Using approximate inertial manifold approach to model turbulent non-premixed combustion

TL;DR

This paper introduces an approximate inertial manifold (AIM) approach for reduced-order modeling of turbulent non-premixed combustion, capturing complex flame behaviors without relying on traditional assumptions.

Contribution

The study develops an AIM-based model that accurately captures turbulent combustion dynamics directly from governing equations, without needing laminar or statistical assumptions.

Findings

AIM effectively captures flame extinction and reignition behaviors.

The model provides scalar dissipation rates and mixing times without extra modeling.

AIM shows promise as a new approach for turbulent combustion modeling.

Abstract

The theory of inertial manifolds (IM) is used to develop reduced-order models of turbulent combustion. In this approach, the dynamics of the system are tracked in a low-dimensional manifold determined in-situ without invoking laminar flame structures or statistical assumptions about the underlying turbulent flow. The primary concept in approximate IM (AIM) is that slow dominant dynamical behavior of the system is confined to a low-dimension manifold, and fast dynamics respond to the dynamics on the IM instantaneously. Decomposition of slow/fast dynamics and formulation of an AIM is accomplished by only exploiting the governing equations. Direct numerical simulations (DNS) of initially non-premixed fuel-air mixtures developing in forced isotropic turbulence have been carried out to investigate the proposed model. Reaction rate parameters are varied to allow for varying levels of extinction and reignition. The AIM performance in capturing different flame behaviors is assessed both a priori and a posteriori. It is shown that AIM captures the dynamics of the flames including extinction and reignition. Moreover, AIM provides scalar dissipation rate, mixing time for reactive scalars, and closures for nonlinear terms without any additional modeling. The AIM formulation is found promising, and provides a new approach to modeling turbulent combustion.