Aerodynamic Coupling Research Articles

Effect of Yaw Angle on Flutter of Rectangular Plates at Low Supersonic Speeds

The stability of the infinite series of thin elastic rectangular plates simply supported along all edges and exposed to a supersonic flow is investigated. The nonzero flow yaw angle with supersonic leading edge is considered. To derive expression for the unsteady aerodynamic pressure distribution over the oscillating plate, potential flow theory was used, and an integrodifferential eigenvalue problem for finding complex eigenvalues was obtained. Flutter boundaries for the first and second modes are computed. Changing of the single-mode and coupled-mode flutter boundaries with the change of the yaw angle was shown. While they are smooth at zero angle, the boundaries become irregular, and additional isolated regions of stability and instability appear when increasing the yaw angle. This irregularity occurs due to the interaction of multiple spanwise modes, which takes place at nonzero yaw angle due to their aerodynamic coupling.

Investigation on a Flow Coupling Rudder for Directional Control of a Low-Aspect Tailless Configuration with Diamond-Shaped Wing

To solve the issues of directional control and aerodynamic moment coupling for a low-aspect tailless configuration with a diamond-shaped wing, we herein propose the concept of a flow coupling rudder (FCR). The FCR was composed of two basic control surfaces: a spoiler slot deflector (SSD) on the upper surface of the wing and the corresponding elevon. With the constraints of the fixed area and spanwise position of the SSD, the effects of the leading-edge sweep angle, chord position of the SSD, and collocating deflection angles of the SSD and elevon on the control characteristics of the configuration were analyzed using a numerical method. Based on the analysis, the selection principle of the key parameters for designing the FCR for the configuration was proposed. This proves that the leading edge of the selected SSD should be swept back instead of being parallel to the trailing edge of the wing to design an FCR with favorable aerodynamic performance for such a configuration. By accurately adjusting the parameters of the SSD and elevon, the FCR on the one-side wing could supply an effective yawing moment while simultaneously weakening or even eliminating the coupling pitching and rolling moments of traditional drag-type control surfaces. In this study, we provide a method for the directional control surface design of a low-aspect tailless configuration with a diamond-shaped wing.

The use of augmented rotor inflow to predict rotorcraft responses in hover and low-speed manoeuvres

AbstractThe rotorcraft is a complex dynamical system that demands specialist modelling skills, and a high level of understanding of the aeromechanics arising from the main rotor wake and aerodynamic couplings. One such example is the difficulty predicting off-axis responses, particularly in hover and low-speed flight, associated with induced velocity variation through the rotor disk resulting from the rotor wake distortions. Various approaches have been developed to deal with this phenomenon but usually demand prerequisites of high levels of expertise and profound aerodynamic knowledge. This paper presents a new and practical approach to capturing this wake distortion through an augmented rotor inflow model. The proposed model is coupled with a nonlinear simulation using the FLIGHTLAB environment, and comparisons are made between the simulation results and flight test data from the National Research Council of Canada’s Advanced System Research Aircraft in hover and low speed. Results show good predictability of the proposed nonlinear model structure, demonstrated by its capability to closely match the time responses to multi-step control inputs from flight test. The results reported are part of ongoing research at Liverpool and Cranfield University into rotorcraft simulation fidelity.

Aero-Structural Coupling Strategy for a Morphing Blade Cascade Study

Abstract The coupling of aerodynamics and structural mechanics is an important step in the design process of aeronautical devices with morphing parts. In this article, a 2D–3D coupling approach is developed to study a morphing blade cascade. Two shape memory alloy actuators are placed on the upper and lower sides of the blade to make possible the change in shape of the leading edge. In the present study, a preliminary design study is conducted by considering a two-dimensional computational fluid dynamics (CFD) analysis of an airfoil cascade coupled with a three-dimensional structural analysis of the whole 3D blade. A methodology is developed to match 2D and 3D meshes such that the aerodynamic loads can be easily transferred to the structural analysis. From there, the deformed blade geometry due to both aerodynamic loads and actuator work can be transferred back to the CFD solver, and the iterative aero-structural coupling loop can be repeated until convergence. The aero-structural coupling strategy developed in this study is also applied to a blade cascade study aiming to improve its performance by morphing the leading-edge of the blade. The results of this application show that by morphing the leading-edge blade of only few millimeters (less than 2 mm), it is possible to achieve a relevant performance improvement in terms of total pressure loss coefficient decrease of about 53% considering off-design conditions.

