Roll Oscillations Research Articles

The suppression of flying-wing roll oscillations with open and closed-loop spanwise blowing

Uncommanded self-induced roll oscillations cause significant challenges in flight control and are ubiquitous in high-attack-angle flights in the flying-wing configuration. Spanwise blowing slots were designed in this article to suppress these roll oscillations with nonzero mean angles of a 53° swept flying-wing model. Three flow control strategies were proposed and studied successively. The open-loop symmetric blowing successfully suppressed oscillations below the nominal angle of attack of 24° before losing its effectiveness. Subsequently, adaptive continuous blowing using the proportion-integral-differential algorithm was performed with symmetric pre-blowing to eliminate the ineffective region with a small blowing coefficient. Using this strategy, roll oscillations under all tested nominal angles of attack were successfully addressed as the nonzero trim angles were eliminated and the oscillations were suppressed. However, the air consumption needed to maintain the model balance was too large, which necessitated the development of pulsed blowing. Static force measurements showed that the blowing-induced rolling moment had a linear relationship with the duty cycle of blowing. The results from the particle-image-velocimetry tests revealed that the mechanism of the linear relationship was the increased duration of coherent vortices over a period at longer duty cycles. Based on the static experimental results, the model was stabilized via proportion-integral-differential adaptive blowing, which utilized the duty cycle as the control variable. Compared to the second strategy, the last one reduced the required mean blowing momentum coefficient by two orders of magnitude while maintaining a great control effect.

Transitions near the onset of low Prandtl-number rotating convection in presence of horizontal magnetic field

We investigate the transitions near the onset of thermal convection in electrically conducting low Prandtl-number (Pr) fluids in the presence of rotation about a vertical axis and external horizontal magnetic field. Three-dimensional direct numerical simulations (DNSs) and low dimensional modeling are performed with the Rayleigh–Bénard convection system in the ranges 0 < Q ≤ 1000 and 0 < Ta ≤ 500 of the Chandrasekhar number (Q) and the Taylor number (Ta), respectively, for that purpose. For larger Q(≥32.7), DNSs show substantial enhancement of convective heat transport and only finite amplitude steady two dimensional roll patterns at the onset. On the other hand, for smaller Q(<32.7), very rich dynamics involving different stationary as well as time dependent patterns, including stationary two-dimensional rolls, cross rolls, and oscillatory cross rolls, are observed at the onset of convection. Our investigation uncovers the cause of enhancement of heat transport and the origin of different flow patterns at the onset. We establish that a first order transition to convection occurring at the onset is responsible for the enhancement of the heat transport there. Furthermore, as the Rayleigh number (Ra) is increased beyond the onset, subsequent transitions near it are also explored in detail for smaller Q, and these are found to be associated with a variety of bifurcations including subcritical/supercritical pitchfork, Hopf, imperfect pitchfork, imperfect gluing, and Neimark–Sacker.

Two constant amplitude pulses’ input shaper to maneuver an attitude of precise-oriented flexible spacecraft

This paper proposes an integrated feed-forward input shaper for flexible spacecraft maneuvering involving coupled roll and yaw motion interactions. The shaper affects both the roll and yaw inputs, and each individual input consists of two constant amplitude pulses. The cross-contribution of the roll and yaw inputs is considered in the formulation of the residual roll and yaw oscillation constraints. The resulting shaped roll and yaw inputs are then applied to several maneuver cases of a satellite with two symmetrical flexible solar panels. The simulation results show that the proposed constraint equations to limit the residual roll and yaw oscillations are valid and correct.

Review of self-induced roll oscillations and its attenuation for low-aspect-ratio wings

Micro aerial vehicles are currently receiving growing interest because of their broad applications in many fields. In their flight tests, the onset of unwanted large amplitude roll oscillations was reported, which resulted in difficulties with flight control, and this has become one of the major challenges of current micro aerial vehicles design. In this review type of article, the low Reynolds number flow characteristics of a low-aspect-ratio wing are reviewed, and the self-induced roll oscillations are discussed with special attention being payed to the interaction between the three-dimensional flow structure and wing in reciprocatively rolling motion. The roll attenuation methods are introduced via flow control approaches, which can suppress the roll oscillations effectively by manipulating the leading-edge flow separation and tip vortices of the low-aspect-ratio wings.

