Unsteady Aerodynamic Model Research Articles

Aerodynamic Analysis of a Jet Transport in Windshear Encounter During Landing

Stability and control characteristics of a nominally controllable jet transport airplane that ran off the runway after touchdown during windshear encounter are evaluated based on the data in the onboard flight data recorder (FDR). To determine these characteristics, the recorded wind profile is first improved, and then the unsteady aerodynamic models for the aircraft in dynamic ground effect are estimated. The recorded wind field is improved through the extended-Kalman-filter (EKF) technique to reconstruct the wind profile along the flight path from the data in the FDR. The windshear guideline is reviewed and compared with the airport weather data. To analyze the windshear effect in more detail, unsteady aerodynamic models for the aircraft are developed based on two artificial intelligent methods, the fuzzy-logic modeling and the feed-forward neural networks, applied to the processed FDR data. The stability and control characteristics are then estimated by using these aerodynamic models. The results indicate that a less favorable dynamic ground effect exists near touchdown in crosswind. In addition, the dynamic motion is shown to exhibit directional instability, unstable yaw damping, and loss of control effectiveness near the ground in a combined crab and sideslip landing in unsteady windshear conditions.

Non-linear unsteady aerodynamic model for insect-like flapping wings in the hover. Part 1: Methodology and analysis

The essence of this two-part paper is the analytical, aerodynamic modelling of insect-like flapping wings in the hover for microair vehicle applications. A key feature of such flapping-wing flows is their unsteadiness and the formation of a leading-edge vortex in addition to the conventional wake shed from the trailing edge. What ensues is a complex interaction between the shed wakes which, in part, determines the forces and moments on the wing. In an attempt to describe such a flow, two-novel coupled, non-linear, wake-integral equations are developed in this first part of the paper, and these form the foundation upon which the rest of the work stands. The circulation-based model thus developed is unsteady and inviscid in nature and essentially two-dimensional. It is converted to a ‘quasi-three-dimensional’ model using a blade-element-type method, but with radial chords. The main results from the model are force and moment data for the flapping wing and are derived as part of this article using the method of impulses. These forces and moments have been decomposed into constituent elements. The governing equations developed in the study are exact, but do not have a closed analytic form. Therefore, solutions are found by numerical methods. These are described in the second part of this paper.

Unsteady Aerodynamic Modeling with Time-Varying Free-Stream Mach Numbers

Unsteady Aerodynamic Modeling with Time-Varying Free-Stream Mach Numbers

INVESTIGATION OF SUITABILITY FOR THE LINEAR SUPERPOSITION MODEL

An aircraft model was tested at the 3-meter low speed wind tunnel as it was oscillated with large amplitude. The unsteady aerodynamic behavior was acquired during the oscillation in yawing, rolling and yawing-rolling. The lateral-directional dynamic derivative was obtained using the mathematic model of unsteady aerodynamics and the dynamic derivative simulation. According to the principle of linear superposition, the unsteady aerodynamic parameters of the model about yaw-roll coupled motion can be obtained by the quasi-steady aerodynamic model and the result was compared with the experimental test. It was found that for the quasi-steady aerodynamic model the unsteady aerodynamic characteristic was in agreement with the test at the middle and large angle of attack (for example α ≤ 45°), but was opposite at the extremely large angle of attack (α > 45°).

Aeroelastic Stability Enhancement and Vibration Suppression in a Composite Helicopter Rotor

An optimization procedure to 1) reduce the 4/revolution oscillatory hub loads and 2) increase the lag mode damping of a four-bladed soft-in-plane hingeless helicopter rotor is developed using a two-level approach. At the upper level, response surface approximations to the objective function and constraints are used to find the optimal blade mass and stiffness properties for vibration minimization and stability enhancement. An aeroelastic analysis based on finite elements in space and time is used. The numerical sampling needed to obtain the response surfaces is done using the central composite design of the theory of design of experiments. The approximate optimization problem expressed in terms of quadratic response surfaces is solved using a gradient-based method. Optimization results for the vibration problem in forward flight with unsteady aerodynamic modeling show a vibration reduction of about 15%. The dominant loads are the vertical hub shear and the rolling and pitching moments, which are reduced by 22-26%. The results of stability enhancement problem show an increase of 6-125% in the lag mode damping. At the lower level, a composite box beam is designed to match the upper-level beam blade stiffness and mass using a genetic algorithm which permits the use of discrete ply angle design variables such as 0, +or-45, and 90 deg, which are easier to manufacture. Three different composite materials are used for designing the composite box beam, thus, showing the robustness of the genetic algorithm approach. Boron/epoxy composite gives the most compact box beam, whereas graphite/epoxy gives the lightest box beam

