Investigations of Incompressible Variable-Density Turbulence in an External Acceleration Field

Abstract

Of interest to turbulence modeling is the behavior of variable-density flow at high Reynolds numbers — a flow difficult to model. This thesis provides insight into variable-density flow behavior by examining the dynamics and mixing of variabledensity turbulence subject to an externally imposed acceleration field. The flow is studied in the zero-Mach-number limit with a series of direct numerical simulations. The flow configuration consists of alternating slabs of high- and low-density fluid in a triply periodic domain. Density ratios in the range of 1.005 ≤ R ≡ ρ1/ρ2≤ 10 are investigated. The flow produces temporally evolving shear layers.

A perpendicular mean density–pressure gradient is maintained as the flow evolves, with multi-scale baroclinic torques generated in the turbulent flow that ensues. For all density ratios studied, the simulations attain Reynolds numbers at the beginning of the fully developed turbulence regime.

An empirical relation for the convection velocity predicts the observed entrainmentratio and dominant mixed-fluid composition statistics. Two mixing-layer temporal evolution regimes are identified: an initial diffusion-dominated regime with a growth rate ∼t ^1/2 followed by a turbulence-dominated regime with a growth rate ∼ t ^3.In the turbulent regime, composition probability density functions within the shear layers exhibit a slightly tilted (‘non-marching’) hump, corresponding to the most probable mole fraction. The shear layers preferentially entrain low-density fluid by volume at all density ratios, which is reflected in the mixed-fluid composition.

The mixed-fluid orientations of vorticity, baroclinic torques, density gradients, and pressure gradients are presented. Baroclinic torques, the cross product of the density and pressure gradients, tend to be aligned with positive or negative vorticity direction, with vorticity preferentially aligning with the intermediate eigenvector of the local strain-rate tensor, with some variance.