Theoretical study of the expansion of Roper's theory on the laminar jet diffusion flame length in 2D and 3D in natural gas and hydrogen mixtures

Abstract

In this work, three mathematical models were developed to study the laminar jet diffusion flame in mixtures of natural gas, hydrogen, and CO2 by extending and applying Roper's theory. Model M1 consists of derivation of the Roper's original equation described in the two-dimensional steady state without convection, thus showing the theoretical equations for the length of the diffusion flame for burners with circular, square, and rectangular cross sections and for regimes in which the flames are dominated by the momentum effects, the buoyancy effect, and in the transition regime. Models M2 and M3 extend the Roper's original theory by deriving analytical solutions of the two- and three-dimensional diffusion flame equation with convection in steady and transient states, taking into account the spatially variable velocity and diffusion coefficients. The flame lengths obtained with models M1 and M2 were compared with model M3 by Relative Percentage Difference (RPD) considering 5 mixtures of NG-H2-CO2. For t = 0.1, the maximum RPD in the circular cross-section for M1 in Gas20:60%NG-25%H2–15%CO2 was 14.75%, while for M2 in Gas14:70%NG-15%H2–15%CO2 was 6.47% and the minimum RPD in Gas1:100%NG was 9.78% and 4.83% for M1 and M2, respectively. The same analysis was developed for the square and rectangular (Fr ≪ 1) cross-sections and showed good agreement. The model M3 was tested under transient conditions, studying the effects of time and velocity on the distribution of the profile in the radial direction, in order to better understand the flame phenomenon, which cannot be observed with the Roper's original model M1. Finally, the models M2 and M3 were validated with experimental results and other analytical solutions showing a good performance considering the characteristics of each mixture.