Quasi-Steady Diffusion Flame Theory with Variable Specific Heats and Transport Coefficients

Abstract

A theory is developed to account for the variable nature of the specific heats C and the transport coefficients of thermal and mass diffusion, λ and D, in quasi-steady one-dimensional diffusion flames, using bipropellant droplet combustion as an illustration. In the theory C, λ and D are all temperature dependent whereas C and λ are further concentration-weighted; consequently all the existing variable-property droplet combustion models are special cases of the present generalized model. By allowing these coefficients to assume realistic functional forms, explicit expressions are derived for the concentration-weighted coefficients, the temperature and species profiles, the mass burning rate, and the flame-front standoff ratio. Predicted results yield improved, yet much less ambiguous, agreement with experimental observations. Finally it is shown that such good agreement can also be achieved by utilizing a simplified, temperature-independent, model and by evaluating the concentration-weighted coefficients at the arithmetic mean of the boundary temperatures in each diffusive-convective region.