Turbulent Flame Speeds of G-equation Models in Unsteady Cellular Flows

TL;DR

This study computationally investigates the effects of unsteady cellular flows on turbulent flame speeds modeled by G-equations, revealing frequency locking phenomena in certain models and flow conditions.

Contribution

It provides the first detailed computational analysis of G-equation models in unsteady cellular flows, highlighting differences between viscous and inviscid models.

Findings

Frequency locking occurs in curvature-strain G-equations with periodic flows.

Frequency locking disappears in viscous G-equations.

Stochastic oscillations eliminate frequency locking in inviscid G-equations.

Abstract

We perform a computationl study of front speeds of G-equation models in time dependent cellular flows. The G-equations arise in premixed turbulent combustion, and are Hamilton-Jacobi type level set partial differential equations (PDEs). The curvature-strain G equations are also non-convex with degenerate diffusion. The computation is based on monotone finite difference discretization and weighted essentially nonoscillatory (WENO) methods. We found that the large time front speeds lock into the frequency of time periodic cellular flows in curvature-strain G-equations similar to what occurs in the basic inviscid G-equation. However, such frequency locking phenomenon disappears in viscous G-equation, and in the inviscid G-equation if time periodic oscillation of the cellular flow is replaced by time stochastic oscillation.