AIAA 98–0697 Velocity Field of the Planar Shear Layer: Compressibility Effects

Particle image velocimetry (PIV) is used to measure the instantaneous two-dimensional velocity field in turbulent, planar mixing layers at varying levels of compressibility. The structure of the instantaneous velocity and vorticity fields are seen to display similar variation with compressibility as the scalar field, with the spatial intermittency of the velocity field tied to the interfaces of the large-scale structures. The compressible case displays multiple thin sheets of vorticity within the layer, rather than diffuse regions spanning its transverse extent. The importance of the lab-frame Mach number, particularly in compressible layers, is suggested by the presence of steep velocity gradients near the instantaneous sonic line within the mixing layer. In addition to lending structural interpretations such as these, the PIV data may also be used in large-ensemble fashion to provide turbulence statistics previously obtained using pointwise measurement techniques. Finally, the effect of sub-boundary layer mixing enhancement techniques on the velocity field is observed by means of plan-view measurements. Nomenclature a Sound speed ˙ m Mass flow rate M Mach number P Pressure r Velocity ratio Re Reynolds number s Density ratio St Stokes number T Temperature U Freestream or structure velocity u Streamwise velocity component v Cross-stream velocity component w Spanwise velocity component x Streamwise coordinate y Cross-stream coordinate z Spanwise coordinate δ Mixing layer thickness ∆t Laser pulse separation ρ Density σ RMS turbulence intensity τ Characteristic time ν Kinematic viscosity Ensemble average * AIAA Student Member † AIAA member; Subscripts 1 High-speed stream 2 Low-speed stream c Convective cl Centerline ex Nozzle exit img Imaging station p Particle vis Visual Introduction H IGH-MACH number aerospace propulsion applications require rapid molecular mixing between gaseous streams in the presence of compress-ibility effects. The two-stream plane shear layer has served as an important model for this family of flows; its relatively simple initial and boundary conditions and well-defined parameter space facilitate numerical and experimental studies alike. For incompressible layers, the primary variables are the density and velocity ratios s and r, and the Reynolds number of the shear, Re δ ≡ ∆U δ/ν. Since the mixing layer is ideally a free shear flow, the frame of reference in which to define a Mach number parametrizing compressibility has proved to be problematic. Early workers 1, 2 defined a reference frame convecting downstream with the large-scale turbulent structures within the layer, at some velocity U c. Given U c , the Mach number …