Nonlinear Aerodynamics Research Articles

Development and Validation of a Fluid–Structure Solver for Transonic Panel Flutter

A partitioned fluid–structure coupling code for transonic panel flutter has been developed and validated. The Reynolds-averaged Navier–Stokes equations are solved numerically by means of an implicit finite volume method to account for nonlinear aerodynamics, as there are shock waves and a viscous boundary layer at the panel surface. An implicit finite element formulation of the structural equations, as well as a Galerkin solution of the von Kármán plate equation are employed to solve elastic panel deformations with respect to geometric nonlinearities. A detailed validation process has shown good agreement with results from the literature for high subsonic and low supersonic Mach numbers. Thereby, a recent comparison between theory and experiment is confirmed. The validated solver is then used for further studies focusing on the impact of turbulent boundary layers on aeroelastic stability boundaries and instabilities. An increase in aerodynamic damping due to a viscous boundary layer is identified by an increase of the aeroelastic stability boundary. Furthermore, a significant damping on high flutter frequencies and mode shapes is revealed. The application of either a one-equation or two-equation turbulence model did not cause any major deviations in the results.

Nonlinear dynamic performance of long-span cable-stayed bridge under traffic and wind

Long-span cable-stayed bridges exhibit some features which are more critical than typical long span bridges such as geometric and aerodynamic nonlinearities, higher probability of the presence of multiple vehicles on the bridge, and more significant influence of wind loads acting on the ultra high pylon and super long cables. A three-dimensional nonlinear fully-coupled analytical model is developed in this study to improve the dynamic performance prediction of long cable-stayed bridges under combined traffic and wind loads. The modified spectral representation method is introduced to simulate the fluctuating wind field of all the components of the whole bridge simultaneously with high accuracy and efficiency. Then, the aerostatic and aerodynamic wind forces acting on the whole bridge including the bridge deck, pylon, cables and even piers are all derived. The cellular automation method is applied to simulate the stochastic traffic flow which can reflect the real traffic properties on the long span bridge such as lane changing, acceleration, or deceleration. The dynamic interaction between vehicles and the bridge depends on both the geometrical and mechanical relationships between the wheels of vehicles and the contact points on the bridge deck. Nonlinear properties such as geometric nonlinearity and aerodynamic nonlinearity are fully considered. The equations of motion of the coupled wind-traffic-bridge system are derived and solved with a nonlinear separate iteration method which can considerably improve the calculation efficiency. A long cable-stayed bridge, Sutong Bridge across the Yangze River in China, is selected as a numerical example to demonstrate the dynamic interaction of the coupled system. The influences of the whole bridge wind field as well as the geometric and aerodynamic nonlinearities on the responses of the wind-traffic-bridge system are discussed.

Nonlinear Vibration and Multimodal Interaction Analysis of Transmission Line with Thin Ice Accretions

A study of multimodal galloping is carried out on an iced transmission line with thin ice accretions. The partial differential governing equations of iced transmission line are established to describe the nonlinear interactions between the in-plane, out-of-plane and torsional vibration, in which geometrical and aerodynamic nonlinearities are considered. The transformation of modal galloping with the continuous variations of parameters and modal interactions are analyzed based on the reduced model obtained by employing Galerkin spatial discretization. Eigenvalue analysis is applied on linear system to determine the switch of different modal galloping in plane U -l, where Hopf bifurcation occurs and mono-modal, bi-modal and multi-modal galloping are observed. Various numerical procedures are implemented to capture the outstanding nonlinear dynamic features of every regional galloping in plane U -l. Internal resonance is observed and investigated to interpret the phenomenon of modal transition which is also analyzed by accounting for the influence of initial conditions on galloping with either symmetric or anti-symmetric modes.

Fixed-Wing Unmanned Aircraft In-Flight Pitch and Yaw Control Moment Sensing

Unsteady, nonlinear aerodynamics at high angles of attack challenges small unmanned aircraft system autopilots that rely heavily on inertial-based instrumentation. This work introduces an expanded aerodynamic sensing system for poststall flight conditions that incorporate high angle of attack and prop-wash aerodynamic forces based on in-flight measurement. A flight vehicle with a 1.8 m wingspan is used in wind-tunnel tests to measure the pitch and yaw moments due to freestream and prop-wash over the tail surfaces at high-thrust, low-airspeed conditions including hover. Test data are used to develop two methods to determine in-flight real-time pitch and yaw moments: a probe designed specifically to measure prop-wash flow and a set of pressure sensors embedded throughout the tail surfaces. Through comparisons with torque-transducer measurements also acquired in the wind-tunnel tests, both methods are shown to provide accurate moment estimates at hover and forward-flight conditions. With information directly provided by in-flight measurement, real-time pitch and yaw control can be enhanced using a simple and reliable framework.

