An Original Method for Computing Complex Non-Premixed Flows in Chemical Equilibrium

A novel method for computing chemical equilibrium reactions in three-dimensional reacting fluid flows is introduced in this paper. The originality of the method is that continuity equations are solved for the atomic densities rather than for the molecular species densities, as is the case for non-equilibrium flow calculations. The method is suited for applications to mixing flows in rocket engine combustors, where, due to the typical low convective speed, chemical reaction is best modeled as an equilibrium process. Equilibrium formulations usually describe the flow as a perfect, atomically uniform mix between the fuel and the oxidizer. This assumption tends to overpredict performance. Solving for the atomic densities permits the assumption of a flow in chemical equilibrium, and still allows for the spatial and temporal resolution of the molecular composition, pressure and temperature of the mixture. Properly accounting for the physical configuration of a rocket combustor, particularly the presence of separate fuel and oxidizer injectors, requires that the flow be treated as non-premixed. In this way, overall performance, and combustion instabilities, can be more accurately predicted. Transport phenomena due to molecular motion such as diffusion of the elemental masses, viscosity and conductivity are also considered, and their properties are modeled with the Chapman-Enskog theory. This study developed successively the equilibrium constants approach and the minimizations of Gibbs and Helmholtz free energies. Minimization of Helmhotz free energy was found to be the most appropriate method for Computational Fluid Dynamics (C.F.D.) implementation. In future works, we will implement this method to run test cases in parallel on the university cluster for the structured grid of a combustion chamber and exhaust nozzle of a rocket designed by the class of the thesis advisor