Effect of gusty inflow on the jet-switching characteristics of a plunging foil
12 Nov 2020-Physics of Fluids (AIP Publishing LLC AIP Publishing)-Vol. 32, Iss: 11, pp 117105-117105
TL;DR: In this article, the effect of stochastic inflow fluctuations on the jet-switching characteristics of a harmonically plunging elliptic foil at a low Reynolds number regime has been analyzed.
Abstract: The effect of stochastic inflow fluctuations on the jet-switching characteristics of a harmonically plunging elliptic foil at a low Reynolds number regime has been analyzed in the present study. The inflow fluctuations are generated by simulating an Ornstein–Uhlenbeck process—a stationary Gauss–Markov process—with a chosen correlation function. In the absence of fluctuations, quasi-periodic movement of the wake vortices plays a key role in bringing out jet-switching at κh ≥ 1.5. However, fluctuating inflow alters the organized arrangement of the vortex street even at a lower κh (κh = 1.0), giving way to an advanced jet-switching onset. More frequent switching with a larger deflection angle is also observed at κh = 1.5 as compared to the no fluctuation case. Effects of inflow timescales on the deflection angle and switching frequency of the wake are investigated by varying the input correlation-lengths. The underlying flow physics are investigated through a qualitative study of the near-field interactions as well as various quantitative measures derived from the unsteady flow-field.
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TL;DR: In this article , an order-to-chaos map for the unsteady flow field of a flapping foil in the low Reynolds number regime is presented, which can capture the physical effect of the parametric variations on the wake dynamics.
Abstract: Abstract The present study focuses on identifying dynamical transition boundaries and presents an order-to-chaos map for the unsteady flow field of a flapping foil in the low Reynolds number regime. The effect of an extensive parametric space, covering a large number of kinematic conditions, has been investigated. It is shown that the conventional non-dimensional parameters cannot effectively capture the changes in the flow field due to the variations in the relevant kinematic parameters and are unable to demarcate the dynamical transition boundaries. Two new non-dimensional measures – maximum effective angle of attack and a leading-edge amplitude-based Strouhal number – are proposed here, which can capture the physical effect of the parametric variations on the wake dynamics. The study proposes generalised transition boundaries and an order-to-chaos map through a transitional regime in terms of these two newly proposed parameters. Published data from the existing literature have also been tested to verify the proposed transition model. It is seen that despite the wide variety of the parametric combinations, the dynamical states from both the new and the published data corroborate well the proposed boundaries, giving credibility to the order-to-chaos map.
3 citations
TL;DR: In this paper , the effect of a chordwise flexible aft-tail of a rigid heaving aerofoil on the dynamical transitions of the trailing-wake is studied using an in-house fluid-structure interaction (FSI) platform, comprising a discrete forcing immersed boundary method based incompressible Navier-Stokes solver, weakly coupled with a finite difference method based structural solver.
Abstract: Abstract The effect of a chordwise flexible aft-tail of a rigid heaving aerofoil on the dynamical transitions of the trailing-wake is studied here. The two-way coupled fluid–solid dynamics is simulated using an in-house fluid–structure interaction (FSI) platform, comprising a discrete forcing immersed boundary method based incompressible Navier–Stokes solver, weakly coupled with a finite difference method based structural solver. The FSI dynamics is studied in comparison to the corresponding rigid tail configuration. For the latter, mild jet-switching due to quasi-periodic movement of the wake vortices gives way to vigorous jet-switching as the dynamics transitions to a state of intermittency, where the quasi-periodic behaviour gets interspersed with chaotic windows. Introduction of a moderately flexible tail regularises this intermittent dynamics, eliminating jet-switching. The wake exhibits a deflected reverse Kármán pattern with fluctuating angles, governed by quasi-periodicity. With a highly flexible tail (very low rigidity), the wake shows almost a symmetric reverse Kármán street as periodicity is restored. Flexibility of the aft-tail is next controlled by changing its length, and flow is regularised and periodicity retained for moderate rigidity for increased length. Different dynamical states are established through robust nonlinear dynamical tools. The underlying flow-field behaviour, instrumental in suppressing the jet-switching phenomenon, is identified through a detailed investigation of the near-field vortex interactions dictated by the dynamics. A suite of measures has also been derived from the unsteady flow field to quantify the interactions of the key near-field vortices with a view to understanding the mechanism of switching and its subsequent suppression through flexibility.
