Aeroelastic Design Research Articles

Experimental Investigations on Aeroelastic Stability of Combined Plunge-Pitch Mode Shapes in a Linear Compressor Cascade

Abstract The effect of mode shape and reduced frequency on the flutter stability of a linear low-speed compressor cascade was investigated experimentally, employing the aerodynamic influence coefficient (AIC) approach. This paper describes in detail the methodology, experimental setup, and measurement techniques. The paper presents experimentally determined influence coefficients, and discusses the findings with regard to the aeroelastic design parameter “plunge-to-twist incidence ratio” (PTIR), which combines reduced frequency and torsion axis setback in an attempt a design variable reduction. The influence of the vibrating blade on itself was always stabilizing, while other blades, mainly the first pressure side neighbor, vibrating at forward-traveling, low nodal diameter inter-blade phase angles (IBPAs), can destabilize the reference blade. As PTIR is increased, the phase of the complex modal force coefficients (AICs) of all blades is decreased, increasing the stabilizing effect of the vibrating blade on itself and overall cascade stability. Within the considered parameter range, the impact of reduced frequency is eliminated to a large extent if the incidence ratio is kept constant, requiring the torsion axis setback to be adjusted accordingly. The findings show that the plunge-to-twist incidence ratio is a meaningful aeroelastic design parameter that can explain the global effect of mode shape on flutter stability and should be considered early in the aeromechanical blade design process to ensure flutter-free blading.

Flutter Characteristics of a Modified Z-Shaped Folding Wing Using a New Non-Intrusive Model

Unmanned aerial vehicles (UAVs) with folding wings can serve in multiple mission profiles, usually accompanied by sudden changes in flight speed. These bring great challenges to the aeroelastic design of UAVs, especially in the calculation of flutter characteristics. This paper developed a new non-intrusive aeroelastic model to quickly calculate the flutter characteristics of Z-shaped folding wings at different folding angles. First, the original Z-shaped folding wing was designed to be enhanced. Beams and ribs were arranged inside each wing segment to enhance the structural strength performance. Control surfaces were arranged in the middle-wing and outer-wing to enhance the aerodynamic control performance. Second, a parametric aeroelastic model at any folding angle was reconstructed based on the input file of Nastran software for the flutter calculation of the folding wing in the unfolded state. Finally, the effects of parameters such as folding angle, hinge stiffness between different wing segments, and hinge stiffness of the control surfaces on the flutter characteristics of the folding wing were investigated. The results show that the enhancement scheme could significantly increase the flutter speed and flutter frequency of the folding wing. The hinge stiffness between each wing segment had a significant impact on the flutter characteristics of the folding wing, but flutter at the control surface basically did not occur.

Numerical Analysis of Free Play-Induced Aeroelastic Phenomena: A Numerical Approach With Adaptive Step Size Control

This study presents a detailed numerical analysis of nonlinear aeroelastic behavior in a two degree of freedom (DOF) model, focusing on plunge and pitch motions and employing the continuation method (CM) with an adaptive step size control algorithm. The research incorporates free-play nonlinearity at the plunge hinge, a common structural nonlinearity in aeronautics that can induce detrimental limit cycle oscillations (LCOs) during flight. By examining three scenarios—linear response, unhindered plunge motion, and nonlinear stiffness behavior—the study assesses the effects of free play on flutter and LCO phenomena, including discontinuity-induced bifurcations like grazing bifurcation. Additionally, the study explores parameter variation for nonlinear flutter analysis, revealing the dynamics of grazing bifurcation and its impact on LCO behavior. The research also demonstrates the method’s superior accuracy in flutter speed estimation and mode-switching identification, despite higher computational demands. The findings underscore the diminishing influence of nonlinear free-play behavior on LCO amplitude, providing insights with significant implications for aeroelastic design and aircraft safety.

