Aeroelastic Framework Research Articles

Loads-based optimal fuel-usage strategy by using a neural-network-based reduced-order model for vertical sloshing

This paper explores methods to reduce aircraft design loads through an optimal fuel usage strategy, which maximises the beneficial effects of wing-tank sloshing-induced damping. A reduced-order neural network models the nonlinear sloshing behaviour in various tank fill level scenarios. Integrated into an aeroelastic framework, this model allows for the assessment of incremental sloshing-induced damping in gust response of wings. The optimised fuel usage strategy enables control of fuel consumption from each individual tank to provide maximisation of load alleviation.

Wake interference effects on flow-induced vibration of flexible membrane wings

This work investigates the effect of wake interference on the nonlinear coupled dynamics and aerodynamic performance of flexible membrane wings at a moderate Reynolds number. A high-fidelity computational aeroelastic framework is employed to simulate the flow-induced vibration of flexible membrane wings in response to unsteady vortex wake flows produced by an upstream stationary circular cylinder. The coupled dynamics of the downstream membrane are investigated at different gap ratios, aeroelastic numbers, and offset distances. The variations in flow features, membrane responses, and frequency characteristics are analyzed to understand the wake interference effect on membrane aeroelasticity. The results indicate that the aerodynamic performance and flight stability of the downstream membrane are degraded under the wake interference effect. Four distinct flow regimes are classified for the cylinder–membrane configuration, namely (i) single body flow, (ii) co-shedding I, (iii) co-shedding II, and (iv) detached vortex-dominated vibration, respectively. The mode transition is found to build new frequency synchronization between the flexible membrane and its own surrounding flows, or the wake flows of the cylinder, to adjust the aerodynamic performance and membrane vibration. This study sheds new light on membrane aeroelasticity in response to wake flows and enhances understanding of the fluid–membrane coupling mechanism. These findings can facilitate the development of next-generation bio-inspired drones that have high flight efficiency and robust flight stability in gusty flows.

Multi-fidelity, steady-state aeroelastic modelling of a 22-megawatt wind turbine

In this work we present multi-fidelity steady-state aeroelastic framework that leverages the state-of-the-art simulation tool HAWC2 for the structural model, and a variety of aerodynamic models, comprising of the low fidelity blade element momentum (BEM) method, the medium fidelity blade element vortex cylinder (BEVC) method and the coupled near wake and vortex cylinder method, and finally the high-fidelity CFD solver EllipSys3D. The aeroelastic framework is part of AESOpt, an aerostructural framework for design of wind turbine blades. The different aerodynamic models are applied to compute the aeroelastic steady state of the newly designed IEA 22 MW Reference Wind Turbine. The results show a very good agreement between the medium- and high-fidelity aerodynamic models with a maximum of 2.7% difference between the high-fidelity aeroelastic response and that of the lower fidelities.

Rapid dynamic aeroelastic response analysis of the highly flexible wing with distributed propellers influence

Abstract A rapid nonlinear aeroelastic framework for the analysis of the highly flexible wing with distributed propellers is presented, validated and applied to investigate the propeller effects on the wing dynamic response and aeroelastic stability. In the framework, nonlinear beam elements based on the co-rotational method are applied for the large-deformation wing structure, and an efficient cylinder coordinate generation method is proposed for attached propellers at different position. By taking advantage of the relatively slow dynamics of the high-aspect-ratio wing, propeller wake is modeled as a quasi-steady skewed vortex cylinder with no updating process to reduce the high computational cost. Axial and tangential induced velocities are derived and included in the unsteady vortex lattice method. For the numerical cases explored, results indicate that large deformation causes thrust to produce wing negative torsion which limits the displacement oscillation, and slipstream mainly increases the response values. In addition, an improvement of flutter boundary is found with the increase of propeller thrust while slipstream brings a destabilising effect as a result of the increment of dynamic pressure and local lift. The great potential of distributed propellers in gust alleviation and flutter suppression of such aircraft is pointed out and the method as well as conclusions in this paper can provide further guidance.

