  Lean turbulent premixed hydrogen/air flames have substantially increased
flame speeds, commonly attributed to differential diffusion effects. In this
work, the effect of turbulence on lean hydrogen combustion is studied through
Direct Numerical Simulation using detailed chemistry and detailed transport.
Simulations are conducted at six Karlovitz numbers and three integral length
scales. A general expression for the burning efficiency is proposed which
depends on the conditional mean chemical source term and gradient of a progress
variable. At a fixed Karlovitz number, the normalized turbulent flame speed and
area both increase linearly with the integral length scale ratio. The effect on
the mean source term profile is minimal, indicating that the increase in flame
speed can solely be attributed to the increase in flame area. At a fixed
integral length scale, both the flame speed and area first increase with
Karlovitz number before decreasing. At higher Karlovitz numbers, the
diffusivity is enhanced due to penetration of turbulence into the reaction
zone, significantly dampening differential diffusion effects.
