Unsteady Aerodynamic Model Research Articles

A modified unsteady-nonlinear aeroelastic model for flapping wings

A novel integrated aeroelastic model of flapping wings (FWs) undergoing a prescribed rigid body motion is presented. In this respect, the FW nonlinear structural dynamics is enhanced via a newly proposed modification of implicit condensation and expansion (MICE) method that better considers the structural nonlinear effects. In addition, the unsteady aerodynamic model is also an extension of the widely utilized modified strip theory (MST) in which the flexibility effects are accounted for (MST-Flex). The integrated utility of the proposed generalized MICE and MST-Flex is demonstrated to be more realistic for elastic FW flight simulation applications. The prescribed rigid body motion is produced via a servo motor whose dynamics is also considered for the analysis. A special case study is also performed whose combined aeroelastic solution is determined and validated under a sinusoidal flapping motion. To this end, an experimental setup is designed and tested in order to validate the proposed integrated approach for aeroelastic modeling of FWs. There is very good agreement between the numerical and experimental results for elastic FW aerodynamics. It should be noted that the proposed integrated aeroelastic approach is readily adaptable to all kinds of elastic wings with arbitrary geometry and various combination of structural elements.

Transonic flutter suppression with tuned mass damper by model-based stability analysis method

Flutter as a self-excited oscillation can cause catastrophic damage to the aircraft structure. Tuned mass damper (TMD) is one of the vibration suppression methods widely used in engineering. However, traditional linear aerodynamic methods are not accurate in transonic flow. In this study, we first establish an unsteady aerodynamic model of the NACA0012 airfoil using the system identification method based on the Auto-Regressive with eXogenous input (ARX) model. Then, a flutter suppression model is constructed by coupling the TMD with the aeroelastic system. The parameters of the TMD are investigated using the model-based aeroelastic stability analysis. It is found that the flutter instability mode of the original system has changed due to the participation of the TMD in the system modal coupling. The proposed reduced-order model (ROM) provides a fast stability analysis method for flutter suppression with TMD as well as significant guidance for TMD design and optimization.

Unsteady aerodynamic force modelling for 3-DoF-galloping of four-bundled conductors

Galloping of overhead transmission lines is characterised by large-amplitude, low-frequency, vertical–horizontal–torsional three degree-of-freedom (DoF) oscillations, which can potentially induce interphase short circuits and fatigue in the conductors and support structures. Numerical analyses are useful for estimating the galloping response of transmission lines, and unsteady aerodynamic forces should be evaluated for accurate simulation. In this study, the unsteady aerodynamic force modelling of four-bundled conductors is investigated based on aerodynamic force measurement test results. Three types of unsteady aerodynamic force measurement tests were performed: under constant torsional angular velocity and under torsional and vertical 1-DoF sinusoidal oscillations. Evaluating the dependence of the aerodynamic forces on the various motions enabled an improved unsteady aerodynamic force model to be developed, considering the effect of angular velocity. First, two-variable aerodynamic coefficients were proposed as a function of the angle of attack and non-dimensional angular velocity. These coefficients were determined via tests performed at constant torsional angular velocities; results with different combinations of wind speed and angular velocity confirmed that the non-dimensional angular velocity can be used to define the unsteady aerodynamic forces. Then, the validity of the two-variable aerodynamic force formulation was confirmed for predicting torsional or vertical 1-DoF oscillations, by comparing the unsteady aerodynamic force obtained via the sinusoidal forced-vibration tests and via the constant angular-velocity tests. Finally, results of the time-history​ analyses using the two-variable aerodynamic coefficients were compared with those of previous wind-response measurement tests to obtain the best unsteady aerodynamic force model for simulating large-amplitude 3-DoF galloping. These results indicate that the unsteady aerodynamic forces for 3-DoF-galloping of four-bundled conductors can be evaluated using the relative angle of attack, the rate of change of the relative angle of attack, and the relative wind speed, using two-variable aerodynamic coefficients measured under constant angular velocity conditions.

Dynamic inflow and unsteady aerodynamics models for modal and stability analyses in OpenFAST

This work presents two aerodynamic models that are used to perform modal and stability analyses of wind turbines. Including aerodynamic effects in stability analyses is important to capture aerodynamic inertia, stiffness, and damping. The two models consist of a dynamic inflow model based on Øye’s model and an unsteady aerodynamics model based on a simplified Beddoes-Leishman dynamic stall model. Both models are written in a continuous-time state-space form, which is the form needed to perform linearizations within OpenFAST. In this article, we present the new models, perform some simple verifications against HAWC2 results, and then perform stability analyses. We investigate the contribution of the aerodynamic effects on the turbine modes, particularly the flapwise modes, which are the most affected. Because of the development presented in this work, Campbell diagrams accounting for dynamic stall and dynamic wake effects were generated for the first time using OpenFAST.