Aerodynamic design, analysis, and validation techniques for the Tianwen-1 entry module

The clear differences between the atmosphere of Mars and the Earth coupled with the lack of a domestic research basis were significant challenges for the aerodynamic prediction and verification of Tianwen-1. In addition, the Mars entry, descent, and landing (EDL) mission led to specific requirements for the accuracy of the aerodynamic deceleration performance, stability, aerothermal heating, and various complex aerodynamic coupling problems of the entry module. This study analyzes the key and difficult aerodynamic and aerothermodynamic problems related to the Mars EDL process. Then, the study process and results of the design and optimization of the entry module configuration are presented along with the calculations and experiments used to obtain the aerodynamic and aerothermodynamic characteristics in the Martian atmosphere. In addition, the simulation and verification of the low-frequency free oscillation characteristics under a large separation flow are described, and some special aerodynamic coupling problems such as the aeroelastic buffeting response of the trim tab are discussed. Finally, the atmospheric parameters and aerodynamic characteristics obtained from the flight data of the Tianwen-1 entry module are compared with the design data. The data obtained from the aerodynamic design, analysis, and verification of the Tianwen-1 entry module all meet the engineering requirements. In particular, the flight data results for the atmospheric parameters, trim angles of attack, and trim axial forces are within the envelopes of the prediction deviation zones.

A CFD–CSD coupling method for simulating the dynamic impact and expulsion of fragile foreign objects from the ‘inlet–bypass duct’ junction of a turboprop aircraft

Frequently appearing fragile hail, ice and other foreign objects pose great threats to advanced turboprop aircraft when they enter the intake system of the engine. However, it is difficult to simulate the effects of these objects as complicated aerodynamic and dynamic impact coupling phenomena are involved. Regarding a turboprop aircraft inlet with a bypass duct as the subject of the research reported in this article, a coupled Computational Fluid Dynamics–Computational Structural Dynamics (CFD–CSD) numerical simulation method is established based on an unstructured dynamic mesh and impact dynamics technology to solve the phenomena of ‘motion–collision–fragmentation–fragment motion’ for foreign objects such as fragile ice and hail entering the inlet. Based on airworthiness specifications, external hail and ice at the lip and inner lower wall of the inlet are modelled. Moreover, the dynamic motion of these foreign objects and their effects on the aerodynamic performance of the inlet system during the process are simulated and analysed in depth. The results show that high-speed hail breaks into small debris after collision, which may not cause a serious threat to the engine. In addition, the total pressure recovery coefficient and distortion rate are not heavily changed during the process. However, large pieces of ice at the lip of the inlet may lead to large-size fragments that impact the inner wall of the inlet, thus increasing the threat to the safety of the engine. Also, serious shielding and interference of large pieces debris with the inner flow in the dynamic process decrease the total pressure recovery coefficient while increasing the distortion rate, especially in the junction area between the inlet and the bypass duct. In particular, ice in the icing zone located in the inner lower part of the inlet should be of much more concern owing to the fact that ice in this region is more likely to fly directly into the main engine and cause a serious threat.