Study regarding the influence of the flexible lamella on the elastic characteristic for a suspension with longitudinal torsion bars

A main component of the car suspension is the stabiliser bar, that has the role to reduce the roll oscillations, and it is constructively materializes, within the conventional suspension, via a transversal torsion bar connected direct and indirect between the wheels of the axle. There are constructive solutions of suspensions with torsion bar as elastic element, longitudinal disposed, and that replaces the conventional stabiliser bar with a flexible lamella connected between the ends of the longitudinal torsion bars. So, the flexible lamella has two functions: reduces the roll oscillations and works as an additional elastic element of the suspension. Via this second function it is improved the elastic characteristic aspect of the suspension with positive consequences on the comfort and safety. The paper aims to highlight this influence by the experimental determination of the elastic characteristic of the suspension with and without lamella and the comparing of the two elastic characteristics. It is carried out and a complex theoretical model of the suspension with longitudinal torsion bars and flexible lamella, validated via the experimental research, that allows the optimization of such a suspension.

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

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

Suppression of Roll Oscillation in Turning of Quadruped Robot by Asymmetric Amplification of Central Pattern Generator Output Waveform

Quadruped robots experience excessive vibrations in the roll direction when turning by controlling their hip yaw joint. In the case of image-based teleoperation of the robot, the operator cannot aware the situation of the robot, due to excessive vibrations of the viewpoint of the image from the camera mounted on the robot. Especially, it is known that vibration in the roll direction is most likely to cause motion sickness. To overcome this problem, we proposed the asymmetric amplification of the output waveforms of central pattern generators. We implemented the proposed method on a robot in a dynamic simulator and verified the effectiveness of the proposed method, during the turning operation. As a result, we confirmed that the proposal method can suppress 43.7% vibration of the robot body in the roll direction and 7.4% vibration in the pitch direction compared with the conventional method.

Numerical study of a container ship model for the uncoupled parametric rolling

Parametric roll on ships is a resonance phenomenon whose onset causes heavy roll oscillations leading to dangerous situations for the ship, the cargo and the crew. It affects both small vessels with marginal stability and large container ships if four conditions are met simultaneously: the wave length and ship length are approximately equal, the frequency of encounter wave is twice the roll natural frequency, the ship’s roll damping is low enough and the wave height exceeds a limit value characteristic to each vessel. For a container ship, the first two conditions result in a time-varying geometry of the submerged hull and thus to a periodic variation of the transverse stability. In the last two decades, several mathematical models for parametric rolling have been proposed by scientists. In the paper, we cancelled the couplings terms between heave, pitch and roll in a 3 DOF model proposed by Neves and Rodriguez to obtain an uncoupled 1 DOF model for the parametric roll. Even if it seems too simplistic, such a model based on Mathieu type equation is a good start to capture the basic features of the analysed phenomenon. There are no less than seven parameters that can influence the ship stability and the appearance of large roll amplitudes. By modifying two of these parameters one by one and keeping the others constant, a series of colour plots have been drown that capture the role played by the ship’s parameters in obtaining dangerous roll amplitudes or too short times to take countermeasures. Analysing the instability regions suggested by these colour plots, one can imagine control measures to reduce the roll amplitudes, such as changing the forward velocity or the heading angle. The data used in the paper have been obtained from experiments with a container ship model in a towing tank followed by expansion to a full scale ship.

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°.

Transition from convection rolls to large-scale cellular structures in turbulent Rayleigh-Bénard convection in a liquid metal layer

A new coherent structure appears on turbulent Rayleigh-B\'enard convection in a liquid metal layer; transitions to large-scale cellular structures from oscillatory roll structures occur with Rayleigh numbers. A scaling law describing characteristic length of the structures is suggested.

