reduced computational cost. In another study, Khalifa et al. [8] examined the 3-D aspects of dynamic stall on a NACA 0012 airfoil using DES solvers. In conclusion, the findings underlined the superiority of 3-D simulations over two-dimensional approaches, particularly in predicting the lift coefficient values and capturing dynamic stall stages more precisely.

97 MATHEMATICS AND COMPUTING↗