Aeroelastic Behavior of Two Airfoils in Proximity

This paper investigates the aeroelastic behavior of elastically supported airfoils due to structural and aerodynamic coupling effects between them in an incompressible uniform flow. The flow is modeled based on a potential theory for thick and thin airfoils considering the coupled interference effect. Coupled aeroelastic equations of motion are formulated in a state-space form and solved explicitly using a predictor–corrector scheme. The numerical analyses are presented for airfoils in proximity with and without structural coupling. It is shown that the airfoils in proximity oscillate out of the phase and destabilized the airfoils at lower speeds. The closer the airfoils are, the lower the speed at which flutter instability occurs. Also, the interference effect becomes more significant on reducing the flutter speed for thick airfoils in proximity. For structurally coupled airfoils, the flutter instability occurs at lower speeds for the lower coupling stiffness value. It is further worsened in the presence of aerodynamic interference. Although, for a larger stiffness value, the flutter instability could be delayed in the presence of aerodynamic interference. This study finds that the lifting surfaces in proximity without structural coupling can become unfavorable in the aeroelastic design. The results provide preliminary insights into the coupled structural and aerodynamic interference effects on the flutter instability for a multiple lifting surface configuration.

Effects of aerodynamic coupling and non-linear behaviour on galloping of ice-accreted conductors

Wind action on ice-covered transmission lines causes galloping, which is a problem because it can introduce interphase short circuits and cause fatigue of the cross-arms of the power line’s towers and insulators. The galloping phenomenon is characterised by a combination of large-amplitude, low-frequency vertical, horizontal, and torsional oscillations. To better understand the dynamic responses of vertical, horizontal and torsional 3-degree-of-freedom (DoF) galloping on four-bundled conductors, time–history analyses were conducted for 2D systems of varying DoFs and frequency ratios. The fundamental characteristics of the conductor’s non-linear 1-DoF vertical response were analysed via time–history analysis, indicating that large oscillations were caused by inclusion of an angular range of relative angle of attack with a high negative lift-coefficient slope. By considering the energy balance of the vertical motion over one oscillation period, we estimated the stable and unstable limit-cycle amplitudes. Then, by comparing the results of the 1-, 2-, and 3-DoF systems, we clarified the effect of aerodynamic coupling on 3-DoF galloping. The oscillation types in the 3-DoF systems were categorised as vertical–horizontal 2-DoF coupling oscillations, vertical–torsional 2-DoF coupling oscillations, and vertical 1-DoF oscillations according to the stationary torsional angle. Finally, we indicated the coupling effects on vertical oscillation by considering the energy balance of the vertical motion with the defined amplitudes and phase differences of the horizontal and torsional motions. The vertical amplitude of the vertical–horizontal 2-DoF coupling oscillation can become very large if the horizontal amplitude increases and the phase difference between horizontal and vertical displacements approaches 180°. Meanwhile, the range of the stationary torsional angle in which the vertical–torsional 2-DoF coupling oscillation occurs becomes wide as the phase difference between the torsional and vertical displacements approaches 90°. However, without horizontal motion, the vertical amplitude has a limited value, even if the torsional amplitude becomes large.

Comparison of Theoretical and Multifidelity Optimum Aerostructural Solutions for Wing Design

As contemporary aerostructural research for aircraft design trends toward high-fidelity computational methods, aerostructural solutions based on theory are often neglected or forgotten. In fact, in many modern aerostructural wing optimization studies, the elliptic lift distribution is used as a reference in place of theoretical aerostructural solutions with more appropriate constraints. In this paper, the authors review several theoretical aerostructural solutions that could be used as reference cases for wing design studies, and these are compared to high-fidelity solutions with similar constraints. Solutions are presented for studies with 1) constraints related to the wing integrated bending moment, 2) constraints related to the wing root bending moment, and 3) structural constraints combined with operational constraints related to either wing stall or wing loading. It is shown that, under appropriate design constraints, theoretical solutions for the optimum lift distribution may capture aerostructural coupling sufficiently to serve as appropriate reference cases for higher-fidelity solvers. A comparison of theoretical and high-fidelity solutions for the optimum wingspan and corresponding drag reveals important insights into the effects of certain aerodynamic and structural parameters and constraints on the aerodynamic and structural coupling involved in aerostructural wing design and optimization.

A spectral approach for efficient fatigue damage evaluation of floating support structure for offshore wind turbine taking account of aerodynamic coupling effects

A spectral approach for efficient fatigue damage evaluation of floating support structure for offshore wind turbine taking account of aerodynamic coupling effects

On the dynamic fluid–structure stability response of an innovative airplane configuration

This paper provides, for the first time, a physical explanation of the dynamic fluid–structure stability response of an unconventional aircraft configuration called PrandtlPlane, which has been recently acknowledged as a possible candidate to foster the ambition of a greener aviation. As observed in previous literature efforts on this configuration, flutter onset is significantly different when considering the aircraft being free in the air or fixed in space. Thanks to the formulation adopted in this effort, it is shown how the aerodynamic coupling of elastic and rigid modes has a beneficial effect on dynamic aeroelastic instability (flutter) onset. However, the different modal properties, consequence of the diverse boundary conditions, when switching from fixed-in-space to free-flying aircraft, also play a relevant role in determining the flutter occurrence. Whereas for the longitudinal case both effects are synergistic, contributing to increase flutter speed, for the lateral-directional case the variation in modal properties has a detrimental and dominating effect, leading to a flutter speed well within the flight envelope. Not only effects of rigid and elastic modes interaction have been addressed with respect to the aeroelastic side but the consequent effect on the flexible flight dynamics in terms of deterioration of the flying qualities has been quantified. Within the adopted formulation, unsteady aerodynamic forces are modeled by means of an enhanced Doublet Lattice Method able to take into account terms typically neglected by classic formulations. The work also discusses the relevance of such extra contributions to the dynamic response of the aircraft.

Wake-induced instabilities of parallel circular cylinders with tandem and staggered arrangements

When two circular cylinders are closely arranged in parallel, the downstream cylinder frequently exhibits wake-induced vibrations (WIVs). This study investigates the classifications of WIVs in various arrangements of cylinders by considering the generation mechanisms of WIVs through a series of wind tunnel tests. The generation mechanisms are defined through flutter and time-history analyses using the quasi-steady theory. Finally, this study suggests a classification map of the arrangements with four types of generation mechanisms: vertical flutter, anti-phase coupled flutter, in-phase coupled flutter (quasi-steady applicable), and in-phase coupled flutter (quasi-steady inapplicable). Vertical flutter occurs in closely staggered cylinders and tandem cylinders with a horizontal center distance measuring 2.5–9.5 times the cylinder diameter. A key parameter for distinguishing coupled flutter is the contribution of the aerodynamic coupling terms. Furthermore, for closely staggered cylinders, two types of vibrations occur, depending on the reduced wind velocity. The arrangement of the two cylinders is slightly changed because of the static displacement of the downstream cylinder depending on the wind velocity, resulting in a change in the generation mechanism. The results pertaining to the generation mechanisms effectively explain the WIV responses of the two cylinders in various arrangements.

Flexural-Torsional Galloping of Prismatic Structures with Double-Symmetric Cross-Section

The linear galloping of prismatic structures having double-symmetric cross-section, subjected to steady wind flow acting along a symmetry axis, is investigated. The continuous system is reduced to a three degree-of-freedom system via a Galerkin approach. The quasi-steady assumption for the aerodynamic forces is applied, under the hypothesis that the galloping instability is well-separated from the vortex induced vibration phenomenon. Due to the structural symmetry conditions and accounting for the aerodynamic coupling, galloping is of flexural-torsional type, occurring in the direction orthogonal to the incident wind. Moreover, coupling is stronger close to the resonance between the flexural and torsional degrees of freedom. A linear stability diagram is built up in a two-parameter space, highlighting the role of coupling in modifying the critical wind velocity, and in producing a veering phenomenon between the two modes. The existence of points at which a double-Hopf bifurcation manifests itself is detected. Both exact and perturbation solutions are provided, these latter in the non-resonant and resonant cases, useful to throw light on the interactive mechanisms. The resonant perturbation solution permits to analytically investigate under which conditions coupling has a detrimental effect on galloping, which manifests at a wind velocity lower than the flexural and torsional critical velocities. Situations where coupling between modes leads to beneficial effect with respect to the Den Hartog's critical wind velocity are also highlighted. As an application, galloping of a family of multi-story tower buildings having a square cross-section is studied.

