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The mixing region in freely decaying variable-density turbulence

Published online by Cambridge University Press:  05 May 2015

Pooya Movahed  and
Eric Johnsen
Pooya Movahed*
Affiliation:
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
Eric Johnsen
Affiliation:
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
*
†Email address for correspondence: [email protected]
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Abstract

A novel set-up is proposed to numerically study turbulent multimaterial mixing, starting from an unperturbed material interface between a light and a heavy fluid. We conduct direct numerical simulation (DNS) to better understand the role of density gradient alone on the turbulence, specifically with regard to the mixing region dynamics and anisotropy across scales. Freely decaying isotropic turbulent fields of different densities but identical kinematic viscosities are juxtaposed. The rationale for this strategy is that conventional turbulence scalings are based on kinetic energy per unit mass and kinematic viscosity. Thus, by matching the initial kinematics (root-mean-square velocity) and the dissipation (kinematic viscosity), the turbulence (kinetic energy per unit mass) decays at the same rate in both fluids. With this set-up, the effect of the density gradient alone on the turbulence can be considered, independently from other contributions (e.g. mismatch in kinetic energy per unit mass, acceleration field, etc.). We examine the mixing region dynamics at large and small scales for different density ratios and Reynolds numbers. After an initial transient, we observe a self-similar growth of the mixing region, which we explain via theoretical arguments verified by the DNS results. Inside the mixing region, the momentum of the heavier eddies causes the mean interface location to shift toward the light fluid. A higher density ratio leads to a wider, less molecularly mixed mixing region. Although anisotropy is evident at the large scales, the dissipation scales remain essentially isotropic, even at the highest density ratio under consideration (12:1). The intermittency of the velocity field exhibits isotropy, while the mass fraction field is more intermittent in the direction of the density gradient.

JFM classification

Turbulent Flows: Intermittency Turbulent Flows: Isotropic turbulence Mixing: Turbulent mixing
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Papers
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Journal of Fluid Mechanics , Volume 772 , 10 June 2015 , pp. 386 - 426
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© 2015 Cambridge University Press 

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