Suppression of Roll Oscillation in Turning of Quadruped Robot by Asymmetric Amplification of Central Pattern Generator Output Waveform

Suppression of Roll Oscillation in Turning of Quadruped Robot by Asymmetric Amplification of Central Pattern Generator Output Waveform

Nonlinear roll oscillation of semisubmersible system and its control

The control and dynamic stability analysis of roll oscillation of the strongly nonlinear semisubmersible system are not widely investigated in the frequency domain. In particular, the suppression of undesirable nonlinear responses like period doubling route to chaos, subharmonic oscillation etc. of such a system under harmonic excitation has not been attempted so far. The nonlinear semisubmersible system is characterized by a fairly strong quintic nonlinearity arising out of the restoring action. In the present study, the incremental harmonic balance method along with arc-length continuation technique (IHBC) is employed to identify the primary and higher order subharmonic responses of the system. Stability of the responses is checked by the Floquet’s theory. A reformulation of the IHBC is then presented to control the responses of the semisubmersible system with quintic nonlinearity under state feedback control with time delay. The stability of the controlled responses is examined by applying the semi-discretization method for delay differential equation. It is shown that by considering appropriate feedback gains and time delay, (i) appreciable reduction of the amplitudes of primary responses, (ii) exclusion of all higher order subharmonics 2T, 3T, 4T, 8T, and (iii) the reduction of the extent of domain of various types of instability phenomena like, bifurcation of solutions, jump phenomena, chaotic responses etc. are possible. Further, it is found that the negative velocity feedback gain is much more effective than the full state feedback gains or varying the time delay parameter for better control of the roll oscillation of the system.

Gravitational thermal flows of liquid metals in 3D variable cross-section containers: Transition from low-dimensional to high-dimensional chaos.

This study extends the numerical results presented in author's past work [M. Lappa and H. Ferialdi, Phys. Fluids 29(6), 064106 (2017)] about the typical instabilities of thermogravitational convection (the so-called Hadley flow) in containers with inclined (converging or diverging) walls. The flow is now allowed to develop along the third dimension (z). In a region of the space of parameters where the two-dimensional solutions were found to be relatively regular in time and with a simple structure in space (supporting transverse waves propagating either in the downstream or in the upstream direction), the 3D flow exhibits either waves traveling along the spanwise direction or spatially disordered and chaotic patterns. In order to identify the related mechanisms, we analyze the competition between hydrodynamic and hydrothermal (Oscillatory Longitudinal Roll) modes of convection for different conditions. A peculiar strategy of analysis is implemented, which, on the one hand, exploits the typical properties of systems developing coexisting branches of solutions ("multiple" states) and their sensitivity to a variation of the initial conditions and, on the other hand, can force such systems to select a specific category of disturbances (by enabling or disabling the related "physical" mechanisms). It is shown that hydrodynamic modes can produce early transition to chaos. The dimensionality of such states is investigated through evaluation of the "fractal" (correlation) dimension on the basis of the algorithm by Grassberger and Procaccia. When low-dimensional chaos is taken over by high-dimensional chaos, the flow develops a recognisable interval of scales where turbulence obeys the typical laws of the so-called "inertial range" and produces small-scale features in agreement with available Kolmogorov estimates.

Forced Synchronization of Electroconvective Roll Oscillations in Nematic Liquid Crystals

The forced phase locking in a system of the oscillating electroconvective rolls that form in a nematic liquid crystal layer in a dc electric field is studied. As a result of the action of an additive ac electric field with a small amplitude, the system of oscillators is found to be divided into clusters, where oscillations are fully phase locked. The electroconvective rolls in neighboring clusters oscillate in antiphase and the clusters are separated by Ising walls. The phase locking is shown to be maximal at the forcing frequency that is close to the double frequency of the natural oscillations of rolls. A model is proposed to describe spatially distributed phase oscillators, and it takes into account the symmetries of a system of electroconvective rolls and external forcing. The results of numerical simulations agree well with the experimental data.

