Pitch-up Maneuver Research Articles

Vorticity dynamics of fully developed leading-edge vortices on revolving wings undergoing pitch-up maneuvers

In nature, birds and insects usually execute pitch-up maneuvers, which is either an active perching or a passive response against gusts. During such maneuvers, their wings flap with a concomitant nose-up rotation around an axis, and thus, both vortex structures and aerodynamic forces of the wings are influenced. This research focuses on the impact of pitch-up maneuvers on the evolution and underlying vorticity dynamics of a fully developed leading-edge vortex (LEV), which has received limited interest in previous research. Based on data obtained from numerical simulations, an analysis of vortex dynamics and vorticity transport is conducted at different pitch rates and pitch axis locations. Our findings show that an increase in pitch rate and a shift of pitch axis toward the trailing edge can both terminate the growth of LEV and then initiate its movement toward the trailing edge via strong downward convection. However, the contributions of spanwise convection and vortex stretching (or compression) are distinct in these two scenarios, leading to different lift generations. Other vortex-tilting-based mechanisms, e.g., the planetary vorticity tilting and the dual-stage radial-tangential vortex tilting, are reduced during pitch-up maneuvers. Moreover, a rapid pitch-up around the leading edge is encouraged to maximize the lift during the maneuver, although this should be accompanied by constraints in flight height and kinetic energy when being applied to guide the perching of bio-inspired flapping wing micro air vehicles.

Transition Flight Trajectory Optimization for a Flapping-Wing Micro Air Vehicle with Unsteady Vortex-Lattice Method

Flapping-wing micro air vehicles (FWMAVs) have the capability of performing various flight modes like birds and insects. Therefore, it is necessary to understand the various flight modes of FWMAVs in order to fully utilize the capability of the vehicle. The unique flight modes of FWMAVs can be studied through the trajectory optimization. This paper proposes a trajectory optimization framework of an FWMAV. A high-fidelity simulation model is included in the framework to sufficiently consider the complicated dynamics of the FWMAV. The unsteady aerodynamics are modeled with the unsteady panel method (UPM) and the unsteady vortex-lattice method (UVLM). The effect of wing inertia is also considered in the simulation model. In this study, transition flight trajectories are searched with the proposed framework. An optimal control problem is formulated for the transition flight from hovering to forward flight and transcribed to the parameter optimization problem with the direct shooting method. The cost function is defined as energy consumption. The same converged solution can be obtained with different initial guesses. The optimization results show that the FWMAV utilizes the pitch-up maneuver to increase altitude, although the forward speed is reduced. This pitch-up maneuver is performed more actively when the target velocity of transition is low, or the wind condition is favorable to acceleration.

Machine-Learning-Based Detection of Aerodynamic Disturbances Using Surface Pressure Measurements

Aerodynamic disturbances (due to gusts, maneuvers, or a combination) leave a signature in the pressures exerted on the wing surface. In this work, the following question is explored: To what extent can the characteristics of these disturbances be parsed from the measured pressures alone? A supervised learning algorithm based on several layers of neural networks is applied. The overall machine-learning architecture is trained and tested on aerodynamic disturbance data generated by an inviscid vortex method applied to a two-dimensional flat plate undergoing a smooth pitchup maneuver. As a surrogate for an incident gust, the critical leading-edge suction parameter (LESP) is perturbed, which in turn dynamically changes the flux of the vorticity from the leading edge. The results are used to train the algorithm to estimate the LESP and angle-of-attack histories from the surface pressure. Two different approaches are used. In the first, which is a purely machine-learning strategy, a combination of convolutional and recurrent neural networks that accept surface pressure measurements as input is used. The overall architecture is shown to achieve an accurate estimation of the LESP and angle of attack. In the second approach, machine learning is integrated with a dynamical systems framework to learn a dynamical model for the angle of attack and the LESP. It is shown that this machine-learned system identification approach achieves somewhat higher accuracy as compared to the purely machine-learning approach with fewer parameters. In both approaches, it is shown that overfitting is mitigated by injecting random noise into the input pressures.

