Pitch Damping Research Articles

Aerodynamic Characterization of a Hypersonic Projectile Using Acceleration-Based Measurements and Numerical Methods

Armor-piercing fin-stabilized projectiles stand out by their exceptionally high slenderness ratios and ground-level flight at super- and hypersonic speeds. As space constraints limit the integration of measurement equipment into such slender test models, nonintrusive measurement techniques become favorable. The present analysis demonstrates a renewed approach to the free-flight technique, which sets models into unconstrained flight through the test section. It enabled the evaluation of the quasi-steady drag, lift, and pitching moment characteristics, and, to some extent, also the dynamic pitch damping characteristics. An alternative to the free-flight technique is the free-oscillation technique, which limits the motion to a rotation around the center of gravity. The free-oscillation technique allowed a higher-fidelity analysis of the static and dynamic pitching moments. Both methods were based on the analysis of the accelerations derived from trajectory tracking. This acceleration-based approach enabled the evaluation of the highly nonlinear characteristics. The high slenderness of the investigated projectile leads to a significant contribution of the viscous forces to the overall drag. These viscous forces are sensitive to the laminar-turbulent boundary-layer state, as well as the thermal boundary conditions. The application of a high-resolution schlieren system enabled the assessment of the local laminar-turbulent boundary-layer state, while the use of low- and high-enthalpy testing facilities enabled the assessment of the aerothermal influence. Steady-state Reynolds-averaged Navier–Stokes simulations, which included laminar-turbulent transition modeling, were employed to replicate the results of the experimental efforts.

Effects of Pitch Stabilization Buffer on the Dynamic Performance of Frame-Type Landing Gear

During the landing and taxiing process of aircraft, the frame-type landing gear (FTLG) usually generates large pitch vibrations under external excitation. Excessive vibration increases localized loads on the landing gear, which may lead to localized failure of the structure. To minimize this undesirable vibration, a passive oil–pneumatic pitch-stabilizing buffer (PSB) is designed in this paper to provide pitch damping. This paper applies the basic principles of dynamics to establish a dynamic model of FTLG considering the influence of PSB. And based on the design of experiments (DOE) method, by changing the filling parameters and structural parameters of PSB, the results of the changes of the frame vibration angle, angular velocity, and landing gear load are obtained, so as to analyze the effects of different parameters on the dynamic performance of the landing gear in the landing and taxiing process. The results demonstrate that increasing the oil damping coefficient of PSB and decreasing the installation angle of PSB on the main strut during the landing period resulted in less frame vibration and lower wheelset load ratios, but increased the landing overloads of landing gears. In the taxiing phase, increasing the PSB air spring stiffness can effectively reduce the frame vibration caused by the uneven road surface. The PSB structural parameters have little effect on the dynamic performance of FTLG.

Analysis of uncertainty factors in the prediction of missile pitch damping derivatives by unstructured CFD solver

Based on the transient planar pitching method, the dynamic derivative calculation function is implemented on an unstructured computational fluid (CFD) software NNW-FlowStar. Then the pitch-damping dynamic derivatives of the standard model of the ANF missile at zero angles of attack and different Mach numbers (0.5∼4.5) are calculated. The influence of various numerical and physical parameters on the calculation results of dynamic derivatives is studied in detail. It is found that the dynamic derivatives of pitch damping are independent of the values of amplitude (0.125° ≤ A ≤ 1°) and reduction frequency (0.025 ≤ k ≤ 0.2). When the number of calculation steps of the sine oscillation period is 200 and the number of inner iterations is 40, the prediction accuracy and computing efficiency can meet the engineering requirements simultaneously in this case. The influence of different grid resolutions on the dynamic derivative calculation results is studied. Results show that the grid requirements of dynamic derivative calculation are consistent with those of steady-state calculations. Finally, the calculation results are compared with the free flight test results, which verifies the reliability of the methods and parameters suggested in this paper.