Multi-Objective Aerodynamic and Aeroelastic Coupled Design Optimization Using a Full Viscosity Discrete Adjoint Harmonic Balance Method

Abstract With increasing requirements for high-loading and high-efficiency turbomachines, blades become thinner and thinner and thus design optimizations considering both aerodynamic performances and aeroelastic stability become more and more necessary. In this study, a full viscosity discrete adjoint harmonic balance solver has been developed using algorithmic differentiation (AD), verified by a discrete linear solver based upon duality property, and then adopted to perform multi-disciplinary coupled design optimizations. To this end, a framework of multi-objective adjoint design optimizations has been developed to improve both aerodynamic performances and the aeroelastic stability of turbomachinery blades. This framework is divided into two steps: aeroelastic design initialization and aerodynamic Pareto front determination. First, the blade profiles are optimized to improve the aeroelastic stability only and constrain the variations of aerodynamic performances. Second, the optimized blade profiles in the first step are used as the initial ones and then further optimized with the objective function of aerodynamic parameters and the constraints of aeroelastic parameters. The effectiveness of the multi-objective design optimization method is demonstrated by comparing the optimization results with those from a single-objective aerodynamic and aeroelastic coupled design optimization method. The results from the transonic NASA Rotor 67 subjected to a hypothetical vibration mode show that the multi-objective coupled design optimization method is capable of improving performances in both disciplines.

Integrated flutter test of a horizontal-tail model in the large-scale continuous transonic wind tunnel

Wind tunnel test is a critical way to investigate flutter characteristics of aircraft, particularly in identifying the transonic dip phenomenon in the aeroelastic design. The continuous wind tunnel has advantages over the blow-down wind tunnel in long running time, wide bandwidth of dynamic pressure, and stable flow field. Thus, the continuous wind tunnel is more suitable for transonic flutter tests. Flutter test techniques are studied for FL-62 wind tunnel, the first large-scale continuous transonic wind tunnel in China. A protection system and a real-time signal processing are developed to ensure the safety and efficiency. Flutter boundaries of a horizontal-tail model are investigated in FL-62 wind tunnel in the Mach number regime between 0.65 and 0.98. In the test, structural vibrations are measured via strain gauges, deformations and pressure distributions are measured via non-contact optical techniques, and flutter boundaries are predicted via a modal identification method.

Functional Hazard Assessment of a Modular Re-Configurable Morphing Wing Using Taguchi and Finite Element Methodologies

Growing concerns over the CO2 footprint due the exponential demand of the aviation industry, along with the requirements for high aerodynamic performance, cost saving, and manoeuvrability during different phases of a flight, pave the path towards adaptable wing design. Morphing wing design encompasses most, if not all, of the flight condition variations, and can respond interactively. However, functional failure of the morphing wing might bring devastating impacts on the passengers, crew, and/or aircraft. In the present work, the dynamic characteristics of a re-configurable modular morphing wing developed in-house by a research group at the Toronto Metropolitan University, are investigated from the perspective of a functional hazard assessment (FHA). This modular morphing wing, developed based on the idea of a parallel robot, consists of a number of structural elements connected to each other and to the wing ribs through eye-bolt joints. Timoshenko’s bending beam theory, in conjunction with the finite element method (FEM), is exploited to model the structural members. Possible hazards, assumed here to be the structural failure of the beam components, have been identified and their failure conditions are assessed. Numerical simulations have been presented to show the impact of various combinations of the identified hazards on the vibration signature of the morphing wing in unmorphed and morphed configurations. Identification of changes in the wing’s vibration signature is a vital component in the fail-safe structural and aeroelastic design of an aircraft. The present study is geared towards the structural response of the system in the absence of any aerodynamic loads.