COMPUTATIONAL AERODYNAMIC OPTIMIZATION OF LOW-SPEED WING

An optimization method consisting of genetic and evolution optimization algorithm and a solver using nonlinear aerodynamics was applied on design of low-speed wing. Geometric parameterization of wing uses standard geometric quantities commonly used for the description of wing geomtery. The method seems to provide good teliable results at low computer capacity requirements.

Nonlinear aerodynamic model identification using empirical mode decomposition

A conceptual method based on the empirical mode decomposition algorithm is proposed to identify a high-fidelity full-flight envelope aerodynamic model, utilising flight data. The key idea is to recognise dominant phenomena of flight containing dissimilar amplitudes and frequencies by means of the empirical mode decomposition. Being distinguished and separated from each other, flight modes can be considered in the aerodynamic model, independently. To achieve the goal, an equation error method is utilised to identify six multi-input single-output systems for aerodynamic forces and moments. The inputs of the identification systems are intrinsic mode functions of flight parameters. The nonparametric identification problem uses the Hammerstein nonlinear ARMAX structure and estimates parameters by the least squares iterative algorithm. Flight tests of an unmanned aircraft in two complex manoeuvres are employed for the modelling and simulation. Several models with different nonlinear functions are introduced and trained by the first dataset. Then, to verify the identified model, the flight simulation is performed for the second dataset. Results indicate the appropriate performance of the identification method in nonlinear aerodynamics.

A shear–shear torsional beam model for nonlinear aeroelastic analysis of tower buildings

In this paper, an equivalent one-dimensional beam model immersed in a three-dimensional space is proposed to study the aeroelastic behavior of tower buildings: linear and nonlinear dynamics are analyzed through a simple but realistic physical modeling of the structure and of the load. The beam is internally constrained, so that it is capable to experience shear strains and torsion only. The elasto-geometric and inertial characteristics of the beam are identified from a discrete model of three-dimensional frame, via a homogenization process. The model accounts for the torsional effect induced by the rotation of the floors around the tower axis; the macroscopic shear strain is produced by bending of the columns, accompanied by negligible rotation of the floors. Nonlinear aerodynamic forces are evaluated through the quasi-steady theory. The first aim is to investigate the effect of mechanical and aerodynamic coupling on the critical galloping conditions. Furthermore, the role of aerodynamic nonlinearities on the galloping post-critical behavior is analyzed through a perturbation solution which permits to obtain a reduced one-dimensional dynamical system, capable of capturing the essential dynamics of the problem.

Efficient Surrogate Modelling of Nonlinear Aerodynamics in Aerostructural Coupling Schemes

This paper considers the substitution of the computational-fluid-dynamics solver within an aerostructural coupling scheme by an efficient reduced-order surrogate model to realize high-fidelity nonlinear aeroelastic analyses within a fraction of the time compared to the corresponding coupled computational-fluid-dynamics analysis. The presented surrogate model approach is a combination of parameter reduction via proper orthogonal decomposition and system identification methods designed to cover nonlinear aerodynamic effects such as viscosity as well as transient effects. The investigated test case is the thick NLR7301 airfoil that shows significant nonlinear aerodynamic behavior along with nonnegligible viscous effects. The model is identified from a set of transient forced motion computational-fluid-dynamics analyses. After identification, the model is used to predict the discrete surface force distribution of the NLR7301 airfoil in static as well as transient coupled analyses. It is shown that the static aeroelastic equilibrium and the limit cycle oscillation case is predicted by the surrogate model with sufficient accuracy.

