Fine scale structure of conserved scalar mixing in turbulent shear flows: Sc much greater than 1 and Sc approximately equal to 1.

Abstract

This work deals with an experimental investigation of the fine scale structure of conserved scalar mixing in turbulent flows, and presents three-dimensional spatio-temporal (x-y-t) measurements of the conserved scalar field $\zeta$(x,t) on the inner scales of a turbulent flow. The measurement resolution reaches down to the local strain-limited molecular diffusion scale of the flow, so that, together with the signal quality achieved, the resulting scalar field measurements are directly differentiable to allow determination of the scalar energy dissipation rate field (ReSc)$\sp{-1}\nabla\zeta{\cdot}\nabla\zeta$(x,t), giving the molecular mixing rate field in the flow. Experiments were conducted at two different values of the Schmidt number, specifically Sc $\approx$ 2075 using planar laser induced fluorescence in water and Sc $\approx$ 1.36 using planar laser Rayleigh scattering in a gaseous turbulent flow, with Reynolds numbers ranging from 2,100 to 14,000. This range of Schmidt numbers allows a direct study of the effect of the molecular diffusivity on the fine structure of the mixing rate field. Results show that the canonical structural element of the mixing rate field is the same for Sc $\gg$ 1 and Sc $\approx$ 1 turbulent mixing, and consists of strained laminar diffusion layers whose internal structure is well described by the classical solution of Burgers and Townsend for diffusion in the presence of a spatially uniform and locally planar strain rate field. Various aspects of this fine scale structure are quantitatively analyzed in considerable detail. In addition, differences between the Sc $\gg$ 1 and Sc $\approx$ 1 mixing processes are identified. These measurements of the conserved scalar field and its dissipation rate field in non-reacting turbulent flows are also extended to study the structure of reacting turbulent flows in the equilibrium chemistry limit. In such mixing-limited reacting flows, the reaction rate field and the mass fraction fields of all species are determined from the local instantaneous values of a conserved scalar and its dissipation rate.