Innovatives Supercomputing in Deutschland
inSiDE • Vol. 11 No. 2 • Autumn 2013
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Aircraft Wake Vortex Evolution during Approach and Landing

With and without Plate Lines

As an unavoidable consequence of lift aircraft generate a pair of counter-rotating and long-lived wake vortices that may pose a potential risk to following aircraft. The empirically motivated separation standards between consecutive aircraft which were introduced in the 1970s still apply at most airports. These aircraft separations limit the capacity of congested airports in a rapidly growing aeronautical environment. The highest risk to encounter wake vortices prevails in ground proximity where the vortices cannot descend below the glide path but tend to rebound due to the interaction with the ground surface [1]. Weak crosswinds may compensate the self-induced lateral propagation of the upwind vortex such that it may hover over the runway directly in the flight path of the following aircraft. From large eddy simulation as well as from lidar field measurements it is known that wake vortices may live significantly longer than 2 min corresponding to the 5 NM separation between a leading heavy weight class aircraft and a medium follower. Consequently, most encounters are reported at flight altitudes below 300 ft. At such low flight altitudes the possibilities of the pilot to recover from a vortex encounter are limited.

Figure 1: Simulation of wake vortex evolution during final approach of A340 aircraft in high-lift configuration. Iso-surface of vorticity magnitude colored by span-wise vorticity component.

All this suggests that comprehensive understanding of wake vortex behavior in ground proximity is of primary interest. The research activities described here are motivated by two questions:

“Why is approach and landing safe under these conditions?”

“Can we actively promote WV decay in ground proximity?”

Appropriate answers to these questions are crucial for the design of a most efficient and safe wake vortex advisory system (WVAS). Such a WVAS is conceived to adjust aircraft separations during approach and landing depending on the respective combinations of leading and following aircraft types and the prevailing meteorological conditions [2]. Although full answers to these questions are not yet tangible the numerical simulations and the related field measurement campaign described here may substantially contribute to understanding and solving the problems. Highly resolving large eddy simulations (LES) conducted on SuperMUC provide valuable insights into the physics of wake vortex behavior under various atmospheric conditions and in ground proximity. These LES also contribute indispensable guidance for the development of the real-time/fast-time wake vortex models needed in WVAS.

LES is performed using the incompressible Navier-Stokes code MGLET developed at Technische Universität München. To conduct wake vortex simulation in various atmospheric conditions, an additional equation for potential temperature is solved to take into account buoyancy effects (Boussinesq approximation).

where ui, p’ and θ’ represent the velocity components in three spatial directions (i = 1, 2, or 3), pressure and potential temperature, respectively. The summation convention is used for the velocity components ui and δij denotes Kronecker's delta. The primes for pressure and potential temperature indicate that these are defined by the deviation from the reference states, hence p = p0+p’, θ = θ0+θ’. Kinematic viscosity in the momentum equations is defined by the sum of molecular viscosity and eddy viscosity obtained from a subgridscale model. The corresponding diffusion coefficients in the potential temperature equation are obtained by assuming constant molecular and turbulent Prandtl numbers of 0.7 and 0.9, respectively.

Figure 2: Wall resolving LES of wake vortex evolution in ground proximity with turbulent crosswind (a) without and (b) with a barrier on the ground surface at a vortex age of 32 s. Iso-surface of vorticity magnitude colored by span-wise vorticity component.

The above equations are solved by a finite-volume approach with the fourth-order finite-volume compact scheme. A split-interface algorithm is used for the parallelization of a tridiagonal system for the compact scheme, which realizes good overhead time and scalability in parallel environments. In addition, a divergence free interpolation is employed for obtaining advection velocity, which ensures conservation of velocity and passive tracer fields. The pressure field is obtained by the velocity-pressure iteration method by Hirt and Cook. For time integration the third-order Runge-Kutta method is used. The Lagrangian dynamic model is employed as turbulence closure which prevents excessive eddy viscosity in the vortex cores. The closure accumulates the required averages of subgrid model coefficients along flow pathlines. This enables the Lagrangian dynamic model to distinguish the centrifugally stable vortex core regions as well as boundary layer flows from the external turbulent flow. All computations are performed in parallel by a domain decomposition approach.

Numerical simulations of wake vortices usually neglect vortex roll-up and are initialized by some analytical vortex model as for example co-rotating Lamb-Oseen vortices. A new method has been developed where an aircraft model and its surrounding flow field, obtained from high-fidelity Reynolds-averaged Navier-Stokes simulation (RANS), are swept through a ground-fixed computational domain to initialize the wake [3]. This allows the simulation of vortex evolution from the roll-up until the final decay. Close to the surface of the aircraft model the velocity field is represented by a combination of the RANS velocity field VRANS and the LES velocity field VLES with a weighting function f(y) In this study, VRANS is used as a constant forcing term of the Navier-Stokes equations solved in the LES. Since the aircraft model is swept through the computational domain, the forcing term acts as a moving boundary condition for the LES. This kind of approach might be referred to as a fortified solution algorithm or as a nudging technique as it is frequently used to assimilate meteorological measurement data into weather prediction models. In conjunction with the wake vortex evolution in ground proximity, the impact of obstacles erected on the ground surface on wake vortex evolution and decay is investigated. These obstacles are modeled by the immersed boundary method where the velocity field is modified by a forcing term such that the modified velocity field represents the obstacles on the ground.

The amount of memory used is approximately 1.5 - 3.0 GB per core. The total memory usage depends on the number of cores used, and typically is 2,048 GB for the parallel computations using 1,024 cores. For pre- and post-processing, spectral analysis requires relatively large amount of memory, e.g., 170 GB for a 1,0243 mesh case. Typical numbers of CPU cores currently used for the simulations are 512 to 2,048 cores for cases from 67 million to 1,0243 ≈ 1.07 billion mesh points. The transition to SuperMUC went smoothly without larger complications.

