Aeroelastic Analysis Research Articles

Aeroelastic Structural Analysis to Calculate Symmetrical Divergence Modes of an Aircraft Wing Using Aerodynamic Lifting Line Theory

This work explores the use of numerical matrix iteration to determine an aircraft wing's divergence speed using the aerodynamic span effects approach. The present work begins with the construction of equilibrium equations in differential and integral forms. In this paper, integral formulas are used because it serves as a convenient basis for numerical solutions of complex practical problems. Second, the straight-tapered wing is divided into a number of Multhopp stations. Subsequently, the stations' torsional influence coefficient matrix has been calculated. Third, lifting line theory was used as a suitable choice of aerodynamic theory, and the governing equations were represented in matrix form. Finally, aerodynamic span effects are taken into consideration with induction effects according to Prandtl’s lifting line theory to calculate the symmetrical divergence speed from the lowest eigenvalue of the homogenous governing integral equation. To get the solution to converge, a matrix has been iterated using the MATLAB environment. The obtained results will aid modern aircraft designers in their understanding of wing instability in steady motion.

Exploration on flutter mechanism of a damaged transonic rotor blade using high-fidelity fluid–solid coupling method

Structural damage in turbomachinery is a primary origin of aeronautic accidents, which is receiving increased attention. This study is thus focused on the aeroelastic analysis of damaged blades, including the onset of flutter and underlying mechanisms. First, a high-fidelity fluid–solid coupling system is established with computational fluid dynamics (CFD) and computational structural dynamics (CSD) technologies, via which the dynamic aeroelastic analysis is conducted based on static aeroelastic deformation. Second, a damaged rotor blade is parametrically modelled with variable damage levels, extents, and positions. Finally, the modal identification method of spectral proper orthogonal decomposition (SPOD) is applied to observe flow details and provide physical insight into the flutter mechanism for damaged blades. Numerical analysis finds that there is a critical damage level below which the aeroelastic stability is positively improved with increasing damage level; otherwise, a significant loss of stability is induced. The damage location and extent further affect this critical damage level and the change rate crossing the threshold. The simulation with CFD/CSD finds that the high pressure near the trailing edge induced from boundary layer separation suppresses vibrations in stable conditions, but motivates vibrations during flutter, which is because of the high-pressure spread to nearing blades. SPOD modes reveal that high-frequency disturbances with large scale are primary factors inducing flutter, which is further stimulated by the high-order disturbances with small scale. This study provides a crucial foundation for the fatigue prediction for rotor blades in service and the optimisation design for high-performance turbomachinery in the near future.

The impact of extreme wind conditions and yaw misalignment on the aeroelastic responses of a parked offshore wind turbine

As global energy demands rise and the urgent need to reduce carbon emissions, offshore wind energy technology has evolved rapidly, becoming a vital component of the world’s energy portfolio. However, offshore wind turbines face new challenges due to complex marine environments. Under extreme conditions such as strong winds and yaw misalignment, parked wind turbines exhibit complex aerodynamic and structural responses that significantly differ from those in normal operating conditions. These responses, crucial to the integrity and safety of wind turbines, demand thorough analysis. This article presents an in-depth aeroelastic analysis of a parked 5 MW offshore wind turbine using a sophisticated and precise numerical model. It explores the impacts of incoming wind speed and yaw misalignment on the aerodynamic loads and structural behaviors of the wind turbine. The findings indicate that gravity plays a significant role in blade structural responses for a parked wind turbine. Additionally, higher wind speeds elevate aerodynamic forces, leading to more pronounced fluctuations in root forces and tip deflections. The increase in wind speed triggers and exacerbates high-frequency edgewise vibrations of the blade, further leading to fluctuations and instability in the loads. The study also reveals that yaw misalignment causes the AOA changes significantly over time, and generates intermittent fluctuations in lift and drag, leading to extra blade vibrations with the maximum amplitude exceeding 10% of the blade length. This research enhances the current understanding of the operational safety of offshore wind turbines, particularly under extreme conditions. It aims to provide valuable insights and guidance for researchers and developers in designing and monitoring the performance of offshore wind turbines, ensuring their resilience and efficiency in challenging environments.

