Unsteady Aerodynamic Forces Research Articles

Time-delay feedback control on vertical vibration of maglev train under unsteady aerodynamic force

The stability and safety of maglev trains are significantly affected by unsteady aerodynamic forces during high-speed operation. In this paper, we employ a time-delay feedback control strategy to suppress the nonlinear vertical vibrations of maglev train under periodic unsteady aerodynamic force. Firstly, the amplitude-frequency response equation of the maglev vehicle is derived using the multiple scales method, and the stability of the steady-state solutions is determined. Then, the influences of velocity feedback gain coefficient and velocity time delay on the nonlinear vibrations of the maglev vehicle are investigated. The optimal value range of the time delay is identified. The results demonstrate that the time delay feedback control can effectively suppress the nonlinear vibration of maglev vehicles and enhance their operational stability under the premise of reasonable selection of time delay parameters. The theoretical research presented in this paper can serve as a theoretical reference for the design, improvement, and optimization of control systems for high-speed maglev trains.

Nonlinear unsteady aerodynamic forces prediction and aeroelastic analysis of wind-induced bridge response at multiple wind speeds: A deep learning-based reduced-order model

Machine learning-based aerodynamic reduced-order models (ROMs) combine high accuracy with extremely low computational costs, making them highly effective in predicting nonlinear and unsteady bridge aerodynamic forces. Although several machine learning-based nonlinear aerodynamic models have been developed, the majority are built on a single wind speed parameter. However, in nonlinear aerodynamic prediction and aeroelastic analysis of bridges, the variability in incoming wind speed significantly influences the computed results. A ROM relying solely on a single wind speed lacks the ability to accurately forecast the intricate dynamic behaviors arising from changes in wind speed. When the incoming wind speed changes, the model's prediction accuracy significantly decreases. Usually, it is necessary to establish a new database and train a new model, which not only increases time and cost but also greatly reduces the convenience of the ROM. Addressing this challenge, this study proposes a multiple-wind-speed (MWS) nonlinear unsteady bridge aerodynamic model based on the LSTM deep neural network. Taking the Taohuayu Yellow River Bridge in the Henan Province of China as an example, the modeling process of the proposed MWS-ROM is demonstrated, along with non-linear aerodynamic predictions of the deck under various conditions and aerodynamic-elastic analysis of the deck under different wind speeds. The research results show that the trained LSTM network can accurately predict the nonlinear aerodynamic forces of bridges under single and double degrees of freedom vibration conditions. The MWS-ROM performed well in predicting convergent vibrations at low wind speeds and limits cycle oscillations at high wind speeds, aligning closely with results from the CFD full-order model. Compared to CFD, the aerodynamic ROM based on the LSTM network significantly enhances computational efficiency, consequently boosting the convenience and efficiency of bridge flutter analysis. Additionally, the methodology proposed herein can be extended for wind-induced vibration control and response prediction in other types of deck sections.

Active Maneuver Load Alleviation for a Pitching Wing via Spanwise-Distributed Camber Morphing

This paper presents the design and verification of a nonlinear model inversion (NMI) controller for the maneuver load alleviation of a pitching oscillating wing based on spanwise-distributed active camber morphing. Recurrent neural networks (RNNs) are used to predict nonlinear and unsteady aerodynamic forces due to wing's large amplitude pitching maneuver, and a fully connected neural network is introduced to build the dynamic inversion of the aeroelastic system for control law design. The inversed system is concatenated with a PI controller to assemble a nonlinear active controller. The controller is first utilized in an offline environment for a 1DoF pitching finite-span wing with spanwise-distributed active camber morphing and then verified in CFD-based fluid-structure-control coupling simulation. The results show that the offline controller could eliminate the maneuver load. In the online CFD-based fluid-structure-control simulation, the bending moment can be alleviated by 38%.