Coupled Dynamics of Steady Jet Flow Control for Flexible Membrane Wings

We present a steady jet-flow-based flow control of flexible membrane wings for the adaptive and efficient motion of bat-inspired drones in complex flight environments. A body-fitted variational computational aeroelastic framework is adopted for the modeling of fluid–structure interactions. High-momentum jet flows are injected from the leading edge and transported to the wake flows to alter the aerodynamic performance and the membrane vibration. The coupled dynamic effect of active jet flow control on membrane performance is systematically explored. While the results indicate that the current active flow control strategy performs well at low angles of attack, its effectiveness degrades at high angles of attack with large flow separation. To understand the coupling mechanism, the variations of the vortex patterns are examined by the proper orthogonal decomposition modes, and the fluid transport process is studied by the Lagrangian coherent structures. Two scaling relations that quantitatively connect the membrane deformation with the aerodynamic loads presented in our previous work are verified even when active jet flow control is applied. A unifying feedback loop that reveals the fluid–membrane coupling mechanism is proposed. These findings can facilitate the development of next-generation bio-inspired drones that incorporate smart sensing and intelligent control.

Power Benefits of High-Altitude Flapping Wing Flight at the Monarch Butterfly Scale.

The long-range migration of monarch butterflies, extended over 4000 km, is not well understood. Monarchs experience varying density conditions during migration, ranging as high as 3000 m, where the air density is much lower than at sea level. In this study, we test the hypothesis that the aerodynamic performance of monarchs improves at reduced density conditions by considering the fluid-structure interaction of chordwise flexible wings. A well-validated, fully coupled Navier-Stokes/structural dynamics solver was used to illustrate the interplay between wing motion, aerodynamics, and structural flexibility in forward flight. The wing density and elastic modulus were measured from real monarch wings and prescribed as inputs to the aeroelastic framework. Our results show that sufficient lift is generated to offset the butterfly weight at higher altitudes, aided by the wake-capture mechanism, which is a nonlinear wing-wake interaction mechanism, commonly seen for hovering animals. The mean total power, defined as the sum of the aerodynamic and inertial power, decreased by 36% from the sea level to the condition at 3000 m. Decreasing power with altitude, while maintaining the same equilibrium lift, suggests that the butterflies generate lift more efficiently at higher altitudes.

High-fidelity aeroelastic transonic analysis using higher-order structural models

A novel computational approach for static aeroelastic analysis of metal and composite wings in transonic flows is proposed. Static aeroelastic analysis is often performed coupling beam/plate structural formulations with low-fidelity inviscid and irrotational aerodynamics. When high subsonic, transonic or supersonic regimes are met, low-fidelity aerodynamics is unable to accurately describe flow separation, viscous phenomena, and/or shock waves, unless suitable corrections are considered. This work combines the use of a variable-order kinematics structural model with Computational Fluid Dynamics (CFD), with the aim of developing a flexible computational aeroelastic framework. In particular, the structural model is based on the Carrera Unified Formulation and Equivalent Plate Modelling, whose governing equations are then solved through the Finite Element Method. The CFD analysis is performed using the high-fidelity open-source software SU2. The fluid–structure interaction is captured resorting to an energetic approach based on the Moving Least Squares patch technique. The generality and flexibility of the developed tool is demonstrated considering: the structural analysis of a wing exhibiting taper ratio, sweep angle, spars and ribs; the aeroelastic static analysis of a transonic AGARD 445.6 wing; and a prototype aeroelastic tailoring study on a composite wing. Comparison with available literature results confirms the robustness of the approach.

A computational aeroelastic framework based on high-order structural models and high-fidelity aerodynamics

A computational framework for high-fidelity static aeroelastic analysis is presented. Aeroelastic analysis traditionally employs a beam stick representation for the structure and potential, inviscid and irrotational flow assumptions for the aerodynamics. The unique contribution of this work is the introduction of a high-order structural formulation coupled with a high-fidelity method for the aerodynamics. In more details, the Carrera Unified Formulation coupled with the Finite Element Method is implemented to model geometrically complex composite, laminated structures as equivalent bi-dimensional plates. The open-source software SU2 is then used for the solution of the aerodynamic fields. The in-house fluid-structure coupling algorithm is based on the Moving Least Square technique. The paper contains a thorough validation of each disciplinary solver of the aeroelastic framework, and provides a few application test cases. For an unswept, untapered and isotropic wing, it was found that the method provides results in agreement with predictions from models based on potential flow theory for moderate freestream velocities. Departures were reported for very low speed and in the high-subsonic regime, alerting the need of adopting high-fidelity flow solutions at these flow conditions. The computational framework was then applied to the static aeroelastic tailoring of a composite wing. The paper concludes providing an overview of future implementation steps towards a tool for the seamless analysis of composite structures subject to different flow conditions, from low to high speed.