Time-Dependent Coefficient Reduced-Order Model for Unsteady Aerodynamics of Proprotors

We present a methodology for the identification of a periodic-coefficient reduced-order model (ROM) for the prediction of perturbation aerodynamic loads on tiltrotor propellers in cruise flight. Although the result is a periodic-coefficient model, the process requires only frequency-domain aerodynamic solutions. Assuming the unperturbed proprotor in axial flow, the matrix that collects the aerodynamic transfer functions between blade perturbative boundary conditions and generalized aerodynamic forces is first derived. Then its rational matrix approximation, followed by combination with the equations describing the wing/pylon/proprotor kinetic coupling, yields the aerodynamic ROM. This ROM is expressed in terms of a set of linear equations that relate the time evolution of the aerodynamic loads acting on the proprotor blades to wing/pylon and deformable-blade degrees of freedom

Application of System Identification to Aircraft at NASA Langley Research Center

The past, present, and future of system identification applied to aircraft at NASA Langley Research Center (LaRC) in Hampton, Virginia, are discussed. Significant research advances generated at NASA LaRC in the past are summarized, including some perspective on the role these developments played in the practice of system identification applied to aircraft. Selected recent research efforts are described, to give an idea of the type of activities currently being pursued at NASA LaRC. These efforts include real-time parameter estimation, identifying flying qualities models, advanced experiment design and modeling techniques for static wind-tunnel database development, and indicial function identification for unsteady aerodynamic modeling. Projected future developments in the area are outlined

An Investigation of the Aerodynamic Response of a Wind Turbine Blade to Tower Shadow

This paper presents results from a wind tunnel based examination of the response of a wind turbine blade to tower shadow in head-on flow. In the experiment, one of the blades of a small-scale, two-bladed, downwind turbine was instrumented with miniature pressure transducers to allow recording of the blade surface pressure response through tower shadow. The surface pressures were then integrated to provide the normal force coefficient responses presented in this paper. It is shown that it is possible to reproduce the measured responses using an indicially formulated unsteady aerodynamic model applied to a cosine wake velocity deficit. It is also shown that agreement between the model and the measured data can be improved by careful consideration of the velocity deficit geometry.

Unsteady aerodynamic model of a cargo container for slung-load simulation

AbstractThe problem of simulation models capable of predicting the aerodynamic instability of helicopter slung-load cargo containers and bluff bodies is addressed. Instability for these loads is known to depend on unsteady frequency-dependent aerodynamics, but simulation models that include the unsteady aerodynamics do not currently exist. This paper presents a method for generating such models using computational fluid dynamics (CFD) to generate forced-oscillation aerodynamic data and frequency domain system identification techniques to generate a frequency response from the CFD data and to identify a transfer function fit to the frequency response. The method is independent of the responsible flow phenomenon and is expected to apply to bluff-bodies generally. Preliminary results are presented for the case of the 6- by 6- by 8-ft CONEX (container express) cargo container. The present work is based on two-dimensional (2D) aerodynamic data for the CONEX side force and yaw moment generated by a forced oscillation in which frequency is varied smoothly over the range of interest. A first-order rational polynomial transfer function is found adequate to fit the aerodynamics, and this is shown to provide a good match with flight test data for the yawing motion of the CONEX.

Helicopter vibration reduction in forward flight with induced-shear based piezoceramicactuation

Governing equations are obtained for helicopter rotor blades with surface bondedpiezoceramic actuators using Hamilton’s principle. The equations are then solved fordynamic response using finite element discretization in the spatial and time domains. Atime domain unsteady aerodynamic model is used to obtain the airloads. The nonlinearrelationship between the piezoelectric shear coefficient and applied ac field is represented asa polynomial curve fit. The nonlinear effects are investigated by applying a sinusoidalvoltage to the helicopter rotor blade. The rotor blade is modeled as a two-cell box sectionwith piezoelectric layers surface bonded to the top and bottom of the box beam.Comparison of results with linear and nonlinear shear coefficients is presented. Use of anonlinear relationship (compared to linear) to achieve targeted reductions in strains ordisplacements results in a reduction in the requirement of applied amplitude of thesinusoidal field. A rate feedback control law is implemented which feeds back the higherharmonics of the time rate of change of strain in the azimuthal direction. Thesensed voltage is then applied to the rotor blade, resulting in a vibration reductionof approximately 43% for a four-bladed, soft-in-plane hingeless rotor in forwardflight.

