© 2025, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.This paper showcases the collaborative efforts between ITA (academic) and Embraer (aircraft manufacturer) in developing advanced methods to address the upcoming challenges of the 4th Aeroelastic Prediction Workshop. For predicting static wing loads, a rapid conceptual design method that accounts for structural geometric nonlinearity is introduced. A matched flutter solution is proposed for control surface flutter in geometrically nonlinear wings. For predicting limit cycle oscillations, the approach combining an unsteady vortex lattice with a transient structural geometric nonlinear solver is presented. Furthermore, a framework that integrates an open-source Reynolds-Averaged Navier-Stokes solver with a geometric nonlinear structural solver is developed to handle transonic static deflections.

© 2025 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.The Actuator Line Method (ALM) is a technique that replaces the detailed airfoil geometry with distributed body forces to predict the flow field. ALM has been widely employed for simulating rotating blade wakes due to its flexibility and accuracy in the far field. In this study, the applicability of ALM for unsteady aerodynamics and acoustic field prediction is evaluated. The case study considered is the harmonic transverse oscillation of a thin airfoil in uniform flow. The ALM body forces are distributed over a few grid points following a Gaussian function, with a range of smearing ratio of ε/c (smearing parameter over the chord length) between 0.4 and 1. These forces are computed using thin airfoil theory with the Prandtl-Glauert correction for compressible regime. Based on these computations, the compressible Navier-Stokes equations are numerically solved, yielding the velocity and pressure fields. ALM lift results are validated against unsteady aerodynamic theory in the subsonic regime. Moreover, results demonstrate an acoustic field consistent with a dipole distribution and a spectrum exhibiting a frequency corresponding to the plunging motion. Furthermore, the acoustic results are validated through an acoustic analogy approach, involving the prediction of the acoustic field via Green’s function. The prediction of the acoustic far-field using ALM is expected to significantly reduce the computational cost of compressible simulations applied to propeller and wind turbine aeroacoustics.

© 2023, AIAA International. All rights reserved.Two configurations typical of fixed-wing aircraft are simulated with the actuator line method (ALM): a wing with winglets, and a T tail. The ALM is extensively used in rotor simulations to model the blades by body forces, which are calculated from airfoil data and the relative flow velocity. This method has not been used to simulate airplane aerodynamics, despite its advantage of allowing coarser grids. This may be credited to the failure of the uncorrected ALM to accurately predict forces near the tip of the wings, even for simple configurations. The recently proposed vortex-based smearing correction shows improved results, suggesting those limitations are part of the past. For the nonplanar configurations studied in this work, differences between the ALM with the original smearing correction and a nonlinear lifting line (LL) method are observed near the intersection of surfaces because the circulation generated in the numerical simulation differs from the calculated corrected circulation. A vorticity magnitude correction is proposed, which improves the agreement between the ALM and the LL method. This second-order correction resolves the ambiguity in the velocity used to define the lift force. The good results indicate that the improved ALM can be used for airplane aerodynamics, with an accuracy similar to the LL method.

© The Author(s), 2023. Published by Cambridge University Press.The actuator line method (ALM) is used extensively in wind turbine and rotor simulations. However, its original uncorrected formulation overestimates the forces near the tip of the blades and does not reproduce well forces on translating wings. The recently proposed vortex-based smearing correction for the ALM is a correction based on physical and mathematical properties of the simulation that allows for a more accurate and general ALM. So far, to correct the forces on the blades, the smearing correction depended on an iterative process at every time step, which is usually slower, less stable and less deterministic than direct methods. In this work, a non-iterative process is proposed and validated. First, we propose a formulation of the nonlinear lifting line that is equivalent to the ALM with smearing correction, showing that the results are practically identical for a translating wing. Then, by linearizing the lifting line method, the iterative process of the correction is substituted by the direct solution of a small linear system. No significant difference is observed in the results of the iterative and non-iterative corrections, in both wing and rotor simulations. Additional contributions of the present work include the use of a more accurate approximation for the velocity induced by a smeared vortex segment and the implementation of a free-vortex wake model to define the vortex sheet, which contribute to the accuracy and generality of the method. The results presented here may motivate the adoption of the ALM by other communities, for example, in fixed-wing applications.

© 2022 Author(s).Floating offshore wind turbines (FOWTs) are subjected to platform motion induced by wind and wave loads. The oscillatory movement trigger vortex instabilities, modifying the wake structure and influencing the flow reaching downstream wind turbines. In this work, the wake of a FOWT is analyzed by means of numerical simulations and a comparison with linear stability theory. Two simplified models based on the stability of vortices are developed for all degrees of freedom of turbine motion. In our numerical simulations, the wind turbine blades are modeled as actuator lines and a spectral-element method with low dispersion and dissipation is employed to study the evolution of the perturbations. The turbine motion excites vortex instability modes predicted by the linear stability of helical vortices. The flow structures that are formed in the non-linear regime are a consequence of the growth of these modes and preserve some of the characteristics that can be explained and predicted by the linear theory. The number of vortices that interact and the growth rate of disturbances are well predicted by a simple stability model of a two-dimensional row of vortices. For all types of motion, the highest growth rate is observed when the frequency of motion is one and a half the frequency of rotation of the turbine that induces the out-of-phase vortex pairing mechanism. For lower frequencies of motion, several vortices coalesce to form large flow structures, which cause the high amplitude of oscillations in the streamwise velocities, which may increase fatigue or induce high amplitude motion on downstream turbines.

