Unsteady Aerodynamic Model Research Articles

Nonlinear Aeroelastic Analysis of Bending-Torsion Wings Subjected to a Transverse Follower Force

This paper deals with the nonlinear aeroelastic behaviors of bending-torsion wings subjected to a transverse follower force. The nonlinear structural wing formulation is based on von Karman large deformation theory. In order to accurately consider the spanwise location of the follower force, the generalized function theory is used. Also, Peter’s finite-state unsteady aerodynamic model is considered. The governing equations are obtained using Hamilton’s principle. Furthermore, the Galerkin method is applied to convert the partial differential equations into a set of nonlinear ordinary differential equations, which will be solved through the numerical integration scheme. Wing dynamic behaviors are investigated through frequency spectra and the bifurcation diagrams of Poincaré maps. In addition, the postcritical region, which includes all periodic, quasiperiodic, and chaotic pockets, is indeed found to exist. Furthermore, the results indicate noticeable effects of the follower force magnitude and location as well as the air stream velocity on critical and postcritical behaviors of a wing.

A Review of the Research on Blade Flutter in Turbomachinery

Aeroelastic stability in the form of blade flutter is a major concern for designers in the field of turbomachinery. This paper presents a review of the research and development on blade flutter models, including unsteady aerodynamic modeling, structural modeling and flutter prediction methods. Based on the introduction of these models, the fundamental mechanism and effects of different treatments are discussed. In the end, some questions about the research of flutter and the works about fluid-solid coupling model are pointed out, which should be paid attention to in future.

Modeling and Analysis of Piezoelectric Energy Harvesting From Aeroelastic Vibrations Using the Doublet-Lattice Method

Multifunctional structures are pointed out as an important technology for the design of aircraft with volume, mass, and energy source limitations such as unmanned air vehicles (UAVs) and micro air vehicles (MAVs). In addition to its primary function of bearing aerodynamic loads, the wing/spar structure of an UAV or a MAV with embedded piezoceramics can provide an extra electrical energy source based on the concept of vibration energy harvesting to power small and wireless electronic components. Aeroelastic vibrations of a lifting surface can be converted into electricity using piezoelectric transduction. In this paper, frequency-domain piezoaeroelastic modeling and analysis of a cantilevered platelike wing with embedded piezoceramics is presented for energy harvesting. The electromechanical finite-element plate model is based on the thin-plate (Kirchhoff) assumptions while the unsteady aerodynamic model uses the doublet-lattice method. The electromechanical and aerodynamic models are combined to obtain the piezoaeroelastic equations, which are solved using a p-k scheme that accounts for the electromechanical coupling. The evolution of the aerodynamic damping and the frequency of each mode are obtained with changing airflow speed for a given electrical circuit. Expressions for piezoaeroelastically coupled frequency response functions (voltage, current, and electrical power as well the vibratory motion) are also defined by combining flow excitation with harmonic base excitation. Hence, piezoaeroelastic evolution can be investigated in frequency domain for different airflow speeds and electrical boundary conditions.

Influence of Geometric Coupling on the Whirl Flutter Stability in Tiltrotor Aircraft with Unsteady Aerodynamics

A further improvement is attempted of an existing analytical model for an accurate prediction of the aeroelastic stability of a tiltrotor aircraft. A rigid-bladed rotor structural model with the natural frequencies selected appropriately in both the flapping and lagging motions is used. The geometric coupling between the wing vertical bending and torsion is also included. The pitch-flap and pitch-lag couplings are also added. Three different aerodynamic models are combined with the structural model: two quasi-steady models and one full unsteady aerodynamics model. Frequency domain analysis is conducted to predict the whirl flutter stability boundary. It was found that the geometric coupling must be included at an appropriate level to predict the whirl flutter boundary accurately. The addition of the wing bending/torsion coupling and the control system flexibility improves the prediction accuracy significantly. Unsteady aerodynamics influences the stability prediction. The whirl flutter boundary is predict...

