Unsteady Aerodynamic Loads Research Articles

Study on semi-active control of running stability in the high-speed train under unsteady aerodynamic loads and track excitation

With the growing trend of higher running speed and lighter body weight in the high-speed train, the influences of fluctuating crosswind on running stability and safety are becoming more and more not negligible, especially under the combined action of unsteady aerodynamic loads and random orbital excitation. In order to investigate this problem, a vehicle dynamic model of with 42 degree of freedom is built, in which the major body, two bogies and eight wheels are involved. The unsteady aerodynamic loads under stochastically fluctuating crosswind are obtained based on Cooper theory and the harmonic superposition method, and the random excitation of the track is also taken into consideration. For the vertical vibration originated from the fluctuating crosswind and the random track spectrum, the skyhook damping and the magneto-rheological fuzzy semi-active control strategies are individually applied to suppress the vibrating amplitude and improve the running stability. It is indicated that the vertical vibration under the coupling influence of the unsteady aerodynamic loads and the random orbital excitation are significantly increased, and the vibrating amplitude can be effectively suppressed by both the two different control approaches. It is also shown that the index of running stability in the case of the fuzzy control is evidently better than the skyhook damping.

Aerodynamic Modeling and Flight Simulator Evaluation of Aircraft's Response to Varying Crosswind

Varying crosswind is the crosswind with varying magnitude and/or direction as that being encountered by an aircraft. It includes horizontal gust wind and horizontal wind shear. As a result of this encounter, the aircraft may develop roll oscillation with large amplitude to affect flight safety. The main purpose of this paper is to show that this phenomenon can be reproduced in an existing flight simulator with high fidelity for pilot training based on unsteady aerodynamic models developed in a tabulated form. Five sets of flight data involving various varying crosswind in landing are available and are combined for developing into one set of unsteady aerodynamic models for six aerodynamic coefficients at low Mach numbers. A least-square-error method is used to smooth any discrepancy among these five sets of flight variables which are in the form of dynamic similitude. The tabulation is arranged only in the subspace of angles of attack because of low Mach numbers. It has been demonstrated that the same set of aerodynamic models in tabulated form is applicable to all five flights with good prediction accuracy. In this paper, the prediction accuracy will be demonstrated only for one flight. One unique feature of the aerodynamic models is that the models can predict the main reasons for flights becoming uncontrollable in a motion with large amplitudes and highly coupled longitudinal and lateral-directional modes. Another feature is that in addition to predicting accurate response for display in a simulator, it can predict the unsteady aerodynamic loads as well. These aerodynamic models, when implemented in a flight simulator, are shown to produce realistic response to varying crosswind. Fidelity of the simulation has been verified by pilots.

Multidisciplinary design optimization of long-range slender guided rockets considering aeroelasticity and subsidiary loads

Due to the insufficient rigidity feature and long-range requirement, it is crucial to consider the aeroelasticity and subsidiary loads caused by the Earth rotation and fuel consumption when designing long-range slender guided rockets (LRSGRs). As a typical multidisciplinary design optimization (MDO) problem, the design optimization of LRSGRs confronts two critical challenges, i.e., accurate multidisciplinary modeling and efficient global optimization. To address the challenges, a novel MDO framework including MDO problem definition, multidisciplinary modeling, and metamodel-based optimizer is developed for LRSGR design. The LRSGR MDO problem is formulated to minimize the total mass subject to a number of practical engineering constraints such as bending mode frequencies, miss distance, and fall angle. Several disciplinary models including structure, aerodynamics, propulsion, mass, aeroelasticity, guidance control, and trajectory are established. To enhance the analysis accuracy, structural finite element analysis (FEA), three-channel autopilot, and high-fidelity trajectory models are adopted. In the aeroelasticity model, the unsteady aerodynamic loads are calculated by slender body theory and aerodynamic derivative method. The subsidiary loads including subsidiary Coriolis force, centrifugal inertial force, Coriolis force, and subsidiary Coriolis moment are incorporated in the trajectory model of LRSGRs. Since structural finite element, aeroelasticity, and trajectory models are computationally expensive (about 1.8 hours for one trial of system analysis on a well-equipped workstation), an adaptive radial basis function metamodel-based optimizer is integrated in the framework to solve the LRSGR MDO problem with moderate computational cost. The total mass of the studied LRSGR is decreased by 88 kg (i.e., 14% of the total mass) after optimization, which demonstrates the effectiveness and practicability of the proposed MDO framework for LRSGRs.