A multi-input multi-output adaptive feed-forward controller for vibration alleviation on a large blended wing body airliner

Turbulent atmosphere, gusts, and manoeuvres significantly excite aircraft rigid body motions and structural vibrations, which leads to reduced ride comfort and increased structural loads. In particular BWB (Blended Wing Body) aircraft configurations, while promising a significant fuel efficiency improvement compared to wing-tube configurations, exhibit severe sensitivity to gusts. In general, a flexible aircraft represents a lightly damped structure involving a large variety of uncertainties due to fuel mass variations during flight, control system nonlinearities, aerodynamic nonlinearities, and structural nonlinearities, to name just a few. Especially at the beginning of flight testing of a newly developed aircraft type, plant models generally require a lot of verification and adjustment based on obtained flight test data, before they can be used reliably for control law design. Adaptive control already is a well-established method for many active noise and vibration control problems, and thus is proposed here for application to the problem of gust load alleviation. However, safety requirements are significantly higher for gust load alleviation systems than for most noise and vibration control systems. This paper proposes a MIMO (Multi-Input Multi-Output) adaptive feed-forward controller for the alleviation of turbulence-induced rigid body motions and structural vibrations on aircraft. The major contribution to the research field of active noise and vibration control is the presentation of a detailed stability analysis of the MIMO adaptive algorithm in order to support potential certification of this method for a safety-critical application. Finally, the proposed MIMO adaptive feed-forward vibration controller is applied to a longitudinal flight dynamics model of a large flexible BWB airliner in order to verify the derived vibration controller on a challenging control problem.

Nonlinear Multivariate Spline-Based Control Allocation for High-Performance Aircraft

High-performance flight control systems based on the nonlinear dynamic inversion principle require highly accurate models of aircraft aerodynamics. In general, the accuracy of the internal model determines to what degree the system nonlinearities can be canceled; the more accurate the model, the better the cancellation, and with that, the higher the performance of the controller. In this paper, a new control system is presented that combines nonlinear dynamic inversion with multivariate simplex spline-based control allocation. Three control allocation strategies that use novel expressions for the analytic Jacobian and Hessian of the multivariate spline models are presented. Multivariate simplex splines have a higher approximation power than ordinary polynomial models and are capable of accurately modeling nonlinear aerodynamics over the entire flight envelope of an aircraft. This nonlinear spline based controller is applied to control a high-performance aircraft (F-16) with a large flight envelope. The simulation results indicate that perfect feedback linearization can be achieved throughout the entire flight envelope, leading to a significant increase in tracking performance compared with ordinary polynomial-based nonlinear dynamic inversion.

Transonic Limit Cycle Oscillation Analysis Using Aerodynamic Describing Functions and Superposition Principle

Limit cycle oscillation for an airfoil in transonic air flow considering aerodynamic nonlinearity is studied. Transonic nonlinear aerodynamic forces are calculated by solving Euler equations or Navier–Stokes equations with respect to harmonic airfoil plunging/pitching motion, and then the aerodynamic describing functions and the superposition principle are used to build an equivalent linearized aerodynamic model in the frequency domain; hence, the transonic limit cycle oscillation solutions can be obtained by the frequency domain flutter analysis method. The procedures for building the aerodynamic describing function and obtaining the limit cycle oscillation solution are described in detail. Four examples are adopted to verify the accuracy of the present method. The Isogai wing model with NACA 64A010 airfoil is used as the first example to verify the accuracy of the transonic linear flutter solution of the present method. Another NACA 64A010 airfoil model with different structural parameters is then adopted to study its transonic limit cycle oscillation characteristics considering only aerodynamic nonlinearity, and the NACA 0012 airfoil model with both aerodynamic and structural nonlinearities is investigated for its transonic limit cycle oscillation properties. The NLR 7301 airfoil is studied for its limit cycle oscillation characteristics in inviscid and viscous transonic flows, respectively. The results obtained by the present method are in good agreement with those obtained by the existing research with the harmonic balance method and time-marching method. The limitations of the present method are also discussed.

Limit Cycle Flutter Analysis of a High-Aspect-Ratio Wing with an External Store

Limit cycle flutter analysis of a high-aspect-ratiowing with an external store is presented. The concentrated store mass iscombined into the governing equations which are obtained using the extendedHamilton’s principle. The high-aspect-ratio wing structural model, which alsoconsiders the in-plane bending motion, is used. Three possible nonlinearitiesare considered including structural nonlinearities, aerodynamic nonlinearities,and store nonlinearities. Time simulation and bifurcation diagrams areperformed to analysis systems with three nonlinearities.