Numerical modelling of wave run-up heights and loads on multi-degree-of-freedom buoy wave energy converters

With the development of wave energy converters (WECs), multi-degree-of-freedom (multi-DOF) buoy has become popular. The effect of nonlinear phenomena, such as wave run-up and wave impact, on an oscillating buoy WEC, may decrease its efficiency and even lead to overturning, plastic deformation, and fatigue failure. This study used a Fortran code for the custom development of Flow-3D software to apply independent power take-off (PTO) damping to each DOF. A hydrodynamic simulation model of the interaction between a wave and cylindrical buoy under six types of motions was developed and verified through model tests of the motion response of the buoy and wave run-up on it. Wave run-up heights and maximum wave loads on buoys with different motions and PTO combinations were investigated and compared. The numerical results show that coupled motion can lead to a less intense wave field distribution than a single motion and reduce the risk of overtopping. In addition, the bottom pressure of the buoy for the pitch–surge motion increased by a maximum of 101.6 % compared to the initial pressure. For independent linear PTO damping, heave damping has the most significant influence on the maximum wave load on the coupled motion buoys, followed by surge damping, while pitch damping has no significant effect. The results of this study can guide the designing of safe and reliable multi-DOF buoy WECs.

Flutter of a finite rectangular Wing’D mill in pitch and heave

Exact solutions of flutter are explored for a mode suitable for an oscillating 2D hydrofoil version of the summarised FlutterWing windpump which radically surpasses the old rotary fanpump. The imaginary part G of the 1D Theodorsen wake lift factor T rises singularly from the steady to allow 1D pure pitch flutter around the leading edge at low frequency. But its logarithmic infinite negative pitch damping by the shed vorticity is capped by the log of the 2D span. The downwash of an oscillating trailing (tip) vortex is reduced by a function of the reduced frequency based on spanwise distance. Its lag damps pitch and further raises the pitch unstable aspect ratio A to above 36. All binary pitch & heave neutral flutter frequency contours in (inertia, imbalance) space still pass through a nexus of the same total pitch inertia and imbalance as the corrected virtual mass concentrated at ¾ chord, a very high total in water. The internal bound windwise vortex from ¼ chord to trailing edge reduces as A−2 the 1D lift slope at all frequencies. It expands the 1D T = ½ double root of high frequency elliptical contours kissing the low frequency limit line at the nexus to make them dip below the line to the right of the nexus as hyperbolae with the nexal ray as left asymptote. Thus low A discovers a new wedge of high frequency binary flutter with real mass moments less than the virtual, as in water.

Pitch motion reduction of semisubmersible floating offshore wind turbine substructure using a tuned liquid multicolumn damper

A tuned liquid multicolumn damper (TLMCD) composed of three liquid columns and bottom connecting pipes is proposed to reduce the pitch motion of a semisubmersible substructure for wind turbine. The pitch damping of the semisubmersible floating offshore wind turbine (FOWT) substructure scale model with TLMCD in regular waves is studied experimentally. The TLMCD with the optimized mass ratio and tuning ratio provides effective pitch motion control especially near resonance period. The OpenFOAM is further developed to simulate dynamic response of the FOWT substructure under internal sloshing and external wave excitations, where the wave elevation and the FOWT substructure response have been validated against the experimental data. The design natural frequency of the TLMCD is equal to that of the FOWT substructure, and the analytical solutions and numerical results of liquid column decay are in good agreements. The motion response of the FOWT substructure, velocity distribution and the wall pressure are used to analyze the damping mechanism of the TLMCD. Based on the hydrodynamic moment, the energy dissipation characteristics of the TLMCD are analyzed quantitatively, where the damping and exciting moment are distinguished from each other. The analyses show that the TLMCD has the best damping effect near resonance frequency, where the 2.0% mass ratio of the liquid can reduce the maximum pitch motion by 10.84% to 18.53%.