Effect of Blade Material of Steam Turbine Rotor on Aeroelastic Characteristics

Elements of powerful steam turbines are subjected to significant unsteady loads, in particular the rotor blades of the last stages. These loads, in some cases, can cause self-excited oscillations, which are extremely dangerous and have a negative impact on the efficiency and service life of the blade cascade. Therefore, when designing new or modernizing existing steam turbine stages, it is recommended to study the aeroelastic characteristics of the blades. The conditions for the occurrence of self-excited oscillations are influenced by both the geometric characteristics and the alloy from which the blade is made. To determine the effect of the blade material on the aeroelastic behaviour, a numerical analysis of the aeroelastic characteristics of the last stage blades made of steel and titanium alloy was performed. For the analysis, the method of simultaneous modeling of unsteady gas flow through the blade cascades and elastic vibrations of the blades (coupled problem) was used, which allows obtaining the amplitude-frequency spectrum of the interaction of unsteady loads and blade vibrations. The paper presents the results of numerical analysis for harmonic oscillations with a given amplitude and a given inter-blade phase angle, as well as for the regime of coupled vibration of blades under the action of unsteady aerodynamic forces. The dependences of the aerodamping coefficient on the inter-blade phase angle and the distribution of the coefficient along the blade are presented. The results of modeling the coupled vibration of the blades for the first six natural forms are presented in the form of a time-evolving displacement of the blade peripheral section, as well as forces and moments acting on the peripheral section. The corresponding amplitude-frequency spectra of displacements and loads in the peripheral section are also presented. The analysis of the results showed an insignificant difference in the characteristics of the proposed blade materials. For the first natural form of blade oscillations, the possibility of self-excited oscillations was found, and for the second form, there are conditions for the appearance of stable self-oscillations.

Moving-fuzzy sliding mode control of aircraft wing-rock motion

This work represents a moving fuzzy sliding mode controller (SMC) to suppress the wing-rock motion, a self-sustaining cycle oscillation caused by the nonlinear coupling between the unsteady aerodynamic forces and the dynamic response of the aircraft. Based on fuzzy systems, a moving algorithm is designed to estimate the unknown nonlinear dynamic function of the system in the control topology. The fuzzy algorithm is formulated by taking the width’s value, and based on Lyapunov theory, the membership function’s mean vector is adapted online. Simulation results, for examples that include small and large initial conditions, demonstrate the effectiveness of the proposed fuzzy sliding mode controller.

Efficient multi-fidelity reduced-order modeling for nonlinear flutter prediction

Flutter prediction is an important part of aircraft design. However, high-fidelity predictions for transonic flutter are difficult to make because of the associated computational costs. This paper proposes a multi-fidelity reduced-order modeling (MFROM) framework for flutter predictions to achieve high-fidelity simulations with limited computational costs. The high-fidelity data were obtained from a Navier–Stokes-equation-based solver, while the low-fidelity data were taken from an Euler-equation-based flow solver. By employing a multi-fidelity neural network trained with two types of data, this methodology enables nonlinear predictions for transonic results. To demonstrate the multi-fidelity process, a widely used pitching and plunging airfoil case is considered. Verification of the approach was performed by comparing with results from time-domain aeroelastic solvers. The results showed that the proposed multi-fidelity neural network modeling framework could realize online predictions of unsteady aerodynamic forces and flutter responses across multiple Mach numbers. Compared with the typical multi-fidelity method, the proposed neural network has a higher accuracy and a stronger generalization capability. Finally, the potential of the method to reduce the computational effort of high-fidelity aeroelastic analysis was demonstrated.

Unsteady Aerodynamic Forces of Tandem Flapping Wings with Different Forewing Kinematics.

