Pitch Oscillations Research Articles

Mitigation of Dynamic Stall over a Pitching Finite Wing Using High-Frequency Actuation

A novel high-frequency flow control strategy for mitigation of dynamic stall is demonstrated for the case of a finite wing using high-fidelity wall-resolved implicit large-eddy simulations. A NACA 0012 wing of aspect ratio is considered at freestream Mach number and chord Reynolds number . The wing undergoes an oscillatory pitching motion with reduced frequency and maximum angle of attack , resulting in deep dynamic stall for the baseline case. Very-high-frequency () spanwise uniform low-amplitude pulsed forcing is imparted through a zero-net mass flow blowing/suction slot located on the wing lower surface near the leading edge. The imposed small fluctuations are amplified by the laminar separation bubble (LSB) and inhibit LSB bursting and the formation of large-scale dynamic stall vortices. By maintaining effectively attached flow throughout the pitching cycle, actuation provides a significant reduction in the cycle-averaged drag and in the force and moment excursions. In addition, the negative (unstable) net-cycle pitch damping found in the baseline case is eliminated.

Untethered quadrupedal hopping and bounding on a trampoline

For quadruped robots with springy legs, a successful jump usually requires both suitable elastic parts and well-designed control algorithms. However, these two problems are mutually restricted and hard to solve at the same time. In this study, we attempt to solve the problem of controller design with the help of a robot without any elastic mounted parts, in which the untethered robot is made to jump on a trampoline. The differences between jumping on hard surfaces with springy legs and jumping on springy surfaces with rigid legs are briefly discussed. An intuitive control law is proposed to balance foot contact forces; in this manner, excessive pitch oscillation during hopping or bounding can be avoided. Hopping height is controlled by tuning the time delay of the leg stretch. Together with other motion generators based on kinematic law, the robot can perform translational and rotational movements while hopping or bounding on the trampoline. Experiments are conducted to validate the effectiveness of the proposed control framework.

Stiffness effects on laminar separation flutter

This work explores self-sustained pitching oscillations of a NACA0012 airfoil operating at low-to-moderate Reynolds numbers in which the aerodynamic flow is in a transitional regime. One-degree of freedom (1-DOF) pitching oscillations are explored for chord-based Reynolds numbers of Rec=77,000 and 110,000, which fall on the lower end of the flutter regime, over a large range of torsional spring constants. Laminar separation flutter (LSF) is shown to persist over several orders of magnitude of structural rigidity. At the Reynolds numbers tested, the effect of changing structural rigidity at a fixed Reynolds number exhibits remarkable similarity to the effect of varying Reynolds number at a fixed stiffness. Although the two effects are not perfectly analogous, both parameters influence the timing of transition events relative to the limit-cycle. Raising stiffness values at either Reynolds number causes the structural response to outpace boundary layer transition which in turn yields an increasingly nonlinear aeroelastic response. Oscillations are no longer sustained when the structural frequency merges with the frequency of the aeroelastic response. At this point, the slow relaxation time of boundary layer transition fails to keep pace with the structural frequency and the processes that sustain LSF are inhibited. Oscillations terminate at a lower stiffness in the lower Reynolds number case—an apparent effect of slower boundary layer transition. Interestingly, hysteresis patterns and flow topologies coalesce into nearly identical topologies for both Reynolds numbers when stiffness is very low.

On the drag–thrust transition of a pitching foil

The drag–thrust transition of a symmetric foil undergoing pitching oscillation in a uniform flow is numerically studied in the present work. Under a certain thickness-based Reynolds number ReD=255, the fluid dynamics around the oscillated foil at a series of values for the chord-based Reynolds number, Rec, are investigated. The various values of Rec are obtained by keeping the maximum thickness of the foil fixed while rhythmically changing the chord length of the foil. Depending on the numerical results, we uncover a scaling relation that links the amplitude-based Strouhal number SrA to the Rec at the drag–thrust transition boundary, which is briefly expressed as SrA∼Rec−1. Through analysing the velocity field of the foil, it is found that the drag–thrust transition of the pitching foil is closely associated with the critical velocity of the latest vortex produced by the foil. These findings helps in understanding the kinematic behaviour of aquatic animals and designing bio-inspired underwater robots.

