A Linear- Eddy Model of Turbulent Scalar Transport and Mixing

TLDR

Transport and mixing of diffusive scalars in turbulent flows are simulated using a novel representation of temporal evolution along a transverse line moving with the mean fluid velocity. The study demonstrates the model’s performance by computing the spatial evolution of diffusive scalar fields downstream of various source configurations in homogeneous turbulence, and discusses extensions to inhomogeneous turbulence, Reynolds and Schmidt number dependencies, and finite‑rate chemical reactions. The model evolves the scalar field along the line by Fickian diffusion and stochastic block inversions, where each inversion randomly selects an interval and replaces the scalar field within that interval, with a fixed or random size, and for fixed interval size the model requires only the Peclet number as input.

Abstract

Abstract Transport and mixing of diffusive scalars in turbulent flows are simulated computationally based on a novel representation of the temporal evolution along a transverse line moving with the mean fluid velocity. The scalar field along this line evolves by Fickian diffusion, representing molecular processes, and by randomly occurring events called block inversions. Block inversion, representing the effect of turbulent convection, consists of the random selection of an interval (Y0 − 1/2, Y0 + 1/2) of the line, where the interval size l may he either fixed or randomly selected, and replacement of the scalar field θ(y) within that interval by θ(2y0 For fixed l, the model requires a single input parameter, the Peclet number. To demonstrate the performance of the model, this formulation is used to compute the spatial development of diffusive scalar fields downstream of several source configurations in homogeneous turbulence. Generalization to inhomogeneous turbulence is discussed, as well as a formulation which incorporates dependences on Reynolds number and Schmidt number. Finite rate chemical reactions can also be incorporated.