Analysis of the Behavior in the Wind Tunnel of an Experimental Model of Savonius with Interlocking Cups with the Classic Ones with 2, 3 and 4 Semi-Cylindrical Cups

The paper is based on experiments conducted on the wind tunnel at low wind speeds (<9.5 m/s), on an experimental model of S-rotor wind turbine type with four blades and a D/H ratio of 1. Semi-cylindrical cups opposite 180 degrees are aerodynamically coupled by overlap and with an air passage gap to equalize the pressures. The formed channel is shaped to allow the same for pairs of blades at 90 degrees. The experimental model has an area of 0.025 m2 which represents 10% of the surface of the measuring section of the wind tunnel (0.25 m2). The behavior of the experimental model was compared with the experimental models of S-rotor with 2, 3 and 4 semi-cylindrical cups, with the same interception surface. The results confirm the better start of the experimental model by reducing dead zones and operating more evenly and stably over a longer range of wind speeds. The results confirm the validity of the proposed concept of interwoven aerodynamic coupling of semi-cylindrical cups.

An Efficient Aeroelastic Eigenvalue Method for Analyzing Coupled-Mode Flutter in Turbomachinery

Abstract In this paper, a method for analyzing flutter for a turbomachinery row with aerodynamically coupled structural modes is presented. The majority of observed turbomachinery flutter incidents involve only one structural mode family due to high mass ratio, high solidity and significant natural frequency separation for blades of traditional design. However, with the trend of higher aerodynamic loading, the wide usage of light weight composite materials and lower blade counts, the likelihood of coupled-mode flutter increases, particularly for turbofans or open rotors. Under such circumstances, the widely used energy method for flutter analysis is not valid. To model this situation, a novel aeroelastic eigenvalue method that is capable of modeling both single- and coupled-mode flutter is proposed. This method takes into account the aerodynamic coupling effects between different vibration modes through the influence coefficient cross sub-matrices, which can be efficiently computed by a harmonic balance solver. The new method is efficient as the required computational effort is only two times that of the traditional single mode analysis approach. The new method is demonstrated and validated by presenting results for Standard Configuration Eleven and NASA Rotor 67 flutter test cases in this paper.

Coupled Mode Flutter Analysis of Turbomachinery Blades Using an Adaptation of the p–k Method

Abstract Current trends in turbomachinery design significantly reduce the mass ratio of structure to air, making them prone to flutter by aerodynamic coupling between mode shapes, also called coupled-mode flutter. The p–k method, which solves an aeroelastic eigenvalue problem for frequency and damping, respectively, excitation of the aerodynamically coupled system, was adapted for turbomachinery application using aerodynamic responses computed in the frequency domain (FD). A two-dimensional (2D) test case is validated against time-marching fluid–structure coupled simulations for subsonic and transonic conditions. A span of mass ratios is investigated showing that the adapted p–k method is able to predict the transition between aeroelastically stable and unstable cascades depending on the mass ratio. Finally, the p–k method is applied to a low mass ratio fan showing that the flutter-free operating range is significantly reduced when aerodynamic coupling effects are taken into account.

Identification of aerodynamic damping matrix for operating wind turbines

Accurate knowledge of wind turbine tower vibration damping is essential for the estimation of fatigue life. However, the responses in the fore-aft and side-side directions are coupled through the wind-rotor interaction under operational conditions. This causes energy transfers and complicates aerodynamic damping identification using conventional damping ratios. Employing a reduced two-degree of freedom wind turbine model developed in this paper, this coupling can be accurately expressed by an unconventional aerodynamic damping matrix. Simulated time series obtained from this model were successfully verified against the outputs from the wind turbine simulation tool FAST. Based on the reduced system obtained, a matrix-based identification method is proposed to identify the aerodynamic damping for numerically simulated wind turbine tower responses. Applying harmonic excitations to the tower allowed the frequency response functions of the wind turbine system to be obtained and the aerodynamic damping matrix to be extracted. Results from this identification were compared to traditional operational modal analysis methods including standard and modified stochastic subspace identification. The damping in the fore-aft direction was successfully identified by all methods, but results showed that the identified damping matrix performs better in capturing the aerodynamic damping and coupling for the side-side responses.

