Combustion in Laminar Mixing Regions and Boundary Layers

Citation

Dooley, Donald Allen (1956) Combustion in Laminar Mixing Regions and Boundary Layers. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/MGTH-TS83. https://resolver.caltech.edu/CaltechETD:etd-03222004-162749

Abstract

The governing relations for gaseous flow systems with chemical reaction are briefly discussed. A mixture of mechanically similar Maxwellian molecules is assumed and the general relations are then reduced to the simplified forms appropriate for reacting, laminar boundary layer type flow systems. One-step unopposed, "global" reactions following first-order, second-order, and third-order kinetics are considered. The simplified governing relations are transformed to an equivalent constant density plane by application of the Howarth transformation. A similarity function relating the specie concentrations to the local temperature is found for the case of equal Prandtl and Schmidt numbers. The similarity function is shown to be equal to the dimensionless streamwise velocity when the Prandtl and Schmidt numbers are both equal to unity. The remaining governing relations are then transformed to the Blasius plane in which the velocity field has known solutions. The energy equation is solved by an iteration process; a general analytic solution for the N'th approximation is obtained. The analytic techniques developed are applied to the problems of combustion within laminar mixing regions and boundary layers. Temperature and concentration profiles are calculated and the dependence of the characteristic stay time upon the parameters of the system is determined. The application of the similarity techniques to the problem of chemical reaction within a hypersonic boundary layer is briefly discussed in an Appendix.

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