Active Control Law Design for Flutter/LCO Suppression Based on Reduced Order Model Method

Active stability augmentation system is an attractive and promising technology to suppress flutter and limit cycle oscillation (LCO). In order to design a good active control law, the control plant model with low order and high accuracy must be provided, which is one of the most important key points. The traditional model is based on low fidelity aerodynamics model such as panel method, which is unsuitable for transonic flight regime. The physics-based high fidelity tools, reduced order model (ROM) and CFD/CSD coupled aeroservoelastic solver are used to design the active control law. The Volterra/ROM is applied to constructing the low order state space model for the nonlinear unsteady aerodynamics and static output feedback method is used to active control law design. The detail of the new method is demonstrated by the Goland+ wing/store system. The simulation results show that the effectiveness of the designed active augmentation system, which can suppress the flutter and LCO successfully.

Micro air vehicle-motivated computational biomechanics in bio-flights: aerodynamics, flight dynamics and maneuvering stability

Aiming at developing an effective tool to unveil key mechanisms in bio-flight as well as to provide guidelines for bio-inspired micro air vehicles (MAVs) design, we propose a comprehensive computational framework, which integrates aerodynamics, flight dynamics, vehicle stability and maneuverability. This framework consists of (1) a Navier–Stokes unsteady aerodynamic model; (2) a linear finite element model for structural dynamics; (3) a fluid-structure interaction (FSI) model for coupled flexible wing aerodynamics aeroelasticity; (4) a free-flying rigid body dynamic (RBD) model utilizing the Newtonian-Euler equations of 6DoF motion; and (5) flight simulator accounting for realistic wing-body morphology, flapping-wing and body kinematics, and a coupling model accounting for the nonlinear 6DoF flight dynamics and stability of insect flapping flight. Results are presented based on hovering aerodynamics with rigid and flexible wings of hawkmoth and fruitfly. The present approach can support systematic analyses of bio- and bio-inspired flight.

Approximate Modeling of Unsteady Aerodynamics for Hypersonic Aeroelasticity

DOI: 10.2514/1.C000190 Various approximations to unsteady aerodynamics are examined for the aeroelastic analysis of a thin doublewedge airfoil in hypersonic flow. Flutter boundaries are obtained using classical hypersonic unsteady aerodynamic theories: piston theory, Van Dyke’s second-order theory, Newtonian impact theory, and unsteady shock-expansion theory. The theories are evaluated by comparing the flutter boundaries with those predicted using computational fluid dynamics solutions to the unsteady Navier–Stokes equations. Inaddition, several alternative approaches to the classical approximations are also evaluated: two different viscous approximations based on effective shapes and combined approximate computational approaches that use steady-state computational-fluid-dynamics-based surrogatemodelsinconjunction withpistontheory.Theresultsindicatethat,with theexceptionof first-order piston theory and Newtonian impact theory, the approximate theories yield predictions between 3 and 17% of normalized root-mean-square error and between 7 and 40% of normalized maximum error of the unsteady Navier–Stokes predictions. Furthermore, the demonstrated accuracy of the combined steady-state computational fluid dynamics and piston theory approaches suggest that important nonlinearities in hypersonic flow are primarily due to steadystate effects. This implies that steady-state flow analysis may be an alternative to time-accurate Navier–Stokes solutions for capturing complex flow effects.

Reduced-Order Nonlinear Unsteady Aerodynamic Modeling Using a Surrogate-Based Recurrence Framework

