A general study of counterflow diffusion flames at subcritical and supercritical conditions: Oxygen/hydrogen mixtures

A theoretical framework is established to study the effect of flow strain rate on counterflow diffusion flames for general fluids over the entire thermodynamic regime. The formulation accommodates fundamental thermodynamics and transport theories, along with detailed chemical mechanisms. Both steady and unsteady burning branches of a complete flame-response curve (the S-curve) are considered. An improved two-point flame-controlling continuation method is employed to solve the singularity problem at the turning points on the S-curve. As a specific example, oxygen/hydrogen flames are systematically investigated over a pressure range of 0.5-200 atm. The strain rate is varied from 102 to 108 s−1. Two different inlet temperatures for oxygen (120 and 300 K) and hydrogen (20 and 300 K) are treated to explore flame behaviors at the ideal-gas and cryogenic-liquid states. General flame similarities (in terms of flame temperature, flame thickness, species concentrations, reaction rates, and heat release rate) are developed in a normalized strain-rate space (a/aext) for the entire range of pressures under consideration. Quantitative mapping of flame properties from one pressure to another is obtained. In addition, an analytical model is developed to refine and elucidate a previously established relationship between the heat release rate and pressure and strain rate in the form of q̇∼p0.534a. The heat release rate, when normalized with respect to p0.534aext, correlates well with the normalized strain rate (a/aext). Both numerical and analytical results show that the extinction strain rate is approximately proportional to pressure; this allows for a priori mapping of flame solutions between different pressure conditions. This in turn will significantly improve the computational efficiency of combustion modeling using tabulated chemistry, including the flamelet, FGM, and FPI models. Cryogenic inlet temperature affects only the flame location, without discernibly modifying the flame structures, which suggests that the ideal-gas flame solutions can be used for flame tabulation.