Direct numerical simulation of the early development of a turbulent mixing layer downstream of a splitter plate

Abstract

A direct numerical simulation is carried out of the initial stages of development of a mixing layer with a velocity ratio of ten, a fast stream Mach number of 0.6 and equal free-stream temperatures. The fast stream is a fully developed turbulent boundary layer with a trailing-edge displacement thickness Reynolds number of 2300, while the slow stream is laminar. The computations include a splitter plate with zero thickness. The initial flow development is dominated by the rapid spreading of an internal shear layer formed as the viscous sublayer of the upstream turbulent boundary layer crosses the trailing edge. A tendency towards spanwise-coherent structures is observed very early in the shear layer development, within five displacement thicknesses of the trailing edge, despite such structures not being present in the upstream boundary layer. A numerical search for a global mode in the vicinity of the splitter plate trailing edge found only convective growth of disturbances. Instead, a convective mechanism is examined and found to be a plausible explanation for the rapid change of observed flow structure near the trailing edge. The same mechanism indicates a trend towards more two-dimensional structures in the fully developed mixing layer.

Keywords:

• DNS
• mixing layer
• compressible
• coherent structure
• trailing edge
• splitter plate

Acknowledgments

The first author would like to acknowledge support from EPSRC under research grant EP/E032028/1. Computer time for the present study was provided via the UK Turbulence Consortium (EPSRC grant EP/D044073/1) and the simulations were run on the UK High Performance Computing Service HECToR. A short version of this study was presented at the DLES7 Conference, Trieste, Italy, 8–10 September 2008 (conference proceedings to appear).