Unsteady aerodynamic effects in landing operation of transport aircraft and controllability with fuzzy-logic dynamic inversion

Aircraft landing in strong wind has been a safety problem for all types of aircraft. The specific issues involve hard landing, roll oscillation and runway veer-off. These issues are related to atmospheric disturbances, and/or dynamic ground effect. As a result, the aerodynamics will be different from those in steady flow concept. In this paper, some of the pertinent stability and control derivatives based on a small-disturbance concept will be presented. How these local stability and control characteristics affect global controllability will be examined with Fuzzy-Logic Dynamic Inversion. Controllability is judged from whether necessary control deflections exceed the imposed limits. Specific examples involving a twin-jet transport with hard landing, rolling oscillation before touchdown and runway veer-off event due to varying crosswind after touchdown are illustrated.

Numerical study of forced roll oscillation of FPSO with bilge keel

This work shows a study about the bilge keel and its influence, width and form, on the roll damping of FPSO sections. A computational code was developed to simulate forced roll oscillation of a middle section of FPSO with different bilge keels types. The computational code calculates the solution of the Navier-Stokes equations in 2D, using the finite volume method and the upwind TVD scheme of Roe-Sweby. The effect of wave radiation is neglected. This work shows how the generated vortices influence the pressure distribution around the middle section of FPSO. The numerical results are compared with experimental results to validate the computational code. New bilge keel configurations were studied to improve the roll damping of FPSO.

Onset of Primary and Secondary Instabilities of Viscoelastic Fluids Saturating a Porous Layer Heated from below by a Constant Flux

We analyze the thermal convection thresholds and linear characteristics of the primary and secondary instabilities for viscoelastic fluids saturating a porous horizontal layer heated from below by a constant flux. The Galerkin method is used to solve the eigenvalue problem by taking into account the elasticity of the fluid, the ratio between the viscosity of the solvent and the total viscosity of the fluid and the lateral confinement of the medium. For the primary instability, we found out that depending on the rheological parameters, two types of convective structures may appear when the basic conductive solution loses its stability: stationary long wavelength instability as for Newtonian fluids and oscillatory convection. The effect of the lateral confinement of the porous medium by adiabatic walls is to stabilize the oblique and longitudinal rolls and therefore selects transverse rolls at the onset of convection. In the range of the rheological parameters where stationary long wave instability develops first, we use a parallel flow approximation to determine analytically the velocity and temperature fields associated with the monocellular convective flow. The linear stability analysis of the monocellular flow is performed, and the critical conditions above which the flow becomes unstable are determined. The combined influence of the viscoelastic parameters and the lateral confinement on the characteristics of the secondary instability is quantified. The major new findings concerning the secondary instabilities may be summarized as follows: (i) For concentrated viscoelastic fluids, computations showed that the most amplified mode of convection corresponds to oscillatory transverse rolls, which appears via a Hopf bifurcation. This pattern selection is independent of both the fluid elasticity and the lateral confinement of the porous medium. (ii) For diluted viscoelastic fluids, the preferred mode of convection is found to be oscillatory transverse rolls for a very laterally-confined medium. Otherwise, stationary or oscillatory longitudinal rolls may develop depending on the fluid elasticity. Results also showed the destabilizing effect of the relaxation fluid elasticity and the stabilizing effect of the viscosity ratio for the onset of both primary and secondary instabilities.

Rattleback dynamics and its reversal time of rotation.