15 years of experience with the Triple Plane Pressure Mode Matching technique

The so-called Triple-Plane-Pressure-Mode-Matching technique (TPP for short) is a method used to isolate and quantify the acoustic part in numerical simulations of turbomachinery. Nowadays, simulations such as Harmonic Balance are commonly applied during the design phase of new turbomachinery components for both aeroacoustic and aeroelastic analyses. The TPP method was first published 20 years ago by Ovenden and Rienstra. The principle is to match the periodic pressure data from three or more neighbouring analysis planes with a subset of acoustic eigenmodes. The original method assumes that the flow in the channel section is potential so that the eigenmodes can be determined analytically. This approach can also be applied in slowly varying ducts. The TPP method is a powerful technique that is used at DLR and MTU Aero Engines. For nearly 15 years, constant joint efforts have been made to improve its applicability in industrial environment. Targeted applications are turbine stages, where the mean flow is complex and vortical wakes contaminate the results. In this paper, the latest developments of the method are presented, including the extension to curved extraction surfaces to enable its application to small blade-row spacing. The utility of the technique is illustrated by an industrial application.

Nonlinear unsteady aerodynamic forces prediction and aeroelastic analysis of wind-induced bridge response at multiple wind speeds: A deep learning-based reduced-order model

Machine learning-based aerodynamic reduced-order models (ROMs) combine high accuracy with extremely low computational costs, making them highly effective in predicting nonlinear and unsteady bridge aerodynamic forces. Although several machine learning-based nonlinear aerodynamic models have been developed, the majority are built on a single wind speed parameter. However, in nonlinear aerodynamic prediction and aeroelastic analysis of bridges, the variability in incoming wind speed significantly influences the computed results. A ROM relying solely on a single wind speed lacks the ability to accurately forecast the intricate dynamic behaviors arising from changes in wind speed. When the incoming wind speed changes, the model's prediction accuracy significantly decreases. Usually, it is necessary to establish a new database and train a new model, which not only increases time and cost but also greatly reduces the convenience of the ROM. Addressing this challenge, this study proposes a multiple-wind-speed (MWS) nonlinear unsteady bridge aerodynamic model based on the LSTM deep neural network. Taking the Taohuayu Yellow River Bridge in the Henan Province of China as an example, the modeling process of the proposed MWS-ROM is demonstrated, along with non-linear aerodynamic predictions of the deck under various conditions and aerodynamic-elastic analysis of the deck under different wind speeds. The research results show that the trained LSTM network can accurately predict the nonlinear aerodynamic forces of bridges under single and double degrees of freedom vibration conditions. The MWS-ROM performed well in predicting convergent vibrations at low wind speeds and limits cycle oscillations at high wind speeds, aligning closely with results from the CFD full-order model. Compared to CFD, the aerodynamic ROM based on the LSTM network significantly enhances computational efficiency, consequently boosting the convenience and efficiency of bridge flutter analysis. Additionally, the methodology proposed herein can be extended for wind-induced vibration control and response prediction in other types of deck sections.

Aerostructural Analysis of a Deployable Aeroshell in Transonic Flow

The deployable aeroshell, a contemporary reentry system, utilizes a thin flexible membrane surface sustained by pressurized gas to efficiently decelerate a reentry vehicle at high altitudes while enabling low-ballistic-coefficient flight. When an in-flight aerodynamic force is applied, the membrane structure undergoes large deformation that may affect its performance. Hence, a coupled analysis that considers the feedback effect of structural deformation is essential for accurately predicting the behavior of such reentry vehicles. In this study, a numerical framework for coupled aeroelastic analysis was constructed in a partitioned manner using open-source software to elucidate the combined effect of structural deformation and compressible flow dynamics and characterize the aerodynamic performance of reentry vehicles with inflatable structures. The results revealed that the membrane surface was deformed elastically by the aerodynamic force owing to the large difference in pressure distribution between the front and back of the aeroshell. Fluctuating behavior was observed in the aerodynamic coefficients owing to the small-amplitude oscillation of the capsule. This oscillation was induced by the large wake behind the vehicle. Several wrinkles and concave-shaped depressions formed on the membrane surface, which exhibited a circumferential movement tendency with time.

Efficient multi-fidelity reduced-order modeling for nonlinear flutter prediction

Flutter prediction is an important part of aircraft design. However, high-fidelity predictions for transonic flutter are difficult to make because of the associated computational costs. This paper proposes a multi-fidelity reduced-order modeling (MFROM) framework for flutter predictions to achieve high-fidelity simulations with limited computational costs. The high-fidelity data were obtained from a Navier–Stokes-equation-based solver, while the low-fidelity data were taken from an Euler-equation-based flow solver. By employing a multi-fidelity neural network trained with two types of data, this methodology enables nonlinear predictions for transonic results. To demonstrate the multi-fidelity process, a widely used pitching and plunging airfoil case is considered. Verification of the approach was performed by comparing with results from time-domain aeroelastic solvers. The results showed that the proposed multi-fidelity neural network modeling framework could realize online predictions of unsteady aerodynamic forces and flutter responses across multiple Mach numbers. Compared with the typical multi-fidelity method, the proposed neural network has a higher accuracy and a stronger generalization capability. Finally, the potential of the method to reduce the computational effort of high-fidelity aeroelastic analysis was demonstrated.

