Analysis of the Evolution of the Surface Density Function During Premixed V-Shaped Flame–Wall Interaction in a Turbulent Channel Flow at 𝑅⁢𝑒𝜏 = 395

Abstract

The flame–turbulence interaction and statistical behavior of the surface density function (SDF; i.e. magnitude of the reaction progress variable gradient) in the vicinity of the wall for a stoichiometric methane-air flame are investigated using a three-dimensional direct numerical simulation of a turbulent premixed V-flame interacting with an isothermal inert wall in a fully developed turbulent channel flow at a friction Reynolds number 𝑅⁢𝑒𝜏 = 395. The results show that the mean SDF significantly decreases in the viscous sublayer in comparison to the corresponding values for the same reaction progress variable in the unstretched laminar flame. Moreover, the mean values of SDF for a given value of reaction progress variable decrease in the downstream direction with the progress of flame quenching in all zones of turbulent boundary layer. The effective normal strain rate 𝑎ₙᵉᶠᶠ (= 𝑎ₙ + 𝑛⋅∇𝑆𝑑), which acts to reduce the SDF as it increases, is much higher in the viscous sublayer than in the other layers. In the viscous sublayer, the contribution of the gradient of displacement speed in the flame-normal direction (𝑛⋅∇𝑆𝑑) to 𝑎ₙᵉᶠᶠ has been shown to dominate the fluid-dynamic normal strain rate (𝑎ₙ). This tendency is qualitatively similar to the previous findings for a V-flame interacting with an isothermal inert wall at 𝑅⁢𝑒𝜏 = 110. However, the maximum mean value of 𝘢ₙᵉᶠᶠ at 𝑅⁢𝑒𝜏 = 395 is approximately twice of that at 𝑅⁢𝑒𝜏 = 110, which causes a sharper drop in the SDF in the viscous sublayer at higher 𝑅⁢𝑒𝜏.