A Machine Learning Approach to Predicting Unsteady Transonic Flow of Pitching Airfoils

Abstract A machine learning methodology has been proposed in this paper to study the unsteady transonic aerodynamics in the flutter regime. The methodology is based on a well-established regularization technique, and it compares very well with the data modeling approach proposed recently by the author in the prediction of the lift coefficient, cl, of NACA00 series airfoils over a range of reduced frequency. The present methodology has been extended to the prediction of the airfoil pitching moment coefficient, cpm, also. Just as in the case of the data model proposed earlier, the regularization-based machine learning model is trained on a subset of the considered reduced frequency range and a subset of the NACA00 series airfoils. The model predictions are in good agreement with the computational fluid dynamics (CFD) results, in the reduced frequency range for the selected test NACA00 profiles including those with a thickness typical of supercritical wing sections. The machine learning methodology presented here represents a new technology that can be used in the prediction of transonic flutter aerodynamics of wings using a strip theory approach. This new approach can be coupled with a simple finite element model such as a beam element model offering a rapidly implementable aeroelastic framework for the design of new transonic wings.

Nonlinear Aeroelastic Analysis for Highly Flexible Flapping Wing in Hover

Aeromechanics of highly flexible flapping wings is a complex nonlinear fluid–structure interaction problem and, therefore, cannot be analyzed using conventional linear aeroelasticity methods. This paper presents a standalone coupled aeroelastic framework for highly flexible flapping wings in hover for micro air vehicle (MAV) applications. The MAV-scale flapping wing structure is modeled using fully nonlinear beam and shell finite elements. A potential-flow-based unsteady aerodynamic model is then coupled with the structural model to generate the coupled aeroelastic framework. Both the structural and aerodynamic models are validated independently before coupling. Instantaneous lift force and wing deflection predictions from the coupled aeroelastic simulations are compared with the force and deflection measurements (using digital image correlation) obtained from in-house flapping wing experiments at both moderate (13 Hz) and high (20 Hz) flapping frequencies. Coupled trim analysis is then performed by simultaneously solving wing response equations and vehicle trim equations until trim controls, wing elastic response, inflow and circulation converge all together. The dependence of control inputs on weight and center of gravity (cg) location of the vehicle is studied for the hovering flight case.

Geometrically nonlinear flutter analysis with corotational shell finite element analysis and unsteady vortex-lattice method

In this paper, an aeroelastic framework developed in the previous works has been extended for a geometrically nonlinear aeroelastic stability analysis. In the aeroelastic stability analysis, modal mass and stiffness matrices are constructed using shell finite elements with the corotational approach, which can take into account the geometric stiffening under large deformations. A generalized aerodynamic force matrix is derived by accommodating the unsteady vortex-lattice method based on a modal approach. The derived modal aeroelastic equations are solved using the p-k method. Individual modules to calculate generalized structural matrices with the corotational approach and aerodynamic forces based on the unsteady vortex-lattice method are verified. The present geometrically nonlinear aeroelastic framework for aeroelastic stability analysis is also validated in a comparison with an experimental result in the flutter wind tunnel test showing a reasonable accuracy for a prediction of flutter speed, while there still is room for further improvement in the estimation of flutter frequency. In addition, the present method allows studying the flutter characteristics of flexible wings with different incident angles, which cannot be evaluated by traditional linear flutter simulations. Finally, effects of geometric nonlinearity and large deformation on flutter characteristics of flexible and high-aspect-ratio wings were explored by using the present method. The present method can help to understand aeroelastic stability characteristics for such high-aspect-ratio wings.

A transonic, viscous nonlinear frequency domain Vortex Lattice Method for aeroelastic analyses