Modelling and analysis of two-dimensional static and dynamic aeroelasticity of Fish Bone Active Camber morphing aerofoils

As a continuous and smooth morphing concept for aerofoils, the Fish Bone Active Camber (FishBAC) concept has demonstrated significant aerodynamic efficiency improvements over traditional hinged flaps. In this paper, to investigate the static and dynamic aeroelasticity of FishBAC aerofoils, an unsteady two dimensional coupled fluid-structure interaction model is developed, which includes the structural response of the FishBAC spine, skin, stringers, tendons and actuator, coupled to an unsteady aerodynamics model. The structural dynamic model is Timoshenko beam-theory-based, while the aerodynamic model is based on Peters’ unsteady model. The static and dynamic aeroelasticity is studied after the model is validated. Results show that the increase in pulley rotational angle reduces the zero-lift angle of attack, while keeping the slope between the lift coefficient and angle of attack the same. A shorter morphing region closer to the trailing edge is beneficial for generating larger lift coefficient with the same tendon moment and angle of attack. Flutter occurs with the increase of the air speed. When the morphing end position is fixed at 0.9 chord, increasing the morphing length reduces the critical flutter speed significantly, with the second bending mode tending to drive instability. With the same morphing length, moving the morphing region closer to the leading edge increases the critical flutter speed, and the unstable mode changes from the second mode into the first mode.

A Jacobi-Ritz Approach for Aeroelastic Analysis of Swept Distributed Propulsion Aircraft Wing

Abstract This paper presents a Jacobi-Ritz approach for conducting flutter and divergence analysis of a complex distributed propulsion aircraft wing like NASA X-57. The general orthogonal Jacobi polynomials are used to approximate the bending displacement and torsional rotation angle in the Ritz method based structural and aeroelastic analysis. The Jacobi polynomials satisfy the orthogonality condition using weight functions which are easily modified to satisfy different essential and natural boundary conditions. Compared to simple polynomials, Jacobi polynomials can eliminate the well-known ill-conditioning numerical issues when considering higher-order polynomials. The Jacobi-Ritz method is also found to alleviate mode switching often encountered in tracking the changes of modes with the varying airspeed. The Jacobi-Ritz method is later used to investigate the flutter and divergence speeds under distributed propulsor mass and their locations, nonuniform aerodynamic model in the presence of multiple propulsors, and the sweep angle. Results show that placing the distributed propulsors on the wing's leading edge increases the flutter speed even though the bending and torsion modal frequencies are decreased compared to those of the wing without propulsors. The presence of pods for the middle high-lift motors causes an extra aerodynamic moment which reduces the flutter speed. Parametric studies also show that the divergence speed is lower than the flutter speed for a uniform and straight distributed propulsor wing. Using swept-back wing configuration and placing the tip propulsor near the wing's leading edge can help to increase both flutter and divergence speeds.

High-fidelity fluid-structure interaction applied to static aeroelasticity in transonic flows

Transonic flows at high Reynolds numbers can lead to high dynamic pressures and, consequently, to aerostructural deflections of aircraft structures. This study aims to develop and validate a high-fidelity static aeroelastic analysis environment that is efficient and that can be used in an industrial setting. The aerodynamics is represented by numerical solutions of the Reynolds-averaged Navier-Stokes equations with appropriate turbulence closures. The load transfer process uses finite element shape functions in order to distribute the aerodynamic loads into the structural discretization. The structural analysis employs a modal basis approach, and a wingtip deflection convergence study is performed to find an adequate modal basis size. Radial basis functions are used for the fluid mesh displacement, and the influence of the support radius is evaluated to determine the optimal values relative to the wing mean aerodynamic chord. The capability is tested using the static aeroelastic benchmarks of the High Reynolds Aerostructural Dynamics Project (HIRENASD) and NASA's Common Research Model (CRM). The static aeroelastic results demonstrate robustness and consistency for the aerodynamic coefficients, pressure distributions, and structural deflection predictions at different normalized dynamic pressure values and grid refinement levels.

