Velocity Spectra and Model Spectrum in Non-Premixed Jet Flames

TL;DR

This study analyzes velocity and dissipation spectra in turbulent non-premixed jet flames using DNS data, revealing scaling laws, spectral peak shifts, and proposing an adapted dissipation model spectrum.

Contribution

It provides new insights into spectral behaviors in turbulent flames and introduces an adapted 3D dissipation spectrum model based on DNS results.

Findings

Inertial range follows $\, ext{k}^{-5/3}$ scaling with $C_K=2.3.

Dissipation range exhibits $\, ext{exp}(eta ext{k})$ scaling with $eta=7.2$.

Normalized dissipation spectra peaks shift compared to non-reactive models.

Abstract

In this contribution, velocity and its dissipation spectra in turbulent non-premixed jet flames are investigated by using two Direct Numerical Simulation (DNS) databases of temporally evolving jets with different bulk jet Reynolds numbers. In the DNS differential diffusion and flame dynamics effects have been accounted for and the flames experience high levels of extinction followed by re-ignition. It turns out that the spectra extracted from different statistically homogeneous planes across the jets and selected times corresponding to various occurring flame regimes (extinction and re-ignition phases) collapse reasonably when normalized by Favre averaged turbulent quantities. Especially (1) in the inertial range, the $\kappa^{-5/3}$ power law is observed with the constant of proportionality of $C_{K}=2.3$. (2) In the dissipation range $\exp(\beta\kappa)$ scaling exists with $\beta=7.2$ (instead of $\beta=5.2$). (3) The location of the peak of the normalized 1D dissipation spectra is in a lower normalized waver number ($\approx 0.08$) compared to the peak of non-reactive model spectrum ($\approx 0.11$). (4) Finally, an adapted 3D dissipation model spectrum proposed which peaks at a normalized waver number $\approx 0.19$ (instead of $\approx 0.26$).