Mixing and chemical reaction in an idealied swirl chamber

A vorticity-based, low-Mach-number model for the simulation of combustion in closed chambers is constructed. The numerical scheme is based on a mixed finite-difference pseudo-spectral discretization of the governing equations. Discrete evolution equations are integrated in time using a predictor-corrector scheme, whereas discrete elliptic systems are inverted with the help of a fast-Poisson solver. The model is applied to analyze mixing and combustion in an idealized swirl cavity, which consists of the annular space between a spinning inner cylinder and a stationary outer cylinder. Attention is focused on the effect of partial mixing on the development of the reaction. To this end, we assume that the oxidizer and fuel are initially separated by a thin mixed region and carefully control mixing levels by varying the duration of the swirl-driven mixing period. The mixture is then ignited along the boundary of the inner cylinder. When premixing is complete, an axisymmetric flame front is established, and the reactants are consumed as the front propagates radially outward. When the charge is partially mixed, combustion in the early stages predominantly occurs within a nonuniform premixed front. As this nonuniform front approaches the outer cylinder, a transition to a distributed combustion regime occurs. Following the transition, the remaining fuel burns at a slow rate within nonpremixed flames that wrap around the inner cylinder. Results show that the mixing time has substantial effects on the pressure rise within the cavity and on the evolution of the burnt fraction and that these effects become more pronounced as the Damköhler number increases.