Dragonflies can independently control the movement of their forewing and hindwing to achieve the desired flight. In comparison with previous studies that mostly considered the same kinematics of the fore- and hindwings, this paper focuses on the aerodynamic interference of three-dimensional tandem flapping wings when the forewing kinematics is different from that of the hindwing. The effects of flapping amplitude (Φ1), flapping mean angle (ϕ1¯), and pitch rotation duration (Δtr1) of the forewing, together with wing spacing (L) are examined numerically. The results show that Φ1 and ϕ1¯ have a significant effect on the aerodynamic forces of the individual and tandem systems, but Δtr1 has little effect. At a small L, a smaller Φ1, or larger ϕ1¯ of the forewing can increase the overall aerodynamic force, but at a large L, smaller Φ1 or larger ϕ1¯ can actually decrease the force. The flow field analysis shows that Φ1 and ϕ1¯ primarily alter the extent of the impact of the previously revealed narrow channel effect, downwash effect, and wake capture effect, thereby affecting force generation. These findings may provide a direction for designing the performance of tandem flapping wing micro-air vehicles by controlling forewing kinematics.

Time-Varying Aeroelastic Modeling and Analysis for a Morphing Wing

The paper presents a novel time-varying aeroelastic modeling approach for the morphing wing with the process of camber changing. The time-varying modeling methodology includes structural dynamics modeling, unsteady aerodynamic modeling, and interpolation for fluid–structure coupling. Firstly, the morphing wing is modularized and divided into fixed and variable parts by the floating frame of reference formulation. It is combined with the Craig–Bampton method to reduce order and eliminate nonindependent degrees of freedom. Then, the unsteady vortex-lattice method is used to calculate the transient, unsteady aerodynamic force for time evolution. Furthermore, the above time-varying structural dynamics modeling and a fluid–structure coupling interpolation are integrated to construct overall aeroelastic modeling, obtaining a set of differential-algebraic equations. Finally, these equations are numerically solved by the generalized-α method. The proposed approach provides an innovative idea to deal with the incredible complexity of the aeroelastic effect as structural characteristics change over time. It can efficiently and accurately analyze the morphing wing’s transient response or flutter property. To verify and utilize the time-varying aeroelastic modeling approach, numerical calculations and comparative studies were carried out regarding the time-varying characteristics of the structural modes, aerodynamic calculations, and flutter prediction of the morphing wing.

Hysteresis behavior and generalized Hopf bifurcation in a three-degrees-of-freedom aeroelastic system with concentrated nonlinearities

A three-degrees-of-freedom aeroelastic system with concentrated structural nonlinearities is considered. The aerodynamic loads in the model are simulated by using unsteady aerodynamic forces. First, we evaluate the linear stability region of the aerodynamic system employing the Lienard–Chipart criterion so that the stability boundaries of the center of gravity position and the uncoupled pitch natural frequency are obtained. Next, we present the distribution of the first Lyapunov coefficient l1 in the parameter space by using the Poincaré projection method to determine the type of Hopf bifurcation (subcritical or supercritical). We identify three types of hysteresis loops associated with Hopf bifurcations: the first type contains one stable equilibrium point and one stable limit cycle, the second type consists of one stable equilibrium point and two stable limit cycles, and the third type comprises two stable limit cycles. Nonlinear analysis shows that the variations in hysteresis loop types are mainly caused by the nonlinear flutter critical points, namely the saddle–node bifurcation points of limit cycles. Furthermore, we determine a degenerate Hopf bifurcation type known as generalized Hopf bifurcation (Bautin bifurcation) and its corresponding second Lyapunov coefficient, l2. Subsequently, we conduct nonlinear flutter analyses for positive and negative values of l2 by using bifurcation diagrams and phase portraits. The results show that when the uncoupled pitch natural frequency is used as the control parameter, the occurring generalized Hopf bifurcations are all supercritical (l2<0). However, when the center of gravity position is used as the control parameter, the generalized Hopf bifurcations that occur have both supercritical and subcritical (l2>0) modes.