A numerical investigation on direct and data-driven flutter prediction methods

Three alternative algorithms for dynamic aeroelastic stability analysis are investigated. They are based either on direct search of oscillatory conditions of the coupled system or on eigenvalue analysis from frequency-domain sampling of the unsteady aerodynamics. The aerodynamic forcing is obtained with a harmonic-balanced solver developed for a general-purpose finite-volume fluid dynamics solver. This new implementation is first verified against experimental flutter results from the literature. A wing with relatively low bending stiffness is then used to explore the relative performance of each approach, both in terms of the numerical robustness and of their usability to support aeroelastic design.

Nonlinear aeroelastic analysis and active flutter control of functionally graded piezoelectric material plate

The nonlinear aeroelastic characteristics and active flutter control of functionally graded piezoelectric material (FGPM) plate under thermo-electro-mechanical loads are studied. An analytical model is developed to explore the nonlinear aeroelastic behaviors of the supersonic FGPM plate, in which the nonlinear effects caused by geometry, aerodynamic force and piezoelectric effect are considered. Based on power law and sigmoid distribution, an improved sigmoid distribution is proposed for the aeroelastic design of the FGPM plate. Numerical examples are carried out to demonstrate that material volume fraction and gradient distribution can significantly affect flutter and thermal buckling of the FGPM plate. Additionally, the effects of thermal and electric loads on limit cycle oscillations and dynamic bifurcations of nonlinear FGPM plate are explored. Results indicate that the applied voltage can cause the static deflection of the plate and the thermal load can result in a more complex dynamic evolution process, and they reveal the competition mechanism of mechanical instabilities of the FGPM plate. Furthermore, the active flutter control of FGPM plate based on displacement feedback, actuated by FGPM plate itself, is carried for improving the aeroelastic stability of the system. The influence factors of active control are explored through parameter analysis, and results show that the volume fraction of piezoelectric material and thermal loads can significantly affect the active control effect. The present work demonstrates that the flutter stability of the FGPM plate can be improved by optimization of the material distribution and self-actuated active control.

A framework for the bi-level optimization of a generic transport aircraft fuselage using aeroelastic loads

The aeroelastic loads and design processes at the German Aerospace Center, Institute of Aeroelasticity in the framework of multi-disciplinary optimization are constantly evolving. New developments have been made in the in-house model generation tool ModGen, which allow us to create detailed fuselage models for preliminary design. As a part of the subsequent developments to integrate the fuselage structure in our aeroelastic design process, a new framework for optimizing the fuselage structure has been developed. The process is based on a bi-level optimization approach which follows a global–local optimization methodology to simplify a large optimization problem. A sub-structuring procedure is used to define stiffened panels as independent structures for local optimization. The panels are sized with stress and buckling constraints with consideration of several aeroelastic load cases. Furthermore, in this paper, we present a physical sub-structure grouping process which enables reduced number of panel optimizations and saves considerable computational effort with little compromise in the solution accuracy.

Aeroelastic Design and Comprehensive Analysis of Composite Rotor Blades Through Cluster-Based Kriging

Excessive vibration during high-speed flights is a critical issue in modern rotorcraft. The aeroelastic design of the composite rotor blades can relieve the hub vibratory loads of the rotor that are a dominant source of these vibrations. However, it has many technical problems, such as a high-dimensional design space, narrow and discontinuous feasible regions, and highly nonlinear design indices. Although the surrogate-based design is known to improve the design results, the conventional surrogate models have an insufficient capacity to represent the nonlinearity of aeroelastic responses. Because the inaccuracy of the surrogate model is combined with the discontinuity of feasible regions during the optimization process, it is likely to converge to local optima. Cluster kriging could accurately represent the complicated physical relations using machine learning techniques, such as soft clustering and classification algorithms. The accurate surrogate model results in a global optimization with 56% vibration reduction, whereas the global approximation using a single kriging yields local optima with 39% vibration reduction. Furthermore, a comprehensive design analysis, conducted to investigate the underlying physics of the vibration reduction, confirms the global optimization. The proposed design method can fully use the multidisciplinary nature of aeroelastic responses, which is not considered in conventional design methods.

