A multiple length and time scale approach is adopted to perform large eddy simulation (LES) of combustion instability in a model afterburner. In this framework, the full compressible Navier-Stokes equations are decomposed into incompressible flow to leading order and acoustic equations to first order. The basis for this decomposition is the disparity in the time and length scales of the flow and acoustic propagation respectively. The present framework yields a coupling between the flow field and acoustic field, in terms of the flow dilatation and acoustic Reynolds stress (ARS). Test cases for various Reynolds numbers (based on mass flow rates) are simulated within this framework, and used to study the dynamics of transition and instability in a model afterburner. As the Reynolds number is increased, the dominant frequency switches from being that of the acoustic mode to the hydrodynamic mode. When the excitation to the acoustic field from the combustion is switched off, a high frequency relating to the transverse acoustic mode of the combustor is observed to be excited in the flow field as an acoustic feedback to the flow. When the acoustic excitation is turned back on, the transverse acoustic mode excitation of the hydrodynamics continues to prevail, illustrating a hysteretic effect. The dominant excitation of hydrodynamic mode at high Reynolds number clearly shows a rapid mixing and shortened length of heat release rate zone, when compared to the case at low Reynolds number as well as when the flow and acoustic simulations are uncoupled. Copyright © 2017 ASME.