Direct Numerical Simulation of Transition to Turbulence on a Laminar Morphing Wing

INTRODUCTION Controlling transition to turbulence is important in optimizing aircraft performance. In some cases, it is desirable to accelerate its occurrence to prevent flow separation. In other cases, it is more important... [ view full abstract ]

INTRODUCTION
Controlling transition to turbulence is important in optimizing aircraft performance. In some cases, it is desirable to accelerate its occurrence to prevent flow separation. In other cases, it is more important for the flow to remain laminar as long as possible. Both approaches aim to reduce drag. The concept of a morphing wing arises, capable of adapting its shape to ensure the flow remains laminar further down the wing’s surface. The proposed paper aims to describe the methodology used and results obtained for the direct numerical simulation prediction of transition on such a wing profile.

METHODOLOGY
The airfoil studied is an experimental morphing wing model at α = 0° and Re between 300,000 and 500,000. Direct numerical simulation (DNS) using the spectral element method (SEM) is used to compute the flow. The solver is Nek5000, a DNS SEM solver of the incompressible Navier-Stokes equations [1]. The domain is decomposed into K = 76,393 spectral elements, upon which the solution is approximated by tensor products of Legendre polynomial Lagrangian interpolants. The highest degree of the Legendre polynomials included is N = 10 and N = 8 for the velocity and pressure grids respectively (PN-PN−2 staggering). As DNS is used to compute the flow, adequate grid generation is essential in capturing the smallest scales of the flow without overly sacrificing performance. A close-up of the grid of Fig. 1a surrounding the airfoil is shown in Fig. 1b with the distribution of collocation points.

The initial and boundary conditions are imposed from an inviscid vortex panel method solution [2]. The solution is computed at Re = 100,000 increments, using the solution of the previous Re increment as an initial condition to the next. An outflow with a 10% chord-length dampening function (“sponge”) is used to prevent pressure waves from re-entering the computational domain [3]. The computational domain’s dimensions along with the initial and boundary conditions are shown in Fig. 2.

DETERMINATION OF THE TRANSITION POINT
Transition point (xtr) detection is performed by measuring the skin friction distribution on the airfoil’s upper surface, and by averaging out large frequency scales from the velocity field. The second method implies the calculation of the mean perturbation kinetic energy at a time-averaging frequency small enough to eliminate periodic velocity variations, and large enough to capture turbulent fluctuations. Figs. 3 and 4 show the instantaneous x-velocity field and time-averaged skin friction distribution with comparison to Xfoil [4] respectively for a test case at Re = 400,000. The final paper will provide DNS prediction of the transition point with respect to the chord Re. For validation, results are to be compared to wind tunnel experiments [5].

ACKNOWLEDGMENTS
This problem was suggested to us by Éric Laurendeau of École Polytechnique de Montréal based on work done while at Bombardier Aerospace. A special thanks to Thomas Burel for his contributions to the grid generator implementation. Support from NSERC is gratefully acknowledged.

REFERENCES

[1] Fischer P., Lottes J., Kerkemeier S., Obabko A., Heisey K. Nek5000 [Software]. Mathematics and Computer Science Division of Argonne National Library. Available from: http://nek5000.mcs.anl.gov/index.php/GETNEK
[2] Kuethe, A.M. and Chow, C.-Y., Foundations of Aerodynamics, Fifth Edition, John Wiley & Sons, 1998.
[3] Tempelmann, D., Schrader, L.-U., Hanifi, A., Brandt, L. & Henningson, D. S. 2011, a Numerical study of boundary-layer receptivity on a swept wing. AIAA Paper 2011-3294.
[4] Drela, M., XFOIL: an analysis and design system for low Reynolds number airfoils. Conference on Low Reynolds Number Airfoil Aerodynamics, University of Notre Dame, 1989.
[5] Coutu, D., Brailovski, V., Terriault, P., Mamou, M., Mébarki, Y., Laurendeau, E., “Lift-to-Drag Ratio and laminar flow control of a laminar morphing wing in a wind tunnel”, Smart Mater. Struct., 20, 2011 035019