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Influence of Thermal Expansion on Potential and Rotational Components of Turbulent Velocity Field Within and Upstream of Premixed Flame Brush

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Abstract

Direct Numerical Simulation (DNS) data obtained earlier from two statistically stationary, 1D, planar, weakly turbulent premixed flames are analyzed in order to examine the influence of combustion-induced thermal expansion on the flow structure within the mean flame brushes and upstream of them. The two flames are associated with the flamelet combustion regime and are characterized by significantly different density ratios, i.e. \(\sigma = 7.53\) and 2.5. The Helmholtz–Hodge decomposition is applied to the DNS data in order to extract rotational and potential velocity fields. Comparison of the two fields shows that combustion-induced thermal expansion can significantly change the local structure of the incoming constant-density turbulent flow of unburned reactants by significantly increasing the relative magnitude of the potential velocity fluctuations when compared to the rotational velocity fluctuations in the flow. Such effects are documented not only within the mean flame brush, but also well upstream of it. The effect magnitude is increased by the density ratio \(\sigma\), with the effects being well (weakly) pronounced at \(\sigma = 7.53\) (2.5, respectively). Moreover, the potential and rotational velocity fields can cause opposite variations of the local area of an iso-scalar surface \(c\left( {{\mathbf{x}},t} \right) = {\text{const}}\) within flamelets by generating the local strain rates of opposite signs.

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Notes

  1. While the Kolmogorov theory should not be applied to turbulence generated in the present DNS due to too low Reynolds number, weakly turbulent premixed combustion characterized by \(u^{{\prime }} /S_{L} = {\text{O}}\left( 1 \right)\) can occur at high \(Re_{t} \gg 1\) if a ratio of \(L/\delta_{L}\) is sufficiently large.

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Acknowledgements

ANL gratefully acknowledges the financial support by the Combustion Engine Research Center. VAS gratefully acknowledges the financial support by ONERA and by the Grant of the Ministry of Education and Science of the Russian Federation (Contract No. 14.G39.31.0001 of 13.02.2017).

Funding

This study was funded by the Combustion Engine Research Center (CERC) and the Ministry of Education and Science of the Russian Federation (Grant Number 14.G39.31.0001 of 13.02.2017).

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Authors and Affiliations

  1. Chalmers University of Technology, 41296, Gothenburg, Sweden

    A. N. Lipatnikov

  2. ONERA - The French Aerospace Lab., 91761, Palaiseau, France

    V. A. Sabelnikov

  3. Moscow State University, Moscow, Russian Federation

    N. V. Nikitin

  4. Teikyo University, Utsunomiya City, Tochigi Prefecture, 320-8551, Japan

    S. Nishiki

  5. Nagoya University, Nagoya, 464-8603, Japan

    T. Hasegawa

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  1. A. N. Lipatnikov
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Correspondence to V. A. Sabelnikov.

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Lipatnikov, A.N., Sabelnikov, V.A., Nikitin, N.V. et al. Influence of Thermal Expansion on Potential and Rotational Components of Turbulent Velocity Field Within and Upstream of Premixed Flame Brush. Flow Turbulence Combust 106, 1111–1124 (2021). https://doi.org/10.1007/s10494-020-00131-3

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