Linear forcing in physical space for premixed turbulent combustion

In the present paper, improvements of the linear forcing method in physical space are developed for both isotropic and anisotropic turbulence. The enhancements achieved are then applied to direct numerical simulations of premixed methane-air flame simulations with inflow-outflow conditions. The first enhancement introduces an individual forcing scheme for each momentum equation, which – unlike previous approaches – removes the constraint that the three space-averaged normal Reynolds stresses must increase or decrease synchronously in time. The second enhancement targets engineering applications involving premixed flames with inflow-outflow conditions. Here, the linear forcing scheme is extended for a flow in a divergent domain, enabling the flame to better stabilise within the computational domain. The third enhancement involves adapting the linear forcing scheme for anisotropic turbulence and applying it to a flame within the divergent domain. Results show that the proposed enhancements – each based on the numerical scheme suggested by Bassenne et al. (2016, Physics of Fluids 28, 035114) – are computationally inexpensive, requiring only 0.26% of the total CPU-time of the simulation. Moreover, it is demonstrated that for anisotropic turbulence, starting from isotropic conditions, the normal Reynolds stresses attain the prescribed levels rapidly, within just one characteristic time interval. When applied to the premixed flame setup, the proposed scheme is used only in the cold, near-inflow region of the domain, which continuously changes shape and size depending on the instantaneous flame position. Results show that with the proposed forcing scheme, the cold volume occupies only a small portion of the domain (11.5–18.0%), demonstrating its numerical efficiency. The consumption flame speed correlates well with the energy dissipation rate (correlation coefficient of 0.86) but negatively with the integral length scale (correlation coefficient of − 0.70). Anisotropic turbulence of the same intensity reduces the consumption speed by a factor of 1.11.