59th Annual Report on Research 2014

During the second year of our research the highly parallel code developed and validated during the first year is used to perform DNS of turbulent compressible temporally evolving mixing layer with several convective Mach numbers between 0.2 to 1.8. The DNS data is used to characterize the flow dynamics in proximity of the turbulent/non-turbulent interface separating the turbulent from the irrotational flow regions. For this purpose, the conditional mean statistics of the flow with respect to the distance from the turbulent/non-turbulent interface (TNTI) are analyzed in interface coordinate system whose origin is at the TNTI and whose axes are tangent and normal to the TNTI.

The interface between turbulent and non-turbulent regimes can be detected either with the vorticity norm, or with the conserved scalar convected by the turbulent flow, as usually done in experimental studies. In present work, a certain threshold for vorticity norm is chosen for turbulent region, below which flow can be considered to be irrotational.

Conditional statistics with respect to the TNTI are calculated. Since the flow is homogenous in spanwise (z) direction, the detection of the interface and calculation of the corresponding statistics are done in x-y planes. In each plane, two interfaces are detected, for upper and lower streams, whose vorticity magnitudes are constant and equal to the predefined threshold. The location of each interface is found using linear interpolation for each grid point in x-direction. Since the shape of the interface can be quite complex, it is more common to use interface envelope rather than the interface. For each stream, the interface envelope is defined as the outermost point of the interface in vertical direction.

The budget of different terms in transport equations for total and turbulent kinetic energy and vorticity are assessed in interface coordinates to understand the evolution of these terms near the TNTI. For both incompressible and compressible mixing layers, the TNTI layer thickness, which corresponds to the sharp jump in conditional profile of vorticity norm, is found to be approximately one Taylor length scale. In compressible mixing layers, the mean density undergoes a sharp drop at the TNTI, and, in the regions close to the TNTI, the density gradient vector is normal to the interface direction.

It is shown that for all the convective Mach numbers considered, the terms in the transport equations for total kinetic energy, turbulent kinetic energy, and spanwise vorticity, are scaled with the Taylor length and velocity scales in interface coordinates.

The total kinetic energy starts to change in irrotational region, , where is the normal distance from the TNTI and λ is the Taylor length scale. The pressure-advection is the dominant mechanism for variation of the total kinetic energy in irrotational region and interface layer. The maximum contribution of this term occurs within . For  the viscous dissipation acts as a sink for total kinetic energy and deep inside the turbulent region, it is the only term affecting the total variation of K in the average. The turbulent diffusion, the pressure diffusion, the production and the dissipation are the dominant terms for total variation of the turbulent kinetic energy near the TNTI. The last two terms become the most important ones inside the turbulent region for .

In compressible mixing layers, the dominant terms contributing to the total variation of vorticity (in spanwise direction) in proximity of the TNTI are viscous diffusion, vortex stretching, and baroclinic torque. For incompressible mixing layer, the first two terms are important. For compressible cases, viscous diffusion and baroclinic terms have the highest correlations with total variation of vorticity in . For  the vortex stretching is the most correlated term. It is observed that the intense vortical structures (IVS) generate a baroclinic torque as they become close to the TNTI. A plausible explanation is that the IVS generates a pressure gradient from the core of the vortex (low pressure) towards the region outside of the vortex. When an IVS becomes close to the TNTI, this pressure gradient field becomes misaligned with the density gradient field, which is aligned with the direction normal to the TNTI, and generates a baroclinic torque.