Critical parameters for the partial coalescence of a droplet

The partial coalescence of a droplet onto a planar liquid/liquid interface is investigated experimentally by tuning the viscosities of both liquids. The problem mainly depends on four dimensionless parameters: the Bond number (gravity vs. surface tension), the Ohnesorge numbers (viscosity in both fluids vs. surface tension), and the density relative difference. The ratio between the daughter droplet size and the mother droplet size is investigated as a function of these dimensionless numbers. Global quantities such as the available surface energy of the droplet has been measured during the coalescence. The capillary waves propagation and damping are studied in detail. The relation between these waves and the partial coalescence is discussed. Additional viscous mechanisms are proposed in order to explain the asymmetric role played by both viscosities.Comment: 16 pages, 14 figures, submitted to Physical Review

Phenomenology and scaling of optimal flapping wing kinematics

Biological flapping wing fliers operate efficiently and robustly in a wide range of flight conditions and are a great source of inspiration to engineers. The unsteady aerodynamics of flapping-wings are dominated by large-scale vortical structures that augment the aerodynamic performance but are sensitive to minor changes in the wing actuation. We experimentally optimise the pitch angle kinematics of a flapping wing system in hover to maximise the stroke average lift and hovering efficiency using a evolutionary algorithm and in-situ force and torque measurements at the wing root. Additional flow field measurements are conducted to link the vortical flow structures to the aerodynamic performance for the Pareto-optimal kinematics. The optimised pitch angle profiles yielding maximum stroke-average lift coefficients have trapezoidal shapes and high average angles of attack. These kinematics create strong leading-edge vortices early in the cycle which enhance the force production on the wing. The most efficient pitch angle kinematics resemble sinusoidal evolutions and have lower average angles of attack. The leading-edge vortex grows slower and stays close-bound to the wing throughout the majority of the stroke-cycle. This requires less aerodynamic power and increases the hovering efficiency by 93% but sacrifices 43% of the maximum lift. In all cases, a leading-edge vortex is fed by vorticity through the leading edge shear-layer which makes the shear-layer velocity a good indicator for the growth of the vortex and its impact on the aerodynamic forces. We estimate the shear-layer velocity at the leading edge solely from the input kinematics and use it to scale the average and the time-resolved evolution of the circulation and the aerodynamic forces

Dynamic stall development

Dynamic stall on an oscillating airfoil was investigated by a combination of surface pressure measurements and time-resolved particle image velocimetry. Following up on previous work on the onset of dynamic stall (Mulleners and Raffel in Exp Fluids 52(3):779-793, 2012), we combined time-resolved imaging with an extensive coherent structure analysis to study various aspects of stall development. The formation of the primary dynamic stall vortex was identified as the growth of a recirculation region and the ensuing instability of the associated shear layer. The stall development can be subdivided into two stages of primary and secondary instability with the latter being the effective vortex formation stage. The characteristic time scales associated with the primary instability stage revealed an overall decrease in dynamic stall delay with increasing effective unsteadiness of the pitching airfoil. The vortex formation stage was found to be largely unaffected by variations of the airfoil’s dynamics

Discrete shedding of secondary vortices along a modified Kaden spiral

When an object is accelerated in a fluid, a primary vortex is formed through the roll-up of a shear layer. This primary vortex does not grow indefinitely and will reach a limiting size and strength. Additional vorticity beyond the critical limit will end up in a trailing shear layer and accumulate into secondary vortices. The secondary vortices are typically considerably smaller than the primary vortex. Here, we focus on the formation, shedding, and trajectory of secondary vortices generated by a rotating rectangular plate in a quiescent fluid using time-resolved particle image velocimetry. The Reynolds number (Re) is varied from 840 to 11150. At low Re, the shear layer is a continuous uninterrupted layer of vorticity that rolls up into a single coherent primary vortex. At Re=1955, the shear layer becomes unstable. For Re>4000, secondary vortices are discretely released from the plate tip. First, we demonstrate that the roll-up of the shear layer, the trajectory of the primary vortex, and the path of secondary vortices can be predicted by a modified Kaden spiral. Second, the timing of the secondary vortex shedding is analysed. The time interval between the release of successive secondary vortices is not constant during the rotation but increases the more vortices have been shed. The shedding time interval also increases with decreasing Reynolds number. The increased time interval under both conditions is due to a reduced circulation feeding rate

Timescales of dynamic stall development on a vertical-axis wind turbine blade

Vertical-axis wind turbines are great candidates to diversify wind energy technology, but their aerodynamic complexity limits industrial deployment. To improve the efficiency and lifespan of vertical axis wind turbines, we desire data-driven models and control strategies that take into account the timing and duration of subsequent events in the unsteady flow development. Here, we aim to characterise the chain of events that leads to dynamic stall on a vertical-axis wind turbine blade and to quantify the influence of the turbine operation conditions on the duration of the individual flow development stages. We present time-resolved flow and unsteady load measurements of a wind turbine model undergoing dynamic stall for a wide range of tip-speed ratios. Proper orthogonal decomposition is used to identify dominant flow structures and to distinguish six characteristic stall stages: the attached flow, shear-layer growth, vortex formation, upwind stall, downwind stall, and flow reattachment stage. The timing and duration of the individual stages are best characterised by the non-dimensional convective time. Dynamic stall stages are also identified based on aerodynamic force measurements. Most of the aerodynamic work is done during the shear-layer growth and the vortex formation stage which underlines the importance of managing dynamic stall on vertical-axis wind turbines

Greenberg’s force prediction for vertical axis wind turbine blade

We present a method to adapt Greenberg's potential flow model for coupled pitching and surging flow such that it can be applied to predict the loads on a vertical-axis wind turbine blade. The model is extended to compute loads on a blade undergoing multi-harmonic oscillations in effective angle of attack and incoming flow velocity by formulating the blade kinematics as a sum of simple harmonic motions. Each of these functions is a multiple of the main turbine rotational frequency, associated with an individual amplitude, as suggested by Greenberg. The results of the adapted model are compared with experimental data from a scaled-down model of a single-bladed H-type Darrieus wind turbine. The comparison between the predictions by the Greenberg model and experimentally obtained phase-averaged radial force evolutions show that the inviscid Greenberg model predicts well the loads at the start of the upwind portion and the maximum loads during upwind, but fails during the downwind portion when flow separation occurs. The proposed application of Greenberg's model to vertical-axis wind turbine kinematics shows a great potential to diagnose regions of separated flow and for quantifying the relative influences of dynamic stall and intrinsic turbine kinematics on the blade loading. Future research can readily extend this method to any airfoil undergoing an arbitrary combination of pitching, surging, and heaving, following a kinematic profile that can be approximated by a Fourier series