Dynamic behavior of a dense spray diffusion flame in a potential vortex.

Abstract

The interaction of a dense spray diffusion flame and a plane potential vortex is analytically investigated assuming constant property, sheath spray combustion, the flame sheet approximation, and the locally one-dimensional approximation. The problem is a modification of the original Marble problem with the gaseous fuel and the viscously decaying vortex replaced by a liquid fuel spray and a non-decaying potential vortex. The study is divided into three stages: (i) the interaction of a nonsteady gaseous diffusion flame and a potential vortex, (ii) the time-dependent sheath combustion of a planar fuel droplet cloud, and (iii) the interaction of a dense spray diffusion flame and a potential vortex. In stage (i) the validity of a proposed patching method as applied to an unsteady gaseous diffusion flame scope is justified for application in subsequent stages. Stage (ii) considers the plane case of stage (iii) and provides a basis for evaluating the vortex effect on a spray diffusion flame. The final stage investigates the dynamic behavior of the vortex interaction with a spray diffusion flame and its influence on the global fuel consumption rate and the growth of a core-like reacted region. Subject to the approximations made in this study, the diffusion layer structure of the spray flame is shown to be self similar in time and space. The global flame is also self similar, and is governed by the ratio of the vortex strength to the diffusion coefficient, $\Gamma /D.$ The radius of the reacted core normalized by $\sqrt{Dt}$ is proportional to $(\Gamma/D)\sp{1\over3}.$ The augmentation in fuel consumption rate normalized by D is proportional to $(\Gamma/D)\sp{2\over3}.$ Criteria for approximation of a viscous vortex by a potential vortex are also developed. It is concluded that analytical solutions for the interaction of a dense spray diffusion flame with a potential vortex can be determined, provided the spray undergoes sheath combustion, and that the results can be related to those of the original Marble problem.