Analysis and simulation for a system of chemical reaction equations with a vortex formulation

Abstract

This work presents analytical and numerical results for the two dimensional molecular mixing and chemical reaction processes using a vortex formulation. The particular model studied here is the single-step, irreversible, exothermic Arrhenius type reaction c A + c B → c P , in an incompressible fluid under Neumann boundary conditions. We establish the existence of a unique classical solution considering the weak coupling of the reactants via advection by a independently developing velocity, and we prove the existence and uniqueness of the solution via a semigroup formulation and the maximum principle. For the numerical solution a second order accurate spatial finite difference scheme is used with a second order accurate Runge–Kutta method for the time step. The behaviour of the concentrations c A and c B , the temperature, the reaction rate, and product concentration c P , are obtained over a wide range of Reynolds and Damköhler numbers.