Detection and tracking of vortex phenomena using Lagrangian coherent structures

The formation and shedding of vortices in two vortex-dominated flows around an actuated flat plate are studied to develop a better method of identifying and tracking coherent structures in unsteady flows. The work automatically processes data from the 2D simulation of a flat plate undergoing a \(45^{\circ }\) pitch-up maneuver, and from experimental particle image velocimetry data in the wake of a continuously pitching trapezoidal panel. The Eulerian \(\varGamma _1\), \(\varGamma _2\), and Q functions, as well as the Lagrangian finite-time Lyapunov exponent are applied to identify both the centers and boundaries of the vortices. The multiple vortices forming and shedding from the plates are visualized well by these techniques. Tracking of identifiable features, such as the Lagrangian saddle points, is shown to have potential to identify the timing and location of vortex formation, shedding, and destruction more precisely than by only studying the vortex cores as identified by the Eulerian techniques.

A Maneuvering Flight Noise Model for Helicopter Mission Planning

A new model for estimating the noise radiation during maneuvering flight is developed in this paper. The model applies the quasi-static acoustic mapping (Q-SAM) method to a database of acoustic spheres generated using the fundamental rotorcraft acoustics modeling from experiments (FRAME) technique. A method is developed to generate a realistic flight trajectory from a limited set of waypoints and is used to calculate the quasi-static operating condition and corresponding acoustic sphere for the vehicle throughout the maneuver. By using a previously computed database of acoustic spheres, the acoustic impact of proposed helicopter operations can be rapidly predicted for use in mission planning. The resulting FRAME-QS model is applied to near-horizon noise measurements collected for the Bell 430 helicopter undergoing transient pitch-up and roll maneuvers, with good agreement between the measured data and the FRAME-QS model.

Lattice Boltzmann simulations of a pitch-up and pitch-down maneuver of a chord-wise flexible wing in a free stream flow

A rapid pitch-up and pitch-down maneuver of a chord-wise flexible wing in a steady free stream is studied by using a lattice Boltzmann flexible particle method in a three-dimensional space at a chord based Reynolds number of 100. The pitching rates, flexibility, and wing density are systematically varied, and their effects on aerodynamic forces are investigated. It is demonstrated that the flexibility can be utilized to significantly improve lift forces. The flexible wing has a larger angular momentum due to elasticity and inertia and generates a larger leading edge vortex as compared with a rigid wing. Such lift enhancement occurs mainly during the pitch-down motion while a large stall angle is produced during the pitch-up motion. At a low pitch rate, the flexibility cannot improve lift.

Determining Aerodynamic Characteristics of a Micro Air Vehicle Using Motion Tracking

The aerodynamic performance of small-scale fixed-wing flight is not well understood, and flight data is needed to gain a better understanding of the aerodynamics of micro air vehicles. The flight characteristics of micro air vehicles are difficult to measure because the small size and low weight prevent the use of conventional onboard instrumentation systems. In this research, an offboard motion tracking system captured the motion trajectory during the flights of a small off-the-shelf radio-controlled airplane that weighed 14.44 g (0.5094 oz) and had a span of 37.47 cm (14.75 in.). The recorded motion-path time histories were analyzed to determine the aerodynamic characteristics of the airplane during unpowered flight. The results presented show the longitudinal aerodynamic characteristics of the micro air vehicle over a wide range of angles of attack at a nominal Reynolds number of 25,000. Specifically, lift and drag characteristics of the airplane were obtained from the analysis of the flight trajectories during quasi-steady nominal gliding flight, as well as unsteady high angle-of-attack flight. The nominal-gliding flights showed an almost linear lift curve and small unsteady effects that were in part due to the angle-of-attack rate. During the unsteady high angle-of-attack flight, as would be seen during perching maneuvers, deep stall maneuvers, and highly dynamic flight in confined spaces, the unsteady effects of rapid changes in the angle of attack significantly increased the lift coefficient during pitch-up maneuvers and then decreased the lift coefficient during pitch-down maneuvers. By using numerous flight tests in both regimes (nominal-gliding and unsteady high angle-of-attack flight), the results show the effect of the angular rate and expand on the limited existing work. The flight-test results presented show the influence of unsteady aerodynamic effects on the longitudinal aerodynamic characteristics of a micro air vehicle in both quasi-steady nominal gliding flight and unsteady high angle-of-attack flight.

