Interrelation Between Dilatation Rate and Displacement Speed in Premixed Turbulent Flames

The interrelation between displacement speed and dilatation rate in premixed turbulent flames has been analysed using three-dimensional Direct Numerical Simulation (DNS) data. The study focuses on statistically planar turbulent premixed flames with single-step chemistry at a unity Lewis number, representing stoichiometric methane-air premixed combustion, and detailed chemistry NH₃-air premixed flames with an equivalence ratio of 1.2. It has been shown analytically that the dilatation rate based on fluid velocity is proportional to the product of the density-weighted displacement speed and the reaction progress variable gradient for unity Lewis number adiabatic conditions. This is demonstrated using unity Lewis number single-step chemistry DNS data and detailed chemistry DNS results of NH₃-air premixed flames with an effective Lewis number close to unity. The study reveals that density-weighted displacement speed positively correlates with dilatation rate based on fluid velocity, though the relationship is non-linear due to the non-linear relationship between density-weighted displacement speed and the reactive scalar gradient magnitude. The density-weighted displacement speed and the dilatation rate based on flame propagation velocity are negatively correlated for the flames belonging to the wrinkled/corrugated flamelets regime, while their joint PDFs in thin reaction zones regime flames show both positive and negative correlation branches. The curvature stretch rate primarily causes these positive and negative correlation branches, a tendency that strengthens with an increase in Karlovitz number. Additionally, the mean dilatation rate in premixed turbulent flames is found to be proportional to the mean reaction rate in Reynolds Averaged Navier-Stokes simulations, suggesting that the mean dilatation rate could be linked to mean reaction rate closure.