Keywords

Transported probability density function, Nonpremixed, Ethylene, Syngas, Mixing, Particle method

Abstract

Transported probability density function (TPDF) methods are well suited to modelling turbulent, reacting, variable density flows. One of the main challenges to the successful deployment of TPDF methods is accurately modelling the unclosed molecular mixing term. This study examines three of the most widely used mixing models: the Interaction by Exchange with the Mean (IEM), Modified Curl (MC) and Euclidean Minimum Spanning Tree (EMST) models. Direct numerical simulation (DNS) data-sets were used to provide both initial conditions and inputs needed over the course of the runs, including the mean flow velocities, mixing frequency, and the turbulent diffusion coefficient. The same chemical mechanism and thermodynamic properties were used, allowing the study to focus on the mixing model. The simulation scenario was a one-dimensional, nonpremixed, turbulent jet flame burning either a syngas or ethylene fuel stream that featured extinction and reignition. This test scenario was selected because extinction and reignition phenomena are sensitive to the mixing model. Three DNS cases were considered for both the syngas and ethylene cases with a parametric variation of Reynolds and Damköhler numbers, respectively. Extinction events became more prevalent with increasing Reynolds number in the syngas cases and with decreasing Damköhler number in the ethylene cases. The model was first tested with the mixing frequency defined from the dissipation rate and variance of mixture fraction. With this definition, for the syngas cases this study finds that the TPDF method is successful at predicting flame extinction and reignition using all three mixing models for the relatively lower and intermediate Reynolds number cases, but that all models under-predict reignition in the relatively higher Reynolds number case. In the ethylene fuelled cases, only the EMST mixing model correctly predicts the reignition event for the two higher Damköhler number cases, however, in the lowest Damköhler number case the EMST model over-predicts reignition and the IEM and MC models under-predict it. Mixing frequency was then modelled based on the turbulence frequency and a model constant CΦ, the ratio of scalar to mechanical mixing rates. The DNS cases were reexamined with this definition and the results suggested that the optimal value for CΦ is mixing model and case dependent. In particular, it was found in the ethylene case considered that reignition could be achieved with the IEM and MC models by adjusting the value of CΦ.

Original Publication Citation

Alex Krisman, Joshua C.K. Tang, Evatt R. Hawkes, David O. Lignell, Jacqueline H. Chen, A DNS evaluation of mixing models for transported PDF modelling of turbulent nonpremixed flames, Combustion and Flame, Volume 161, Issue 8, 2014, Pages 2085-2106, ISSN 0010-2180, https://doi.org/10.1016/j.combustflame.2014.01.009.

Document Type

Peer-Reviewed Article

Publication Date

2014-02-01

Publisher

Elsevier

Language

English

College

Ira A. Fulton College of Engineering

Department

Chemical Engineering

University Standing at Time of Publication

Full Professor

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