Transformation of flow structure on a delta wing of moderate sweep angle during pitch-up maneuver

The transformation of flow structure on a delta wing of moderate sweep angle is investigated during pitch-up via quantitative imaging in crossflow planes, in relation to qualitative dye visualization. The comparisons are made with the corresponding stationary wing. The effects of different pitch-up maneuver rates and Reynolds numbers on evolution of flow patterns are also addressed. A technique of high-image-density particle image velocimetry is employed for the quantitative analysis. The transformation of the flow structure starts with intertwining of the dual vortex structure which is distinctively seen at a low angle of attack of 50° swept wing, and then continues with the disappearance of one of the vortices of the dual vortex structure, in particular, the vortex located closest to the leading-edge of the wing. At further stages, a single, large-scale, leading-edge vortex, and distinctive form of vortex breakdown is witnessed. This distinctive type of vortex breakdown turns into a more traditional form at later stages of the maneuver. During the final stage of the pitch-up maneuver, the onset of vortex breakdown moves toward the apex of the wing. The general trend of aforementioned flow transformation happens irrespective of the values of pitch rates and Reynolds numbers. When the foregoing patterns are compared with the corresponding patterns on the stationary wing, it is evident that a significant time lag of development of the flow patterns occurs, relative to the motion of the wing.

Landing, perching and taking off from vertical surfaces

An approach is presented whereby small, unmanned aircraft can land on walls. The approach is demonstrated with a plane that uses an ultrasonic sensor to initiate a pitch-up maneuver as it flies toward a wall. The plane contacts the wall with spines that engage asperities on the surface. A non-linear suspension absorbs the kinetic energy while keeping the spines attached. A planar dynamic model is used to evaluate pitch-up maneuvers and determine suspension parameters that satisfy constraints on the contact forces for a range of flight velocities. Simulations conducted using the model are compared with data obtained using high-speed video and a force plate embedded in a wall.

Simulator Development for Transition Flight Dynamics of a VTOL MAV

This paper presents the simulation and validation of models for transition between forward flight and hover for a micro air vehicle (MAV). A dynamical simulation environment is developed, based on measured aerodynamic properties of a fixed-wing tail-sitter MAV with vertical take-off and landing (VTOL) capabilities. The simulator is validated against recorded flight data of transition from forward flight to hover using the physical platform. Specifically, the flight transition maneuver in the vertical plane (vertical-to-horizontal and horizontal-to-vertical) is studied in detail. The development and evaluation of a VTOL MAV called Mini-Vertigo 2 (MV2) is presented. A non-linear longitudinal dynamic model of MV2 flight is derived, and semi-empirical aerodynamic formulas for thrust, lift, drag and pitching moment based on wind tunnel testing are applied to the dynamic model. Nonlinearities during transition to/from hover are addressed, and (using the developed dynamic model) a numerical vehicle dynamic simulator is presented. The MV2 autopilot is discussed and flight test data are presented. Flight data from pitch-up maneuvers was compared to results of simulations. This comparison enables the future application of the simulation system throughout the flight envelope. This work presents a significant extension of [1].

Experimental Investigation of Unsteady Flow Separation on a Maneuvering Axisymmetric Body

An experimental study on maneuvering-undersea-vehicle geometry was conducted to give detailed information on unsteady turbulent flow separation and to investigate different time-lag models for approximating the unsteady separation locations. Both unsteady and steady results are presented for the axisymmetric configuration of the model, which can also be thought of as a missile or aircraft-fuselage geometry. Steady and unsteady skin-friction magnitudes were measured using hot-film sensors. The minimum of the circumferential skin-friction distribution at each axial-measurement station was used to detect the separation locations. The linear pitch-up maneuver studied is comparable to the dynamic motion of full-scale vehicles of interest, in terms of the nondimensional time. Significant time lags observed between unsteady and steady crossflow separation locations indicate the increase in attached circulation over the maneuvering model, which may explain why unsteady forces measured on similar geometries lead the steady values. A first-order differential time-lag model approximates the unsteady separation locations reasonably well. This model can be considered as a method of correlating the unsteady measurements to the quasi-steady data with a time lag. Using this model, the prediction of the unsteady flow characteristics from the steady data can be possible with the development of methods for estimating the time lags that vary based on the geometry and the maneuvers performed. The results of the unsteady experiments presented in this paper show that the time required to displace the volume of leeside inviscid fluid during a maneuver with vortical separated flow may be the main factor creating the difference in the time-lag magnitudes and their spatial variation observed for different axisymmetric geometries and points of rotation.

