The modelling approach of turbulent reacting flows deals with the description of the complex interaction between turbulent transport processes and chemical reactions. Probability density function (PDF) methods have the main advantage to treat this interaction in closed form. However, the computational effort required to solve the chemical kinetics can limit its application in real combustion systems. This is particularly true when filtered density function (FDF) methods are applied in large eddy simulation (LES), due to the fine spatial discretisation and the large number of stochastic particles per cells required to guarantee an instantaneous accuracy. In the present work, the formulation of a hybrid method, which combines a LES with a conditional Reynolds-Average Navier-Stokes probability density function (RANS-PDF) method for non-premixed reacting flows is developed. The objective of the hybrid approach is to effectively incorporate a conditional composition RANS-PDF method to perform the turbulence-combustion closure in the LES, allowing a significant reduction of the computational costs. Under the assumption that the conditional variables undergo slower spatial variations than the corresponding filter variables, the conditional RANS-PDF can be solved on a coarser mesh than the LES, keeping the evaluation of the reaction rates within the RANS spatial resolution. The LES solves the filtered turbulent flow field, while the RANS-PDF provides the solution of the conditional composition-PDF, evolving Lagrangian particles on the time-averaged LES solution. As in other conserved scalar methods, the mixture fraction field is fundamental in the hybrid approach: it is used to determine the conditional variables in the RANS-PDF and to account for the combustion effects into the LES. Additionally, the averaged LES mixture fraction PDF including a sub-grid β distribution is applied to determine the mean reactive scalars from the conditional RANS-PDF solution. The development of consistent strategies for the two-way coupling between LES and RANS-PDF is addressed in this work. The time-averaged velocity and the resolved stress tensor are transferred from the LES to the RANS to accomplish the particle evolution and the turbulence closure; whereas an indirect conditional equivalent enthalpy method performs the density coupling from the particle solution back to the LES. Additionally, with the aim of further reducing the computational effort, a GPU-based ODE solver is included into the RANS-PDF algorithm to accelerate the integration of chemical reactions. Simulations of the Sandia flame series are performed to validate the hybrid method and to investigate its prediction ability under different turbulent combustion conditions. The sensitivity to some model parameters with different kinetic schemes is also analysed. The results show that the hybrid method is able to correctly predict the evolution of the flow field, the temperature and the reactive scalars as well as the amount of local extinction. The performance of the method is analysed in terms of computational costs and accuracy.    «

The modelling approach of turbulent reacting flows deals with the description of the complex interaction between turbulent transport processes and chemical reactions. Probability density function (PDF) methods have the main advantage to treat this interaction in closed form. However, the computational effort required to solve the chemical kinetics can limit its application in real combustion systems. This is particularly true when filtered density function (FDF) methods are applied in large eddy...    »