Flow physics and dynamics of flow-induced pitch oscillations of an airfoil

We conduct a computational study of flow-induced pitch oscillations of a rigid airfoil at a chord-based Reynolds number of 1000. A sharp-interface immersed boundary method is used to simulate two-dimensional incompressible flow, and this is coupled with the equations for a rigid foil supported at the elastic axis with a linear torsional spring. We explore the effect of spring stiffness, equilibrium angle-of-attack and elastic-axis location on the onset of flutter, and the analysis of the simulation data provides insights into the time scales and mechanisms that drive the onset and dynamics of flutter. The dynamics of this configuration includes complex phenomena such as bifurcations, non-monotonic saturation amplitudes, hysteresis and non-stationary limit-cycle oscillations. We show the utility of ‘maps’ of energy exchange between the flow and the airfoil system, as a way to understand, and even predict, this complex behaviour.

Statistical analysis on the effect of reduced frequency on the aerodynamic behavior of an airfoil in dynamic physical motions

In this paper, an extensive experimental tests were performed to determine the aerodynamic characteristics of an airfoil undergoing static, dynamic pitch, dynamic plunge and dynamic combined pitch and plunge motions for various cases. This paper, however, focuses on the effects of reduced frequencies and mean angles of attack on the surface pressure distribution and on the corresponding lift of the airfoil oscillating in either pure pitch or in combined pitch–plunge motions. The angles of attack variations were set such that the model motion would be ceased lower than the static stall, near the static stall and beyond the static stall angles of attack. All tests were conducted at a constant Reynolds number and at various reduced frequency. The plunging motion which is created by the vertical displacement of the model inside the test section, is transformed to the equivalent angle of attack and is added to the pitch angle of attack for the case of the combined pitch and plunge motion. The differences in the pressure distribution and the corresponding aerodynamic loads as a function of the equivalent angle of attack, represent an extreme dependence of the pitch–plunge motion on the reduced frequency. Pitch oscillation seems to have dominant role in the pitch–plunge oscillation case. For the same situation, same frequency and mean angles of attack, the corresponding aerodynamic lift of the pitch–plunge motion was seen to be much higher than the pitch alone oscillation case.

Reprint of: Boundary layer tripping on moderate Reynolds number oscillating foils

An experimental study was conducted to assess fidelity of model-scale representations of full-scale oscillating-foil turbines operating at high Reynolds numbers. The experiments were performed using a NACA 0015 foil with an aspect ratio of 7.5 undergoing controlled oscillations in pitch and heave in a water tunnel. We considered Reynolds numbers ranging from 20,000 to 50,000 to investigate the effects of dynamic stall, channel confinement and forced transition to turbulence using distributed surface roughness. Direct force measurements were used to quantify the performance of the turbine, and quantitative flow imaging was performed using particle image velocimetry. Oscillations of the foil resulted in formation of turbulent boundary layers, particularly in the cases involving the roughened foils. This accelerated transition led to turbine performance characteristics (i.e. efficiency and extracted power coefficient) comparable to those reported for a numerical benchmark case of Re=500, 000.

Wake and power fluctuations of a model wind turbine subjected to pitch and roll oscillations

Wind-tunnel experiments were performed to inspect the impact of a variety of pitch and roll oscillations of a model wind turbine on the instantaneous power output and wake. Particle image velocimetry and hotwire anemometry were used to characterize the flow in the wake; instantaneous power output was also obtained in each of the configurations. For comparison, measurements were also performed in a fixed wind turbine. Results show that the wake at the turbine symmetry plane is significantly altered by the imposed motions, where rolling induced the lowest momentum deficit. The mean power output of the turbine increased with moderate tower oscillations, namely ≲10°, independent of the type of motion. We argue that this is due to, at least, two distinctive processes. Namely, a relative gain due to the cube of the relative incoming velocity impinging the rotor in the pitching, and a momentum replenish in the rolling motion The power fluctuations exhibited a peak on the spectral content of the spectrum ΦP coincident with the frequencies of the pitching and rolling. They also revealed the effects of the oscillation within the low-frequency content of ΦP, which was likely due to the oscillation-driven changes in the aerodynamics of the blades. In particular, the pitch reduced the energy of the power fluctuations within frequencies below that of the pitching frequency, with stronger effect at larger amplitude of oscillations, θ. However, the roll motions reduced the energy of the power fluctuations in a relatively narrow band, and notorious only with θ≳10°.

Comparing Models of Lateral Station-Keeping for Pitching Hydrofoils.

