# Passive Front Propagation in Intense Turbulence: Early Transient and Late Statistically Stationary Stages of the Front Area Evolution

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## Abstract

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## 1. Introduction

## 2. Analysis and Results

#### 2.1. Earlier Transit Stage

#### 2.2. Statistically Stationary State

## 3. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${A}_{0}$ | initial surface area |

${A}_{F}$ | area of self-propagating front |

${A}_{M}$ | material surface area |

$D$ | fractal dimension |

$\overline{d}$ | mean distance between neighboring front elements |

$L$ | integral length scale of turbulence |

${L}_{G}$ | Gibson scale |

$\overline{l}$ | mean thickness of layer consumed by self-propagating front |

${l}_{0}={u}_{0}{\tau}_{K}$ | newly introduced microscale |

${\ell}_{in}$ | inner cut-off scale |

${\ell}_{out}$ | outer cut-off scale |

$R{e}_{L}$ | turbulent Reynolds number |

$t$ | time |

$u$ | velocity vector |

${u}^{\prime}$ | rms turbulent velocity |

${u}_{0}$ | speed of a self-propagating front |

${u}_{K}$ | Kolmogorov velocity |

${\overline{u}}_{T}$ | mean turbulent consumption velocity |

${V}_{F}$ | volume occupied by self-propagating front |

${V}_{M}$ | volume occupied by material surface |

${\mathsf{\Delta}}_{F}$ | streamwise dispersion of self-propagating front |

${\mathsf{\Delta}}_{M}$ | streamwise dispersion of material surface |

$\epsilon $ | viscous dissipation rate of turbulent kinetic energy |

${\eta}_{K}$ | Kolmogorov length scale |

$\nu $ | kinematic viscosity |

$\xi $ | constant |

${\tau}_{K}$ | Kolmogorov time scale |

${\tau}_{T}$ | turbulence time scale |

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**MDPI and ACS Style**

Sabelnikov, V.A.; Lipatnikov, A.N. Passive Front Propagation in Intense Turbulence: Early Transient and Late Statistically Stationary Stages of the Front Area Evolution. *Energies* **2021**, *14*, 5102.
https://doi.org/10.3390/en14165102

**AMA Style**

Sabelnikov VA, Lipatnikov AN. Passive Front Propagation in Intense Turbulence: Early Transient and Late Statistically Stationary Stages of the Front Area Evolution. *Energies*. 2021; 14(16):5102.
https://doi.org/10.3390/en14165102

**Chicago/Turabian Style**

Sabelnikov, Vladimir A., and Andrei N. Lipatnikov. 2021. "Passive Front Propagation in Intense Turbulence: Early Transient and Late Statistically Stationary Stages of the Front Area Evolution" *Energies* 14, no. 16: 5102.
https://doi.org/10.3390/en14165102