Nonlinear Autopilot Design and Guidance-in-Loop Validation for a Tactical Air-to-Air Flight Vehicle

In this paper, design and analysis of nonlinear autopilot of a tactical flight vehicle has been carried out for surface to air application. The lateral autopilot design is based on dynamic inversion and time scale separation principle. The roll autopilot design is based on back stepping technique. At first, better tracking performance of present autopilot with respect to linear design at higher angles of attack in presence of side force and aerodynamic nonlinearity and its robustness study with respect to plant parameter variation has been carried out through six degrees of freedom simulation. Later, successful tracking performance of the pursuer nonlinear autopilot while tracking guidance command has also been demonstrated through realistic six degrees of freedom simulation of a pursuer evader engagement.

Modified Unsteady Vortex-Lattice Method to Study Flapping Wings in Hover Flight

A numerical-simulation tool is developed that is well suited for modeling the unsteady nonlinear aerodynamics of flying insects and small birds as well as biologically inspired flapping-wing micro air vehicles. The present numerical model is an extension of the widely used three-dimensional general unsteady vortex-lattice model and provides an attractive compromise between computational cost and fidelity. Moreover, it is ideally suited to be combined with computational structural dynamics to provide aeroelastic analyses. The present numerical results for a twisting, flapping wing with neither leading-edge nor wing-tip separations are in close agreement with the results obtained in previous studies with the Euler equations and a vortex-lattice method. The present results for unsteady lift, mean lift, and frequency content of the force are in good agreement with experimental data for the robofly apparatus. The actual wing motion of a hovering Drosophila is used to compute the flowfield and predict the lift force. The downward motion of the fluid particles revealed in the graphics of the calculated wake indicates the presence of lift. Moreover, the calculated mean lift is in close agreement with the weight of a Drosophila. The results presented in this paper definitely show that the interaction between vortices is the main feature that allows insects to generate enough lift to stay aloft. The present results warrant the use of this general version of the unsteady vortex-lattice method for future studies.

About the Aerothermoelastic Stability of Panels in Supersonic Flows

This article provides new insights into the aerothermoelastic stability of thin plates. Particularly, the issue of loss of stability of an isotropic plate-strip of constant thickness immersed in a supersonic flow field and subjected to a variable temperature field through the thickness is examined. Using the basic principles of the theory of aerothermoelasticity of isotropic bodies, the theories of flexible panels, and the linear law of temperature field through the thickness of the panel, the stability equations and associated boundary conditions are obtained. As expected, the coefficients of the aerothermoelastic governing equations depend on the thermal load, and consequently the panel-flutter critical speed depends on temperature. The model takes into account quadratic and cubic aerodynamic non-linearities as well as cubic geometric non-linearities. Due to the inhomogeneity of the temperature field distribution across the thickness plate buckling instability occurs. This instability accounts for the deformed shape of the plate and the stability boundary depends on the variables characterizing the flow speed, the temperature of the middle plane and the temperature gradient in the direction normal to the plane. It is shown that the combined effect of the temperature field and free-stream regulates the process of stability and the temperature field can significantly change the flutter critical speed and flutter behavior. The problem of stability is also considered in the non-linear framework. The existence and behavior of flutter-type vibrations is investigated at pre- and post-critical speeds. The influence of the temperature field on the dependency of the limit cycle amplitude as a function of speed is studied. Results and discussions are presented along with pertinent concluding remarks.

Nonlinear dynamics of galloping-based piezoaeroelastic energy harvesters

The normal form is proposed as a tool to analyze the performance and reliability of galloping-based piezoaeroelastic energy harvesters. Two different harvesting systems are considered. The first system consists of a tip mass prismatic structure (isosceles 30° or square cross-section geometry) attached to a multilayered cantilever beam. The only source of nonlinearity in this system is the aerodynamic nonlinearity. The second system consists of an equilateral triangle cross-section bar attached to two cantilever beams. This system is designed to have structural and aerodynamic nonlinearities. The coupled governing equations for the structure’s transverse displacement and the generated voltage are derived and analyzed for both systems. The effects of the electrical load resistance and the type of harvester on the onset speed of galloping are quantified. The results show that the onset speed of galloping is strongly affected by the load resistance for both types of harvesters. The normal form of the dynamic system near the onset of galloping (Hopf bifurcation) is then derived. Based on the nonlinear normal form, it is demonstrated that smaller levels of generated voltage or power are obtained for higher absolute values of the effective nonlinearity. For the first harvesting system, the results show a supercritical Hopf bifurcation for both isosceles 30° or square cross-section geometries. The nonlinear normal form shows that the isosceles triangle section (30°) is more efficient than the square section. For the second harvesting system, the normal form is used to identify the values of the nonlinear torsional spring which changes the harvester’s instability. It is demonstrated that this critical value of the nonlinear torsional spring depends strongly on the load resistance.