Harmonic Decomposition Models of Flapping-Wing Flight for Stability Analysis and Control Design

This paper demonstrates the extension of the harmonic decomposition methodology, originally developed for rotorcraft applications, to the study of the nonlinear time-periodic dynamics of flapping-wing flight. A harmonic balance algorithm based on harmonic decomposition is applied to find the periodic equilibrium and approximate linear time-invariant dynamics about that equilibrium of the vertical and longitudinal dynamics of a hawk moth. These approximate linearized models are validated through simulations against the original nonlinear time-periodic dynamics. Dynamic stability using the linear models is assessed and compared to that predicted using the averaged dynamics. In addition, modal participation factors are computed to quantify the influence of the higher harmonics on the flight dynamic modes of motion. The study shows that higher harmonics play a key role in the dynamics of flapping-wing flight, inducing a vibrational stabilization mechanism that increases the pitch damping and stiffness while reducing the speed stability. This results in stabilization of the pitch oscillation mode and thus of the longitudinal hovering cubic. In addition, the proposed methodology is used to derive open- and closed-loop control laws for attenuating arbitrary state harmonics and to enhance the dynamic response characteristics.

Low-Interference Wind Tunnel Measurement Technique for Pitch Damping Coefficients at Transonic and Low Supersonic Mach Numbers

An experimental method for the determination of the pitch damping moment coefficient sum Cmq+Cmα˙ in a wind tunnel at transonic and low supersonic Mach numbers is developed. With support interference being a major issue for dynamic tests at these velocities, a minimum interference wire suspension approach is used. The motion of the wind tunnel model is restricted to a single-degree of freedom pitching oscillation through the geometry of the support system. A statistical evaluation procedure allows the simultaneous evaluation of multiple tests to increase confidence in the results. The influence of the wires as well as nonlinear effects are accounted for. The method is validated in an extensive test series at Mach numbers ranging from 0.6 to 2.0. Two reference missile models—the Basic Finner and the Army-Navy Spinner Rocket (ANSR)—are used. The results agree very well with CFD calculations throughout the transonic range. In comparison to free-flight tests the accuracy is significantly improved and result uncertainties are reduced by an order of magnitude.

Causation of Supersonic Limit Cycle Oscillations in Atmospheric Entry Vehicles

A successful atmospheric entry vehicle (AEV) design demonstrates manageable aerodynamic heating, bearable structural load, smooth deceleration, and intended trajectory during a descent into the atmosphere. Interestingly, the supersonic regime of the AEV manifests limit cycle oscillations (LCO) that restrict the maneuver potential and deployment of the drag chute. In this paper, efforts are made numerically and analytically to link the causation of LCO with external geometric variables of AEV. Computational fluid dynamics is used to calculate damping derivatives. The numerical results are validated with the Orion Crew Exploration Vehicle. The multiple time scales method, which belongs to the class of perturbation methods, is explored to develop an approximate closed-form solution of the nonlinear dynamic behavior of AEV. The analytical solution identifies that higher-order nonlinearities associated with pitch damping and static lift govern the onset of LCO. Finally, a parametric interaction study is carried out to determine the effect of two design variables, apex angle and length, on the vehicle’s dynamic stability. The mean data values from the main geometric effects plot show the condition of finite-amplitude oscillations. The results indicate that variation in these two parameters significantly impacts the magnitude of identified higher-order nonlinearities.

Hydrodynamic analysis of a hybrid modular floating structure system and its expansibility

