Nonlinear Aeroelastic Analysis of Control Surface with Freeplay Using Computational-Fluid-Dynamics-Based Reduced-Order Models

An experimental model for an all-movable horizontal tail with a free-play gap in the actuating mechanism at the root of the tail wingwas designed and constructed. The flutter response andnonlinear limit-cycle oscillations induced by a free-play gap have beenmeasured in theDukeUniversitywind tunnel, including gust responsemeasurements. A computational code has been developed for aeroelastic analysis using a linear three-dimensional time-domain vortex lattice aerodynamic model. The computational code is used to study the flutter limit-cycle-oscillation response induced by a free-play gap and the gust response with these free-play gaps. The effects of the nominal angle of attack on limit-cycle oscillation andgust excitation are also studied. The theoretical and experimental correlation shows that the angle of attack significantly affects the limit-cycle oscillation behavior and, if sufficiently large, may suppress the limit-cycle oscillation entirely. The computed results are compared with the experimental data with reasonably good quantitative agreement between theory and experiment for flutter and limit-cycle oscillation.

Energy harvesters are designed to convert energy from ambient sources to recharge batteries or power low-power-consumption microsystems. The piezoelectric transduction of aeroelastic vibrations is a scalable option for energy harvesting. To design an efficient harvester, the harvesting performance needs to be studied and hence enhanced. The purpose of this paper is to analyze the dynamic response and harvesting performance of an airfoilbased piezoaeroelastic energy harvester by investigating the effects of the system parameters and external discrete disturbances. The airfoil, with plunge and pitch degrees of freedom (DOFs), is supported by linear flexural springs and nonlinear torsional springs. Piezoelectric transducers are attached to the plunge DOF. The unsteady aerodynamics due to arbitrary motions are obtained from Jones’ approximation of the Wagner function. A state-space model is obtained for numerical simulation. Parameters including the load resistance, the nonlinear torsional stiffness coefficient, the free play gap and the locations of both elastic axis and gravity center axis of the airfoil are concerned. In addition, the effects of 1-cosine gust disturbances are studied. The results show that: as the resistance increases, each of the plunge and pitch motions has a minimum amplitude. But the minimum response amplitudes do not affect the variations of the electric outputs. There is one optimal resistance maximizing the power output. Besides, the increase of the free play gap enhances harvesting performance linearly, whereas large nonlinear torsional stiffness would significantly decrease the power output. The variations of the voltage output with the structural nonlinearities resemble that of the plunge motion. Moreover, there is one optimal eccentricity of the airfoil for the highest harvesting performance as the elastic axis is fixed and the flow velocity is certain. The rearward shift of the elastic axis helps enhance the power output whereas it demands larger eccentricities to maintain limit cycle oscillations (LCOs). Last but not the least, under a relative large wind scale, the discrete gust loads may change the equilibrium position of both plunge and pitch responses under special gust vertical velocities. The jumps may affect the phase of the electric outputs, but they make no difference on the amplitude of power output.

: Unsteady aerodynamic computational models for aeroelastic phenomena such as flutter and limit cycle oscillations are complex and high dimensional. Under this grant, reduced order models are being developed that offer increased physical insight and greatly reduced computational cost. Transonic flows are emphasized because of their practical importance and significant technical challenge.

Flutter analysis is an essential process for developing high-performance aerospace vehicles with salient fuel efficiency and durability. Although several methods are available, a rapid, economical, accurate method for flutter boundary determination is strongly needed. This paper proposes a new method to predict flutter onset conditions using aeroelastic (AE-) reduced-order models (ROM) that are built with optimized model hyperparameters in 2-dimensional (2-D) flight parameter space. Data-driven aerodynamic (A-) ROMs at various flight conditions are first constructed using the AutoRegressive eXogenous (ARX) method to map a relationship between the generalized displacement (GD) and generalized aerodynamic force (GAF) data obtained from FUN3D simulations. They are then combined with a physics-based structural dynamic (S-) ROM to form a fully coupled AE-ROM. Then, the grid search algorithm is implemented to find the best polynomial fit orders for the A-ROMs in AE-ROMs that yield the most accurate prediction of unsteady AE responses. The eigenvalues of the best-performed AE-ROMs are computed in the 2-D parameter space to analyze flutter behavior and determine the flutter onset and boundary of an AGARD 445.6 wing. The response surface of the maximum real part of the eigenvalues is verified by the damping ratio, another widely used flutter indicator. It is demonstrated that the proposed method and AE-ROMs are capable of accurately capturing stability characteristics of aeroelasticity and rapidly determining flutter onset and boundaries. Excellent agreement between the AE-ROM eigenvalues and the dampling ratio is also observed.

