In order to take off and fly, an airplane must generate a force equal to its weight. It is known that when a wing generates lift, it also generates a pair of counter-rotating vortices. These vortices can be very powerful and... [ view full abstract ]
In order to take off and fly, an airplane must generate a force equal to its weight. It is known that when a wing generates lift, it also generates a pair of counter-rotating vortices. These vortices can be very powerful and their intensity is proportional to the weight of the aircraft [1]. They represent a possible hazard for other aircrafts flying nearby, in particular on the outskirts of runways. Aircraft wake vortices are the cause of the delays between two takeoffs / landings in congested airports. The waiting time required between each aircraft is related to the intensity and persistence of these vortices. Dissipation of these structures depends heavily on hydrodynamic instabilities which are the source of fine turbulence in such flows. On their part, instabilities and the wake vortex dynamics depend very much on the internal structure of the vortices, the atmospheric turbulence and eventually the ground effects. A thorough understanding of these dynamics is fundamental and will help to improve flight safety and to reduce airport congestion.
In this work, DNS is carried out to study the reconnection of two vortices. The Navier-Stokes equations are solved using a Fourier pseudospectral algorithm with triply periodic boundary conditions. The focus is set on the reconnection of a simplified system of two orthogonal vortices in order to assess its impact on the longevity of the wake vortex system. In addition to equal-strength vortices, initial configurations consisting of two unequal-strength vortices are also studied. These configurations are common in aircraft wakes, for example when a spoiler is deployed on a wing. Typically, the weak vortex (Γ2) is seen to deform and to wrap itself around the strong one (Γ1) to (partially) reconnect. Recent studies [2-4] suggest that partial reconnection generates a large spectrum of small-scale turbulent structures that should significantly increase the dissipation rate of the wake vortices. In order to quantify the instantaneous reconnection level of the two vortices, an approach using instantaneous vortex lines is employed [4]. The use of vortex lines has already proven to be useful to gain insight into the mechanisms of vortex reconnection [5-7]. For Reynolds numbers (Γ1/ν) of the order of 10^4 and circulation ratios 0.3 ≤ (Γ2/Γ1) ≤ 1.0, the instantaneous reconnection level is computed and the propagating vorticity structures are observed. For the reconnection of two orthogonal, equal-strength vortices, the maximum rate of circulation transfer is found to scale as Re^1, in agreement with results found for the reconnection of two equal-strength, anti-parallel vortices [5].
REFERENCES
1. P.R. Spalart. Airplane trailing vortices. Annual Rev. Fluid Mech., 30, 107-138, 1998.
2. L. Dufresne and G. Winckelmans. LES of the interaction and partial reconnection of unequal strength vortices. In Intl. Conf. High Reynolds Numb. Vortex Interactions, Toulouse, France, 2005.
3. L. Dufresne, G. Beardsell and G. Dumas. Partial reconnection of orthogonal vortices. Bull. Amer. Phys. Soc., 57, 2012.
4. G. Beardsell, L. Dufresne and G. Dumas. Quantifying the reconnection process of two vortices. Bull. Amer. Phys. Soc., 59, 2014.
5. F. Hussain and K. Duraisamy. Mechanics of viscous vortex reconnection. Phys. Fluids, 23, 021701, 2011.
6. W.M. van Rees, F. Hussain and P. Koumoutsakos. Vortex tube reconnection at Re=10^4. Phys. Fluids, 24, 075105, 2012.
7. R.M. Kerr. Swirling, turbulent vortex rings formed from a chain reaction of reconnection events. Phys. Fluids, 25, 065101, 2013.
Topics: Unsteady aerodynamics, vortical flows, aircraft wakevortex dynamics including DES,
