Lagrangian and Eulerian probability density function methods for turbulent reacting flows

Transported probability density function (PDF) methods have been applied widely and effectively for modeling turbulent reacting flows. In most applications of PDF methods to date, Lagrangian particle Monte Carlo algorithms have been used to solve a modeled PDF transport equation. However, Lagrangian particle PDF methods are computationally expensive and are not readily integrated into conventional Eulerian CFD codes. Eulerian field PDF methods have been proposed as an alternative. Here a systematic comparison is performed among three methods for solving the same underlying modeled composition PDF transport equation: a consistent hybrid Lagrangian particle/Eulerian mesh (LPEM) method, a stochastic Eulerian field (SEF) method, and a deterministic Eulerian field method with a direct-quadrature-method-of-moments closure (a multi-environment PDF - MEPDF - method). The comparisons have been made in simulations of a series of three nonpremixed, piloted methane-air turbulent jet flames that exhibit progressively increasing levels of local extinction and turbulence-chemistry interactions: Sandia/Technische Universitat Darmstadt (TUD) flames D, E and F. The three PDF methods have been implemented using the same underlying CFD solver, and results obtained using the three methods have been compared using (to the extent possible) equivalent physical models and numerical parameters. Reasonably converged mean and rms scalar profiles are obtained using 40 particles per cell for the LPEM method or 40 Eulerian fields for the SEF method. Results from these stochastic methods are compared with results obtained using two- and three-environment MEPDF methods. The relative advantages and disadvantages of each method in terms of accuracy and computational requirements are explored and identified. In general, the results obtained from the two stochastic methods (LPEM and SEF) are very similar, and are in closer agreement with experimental measurements than those obtained using the MEPDF method, while MEPDF is the most computationally efficient of the three methods.;The advantages of Eulerian PDF methods over Lagrangian PDF methods are expected to be especially compelling for complex configurations with deforming computational meshes: e.g., in-cylinder flows in reciprocating-piston internal combustion engines. As a first step in that direction, a SEF PDF method has been coupled with a fuel spray model and a soot model, and initial simulations have been performed for constant-volume turbulent spray combustion under diesel-engine-like conditions. Differences in results of simulations with versus without the SEF PDF method suggest that consideration of turbulence-chemistry interactions is of prime importance. These and other findings are discussed in detail.