Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Scaling Laws for Thermodiffusively Unstable Lean Premixed Turbulent Hydrogen-Air Flames

M. Gauding T. Lehmann, T. L. Howarth, L. Berger, M. Rieth, A. Gruber, W. Song, J. H. Chen, M. Day, A. Attili, E. F. Hunt, A. J. Aspden, H. Pitsch

Abstract

Lean premixed hydrogen-air flames are strongly affected by thermodiffusive (TD) instabilities, which can alter the flame structure and enhance the local reactivity many-fold. Two recent models (Howarth et al. (Combust.~Flame 253, 2023) and Rieth et al. (MSC 2023)) describe the scaling of the stretch factor in turbulent hydrogen flames with the Karlovitz number using different parameters, i.e., the $ω_2$ parameter from linear stability theory and the ratio of the Zel'dovich to the Peclet number (${Ze}/{Pe}$). Using a comprehensive set of 91 direct numerical simulation (DNS) cases spanning a wide range of pressures, equivalence ratios, turbulence intensities, and flow configurations, both formulations are systematically evaluated and an adapted formulation is proposed. The analysis of the governing non-dimensional groups reveals a scaling behavior characterized by two distinct regimes. In the first regime, typically relevant for burner and gas turbine conditions, both models reduce to an identical form that depends solely on the Karlovitz number and the stretch factor of laminar flames, independent of $ω_2$ or ${Ze}/{Pe}$. In the second regime, characterized by ultra-low flame speeds, the explicit consideration of $ω_2$ or the ratio ${Ze}/{Pe}$ is required for accurate scaling. In both regimes, the two models predict the DNS data reasonably well and reduce to the same functional form of non-dimensional groups, indicating their physical equivalence.

Scaling Laws for Thermodiffusively Unstable Lean Premixed Turbulent Hydrogen-Air Flames

Abstract

Lean premixed hydrogen-air flames are strongly affected by thermodiffusive (TD) instabilities, which can alter the flame structure and enhance the local reactivity many-fold. Two recent models (Howarth et al. (Combust.~Flame 253, 2023) and Rieth et al. (MSC 2023)) describe the scaling of the stretch factor in turbulent hydrogen flames with the Karlovitz number using different parameters, i.e., the parameter from linear stability theory and the ratio of the Zel'dovich to the Peclet number (). Using a comprehensive set of 91 direct numerical simulation (DNS) cases spanning a wide range of pressures, equivalence ratios, turbulence intensities, and flow configurations, both formulations are systematically evaluated and an adapted formulation is proposed. The analysis of the governing non-dimensional groups reveals a scaling behavior characterized by two distinct regimes. In the first regime, typically relevant for burner and gas turbine conditions, both models reduce to an identical form that depends solely on the Karlovitz number and the stretch factor of laminar flames, independent of or . In the second regime, characterized by ultra-low flame speeds, the explicit consideration of or the ratio is required for accurate scaling. In both regimes, the two models predict the DNS data reasonably well and reduce to the same functional form of non-dimensional groups, indicating their physical equivalence.

Paper Structure

This paper contains 13 sections, 19 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Modeling the TD response
  3. Instability parameter $\omega_2$
  4. Peclet number $\mathit{Pe}$
  5. Turbulence-chemistry interaction
  6. Simulation data
  7. Scaling relations for the stretch factor $I_0$
  8. Scaling of the $\omega_2$-model
  9. Scaling of the $\mathit{Ze}/\mathit{Pe}$-model
  10. Unification of scaling laws
  11. Scaling laws for the low-pressure regime
  12. Scaling laws for the high-pressure regime
  13. Conclusion

Figures (6)

  • Figure 1: Enhancement of reactivity $I_0$ from the laminar freely propagating flame as a function of the Karlovitz number for all cases. Conditions in the high-pressure regime ($p> \Pi_c$) are highlighted in orange. Cases with $\omega_2 = 0$ are marked in red. The streamwise direction of the jet flames is indicated by an arrow.
  • Figure 2: Evaluation of the scaling relation given by Eq. \ref{['eq:TLH']}. Data with $\omega_2 = 0$ are highlighted in red, and data belonging to the high-pressure regime ($p > \Pi_c$) are highlighted in yellow. MAPE is the mean-absolute percentage error.
  • Figure 4: Parameterization of $I_0^*$ with $\mathit{Ze}$ and $\mathit{Pe}$. Conditions in the low-pressure regime are shown in black, conditions in the high-pressure regime are indicated in orange.
  • Figure 5: Evaluation of the scaling relations in the low- (top row) and high-pressure (bottom row) regimes. Left column: modified $\mathit{Ze}/\mathit{Pe}$-model from Eq. \ref{['eq:MRmod']}. Right column: $\omega_2$-model from Eq. \ref{['eq:TLH']}. Coloring as in Fig. \ref{['fig:scaling_tlh']}.
  • Figure 6: Comparison of the scaling coefficients in the high-pressure regime ($p>\Pi_c$) with one-dimensional simulations of unstretched premixed flames over a wide parameter space. Data points are colored by $\mathit{Ze}$. Red crosses indicate conditions considered in this study.
  • ...and 1 more figures