A reduced-order nonlinear unsteady aerodynamic modeling approach suitable for analyzing pitching/plunging airfoils subject to fixed or time-varying freestream Mach numbers is described. The reduced-order model uses kriging surrogates to account for flow nonlinearities and recurrence solutions to account for time-history effects associated with unsteadiness. The resulting surrogate-based recurrence framework generates time-domain predictionsofunsteadylift,moment,anddragthataccuratelyapproximate computational fluiddynamicssolutions, but at a fraction of the computational cost. Results corresponding to transonic conditions demonstrate that the surrogate-based recurrence framework can mimic computational fluid dynamics predictions of unsteady aerodynamic responses when flow nonlinearities are present. For an unsteady aerodynamic modeling problem considered in this study, an accurate reduced-order model was generated by the surrogate-based recurrence framework approach with significantly fewer computational fluid dynamics evaluations compared to results reported in the literature for a similar problem in which a proper-orthogonal-decomposition-based approach was applied. Furthermore, the results show that the surrogate-based approach can accurately model time-varying freestream Mach number effects and is therefore applicable to rotary-wing applications in addition to fixed-wing applications.

Ionic Polymer Metal Composite Flapping Actuator Mimicking Dragonflies

In this study, variational principle is used for dynamic modeling of an Ionic Polymer Metal Composite (IPMC) flapping wing. The IPMC is an Electro-active Polymer (EAP) which is emerging as a useful smart material for `artificial muscle' applications. Dynamic characteristics of IPMC flapping wings having the same size as the actual wings of three different dragonfly species Aeshna Multicolor, Anax Parthenope Julius and Sympetrum Frequens are analyzed using numerical simulations. An unsteady aerodynamic model is used to obtain the aerodynamic forces. A comparative study of the performances of three IPMC flapping wings is conducted. Among the three species, it is found that thrust force produced by the IPMC flapping wing of the same size as Anax Parthenope Julius wing is maximum. Lift force produced by the IPMC wing of the same size as Sympetrum Frequens wing is maximum and the wing is suitable for low speed flight. The numerical results in this paper show that dragonfly inspired IPMC flapping wings are a viable contender for insect scale flapping wing micro air vehicles.

A dragonfly inspired flapping wing actuated by electro active polymers

An energy-based variational approach is used for structural dynamic modeling of the IPMC (Ionic Polymer Metal Composites) flapping wing. Dynamic characteristics of the wing are analyzed using numerical simulations. Starting with the initial design, critical parameters which have influence on the performance of the wing are identified through parametric studies. An optimization study is performed to obtain improved flapping actuation of the IPMC wing. It is shown that the optimization algorithm leads to a flapping wing with dimensions similar to the dragonfly Aeshna Multicolor wing. An unsteady aerodynamic model based on modified strip theory is used to obtain the aerodynamic forces. It is found that the IPMC wing generates sufficient lift to support its own weight and carry a small payload. It is therefore a potential candidate for flapping wing of micro air vehicles.

Aeroelastic Characteristics of Slender Wing/Bodies with Freeplay Non-Linearities

This article presents a time domain approach to the flutter analysis of a missile-type wing/body configuration with concentrated structural non-linearities. The missile wing is considered fully movable and its rotation angle contains the structural freeplay-type non-linearity. Although a general formulation for flexible configurations is developed, only two rigid degrees of freedom are taken into account for the results: pitching of the whole wing/body configuration and wing rotation angle around its hinge. An unsteady aerodynamic model based on the slender-body approach is used to calculate aerodynamic generalized forces. Limit-cycle oscillations and chaotic motion below the flutter speed are observed in this study.

Non-linear Dynamic Analysis of a Piezoelectrically Actuated Flapping Wing

An energy method is used in order to derive the non-linear equations of motion of a smart flapping wing. Flapping wing is actuated from the root by a PZT unimorph in the piezofan configuration. Dynamic characteristics of the wing, having the same size as dragonfly Aeshna Multicolor, are analyzed using numerical simulations. It is shown that flapping angle variations of the smart flapping wing are similar to the actual dragonfly wing for a specific feasible voltage. An unsteady aerodynamic model based on modified strip theory is used to obtain the aerodynamic forces. It is found that the smart wing generates sufficient lift to support its own weight and carry a small payload. It is therefore a potential candidate for flapping wing of micro air vehicles.

