A probability density function method for turbulent mixing and combustion on three-dimensional unstructured deforming meshes

Abstract

A hybrid Lagrangian-Eulerian methodology is developed for numerical simulation of turbulent mixing and combustion in arbitrary three-dimensional time-dependent geometric configurations. The context is a probability density function (PDF) based approach intended for modelling in cylinder processes in reciprocating piston internal combustion (IC) engines. Issues addressed include mean estimation, particle tracking and particle number-density control on three-dimensional unstructured deforming meshes. The suitability of the methodology for statistically time-dependent three-dimensional turbulent flow with large density variations is demonstrated via simulations of turbulent freon vapour/air mixing on an unstructured deforming mesh representing an idealized IC engine [13]. Computed profiles of mean and r.m.s. freon mole fractions show good quantitative agreement with measurements. Moreover, inherent advantages of the Lagrangian-Eulerian PDF approach are demonstrated, compared to Eulerian finite volume solutions of an (approximately) equivalent set of moment equations. The new approach is, by design, compatible with existing computational fluid dynamics codes that are used for multidimensional modelling of in-cylinder thermal fluids processes. This work broadens the accessibility of PDF methods for practical turbulent combustion systems.