Strategies for modeling homogeneous isotropic turbulence and investigation of spatially correlated aerodynamic forces on a stationary model

A numerical simulation method is proposed for the generation of homogeneous isotropic turbulence and is applied to the investigation of the spanwise coherence aerodynamic force on a stationary airfoil. First, the inflow turbulence is generated by modeling a grid at the inlet of the computational domain. To verify the accuracy of the generated turbulence field, a series of relevant parameters are compared with the results of wind tunnel tests and previous studies. A model with NACA 0015 profile is then placed in the downstream turbulence. The relationship between the spanwise correlation width of the vertical turbulence component and the lift force is determined. Possible mechanisms for the result are discussed. This study demonstrates that the proposed turbulence generation method is an effective tool for investigating the spatial distribution of unsteady aerodynamic loads on elongated bodies.

Multi-variable Volterra kernels identification using time-delay neural networks: application to unsteady aerodynamic loading

In the last decades, the Volterra series theory has been used to construct reduced-order models of nonlinear systems in engineering and applied sciences. For the particular case of weakly nonlinear aerodynamic and aeroelastic systems, the Volterra series theory has been tested as an alternative to the high computing costs of CFD methods. The Volterra series model determination depends on identifying the kernels associated with the respective convolution integrals. The Volterra kernels identification has been tried in many ways, but the majority of them addresses only the direct kernels of single-input, single-output nonlinear systems. However, multiple-input, multiple-output relations are the most typical case for many dynamic systems. In this case, the so-called Volterra cross-kernels represent the internal couplings between multiple inputs. Not many generalizations of the single-input kernel identification methods to multi-input Volterra kernels are available in the literature. This work proposes a methodology for the identification of Volterra direct kernels and cross-kernels, which is based on time-delay neural networks and the relationship between the kernels functions and the internal parameters of the network. Expressions to derive the pth-order Volterra direct kernels and cross-kernels from the internal parameters of a trained time-delay neural network are derived. The method is checked with a two-degree-of-freedom, two-input, one-output nonlinear system to demonstrate its capabilities. The application to a mildly nonlinear unsteady aerodynamic loading due to pitching and heaving motions of an airfoil is also evaluated. The Volterra direct kernels and cross-kernels of up to third order are successfully identified using training datasets computed with CFD simulations of the Euler equations. Comparisons between CFD simulations and Volterra model predictions are presented, thereby ensuring the potential of the method to systematically extract kernels from neural networks.

Experimental investigation of shock-induced separation and flow control in a transonic compressor cascade

The influence of transition control on shock-induced flow separation was investigated in a highly loaded transonic compressor cascade at an inlet Mach number of 1.21 and a chord-based Reynolds number of $$1.4 \times 10^6$$ . Transition was influenced by raising the free-stream turbulence from 0.5 to 2.5%. Two further cases employed either air-jet vortex generators (AJVG) or a surface roughness patch as transition control devices. Velocity fields in the vicinity of the unsteady transonic separation were captured by particle image velocimetry (PIV). Blade flexure induced by the unsteady aerodynamic loading was tracked for each image and compensated individually prior to PIV processing. The captured flow fields indicate shape variations of the separation region, while the shock foot moves within a range of up to 20% of chord. The frequency of separation for each investigated case was assessed on the number of vectors with negative velocity in each PIV sample. To further quantify the size of the separation region, the statistically independent PIV samples were conditionally averaged for various passage shock positions at a resolution of 1% chord length. Insight to the dynamics and frequency of the passage shock motion was further provided by high-speed shadowgraphy. Large bubble separation occurs if the turbulence of the incoming flow is low. The size of separation region decreases when AJVGs are applied but still exhibits bubble separation as the passage shock moves downstream. The size of the separation region is significantly reduced either if a roughness patch is applied or if the turbulence level of the incoming flow is high. The flow conditions showing bubble separation in the mean flow also exhibit distinct spectral peaks indicating periodic shock oscillations.

