LES of an inclined jet into a supersonic cross-flow

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). Helium is injected through an inclined round jet into a supersonic air flow at Mach 3.6. The video shows 2D contours of Mach number and magnitude of density gradient, and 3D iso-surfaces of Helium mass-fraction and vortical structures. Large eddy
  LES of an inclined jet into a supersonic cross-flow Antonino Ferrante 1 , Carlos Pantano-Rubino 2 ,Georgios Matheou 1 , Paul E. Dimotakis 1 ,Mike Stephens 3 , Paul Adams 3 , Richard Walters 3 , Randall Hand 31 Graduate Aeronautical Laboratories,California Institute of Technology, CA 91125, USA 2 Mechanical Science and Engineering,University of Illinois at Urbana-Champaign, IL 61801, USA 3 Data Analysis and Assessment Center, U.S. ArmyEngineer Research and Development Center, MS 39180, USAOctober 10, 2008 Abstract This short article describes flow parameters, numerical method,and animations of the fluid dynamics video LES of an Inclined Jetinto a Supersonic Cross-Flow. Helium is injected through an inclinedround jet into a supersonic air flow at Mach 3.6. The video shows2D contours of Mach number and magnitude of density gradient, and3D iso-surfaces of Helium mass-fraction and vortical structures. Largeeddy simulation with the sub-grid scale (LES-SGS) stretched vortexmodel of turbulent and scalar transport captures the main flow fea-tures: bow shock, Mach disk, shear layers, counter-rotating vortices,and large-scale structures. Flow description Helium is injected through an inclined round jet into a supersonic air flow(Fig. 1). In the present investigation, the jet axis forms a 30 ◦ angle with thestreamwise direction of the air flow. The flow parameters of air and heliumare reported in Table 1. The jet diameter,  d , is 3.23 × 10 − 3 m, and the bound-ary layer thickness,  δ  , of the air flow is 2 × 10 − 2 m, as in the experimentalstudy of  Maddalena, Campioli & Schetz (2006). The air free-stream Mach 1   a  r   X   i  v  :   0   8   1   0 .   1   9   5   7  v   1   [  p   h  y  s   i  c  s .   f   l  u  -   d  y  n   ]   1   0   O  c   t   2   0   0   8  number is 3.6, the jet Mach number is 1.0, and the jet to free-stream momen-tum ratio,  q  , is 1.75. The Reynolds number of the air flow based on the mo-mentum thickness is  Re θ  =  U  e θ/ν  w  = 13 × 10 3 ( Re δ  =  U  e δ/ν  w  = 113 × 10 3 ),where  U  e  is the free-stream air velocity and  ν  w  is the kinematic viscosity of air computed at the wall for adiabatic wall conditions. He,  M   = 1   30 O Air,  M  e  > 1   Figure 1: Flow schematic. Mach  ρ  (kg/m 3 ) m  j  (g/s)  p  (kPa) T   (K)  p 0 (kPa) T  0  (K) Air 3.6 0.50 - 12 82 1,034295 He 1.0 0.46 3.4 225 235460 313 Table 1: Flow parameters. I. ., . .. .   Numerical method We performed large-eddy simulation with the sub-grid scale (LES-SGS)stretched vortex model of turbulent and scalar transport developed by Pullinand co-workers (Misra & Pullin, 1997; Pullin, 2000; Voelkl  et al. , 2000;Kosovi´c  et al. , 2002). The governing equations are solved on a Cartesianmesh with adaptive mesh refinement (AMR) (Deiterding, 2003). The level- set approach with the ghost-fluid method (Fedkiw  et al. , 1999) is used totreat the complex boundary (Fig.1) where no-slip and adiabatic boundaryconditions are applied. The numerical method is a hybrid approach with lownumerical dissipation (Hill & Pullin, 2004; Pantano  et al. , 2007) that usestuned centered finite differences (TCD) (Hill & Pullin, 2004) in smooth flow regions, and weighted essentially non-oscillatory (WENO) (Liu  et al. , 1994;Jiang & Shu, 1996) scheme around discontinuities and ghost-fluid bound- aries.2  Video The video LES of an Inclined Jet into a Supersonic Cross-Flow shows fiveanimations:1. Mach number contours in mid-span plane;2. magnitude of density gradient contours in mid-span plane;3. iso-surface of Helium mass fraction  Y  He  = 0 . 