A rattleback is a rigid, semielliptic toy which exhibits unintuitive behavior; when it is spun in one direction, it soon begins pitching and stops spinning, then it starts to spin in the opposite direction, but in the other direction, it seems to spin just steadily. This puzzling behavior results from the slight misalignment between the principal axes for the inertia and those for the curvature; the misalignment couples the spinning with the pitching and the rolling oscillations. It has been shown that under the no-slip condition and without dissipation the spin can reverse in both directions, and Garcia and Hubbard obtained the formula for the time required for the spin reversal t_{r} [Proc. R. Soc. Lond. A 418, 165 (1988)1364-502110.1098/rspa.1988.0078]. In this work, we reformulate the rattleback dynamics in a physically transparent way and reduce it to a three-variable dynamics for spinning, pitching, and rolling. We obtain an expression of the Garcia-Hubbard formula for t_{r} by a simple product of four factors: (1) the misalignment angle, (2) the difference in the inverses of inertia moment for the two oscillations, (3) that in the radii for the two principal curvatures, and (4) the squared frequency of the oscillation. We perform extensive numerical simulations to examine validity and limitation of the formula, and find that (1) the Garcia-Hubbard formula is good for both spinning directions in the small spin and small oscillation regime, but (2) in the fast spin regime especially for the steady direction, the rattleback may not reverse and shows a rich variety of dynamics including steady spinning, spin wobbling, and chaotic behavior reminiscent of chaos in a dissipative system.

Cross-coupling vestibular stimulation: motion sickness and the vestibulo-sympathetic reflex.

Motion sickness is associated with a variety of autonomic symptoms, presumably due to proximity or functional interconnectivity between the autonomic centers in the brainstem and the vestibular system. A direct influence of the vestibular system on cardiovascular variables, defined as the vestibulo-sympathetic reflex, has been reported previously. Our aim was to investigate the sudomotor components of the autonomic responses associated with motion sickness during passive cross-coupling stimulation ("roll while rotating"). Healthy subjects (n=17) were rotated at 40°/s around an earth-vertical yaw axis alone and in combination with sinusoidal roll oscillations (0.2Hz). Motion sickness was assessed verbally every minute using a 1-10 scale, while recording DC and AC skin conductance levels (SCL) from the forehead. Yaw rotation alone provoked neither motion sickness nor variations of forehead sweating. Yet during cross-coupling stimulation all subjects reported motion sickness. Higher motion sickness scores (>5) were associated with significantly higher amplitudes of AC-SCL events compared to the lower scores (0.22±0.01 vs. 0.11±0.01µS, respectively). Frequency domain analysis of the AC-SCL events revealed a peak at 0.2Hz, coinciding with the frequency of the chair rolls. The total power of AC-SCL signals did not match the trend of motion sickness scores across conditions. We conclude that: (1) although SCL is related to motion sickness, it does not follow the perceived sickness closely; (2) the discrepancy between SCL and motion sickness and the rhythmic AC-SCL events could reflect a sudomotor component of the vestibulo-sympathetic reflex.

Fluid-structure interaction of a rolling restrained body of revolution at high angles of attack

The current work investigates numerically rolling instabilities of a free-to-roll slender rigid-body of revolution placed in a wind tunnel at a high angle of attack. The resistance to the roll moment is represented by a linear torsion spring and equivalent linear damping representing friction in the bearings of a simulated wind tunnel model. The body is subjected to a three-dimensional, compressible, laminar flow. The full Navier-Stokes equations are solved using the second-order implicit finite difference Beam-Warming scheme, adapted to a curvilinear coordinate system, whereas the coupled structural second order equation of motion for roll is solved by a fourth-order Runge-Kutta method. The body consists of a 3.5-diameter tangent ogive forebody with a 7.0-diameter long cylindrical afterbody extending aft of the nose-body junction to x/D = 10.5. We describe in detail the investigation of three angles of attack 20°, 40°, and 65°, at a Reynolds number of 30 000 (based on body diameter) and a Mach number of 0.2. Three distinct configurations are investigated as follows: a fixed body, a free-to-roll body with a weak torsion spring, and a free-to-roll body with a strong torsion spring. For each angle of attack the free-to-roll configuration portrays a distinct and different behavior pattern, including bi-stable limit-cycle oscillations. The bifurcation structure incorporates both large and small amplitude periodic roll oscillations where the latter lose their periodicity with increasing stiffness of the restraining spring culminating with distinct quasiperiodic oscillations. We note that removal of an applied upstream disturbance for a restrained body does not change the magnitude or complexity of the oscillations or of the flow patterns along the body. Depending on structure characteristics and flow conditions even a small rolling moment coefficient at the relatively low angle of attack of 20° may lead to large amplitude resonant roll oscillations.