Numerical simulation of unsteady combustion using the transport element method

¹ Dept. of Mechanical Engineering University of Connecticut Storrs, CT 06269-3139, USA
² Dept. of Mechanical Engineering Massachusetts Institute of Technology Cambridge, MA 02139, USA

Abstract

The transport element method is described and implemented in the simulation of the non-premixed reacting shear layer. The method, a natural extention of the vortex element method, resolves the low Mach number variable density flow and the exothermic reacting field. The effect of combustion on the flow is accommodated by incorporating a volumetric expansion velocity component and by modifying the integration of the vorticity equation to include expansion-related and baroclinic terms. The reacting field equations describing a single step, irreversible, chemical reaction, are simplified by the introduction of Schvab-Zeldovich (SZ) conserved scalars whose transport is sufficient to compute the evolution of combustion in the case of infinite reaction rate. In the case of finite rate chemistry the evolution of one primitive scalar, the product mass-fraction, is also computed. The vorticity, conserved scalar gradient and product mass fraction are discretized amongst fields of transport elements. Their time evolution is implemented by advecting the elements at the local velocity while simultaneously integrating their transport equations along particle trajectories. The integration of the vorticity and the conserved scalar gradient equations is simplified using ideas from kinematics. A novel core expansion scheme that avoids the problems associated with the conventional implementation is used to simulate diffusion. Field quantities are obtained using convolutions over the elements. Results indicate that the method is able to accurately reproduce the essential features of the flow. Convergence of the solution in time is approximately linear. Moreover, the finite reaction rate solution at low Karlovitz number bear strong similarities to that of the infinite reaction rate model. This similarity is exploited in validating the part of the numerical methodology related to the integration of the product mass-fraction equation.