Evolution of spatial correlations and spectra of velocity fluctuations during head-on interaction of premixed flames within turbulent boundary layers

The statistical behaviors of the two-point spatial correlations of the turbulent velocity fluctuations based on Reynolds decomposition, Favre decomposition, and density-compensated Favre decomposition have been analyzed at different wall-normal distances for different stages of head-on quenching of premixed flames due to wall heat loss within turbulent boundary layers. Using a Direct Numerical Simulation database for friction Reynolds numbers Reτ of 110 and 180, it has been demonstrated that Favre fluctuation-based correlations differ quantitatively from Reynolds and density-compensated Favre fluctuation correlations, particularly in the early stages of quenching and when the flame is away from the wall. Despite these differences, the overall qualitative trends remain unaffected by the choice of definition of spatial correlations. As quenching progresses, the quantitative differences reduce due to weakening thermal expansion effects and increasing presence of burned gas in the boundary layer. This effect is strongest for wall-normal velocity fluctuations, as flame-normal acceleration due to thermal expansion primarily influences this direction in this configuration. However, momentum redistribution due to this flame normal acceleration also impacts streamwise and spanwise velocity correlations. These effects manifest in the integral length scales derived from two-point spatial correlations, with their variations evolving as quenching progresses. The longitudinal integral length scale in the streamwise direction exhibits the highest peak value among all considered length scales. While qualitative behaviors of correlations and integral length scales remain largely unaffected by the variation in Reτ considered here, a higher Reτ results in a broader wavenumber range before viscous roll-off occurs in the one-dimensional velocity spectrum.