Fish must maneuver laterally to maintain their position in schools or near solid boundaries. Unsteady hydrodynamic models, such as the Theodorsen and Garrick models, predict forces on tethered oscillating hydrofoils aligned with the incoming flow. How well these models predict forces when bio-inspired hydrofoils are free to move laterally or when angled relative to the incoming flow is unclear. We tested the ability of five linear models to predict a small lateral adjustment made by a hydrofoil undergoing biased pitch oscillations. We compared the models to water channel tests in which air bushings gave a rigid pitching hydrofoil lateral freedom. What we found is that even with no fitted coefficients, linear models predict some features of the lateral response, particularly high frequency features like the amplitude and phase of passive heave oscillations. To predict low frequency features of the response, such as overshoot and settling time, we needed a semiempirical model based on tethered force measurements. Our results suggest that fish and fish-inspired vehicles could use linear models for some aspects of lateral station-keeping, but would need nonlinear or semiempirical wake models for more advanced maneuvers.

The computation of the pitch damping stability derivatives of supersonic blunt cones using unsteady sensitivity equations

The numerical methods for computing the stability derivatives of the aircraft by solving unsteady sensitivity equations which was proposed in our previous papers was extended to solve three-dimensional problems in this paper. Both the static and dynamic derivatives of the hypersonic blunt cone undergoing pitching oscillation around a fixed point were computed using the new methods. The predicted static derivative and dynamic derivative were found to be in reasonable agreement with the experimental data. For the present method, it is possible to distinguish the components of dynamic derivatives caused by different state parameters. It is found that {C}_{m_{dot{alpha}}} and {C}_{m_q} are usually of opposite signs and tend to eliminate each other, which makes {C}_{m_{dot{alpha}}}+{C}_{m_q} being much smaller than its individual components. Another feature of this method is that the moment of pressure derivatives proposed in the present paper can be used to predict the contribution of each part of the blunt cone to the overall stability quantitatively. It is found that the head region is crucial for the static stability and the body region contributes most to the dynamic stability.

A methodology for simulating 2D shock-induced dynamic stall at flight test-based fluctuating freestream

A comprehensive methodology for simulating 2D dynamic stall at fluctuating freestream is proposed in this paper. 2D CFD simulation of a SC1095 airfoil exposed to a fluctuating freestream of Mach number 0.537 ± 0.205 and Reynolds number 6.1 × 106 (based on the mean Mach number) and undergoing a 10° ± 10° pitch oscillation with a frequency of 4.25 Hz was conducted. These conditions were selected to be representative of the flow experienced by a helicopter rotor airfoil section in a real-life fast forward flight. Both constant freestream dynamic stall as well as fluctuating freestream dynamic stall simulations were conducted and compared. The methodology was carefully validated with experimental data for both transonic flow and dynamic stall under fluctuating freestream. Overall, the results suggest that the fluctuating freestream alters the dynamic stall mechanism documented for constant freestream in a major way, emphasizing that inclusion of this effect in the prediction of dynamic stall related rotor loads is imperative for rotor performance analysis and blades design.

Multi-DOF WEC Performance in Variable Bathymetry Regions Using a Hybrid 3D BEM and Optimization

In the present work a hybrid boundary element method is used, in conjunction with a coupled mode model and perfectly matched layer model, for obtaining the solution of the propagation/diffraction/radiation problems of floating bodies in variable bathymetry regions. The implemented methodology is free of mild-slope assumptions and restrictions. The present work extends previous results concerning heaving floaters over a region of general bottom topography in the case of generally shaped wave energy converters (WECs) operating in multiple degrees of freedom. Numerical results concerning the details of the wave field and the power output are presented, and the effects of WEC shape on the optimization of power extraction are discussed. It is demonstrated that consideration of heave in combination with pitch oscillation modes leads to a possible increase of the WEC performance.

Influence of Aspect Ratio on Dynamic Stall of a Finite Wing

The influence of aspect ratio () on dynamic stall was studied by comparing experimental performance data and three-component velocity measurements acquired for wings of , 4, and 5, and an airfoil during an unsteady pitch maneuver. A NACA 0012 airfoil was used for all wing models, which were subject to a sinusoidal pitch oscillation between 4 and 22 deg at a reduced frequency of 0.1 and a Reynolds number of . After acquiring the experimental performance data, it was found that decreasing the leads to a decrease in the nonlinear unsteady loading of the wing and postpones the dynamic stall process, which also leads to variations in the pitch damping characteristics. Velocity field measurements revealed that the dynamic stall vortex originates from flow separation at the leading edge across the wing inboard section and convects downstream across the chord, whereas the unsteady separation progresses toward the wing tips with increasing angle of attack. The formation of this vortex was delayed to higher angles of attack with reductions in , and the three-dimensional nature of the unsteady separation process led to a significant spanwise flow component identified in the acquired velocity fields.

