Large eddy simulation of a turbulent flame using tabulated chemistry with a novel multivariate PDF

ABSTRACT

A novel, efficient method to account for multivariate probability density functions (PDFs) in the context of the flamelet generated manifolds (FGM) approach in a large eddy simulation (LES) framework is presented and discussed. It consists of applying the ‘Correlation Set by Simulated Annealing (CSSA)’ algorithm on univariate samples of each control variable to recombine them into multivariate samples in joint space, while accounting for the needed covariances. This is done on the fly and on a cell-by-cell basis. Thereby, the assumption of statistical independence of the control variables has been relaxed. The PDF is represented in a discrete manner and the integration is replaced through ensemble averaging. Consequently, the shape of the PDF no longer appears in the look-up table. The algorithm has been validated in the context of LES calculations of two configurations. Compared to a conventional pre-integrated FGM approach, the required CPU time has increased only modestly.

KEYWORDS:

• Turbulent combustion
• large eddy simulation
• turbulence-chemistry interaction
• flamelet generated manifold
• multivariate joint probability density function
• simulated annealing

Acknowledgements

Our sincere thanks go to our colleague, Mr Cooper Welch, for proofreading the manuscript. Calculations for this research were conducted on the Lichtenberg high performance computer of the TU Darmstadt.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Alija Bevrnja http://orcid.org/0000-0002-4930-8634

Additional information

Funding

This work was funded through the ‘Excellence Initiative’ of the German Federal and State Governments and the Graduate School of Computational Engineering at Technische Universität Darmstadt as well as the DFG-Project TRR 150.

Notes on contributors

David Jesch

David Jesch received his elementary education in his homeland Hungary. He then proceeded to obtain an MSc in physics, followed by BSc in mechatronics engineering and MSc in fluid mechanics. Afterwards, he enrolled as a PhD student at the TU Darmstadt which he successfully finished in 2016. He always showed interest in astronomy, so soon after the completion of the PhD, he landed a job at the ESA (European Space Agency). His research work during his PhD was in the field of combustion modelling and using PDFs (Probability Density Functions) to describe sub-grid states.

Alija Bevrnja

Alija Bevrnja got his education in his hometown Sarajevo, Bosnia and Herzegovina. There, he received several prizes for above-average results. He enrolled at the TU Darmstadt to do combustion research under the leadership of prof. Janicka and prof. Sadiki, where he worked together with David Jesch and others. He is currently in the last phase of his PhD.

Francesca di Mare

Francesca di Mare, a professor of mechanical engineering and head of department at the Rhur University Bochum, conducts active research in the fields of numerical modelling and simulation of propulsion and energy transformation systems. With respectable experience working in applications-oriented projects also at the institute of propulsion engines (DLR Köln), her research includes turbulent reacting flows, non-ideal working fluids in turbomachinery, complex geometrical configurations (IC-engines, gas turbines, turbomachines, etc.), turbulent compressible combustion, etc. She published a number of scientific papers.

Johannes Janicka

Johannes Janicka, a professor of mechanical engineering of the Technical University of Darmstadt (TU-Da) and head of the institute of Energy and Power Plant Technology (EKT). His research interests focus on developing new techniques for modelling and simulating of combustion and energy systems (IC-engines, power plants, gas turbines) based on direct numerical simulation, RANS, Large Eddy Simulation, probability density function, etc. He published a large number of scientific papers. The application objects are especially power plants, gas turbines and IC-engines. He is initiating various research activities in Germany and involved in various European and international research cooperations as well as in various steering committees in Germany.

Amsini Sadiki

Amsini Sadiki, professor and leader of the numerical simulation and rheology group at the institute of Energy and Power Plant Technology (EKT) at the mechanical engineering department of the Technical University of Darmstadt (TU-Da). His research interests focus on developing new techniques for modelling and simulating of combustion and energy systems (IC-engines, power plants, gas turbines) based on direct numerical simulation, RANS, Large Eddy Simulation, probability density function, etc. Using the second law of thermodynamics he also analyses various engineering systems of applied fluid mechanics, applied thermodynamics, turbulent multiphase flows and non-Newtonian fluids. He published a large number of scientific papers and few books. He is involved in various European and international researches and collaborations.