© (2022) by International Council of Aeronautical Sciences (ICAS) All rights reserved.The system of vortices created by the hub and tip vortices of rotors and propellers is composed of two subsystems of helical vortices that have different radii and pitches. A similar system of external and internal vortices is created by some blade devices proposed to destabilize the tip vortices of helicopters. The steady solution of these systems of vortices was recently described. However, their stability was not studied. The stability of a system of multiple helical vortices was studied in this work using a complex-step technique to linearize the Biot-Savart law and the vorticity transport equations. It was noted that the hub and tip vortices do not interact and their linear stability can be treated separately, if the velocity field induced by one system is considered in the stability of the other. For a ratio of radius of 0.8, strong interaction between the vortices was observed, with an out-of-phase mechanism appearing as one of the main phenomena.

© 2022 Royal Society Publishing. All rights reserved.The use of the complex velocity potential and the complex velocity is widely disseminated in the study of two-dimensional incompressible potential flows. The advantages of working with complex analytical functions made this representation of the flow ubiquitous in the field of theoretical aerodynamics. However, this representation is not usually employed in linear stability studies, where the representation of the velocity as real vectors is preferred by most authors, in order to allow the representation of the perturbation as the complex exponential function. Some of the classical attempts to use the complex velocity potential in stability studies suffer from formal errors. In this work, we present a framework that reconciles these two complex representations using bicomplex numbers. This framework is applied to the stability of the von Kármán vortex street and a generalized formula is found. It is shown that the classical results of the symmetric and staggered von Kármán vortex streets are just particular cases of the generalized dynamical system in bicomplex formulation.

© 2021 Acoustical Society of America.Parabolized stability equations (PSE) have been shown to model wavepackets and, consequently, the near-field of turbulent jets with reasonable accuracy. In this work, PSE were employed to obtain a reduced-order model that could estimate both the fluid-dynamic and the acoustic fields of a supersonic jet in a computationally efficient approximation for resolvent-based estimation based on a single input. From the unsteady pressure data at an input position, the time-domain pressure field was estimated using transfer functions obtained using PSE and a data-driven method based on a well-validated large-eddy simulation (LES). The prediction scheme employed is a single-input single-output, linear model. The unsteady pressure predicted by the PSE showed good agreement with the LES results, especially if the input position is outside the mixing layer, where the prediction capabilities of the PSE are comparable to those of the data-driven transfer functions. The good agreement indicates that PSE could not only be used to predict the sound generation but also to open up different potentialities to attenuate the noise by flow control. The exploration of the regions where the method displayed good agreement, which are presented in this work, can guide the positioning of the sensors for experimental implementation of closed-loop control in a jet.

© Published under licence by IOP Publishing Ltd.Floating offshore wind turbines (FOWTs) are the next frontier in offshore wind energy, allowing exploration of deep-water regions previously unavailable to fixed-foundation turbines. Since offshore turbines operate in lower turbulence levels, the intrinsic hydrodynamic unstable modes of the tip vortices can have even more relevance than in onshore turbines. For floating turbines, platform motion induced by wind and wave loads can trigger vortex instabilities, modifying the wake structure, possibly influencing the flow reaching downstream wind turbines. In the present paper, we study those effects by the means of numerical simulations and their comparison with analytical studies. In our simulations, the wind turbine blades are modeled as actuator lines in the incompressible Navier-Stokes equations. Heave motion with different amplitudes and frequencies are studied. The effect of increasing amplitude is to advance the onset of vortex interaction. For the lower frequency of heave motion, several vortices coalesce to form a large flow structure. High amplitude of oscillations in the streamwise velocity were observed due to these flow structures, which may increase fatigue or induce high amplitude motion on downstream turbines. The number of vortices that interact, as other qualitative phenomena of the numerical simulation, were well predicted by a simple stability model of two-dimensional row of vortices. The disturbances imposed by the heave motion were also compared to the eigenvectors resulting from linear stability theory for helical vortices and the predicted growth rates for the wavenumbers resulting from this comparison were consistent with the model of a row of vortices. These results motivate further studies to understand the impact of the larger flow structures on downstream turbines.

© 2019 IOP Publishing Ltd. All rights reserved.The hydrodynamic stability of a vortex system behind two in-line wind turbines operating at low tip-speed ratios is investigated using the actuator-line method in conjunction with the spectral-element flow solver Nek5000. To this end, a simplified setup with two identical wind turbine geometries rotating at the same tip-speed ratio is simulated and compared with a single turbine wake. Using the rotating frame of reference, a steady solution is obtained, which serves as a base state to study the growth mechanisms of induced perturbations to the system. It is shown that, already in the steady state, the tip vortices of the two turbines interact with each other, exhibiting the so-called overtaking phenomenon. Hereby, the tip vortices of the upstream turbine overtake those of the downstream turbine repeatedly. By applying targeted harmonic excitations at the upstream turbine's blade tips a variety of modes are excited and grow with downstream distance. Dynamic mode decomposition of this perturbed flow field showed that the unstable out-of-phase mode is dominant, both with and without the presence of the second turbine. The perturbations of the upstream turbine's helical vortex system led to the destabilization of the tip vortices shed by the downstream turbine. Two distinct mechanisms were observed: for certain frequencies the downstream turbine's vortices oscillate in phase with the vortex system of the upstream turbine while for other frequencies a clear out-of-phase behaviour is observed. Further, short-wave instabilities were shown to grow in the numerical simulations, similar to existing experimental studies [1].