Modeling the displacement speed in the flame surface density method for turbulent premixed flames at high pressures

We propose a model of the local displacement speed for the large-eddy simulation (LES) of turbulent premixed combustion with the flame surface density (FSD) method. This model accounts for flame stretch and curvature effects in order to improve the prediction of LES-FSD for turbulent premixed flames with the non-unity Lewis number at high pressures. The proposed model is validated by a priori and a posteriori tests, with the direct numerical simulation (DNS) and LES-FSD of statistically planar turbulent premixed flames of lean hydrogen at 1 and 10atm and a range of turbulence intensities. The a priori test confirms that the proposed model accurately estimates the negative correlation of the displacement speed and the flame curvature. In the a posteriori test, the comparison of DNS and LES-FSD results demonstrates that the proposed model improves the prediction on the turbulent burning velocity and the turbulent flame thickness, compared with those from the existing displacement-speed model. The stretch effect in the present model leads to the rise of the turbulent burning velocity and the suppression of the "bending" phenomenon in LES-FSD, consistent with the DNS result.