昆虫の形状と構造のデジタイジング及び計算力学モデルの構築(J07-3 生物の運動機能/バイオミメティクスとバイオメカニクス/バイオロボティクスとバイオメカトロニクス(3),J07 生物の運動機能/バイオミメティクスとバイオメカニクス/バイオロボティクスとバイオメカトロニクス)

We have developed a biology-inspired dynamic flight simulator on a basis of realistic insect morphology which is capable to mimic free flight of a real insect. It aims at analyzing the aerodynamic phenomena associated with the insect free flight and revealing the force-generation mechanisms. Using a moth, Agrius convolvuli LINNE, we have made a digitizing analysis of the shape and the internal structure of insect wings and body, and succeeded in constructing a realistic wing-body moth model with high resolution. A CFD modeling of unsteady aerodynamics in a flapping flight is also established.

Passive control of discrete-frequency tones generated by coupled detuned cascades

Discrete-frequency tones generated by rotor–stator interactions are of particular concern in the design of fans and compressors. Classical theory considers an isolated flat-plate cascade of identical uniformly spaced airfoils. The current analysis extends this tuned isolated cascade theory to consider coupled aerodynamically detuned cascades where aerodynamic detuning is accomplished by changing the chord of alternate rotor blades and stator vanes. In a coupled cascade analysis, the configuration of the rotor influences the downstream acoustic response of the stator, and the stator configuration influences the upstream acoustic response of the rotor. This coupled detuned cascade unsteady aerodynamic model is first applied to a baseline tuned stage. This baseline stage is then aerodynamically detuned by replacing alternate rotor blades and stator vanes with decreased chord airfoils. The nominal aerodynamically detuned stage configuration is then optimized, with the stage acoustic response decreased 13 dB upstream and 1 dB downstream at the design operating condition. A reduction in the acoustic response of the optimized aerodynamically detuned stage is then demonstrated over a range of operating conditions.

LIMIT CYCLE FLUTTER OF AIRFOILS IN STEADY AND UNSTEADY FLOWS

The limit cycle flutter of a two-dimensional wing with non-linear pitching stiffness is investigated. For modelling the aerodynamic forces of the wing steady linear and non-linear models as well as an unsteady model were used. The flutter speed was calculated using the harmonic balance method and by predicting Hopf bifurcation. Analytical solutions based on the centre manifold theory and normal forms were obtained as were results given by the harmonic balance method. The analytical solutions were compared with those obtained by numerical integration. The results show that the harmonic balance method can forecast flutter speed with a good accuracy while analytical solutions based on centre manifold theorem are accurate only in a small neighbourhood of the bifurcation point. The oscillation of the airfoil after flutter for two different models, linear and non-linear pitching stiffness were compared with each other and the flutter speeds for two linear steady and an unsteady aerodynamic model calculated. The obtained results show that flutter analysis based on the linear steady model is conservative only for the ratios of plunge frequency to pitch frequency lower than 1.