Experimental Investigation on the Mechanism of Impeller Synchronous and Nonsynchronous Vibrations in an Industrial Centrifugal Compressor

Abstract Understanding of the fluid–structure interaction phenomena in centrifugal compressors is essential for the impeller structural integrity design. To enhance the understanding of blade vibration in a realistic flow environment, a single-stage centrifugal compressor representative of industrial architecture has been investigated experimentally. For deterministic synchronous vibrations, the response amplitudes at different operating lines are measured and compared. The fundamental relations between flow excitation and rotor modal resonance are established by pairwise strain gages from experimental perspective. Compared with the third mode, the impeller first bending mode shows traveling wave response characteristic only within the frequency band where two adjacent blades have the same resonant frequency. Besides, the impeller encounters unexpected nonsynchronous vibrations when operating near the flow instability boundary. Speed ramp tests show that the stall cell propagating speed increases along with the rotor rotational speed without changing the cell count. Response amplification is further measured when throttling the compressor into stall. Experimental findings point toward vaned diffuser rotating stall and the corresponding propagating pressure waves in circumference leads to the impeller vibration. The aerodynamic asymmetry of stall cells increases the possibility of aeroelastic coupling with the blade modes. These results contribute to an in-depth understanding of the aeroelastic phenomena in industrial centrifugal compressors. The observed nonsynchronous vibration is important for the aeroelastic design and also of great interest for numerical predictions near stall.

An engineering modification to the blade element momentum method for floating wind turbines

The design of next-generation offshore wind rotors for floating applications carries large uncertainties that make it harder to bring costs down. A significant share of this uncertainty is associated with the use of Blade Element Momentum (BEM) methods to run aeroelastic design and loadcase calculations, because the assumptions underlying the momentum theory are violated by the floater motion. This work presents an engineering method for BEM that allows to model generic floater motions and improves the aerodynamic modelling of floating wind turbines. The new model overcomes the challenge of estimating the apparent wind caused by the platform motion in a simple way, which proves to be very effective for rigid aerodynamic simulations. To verify its impact, BEM results with and without the proposed correction are compared to high-fidelity free vortex wake simulations, imposing the same harmonic motion first to the pitch and then to the yaw degree of freedom of the platform. While little differences are found for the yaw motion, the new floating model clearly improves predictions for the platform pitch case in terms of both aerodynamic loads and induction, finding a very good match with the high-fidelity results. An analysis of the verification data provides new valuable insights on the effect of these motions on aerodynamic loads and performance of a floating wind turbine.

Multi-Fidelity Gradient-Based Optimization for High-Dimensional Aeroelastic Configurations

The simultaneous optimization of aircraft shape and internal structural size for transonic flight is excessively costly. The analysis of the governing physics is expensive, in particular for highly flexible aircraft, and the search for optima using analysis samples can scale poorly with design space size. This paper has a two-fold purpose targeting the scalable reduction of analysis sampling. First, a new algorithm is explored for computing design derivatives by analytically linking objective definition, geometry differentiation, mesh construction, and analysis. The analytic computation of design derivatives enables the accurate use of more efficient gradient-based optimization methods. Second, the scalability of a multi-fidelity algorithm is assessed for optimization in high dimensions. This method leverages a multi-fidelity model during the optimization line search for further reduction of sampling costs. The multi-fidelity optimization is demonstrated for cases of aerodynamic and aeroelastic design considering both shape and structural sizing separately and in combination with design spaces ranging from 17 to 321 variables, which would be infeasible using typical, surrogate-based methods. The multi-fidelity optimization consistently led to a reduction in high-fidelity evaluations compared to single-fidelity optimization for the aerodynamic shape problems, but frequently resulted in a cost penalty for cases involving structural sizing. While the multi-fidelity optimizer was successfully applied to problems with hundreds of variables, the results underscore the importance of accurately computing gradients and motivate the extension of the approach to constrained optimization methods.