Space–time discontinuous Galerkin method for the compressible Navier–Stokes equations

A space–time discontinuous Galerkin finite element method for the compressible Navier–Stokes equations is presented. We explain the space–time setting, derive the weak formulation and discuss our choices for the numerical fluxes. The resulting numerical method allows local grid adaptation as well as moving and deforming boundaries, which we illustrate by computing the flow around a 3D delta wing on an adapted mesh and by simulating the dynamic stall phenomenon of a 2D airfoil in rapid pitch-up maneuver.

Aerodynamic Analysis of a Spinning Missile with Dithering Canards

A generic spinning missile with dithering canards is used to demonstrate the utility of an overset structured grid approach for simulating the aerodynamics of rolling airframe missile systems. A grid convergence study andassessment of viscous effects shows that a medium-resolution viscous grid with 8 million grid points provides a good compromise between solution accuracy and throughput. Viscous effects should be included in detailed studies to capture the interaction between the inboard canard vortex and the fuselage and tail boundary layers. The computed results agree well with experimental data. A database of cases with variation of angle of attack and the strength of control authority of a pitch-up maneuver is computed to evaluate missile performance. The case throughput rates are sufficient to contemplate population of aerodynamic databases with Navier-Stokes computations. Overall, the structured overset grid approach enables accurate and efficient simulation of rolling airframe missile configurations that involve relative motion between system components.

Unsteady Crossflow Separation Location Measurements on a Maneuvering 6:1 Prolate Spheroid

The crossflow separation of a 6:1 prolate spheroid undergoing transient maneuvers is studied. The dynamic plunge-pitch-roll model mount provides the unique capability to simulate unsteady maneuvers in a wind tunnel. Hot-film sensors are used with constant-temperature anemometers to measure the time-depcndent wall shear at points over the entire model surface. Minima in wall shear are used to indicate separation locations. Steady and unsteady data are presented for two fast maneuvers: a 0-30-deg, 0.33-s(t' = tU /L = 11) ramp pitchup about the model center (pitchup maneuver) and a 0-13.5-deg, 0.25-s (t' = 8.3) pitchup about the model center that simulates the time-dependent sideslip angle of a submarine entering a turning maneuver (submarine maneuver). Data show that, especially at higher angles of attack, significant lags occur in the flowfield during the maneuvers compared with the steady cases. In particular, separation is delayed at all locations of the model by up to a 10-deg higher angle of attack in the unsteady maneuvers compared with the steady data. Equivalently, the separation structure during the unsteady maneuvers lags the steady data by from 1.5 to 3.5 nondimensional time units t'

Preconditioned Multigrid Methods for Unsteady Incompressible Flows

A highly efficient numerical approach based on multigrid and preconditioning methods is developed for modeling 3D steady and time-dependent incompressible flows. Thek-ω turbulence model is used to estimate the effects of turbulence. The model equations are solved together with the N-S equations in a strongly coupled way, and acceleration techniques like the multigrid method are also used for the turbulence model equations. For unsteady problems, a dual-time stepping procedure is adopted to satisfy the divergence-free constraint and to obtain a time-accurate solution. To improve the performance of this approach for small physical time steps, a modification to residual smoothing parameters is proposed. The numerical algorithm and the turbulence model are validated first by calculating unsteady inviscid flow around an oscillating cylinder, unsteady laminar flow past a circular cylinder, and steady high-Reynolds number turbulent flow over a 6:1, prolate spheroid. Then the three-dimensional time-dependent turbulent flow over a spheroid when it is undergoing a pitch-up maneuver is calculated and compared with experimental data.

Surface pressure measurements on a pitching swept wing in a water channel

We present the results of surface pressure measurements on a swept wing of NACA 0015 profile and a back sweep angle of 15 deg, which was pitched at a uniform angular velocity. The pitching axis was perpendicular to the flow direction so that the experiment simulated the pitch-up maneuver of a fixed-wing aircraft. The experiments were performed in an open-surface water channel. The object of the study was to understand the mechanics of vorticity production and dynamic stall in three-dimensional unsteady flows. The phase-locked pressure data which were obtained at several closely spaced spanwise locations of the wing were used to obtain information on the fluxes of spanwise and chordwise vorticity components, in addition to the usual information on the aerodynamic coefficients. The study showed that the three-dimensional dynamic stall over the slightly swept wing is less catastrophic and more gradual than the two-dimensional process over an unswept wing. Other important effects observed were a spanwise variation of the aerodynamic coefficients and the presence of spanwise periodicity in the production of vorticity following the onset of dynamic stall.