The Unsteady Vortex Lattice Method has interesting capabilities for nonlinear subsonic aeroelastic analyses. This paper aims to develop an aeroelastic framework based on the UVLM that is suitable for compressible, transonic and viscous unsteady flows. To achieve these modeling capabilities, the UVLM is first extended to the nonlinear frequency domain using the harmonic balance approach. Secondly, sectional corrections are applied from a steady 2D/2.5D database of aerodynamic forces computed with high-fidelity Euler/RANS flow solvers. The angle of attack coupling scheme on the lift force is complemented by a least-square procedure also coupling the pitching moment. Finally, an approximation of the retarded time is implemented in the influence kernel of the harmonic balance formulation of the UVLM to account for unsteady compressibility. The aerodynamic model is verified against time domain high-fidelity solutions with pitching airfoils in 2D and in 3D with a pitching constant chord NACA 0012 swept wing. Thereafter, the HB/LCO approach is applied with the frequency domain UVLM to 2D and 3D aeroelastic problems and compared against high-fidelity solutions. The proposed framework is capable of capturing strong nonlinear Limit Cycle Oscillation behaviors at high Mach numbers, as well as the flutter boundary for a wide range of Mach numbers while maintaining a low computational cost. As a result, the proposed framework could be of interest for preliminary design and Multi-Disciplinary Design (MDO) optimizations in the context of subsonic and transonic aircraft design.

Aeroelastic Simulation of High-Aspect Ratio Wings with Intermittent Leading-Edge Separation

We present a medium-fidelity aeroelastic framework for computing intermittently separating three-dimensional (3-D) flows around high-aspect ratio wings with a significantly reduced computational cost compared to the computational-fluid- dynamics-based method. To achieve that, we propose a modified three-dimensional vortex panel method with leading-edge separation controlled by leading-edge suction parameter theory, and its incorporation in a coupled aeroelastic solver for the dynamic response of these systems. Numerical verifications and simulations are presented on both attached and separated aeroelastic test cases, demonstrating the method on postflutter limit-cycle oscillation of a cantilever wing, and leading-edge separation on a deploying wing, a complex kinematic response. In both cases we were able to capture three-dimensional interactions on intermittently separating dynamic flowfields using a low computational cost.

Resolving Pitching Airfoil Transonic Aerodynamics by Computational Fluid Dynamics Data Modeling1

Abstract A detailed numerical study of harmonically pitching airfoils of NACA00 series is presented here. Based on the analysis of the computational fluid dynamics (CFD) results, a hypothesis is made that a simple data model can capture the dynamics of the airfoils in pitch. The data model is based on the cl−α (lift coefficient–angle of attack) hysteresis loops that retain generic geometrical characteristics for a wide range of reduced frequency, k, encountered in flutter in transonic flows for all the NACA00 airfoils considered. The model was trained on a subset of the considered NACA00 airfoils and then tested on the remaining NACA00 set, for a subset of the reduced frequencies. The model predictions of the cl−α hysteresis loops for the test set are shown to be in excellent agreement with the CFD results for the range of k typical of transonic flutter. The data model offers a paradigm shift in the prediction of transonic flow dynamics of pitching airfoils and will guide the development of a new transfer function that will be incorporated in a new aeroelastic framework leading to an appropriate transonic flutter model for use in the development of future aircraft.

Nonlinear aeroelastic analysis of airfoil section under stall flutter oscillations and gust loads

As the desire for more flexible aircraft structures increases, so does the need to incorporate the intrinsic nonlinearities in their aeroelastic analyses. In that manner, it becomes essential to fully characterize the aeroelastic behavior and to investigate the effects that common external disturbances, such as atmospheric gust turbulence, might induce. In this work, an augmentation of the semi-empirical Beddoes–Leishman dynamic stall model to include gust loads is presented. This augmented dynamic stall model is coupled with the typical section equations of motion to yield a complete aeroelastic framework for gust-induced stall flutter analyses. The stability boundary of a classic 2-DOF typical section is investigated, and a stochastic gust response study reveals that depending on the turbulence intensity, the probabilities of reaching aeroelastic instability can be quite high even for airspeeds well below the one for linear flutter.

A variational flexible multibody formulation for partitioned fluid–structure interaction: Application to bat-inspired drones and unmanned air-vehicles