ABSTRACT This paper reports a hybrid modular floating structure (HMFS) system preliminarily designed for mild marine environment. It is composed of a certain number of inner semi-sub modules and outermost box-type modules. The box-type modules are connected to adjacent semi-sub modules with hinges and additional Power Take-Off (PTO) damping systems. The hydrodynamic characteristics of several representative simplified serially connected HMFS systems under typical sea conditions are compared. The functions of the outermost module, the effects of different outermost module types and the expansibility of the HMFS system are emphatically analysed. The results indicate that compared with the outermost semi-sub module, the outermost box-type module is more effective in reducing the motion responses of inner semi-sub modules, connector forces and mooring forces. The additional PTO damping systems can produce substantial wave energy. The HMFS system shows good expansibility for mild sea zones. Abbreviations: HMFS, Hybrid Modular Floating Structure; VLFS, Very Large Floating Structure; RMFC, Rigid Module and Flexible Connector; MOB, Mobile Offshore Base; FEM, Finite Element Method; PTO, Power Take-Off; MFS, Modular Floating Structure; Ks, Pitch Elastic Stiffness; Kp, Pitch Damping Coefficient; DOF, Degree of Freedom; Fx, Horizontal Force of Connector; Fz, Vertical Shear Force of Connector; My, Pitch Bending Moment of Connector

Enhanced performance of airfoil-based piezoaeroelastic energy harvester: numerical simulation and experimental verification

This paper performs the detailed simulation analyses of airfoil-based piezoaeroelastic energy harvester with two degrees of freedom self-induced plunge-pitch motions, for exploring the flow field characteristic and enhancing the harvesting performance. The designing of the harvester for achieving flutter is first accomplished, finite element model is then built and simulation analyses are performed, and a prototype of the harvester system is finally fabricated. The obtained simulation results are in good agreement with the experimental and theoretical values. The effects of the key structural parameters of the harvester on flow field, aeroelastic vibration, and harvesting performance are numerically investigated. The results demonstrated that the structural parameters of the harvester determine primarily flutter onset of velocity, and consequently affect the dynamic behavior and harvesting performance. The harvester system takes place flutter and occurs limit cycle oscillations after flutter onset of velocity, which is suitable for harvesting energy. The smaller pitch structural stiffness coefficient and the more moderate both plunge stiffness and pitch damping coefficients are, the better aeroelastic vibration and output performance can be captured. A maximum output voltage of 29.08 V and output power of 3.382 mW can be harvested when the linear and cubic structural stiffness coefficients in pitch are 2.5 N·m and 100 N·m at 14 m/s, respectively, which corresponds to the power density of 21.138 mW/cm3 and demonstrates the superior harvesting performance over others. This work provides a significant guidance for designing the more efficient airfoil-based piezoaeroelastic energy harvester utilized in unmanned aerial vehicles.

Dynamic stall of the wind turbine airfoil and blade undergoing pitch oscillations: A comparative study

Dynamic stall significantly causes the unsteady aerodynamic loads on horizontal axis wind turbines. However, many studies are about dynamic stall of 2D airfoils rather than 3D rotating blades. The 3D dynamic stall is therefore still poorly understood and also challenging to predict accurately. This paper presents comparative analyses of dynamic stall among the 2D airfoil, 3D non-rotating blade and 3D rotating blade undergoing sinusoidal pitch oscillations. The parameters of 2 radial locations and 11 pitch conditions are also studied. All 3D aerodynamic responses come from the NREL Phase VI experiment. URANS simulations are used to predict the 2D aerodynamic responses of NREL S809 airfoil. Rotational augmentation is found to make the key difference between 2D airfoil flow and 3D blade flow. Rotational augmentation effectively suppresses the extension of separated flow during the upstroke process, and significantly accelerates the flow reattachment during the downstroke process. The onset of dynamic stall is therefore delayed with the maximum lift coefficient increased by 46%. The aerodynamic hysteresis intensity is also greatly reduced by 61%. Increasing the mean angle of attack (AOA), AOA amplitude and reduced frequency can further delay the onset of dynamic stall. On the other hand, rotational augmentation may unexpectedly produce a negative aerodynamic pitch damping and cause stall flutter on the inboard blade. Increasing AOA amplitude could reduce this negative damping and improve the torsional aeroelastic stability. This work might deepen the understanding of 3D dynamic stall with rotational augmentation on wind turbines.

