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Combustion research is at the forefront of development of clean and efficient IC engines, gas turbines, rocket propulsion systems etc. With the advent of faster computers and parallel programming, computational studies of turbulent combustion is increasing rapidly. Many turbulent combustion models have been previously developed based on certain underlying assumptions. One of the major assumptions of the models is the regime it can be used for: either premixed or non-premixed combustion. However in reality, combustion systems are multi-regime in nature, i.e.,\ co-existence of premixed and non-premixed modes. Thus, there is a need for development of multi-regime combustion models which closely follows the physics of combustion phenomena. Much of previous modeling efforts for multi-regime combustion was done using flamelet-type models. As a first, the current study uses the highly robust transported Probability Density Function (PDF) method coupled with Large Eddy Simulation (LES) to develop a multi-regime model. The model performance is tested for Sydney Flame L, a piloted methane-air turbulent flame. The concept of flame index is used to detect the extent of premixed and non-premixed combustion modes. The drawbacks of using the traditional flame index definition in the context of PDF method are identified. Necessary refinements to this definition, which are based on the species gradient magnitudes, are proposed for the multi-regime model development. This results in identifying a new model parameter beta which defines a gradient threshold for the calculation of flame index. A parametric study is done to determine a suitable value for beta, using which the multi-regime model performance is assessed for Flame L by comparing it against the widely used non-premixed PDF model for three mixing models: Modified Curl (MCurl), Interaction by Exchange with Mean (IEM) and Euclidean Minimum Spanning Trees (EMST). The multi-regime model shows a significant improvement in prediction of mean scalar quantities compared to the non-premixed PDF model when MCurl mixing model is used. Similar improvements are observed in the multi-regime model when IEM and EMST mixing models are used. The results show potential foundation for further multi-regime model development using PDF model.

<div>Studies of turbulent combustion in the past mainly focus on problems with single-regime combustion. In practical combustion systems, however, combustion rarely occurs in a single regime, and different regimes of combustion can be observed in the same system. This creates a significant gap between our existing knowledge of combustion in single regime and the practical need in multi-regime combustion. In this work, we aim to extend the traditional single-regime combustion models to problems involving different regimes of combustion. Among the existing modeling methods, Transported Probability Density Function (PDF) method is attractive for its intrinsic closure of treating detailed chemical kinetics and has been demonstrated to be promising in predicting low-probability but practically important combustion events like local extinction and re-ignition. In this work, we focus on the model assessment and advancement of the Large Eddy Simulation (LES)/ PDF method in predicting turbulent multi-regime combustion.</div><div><br></div><div><div>Two combustion benchmark problems are considered for the model assessment. One is a recently designed turbulent piloted jet flame that features statistically transient processes, the Sydney turbulent pulsed piloted jet flame. A direct comparison of the predicted and measured time series of the axial velocity demonstrates a satisfactory prediction of the flow and turbulence fields of the pulsed jet flame by the employed LES/PDF modeling method. A comparison of the PLIF-OH images and the predicted OH mass fraction contours at a few selected times shows that the method captures the different combustion stages including healthy burning, significant extinction, and the re-establishment of healthy burning, in the statistically transient process. The temporal history of the conditional PDF of OH mass fraction/temperature at around stoichiometric conditions at different axial locations suggests that the method predicts the extinction and re-establishment timings accurately at upstream locations but less accurately at downstream locations with a delay of burning reestablishment. The other test case is a unified series of existing turbulent piloted flames. To facilitate model assessment across different combustion regimes, we develop a model validation framework by unifying several existing pilot stabilized turbulent jet flames in different combustion regimes. The characteristic similarity and difference of the employed piloted flames are examined, including the Sydney piloted flames L, B, and M, the Sandia piloted flames D, E, and F, a series of piloted premixed Bunsen flames, and the Sydney/Sandia inhomogeneous inlet piloted jet flames. Proper parameterization and a regime diagram are introduced to characterize the pilot stabilized flames covering non-premixed, partially premixed, and premixed flames. A preliminary model assessment is carried out to examine the simultaneous model performance of the LES/PDF method for the piloted jet flames across different combustion regimes.</div><div><br></div><div>With the assessment work in the above two test cases, it is found that the LES/PDF method can predict the statistically transient combustion and multi-regime combustion reasonably well but some modeling limitations are also identified. Thus, further model advancement is needed for the LES/PDF method. In this work, we focus on two model advancement studies related to the molecular diffusion and sub-filter scale mixing processes in turbulent combustion. The first study is to deal with differential molecular diffusion (DMD) among different species. The importance of theDMD effects on combustion has been found in many applications. However, in most previous combustion models equal molecular diffusivity is assumed. To incorporate the DMD effects accurately, we develop a model called Variance Consistent Mean Shift (VCMS) model. The second model advancement focuses on the sub-filter scale mixing in high-Karlovitz (Ka) number turbulent combustion. We analyze the DNS data of a Sandia high-Ka premixed jet flame to gain insights into the modeling of sub-filter scale mixing. A sub-filter scale mixing time scale is analyzed with respect to the filter size to examine the validity of a power-law scaling model for the mixing time scale.</div></div>