An overview of recent applications of the FUN3D CFD code to computational aeroelastic, sonic boom, and aeropropulsoservoelasticity (APSE) analyses of a low-boom supersonic configuration is presented. The overview includes details of the computational models developed including multiple unstructured CFD grids suitable for aeroelastic and sonic boom analyses. In addition, aeroelastic Reduced-Order Models (ROMs) are generated and used to rapidly compute the aeroelastic response and utter boundaries at multiple flight conditions.

This paper describes an efficient reduced order model (ROM) applied in the aerodynamic analysis of bluff bodies. The proposed method, which is based on eigensystem realization algorithm (ERA), uses the impulse response of the system obtained by computational fluid dynamics (CFD) analysis to construct a ROM that can accurately predict the response of the system to any arbitrary input. In order to study the performance of the proposed technique, three different geometries including elliptical and rectangular sections as well as the deck cross section of Great Belt Bridge (GBB) were considered. The aerodynamic coefficients of the impulse responses of the three sections are used to construct the corresponding ROM for each section. Then, the aerodynamic coefficients from an arbitrary sinusoidal input obtained by CFD are compared with the predicted one using the ROM. The results presented illustrate the ability of the proposed technique to predict responses of the systems to arbitrary sinusoidal and other generic inputs, with significant savings in terms of CPU time when compared with most CFD codes. The methodology described in this paper has wide application in many offshore engineering problems where flexible structures interact with unsteady fluid flow, and should be useful in preliminary design, in design optimization, and in control algorithm development.

Aeroelastic prediction in transonic buffeting flow with data fusion method

Aeroelastic response and limit cycle oscillations for wing-flap-tab section with freeplay in tab

Aerodynamic reduced-order model (ROM) is a useful tool to predict nonlinear unsteady aerodynamics with reasonable accuracy and very low computational cost. The efficacy of this method has been validated by many recent studies. However, the generalization capability of aerodynamic ROMs with respect to different flow conditions and different aeroelastic parameters should be further improved. In order to enhance the predicting capability of ROM for varying operating conditions, this paper presents an unsteady aerodynamic model based on long short-term memory (LSTM) network from deep learning theory for large training dataset and sampling space. This type of network has attractive potential in modeling temporal sequence data, which is well suited for capturing the time-delayed effects of unsteady aerodynamics. Different from traditional reduced-order models, the current model based on LSTM network does not require the selection of delay orders. The performance of the proposed model is evaluated by a NACA 64A010 airfoil pitching and plunging in the transonic flow across multiple Mach numbers. It is demonstrated that the model can accurately capture the dynamic characteristics of aerodynamic and aeroelastic systems for varying flow and structural parameters.

Limit cycle oscillation behavior of transonic control surface buzz considering free-play nonlinearity

A new approach for generating reduced-order models of fluid systems was developed using proper orthogonal decomposition in combination with Volterra theory. The method involves identifying fluid basis functions with proper orthogonal decomposition and applying systems realization theory to generate a low-dimensional model for the scalar coefficients. The method was tested on a two-dimensional inviscid flow over a bump with forcing. Eight fluid basis functions were identified, and the eigensystem realization algorithm was used to identify an eight-state, reduced-order model. Time histories of both the reduced-order coefficients and the expanded flowfield data accurately tracked the full-order results in both amplitude and phase (average error less than 5%). The reduced-order model demonstrated four-orders-of-magnitude reduction in compute time relative to the full system, which represents a computational improvement on the same order as the reduction in degrees of freedom.