Investigating the unsteady flow mechanism at the lip of a ducted fan in crosswind

The unsteady numerical analysis method was utilized to investigate the unsteady flow structure of a contra-rotating ducted fan under crosswind conditions. The development and evolution mechanism of the lip vortex under the combined action of crosswind and rotor were studied. Two perspectives, namely the time-averaged flow field and unsteady time-frequency analysis, were employed for the examination. The results indicate that the unsteady aerodynamic forces exerted on the lip of the ducted fan are primarily influenced by four sets of frequencies, ranked in descending order of magnitude: 1 BPF (Blade Passing Frequency) of the upstream rotor, 1 BPF of the downstream rotor, the combined effect of the 1 BPF of the upstream rotor and 1 BPF of the downstream rotor, and 2 BPF of the upstream rotor. The maximum velocity occurs at the position where the inner surface of the windward side lip is inclined 40° from the freestream velocity direction, and a stable separation vortex is formed below this region. The lip separation vortex triggers the generation of blade suction side separation vortex in the upstream rotor, and its periodic formation, growth, shedding, and dissipation are the primary factors contributing to the unsteady flow. The research findings lay the groundwork for further advancements in active and passive flow control technologies under crosswind conditions.

Unsteady Aerodynamic Forcing Due to Distortion in a Boundary Layer Ingesting Fan

Abstract Boundary Layer Ingestion (BLI) is a concept with the potential to reduce energy consumption needed for aircraft propulsion. For the fan this results in a need to work well in an environment of increased continuous distortion. The objective of this study is to increase the understanding of unsteady aerodynamic forces due to total pressure distortion in a BLI fan. This is done by using computational fluid dynamics to analyze a fan design intended for a BLI installation. Results include low subsonic to transonic operating speeds and distortion in a wide range of wave numbers. The forcing exhibits a significant dependency on the aeroacoustic cut-on/cut-off condition. This is in particular true at part speed where the normalized unsteady force rises sharply before dropping suddenly as the corrected speed or engine order increases. Unsteady pressure in the blade passage is observed to exhibit the same increase in level followed by a sudden drop once the cut-on limit is passed and undamped pressure waves propagating out from the blade row appear. The unsteady forces on the first three modes exhibit different sensitivities to the distortion wavelength but all are affected by the acoustic condition. By comparing results for the reference fan to a similar fan design with a higher blade count the cascade properties of the blade row are found to dominate the interaction. A result of this is that a higher blade count fan may be less affected by the distortion, and be less prone to propagate noise due to low engine order distortion.

Combined Theodorsen and Sears theory: experimental validation and modification

The response of airfoils to unsteady disturbances is a classic problem in the aerodynamics field. Many theoretical models have been proposed in the past to predict the unsteady aerodynamic forces of airfoils. However, these theories focused on individual airfoil motions or incoming flow disturbances, while the theoretical models for multiple disturbances still need to be developed. In this study, a theoretical model to predict the aerodynamic force of an oscillating airfoil encountering vertical gust is derived from a linear combination of Theodorsen's and Sears’ theories. Experimental investigations involving a two-dimensional pitching airfoil encountering a sinusoidal vertical gust are carried out to examine the proposed theory. It is found that the theory effectively captures the trends in the unsteady lift of airfoils subjected to dual disturbances. However, it tends to overestimate the lift amplitude. Notably, when a quasi-steady correction is applied to the theory, the prediction accuracy is greatly improved. The theory correction agrees well with experiment at small pitching frequencies, while deviations exist at higher pitching frequencies. The temporal evolution of the flow velocity reveals that the velocity disturbance induced by the coupled disturbance around the airfoil conforms to the linear superposition of the velocities induced by each individual disturbance, consistent with the prediction of the vortex sheet model. As the pitching frequency increases, significant nonlinear effects appear near the trailing edge of the airfoil, which may be one key factor for the disparities between the theoretical predictions and the experimental lift at higher pitching frequencies.