Pitch damping identification in high speed regimes with a free-to-tumble rig

Many re-entry bodies, even if they are debris or not, have nonlinear dynamic stability characteristics that produce oscillations in flight. The free-to-tumble techniques can be used to extract damping coefficient of specific body for planetary entry. The curve fitting approach is used to predict oscillatory behavior and the damping coefficient for the various test conditions of the wind tunnel obtained after the experimental data. The analysis presented provides an overview of the free-to-tumble test techniques and illustrates the effects of dynamic stability of the inter-stage tronconical system. It is proposed that these test techniques and curve fitting solution be refined in the future to better define the dynamic stability curves for the re-entry bodies.

A survey on modeling and control of thruster-assisted position mooring systems

This review presents a systematic summary of the state-of-the-art development of technological solutions, modeling, and control strategies of thruster-assisted position mooring (TAPM) systems. The survey serves as a starting point for exploring automatic control and real-time monitoring solutions proposed for TAPM systems. A brief historical background of the mooring systems is given. The kinematics and a simplified kinetic control-design model of a TAPM system are derived in accordance with established control methods, including a quasistatic linearized model for the restoring and damping forces based on low-frequency horizontal motions of the vessel. In addition, another two mooring line models, i.e., the catenary equation and the finite element method model, are presented for the purpose of higher-fidelity simulations. The basic TAPM control strategies are reviewed, including heading control, surge-sway damping, roll–pitch damping (for semisubmersibles), and line break detection and compensation. Details on the concepts of setpoint chasing for optimal positioning of a vessel at the equilibrium position are discussed based on balancing the mooring forces with the environmental loads and avoiding mooring line failure modes. One method for setpoint chasing is the use of a structural reliability index, accounting for both mean mooring line tensions and dynamic effects. Another method is the use of a lowpass filter on the position of the vessel itself, to provide a reference position. The most advanced method seems to be the use of a fault-tolerant control framework that, in addition to direct fault detection and isolation in the mooring system, incorporates minimization of either the low-frequency tensions in the mooring lines or minimization of the reliability indices for the mooring lines to select the optimal directions for the setpoint to move. A hybrid (or supervisory switching) control method is also presented, where a best-fit control law and observer law are automatically selected among a bank of control and observer algorithms based on the supervision of the sea-state and automatic switching logic.

Evaluation of Dynamic Stability Derivatives for Hypersonic Vehicle

The dynamic stability derivative is the key parameter of the aircraft control system and the boundary analysis of the dynamic stability criterion. The accurate evaluation of dynamic derivative is of great importance to the design and flight of the aircraft. A method to predict the derivative of pitch damping is presented. The unsteady aerodynamic force is obtained by solving the unsteady flow field, and the static and dynamic derivatives of the aircraft are obtained by using integral method and least square method. By comparing the aerodynamic derivatives at different equilibrium positions and different centers of gravity, it can be seen that the calculated results are in good agreement with the experiment. It indicates that the present method has satisfactory order and efficiency and be suitable for engineering problems.

Effect of Single-Row and Double-Row Passive Vortex Generators on the Deep Dynamic Stall of a Wind Turbine Airfoil

Passive vortex generators (VGs) have been widely applied on wind turbines to boost the aerodynamic performance. Although VGs can delay the onset of static stall, the effect of VGs on dynamic stall is still incompletely understood. Therefore, this paper aims at investigating the deep dynamic stall of NREL S809 airfoil controlled by single-row and double-row VGs. The URANS method with VGs fully resolved is used to simulate the unsteady airfoil flow. Firstly, both single-row and double-row VGs effectively suppress the flow separation and reduce the fluctuations in aerodynamic forces when the airfoil pitches up. The maximum lift coefficient is therefore increased beyond 40%, and the onset of deep dynamic stall is also delayed. This suggests that deep dynamic-stall behaviors can be properly controlled by VGs. Secondly, there is a great difference in aerodynamic performance between single-row and double-row VGs when the airfoil pitches down. Single-row VGs severely reduce the aerodynamic pitch damping by 64%, thereby undermining the torsional aeroelastic stability of airfoil. Double-row VGs quickly restore the decreased aerodynamic efficiency near the maximum angle of attack, and also significantly accelerate the flow reattachment. The second-row VGs can help the near-wall flow to withstand the adverse pressure gradient and then suppress the trailing-edge flow separation, particularly during the downstroke process. Generally, double-row VGs are better than single-row VGs concerning controlling deep dynamic stall. This work also gives a performance assessment of VGs in controlling the highly unsteady aerodynamic forces of a wind turbine airfoil.

