A Priori Study of Inter-Scale Kinetic Energy Transfer and Energy Exchange in a Turbulent Premixed Flame

Velocity, pressure, and density fields computed in earlier three-dimensional direct numerical simulations of a statistically stationary, planar, one-dimensional, low-Mach-number hydrogen–air flame propagating in small-scale, moderately intense, spatially decaying turbulence are filtered out using top-hat filters of four different widths. Certain source/sink filtered terms in the transport equations for resolved and subfilter-scale kinetic energies are analyzed. These are (i) the rate of inertial transfer of kinetic energy between resolved and subfilter scales, (ii) baropycnal work, (iii) subfilter-scale velocity–pressure–gradient term, and (iv) subfilter-scale pressure–dilatation term. These filtered terms are averaged over transverse planes and time or conditioned to the filtered combustion progress variable. Results show that terms (i) and (ii) work to transfer kinetic energy from smaller to larger scales (backscatter) and from larger to smaller scales, respectively, with the baropycnal work dominating the former term. These trends are observed for mean and conditional terms. The mean velocity–pressure–gradient term is positive and works to increase subfilter-scale kinetic energy due to combustion-induced thermal expansion. The pressure–dilatation term changes its sign from negative to positive at the leading and trailing edges, respectively, of the turbulent flame brush. Under conditions of the present study, the magnitudes of the mean velocity–pressure–gradient and pressure–dilatation terms are smaller when compared to the baropycnal work. Probability Density Functions (PDFs) for the explored filtered terms exhibit long tails, are highly skewed, and are characterized by a large kurtosis, thus implying significant intermittency of inter-scale energy transfer and energy exchange between internal and kinetic energy in the flame. These PDFs indicate that the intermittency of the inter-scale energy transfer and energy exchange depends substantially on mechanisms and scales of energy injection.