Data-driven aeroelastic analyses of structures in turbulent wind conditions using enhanced Gaussian Processes with aerodynamic priors

Recent advancements in data-driven aeroelasticity have been driven by the wealth of data available in the wind engineering practice, especially in modeling aerodynamic forces. Despite progress, challenges persist in addressing free-stream turbulence and incorporating physics knowledge into data-driven aerodynamic force models. This paper presents a hybrid Gaussian Process (GPs) methodology for non-linear modeling of aerodynamic forces induced by gusts and motion on bluff bodies. Building on a recently developed GP model of the motion-induced forces, we formulate a hybrid GP aerodynamic force model that incorporates both gust- and motion-induced angles of attack as exogenous inputs, alongside a semi-analytical quasi-steady (QS) model as a physics-based prior knowledge. In this manner, the GP model incorporates the absent physics of the QS model, and the non-dimensional hybrid formulation enhances its appeal from an aerodynamic perspective. We devise a training procedure that leverages simultaneous input signals of gust angles, based on random free-stream turbulence, and motion angles, based on random broadband signals. We verify the methodology through analytical linear aerodynamics of a flat plate and non-linear aerodynamics of a bridge deck using Computational Fluid Dynamics (CFD). The standout feature of the presented methodology is its applicability for aeroelastic buffeting analyses, showcasing robustness when handling broadband excitation. Importantly, the non-linear hybrid model preserves its capability to capture higher-order harmonics in the motion-induced forces and remains applicable for flutter analysis, while incorporating both motion and gust angles as input. Applications of the methodology are anticipated in the aeroelastic analysis and monitoring of slender line-like structures.

Reliability based optimisation of composite plates under aeroelastic constraints via adapted surrogate modelling and genetic algorithms

Composite materials are vital in aerospace for their exceptional strength-to-weight ratio. This study delves into reliability-based optimisation of composite plates within aeroelastic constraints, employing an efficient global optimisation method and genetic algorithms. Initial analysis focuses on aeroelastic responses such as limit flutter speed, gust response, and static loads, emphasising maximum strain assessment. To tackle optimisation challenges of composite stacking sequences, a homogenisation technique with lamination parameters is applied. We then formulate a constrained optimisation problem to minimise gust response while meeting flutter and maximum strain constraints. Surrogate models based on conditioned Gaussian Processes are developed for each aeroelastic response, facilitating optimisation within the composite design space. These models, with potential for local refinement, expedite optimal solution identification. Further, we integrate reliability-based optimisation into the framework to determine a robust stacking sequence using genetic algorithms, accounting for random fibre orientation variations. This holistic approach integrates aeroelastic analysis, constrained optimisation, surrogate modelling, and reliability-based optimisation, proving effective in designing reliable, efficient composite structures for aerospace, thus enhancing performance and safety.

Time-Varying Aeroelastic Modeling and Analysis for a Morphing Wing

The paper presents a novel time-varying aeroelastic modeling approach for the morphing wing with the process of camber changing. The time-varying modeling methodology includes structural dynamics modeling, unsteady aerodynamic modeling, and interpolation for fluid–structure coupling. Firstly, the morphing wing is modularized and divided into fixed and variable parts by the floating frame of reference formulation. It is combined with the Craig–Bampton method to reduce order and eliminate nonindependent degrees of freedom. Then, the unsteady vortex-lattice method is used to calculate the transient, unsteady aerodynamic force for time evolution. Furthermore, the above time-varying structural dynamics modeling and a fluid–structure coupling interpolation are integrated to construct overall aeroelastic modeling, obtaining a set of differential-algebraic equations. Finally, these equations are numerically solved by the generalized-α method. The proposed approach provides an innovative idea to deal with the incredible complexity of the aeroelastic effect as structural characteristics change over time. It can efficiently and accurately analyze the morphing wing’s transient response or flutter property. To verify and utilize the time-varying aeroelastic modeling approach, numerical calculations and comparative studies were carried out regarding the time-varying characteristics of the structural modes, aerodynamic calculations, and flutter prediction of the morphing wing.

Vibration and aeroelastic instability analysis in GPL-porous multi-layered beam with the rotation effect

This research studies the vibrations and instability of a rotating three-layer beam under aerodynamic forces consisting of two functionally graded (FG) composite surfaces and a porous intermediate layer. Linear poroelasticity theory is used for modeling the porous layer while Young’s modulus and density vary along the thickness. Equivalent coefficients of the graphene nanoplatelets-reinforced composite (GPLs) are extracted by modified Halpin-Tsai theory, according to five different configurations. The equations of motion in the GPL-porous multi-layered beam are derived using the Euler–Bernoulli beam (EBB), Timoshenko beam (TB), and Reddy’s higher-order shear deformation theory (HSDT) theories, as well as the energy method and Hamilton’s principle. The most important results show the effect of reinforcements and their different configurations, porosity and its distribution, speed of rotation on natural frequency, critical flutter point, and loss factor for a GPL-porous multi-layered beam. The unique properties of GPL-reinforced porous materials facilitate the design of components capable of effectively managing dynamic loads and resisting aeroelastic instabilities. This results in more efficient, reliable, and durable systems across various industries.

