Several previous experimental and theoretical studies have shown that a leading edge vortex (LEV) on an airfoil or wing can provide lift enhancement. In this paper, unsteady two-dimensional (2D) potential flow theory is employed to model the flow field of a pitching flat plate wing. A multi-vortices model is developed to model both the leading edge and trailing edge vortices (TEVs), which offers improved accuracy compared with using only single vortex at each separation location. The lift is obtained by integrating the unsteady Blasius equation. It is found that the motion of vortices contributes significantly to the overall aerodynamic force on the flat plate. A Kutta-like condition is used to determine the vortex intensity and location at the leading edge for large angle of attack cases; however, it is proposed to relax this condition for small angle of attack cases and apply a 2D shear layer model to calculate the circulation of the new added vortex. The results of the simulation are then compared with classical numerical, theoretical, and experimental data for canonical unsteady flat plat problems. Good agreement with these data is observed. Moreover, these results suggested that the leading edge vortex shedding for small angles of attack should be modeled differently than that for large angles of attack. Finally, the results of vortex motion vs. lift indicate that the slow convection of the LEV creates less negative lift while the rapid shedding of the TEV creates more positive lift. The difference between these two contributions of lift results in a total positive lift that lasts for about two chord-length travel of the plate. It is therefore concluded that the lift enhancement during the LEV “stabilization” above the wing is a combined effect of both the LEV and TEV motion. This also provides the insights for future active flow control of micro aerial vehicles (MAVs) that the formation and shedding process of LEVs and TEVs can be manipulated to provide lift enhancement.

The flickering of buoyant diffusion flames is associated with the periodic shedding of toroidal vortices that are formed under gravity-induced shearing at the flame surface. Numerous experimental investigations have confirmed the scaling, $f\propto D^{-1/2}$ , where $f$ is the flickering frequency and $D$ is the diameter of the fuel inlet. However, the connection between the toroidal vortex dynamics and the scaling has not been clearly understood. By incorporating the finding of Gharibet al.(J. Fluid Mech., vol. 360, 1998, pp. 121–140) that the detachment of a continuously growing vortex ring is inevitable and can be dictated by a universal constant that is essentially a non-dimensional circulation of the vortex, we theoretically established the connection between the periodicity of the toroidal vortices and the flickering of a buoyant diffusion flame with small Froude number. The scaling theory for flickering frequency was validated by the existing experimental data of pool flames and jet diffusion flames.

Unsteady inviscid flow models of wings and airfoils have been developed to study the aerodynamics of natural and man-made flyers. Vortex methods have been extensively applied to reduce the dimensionality of these aerodynamic models, based on the proper estimation of the strength and distribution of the vortices in the wake. In such modelling approaches, one of the most fundamental questions is how the vortex sheets are generated and released from sharp edges. To determine the formation of the trailing-edge vortex sheet, the classical steady Kutta condition can be extended to unsteady situations by realizing that a flow cannot turn abruptly around a sharp edge. This condition can be readily applied to a flat plate or an airfoil with cusped trailing edge since the direction of the forming vortex sheet is known to be tangential to the trailing edge. However, for a finite-angle trailing edge, or in the case of flow separation away from a sharp corner, the direction of the forming vortex sheet is ambiguous. To remove anyad hocimplementation, the unsteady Kutta condition, the conservation of circulation as well as the conservation laws of mass and momentum are coupled to analytically solve for the angle, strength and relative velocity of the trailing-edge vortex sheet. The two-dimensional aerodynamic model together with the proposed vortex-sheet formation condition is verified by comparing flow structures and force calculations with experimental results for several airfoil motions in steady and unsteady background flows.

The off-center collision of binary bouncing droplets of equal size was studied numerically by a volume-of-fluid method with two marker functions, which has been justified and validated by comparing with available experimental results. A nonmonotonic kinetic energy (KE) recovery with varying impact parameters was discovered. This can be explained by the prolonged entanglement time and the enhanced internal-flow-induced viscous dissipation for bouncing droplets at intermediate impact parameters, compared with those at smaller or larger impact parameters. The distribution of the local viscous dissipation rate (VDR) in the droplet interior shows two major concentration areas, and the competition between these two concentration areas accounts for the nonmonotonic viscous dissipation with varying impact parameters. The nonmonotonic KE recovery with varying impact parameters can also be attributed to the competition between the VDR induced by normal strains and shear strains. The nonmonotonicity was further numerically verified for wider ranges of parameters, and a practically useful formula was proposed to correlate the KE dissipation factor with the impact parameter for various Weber numbers and Ohnesorge numbers.

This study numerically investigates the internal jetlike mixing upon the coalescence of two initially stationary droplets of unequal sizes by employing the volume of fluid method with an adaptive mesh refinement algorithm. The emergence of the internal jet is attributed to the formation of a main vortex ring, as the jetlike structure shows a strong correlation with the main vortex ring inside the merged droplet. By tracking the evolution of the main vortex ring together with its circulation, we identified two mechanisms that are essential to the internal-jet formation: the vortex-ring growth and the vortex-ring detachment. Recognizing that the initiation of the vortex-ring-induced jet energetically relies on the merged interface but the manifestation of the jet physically relies on the competition between the convection and viscous dissipation of the vortex ring, we further developed and substantiated a vortex-ring-based Reynolds number $\left(\mathrm{R}{\mathrm{e}}_J={\mathrm{\Gamma }}_{\mathrm{VD}}/4\pi \nu \right)$ criterion, where ${\mathrm{\Gamma }}_{\mathrm{VD}}$ is the circulation of the detached main vortex ring and $\nu$ is the liquid kinematic viscosity, to interpret the occurrence of the internal jet at various Ohnesorge numbers and size ratios. For the merged droplet with apparent jet formation, the average mixing rate after jet formation increases monotonically with $\mathrm{R}{\mathrm{e}}_J$, which therefore serves as an approximate measure of the jet strength. In this respect, stronger internal jet is responsible for enhanced mixing of the merged droplet.