Theory and Application of Multiple Mapping Conditioning for Turbulent Reactive Flows

Abstract

This chapter presents the basic theory and conceptual evolution of the multiple mapping conditioning (MMC) framework, and presents recent applications for turbulent reactive flows. MMC was initially formulated as a method that integrates the probability density function (PDF) and conditional moment closure (CMC) models through a generalisation of mapping closure. MMC models utilise a reference space, whose PDF is prescribed a priori or which is simulated by some means such as a Markov diffusion process. The turbulent fluctuations of all scalars in this method are divided into major and minor groups, and the former are associated with the reference space via a mapping function. The reference space describes a low-dimensional manifold which can fluctuate in any given way, while the fluctuations of the (real) scalars are fully or partially confined relative to that reference space. The dimensionality of the reference space is usually small. For example, in non-premixed combustion a reference space emulating the mixture fraction usually suffices. There are both conditional and probabilistic conceptualisations of MMC and both deterministic and stochastic mathematical formulations. In the past decade, an extension of probabilistic MMC has emerged that is known as generalised MMC that removes some of the formality of the original formulation and extends the type and usage of the reference variables. Generalised MMC is commonly associated, although not exclusively, with large eddy simulations (LES). This chapter reviews the conceptual and theoretical advances in MMC since its original formulation and also reviews some of the recently published applications of MMC in turbulent reactive flows.