Investigation of Static Aeroelastic Analysis and Flutter Characterization of a Slender Straight Wing

Investigation of Static Aeroelastic Analysis and Flutter Characterization of a Slender Straight Wing

Aeroelastic analysis using confocal sensors: experimental study and numerical validation with application to a future particle detector

This study investigates the structural displacements induced by aerodynamic loads in a future particle detector at the Large Hadron Collider (LHC): the Inner Tracking System 3 (ITS3) of the ALICE experiment. The development of an ultralight structure and use of air cooling lead to an unprecedentedly low material budget, resulting in improved accuracy compared to the current detector (ITS2). The airflow applied to the low-mass structure of the ITS3 is expected to cause vibrations, which requires an aeroelastic analysis that is performed using experimental and numerical methods. A novel experimental approach is proposed using confocal chromatic sensors to measure the structural displacements of an ITS3 prototype with submicron accuracy. A simplified mathematical model is developed for the fluid-structure interaction. The results obtained in the experimental setup show that the numerical model predicts the primary peaks in the spectrum of structural displacements induced by airflow. The validated model is used to analyze both the real anticipated configuration of the future ITS3 setup and potential modifications arising from changes in detector cooling and installation requirements.

Floating wind turbine stability and time response analysis with rotating modes

The periodic azimuthal time dependence of a linearized simple floating wind turbine model with four degrees of freedom is dealt with by developing a particular procedure that enables a stability analysis calculation and reduces computational efforts to calculate time responses. We apply Hill’s method for the aeroelastic stability analysis by generating a constant state-space hyper-matrix that takes into account the periodic azimuthal dependence of the system. It is used to compute precisely the time domain response and to solve an overall eigenvalue problem where natural frequency and modal damping are determined through the eigenvalues. For a varying rotational speed with a fixed air density, eigenfrequencies from Hill’s method are displayed on a Campbell diagram that is based on a waterfall plot of the frequencies obtained by decay tests peaks using the time domain model. Through the modal analysis as well, an investigation of the impact of aerodynamic damping is done following the same procedures by rather fixing the rotational speed and varying air density. In the end, a forcing moment of the platform pitch motion is added to analyze the accuracy of fast time response calculations compared to the time domain model benchmark results.

Aeroelastic analysis of a very large wind turbine in various atmospheric stability conditions

With the growing trend towards larger wind turbine rotor diameters, the impact of wind shear on rotor performance and loads becomes increasingly significant. Atmospheric stability strongly influences wind shear, leading to higher wind shear under stable atmospheric conditions. In this study, the aeroelastic performance of the IEA 22 MW rotor is assessed under inflow conditions generated by different methods. Inflow conditions were generated using turbulence models specified in the IEC Standards and also by Large Eddy simulations. Standalone OpenFAST simulations were conducted with the respective inflow conditions.It was found that at rated and above-rated wind speeds, the time-averaged wind turbine design loads were higher in stable atmospheric conditions, in comparison to the IEC NTM inflow conditions, while the opposite held for below-rated wind speeds. Specifically, the time-averaged root flapwise bending moment and rotor thrust were found to be higher by up to 7% in stable atmospheres. However, maximum design and fatigue loads were considerably higher in the IEC NTM case due to elevated turbulence levels. Compared to the IEC NTM case, the damage equivalent root flapwise bending moment was found to be 30% to 70% lower in the different scenarios.

Numerical investigation of vortex induced vibrations on cylinders

The paper addresses Vortex Induced Vibrations (VIV) caused by tower vortex shedding through LES simulations of a wind tunnel experiment. A high-fidelity (HiFi), Fluid Structure Interaction (FSI) framework for aeroelastic analysis of 3D flexible cylinders is established, based on the open-source Computational Fluid Dynamics (CFD) code OpenFOAM and the coupling library preCICE. In the present study, the FSI framework is employed with the aim to replicate a low Reynolds (Re=26000) forced vibrations wind tunnel experiment of a circular cross-section rigid cylinder. The paper compares predictions of the aerodynamic damping of the oscillating cylinder for different oscillation frequencies within the lock-in range and amplitudes against experimental results. While the model consistently predicts the lock-in range of frequencies and the trends in the variation of the aerodynamic damping with the oscillation amplitude, it falls short of accurately capturing the maximum value of the aerodynamic damping at the onset of lock-in.

Multimodal aeroelastic analysis of suspension bridges with aerostatic nonlinearities

Multimodal aeroelastic analysis of suspension bridges with aerostatic nonlinearities