The effects of structural and aerodynamic nonlinearities on the energy harvesting from airfoil stall-induced oscillations

An airfoil may undergo stall-induced oscillations beyond the critical flutter speed with amplitudes determined by aerodynamic nonlinearities due to the dynamic stall. Stall-induced oscillations yield intense periodical motions that can be used to convert the airflow energy into electrical power. The inclusion of structural nonlinearities contributes to the complexity of the aeroelastic response. In this sense, the present work models and analyzes for the first time the effects of structural and aerodynamic nonlinearities in the potential of extracting energy from pitching and plunging motions of an airfoil during stall-induced oscillations. A computational model is employed, based on the electro-aeroelastic differential equations modeling a typical aeroelastic section with two degrees of freedom with an electrical generator connected to the pitching motion and a piezoelectric element connected to the plunging motion. The Beddoes–Leishman semi-empirical model is used to represent the unsteady aerodynamic loading. Concentrated structural nonlinearities, such as the hardening effect and free-play, are also considered. Bifurcation diagrams and harvested power calculations are used to analyze the performance of each energy harvesting scheme. The results show that nonlinear pitching stiffness reduces the average harvested power from this degree of freedom in a range of wind speeds. However, the presence of a free-play spring reduces the flutter velocity and initiates the harvesting at lower wind speeds. In conclusion, the present electro-aeroelastic model can be used to find optimal parameters of a harvester from airfoil stall-induced oscillations for a specific application.

Study on flight dynamics of flexible projectiles based on closed-loop feedback control

Since projectiles with large slenderness ratio are prone to elastic deformation, the effect of structural deformation is necessary to be taken into consideration for dynamic modeling. In order to obtain the precise aerodynamic performance and flight dynamic characteristics of flexible projectiles, a new numerical flight simulation system is developed based on computational fluid dynamics and generalized dynamic-mesh technique. Furthermore, flight dynamic stability of a typical flexible projectile is carried out in detail by introducing PID controller. By means of installing the sensors at various locations, the effect of different mode shapes on the characteristics of the closed-loop flight dynamic system is researched. Numerical results indicate that, when the disturbance due to elastic vibration is added into the mixed signals gained from the angular velocity/acceleration sensors, the feedback response of the closed-loop system becomes adversely divergent. In contrast, the stability of the closed-loop system is not sensitive to the elastic disturbance added to the centroid velocity and acceleration. Moreover, the stability of closed-loop system is much less affected by the unsteady aerodynamic loading due to elastic vibration than the interference of the elastic vibration on the dynamic signals detected by the sensors. The phenomenon can be explained by the requirement on the stability of the long and short period modes of flight dynamics, which can provide some guidance for the layout of the sensor and the design of control system of the projectiles with large slenderness ratio.

Large Eddy simulation of a heaving wing on the Cusp of transition to turbulence

Simulations of the flow over a heaving NACA 0012 wing are conducted to study the separated flow phenomena for a pre-stall and post-stall wing condition. An extensively validated high fidelity large-eddy simulation (LES) approach is used to examine the unsteady aerodynamic loads and flow structures at Reynolds number Rec = 2 × 104 based on the chord. We consider reduced frequencies of k = 0.47 and 0.94 for a chord-normalized peak-to-peak amplitude of A/c=0.5 and angles of attack of 5∘ and 15∘, representing pre-stall and post-stall conditions respectively. Comparison to experiment shows good agreement for the phase-averaged lift, drag and moments of the heaving wing. Characteristic phenomena of dynamic stall are analysed with emphasis on the leading edge vortex (LEV) development. A series of instantaneous spanwise vorticity plots show significant spanwise perturbations in the reverse flow region that develops over the suction surface during the start of the downstroke, giving rise to instabilities in the detached shear layer. The instabilities give rise to the first occurrence of turbulence near the wing surface at the leading edge.