Geometric control analysis of the unsteady aerodynamics of a pitching–plunging airfoil in dynamic stall

Geometric control theory is the application of differential geometry to the study of nonlinear dynamical systems. This control theory permits an analytical study of nonlinear interactions between control inputs, such as symmetry breaking or force and motion generation in unactuated directions. This paper studies the unsteady aerodynamics of a harmonically pitching–plunging airfoil in a geometric control framework. The problem is formulated using the Beddoes–Leishman model, a semi-empirical state space model that characterizes the unsteady lift and drag forces of a two-dimensional airfoil. In combination with the averaging theorem, the application of a geometric control formulation to the problem enables an analytical study of the nonlinear dynamics behind the unsteady aerodynamic forces. The results show lift enhancement when oscillating near stall and thrust generation in the post-stall flight regime, with the magnitude of these force generation mechanisms depending on the parameters of motion. These findings demonstrate the potential of geometric control theory as a heuristic tool for the identification and discovery of unconventional phenomena in unsteady flows.

Active Flutter Suppression of a Wing Section in the Subsonic, Sonic and Supersonic Regimes by the H∞ Control Method

This paper compares various procedures for determining the optimal control law for a wing section in compressible flow. The flow regime includes subsonic, sonic and supersonic flows. For the evolution of the system in the Laplace plane, the present method makes use of the exact unsteady aerodynamic forces in this plane once the control law is established. This is a great advantage over other results previously published, where the unsteady aerodynamics in the Laplace plane are merely approximations of the curve-fitted values in the frequency domain (imaginary axis). A comparison of different control techniques like pole placement, LQR and H-infinity control demonstrates that the H-infinity controller is the optimal choice, exhibiting an H-infinity norm approximately two orders of magnitude lower than the LQR case. Furthermore, the H-infinity controller demonstrates lower pole values than those of the pole placement and LQR compensator, showing the advantage of the H-infinity controller in terms of economic efficiency.

Mechanism of single-mode panel flutter in low supersonic flow

Supersonic panel flutter can be of two possible types: single-mode flutter and coupled-mode flutter. Compared to coupled-mode flutter, the physical mechanism of single-mode flutter is less studied at present. In order to reveal the inducing mechanism of single-mode flutter, the present paper constructed a reduced-order fluid model by using the system identification and the Auto Regressive with eXogenous input (ARX) model. Coupling the reduced-order model (ROM) for unsteady aerodynamics in low supersonic flow with the structural equation, a highly efficient ROM-based aeroelastic model in state space is formulated, then the flutter boundaries are obtained and the stability of aeroelastic modes are investigated by the complex eigenvalue analysis. According to the physical meaning of relevant parameters in unsteady aerodynamic reduced order model ARX, it is found that the unsteady characteristic of the flow, specifically the history effects of the unsteady aerodynamic forces, plays a dominant role in causing the single-mode panel flutter at low supersonic speeds. It is also shown that the higher modes are indeed weakly unstable in the absence of any structural damping or a viscous boundary layer.

Real-Time Ground Aeroservoelastic Test for Slender Vehicles Based on Condensed Aerodynamic Force Loading

Slender vehicles often encounter significant aeroservoelastic challenges due to their low elastic mode frequencies and wide servo control system bandwidths. Traditional analysis methods have limitations, including low modeling accuracy for real vehicles in numerical methods, scale errors in wind tunnel tests, and significant risks in flight tests. The ground aeroelastic stability test is an innovative experimental method designed to address these challenges. This novel method employs shakers to apply condensed unsteady aerodynamic forces in real-time to actual vehicles, serving for both the ground flutter test (GFT) and the ground aeroservoelastic test (GAT). While extensive research exists on the GFT, there is limited exploration of the GAT. For the GAT of a slender vehicle in this paper, the condensed aerodynamic forces are calculated using the quasi-steady aerodynamic derivative method. An improved, partially decoupled inverse model controller is designed for force control, guided by an assessment of coupling strength among different shakers. Ground experiments under various flight control laws and flight dynamic pressures produce accurate results. Numerical simulations and experimental results demonstrate high precision, with excitation force amplitude deviations within ±10% and phase deviations within ±5° within the frequency range relevant to aeroservoelastic stability.