Unsteady aerodynamic modelling for dual-rotor wind turbines with lifting surface method and free wake model

A time-marching aerodynamic model for dual-rotor wind turbines (DRWT) is presented with the lifting surface method and free wake model. The performance of a reference DRWT by two axial connected NREL 5MW wind turbines is calculated to verify the algorithm. The output converges with remarkable oscillation. Free wakes swell under the coupling effect. The accumulated power of DRWT outranges single-rotor wind turbine (SRWT) by a limited extent under certain operating conditions. The front rotor (FR) produces the major portion of the power, especially for low inflow velocity. The unsteadiness of performance and spanwise load is further investigated, and the result shows that the power output of the rear rotor (RR) undergoes greater fluctuation than FR. The rotor-rotor induction strengthens both the rotors’ performance before they align and weakens it when they rotate away. The additional disturbance caused by FR’s tip vortices acts negatively on RR’s torque by upwashing the blade tip.

An unsteady aerodynamic model for three-dimensional wing based on augmented lifting-line method

AbstractA fast numerical method for unsteady aerodynamic calculation of 3D wing is established, which is suitable for the preliminary design. Based on the lifting-line method, the aerodynamic data of the 2D aerofoil obtained by the unsteady CFD simulation is used as the model input to solve the aerodynamic force of the 3D wing. Compared with the traditional steady lifting-line method, the augmented method adopts the unsteady Kutta-Jouowski (K-J) theorem to calculate the circulation and improve the accuracy of the method through the circulation correction. The pitching motion of 3D wing at different aspect ratio and reduction frequencies are studied. The results show that the aerodynamic forces obtained by the augmented lifting-line method have good agreement with the 3D unsteady CFD calculations. Compared with 3D CFD calculation, the calculation efficiency of the improved method is increased by more than 12 times. The improved method has extensive applicability and can be used to estimate the unsteady aerodynamic forces of 3D single or multiple wing configurations.

Nonlinear Aeroelastic Analysis for Highly Flexible Flapping Wing in Hover

Aeromechanics of highly flexible flapping wings is a complex nonlinear fluid–structure interaction problem and, therefore, cannot be analyzed using conventional linear aeroelasticity methods. This paper presents a standalone coupled aeroelastic framework for highly flexible flapping wings in hover for micro air vehicle (MAV) applications. The MAV-scale flapping wing structure is modeled using fully nonlinear beam and shell finite elements. A potential-flow-based unsteady aerodynamic model is then coupled with the structural model to generate the coupled aeroelastic framework. Both the structural and aerodynamic models are validated independently before coupling. Instantaneous lift force and wing deflection predictions from the coupled aeroelastic simulations are compared with the force and deflection measurements (using digital image correlation) obtained from in-house flapping wing experiments at both moderate (13 Hz) and high (20 Hz) flapping frequencies. Coupled trim analysis is then performed by simultaneously solving wing response equations and vehicle trim equations until trim controls, wing elastic response, inflow and circulation converge all together. The dependence of control inputs on weight and center of gravity (cg) location of the vehicle is studied for the hovering flight case.

Nonlinear aeroelastic stability analysis of a two-stage axially moving telescopic wing by using fully intrinsic equations

During the process of span extension for an aircraft wing equipped with a telescopic morphing mechanism, the wing aspect ratio increases, and hence, the geometrical nonlinearities might become more significant. In this regard, this paper aims to investigate the effect of structural nonlinearity on the aeroelasticity of span morphing wings using the exact fully intrinsic equations for the first time. Furthermore, the effects of various parameters such as thrust force, engine location, chord size, flight altitude, initial angle of attack, and overlapping mass on the aeroelasticity of the wing are studied. The applied aerodynamic loads in an incompressible flow regime are determined using Peters’ unsteady aerodynamic model. In order to check the stability of the system, first the resulting nonlinear partial differential equations are discretized by using the central finite difference method and then linearized about the static equilibrium. Finally, by obtaining the eigenvalues of the linearized system, the stability of the wing is evaluated. It is observed that by using the fully intrinsic equations, the instability of the axially moving telescopic wing can be determined more accurately. Moreover, the results show that the morphing length and overlapping mass have significant effects on the aeroelastic stability of the telescopic wing.

