Diffusion-Controlled Reaction in a Vortex Field

• Published in: Combustion science and technology 1989-08, Vol.66 (4-6), p.293-317
• Main Authors: Rehm, Ronald G., Baum, Howard R., Lozier, Daniel W., Aronson, Jonathan
• Format: Article
• Language: English
• Subjects: Applied sciences; Combustion. Flame; Energy; Energy. Thermal use of fuels; Exact sciences and technology; Theoretical studies; Theoretical studies. Data and constants. Metering
• ISSN: 0010-2202; 1563-521X
• DOI: 10.1080/00102208908947155

A two-dimensional model of a constant-density diffusion-controlled reaction between unmixed species initially occupying adjacent half-spaces is formulated and analyzed. An axisymmetric viscous vortex field satisfying the Navies-Stokes equations winds up thc interface between the species as they diffuse together and react. A flame-sheet approximation of the rapid reaction is made using a mixture fraction dependent variable. The problem was originally proposed by F. Marble, who performed a local analysis and determined the total consumption rate along thc flame sheet. The present paper describes a global similarity solution to the problem which is Fourier analyzed in a Lagrangian coordinate system. The Fourier amplitudes are determined both by an asymptotic analysis, valid for large Schmidt numbers,and by numerical solution of the two-point boundary-value ordinary differential equations. The solution is evaluated in both Lagrangian and Eulerian coordinate systems. Comparisons are made between the asymptotic and the numerical solutions for a variety of values of the governing parameters, the Reynolds and Schmidt numbers.