Rotorcraft Lateral-Directional Oscillations: The Anatomy of a Nuisance Mode

High-fidelity rotorcraft flight simulation relies on the availability of a quality flight model that further demands a good level of understanding of the complexities arising from aerodynamic couplings and interference effects. One such example is the difficulty in the prediction of the characteristics of the rotorcraft lateral-directional oscillation (LDO) mode in simulation. Achieving an acceptable level of the damping of this mode is a design challenge requiring simulation models with sufficient fidelity that reveal sources of destabilizing effects. This paper is focused on using System Identification to highlight such fidelity issues using Liverpool's FLIGHTLAB Bell 412 simulation model and in-flight LDO measurements from the bare airframe National Research Council's (Canada) Advanced Systems Research Aircraft. The simulation model was renovated to improve the fidelity of the model. The results show a close match between the identified models and flight test for the LDO mode frequency and damping. Comparison of identified stability and control derivatives with those predicted by the simulation model highlight areas of good and poor fidelity.

Wind tunnel testing and frequency domain buffeting analysis of a 5000 m suspension bridge

Buffeting’s importance is highlighted in the case of super-long bridges. It remains unclear how buffeting will perform and whether the traditional methods still apply when bridge’s span is approaching its upper limitation. To figure out this, a full aeroelastic model testing has been carried out with the span arrangement 2000+5000+2000 m. A comparison with the existing bridges reveals the similarities and differences. It shows vertical and torsional buffetings are important for a 5000 m bridge while lateral response is almost static. Fundamental modes contribute most kinetic energy. With the increasing of wind speed, the aerodynamic coupling effect becomes prominent while the structural coupling effect keeps limited. Afterwards, four analytical methods, namely SRSS and CQC, with and without self-induced forces, are used for the buffeting displacements. The calculation indicates the multi-mode (CQC) analysis is still applicable on a 5000 m bridge but the mode-by-mode (SRSS) method is risky since the neglection of aerodynamic coupling effect. Parameter analysis shows aerodynamic admittance function and force coherence are decisive while the cross terms are of secondary importance. Since all data is experimentally measured, the reliability of analytical results can be ensured.

Horizontal Wind Effect on the Aerodynamic Performance of Coaxial Tri-Rotor MAV

The coaxial Tri-rotor micro air vehicle (MAV) is composed of three coaxial rotors where the aerodynamic characteristics of is complicated in flight especially when the wind effect is introduced. In this paper, the hovering performance of a full-scale coaxial Tri-rotor MAV is analyzed with both the simulations and wind tunnel experiments. Firstly, the wind effect on the aerodynamic performance of coaxial Tri-rotor MAV is established with different rotor speed (1500–2300 rpm) and horizontal wind (0–4 m/s). Secondly, the thrust and power consumption of coaxial Tri-rotor (L/D = 1.6) were obtained with low-speed wind tunnel experiments. Furthermore, the streamline distribution, pressure distribution, velocity contour and vortex distribution with different horizontal wind conditions are obtained by numerical simulations. Finally, combining the experiment results and simulation results, it is noted that the horizontal wind may accelerate the aerodynamic coupling, which resulting in the greater thrust variation up to 9% of the coaxial Tri-rotor MAV at a lower rotor speed. Moreover, the aerodynamic performance is decreased with more power consumption at higher rotor speed where the wind and the downwash flow are interacted with each other. Compared with no wind flow, the shape of the downwash flow and the deformation of the vortex affect the power loading and figure of metric accordingly.