Diffusion Coefficients in Flames and Detonations With Constant Enthalpy

Abstract

It is found that the entropy per gram of mixture remains constant in a flame or a one‐dimensional chemically reacting gaseous flow system if all the binary diffusion coefficients are equal to each other and ${\mathcal{D}}_{\mathrm{ij}}{\mathrm{=\lambda /(C̄}}_p\mathrm{mn)}$ , where C̄_p is the specific heat at constant pressure per gram of the mixture, m is the average molecular weight of the mixture, and n is the number of moles per gram. This value for each of the binary diffusion coefficients corresponds to setting each of the Lewis numbers equal to unity. For detonations, or systems having large kinetic energy, the enthalpy (per gram) including kinetic energy remains constant if, in addition to the diffusion coefficients having this special value, the Prandtl number is equal to ¾. It is clear that the assumption of constant enthalpy should not be applied to hydrogen‐bromine or hydrogen‐oxygen flames where some coefficients of diffusion are very large and others very small. The constant enthalpy assumption is applied to unimolecular decomposition flames supported by the reaction A → sB′. It is found that, to a rough approximation, the flame velocity varies as the 1/12th power of s.