Parametric study on the dynamic aeroelastic analysis of a two-stage axially deploying telescopic wing

In this paper, the flutter instability of a conventional two-stage axially moving telescopic UAV wing is investigated. To this aim, and to be as close as possible to the reality, the effects of temporal variation of mass and length, due to the movement of stages and their overlapping, along with the effects of morphing speed are considered for the first time. The bending-torsional dynamics of the two-stage wing is modeled by modifying the Euler–Bernoulli beam theory to take into account the effects of morphing speed and variations of mass and length. Furthermore, the aerodynamic loads are simulated using Peters' unsteady aerodynamic model. The governing aeroelastic equations are discretized using a finite element approach, and a length-based stability analysis is proposed to investigate the aeroelasticity of the wing. The obtained results are compared with those available in the literature, and a good agreement is observed. It is found that the aeroelastic stability of a telescopic wing is more sensitive to the fixed part parameters than the moving part. Also, it is shown that the wing critical length is sensitive to the morphing speed. Therefore, by selecting the telescopic wing morphing parameters properly, the aeroelastic stability of the system can significantly be improved.

Comparative Study of Lifting Surface and CFD Methods in the Simulation of Morphing Process of Folding Wing

A folding wing aircraft can autonomously change its configuration in flight to respond to different flying environments. Hinge moment during morphing process is an important basis for driving mechanism design and structural strength check, and its calculation depends on the simulation of the morphing process. Existing studies mostly use the simplified lifting surface method for aerodynamic modeling. In this paper, the CFD-based simulation method is studied, and the results are compared with those by the lifting surface method. First, the unsteady aerodynamic modeling method of the folding wing based on the CFD method is studied, an effective description method is given to define the wall mesh motion caused by wing folding and aileron deflection, and an unfolding–refolding strategy is proposed to improve the quality of the internal mesh in the case of large folding angles. Then, the CFD aerodynamic model is coupled through a developed coupling calculation program with the flexible multibody structure model for the simulation of a flight-morphing process. The comparison with the results of the lifting surface method shows that hinge moments obtained according to the two aerodynamic models are markedly different. Analysis of the difference shows that airfoil thickness considerably affects aerodynamic loading distributions and hinge moments of folding wing aircraft. The lifting surface method ignores airfoil thickness, which will cause large simulation errors in hinge moments.

The unsteady aerodynamics of insect wings with rotational stroke accelerations, a systematic numerical study

To generate aerodynamic forces required for flight, two-winged insects (Diptera) move their wings back and forth at high wing-beat frequencies. This results in exceptionally high wing-stroke accelerations, and consequently relatively high acceleration-dependent fluid forces. Quasi-steady fluid force models have reasonable success in relating the generated aerodynamic forces to the instantaneous wing motion kinematics. However, existing approaches model the stroke-rate and stroke-acceleration effects independently from each other, which might be too simplified for capturing the complex unsteady aerodynamics of accelerating wings. Here, we use computational-fluid-dynamics simulations to systematically explore how aerodynamic forces and flow dynamics depend on wing-stroke rate, wing-stroke acceleration and wing-planform geometry. Based on this, we developed and calibrated a novel unsteady aerodynamic force model for insect wings with stroke accelerations. This includes improved versions of the translational-force model and the added-mass force model, and we identify a third novel component generated by the interaction of the two. This term reflects the delay in bound-circulation build-up as the wing accelerates. The physical interpretation of this effect is analogous to the Wagner effect experienced by a wing starting from rest. Here, we show that this effect can be modelled in the context of flapping wings as a stroke-acceleration-dependent correction on the translational-force model. Our revised added-mass model includes a viscous force component, which is relatively small but not negligible. We subsequently applied our new model to realistic wing-beat kinematics of hovering Dipteran insects, in a quasi-steady approach. This revealed that stroke-acceleration-related aerodynamic forces contribute substantially to lift and drag production, particularly for high-frequency flapping mosquito wings.

Real-time prediction framework for frequency-modulated multirotor noise

A comprehensive multirotor noise assessment framework is developed to predict the noise of rotational-speed-controlled rotor configurations in real-time. The key objectives are to synthesize the frequency-modulated multirotor noise and analyze the frequency modulation (FM) characteristics. The framework includes modules associated with the flight control, aerodynamics, time reconstruction, noise prediction, and time-frequency analysis (TFA). In addition to the hybrid blade element momentum model, the aerodynamics module contains a linear inflow model, a Beddoes wake model, and an unsteady aerodynamic correction model. The convective form and source-time dominant algorithms are used in the acoustic analogy for tonal noise prediction. The FM characteristics are identified using the synchrosqueezing-based high-resolution TFA for strongly non-stationary signals. The framework is verified through validation and verification studies for diverse rotor configurations and flight conditions. During the cruise flight of the multirotor, the tonal noise exhibits simultaneous frequency and amplitude modulations. In wind gust conditions, these modulations result from rotational speed variations, acoustic wave interference, and Doppler shifting. By clarifying the non-stationary noise signal in diverse flight environments, the proposed framework can facilitate noise assessment in the perception-influenced design stage of multirotor configurations.

