## Abstract

Three-dimensional compressible Direct Numerical Simulation (DNS) data of freely propagating statistically planar and statistically stationary slot-jet turbulent premixed flames has been used to assess the accuracy of the isotropy-derived correction factors, which relate the two-dimensional projections of the different terms of the Favre-averaged scalar dissipation rate transport equation with their corresponding actual threedimensional counterparts. The accuracy of these correction factors is assessed using both simplified and detailed chemistry-based DNS data, for a range of values of Karlovitz number Ka, heat release parameter s, and turbulent Reynolds number R_{et}. It is shown that the isotropic distribution of the probability density function (pdf) of the angle,between the normal vectors of the measurement plane and of the flame surface provides a simple algebraic relation between the scalar dissipation rates evaluated in two and three dimensions (i.e. Nc and N^{2D}_{c} ), independent of the considered values of Ka, t and Ret. The isotropic relations between two-dimensional and three-dimensional counterparts of the curvature and propagation terms in the transport equation of eNc are also found to work well for all the values of Ka, t and Ret considered here. However, the relation between the value obtained from two-dimensional projection and the true three-dimensional value for the strain rate term in the N_{c} transport equation works well only for large values of Ret and the reasons for this behaviour are explained in detail. It is found that the threshold value of Ret above which the assumption of isotropy yields an accurate relation between two-dimensional projection and three-dimensional values for the strain rate term of the dissipation rate transport equation depends on the regime of the prevailing combustion process.

Original language | English |
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Pages (from-to) | 1151-1162 |

Number of pages | 12 |

Journal | Proceedings of the Combustion Institute |

Volume | 34 |

Issue number | 1 |

DOIs | |

State | Published - 2013 |

### Funding

NC and NS acknowledge the support of ESPRC. The work at Sandia National Laboratories was supported by the Division of Chemical Sciences, Geosciences and Biosciences, the Office of Basic Energy Sciences, the U. S. Department of Energy (DOE). This research used resources of the National Center for Computational Sciences at Oak Ridge National Laboratory (NCCS/ORNL) which is supported by the Office of Science of the DOE under contract No. DE-AC05-00OR22725. ERH acknowledges the support of the Australian Research Council.

## Keywords

- Direct Numerical Simulation
- Isotropy
- Reynolds-Averaged Navier-Stokes (RANS) simulation
- Scalar dissipation rate (SDR)
- Two-dimensional experimental measurements