Rotorcraft blade-vortex interaction noise prediction using the Lattice-Boltzmann method

The aim of this paper is to assess the accuracy, capabilities and computational performances of the Lattice-Boltzmann/Very Large Eddy Simulation Method to predict the unsteady aerodynamic loads, the rotor wake development and the noise radiation of helicopter rotors in strong Blade-Vortex Interaction conditions. The numerical flow solution is obtained by solving the explicit, transient and compressible Lattice-Boltzmann equation implemented in the high-fidelity CFD/CAA solver Simulia PowerFLOW®. The acoustic far-field is computed by using the Ffwocs-Williams & Hawkings integral solution applied to a permeable surface encompassing the whole helicopter geometry. The employed benchmark configuration is the 40% geometrically and aeroelastically scaled model of a BO-105 4-bladed main rotor tested in the open-jet anechoic test section of the German-Dutch wind tunnel in the framework of the HART-II project. In the present study, only the baseline operating condition of the experimental campaign, without Higher-Harmonic Control enabled, is considered. All simulations are performed by assuming a rigid blade motion, but a computational strategy based on a combination of a rigid blade pitching motion and a transpiration velocity boundary condition applied on the blade surface is employed to take into account the blade elastic deformation motion measured during the experiments. As expected, modeling the blade elastic deformation leads to more accurate predictions of control settings, unsteady air-loads and noise footprint. The effects of the computational grid on the aerodynamic and aeroacoustic prediction is documented as well.

Parametric reduced-order modeling of unsteady aerodynamics for hypersonic vehicles

A novel parametric reduced-order model (ROM) is proposed for efficiently predicting hypersonic unsteady aerodynamic responses under different flight conditions. The construction of the ROM is realized by computational fluid dynamics (CFD) simulations under the prescribed motion of the structure, while the results are processed via the proper orthogonal decomposition (POD) to obtain the predominant flow modes. Subsequently, to obtain the ROM valid for varying flight conditions, the method of interpolation in a tangent space to a Grassmann manifold is used to generate a new POD modal matrix for the arbitrary operating point in the considered parameter space. Finally, the least squares support vector machine (LS-SVM) is carried out to obtain the nonlinear relations between the applied excitations and the resulting POD coefficients. Once the parametric ROM is constructed, it can behave as a substitution of the full-order CFD flow solver in the considered parameter space. For demonstration purposes, the parametric ROM is used to predict hypersonic unsteady aerodynamic loads, flutter boundaries and limit-cycle oscillations of a double wedge airfoil over a wide range of the flight conditions, respectively. Numerical investigations show a good agreement between the results obtained by the ROM methodology in comparison to the full-order CFD solution over a wide range of the parameters. In addition, the ROM approach yields a significant speedup regarding unsteady aerodynamic calculations, which is beneficial for aeroelastic analysis, control and optimization applications.

Computational Investigation on Unsteady Loads of High-Speed Rigid Coaxial Rotor with High-Efficient Trim Model

A computational fluid dynamics method is built to study the unsteady aerodynamic loads of a high-speed rigid coaxial rotor model, taking account of lift offset (LOS). The flowfield is simulated by solving Reynolds Averaged Navier–Stokes equations, and moving overset mesh is adopted to include blade motions. A high-efficient trim model for coaxial rotor is developed, where the “delta method” is implemented. Performance of Harrington rotor-1 is calculated for validation. Forward flight cases in three advance ratios are conducted. Results indicate that the temporal thrusts of coaxial rotor at low advance ratio share some fluctuations similar to hover state. In forward flight, the impulsive thrust fluctuations caused by blade-meeting are obviously exhibited around 270° for upper blades, and the strengths increase with the increase of LOS and advance ratio. At higher advance ratios, the blade thrusts of the upper and lower rotors tend to be the same. At the advance ratio of 0.6, two new kinds of Blade–vortex interaction (BVI) are captured. One is the parallel BVI caused by the root vortex and the other is the complex interaction among the tip vortex, root vortex and the rear blade.

