Examination of probability distribution of mixture fraction in LES/FDF modelling of a turbulent partially premixed jet flame

Abstract

An accurate prediction of the probability density function (PDF) of the mixture fraction is crucial to the prediction of combustion since mixing plays an important role in turbulent non-premixed and partially premixed flames. This work provides an assessment of the large-eddy simulation (LES)/filtered density function (FDF) method for the prediction of the PDF of the mixture fraction. The advantage of the LES/FDF method is that it provides the full predictions of the statistical distribution of scalars including the mixture fraction. The predictive accuracy of the method for the PDF is yet to be fully validated. Assessing the prediction of the PDF of the mixture fraction, a conserved scalar, is an important starting point. The Sydney/Sandia inhomogeneous inlet jet flame is used as a test case. A quick comparison shows that the LES/FDF predicted PDF shapes of the mixture fraction deviate significantly from the commonly presumed Beta-PDF as well as from the experimental data in the flame. To examine the source of the discrepancy, we clarify the different PDF definitions used in the comparison among the predictions, measurements, and presumed shape PDFs. The discrepancy observed from the comparison is largely reconciled by clarifying the difference between the PDFs that are examined. The PDF of the resolved mixture fraction is shown to be close to the Beta-PDF in both the measurements and predictions, while the PDF directly deduced from the LES/FDF particles deviates significantly from the Beta-PDF. A multimodal PDF analysis and a pseudo convergence analysis are conducted to provide plausible evidence to support the predicted multimodal PDF shapes. The sub-filter scale FDF is shown to be close to the Beta-PDF too through the construction of a synthesised PDF, which supports the common presumed Beta-PDF assumption used in the presumed PDF methods when combined with LES.

Keywords:

• LES
• transported FDF
• mixture fraction
• PDF
• partially premixed flames

Acknowledgments

The views expressed herein do not necessarily represent the views of the U.S. Department of Energy or the United States Government. The research was supported in part through computational resources provided by Information Technology at Purdue University, West Lafayette, Indiana. We are grateful to Prof. Assaad Masri and Dr. Robert Barlow for providing us the experimental data for the inhomogeneous inlet jet flame.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was supported by the National Science Foundation under Grant No. CBET-1336075 and by the US Department of Energy's Office of Energy Efficiency and Renewable Energy (EERE) under the Vehicle Technologies Office, Award Number DE-EE0008876.