Free hovering of hummingbird hawkmoth and effects of wing mass and wing elevation

This paper presents a computational study on the free hovering flight of an insect-like flapping-wing flyer modelled after the hummingbird hawkmoth (Macroglossum stellatarum), with a Reynold number Re ≈ 3000. The numerical model integrated a Navier-Stokes solver with the Newtonian free-body dynamics of the model insect. The primary cyclic kinematics of wings were assumed to be sinusoidal for simplicity here. A generic PID-based kinematics controller was used to achieve stable quasi-steady hovering flights. Hovering flight with zero wing mass was first simulated and served as a reference for subsequent study into the effects of wing mass. The translational inertia of wings, which was proportional to the longitudinal acceleration and the mass of the wings, accentuated the longitudinal and pitching oscillations of the model hawkmoth. The inertial wing force and torque were dominant over the aerodynamic ones at the morphological wing mass (4.67%) of the hawkmoth. The cyclic pitching oscillation may, however, be significantly suppressed by a suitable adjustment of wing elevation, subject to a small penalty on the aerodynamic power. The flow created by a flapping wing comprised a connected system of vortices, emanating from the leading edge, the inner edge, the trailing edge and the wing tip of the wing – these were shed downwards during stroke reversal to form a vortical wake below each of the wings. The results obtained show good consistency and agreement with available results in the literature.

The Influence of Semi-Active Suspension Adjustment on Vehicle Body Pitch Oscillations

Abstract In this paper the relation between semi-active suspension characteristics and vertical oscillations of the vehicle body on road roughness is analysed. During experimental tests, the damping of semi-active suspension was changed while measuring vehicle's sprung and unsprung mass vertical accelerations, pitch rate, which were transformed into a frequency domain for further analysis. The results of the experimental tests were compared to the simulations using the semi-active dynamic model. Validation has shown that model can be used to analyse the influence of semi-active suspension parameters on vehicle oscillations over the entire range of semiactive suspension settings. The comparison of experimental and theoretical simulation showed that semi-active suspension settings have influence on longitudinal oscillations of the sprung mass and it should be estimated in related researches of modern suspension.

Numerical Investigation of Passive Vortex Generators on a Wind Turbine Airfoil Undergoing Pitch Oscillations

Passive vortex generators (VGs) are widely used to suppress the flow separation of wind turbine blades, and hence, to improve rotor performance. VGs have been extensively investigated on stationary airfoils; however, their influence on unsteady airfoil flow remains unclear. Thus, we evaluated the unsteady aerodynamic responses of the DU-97-W300 airfoil with and without VGs undergoing pitch oscillations, which is a typical motion of the turbine unsteady operating conditions. The airfoil flow is simulated by numerically solving the unsteady Reynolds-averaged Navier-Stokes equations with fully resolved VGs. Numerical modelling is validated by good agreement between the calculated and experimental data with respect to the unsteady-uncontrolled flow under pitch oscillations, and the steady-controlled flow with VGs. The dynamic stall of the airfoil was found to be effectively suppressed by VGs. The lift hysteresis intensity is greatly decreased, i.e., by 72.7%, at moderate unsteadiness, and its sensitivity to the reduced frequency is favorably reduced. The influences of vane height and chordwise installation are investigated on the unsteady aerodynamic responses as well. In a no-stall flow regime, decreasing vane height and positioning VGs further downstream can lead to relatively high effectiveness. Compared with the baseline VG geometry, the smaller VGs can decrease the decay exponent of nondimensionalized peak vorticity by almost 0.02, and installation further downstream can increase the aerodynamic pitch damping by 0.0278. The obtained results are helpful to understand the dynamic stall control by means of conventional VGs and to develop more effective VG designs for both steady and unsteady wind turbine airfoil flow.