Physics of forced unsteady flow for a NACA 0015 airfoil undergoing constant-rate pitch-up motion**This research is supported, in part, by AFOSR Grant No. 90-0249, and by the Ohio Supercomputer Center Grant No. PES080.

The unsteady Navier-Stokes (NS) analysis of Osswald, Ghia and Ghia in velocity-vorticity variables is modified to study the dynamic stall phenomenon for a NACA 0015 airfoil undergoing constant Ω0 pitch-up maneuvers at Reynolds number Re = 10 000 and 45000. The use of third-order accurate biased upwind differencing for the nonlinear convective terms in the vorticity transport equation removes the spurious oscillations observed in the earlier studies by the authors for these values of Re. The fully implicit and vectorized ADI-BGE method of the authors is used to solve the unsteady NS equations. Instantaneous inertial surface vorticity, which is an invariant of the choice of reference frame selected, is employed to determine the location of separation of the boundary-layer flow on the suction surface; also a separation bubble embedded within the boundary layer is observed for both cases somewhere between the leading edge and the quarter-chord point. Primary, secondary, tertiary and quarternary vortices have been observed before the dynamic-stall vortex evolves and gathers its maximum strength.

Unsteady crossflow on a delta wing using particle image velocimetry

5has shown that the vortex breakdown response is typically an order of magnitude slower than the convective time scale; in essence, this means that the location of breakdown substantially lags that expected from quasistatic considerations. In view of these observations of the phase lag of vortex breakdown location, one expects the cross-sectional development of the leading-edge vortices to exhibit an analogous phase lag. Such lag has been demonstrated using qualitative flow visualization.6 For this type of lag, the overall features of the velocity field during pitching maneuvers have been characterized separately.5 Therein, the velocity field at several instants during the wing motion is compared with its quasistatic counterpart to show the consequence of the movement of the location of vortex breakdown through the plane of interest. The unsteady loading in relation to the foregoing features of the flow structure has been reviewed independently7 and illustrates that corresponding phase lags and hysteresis of the unsteady forces are induced during a typical maneuver. The emergence of particle image velocimetry (PIV) provides the potential for detailed characterization of the unsteady velocity field past a moving delta wing with an accuracy comparable to laser-Doppler anemometry (LD A) but without the necessity of phase referencing. This high-resolution optical method allows detailed definition of the flow structure at a given instant, thereby providing a more accurate representation of the flowfield than can be accomplished with phasereferencing techniques. The objective of this note is to report on the first characterization of the unsteady flow structure past a pitching delta wing via particle imaging techniques and to reveal new features of the flow structure during pitch-up and pitch-down maneuvers. The major challenge of applying PIV to this class

High-alpha application of variable-gain output feedback control

This paper describes a recently developed variable-gain, optimal, discrete, output feedback design approach that is applied in a nonlinear flight regime. The flight regime covers a wide angle-of-attack a range that includes the stall region. The paper contains brief descriptions of the variable-gain formulation, the discrete-control structure and flight equations used to apply the design approach, and the high-performance airplane model used in the application. Both linear and nonlinear analyses are shown for a longitudinal four-model integrated design case with a = 5, 15, 35, and 60 deg and two flight control modes. Nonlinear simulations show good time response for both a longitudinal pitch-up and pitch-down maneuver and a regulation within 5 deg from the nominal angle during a high-ex lateral maneuver.

Simulation of dynamic stall phenomenon using unsteady Navier-Stokes equations

A non-inertial body-fixed generalized coordinate frame is employed to develop an unsteady Navier-Stokes (NS) analysis for arbitrary maneuvering bodies. A fully implicit direct numerical simulation (DNS) methodology is implemented for the solution of the governing equations. A velocity-vorticity (disturbance stream function - vorticity in 2-D) formulation is shown to simplify both the theoretical and numerical analysis of maneuvering flight when compared with the primitive-variable formulation. The resulting method is highly vectorizable and currently achieves a computational index of 6 micro-seconds per time step per mesh point using a single processor on the CRAY Y-MP 8 864 at the Ohio Supercomputer Center. Vectorization has been achieved satisfactorily, with the code currently performing in the range of 130–180 Mflops. The rapid pitch-up maneuver of a NACA 0015 airfoil is wxamined at Re=1000 and Re=10 000, with particular emphasis being placed on the development and evolution of the dynamic stall vortex.