We present a three-dimensional (3D) partitioned aeroelastic formulation for a flexible multibody system interacting with incompressible turbulent fluid flow. While the incompressible Navier–Stokes system is discretized using a stabilized Petrov–Galerkin procedure, the multibody structural system consists of a generic interaction of multiple components such as rigid body, beams and flexible thin shells along with various types of joints and connections among them. A co-rotational framework is utilized for the category of small strain problems where the displacement of the body is decomposed into a rigid body rotation and a small strain component. This assumption simplifies the structural equations and allows for the incorporation of multiple bodies (rigid as well as flexible) in the system. The displacement and rotation constraints at the joints are imposed by a Lagrange multiplier method. The equilibrium conditions at the fluid–structure interface are satisfied by the transfer of tractions and structural displacements via the radial basis function approach, a scattered data interpolation technique, which is globally conservative. For the coupled stability in low structure-to-fluid mass ratio regimes, a nonlinear iterative force correction scheme is employed in the partitioned staggered predictor–corrector scheme. The convergence and generality of the radial basis function mapping are analyzed by carrying out systematic error analysis of the transfer of fluid traction across the non-matching fluid–structure interface where a third-order of convergence is observed. The proposed aeroelastic framework is then validated by considering a flow across a flexible pitching plate configuration with serration at the trailing edge. Finally, we demonstrate the flow across a flexible flapping wing of a bat modeling the bone fingers as beams and the flexible membrane as thin shells in the multibody system along with the joints.

Static Geometrically Nonlinear Aeroelastic Framework for Multi-Fidelity Analysis

Static Geometrically Nonlinear Aeroelastic Framework for Multi-Fidelity Analysis

Industrially Inspired Gust Loads Analysis of Various-Aspect-Ratio Wings Featuring Geometric Nonlinearity

This paper considers the effect of geometric nonlinearity on gust load analyses of high-aspect-ratio commercial aircraft. Three variants of a conceptual aircraft, featuring wing aspect ratios of 10, 18, and 26, are sized using an industrially inspired procedure to obtain realistic structures of existing and future designs. These aircraft are modeled in a nonlinear aeroelastic framework, featuring a geometrically exact beam formulation coupled with unsteady aerodynamics, and subjected to a gust loads process adapted for nonlinear systems. The gust analysis is also carried out using a linear approach (linearizing the equations of motion about an undeformed or trimmed geometry) to understand how nonlinearities influence the loads and dynamic behavior of aircraft as the aspect ratio increases. Load envelopes show that vertical shear and bending moments are predicted well by the linear analyses, even for the aspect-ratio-26 case, providing that the linearization is performed about the trimmed geometry. In contrast, the in-plane and axial loads are significantly underestimated using linear analyses. Torque behavior is problem specific and therefore difficult to generalize. Even on the aspect-ratio-10 case, which would traditionally be considered as a linear problem, it can be shown that the torque loads are considerably affected by nonlinearity.

Strongly-coupled aeroelastic free-vortex wake framework for floating offshore wind turbine rotors. Part 2: Application

This two-part paper presents the integration of the free-vortex wake method (FVM) with an aeroelastic framework suitable to model the rotor-wake interactions engendered by floating offshore wind turbine (FOWT) rotors in operation. Part 1 of this paper introduces the numerical development and validation of an aeroelastic framework. Due to a lack of experimental aeroelastic benchmarks for FOWTs, a series of validation studies are conducted against the rotor aerodynamic and structural performance of the National Renewable Energy Laboratory (NREL) 5-MW reference wind turbine. Part 2 of this paper focuses on the modeling and simulating different aeroelastic operational conditions of FOWTs. Numerical results of the current framework capture consistently the aerodynamic rotor performance, such as power, thrust, and torque of wave-induced pitching FOWTs. In addition, the presented aeroelastic framework yields additional information about the power, thrust, and torque fluctuations due to the out-of-phase blade passing frequency and corresponding blade deflections. The fidelity of the presented framework demonstrates, for the first time, an FVM-based aeroelastic method capable of carrying out investigations on rotor-wake interactions and relevant aeroelastic phenomena of FOWTs.

Computational Aeroelasticity Using Modal-Based Structural Nonlinear Analysis

This paper presents the development of an aeroelastic analysis formulation for the dynamic response of a flexible wing. The geometrically nonlinear structure is represented by a reduced-order model that accounts for the large-deformation effects on the inertia and stiffness terms. It is based on a system identification of a built-up finite element model and does not rely on a geometric nonlinear beam-based model as most of the state-of-the-art nonlinear aeroelastic frameworks do. The complexity of the wing structural layout is captured in the built-up finite element model as in traditional industry applications. To preserve a small number of states to represent the structural dynamics of the system, a modal approach is used in a nonlinear sense. Moreover, this approach is easily linked to computational fluid dynamics. For this study, the structural reduced-order model framework is integrated within the aeroelastic framework of the code CFL3D. Using this integrated solution, the aeroelastic response of a high-aspect-ratio wing is investigated.