Aeroelasticity Analysis of Air-Riding Seals for Aero-Engine Applications

This paper presents the results of a feasibility study on air-riding seal aeroelasticity for large-diameter aero-engines. A literature survey of previous seal studies revealed a significant amount of experimental work but numerical modeling using CFD techniques was relatively scarce. Indeed, most existing theoretical studies either deal with the structural behavior, or use simplified flow modeling. The aeroelasticity stability of a simplified air-riding seal geometry, devised for this particular feasibility study, was analyzed in three dimensions for typical engine operating conditions. Both the unsteady flow and structural vibration aspects were considered in the investigation. The boundary conditions and the seal gap were varied to explore the capabilities and limitations of a state-of-the-art unsteady flow and aeroelasticity code. The methodology was based on integrating the fluid and structural domains in a time-accurate fashion by exchanging boundary condition information at each time step. The predicted characteristics, namely lift and flow leakage as a function of pressure and seal gap, were found to be in agreement with the expected behavior. Operating seal gaps were determined from the actual time histories of the seal motion under the effect of the aerodynamic and the restoring spring forces. Both stable and unstable cases were considered. It was concluded that, in principle, the existing numerical tools could be used for the flow and aeroelasticity analyses of hydrostatic seals. However, due to large Mach number variations, the solution convergence rate was relatively slow and it was recognized that a preconditioner was needed to handle seal flows. For small gaps of about 10 microns, typical of spiral groved seals, the flow has a high Knudsen number, indicating that the Navier-Stokes formulations may no longer be valid. Such cases require a totally different treatment for the modeling of steady and unsteady aerodynamics, either by modifying the transport parameters of the Navier-Stokes equations or by considering rarefied gas dynamics.

Unsteady Cascade Aerodynamics in the Time Domain

A linearized unsteady incompressible aerodynamic model for airfoil cascades is developed that is not restricted to harmonic motion at a constant interblade phase angle. This is accomplished by starting with the unsteady aerodynamic coefe cients generated by LINSUB, a semianalyticunsteady cascadeaerodynamics codethat assumes linearity in both space and time. An inverse Fourier transform is then performed to predict the unsteady aerodynamic forces on the airfoils due to an impulsive acceleration. This result, termed the cascade indicial function, is then convolved with the arbitrary motion of the blades to obtain the unsteady aerodynamic forces on the airfoils in the time domain. The aerodynamic damping predicted by the time domain model is shown to compare well to LINSUB results when the interblade phase angle is constant. Results demonstrating the ability of the model to handle arbitrary airfoil motion are also presented. Nomenclature

Effect of Thrust on Bending-Torsion Flutter of Wings

The effect of thrust on the flutter of a high-aspect-ratio wing is investigated. The wing is represented by a beam using a nonlinear mixed finite element method. Aerodynamic forces are calculated using a finite-state, two-dimensional unsteady aerodynamic model. The effect of thrust is modeled as a follower force of prescribed magnitude. Without the thrust force, the wing is shown to become unstable for freestream airspeeds greater than the flutter speed. On the other hand, in the absence of aerodynamic forces, the wing becomes unstable for values of the thrust in excess of a critical magnitude of the force. When both effects are present, the airspeed at which the instability occurs depends on the thrust magnitude. For validation, an analytical solution for the en vacuo case (accounting only for the effect of thrust) was developed and shown to closely match results from the numerical method. Parametric studies show that the predicted stability boundaries are very sensitive to the ratio of bending stiffness to torsional stiffness. Indeed, the effect of thrust can be either stabilizing or destabilizing, depending on the value of this parameter. An assessment whether or not the magnitude of thrust needed to influence the flutter speed is practical is made for one configuration.

On aerodynamic modelling of an insect–like flapping wing in hover for micro air vehicles

This theoretical paper discusses recent advances in the fluid dynamics of insect and micro air vehicle (MAV) flight and considers theoretical analyses necessary for their future development. The main purpose is to propose a new conceptual framework and, within this framework, two analytic approaches to aerodynamic modelling of an insect-like flapping wing in hover in the context of MAVs. The motion involved is periodic and is composed of two half-cycles (downstroke and upstroke) which, in hover, are mirror images of each other. The downstroke begins with the wing in the uppermost and rearmost position and then sweeps forward while pitching up and plunging down. At the end of the half-cycle, the wing flips, so that the leading edge points backwards and the wing's lower surface becomes its upper side. The upstroke then follows by mirroring the downstroke kinematics and executing them in the opposite direction. Phenomenologically, the interpretation of the flow dynamics involved, and adopted here, is based on recent experimental evidence obtained by biologists from insect flight and related mechanical models. It is assumed that the flow is incompressible, has low Reynolds number and is laminar, and that two factors dominate: (i) forces generated by the bound leading-edge vortex, which models flow separation; and (ii) forces due to the attached part of the flow generated by the periodic pitching, plunging and sweeping. The first of these resembles the analogous phenomenon observed on sharp-edged delta wings and is treated as such. The second contribution is similar to the unsteady aerodynamics of attached flow on helicopter rotor blades and is interpreted accordingly. Theoretically, the fluid dynamic description is based on: (i) the superposition of the unsteady contributions of wing pitching, plunging and sweeping; and (ii) adding corrections due to the bound leading-edge vortex and wake distortion. Viscosity is accounted for indirectly by imposing the Kutta condition on the trailing edge and including the influence of the vortical structure on the leading edge. Mathematically, two analytic approaches are proposed. The first derives all the quantities of interest from the notion of circulation and leads to tractable integral equations. This is an application of the von Kármán-Sears unsteady wing theory and its nonlinear extensions due to McCune and Tavares; the latter can account for the bound leading-edge vortex and wake distortion. The second approach uses the velocity potential as the central concept and leads to relatively simple ordinary differential equations. It is a combination of two techniques: (i) unsteady aerodynamic modelling of attached flow on helicopter rotor blades; and (ii) Polhamus's leading-edge suction analogy. The first of these involves both frequency-domain (Theodorsen style) and time-domain (indicial) methods, including the effects of wing sweeping and returning wake. The second is a nonlinear correction accounting for the bound leading-edge vortex. Connections of the proposed framework with control engineering and aeroelasticity are pointed out.