Unsteady aerodynamic modeling based on POD-observer method

A new hybrid approach to constructing reduced-order models (ROM) of unsteady aerodynamics applicable to aeroelastic analysis is presented by using proper orthogonal decomposition (POD) in combination with observer techniques. Fluid modes are generated through POD by sampling observations of solutions derived from the full-order model. The response in the POD training is projected onto the fluid modes to determine the time history of the modal amplitudes. The resulting data are used to extract the Markov parameters of the low-dimensional model for modal amplitudes using a related deadbeat observer. The state-space realization is synthesized from the system’s Markov parameters that are processed with the eigensystem realization algorithm. The POD-observer method is applied to a two-dimensional airfoil system in subsonic flow field. The results predicted by the ROM are in general agreement with those from the full-order system. The ROM obtained by the hybrid approach captures the essence of a fluid system and produces vast reduction in both degrees of freedom and computational time relative to the full-order model.

A Mathematical Model for Helicopter Comprehensive Analysis

This article presents a new mathematical model for helicopter comprehensive analysis with the features of flexibility and mathematical simplicity. The model synthesizes the rigid fuselage motion model with 6 degrees of freedom, coupled flap-lag-torsion elastic rotor blade motion model, unsteady aerodynamics model with dynamic stall and high order generalized dynamic wake model. A new blade structural operator with implicit form is formulated, and the components of the blade structure model are independent of each other so that it is convenient to change or handle any component of blade structure without changing the others. What is more, the entire model is developed in a strict state-space form to simplify the comprehensive analysis. Finally, the UH-60 helicopter is taken as an example to predict the blade natural characteristics, the trim characteristics including controls and fuselage attitudes as well as the airloads at blade section under the flight conditions of high speed with moderate thrust and high thrust with moderate speed. The results are compared with UH-60 flight test data and those predicted by two well-known comprehensive codes. The validity of the model presented in this article is verified.

Piezoaeroelastic Modeling and Analysis of a Generator Wing with Continuous and Segmented Electrodes

Unmanned air vehicles (UAVs) and micro air vehicles (MAVs) constitute unique application platforms for vibration-based energy harvesting. Generating usable electrical energy during their mission has the important practical value of providing an additional energy source to run small electronic components. Electrical energy can be harvested from aeroelastic vibrations of lifting surfaces of UAVs and MAVs as they tend to have relatively flexible wings compared to their larger counterparts. In this work, an electromechanically coupled finite element model is combined with an unsteady aerodynamic model to develop a piezoaeroelastic model for airflow excitation of cantilevered plates representing wing-like structures. The electrical power output and the displacement of the wing tip are investigated for several airflow speeds and two different electrode configurations (continuous and segmented). Cancelation of electrical output occurs for typical coupled bending-torsion aeroelastic modes of a cantilevered generator wing when continuous electrodes are used. Torsional motions of the coupled modes become relatively significant when segmented electrodes are used, improving the broadband performance and altering the flutter speed. Although the focus is placed on the electrical power that can be harvested for a given airflow speed, shunt damping effect of piezoelectric power generation is also investigated for both electrode configurations.

Tonal and Broadband Noise Calculations for Aeroacoustic Optimization of a Pusher Propeller

A multidisciplinary analysis and optimization is carried out for a propeller in a real pusher aircraft configuration with the goal of reducing the radiated noise power levels, while preserving the aerodynamic efficiency. The optimization process involves the shape of the blade and the position of the engine exhaust ducts. A coupling of the unsteady aerodynamic and structural-dynamic blade models provides the aeroelastic propeller model that drives a tonal and broadband aeroacoustic prediction. The tonal noise results from the periodic flow unsteadiness due to the nonaxial flight and to the impingement of the engine exhausts on the propeller disk. The broadband noise is mainly due to the interaction between the blade leading edge and the exhaust turbulence. It is shown that the tonal noise overwhelmsthebroadbandnoiseandthattheoptimizationaffectstheshapeofthebladeatthetipandinthespanwise segment hit by the exhausts. An overall sound pressure level reduction of 3.5 dB is achieved at the takeoff condition, while preserving the design propeller thrust and resulting in a small penalty on the propeller efficiency in cruise.

