The role of the Coriolis effect on the attachment of the leading edge vortex (LEV) is investigated. Toward that end, the Navier–Stokes equations are solved in the non-inertial reference frame of a high angle of attack $\unicode[STIX]{x1D6FC}$ rotating wing with the Coriolis term being artificially tuned. Reynolds numbers in the range $Re\in [100;750]$ are considered to identify the interplay between Coriolis and viscous effects. Similarly, artificial tuning of the centrifugal term is achieved to identify the interplay between Coriolis and centrifugal effects. It is shown that (i) the Coriolis effect is the key element in LEV stability for $Re>200$, (ii) viscous effects are the key element for $Re<200$ and (iii) centrifugal effects have a marginal role. The Coriolis effect is found to promote spanwise flow in the core and behind the LEV, which is known to promote outboard vorticity transport and presumably contributes to stabilizing the aft boundary layer. These mechanisms of LEV stabilization have increased authority as $\unicode[STIX]{x1D6FC}$ decreases.

While a leading-edge vortex on an infinite translating wing is shed after a short distance of travel, its counterpart on a finite span revolving insect wing or maple seed membrane exhibits robust attachment. The latter explains the aerodynamic lift generated by such biological species. Here we analyze the mechanisms responsible for leading-edge vortex attachment. We compute the Navier-Stokes solution of the flow past a finite span wing (i) embedded in a uniform oncoming flow, (ii) embedded in a spanwise varying oncoming flow, and (iii) revolving about its root. We show that over flapping amplitudes typical of insect flight (ϕ = 120°), the spanwise gradient of the local wing speed may suffice in maintaining leading-edge vortex attachment. We correlate this result with the development of spanwise flow, driven by the spanwise gradient of pressure, and we evaluate the sensitivity of such a mechanism to the Reynolds number. It is noted, however, that leading-edge vortex attachment through the spanwise gradient of the local wing speed does not promote large lift, which ultimately arises from centrifugal and Coriolis effects.

This paper aims at understanding the influence of three-dimensional effects in hovering flapping flight. Numerical simulations at a Reynolds number of 1000 are performed to compare two types of flapping kinematics whose plunging phase is characterized by either a rectilinear translation or a revolving motion. In this way, we are able to isolate the three-dimensional effects induced by the free end condition from that induced by the spanwise incident velocity gradient (and the associated implicit Coriolis and centrifugal effects). In the rectilinear translation case, the analysis of the wake and of the aerodynamic loads reveals that the wingspan can be compartmented into three distinct regions whether it is predominantly subjected to an unstable two-dimensional flow, a stable three-dimensional flow or both two-dimensional and three-dimensional effects. It is found that this partitioning exhibits common features for three different aspect ratios of the wing. In conjunction with the previous results of Ringuette, Milano & Gharib (J. Fluid Mech., vol. 581, 2007, pp. 453-468), this suggests that the influence of the tip vortex over the wingspan is driven by a characteristic length scale. In addition, this length scale matches the position of the connecting point between leading and tip vortices observed in the revolving case, providing insight into the connecting process. In both translating and revolving cases, leading edge vortex attachment and strong spanwise velocities are found to be strongly correlated phenomena. Spanwise velocities (that mostly confine at the periphery of the vortices), together with downward velocities, do not only affect the leading edge vortex but also act as an inhibitor for the trailing edge vortex growth. As a consequence, crosswake interactions between leading and trailing edge vortices are locally limited, hence contributing to flow stabilization.

To cite this version:Yannick Bury, Thierry Jardin. Transitions to chaos in the wake of an axisymmetric bluff body. Physics Letters A, Elsevier, 2012, vol. 376, pp. 3219-3222 AbstractThis letter aims at understanding the dynamical process that leads to the onset of chaos in the flow past a blunt-based axisymmetric bluff body. On the basis of direct numerical simulations, conducted for Reynolds numbers ranging from 100 to 900, we show that the flow undergoes multiple transitions, successively giving rise to the SS, RSP a , RSP b , RSP c and RSB wake states. In particular, the RSP c state, revealed in this work via long-term computations, is characterized by intermittent vortex stretching denoting the onset of chaos before the symmetry breaking and the occurence of the RSB state.