IDENTIFICATION AND PREDICTION OF UNSTEADY TRANSONIC AERODYNAMIC LOADS BY MULTI-LAYER FUNCTIONALS

Nonlinear unsteady aerodynamic effects present major modelling difficulties in the analysis and control of aeroelastic response. A rigorous mathematical framework, that can account for the complex nonlinearities and time-history effects of the unsteady aerodynamic response, is provided by the use of functional representations. A recent development, based on functional approximation theory, has achieved a new functional form; namely, multi-layer functionals. The development of a multi-layer functional for discrete-time, finite memory, causal systems has been shown to be realizable via finite impulse response neural networks. Identification of an appropriate temporal neural network model of the nonlinear transonic aerodynamic response is facilitated via a supervised training process using multiple input–output sets, with data obtained by an Euler CFD code. The training process is based on a genetic algorithm to optimize the network architecture, combined with a random search algorithm to update weight and bias values. The approach is examined for two different multiple aerodynamic input–output data sets, and in both cases, the prediction properties of the network model establish the multi-layer functional as a suitable representation of unsteady aerodynamic response.

Vibration Reduction in Rotor Blades Using Active Composite Box Beam

The vibratory load reduction at a rotor hub using smart materials and closed-loop control is investigated. The principal load-carrying member in the blade is represented by a composite box beam, of arbitrary thickness, with surface bonded self-sensing actuators. A comprehensive theory is used to model the smart box beam. The theory, whichisbasedonaree neddisplacemente eld,isathree-dimensionalmodelthatapproximatestheelasticitysolution so that the beam cross-sectional properties are not reduced to one-dimensional beam parameters. Both in-plane and out-of-plane warpings are included automatically in the formulation. Next, an integrated rotor vibratory load analysis procedure is developed by coupling an unsteady aerodynamic model with the rotor blade dynamic model based on the smart composite box beam theory. The dynamic deformations of the blade in all three directions, e ap, lead lag, and torsion, are included in the analysis. The e nite-state, induced-e ow model is used for predicting the dynamic loads. The procedure results in signie cant reductions in the amplitudes of rotor dynamic loads with closed-loop control. Detailed parametric studies are presented to assess the ine uence of number of actuators and their locations in vibratory hub load reduction.

Prediction of the unsteady aerodynamic characteristics of horizontal axis wind turbines including three-dimensional effects

An unsteady aerodynamic model for horizontal axis wind turbine performance prediction has been extended to consider three-dimensional (3D) rotational effects. The method couples a prescribed wake vortex scheme with a semi-empirical unsteady aerofoil model to provide the unsteady response of the blades due to the cyclic variation of incidence. The wake geometry of the turbine and the basic aerodynamic parameters required by the unsteady aerofoil model are calculated from the prescribed wake model using two-dimensional aerofoil data. The 3D rotational effects are then taken into account by a series of corrections to the unsteady aerofoil model. Application of these corrections has yielded substantial improvements in the prediction of aerodynamic force and moment coefficients on inboard blade sections. This is illustrated by a series of comparisons with field data. In general, the method is shown to give accurate predictions over a range of operating conditions and inflow angles.