Figure 3: Wall resolving LES of wake vortex evolution in ground proximity with solid barrier (above) and plate line (below) at a vortex age of 40 s. Iso-surface of vorticity magnitude colored by span-wise vorticity component.

Fig. 1 shows the simulation of the final approach of an A340 aircraft in high-lift configuration including vortex roll-up, aircraft flare and touchdown, vortex interaction with the ground and obstacles in terms of a plate line. In high-lift configuration a manifold of vortex sheets and distinct vortices are formed behind the aircraft (Fig. 1, upper left). The strongest vortices detaching form the wing tips and flap tips merge within a distance of about 10 wing spans behind the aircraft. The wake vortices as well as the bound vortex along the aircraft wing induce a vorticity layer of opposite sign at the ground surface. Shortly after touchdown the bound vortex vanishes and the free ends of the wake vortices start to interact with the vorticity layer at the ground, disturbing the wake vortices starting from the point of touchdown. This process constitutes the end effects propagating as helical disturbances along the wake vortices. Port- and starboard-vortices are no longer linked by the bound vortex and quickly diverge at the point of touchdown. Finally, we observe linking of the vortex ends with the ground. Secondary vorticity structures form at the red plate line, are wound around the primary vortices and propagate by self-induction in axial directions to either sides (lower plots). These helical disturbances finally interact with the end effects leading to rapid vortex decay.

End effects can be considered as good candidates that accelerate vortex decay close to the touchdown zone such that approach and landing can be accomplished safely. In combination with plate lines safety could be further increased by accelerating vortex decay within the whole height range where wake vortices may rebound to the glide path.

Fig. 2a shows the interaction of the wake vortices with the turbulent structures at the ground surface generated by a crosswind blowing from left below. At a vortex age of 32 s the vorticity sheet generated by the lee (rear) vortex detaches from the ground and starts rotating around the primary vortex. Triggered by crosswind streaks the secondary vorticity sheet transforms into so-called omega loops wrapping around the primary vortices and initiating vortex decay. Under unfavorable crosswind conditions the rebounding upwind (front) vortex may hover over the runway directly in the flight corridor of a landing aircraft.

Figure 4: HALO research aircraft flies over plate line consisting in total of 6 wooden plates mounted perpendicular to the flight direction.

The introduction of a barrier at the ground surface may substantially accelerate vortex decay in the critical area close to the threshold where most vortex encounters occur (Fig. 2b) [4]. A respective patent entitled “Surface Structure on a Ground Surface for Accelerating Decay of Wake Turbulence in the Short Final of an Approach to a Runway” has been filed under number DE 10 2011 010 147. Such a setup specifically exploits properties of vortex dynamics to accelerate wake vortex decay in ground proximity with the following characteristics: (i) early detachment of strong omega-shaped secondary vortices, (ii) omega shape causes self-induced fast approach to the primary vortex, (iii) after the secondary vortex has looped around the primary vortex, it separates and travels both ways along the primary vortex, again driven by self induction, (iv) the artificially generated secondary vortex connects to the regular ground effect vortex and thus obtains continued supply of energy, (v) the highly intense interaction of primary and secondary vortices leads to rapid wake vortex decay independent from natural external disturbances.

Fig. 3 demonstrates that the solid barrier can be replaced by a less costly and objectionable plate line that turns out to produce similar effects. A closer look at Fig. 3 reveals that the secondary vortices are even slightly stronger and the propagation speed of the helical structures is even slightly higher with the plate line.

Figure 5: Overflight of HALO research aircraft and vortex roll-up in ground proximity visualized by smoke at special airport Oberpfaffenhofen.

On 29 and 30 April 2013 the WakeOP field measurement campaign has been accomplished at special airport Oberpfaffenhofen with the research aircraft HALO, a modified Gulfstream G550, in order to demonstrate the functionality of the plate line to significantly accelerate vortex decay in ground proximity. During the 72 overflights of HALO at an altitude of 22 m above ground the weather impact on vortex behavior was minimized by folding away the plates alternatingly. The field experiments have successfully demonstrated the efficiency of this way to provoke premature vortex decay in the most critical flight phase prior to touch down. Already the smoke and fog visualizations documented by video and photo indicated that with the plate line the formed vortex structures are less coherent. The lidar measurements corroborate quantitatively that with the plate line vortex decay progresses faster than above flat ground at all relevant vortex ages. Further, lidar measurements in a plane with an offset of 4.5 initial vortex separations to the plate line in flight direction reveal that the disturbances travel quickly along the vortices.

References

[1] Holzäpfel, F., Steen, M. Aircraft Wake-Vortex Evolution in Ground Proximity: Analysis and Parameterization, AIAA Journal, 45, 2007

[2] Holzäpfel, F., Gerz, T., Frech, M., Tafferner, A., Köpp, F., Smalikho, I., Rahm, S., Hahn, K.-U., Schwarz, C. The Wake Vortex Prediction and Monitoring System WSVBS – Part I: Design, Air Traffic Control Quarterly, 17, 2009

[3] Misaka, T., Holzäpfel, F., Gerz, T. Wake Evolution of High-Lift Configuration from Roll-Up to Vortex Decay, AIAA Paper 2013-0362, 2013

[4] Stephan, A., Holzäpfel, F., Misaka, T. Aircraft Wake-Vortex Decay in Ground Proximity - Physical Mechanisms and Artificial Enhancement, Journal of Aircraft, DOI:10.2514/1.C032179, 2013.

Links

http://www.pa.op.dlr.de/wirbelschleppe/

• Frank Holzäpfel
• Anton Stephan DLR, Institut für Physik der Atmosphäre, Oberpfaffenhofen


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