Theoretical and Experimental Investigations of Nonlinear Flame Instability

Doctoral thesis, 1998

Flame instability is both important and difficult to understand. Mechanisms of instability are complex, because instability often involves an interaction between several different physical phenomena, such as an unsteady chemical reaction, unsteady flame propagation generating an unsteady flow, acoustic waves or shock waves. So, it is difficult to control these instabilities in combustion systems. Research on combustion instability will promote understanding and provide some rational approaches to the anticipation, prevention, remedy and utilization of unstable combustion. The investigations in this thesis focus on some nonlinear effects of fundamental importance to combustion theory, flame propagation and stretch effects, shock-induced flame-front instability and tulip flame instability by using experimental and theoretical tools. The main goals of this thesis are to study the intrinsic characteristics of flame instability, to describe the mechanisms of instability, and to derive some asymptotic formulations to quantitatively predict the processes of unstable flame development and it final stage. In order to study this process, a level set technique accounting for heat release effects and flame propagation is adopted together with N.S and Euler equations to track the evolution of the flame front in nonlinear hydrodynamic and shock-induced flame instability for 2D and 3D cases. The Schlieren technique is used for experimental visualization of the processes of tulip flame formation. It was found that tulip flame formation and shock-induced flame-front instability are due to the vorticity generated by the misalignment of density and pressure gradients in the systems. The initial inversion of the flame-front is due to the Richtmyer-Meshkov instability. Results also show that the flame propagation speed of a perturbed flame is asymptotically equal to Up=(1+0.293*sqrt(d-1))*sl, where d is the density ratio and sl is the laminar burning speed and the asymptotic amplitude of the flame is approximately A=0.37*L*sqrt(d-1), where L is the flame wave-length. The burning velocity has a minor effect on the asymptotic shape of the flames. When the turbulence scale is much smaller than the size of the combustion apparatus the results can be directly applied to turbulent flames by replacing sl with the turbulent burning velocity.