2 citations
TL;DR: In this article , the authors considered the idealized case of a pitching-plunging flapping foil and numerically investigated the effects of passive pitching dynamics on the fluid forces and dynamical states, and compared it with a fully actuated wing.
Abstract: Abstract Natural and artificial flapping wing flyers generally do not exhibit chaos or aperiodic dynamic modes, though several experimental and numerical studies with canonical models of flapping foils have reported inevitable chaotic transition at high ranges of dynamic plunge velocity (κh). Here we considered the idealized case of a pitching–plunging flapping foil and numerically investigated the effects of passive pitching dynamics on the fluid forces and dynamical states, and compared it with a fully actuated wing. We found that in comparison to fully actuated foils, aperiodic transition can be avoided even for high κh when passive oscillations are allowed. Passive pitching modulated the relative foil orientation with respect to the incoming free stream to maintain a lower effective angle-of-attack throughout the stroke and reduced the leading-edge-vortex (LEV) strength. Absence of aperiodic triggers such as flow separation and strong LEVs keep the wake periodic, and chaotic transition is averted. In the presence of fluctuating inflow conditions, passive pitching attenuated the fluid loads experienced by the airfoil thus improving the wing’s gust mitigating potential. These findings highlight the favorable properties of passive dynamics in regularizing aerodynamic loads on flapping wing systems and presents viable solutions for artificial flying platforms.
2 citations
References
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TL;DR: The article is built around $10$ MATLAB programs, and the topics covered include stochastic integration, the Euler--Maruyama method, Milstein's method, strong and weak convergence, linear stability, andThe stochastics chain rule.
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TL;DR: In this paper, a new immersed-boundary method for simulating flows over or inside complex geometries is developed by introducing a mass source/sink as well as a momentum forcing.
1,090 citations
TL;DR: In this article, the vortical flow patterns in the wake of a NACA 0012 airfoil pitching at small amplitudes were studied in a low speed water channel, and it was shown that a great deal of control can be exercised on the structure of the wake by the control of the frequency, amplitude and also the shape of the oscillation waveform.
Abstract: The vortical flow patterns in the wake of a NACA 0012 airfoil pitching at small amplitudes are studied in a low speed water channel. it is shown that a great deal of control can be exercised on the structure of the wake by the control of the frequency, amplitude and also the shape of the oscillation waveform. An important observation in this study has been the existence of an axial flow along the cores of the wake vortices. Estimates of the magnitude of the axial flow suggest a linear dependence on the oscillation frequency and amplitude.
672 citations
TL;DR: The exact simulation algorithm used here to illustrate the zero-\ensuremath{\tau} limit theorem is derived for the Ornstein-Uhlenbeck process X(t) and its time integral Y(t).
Abstract: A numerical simulation algorithm that is exact for any time step \ensuremath{\Delta}tg0 is derived for the Ornstein-Uhlenbeck process X(t) and its time integral Y(t). The algorithm allows one to make efficient, unapproximated simulations of, for instance, the velocity and position components of a particle undergoing Brownian motion, and the electric current and transported charge in a simple R-L circuit, provided appropriate values are assigned to the Ornstein-Uhlenbeck relaxation time \ensuremath{\tau} and diffusion constant c. A simple Taylor expansion in \ensuremath{\Delta}t of the exact simulation formulas shows how the first-order simulation formulas, which are implicit in the Langevin equation for X(t) and the defining equation for Y(t), are modified in second order. The exact simulation algorithm is used here to illustrate the zero-\ensuremath{\tau} limit theorem. \textcopyright{} 1996 The American Physical Society.
528 citations