LES of an inclined sonic jet into a turbulent crossflow at Mach 3.6

Abstract

We have performed large-eddy simulation with subgrid scale (LES-SGS) stretched-vortex model of an inclined sonic jet into a supersonic crossflow at Mach 3.6. The main flow features generated by the gas-dynamic interactions of the jet with the supersonic crossflow, such as barrel shock, shear layer, and counter-rotating vortex pair, are numerically captured by the employed LES-SGS. The transition and spatial development of the jet into a supersonic crossflow have been shown to be strongly dependent on the inflow conditions of the crossflow. This result indicates that correct turbulent inflow conditions are necessary to predict the main flow characteristics, dispersion and mixing of a gaseous jet in a supersonic, turbulent crossflow using LES-SGS. This work presents a methodology for the generation of realistic synthetic turbulent inflow conditions for LES of spatially developing, supersonic, turbulent, wall-bounded flows. The methodology is applied to the study of a supersonic turbulent flow over a flat wall interacting with an inclined jet. The effects of inflow conditions on the spatial development of the inclined jet are discussed, and then the results are compared with the available experimental data. Also, the dominant vortical structures generated by the jet/turbulent boundary layer interaction are identified as sheets, tilted tubes and discontinuous rings, and a visualization of their spatiotemporal development is provided. The identified vortical structures are shown to be enveloped by the helium mass-fraction isosurface, thus showing the important role of those structures in the dispersion of a gaseous jet in a supersonic crossflow.

Keywords:

• LES
• stretched-vortex model
• jet
• inflow conditions
• supersonic turbulent boundary layer

Acknowledgements

The authors would like to thank Dr. L. Maddalena and Prof. J. Schetz for providing data from their experimental study. The authors would like to acknowledge useful discussions with Dr. C. Pantano, and contributions to and support of the AMROC computational framework by Drs. R. Deiterding, D. Hill, and C. Pantano. The simulations were performed at the Center of Advanced Computing Research (CACR) at Caltech. The fluid dynamic videos (Movies 1–5) discussed in the paper were produced by the Data Analysis and Assessment Center (DAAC) at the US Army Engineer Research and Development Center, Mississippi. 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 views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the AFOSR or the US Government.

Notes

¹Dimensionless quantities in wall units carry the superscript ‘⁺’, i.e., U ⁺=U/u _τ and y ⁺=yu _τ/ν _w , where u _τ is the wall friction velocity, and ν _w , the air kinematic viscosity at a wall adiabatic temperature.

²Private communications with Dr. L. Maddalena.

³The vortical structures are educed using the λ₂ method [64], where λ₂ is defined as the second largest eigenvalue of the tensor (S_ikS_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 the rotation rate tensor.