Direct Numerical Simulation of Passive Scalars Mixing in a Spatially Evolving Axisymmetric Vortex Breakdown Flow

Direct Numerical Simulation (DNS) of multiple passive scalars with varying molecular diffusivity in a spatially evolving axisymmetric vortex breakdown flow is performed at Reynolds number of 1500. Vortex breakdown is peculiar to swirling flows, and generally occurs when the ratio of azimuthal to axial velocity exceeds a certain level (Billant et al, 1999, J. Fluid Mech. 309, 1-44). Vortex breakdown is known to enhance mixing of scalars. However, little about the mixing characteristic and mechanism behind the transport of passive scalars in such flow have been known. Recent studies of scalar transport in turbulent flows have shown that the evolution of scalar field in the flow depends on the turbulence transport as well as the molecular diffusivity of the scalar (Saylor & Sreenivasan, 1998, Physics of Fluids 10(5), 1135-1146). This process, called differential diffusion, is a potential complication of the mixing process. The present study investigates the role of scalar molecular diffusivity in passive scalar transport in an axisymmetric vortex breakdown flow in swirling jet. Both instantaneous and mean scalar and velocity fields are analysed. The instantaneous radial profiles of velocity and passive scalar are also examined. The convective and diffusive budgets in the passive scalar transport equation are analysed, and diffusion-dominated regions are identified. DNS data reveals that differential diffusion has significant effect on spatial evolution of passive scalar field depending on its Schmidt number. Scalar with lower molecular diffusivity predominantly responds to transport by momentum of the flow. In contrast, molecular diffusion is the predominant transport mechanism for scalar with higher molecular diffusivity. It is shown that turbulence preferentially transport scalars with lower molecular diffusivity relative to one with higher molecular diffusivity even in the presence of high turbulent stirring, e.g. vortex breakdown. Furthermore, the instantaneous scalar radial profiles are shown to deviate from the instantaneous velocity profile depending on the scalar Schmidt number. The result has direct implication on limitations of dye-flow visualisation and on transfer of heat in vortex breakdown flows.