We present an effective reduced-order model (ROM) technique to couple an incompressible flow with a transversely vibrating bluff body in a state-space format. The ROM of the unsteady wake flow is based on the Navier–Stokes equations and is constructed by means of an eigensystem realization algorithm (ERA). We investigate the underlying mechanism of vortex-induced vibration (VIV) of a circular cylinder at low Reynolds number via linear stability analysis. To understand the frequency lock-in mechanism and self-sustained VIV phenomenon, a systematic analysis is performed by examining the eigenvalue trajectories of the ERA-based ROM for a range of reduced oscillation frequency $(F_{s})$, while maintaining fixed values of the Reynolds number ($Re$) and mass ratio ($m^{\ast }$). The effects of the Reynolds number $Re$, the mass ratio $m^{\ast }$ and the rounding of a square cylinder are examined to generalize the proposed ERA-based ROM for the VIV lock-in analysis. The considered cylinder configurations are a basic square with sharp corners, a circle and three intermediate rounded squares, which are created by varying a single rounding parameter. The results show that the two frequency lock-in regimes, the so-called resonance and flutter, only exist when certain conditions are satisfied, and the regimes have a strong dependence on the shape of the bluff body, the Reynolds number and the mass ratio. In addition, the frequency lock-in during VIV of a square cylinder is found to be dominated by the resonance regime, without any coupled-mode flutter at low Reynolds number. To further discern the influence of geometry on the VIV lock-in mechanism, we consider the smooth curve geometry of an ellipse and two sharp corner geometries of forward triangle and diamond-shaped bluff bodies. While the ellipse and diamond geometries exhibit the flutter and mixed resonance–flutter regimes, the forward triangle undergoes only the flutter-induced lock-in for $30\leqslant Re\leqslant 100$ at $m^{\ast }=10$. In the case of the forward triangle configuration, the ERA-based ROM accurately predicts the low-frequency galloping instability. We observe a kink in the amplitude response associated with 1:3 synchronization, whereby the forward triangular body oscillates at a single dominant frequency but the lift force has a frequency component at three times the body oscillation frequency. Finally, we present a stability phase diagram to summarize the VIV lock-in regimes of the five smooth-curve- and sharp-corner-based bluff bodies. These findings attempt to generalize our understanding of the VIV lock-in mechanism for bluff bodies at low Reynolds number. The proposed ERA-based ROM is found to be accurate, efficient and easy to use for the linear stability analysis of VIV, and it can have a profound impact on the development of control strategies for nonlinear vortex shedding and VIV.

In this study, identification of nonlinear aerodynamic systems based on an improved nonlinear state-space modeling approach is presented to predict transonic aeroelastic behaviors of aircraft structures. It starts with identifying a linear state-space aerodynamic model by using the eigensystem realization algorithm and observer/Kalman filter identification methods. Subsequently, the remaining parameters of the nonlinear state-space aerodynamic model are determined through an output error-minimization procedure, based on a new training data generation methodology. To illustrate the approach, two- and three-dimensional transonic aeroelastic configurations are studied. The transonic aeroelastic behaviors predicted via the proposed approach agree well with those obtained via computational fluid dynamics technique in the interested range of dynamic pressure.

Investigation of rotating mode behavior in BWR out-of-phase limit cycle oscillations – Part 1: Reduced order model

The bronchial tree plays a main role in the human respiratory system because the air distribution throughout the lungs and gas exchange with blood occur in the airways whose dimensions vary from several centimeters to micrometers. Organization of about 60,000 conducting airways and 33 million respiratory airways in a limited space results in a complex structure. Due to this inherent complexity and a high number of airways, using target-oriented dimensional reduction is inevitable. In addition, there is no general reduced-order model for various types of problems. This necessitates coming up with an appropriate model from a variety of different reduced-order models to solve the desired problem. Lumped formulation, trumpet, or typical path model of whole or parts of bronchial tree are frequently used reduced-order models. On the other hand, using any of these models results in underestimation of flow heterogeneity leading to inaccurate prediction of the systems whose mechanisms depend on the fluid heterogeneity. In this study, a simple robust model combining mechanistic and non-mechanistic modeling approaches of the bronchial tree is proposed which overcomes the limitations of the previous reduced-order models and gives the same results of a detailed mechanistic model for the first time. This model starts from an accurate multi-branching model of conducting and respiratory airways (i.e., the base model) and suggests a proxy model of conducting airway and reduced-order model of respiratory airways based on the base model to significantly reduce computational cost while retaining the accuracy. The combination of these models suggests various reduced-order surrogate models of the human bronchial tree for different problems. The applications and limitations of each reduced-order model are also discussed. The accuracy of the proposed model in the prediction of fluid heterogeneity has been examined by the simulation of multi-breath inert gas washout because the alveolar slope is the reflection of fluid heterogeneity where the computational time decreases from 121h (using the base model) to 4.8s (using the reduced-order model). A parallel strategy for solving the equations is also proposed which decreases run time by 0.18s making the model suitable for real-time applications. Furthermore, the ability of the model has been evaluated in the modeling of asthmatic lung as an instance of abnormal lungs, and in the modeling of O2-CO2 exchange as an instance of nonlinear reacting systems. The results indicate that the proposed model outperforms previous models based on accuracy, robustness, and run time.