Specific features of the aerodynamic moment and the pitch damping of a re-entry vehicle model exercising free oscillations at supersonic speeds

A method for treating experimental data obtained on a setup with free oscillations over the pitching angle of the model and for determining the unsteady aerodynamic characteristics of the pitching moment coefficient is described. It is found that the pitching moment coefficient of a re-entry vehicle model at Mach numbers M = 2 and 2.25 and fixed angles of attack a depends non-linearly on the rate of change of the angle α. This circumstance makes the concept of aerodynamic derivatives inappropriate for mathematical description of the pitching moment coefficient.

Application of system identification technique in efficient model test correlations for a floating power system

Both the time domain simulations based on potential flow theory and wave tank model tests are used to evaluate the motion responses of a wave energy device. In this work, system identification is applied to obtain the frequency dependent transfer functions (between motions and excitations) from a series of model test runs of a wave energy platform exposed to irregular (random) waves. This is the first application of Reverse-Multiple Input Single Output (R-MISO) to a realistically (catenary) moored system (typical characteristics of wave energy devices) comparing physical model tests with our in-house time domain simulation program with addition of a mooring model. Based on the comparisons between the transfer functions from the time domain simulations and those from the model tests, reasonable frequency dependent dampings have been directly pulled out from the test cases under random sea states. System identification derived corrections to the linear or quadratic damping in pitch significantly improved the accuracy of motion responses. In this sense, this methodology can be a powerful tool in assisting the accurate simulation and design of wave energy devices under random sea states.

Analysis of Damping Derivatives for Delta Wings in Hypersonic Flow for Curved Leading Edges with Full Sine Wave

In this study, an attempt is made to evaluate the effect of first arched ends on the damping derived due to the pitch rate aimed at the variable sine wave bounty, flow deflection angle δ, pivot position, and the Mach numbers. Results show that with the escalation in the bounty of the complete sine wave (i.e., positive amplitude) there is an enlightened escalation in the pitch damping derivatives from h = 0, later in the downstream in the route of the sprawling verge it decreases till the location of the center of pressure and vice versa. At the location where the reasonable force acts, when we consider the stability derivatives in damping for the rate of pitch q, there is a rise in the numerical tenets of the spinoffs. This increase is non-linear in nature and not like for position near the leading edges. The level of the stifling derivatives owing to variations in Mach numbers, flow bend approach δ, and generosity of the sine wave remained in the same range.

Research on Damping Derivatives for Delta Wings in Hypersonic Flow for Curved Leading Edges with Full Sine Wave

In this study, an attempt is made to evaluate the effect of first arched ends on the damping derived due to the pitch rate aimed at the variable sine wave bounty, flow deflection angle δ, pivot position, and the Mach numbers. Results show that with the escalation in the bounty of the complete sine wave (i.e., positive amplitude) there is an enlightened escalation in the pitch damping derivatives from h = 0, later in the downstream in the route of the sprawling verge it decreases till the location of the center of pressure and vice versa. At the location where the reasonable force acts, when we consider the stability derivatives in damping for the rate of pitch q, there is a rise in the numerical tenets of the spinoffs. This increase is non-linear in nature and not like for position near the leading edges. The level of the stifling derivatives owing to variations in Mach numbers, flow bend approach δ, and generosity of the sine wave remained in the same range.