A DNS and transient growth analysis of aircraft wakes. The effect of aircraft tail configuration.

This thesis describes an analysis of the transient growth characteristics of arrangements of parallel vortices including vortex pairs and four-vortex systems. These flows are a useful model for the far-wake created by the combination of a wing and tail of an aircraft. These wakes can be extremely hazardous to aircraft moving through the same airspace, and increase in strength as the lift of the generating aircraft increases. Given that aircraft have undergone a significant jump in size with the Airbus A380 and the C-17 Globemaster aircraft, the investigation of these types of vortex flows has experienced renewed interest. Specifically, this study investigates an equal strength two-vortex system, a symmetric four-vortex system (with the vortex strength equal, but opposing in vorticity sign across the mid-plane for each vortex pair) with varying vertical displacement of the vortex pair that represents the tail vortex pair, and an asymmetric strength four-vortex system (with the vortex strength differing across the mid-plane) with a similar varying vertical displacement of the tail vortex pair. The ‘flat tail’ and ‘high tail’ cases referred to later in the thesis refer to the cases without and with vertical displacement of the tail vortex pair respectively (for example, the Airbus A380 is a ‘flat tail’ aircraft and the C-17 Globemaster is a ‘high tail’ aircraft). It was found in all the cases studied that by seeding various vortex flows with the perturbations that lead to optimal energy growth (created from a transient growth analysis in the linear regime) it is possible to obtain very large reductions in the time required to cause transition into the non-linear regime and subsequent destruction of the coherence of the vortex flow. The transient growth analysis performed on the symmetric four-vortex system demonstrated that both the ‘high tail’ and ‘flat tail’ configurations were most unstable to the transient growth of perturbations at the same axial wavenumber, k a1 = 5.3. This gave the perturbation that leads to optimal energy growth, centered in the tail vortex pair of the system in the form of a mode [-1,1,1] elliptic instability. The three-dimensional direct numerical simulation (DNS) of the four-vortex study demonstrated that there are two main vortex interactions present in the growth and subsequent destruction of four-vortex flows. If the instability has reached a sufficient magnitude in the tail vortex pair before entering the highly strained region between the wing vortex pair, the tail vortices are forced to interact with each other, causing a rapid breakdown into small scale flow structures. Conversely, if the instability inthe tail vortex pair has not reached the critical magnitude before entering this highly strained region, the tail vortex pair will not interact with each other, leading to a slower growth due to the interaction between the wing and tail vortices alone. The asymmetric four-vortex study found an immediate growth of the instability, by seeding the flow with the perturbation that leads to optimal energy growth. One finding of interest is that the perturbation that leads to optimal energy growth is predominantly contained within the weaker tail vortex. The three-dimensional DNS demonstrates that the instability grows in the weaker tail vortex first, causing its destruction, then continuing through the other vortices in order of strength. The implication of this study is that by seeding the wake with specific perturbations, the time that is required to eliminate the hazard of the wake can be decreased significantly, reducing the hazard to trailing aircraft. This would allow a reduction in the spacing of aircraft through airports, increasing throughput. This increase in throughput would allow for airports to reduce the fuel usage of aircraft having to wait to land due to the wakes of other aircraft, while maintaining safety. Another implication of the study for real aircraft is that the seeding of instabilities in the wake is most effective if seeded within the tail vortex pair, which would mean that a control system only needs to be present on the tail, reducing the cost of such a system. An important discovery by this study is the importance of the transition into the non-linear growth for systems comprising of more than two vortices and how the interactions can change due to the magnitude of the instability as the vortices enter favourable regions. A major implication of this study is to elucidate the limitations of vortex filament methods used in previous studies (Crow 1970; Crouch 1997; Fabre & Jacquin 2000; Bristol et al. 2004) compared to methods such as the transient growth method. These limitations are due to the vortex filament ignoring any viscous interaction (such as two-dimensional vortex stripping) between the vortices and the assumption of a specific mode shape of the instability