Velocity Spectra and Model Spectrum in Non-Premixed Jet Flames

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 $\approx 0.26$).