Effects of fiber properties on aerodynamic performance and structural sizing of composite aircraft wings

An advanced carbon fiber is expected to reduce the structural weight of a composite aircraft. Historically, various studies on composite aircraft designs have focused on the challenge to utilize the anisotropy of unidirectional laminates. However, there is still a research interest to consider the impact of changing the fibers for their positive influence on the structural weight and performances of a composite aircraft. In this study, the effects of fiber properties on the static aeroelastic design of aircraft wings were investigated using a multi-scale framework and two-way coupled aeroelastic analysis with structural sizing. The fibers analyzed were T700S, T800S, and T1100G, which have different stiffnesses and strengths. The design analysis was performed under two scenarios: fixing the angle of attack and fixing the lift while changing the angle of attack in the flow condition. The results from the former case indicate that the choice of fiber did not significantly affect the entire shape of the drag polar, while the highest lift coefficient was obtained with the stiffest fiber, T1100G, under the same angle of attack. The results from the latter case indicate that using T1100G can reduce the structural weight by 9.9% and 14% at the same lift compared to T800S and T700S, respectively, owing to its high buckling resistance and high tensile strength, rather than compressive strength.

Aerostructural topology optimization using high fidelity modeling

We investigate the use of density-based topology optimization for the aeroelastic design of very flexible wings. This is achieved with a Reynolds-averaged Navier–Stokes finite volume solver, coupled to a geometrically nonlinear finite element structural solver, to simulate the large-displacement fluid-structure interaction. A gradient-based approach is used with derivatives obtained via a coupled adjoint solver based on algorithmic differentiation. In the example problem, the optimization uses strong coupling effects and the internal topology of the wing to allow mass reduction while maintaining the lift. We also propose a method to accelerate the convergence of the optimization to discrete topologies, which partially mitigates the computational expense of high-fidelity modeling approaches.

Aero-structural optimization-based tailoring of bridge deck geometry

The deck cross-section is usually identified in engineering practice as the most important design variable in the wind-resistant design of long-span bridges. This is certainly true in most cases since it controls the aerodynamic and mechanical contribution of the deck to the global bridge performance. However, the effectiveness of deck shape modifications to handle the aeroelastic constraints is highly influenced by the aeroelastic performance requirements. This paper seeks to delve into the aero-structural design optimization of long-span bridges by analyzing possible design scenarios depending on the ability of the deck shape to meet the imposed aeroelastic requirements. A long-span cable-stayed bridge is optimized focusing on the buffeting response and considering different sets of limit values for the design constraints. According to the effectiveness of the deck shape design variables and other size design variables to manage the aeroelastic design constraints, three types of aero-structural optimization problems are identified: type I, aeroelastic constraints are not active and structural constraints drive the design; type II, aeroelastic constraints are active and effectively controlled by deck shape modifications; and type III, aeroelastic constraints are active and demand both shape and size modifications. The engineering significance for practical design is discussed.

Aeroelastic Optimization Design of the Global Stiffness for a Joined Wing Aircraft

Due to the complexity and particularity of the joined wing layout, traditional design methods for the global stiffness of a high-aspect wing are not applicable for a joined wing. Herein, a beam-frame model and a three-dimensional wing-box model are built to solve the global stiffness aeroelastic optimization design problem for a joined wing. The goal is to minimize the weight, and the constraints are the overall aeroelastic requirements. Based on a genetic algorithm, two methods for the beam-frame model and one method for the three-dimensional model are used for comparative analysis. The results show that the optimization method for a diagonal beam section and the optimization method for an exponential/linear combination function fit are adequate for optimizing and designating the joined wing global stiffness. The distributions obtained using the two methods have good consistency and are similar to the distribution of the three-dimensional model. The stiffness distribution data and the beam section parameters can be converted from each other, which is convenient for redesigning the structure parameters using the stiffness distribution data, and is valuable for engineering applications.