Evaluating Longitudinal Unsteady Aerodynamic Effects in Stall for a T-Tail Transport Model

Although there have been many proposed methods to model unsteady aerodynamic effects in the stall and poststall region, little work has been done to directly assess the impact of unsteady aerodynamic models on stability and control characteristics. In this paper, the state-space method for unsteady aerodynamic modeling is combined with bifurcation analysis to examine the sensitivity of stall and poststall behavior to the choice of aerodynamic modeling method: quasi-steady or unsteady. It is found that quasi-steady modeling can adequately capture the dynamics of the chosen example of a T-tailed transport aircraft with negligible wing–tail coupling. The study is then expanded to investigate a hypothetical situation with highly unsteady aerodynamic characteristics resembling a delta wing configuration—achieved by increasing the time delay constants in the unsteady model. This results in an aircraft with significantly lower flying qualities as indicated by bifurcation analysis. These findings highlight the need to implement unsteady aerodynamic modeling techniques in high-performance aircraft with significant vortex-related unsteady aerodynamics in order to sufficiently capture their stall and poststall dynamics.

Unsteady Aerodynamic Modeling and Analysis of Load Distribution for Helicopter Rotor Blades

The complexity of the kinematics and aerodynamics of rotors is a challenging problem for achieving accurate modeling for prediction of rotor loads. The present paper describes an unsteady aerodynamic model based on strip theory for the prediction of local aerodynamic loads on helicopter blades in translational flights. The proposed model accounts aerodynamically for unsteady behavior, poststall, leading-edge suction, and, structurally, local elastic torsion. Also, the local pitching moment coefficient is calculated according to the local parameters of both aerodynamic characteristics and unsteady angle of attack. A case study with published experimental data is selected to validate the model for the same operating conditions. The case is the 7A rotor high-speed test (point 312) performed in the French Space Lab’s (ONERA) S1MA wind tunnel in Modane-Avrieux, France. The proposed model is capable of predicting, qualitatively, the variation in both local normal force and pitching moment coefficients. Computational solver results are compared with experimental results to qualitatively clarify the physical differences between them. The main conclusion is that the proposed model calculations generally reflect the same trends as the test data, providing confidence in the ability to increase the model’s fidelity in calculating the aerodynamic behavior of rotors.

Recent Progress on Aeroelasticity of High-Performance Morphing UAVs

The high-performance morphing aircraft has become a research focus all over the world. The morphing aircraft, unlike regular unmanned aerial vehicles (UAVs), has more complicated aerodynamic characteristics, making itmore difficultto conduct its design, model analysis, and experimentation. This paper reviews the recent process and the current status of aeroelastic issues, numerical simulations, and wind tunnel test of morphing aircrafts. The evaluation of aerodynamic characteristics, mechanism, and relevant unsteady dynamic aerodynamic modeling throughout the morphing process are the primary technological bottlenecks formorphing aircrafts. The unstable aerodynamic forces have a significant impact on the aircraft handling characteristics, control law design, and flight safety. In the past, the structural analysis of morphing aircrafts, flight dynamics modeling, computational mesh morphing technology, and aerodynamic calculation were performed in promoting the development of next generation UAVs, with nonlinear dynamic challenges includingtransonic aeroelastic problems and high angle of attack aeroelastic problems. At present, many facets of these difficulties, together with the accompanying numerical simulation studies, remain under-explored. In addition, wind tunnel experiments face significant challenges in the dynamic morphing process. Finally, dynamic unsteady aerodynamic characteristics in the continuous morphing process still need to be verified by more related experiments.

適応的空力弾性制御モデルの構築と風洞実験による検証 ---圧力制御と翼端変位推定---

GLA (= Gust Load Alleviation) control is an important active safety technology, especially for light-weight flexible wing aircraft with high aspect ratio wings. This paper proposes an adaptive aero-servo-elastic model for control design, including an aerodynamic load distribution estimator using in-flight partial pressure sensing. The GLA control law obtained based on the proposed model consists of pressure control and mode estimation. In general, aero-servo-elastic models require an wing structure dynamics and an aerodynamic model around the wing. However, it is difficult to construct a generic model in advance for complex unsteady aerodynamic phenomena where turbulence and vibration of flexible wings interact. In this case, the optimality and the reliability of a model-based GLA control is significantly reduced. To minimize the uncertainty of the model for unsteady aerodynamics, this method proposes the use of an autoregressive model with time-varying coefficients, which are updated in real-time based on in-flight pressure sensing. The feasibility of the proposed GLA scheme is demonstrated in terms of both pressure control and wing tip displacement estimation through wind tunnel experiments.