A fully coupled analysis of unsteady aerodynamics impact on vehicle dynamics during braking

This study investigates the impact of unsteady aerodynamic loads on the behavior of car dynamics during braking maneuvers. In the analysis, two independent solvers were coupled to solve an existing fluid structure interaction (FSI) problem. Transient CFD analysis applying Fluent software was used to obtain realistic aerodynamic loads. A full car, nonlinear dynamic model with elastic suspension system was built in a dedicated multibody dynamic system MSC.Adams/Car. Both physics were integrated into one ecosystem via a block diagram environment for multidomain simulation (Matlab/Simulink). Methodology elements were validated against experimental results for a rectangular beam in cross-flow with vortex-induced vibrations. The final results were validated against a full-scale experiment on a real car. The solution of an untypical flow problem (decreasing car speed during a braking maneuver) required an untypical reference frame. The classic case, with an observer at rest (stationary model and moving air), was replaced with a moving observer. The whole domain was translocated during the analysis with a velocity which varied with time. The problem was further complicated by the presence of movable aerodynamic elements. The overset mesh technique was used to allow movement of the car body and active aerodynamic surfaces. The results obtained show the importance of aerodynamic effects on the braking process. It was shown that in the analyzed scenario, movable aerodynamic features can reduce the distance to stop by 6%. The complex interaction between the active aerodynamic surface and the car body with respect to load split is discussed as well. The methodology proposed to determine the behavior car dynamics with unsteady aerodynamic effects taken into account appears to be a significant improvement when compared with existing methodologies used for such an assessment.

Volterra Kernels Assessment via Time-Delay Neural Networks for Nonlinear Unsteady Aerodynamic Loading Identification

Reduced-order modeling using the Volterra series approach has been successfully applied in the past decades to weakly nonlinear aerodynamic and aeroelastic systems. However, aspects regarding the identification of the kernels associated with the convolution integrals of Volterra series can profoundly affect the quality of the resulting reduced-order model (ROM). An alternative method for their identification based on artificial neural networks is evaluated in this work. This relation between the Volterra kernels and the internal parameters of a time-delay neural network is explored for the application in the reduced-order modeling of nonlinear unsteady aerodynamic loads. An impulse-type Volterra-based ROM is also under consideration for comparison. All aerodynamic data used for the construction of the ROMs are obtained from computational fluid dynamics (CFD) simulations of the NACA 0012 airfoil using the Euler equations. Prescribed inputs in pitch and in plunge degrees of freedom at different freestream Mach numbers are used to evaluate the range of applicability of the obtained models. For weakly nonlinear test cases, the modeling performance of the neural network Volterra ROM was comparable to the impulse-type ROM. Additional accuracy and adequate modeling of stronger nonlinearities, however, could only be attained with the inclusion of the neural network kernels of higher order in the Volterra ROM. A generic expression is derived for the kernel function of th-order from the internal parameters of a time-delay neural network.

An Experimental Investigation of the Surface Pressure Fluctuations for Round Cylinders

An experimental study is carried out to investigate the unsteady pressure exerted on the surface of a round cylinder in the subcritical Reynolds number range. Results are presented for the surface pressure fluctuations, spanwise coherence, lateral correlation length, and peripheral coherence. Discussions are provided for the dominance of the first three vortex shedding tones at different regions of the cylinder and the size of the flow structures around the cylinder. The dataset provided have shed new light on the unsteady aerodynamic loading acting on cylinders and provides the impetus for further research on the aerodynamics and aeroacoustics of bluff bodies.

Numerical analysis of transonic buffet flow around a hammerhead payload fairing

During ascent of launcher, the unsteady aerodynamic loads associated with transonic buffet flow have become of considerable concern. To study the unsteady dynamics of buffet flow, delayed detached-eddy simulations of a hammerhead configuration have been conducted at transonic Mach numbers. The results, including mean Cp, Cprms, PSD and Schlieren visualizations, were validated by the measurements obtained from the wind-tunnel experiments. Nevertheless, to perform a good validation for unsteady loads, the numerical data needed to be filtered according to the data acquisition used in the experiments. The studies were performed by means of instantaneous, statistical, spectral and cross-spectral analysis of the numerical data, which identify the fluid dynamic mechanism that produces a relatively strong buffet environment. The mechanism involves a sequence of vortex, which is shed downstream, merges together, and ultimately impinges on the wall leading to large fluctuations. Besides, the cross-spectral analysis also revealed that the subsequent large scale and low frequency vortex shedding of the developed shear layer provides a strong influence on the flows around cone–cylinder conjunction. The fluctuations in this area are highly sensitive to Mach numbers, and the peak of Cprms appears at Ma ≈ 0.81.