25;4. vortical structures 1 ;5. overlapped iso-surface of Helium mass fraction  Y  He  = 0 . 25 and vorticalstructures.Each animation is played at a speed 10,000 times slower than in real life,and shows the flow evolution for about 1 . 8 × 10 − 3 s.The video shows that the main flow features are well captured: bow shock,Mach disk, shear layers, counter-rotating vortices, and large-scale structures(Ferrante  et al. , 2008). Acknowledgments This work was supported by AFOSR Grants FA9550-04-1-0020 and FA9550-04-1-0389, by the Caltech DoE Advanced Simulation and Computing (ASC)Alliance Center under subcontract No. B341492 of DOE contract W-7405-ENG-48, and NSF Grant EIA-0079871. The simulations were performed atthe Center of Advanced Computing Research (CACR) at Caltech. The fluiddynamics video was produced at the Data Analysis and Assessment Center,U.S. Army Engineer Research and Development Center (ERDC). References Deiterding, R.  2003  Parallel Adaptive Simulation of Multi-dimensional Detonation Structures  . Ph.D. Dissertation. Fedkiw, R. P., Aslam, T., Merriman, B. & Osher, S.  1999 A non-oscillatory Eulerian approach to interfaces in multimaterial flows (theGhost Fluid Method).  J. Comput. Physics   152 , 457–492. 1 The vortical structures are educed using the  λ 2 -method (Jeong & Hussain, 1995),where  λ 2  is defined as the second largest eigenvalue of the tensor ( S  ik S  kj  + Ω ik Ω kj ),where  S  ij  ≡  ( ∂  j U  i  +  ∂  i U  j ) / 2 is the strain rate tensor, and Ω ij  ≡  ( ∂  j U  i − ∂  i U  j ) / 2 is therotation rate tensor. 3  Ferrante, A., Pantano-Rubino, C., Matheou, G. & Dimotakis, P. 2008 LES of an inclined jet into a supersonic cross-flow at Mach 3.6.  Bull.Amer. Phys. Soc.  . Hill, D. J. & Pullin, D. I.  2004 Hybrid tuned center-difference-WENOmethod for large eddy simulations in the presence of strong shocks.  J.Comput. Physics   194 , 435–450. Jeong, J. & Hussain, F.  1995 On the identification of a vortex.  J. Fluid Mech.  285 , 69–94. Jiang, G. S. & Shu, C. W.  1996 Efficient implementation of weightedENO schemes.  J. Comput. Physics   126 , 202–228. Kosovi´c, B., Pullin, D. I. & Samtaney, R. 2002 Subgrid-scale modelingfor large-eddy simulations of compressible turbulence.  Phys. Fluids   14 ,1511–1522. Liu, X. D., Osher, S. & Chan, T.  1994 Weighted essentially non-oscillatory schemes.  J. Comput. Physics   115 , 200–212. Maddalena, L., Campioli, T. L. & Schetz, J. A.  2006 Experimentaland computational investigation of light-gas injectors in Mach 4.0 cross-flow.  J. Propulsion and Power   22 , 1027–1038. Misra, A. & Pullin, D. I.  1997 A vortex-based subgrid stress model forlarge-eddy simulation.  Phys. Fluids   9 , 2443–2454. Pantano, C., Deiterding, R., Hill, D. & Pullin, D.  2007 A low-numerical dissipation patchbased adaptive mesh refinement method.  J.Comput. Physics   221 , 63–87. Pullin, D. I.  2000 A vortex-based model for the subgrid flux of a passivescalar.  Phys. Fluids   12 , 2311–2319. Voelkl, T., Pullin, D. I. & Chan, D. C.  2000 A physical-space versionof the stretched-vortex subgrid-stress model for large-eddy simulation. Phys. Fluids   12 , 1810–1825.4
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