Nonlinear Aerodynamics Reduced-Order Model Based on Multi-Input Volterra Series

This paper gives a low-order approximations of multi-input Volterra series as a nonlinear reduced-order model (ROM) based on wavelet multiresolution analysis. The band-limited pseudorandom multilevel sequence (PRMS) is used as the identification signal and the QR decomposition recursive least square (QRD-RLS) method is utilized as identification method. At last, the ROM is applied to model the nonlinear aerodynamic moment of an airfoil undergoing simultaneous forced pitch and plunge harmonic oscillation. The results show that including the second-order Volterra cross kernels in ROM can capture the coupling effect which significantly improves accuracy in predicting nonlinear aerodynamics under simultaneous motion. And the wavelet multiresolution analysis efficiently reduces the number of identification coefficients for Volterra kernels.

Online Aerodynamic Model Identification Using a Recursive Sequential Method for Multivariate Splines

Avoiding high computational loads is essential to online aerodynamic model identification algorithms, which are at the heart of any model-based adaptive flight-control system. Multivariate simplex B-spline methods are excellent function approximation tools for modeling the nonlinear aerodynamics of high-performance aircraft. However, the computational efficiency of the multivariate simplex B-spline method must be improved in order to enable real-time onboard applications, for example, in adaptive nonlinear flight-control systems. In this paper, a new recursive sequential identification strategy is proposed for the multivariate simplex B-spline method aimed at increasing its computational efficiency, thereby allowing its use in onboard system identification applications. The main contribution of this new method is a significant reduction of the computational load for large-scale online identification problems as compared to the existing multivariate simplex B-spline methods. The proposed method consists of two sequential steps for each time interval and makes use of a decomposition of the global problem domain into a number of subdomains, called modules. In the first step, the B-coefficients for each module are estimated using a least-squares estimator. In the second step, the local B-coefficients for each module are then smoothened into a single global B-coefficient vector using a linear minimum mean-square errors estimation. The new method is compared to existing batch and recursive multivariate simplex B-spline methods in a numerical experiment in which an aerodynamic model is recursively identified based on data from a NASA F-16 wind-tunnel model.

Vortex-Induced Vibration of Bridge Decks: Volterra Series-Based Model

AbstractA brief overview of vortex-induced vibration (VIV) of bridge decks is presented, highlighting special VIV features concerning bridge decks. A popular VIV model (Van der Pol–type model) for bridge decks is examined in detail. Alternatively, a truncated Volterra series–based nonlinear oscillator is introduced to model the VIV system. Typical features of VIV such as the limit cycle oscillation (LCO), frequency shift, hysteresis, and beat phenomenon are parsimoniously and accurately captured in the proposed nonlinear model. As a functional expansion of a nonlinear system, the Volterra series is convenient for estimating the linear and nonlinear contributions to VIV. It is demonstrated that the relative contribution of nonlinear effects in VIV is around 50% of the total response for a range of bridge cross sections. The efficacy of the Volterra series as a reduced-order model (ROM) in capturing aerodynamic nonlinearities eliminates the need for reliance on conventional phenomenological models as it pro...

Hysteresis Phenomenon in the Galloping of the D-Shape Iced Conductor

It is well known that there is a hysteresis phenomenon in the amplitude variation in the iced conductor galloping with the wind velocity, which will have more obvious disadvantages to the overhead transmission lines. But hysteresis characteristics in the conductor galloping have not received much attention. In this paper, a continuum model of the conductor galloping with D-shape ice is derived by using Hamilton principle, where the initial deformation, the geometric nonlinearity caused by the large deformation, and the aerodynamic nonlinearity are considered. The aerodynamic forces are described by using the quasi steady hypothesis, where the aerodynamic coefficients are expanded by the polynomial curves with a third order and a ninth order, respectively. The hysteresis phenomenon is analyzed by using the approximate solutions of the Galerkin discretized equation derived from the continuum model by means of the harmonic balance method. The influence of the different factors, dynamic angle of attack, span length, initial tension, and conductor mass, is obtained in different galloping instability intervals. And two important aspects about the point of the hysteresis phenomenon onset and the size of the hysteresis region over the wind velocities are analyzed under different conditions.