Abstract

The difficulties of modelling transport of scalar properties (such as temperature and concentrations) in physical space are well-known. It is conventional to call the turbulent scalar transport as turbulent diffusion. However, if a strict mathematical definition of the term “diffusion” is to be used, this stochastic process is not a diffusion process since its characteristic time is quite long. That is why the gradient-based approximations of the turbulent fluxes, which are precise for the diffusion transport, may have some difficulties when dealing with a turbulent flow. In the present work, we investigated an alternative formulation of the turbulent scalar transport: the transport of one scalar with respect to another scalar. Using DNS data, we demonstrated that this transport can be much better approximated by a diffusion process than the turbulent scalar transport in physical space. This property is effectively used in Conditional Moment Closure (CMC) which deals with turbulent transport of reactive scalers (i.e. scalars participating in chemical reactions) with respect to the conserved scalar.

The similarity with diffusion processes can be used to numerically simulate this process by stochastic differential equations. Although solving such equations would be much easier than using DNS to predict characteristics of the turbulent scalar transport, the idea needs a proper theoretical analysis due to the complicated structure of CMC equations which have, in their conserved form, both forward and inverse parabolic terms. In the present work, we also demonstrated how the CMC equations can be properly represented by a stochastic model.

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