Correction to: Direct Numerical Simulation of head-on quenching of statistically planar turbulent premixed methane-air flames using a detailed chemical mechanism

Correction to: Flow Turbulence Combust

https://doi.org/10.1007/s10494-018-9907-5

In Lai et al. [1] the distributions of reaction progress variable c, non-dimensional temperature $T=(\hat {T}-T_{0})/(T_{ad}-T_{0})$ (where $\hat {T}$ is the instantaneous dimensional temperature, T₀ is the unburned gas temperature and T_ad is the adiabatic flame temperature), normalised heat release rate ${{\Omega }}_{\mathrm {T}}=\dot {\omega }_{\mathrm {T}}\times \delta _{\text {th}}/(\rho _{0}S_{\mathrm {L}}C_{\mathrm {p0}}T_{0})$ (where $\dot {\omega }_{\mathrm {T}}$ is the dimensional heat release rate) and normalised reaction rate of reaction progress variable $\mathrm {{\Omega } }_{c}=\dot {\omega }\times \delta _{\text {th}}/\rho _{0}S_{\mathrm {L}}$ (where $\dot {\omega }$ is the reaction rate of reaction progress variable) in the wall normal direction are shown in Fig. 3 at different time instants for laminar flames using detailed (16 species, 25 reaction steps) [2] and single-step chemical mechanisms (i.e. cases A and B respectively) with ρ₀,C_p0S_L and δ_th being the unburned gas density, mixture specific heat at constant pressure in the unburned gas, unstrained laminar burning velocity and the thermal flame thickness, respectively. Unfortunately, in Fig. 3 of [1] the distributions of reaction progress variable c and non-dimensional temperature T got interchanged for the simple chemistry case B. It was an error in plotting, and this error did not affect any of the results and conclusions in the paper [1]. The revised figure is shown below as Fig. 1 where distributions of c, T, Ω_T and Ω_c in the wall normal direction are shown for cases A (detailed chemistry) and B (single-step chemistry). The non-dimensional temperature T remains 0 at the wall (i.e. x₁/δ_th = 0) due to Dirichlet boundary condition (i.e. temperature at the wall corresponds to the unburned gas temperature) for both cases A and B. However, the value of c increases with time at the wall with the progress of head-on quenching for both cases A and B due to zero gradient boundary condition in the wall normal direction.

Fig. 1

Variations of c, T, Ω_T and Ω_c with x₁/δ_th at different time instants for laminar head-on quenching for both detailed (a) and simple (b) chemistry cases