Modeling of airfoil aeroelastic response to gust and rain coupled loads

The aeroelastic response of an airfoil featuring plunging-pitching coupled motion in an incompressible flow field to gust and rain coupled loads is primarily investigated in this paper. The equations of airfoil coupled motion are derived by the “typical section” approach and the aeroelastic model is achieved by coupling these to 2D unsteady aerodynamics models for incompressible potential flows. The modelings of the unsteady aerodynamic and gust loads are established by the use of the Wagner’s and the Küssner’s functions, respectively. The incorporation of the rain effect is implemented via substituting the values of the slope of lift curve in the rain conditions in the aeroelastic response equations. Numerical modelings of the aeroelastic response to gusts of different velocity distributions and comparisons with the solution obtained for the rigid and elastic models featuring plunging or pitching motion alone and plunging-pitching coupled motion are provided. The pertinent results agree well with the results from other literature. The influences of gust, rain and airfoil control parameters are specially presented and discussed in detail. These results seem new and should have important reference value to the optimization of aircraft structure for the industrial aviation community.

Geometrically nonlinear aeroelastic behavior of pretwisted composite wings modeled as thin walled beams

Geometrically nonlinear aeroelastic behavior of pretwisted composite high aspect ratio wings, structurally modeled as thin walled beams (TWB) is studied. The structural equations of motion are obtained for the circumferentially asymmetric stiffness (CAS) configuration TWB based on the kinematic relations governing the thin walled beams, including the nonlinear strain–displacement relations and utilizing the principles of analytical dynamics. Unsteady aerodynamic loads in the incompressible flow regime are expressed using Wagner’s function in time-domain. The aeroelastic system of equations is augmented by the differential equations governing the aerodynamics lag states to come up with the final coupled fluid–structure equations of motion. The governing equations of the aeroelastic system is solved, for the TWB with CAS composite layup, by means of a Ritz based solution methodology utilizing the mode shapes of the linear structural system to approximate the spatial variation of degrees of freedom in the thin walled beam. Time response of the nonlinear aeroelastic system is obtained via the Runge–Kutta direct integration algorithm. Effects of the fiber angle and pretwist angle of the CAS layup configuration on the nonlinear aeroelastic stability margins and limit cycle oscillation behavior are studied in depth.

Numerical Validation of Floating Offshore Wind Turbine Scaled Rotors for Surge Motion

Aerodynamic performance of a floating offshore wind turbine (FOWT) is significantly influenced by platform surging motions. Accurate prediction of the unsteady aerodynamic loads is imperative for determining the fatigue life, ultimate loads on key components such as FOWT rotor blades, gearbox and power converter. The current study examines the predictions of numerical codes by comparing with unsteady experimental results of a scaled floating wind turbine rotor. The influence of platform surge amplitude together with the tip speed ratio on the unsteady aerodynamic loading has been simulated through unsteady CFD. It is shown that the unsteady aerodynamic loads of FOWT are highly sensitive to the changes in frequency and amplitude of the platform motion. Also, the surging motion significantly influences the windmill operating state due to strong flow interaction between the rotating blades and generated blade-tip vortices. Almost in all frequencies and amplitudes, CFD, LR-BEM and LR-uBEM predictions of mean thrust shows a good correlation with experimental results.

Boundary feedback stabilization of a flexible wing model under unsteady aerodynamic loads

This paper addresses the boundary stabilization of a flexible wing model, both in bending and twisting displacements, under unsteady aerodynamic loads, and in presence of a store. The wing dynamics is captured by a distributed parameter system as a coupled Euler–Bernoulli and Timoshenko beam model. The problem is tackled in the framework of semigroup theory, and a Lyapunov-based stability analysis is carried out to assess that the system energy, as well as the bending and twisting displacements, decay exponentially to zero. The effectiveness of the proposed boundary control scheme is evaluated based on simulations.