A mixture-fraction-based hybrid binomial Langevin-multiple mapping conditioning model

Abstract

Generalized Multiple Mapping Conditioning (MMC) allows for the use of any physical quantity to represent the required reference variable provided that it delivers the desired behavior. The binomial Langevin model (BLM) has been shown to predict higher statistical moments with good accuracy. However, joint-scalar modeling for many scalars becomes problematic because scalar bounds must be specified as conditional on other scalars to preserve elemental balances. The resulting volumes in state space become exceptionally complex for realistic problem sizes. In the current work, this central difficulty is avoided by using only velocity and mixture fraction statistics from the BLM with the latter used as the MMC reference variable. The principal advantage of this method is that the implementation of the binomial Langevin mixture fraction is relatively straightforward and provides a direct physical link to MMC. The MMC model is closed using an augmented modified Curl's model where the selection of particle pairs for (turbulent) mixing ensures proximity in reference space and a corresponding closeness in physical space. The method is evaluated for a lifted methane jet flame undergoing auto-ignition in a vitiated coflow. Most of the major features of the flow are well reproduced and found to generally outperform other modeling approaches, including Large Eddy Simulations using simplified treatments of turbulence-chemistry interactions such as unsteady flamelet/progress variable descriptions.

The impact of molecular diffusion on auto-ignition in a turbulent flow

“…In the current case, comparisons with measurements of temperature, the OH radical, molecular oxygen, molecular hydrogen, carbon monoxide and the PDF of temperature are consistent with the above explanation of the impact of molecular diffusion in physical space. A comparison with results obtained by Wandel and Lindstedt [43] suggests that models for molecular mixing that enforce locality in composition space [20,21,23,55] can mitigate against short comings of simpler models in the treatment of molecular diffusion, particularly when applied in the context of moment based closures. The current work has shown that the developed approach is viable for well-resolved boundary layer flows and it can be expected that the same applies to the computation of premixed turbulent flame structures at high Da numbers [30,52].…”

“…The standard mixing time scale closure given in Eq. ( 15) with C ϕ = 2.3 [48] is applied here for consistency with previous work [42,43].…”

“…The flame has been extensively studied in the past through a range of models for mixing in composition space and different chemical reaction mechanisms by Cabra et al [41]. Gkagkas and Lindstedt [42] used a closure at the jointscalar level and comprehensive chemistry including low-temperature reactions, while Wandel and Lindstedt [43] used a mixture-fraction-based hybrid binomial Langevin-multiple mapping conditioning (BLM-MMC) to show improved predictions. The studies have shown that the main flame structure can be well predicted through JPDF approaches with results for molecular hydrogen and carbon monoxide typically less satisfactory.…”

Mixing in Turbulent Flows: An Overview of Physics and Modelling

“…Another advantage is that a number of constraints are respected, such as the boundedness, linearity, independence and the Gaussian limiting behaviour. In [89], a further study is reported on coupling the BLM with the multiple mapping conditioning (MMC) of [88]. The authors advocate the use of mixture fraction statistics in MMC to outperform other approaches, including those based on LES.…”

Impact of molecular mixing and scalar dissipation rate closures on turbulent bluff-body flames with increasing local extinction

“…Flames HM2 and HM3 have proved more challenging due to the enhanced probability of local extinction and the co-existence of diffusion flames and premixed gas pockets. Multiple Mapping Conditioning (MMC) [30] has also been used for diffusion flames [31] with local extinction [32] and has recently extended to premixed combustion [33]. Transported JPDF method [24][25][26]28] can in principle predict flames with high levels of local extinction as well as re-ignition.…”