The effect of elastic couplings and material uncertainties on the flutter of composite high aspect ratio wings

In this paper, the stochastic aeroelastic stability analysis of a composite high aspect ratio wing with various elastic couplings is investigated. The wing consists of a rectangular spar-box made from composite materials. Due to its high aspect ratio, the wing structure is modelled using the exact beam formulation, and the aerodynamic loads acting on the wing are simulated using an unsteady lifting line theory. A composite spar-box cross section is considered, and the effect of various effective parameters on the aeroelastic stability of the wing is studied. First, a baseline composite wing is designed and the effect of three different elastic couplings on the stability of the wing is determined. These three elastic couplings that affect the aeroelastic design of the composite wing are the out-of-plane (flap)-twist, the in-plane (lag)-twist and the extension-twist. Furthermore, the effect of uniformly distributed load on the aeroelastic stability of the wing is assessed for various layups. Finally, the effect of material uncertainties on the aeroelastic stability of the composite wing with various couplings is studied. It is observed that the type of elastic coupling has a significant effect on the sensitivity of the flutter speed and frequency of the composite wing due to the randomness of the material properties. In particular, the aeroelastic behaviour of the wing with lag-twist coupling is more sensitive to the material uncertainties than other two layups.

Tropical-cyclone-wind-induced flutter failure analysis of long-span bridges

Continuously growing number and span length of long-span bridges in coastal region of China require a robust aeroelastic design to against the tropical-cyclone (TC) -induced flutter instability. Instead of using the deterministic approach, this study presents a Monte-Carlo-technique-based framework to analyze the flutter reliability of a long-span suspension bridge subjected to TC winds. A limit state function formulated as the difference between the flutter capacity and the extreme gust wind, termed as the product of a random gust factor and the TC mean wind hazard is employed. The flutter fragility curve in terms of the critical wind speed is derived using 2D and 3D flutter analysis models accounting for the structural modal and damping randomness as well as experiment-induced errors of aeroelastic flutter derivatives. The TC wind hazard curves at the height of the bridge deck described as the probability of exceedance at any given years of interest versus the extreme 10-min mean wind speed are estimated through generating a large quantity of synthetic tracks around the bridge site. The probabilistic solutions of the gust factor associated with any gust duration of interest are determined utilizing the statistics of observed TCs coupled with a theoretical model. The TC-induced flutter failure probabilities of present bridge are then predicted in different combinations of gust duration, surface roughness length and flutter analysis models, which enables the assessment of flutter risk subjected to TC winds as compared to code-suggested target reliability indices. The present reliability analysis provides some basic information to assist and enhance the flutter-resistant design of long-span bridges due to TC winds during the preliminary stage.

Aeroelastic Behavior of Two Airfoils in Proximity

This paper investigates the aeroelastic behavior of elastically supported airfoils due to structural and aerodynamic coupling effects between them in an incompressible uniform flow. The flow is modeled based on a potential theory for thick and thin airfoils considering the coupled interference effect. Coupled aeroelastic equations of motion are formulated in a state-space form and solved explicitly using a predictor–corrector scheme. The numerical analyses are presented for airfoils in proximity with and without structural coupling. It is shown that the airfoils in proximity oscillate out of the phase and destabilized the airfoils at lower speeds. The closer the airfoils are, the lower the speed at which flutter instability occurs. Also, the interference effect becomes more significant on reducing the flutter speed for thick airfoils in proximity. For structurally coupled airfoils, the flutter instability occurs at lower speeds for the lower coupling stiffness value. It is further worsened in the presence of aerodynamic interference. Although, for a larger stiffness value, the flutter instability could be delayed in the presence of aerodynamic interference. This study finds that the lifting surfaces in proximity without structural coupling can become unfavorable in the aeroelastic design. The results provide preliminary insights into the coupled structural and aerodynamic interference effects on the flutter instability for a multiple lifting surface configuration.