XXIV ICTAM, 21-26 August 2016, Montreal, Canada

HYBRID RANS-LES SIMULATION OF WINGTIP VORTICES OF AN

Dmitry Kolomenskiy1 and Roberto Paoli∗2,3,4 1Graduate School of Engineering, Chiba University, Chiba, Japan 2Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, Illinois, USA 3Argonne National Laboratory, Argonne, Illinois, USA 4CERFACS, Toulouse, France

Summary Numerical simulation of the wake of a realistic model of an airliner have been conducted using a hybrid RANS–LES approach. Dynamics of the trailing vortices is analyzed and a simple analytical model is proposed that accounts for the in the wake.

INTRODUCTION

Modeling of aircraft wakes is an important component of many research areas in the aviation sector, including the pre- diction of wake encounter hazard and the environmental impact of aviation. The latter has caught the attention of scientific community because of its contribution to the general problem of climate change produced by anthropogenic activity [1]. Con- trails, the crystals forming behind jet engines by of water onto exhaust soot particles are the most uncertain contributors to the Earth radiative balance among all aircraft emissions. A good estimation of the radiative pertur- bation depends partly on the accurate description of the long-time development of , which is related to the dynamics of trailing vortices past the tips [2]. Various hydrodynamic effects are involved in the process, such as generation of a sheet from the boundary layers, its subsequent roll-up in a pair of vortices, interaction with the jets and hydrodynamic instabilities. In addition, chemical and micro-physics phenomena have to be considered such as formation and dispersion of soot particles, ice crystal growth, evolution of their optical properties etc. In this work, we focus on the dynamics of the near wake within the distance of about three wing spans downstream.

AIRLINER MODEL AND NUMERICAL METHOD

We consider a medium range twin-engine airliner and model its cruise flight at the altitude of 35000 feet, Mach number M = 0.82 and coefficient cL = 0.5. The with wing span is b = 57.6 m, bilateral symmetry is assumed. Reynolds– Averaged Navier–Stokes (RANS) and Large Eddy Simulations (LES) computations are performed in sequence. Averaged quantities obtained form the RANS simulation are projected (using spline interpolation) on a uniform Cartesian grid at a cross-section downstream from the trailing edge (figure 1a). The location chosen corresponds to the inflow boundary of the LES domain. More information about our RANS–LES hybrid approach can be found in [3]. The LES simulations are performed using NTMIX [5], a research code developed for fundamental study of turbulent reactive two- flows. The LES domain is a rectangular box located downstream from the wing. It spans Ly = 180 m in the vertical direction, Lz = 90 m in the lateral direction and Lx = 192 m in the downstream direction. A Cartesian discretization grid is used that consists of Nx × Ny × Nz = 1280 × 620 × 852 points. It is stretched in the vertical and lateral directions, but the volume that encompasses the wake is discretized uniformly with grid step 0.036 m. In the downstream direction, the grid is uniform with step 0.15 m. The inflow boundary condition is supplied by a RANS computation (see figure 1b). Conservative variables are sampled on a plane past the and extended inside the fuselage.

DISCUSSION

Figure 2 shows a visualization of the wake. The surface of the aircraft is shown in grey, for reference. The two distinctive features clearly visible in this image are trailing vortices and turbulent jets. For the vortices, based on the results of our numerical simulation, we propose a generalized Moore–Saffman model adapted to the turbulent regime. It yields a similarity solution for the tangential velocity in a plane perpendicular to the inflow direction, in the laboratory reference frame,

1 1 v (r, τ) = C ν−1τ α−1 4 V (− r2ν−1τ α−1), (1) θ θ 4 where r is the distance to the vortex core, τ is the time variable, Cθ, ν and α are the parameters of the model. The self-similar profile is expressed in terms of the Kummer confluent hypergeometric function M as   1 1 b V (η) = (−η) 2 M + , 2; (1 − α)η . (2) 2 α − 1

∗Corresponding author. Email: [email protected] Figure 1: (a) Side and top views of the airliner. (b) Flow parameters at the RANS-LES interface.

The original Moore–Saffman model [6] for laminar vortices is recovered if α = 0 and if ν is the kinematic viscosity of the fluid. In our turbulent case, however, the numerical simulation suggests that α = 0.707 and ν = 0.00101 m2/s0.293. Similarity solutions for the deficit and for the axial velocity have also been obtained.

References

[1] Lee, D., D. W. Fahey, P. M. Foster , P. J. Newton, R. C. N. Wit, L. L. Lim, B. Owen, and R. Sausen: Aviation and global climate change in the 21th century. Atmos. Env., 43, 3520–3537, 2009. [2] Paoli R. and K. Shariff: modeling and simulation. Annu Rev. FLuid Mech., 48: 393–427, 2016. [3] Kolomenskiy D., Paoli R. and Boussuge, J.: Hybrid RANS-LES simulation of wingtip vortex dynamics. Proceedings of the ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting and 12th International Conference on Nanochannels, Microchannels, and Minichannels. August 3-7, 2014, Chicago, Illinois, USA, 2014, FEDSM2014-21349. [4] Cambier L., Heib S. and Plot S.: The ONERA elsA CFD software: input from research and feedback from industry. Mech. & Industry 14, 159-174, 2013. [5] Stoessel A.: An efficient tool for the study of 3D turbulent combustion phenomena on MPP computers. Proceedings of the HPCN 95 Conference, Milan, Italy, 1995. [6] Moore D. W. and Saffman P. G.: Axial flow in laminar trailing vortices. Proc. R. Soc. London, Ser. A 333, 491-508, 1973. [7] Paoli R., Nybelen L., Picot J. and Cariolle D.: Effects of jet/vortex interaction on contrail formation in supersaturated conditions. Phys. Fluids 25, 053305, 2013.

Figure 2: Isosurface of λ2 criterion coloured with the .