Wingbeat Shape Modulation for Flapping-Wing Micro-Air-Vehicle Control During Hover

A new method of controlling a flapping-wing micro air vehicle by varying the velocity profiles of the wing strokes is presented in this manuscript. An exhaustive theoretical analysis along with simulation results show that this new method, called split-cycle constant-period frequency modulation, is capable of providing independent control over vertical and horizontal body forces as well as rolling and yawing moments using only two physical actuators, whose oscillatory motion is defined by four parameters. An actuated bob-weight is introduced to enable independent control of pitching moment. A general method for deriving sensitivities of cycle-averaged forces and moments to changes in wingbeat kinematic parameters is provided, followed by an analytical treatment for a case where the angle of attack of each wing is passively regulated and the motion of the wing spar in the stroke plane is driven by a split-cycle waveform. These sensitivities are used in the formulation of a cycle-averaged control law that successfully stabilizes and controls two different simulation models of the aircraft. One simulation model is driven by instantaneous aerodynamic forces derived from blade-element theory, while the other is driven by an empirical representation of an unsteady aerodynamic model that was derived from experiments.

Nonlinear-Aerodynamics/Nonlinear-Structure Interaction Methodology for a High-Altitude Long-Endurance Wing

Nonlinear aeroelastic analysis is essential for high-altitude long-endurance (HALE) aircraft. In the current paper, we have presented a computational aeroelastic tool for nonlinear-aerodynamics/nonlinear-structure interaction. Specifically, a consistent nonlinear time-domain aeroelastic methodology has been integrated via tightly coupling a geometrically exact nonlinear intrinsic beam model and the generalized unsteady vortex-lattice aerodynamic model with vortex roll-up and free wake. The effects of discrete gust as well as flow separation at various angles of attack from attached flow to the stall and poststall ranges are also included in the nonlinear aerodynamic model. A HALE-wing model is analyzed as a numerical example. The trim angle of attack is first found for the wing, and the results show that aeroelastic instability could occur at higher angles of attack. The HALE-wing model under the trim condition is then analyzed for various gust profiles to which it is subject. It is found that for certain gust levels, the elastic deformations of the HALE wing tend to become unstable: notably, the in-plane deflections become very significant. It is noted for the unstable solution of the HALE wing that the flow may be well beyond the stall range. An engineering approach with the use of the nonlinear sectional lift is attempted to consider such stall effects.

Parallel Multigrid Algorithm for Aeroelasticity Simulations

This paper presents the development of a multigrid parallel algorithm for a nonlinear aeroelastic analysis. The aeroelastic model consists of 1) a nonlinear structural model that captures in-plane, out-of-plane, and torsional couplings; 2) an unsteady viscous aerodynamic model that captures compressible flow effects for transonic flows with shock/boundary-layer interaction; and 3) a solution methodology that assures a tightly coupled solution of the nonlinear structure and the fluid flow, including a consistent geometric interface between the highly deforming structure and the flowfield. A domain-decomposition parallel computation algorithm based on a message-passing interface was developed for the flow solver. A three-level multigrid algorithm was implemented in the flow solver to further reduce the computational time. A grid generation and deformation algorithm was developed concurrently with the flow solver in order to improve the efficiency of the computation. The grid deformation methodology kept the mesh topology unchanged as the structure deformed. Consequently, it was not necessary for either the parallel computation or the multigrid algorithm to update their communication pointers while the structure deformed. The validation of the numerical solver was done using experimental results of the F-5 wing. The aeroelastic solver was then used to assess the effect of structural nonlinearities on the aeroelastic response of the heavy Goland wing.

Approximate Modeling of Unsteady Aerodynamics for Hypersonic Aeroelasticity

Approximate Modeling of Unsteady Aerodynamics for Hypersonic Aeroelasticity