Tilt-rotor aircraft fuselage wall aeroacoustics radiation suppression using Higher harmonic control

Aeroacoustics radiation is one of the main sources of tilt-rotor aircraft interior noise. In order to reduce the noise radiation on the surface of tilt-rotor aircraft fuselage, an active rotor control technology based on Higher Harmonic Control (HHC) is proposed. Its control effect is verified by simulation and the control mechanism is studied at the same time. Firstly, a tilt-rotor aeroacoustics prediction model is established based on FW-H equation and Beddoes unsteady aerodynamic model. And the accuracy of the above model is verified according to the flight test data of the XV-15 tilt-rotor aircraft. Furthermore, taking XV-15 as the object, a simulation research of rotor aeroacoustics active control is carried out in both airplane mode and helicopter mode. The simulation research reveals that: the HHC can suppress the aeroacoustics radiation of tilt-rotor to the fuselage through the principle of sound pressure cancellation. By applying appropriate control inputs, the maximum aeroacoustics radiation can be reduced by 9.2 dB in airplane mode; and the maximum aeroacoustics radiation can be reduced by 13.5 dB in helicopter mode.

A reduced order model for coupled mode cascade flutter analysis

A Reduced Order Model (ROM) based analysis method for turbomachinery cascade coupled mode flutter is presented in this paper. The unsteady aerodynamic model is established by a system identification technique combined with a set of Aerodynamic Influence Coefficients (AIC). Subsequently, the aerodynamic model is encoded into the state space and then coupled with the structural dynamic equations, resulting in a ROM of the cascade aeroelasticity. The cascade flutter can be determined by solving the eigenvalues of the ROM. Bending-torsional coupled mode flutter analysis for the Standard Configuration Eleven (SC11) cascade is used to validate the proposed method.

Development of an aeroelastic model based on system identification using boundary elements method

PurposeThe purpose of this paper is to analyze the stability of aeroelastic systems using a novel reduced order aeroelastic model.Design/methodology/approachThe proposed aeroelastic model is a reduced-order model constructed based on the aerodynamic model identification using the generalized aerodynamic force response and the unsteady boundary element method in various excitation frequency values. Due to the low computational cost and acceptable accuracy of the boundary element method, this method is selected to determine the unsteady time response of the aerodynamic model. Regarding the structural model, the elastic mode shapes of the shell are used.FindingsThree case studies are investigated by the proposed model. In the first place, a typical two-dimensional section is introduced as a means of verification by approximating the Theodorsen function. As the second test case, the flutter speed of Advisory Group for Aerospace Research and Development 445.6 wing with 45° sweep angle is determined and compared with the experimental test results in the literature. Finally, a complete aircraft is considered to demonstrate the capability of the proposed model in handling complex configurations.Originality/valueThe paper introduces an algorithm to construct an aeroelastic model applicable to any unsteady aerodynamic model including experimental models and modal structural models in the implicit and reduced order form. In other words, the main advantage of the proposed method, further to its simplicity and low computational effort, which can be used as a means of real-time aeroelastic simulation, is its ability to provide aerodynamic and structural models in implicit and reduced order forms.

Unsteady aerodynamic reduced-order modeling based on machine learning across multiple airfoils

Computational-fluid-dynamics-based prediction of unsteady aerodynamics is an essential research topic in the design of aircraft, which usually requires very high computational cost. Therefore, developing efficient and accurate reduced-order models (ROMs) for unsteady aerodynamics is important. With recent progress in modeling unsteady aerodynamics for a fixed configuration, there is a need of developing reduced-order models across multiple geometrical shapes. In this work, the long short-term memory (LSTM) network, a traditional model in machine learning for modeling time-dependent dynamics, is utilized to construct the unsteady aerodynamic reduced-order model, which takes into account the variation of airfoil geometry. The proposed approach is illustrated by some NACA 6-series airfoils under pitching and plunging motions in the transonic flow, where the geometrical parametrization is based on the maximum camber and thickness. Results show that the model can accurately capture the unsteady aerodynamics for varying shape parameters. Finally, as a proof of concept, the constructed ROM is applied to uncertainty and sensitivity analysis with respect to the variation of geometry parameters.