Boundary layer tripping on moderate Reynolds number oscillating foils

An experimental study was conducted to assess fidelity of model-scale representations of full-scale oscillating-foil turbines operating at high Reynolds numbers. The experiments were performed using a NACA 0015 foil with an aspect ratio of 7.5 undergoing controlled oscillations in pitch and heave in a water tunnel. We considered Reynolds numbers ranging from 20,000 to 50,000 to investigate the effects of dynamic stall, channel confinement and forced transition to turbulence using distributed surface roughness. Direct force measurements were used to quantify the performance of the turbine, and quantitative flow imaging was performed using particle image velocimetry. Oscillations of the foil resulted in formation of turbulent boundary layers, particularly in the cases involving the roughened foils. This accelerated transition led to turbine performance characteristics (i.e. efficiency and extracted power coefficient) comparable to those reported for a numerical benchmark case of Re=500, 000.

Determining strength indicators for the bearing structure of a covered wagon's body made from round pipes when transported by a railroad ferry

Improving the efficiency of transportation process through international transport corridors promotes the development of interoperable systems. Successful functioning of the interoperability of transportation is possible at reliable and well-coordinated work of individual components. In this regard, it is necessary to introduce into service a new generation of rolling stock with improved techno-economic and performance indicators. We have designed a supporting structure of the covered wagon, whose special feature is that the elements of the body are made of round tubes; in order to ensure the reliability of its fastening to the deck of a rail ferry, the nodes for fastening chain couplers are arranged at the pivot beams. To refine the determination of indicators for the strength of the body of a covered wagon, we have investigated its dynamic loading under the most unfavorable estimation scheme ‒ angular displacements of the railroad ferry relative to its longitudinal axis (equivalent to lateral pitching oscillations in the dynamics of railroad cars). We have determined the maximum magnitude of accelerations using mathematical modeling of a railroad ferry oscillations with wagons placed on its decks, applying a second-order Lagrange method. Solving differential equations of a railroad ferry oscillations, with railroad cars on it, employed the Runge-Kutta method in the programming environment MathCad. When determining the total magnitude of acceleration acting on the body of a covered wagon when transported by a railroad ferry, we also accounted for the horizontal component of a free fall acceleration, predetermined by the tilt angle (heeling) of the railroad ferry. The resulting value for acceleration as a component of dynamic loading was taken into account while studying the strength of a load-bearing bodywork of the covered wagon. The calculation employed a finite element method in the programming environment CosmosWorks. To this end, we developed a model of strength of a load-bearing bodywork of the covered wagon made from round tubes when transported by a railroad ferry. It has been established that the maximum equivalent stresses do not exceed those permissible for the grade of steel used for metallic structures of the body and are about 280 MPa. We have determined a design service life of the node for fastening chain screeds at the body of a covered wagon when transported by a railroad ferry. Results of this research could be applied when designing railroad cars of the new generation with improved technoeconomic and performance indicators

Validation of Control Laws at High Angles of Attack Using Three-Degree-of-Freedom Dynamic Rig in Wind Tunnel

Abstract The paper presents a technique for cost-effective and safe study of conventional and critical flight regimes and control validation using an autonomous dynamically scaled aircraft model mounted in a three-degree-of-freedom gimbal in a wind tunnel. The similarity of the dynamics of the model in gimbal and in free flight at high angles of attack is shown. To suppress large amplitude self-sustained pitch oscillations and prevent stalling, several control laws are developed using recent control design techniques based on structured H∞-optimization. The control laws are tested and compared in a dynamic rig with three degrees of freedom in a wind tunnel.

Investigation of Shock Motion in Transonic Flow Using an Oscillating, Straked, Delta Wing

A computational analysis was performed on a straked, delta wing undergoing pitch motion in order to investigate the influence of shock-induced, trailing-edge separation (SITES) on simulated limit-cycle oscillations (LCO). The research presented herein describes an aeroelastic analysis of a wing oscillating in pitch using Euler-based aerodynamics with boundary-layer coupling (BLC). Results indicate that oscillatory shock movement occurs in response to the pitching motion of the wing, both with and without BLC. However, the BLC solution predicted more significant shock movement, and the inviscid solution predicted more aggressive shocks located further aft on the wing. Increasing the amplitude of the pitch oscillations resulted in a greater range of shock motion than lower amplitude cases, but variation of oscillation frequencies tested did not show any noteworthy differences. These findings support the theory that oscillatory shock movement associated with SITES can occur during certain cases of transonic LCO. In addition, based on the results from pure pitch motion of the wing and on the flow solver used, shock motion can occur without a boundary-layer model, although the modeling of viscous effects does affect the range of shock motion.