Lentink & Dickinson (2009 , 2705-2719. (doi:10.1242/jeb.022269)) showed that rotational acceleration stabilized the leading-edge vortex on revolving, low aspect ratio (AR) wings and hypothesized that a Rossby number of around 3, which is achieved during each half-stroke for a variety of hovering insects, seeds and birds, represents a convergent high-lift solution across a range of scales in nature. Subsequent work has verified that, in particular, the Coriolis acceleration plays a key role in LEV stabilization. Implicit in these results is that there exists an optimal AR for wings revolving about their root, because it is otherwise unclear why, apart from possible morphological reasons, the convergent solution would not occur for an even lower Rossby number. We perform direct numerical simulations of the flow past revolving wings where we vary the AR and Rossby numbers independently by displacing the wing root from the axis of rotation. We show that the optimal lift coefficient represents a compromise between competing trends with competing time scales where the coefficient of lift increases monotonically with AR, holding Rossby number constant, but decreases monotonically with Rossby number, when holding AR constant. For wings revolving about their root, this favours wings of AR between 3 and 4.

At high angles of attack, an aircraft wing stalls. This dreaded event is characterized by the development of a leading edge vortex on the upper surface of the wing, followed by its shedding which causes a drastic drop in the aerodynamic lift. At similar angles of attack, the leading edge vortex on an insect wing or an autorotating seed membrane remains robustly attached, ensuring high sustained lift. What are the mechanisms responsible for both leading edge vortex attachment and high lift generation on revolving wings? We review the three main hypotheses that attempt to explain this specificity and, using direct numerical simulations of the Navier-Stokes equations, we show that the latter originates in Coriolis effects.

The aim of this paper is to discuss the advantages and difficulties linked with the experimental application of the momentum equation approach as a non-intrusive way to predict the unsteady loads experienced by an airfoil in motion. First, in order to evaluate the influence of the varying parameters relative to the calculation of the corresponding drag and lift coefficients, numerical flow fields obtained by means of DNS are used. The comprehension of the impact of the spatial and temporal resolutions, velocity accuracy or third velocity component on the estimation of forces allows us to quantify the accuracy of the approach and helps in specifying the parameters setting which could lead to a consistent experimental application. In a second step, the approach is applied to experimental flow fields measured through the use of time resolved particle image velocimetry (TR-PIV). A low Reynolds number flow around an impulsively started airfoil is considered. The loads and vorticity flow fields are correlated and compared with those obtained by DNS.

In this paper, an experimental characterisation of low Reynolds number rotors is performed in an anechoic room. Two commercially available two-bladed rotors as well as four three-dimensional (3D)-printed rotors with different numbers of blades (from two to five) are tested. The latter have canonical geometry, with an NACA0012 blade section profile, extruded in the radial direction with constant chord and constant 10° pitch. The experimental setup and the 3D printing strategy are first validated using results from the literature for the commercially available rotors. For all the tested rotors, four noise characteristics are analysed: the overall sound pressure level (OASPL), the amplitude of the blade passing frequency (BPF), and the amplitude of its first harmonic and the high-frequency broadband noise. For all the rotors, an increase in all noise characteristics is observed with the rotational speed (rpm) for all directivity angles. Moreover, an interesting change of pattern is observed for the amplitudes of the BPF and of its first harmonic, with, in the vicinity of the rotor plane, a minimum value for low rpm and/or high number of blades, and a maximum value for high rpm and/or low number of blades. This change in directivity leads to a similar change of directivity of the OASPL. For the broadband noise, a dipole-like pattern is obtained with a minimum value at θ=−10°, i.e., aligned with the trailing edge and thus indicating the generation of trailing edge noise. Finally, scaling laws that characterise the amplitude of the different noise components with respect to the rpm are proposed.