Investigations on bifurcation behavior of wind turbine airfoil response at a high angle of attack

Design load and vibration for parked conditions are gaining in importance for large-scale modern wind turbines with increasing flexibility, especially edgewise vibration when the blade is at a high angle of attack. In this work, flow-induced vibration of the wind turbine airfoil at 90 degrees of attack angle is studied with the fluid-structure interaction (FSI) simulation. The unsteady aerodynamic force due to flow separation and vortex shedding at the high angle of attack causes the chordwise vibration of the airfoil. When the vortex shedding frequency fv gets close to the chordwise natural frequency fn of the airfoil, vortex-induced vibration (VIV) of high amplitude occurs accompanied with the frequency lock-in phenomenon. In the post lock-in regime, it is found that period-3 and torus bifurcation occur successively and the vibration response becomes aperiodic. Dynamic mode decomposition(DMD) technique is used to investigate the mechanism of bifurcation from the perspective of energy balance, through analyzing the vorticity field in the wake and pressure distribution on the airfoil surface. For the certain incoming velocity in the post lock-in regime, since the frequency of the DMD mode f=2fv/3 is close to the natural frequencyfn, both the vibration of frequency 2fv/3 and fv get excited, leading to the onset of bifurcation. The Lissajou curves are obtained through reconstructing the transient pressure of each DMD mode, which indicates that energy transfer mainly exists in modes f=fv. In addition, the reconstructed Lissajou curves based on the leading DMD modes agree well with the original time-domain Lissajou curves.

Transonic Aerodynamic–Structural Coupling Characteristics Predicted by Nonlinear Data-Driven Modeling Approach

Accurate prediction of nonlinear aerodynamics is essential for the transonic aeroelastic analysis of flight vehicles. Though reduced-order aerodynamic models are cheap and reasonable tools, it is still a tough problem to accurately evaluate the unsteady pressure distributions on the surface of an elastic structure. This paper presents a nonlinear data-driven modeling approach based on the high-fidelity simulations in the following three steps. The first step is to compute the dominant modes of unsteady pressure distributions through the proper orthogonal decomposition. The pressure snapshots used for the feature extraction are sampled under a multilevel sine-sweep excitation. The second step is to obtain the low-dimensional temporal dynamics of the coefficients of these modes via polynomial nonlinear state-space identification. The linear estimation implemented by employing the dynamic mode decomposition with control algorithm serves as the initialization of the nonlinear optimization. The third step is to reconstruct the unsteady pressure distributions under arbitrary structural excitation from the temporal coefficients. The paper validates the approach via two numerical examples of the transonic aerodynamic–structural coupling problem. One is an NACA0012 airfoil, and the other is an AGARD 445.6 wing. The examples show that the proposed approach exhibits both accurate and robust performance in the prediction of unsteady pressure distributions, aerodynamic forces, and aeroelastic responses. In particular, the approach well predicts the physical features at the fluid–structure coupling interface, previously neglected in the system identification of aerodynamic systems. Therefore, the approach serves as a promising tool for data-driven aeroelastic analysis.

Aeroelasticity Analysis of Folding Wing with Structural Nonlinearity Using Modified DLM

The structural nonlinear aeroelastic analysis of folding wings is conducted by integrating the modified Doublet Lattice Method in this paper. Firstly, a modified Doublet Lattice Method is investigated to relax the aspect ratio limitation of aerodynamic elements, and its correctness is verified through numerical examples. Secondly, the rational function approximation method is discussed, and the modified Doublet Lattice Method is approximated using the minimum state method to obtain the unsteady aerodynamic forces in the time domain. Finally, the aeroelastic characteristics of a folding wing with free-play and friction nonlinearity are studied by integrating time-domain unsteady aerodynamics with the nonlinear structural dynamics model. The results show that the modified Doublet Lattice Method, which relaxes the aspect ratio limitation of aerodynamic grid elements, is feasible and effective; Friction can suppress the influence of free-play nonlinearity on aeroelastic response.

Modeling of the unsteady aerodynamic force of turbine blades considering nonuniform vane pitch

Modeling of the unsteady aerodynamic force of turbine blades considering nonuniform vane pitch