Hydrodynamic stability of a premixed flame subjected to transverse shear
Flame instabilities arise intrinsically in combustion systems and have important implication in the operation of engineering devices. The primary intrinsic instability of premixed combustion is caused by thermal gas-expansion, known as the hydrodynamic or the Darrieus-Landau (DL) instability. Consequently, a premixed flame is susceptible to disturbances. The flame tends to develop a wrinkled or corrugated front with a cusp-like structure at a large scale. Once formed, the flame front always spikes towards the burned gas region and bows on the unburned gas region. The DL stability plays a crucial role in the hydrodynamic behaviors of a premixed flame and has many ramifications when premixed combustion takes place in practice. We study the hydrodynamic behavior of a premixed flame under the influence of a transversely shearing flow. A new problem configuration is proposed to gain a fundamental understanding of the premixed flame-shear interaction. The shear flow is introduced such that unburned and burned gases separated by the standard planar flame have opposite flow velocities in the flame transverse direction. This setting idealizes situations found in practical premixed combustion systems, for example, swirl-stabilized burners and gas turbines. Recent studies, made possible by Direct Numerical Simulations (DNS) and Large-Eddy Simulations (LES), have provided rich data for the description of premixed combustion in turbulent shear flows. And yet, little attention has been given to the effects of mean shear on the hydrodynamic stability. This work intends to fill the gap and shed some light on the premixed flame-shear interaction. This thesis presents a three-step study to address the linear, weakly nonlinear, and fully nonlinear stabilities of a premixed flame subjected to a transverse shear. First, the linear analysis extends the classical DL configuration and solves the linearized stability problem. The key result is a dispersion relation and its distinguished limits that reveal the conditions for the onset of hydrodynamic instability. Second, the weakly nonlinear analysis derives the modified Michelson-Sivashinsky (MS) equation, a time-dependent partial differential equation (PDE) describing the evolution of a hydrodynamically unstable premixed flame front in the weak thermal expansion limit. Solutions of the modified MS equation demonstrates the formation process of a skewed cusp-like flame pattern as well as the long-time behaviors beyond the linear regime when the premixed flame is affected by shear. The parametric study identifies the effect of each parameter on the flame dynamics. Third, a computational solver is developed for numerical simulations of premixed flames at the hydrodynamic flame-sheet level, based on the same mathematical formulation of linear and nonlinear analysis. Without restrictions on the amplitude of flame deformation and the density variation, the solver is used to conduct a series of numerical experiments to explore the fully nonlinear behaviors of premixed flames in a shearing flow.
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign