Effects of thermal expansion on moderately intense turbulence in premixed flames

The study aims at analytically and numerically exploring the influence of combustion-induced thermal expansion on turbulence in premixed flames. In the theoretical part, contributions of solenoidal and potential velocity fluctuations to the unclosed component of the advection term in the Reynolds-averaged Navier-Stokes equations are compared and a new criterion for assessing the importance of the thermal expansion effects is introduced. The criterion highlights a ratio of the dilatation in the laminar flame to the large-scale gradient of root-mean-square (rms) velocity in the turbulent flame brush. To support the theoretical study, direct numerical simulation (DNS) data obtained earlier from two complex-chemistry, lean H2-air flames are analyzed. In line with the new criterion, even at sufficiently high Karlovitz numbers, results show significant influence of combustion-induced potential velocity fluctuations on the second moments of the turbulent velocity upstream of and within the flame brush. In particular, the DNS data demonstrate that (i) potential and solenoidal rms velocities are comparable in the unburnt gas close to the leading edge of the flame brush and (ii) potential and solenoidal rms velocities conditioned to unburnt gas are comparable within the entire flame brush. Moreover, combustion-induced thermal expansion affects not only the potential velocity, but even the solenoidal one. The latter effects manifest themselves in a negative correlation between solenoidal velocity fluctuations and dilatation or in the counter-gradient behavior of the solenoidal scalar flux. Finally, a turbulence-in-premixed-flame diagram is sketched to discuss the influence of combustion-induced thermal expansion on various ranges of turbulence spectrum.