Hybrid binomial Langevin-multiple mapping conditioning modeling of a reacting mixing layer

Abstract

A novel, stochastic, hybrid binomial Langevin-multiple mapping conditioning ͑MMC͒ model-that utilizes the strengths of each component-has been developed for inhomogeneous flows. The implementation has the advantage of naturally incorporating velocity-scalar interactions through the binomial Langevin model and using this joint probability density function ͑PDF͒ to define a reference variable for the MMC part of the model. The approach has the advantage that the difficulties encountered with the binomial Langevin model in modeling scalars with nonelementary bounds are removed. The formulation of the closure leads to locality in scalar space and permits the use of simple approaches ͑e.g., the modified Curl's model͒ for transport in the reference space. The overall closure was evaluated through application to a chemically reacting mixing layer. The results show encouraging comparisons with experimental data for the first two moments of the PDF and plausible results for higher moments at a relatively modest computational cost.

Turbulent burning velocity predictions using transported PDF methods

“…In the context of PDF methods, the former closure has been shown to result in significantly ðP 300%Þ lower turbulent burning velocities as compared to the modified Curl's or binomial Langevin models [10]. It can further be argued that mixing models that enforce locality in composition space [6,8] are better suited to handling combustion in the high Da number regime [2]. However, the modified Curl's model has been retained here for reasons of simplicity and computational cost.…”

“…Further details are provided in the review by Haworth [2]. One of the major closure challenges concerns transport in composition space with a range of models proposed [3][4][5][6][7][8] and compared [8][9][10][11][12][13]. Furthermore, the application of the approach typically features non-premixed flames and the number of studies with premixed reactants is much more limited.…”

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

“…Conditioning model has been proposed with the reference variable modeled by the mixture fraction from BLM. This approach promises to improve upon the applicability of the previous formulation [9,10], while resulting in a simpler implementation. The development of a universal methodology that imposes a physical condition on the fraction of particles to be mixed remains desirable.…”

“…The hybrid binomial Langevin-Multiple Mapping Conditioning (MMC) model [9,10] aims to combine some of the benefits of the binomial Langevin model (BLM) [11], such as predictions of higher statistical moments, with the benefits of the MMC approach [12], while overcoming at least some of the deficiencies associated with each individual model component. Previously, the hybrid model utilized a velocity component for mapping the MMC mixture fraction.…”

“…Arguably, the low n p ∆t limit of MMC behaves worse than EMST in terms of stranding: MMC is restricted to isolated pairs of particles, whereas in EMST interactions can occur between multiple par-8 ticles. The method used here and in related work [9,10,20,30] guarantees dissipation in the mixing process for smaller values of n p ∆t than methods that pair neighboring particles. Because the distance between particles in reference space is consequentially greater for individual particles than if they were neighboring, the amount of dissipation per mixing interaction and the number of paired particles must also be different.…”