Displacement-thickness based recycling inflow generation method for spatially developing turbulent boundary layer simulations

A displacement thickness based inflow generation method, for simulation of developing turbulent boundary layer, is proposed. Following existing rescaling/recycling methods, velocities from a plane sufficiently downstream of the inlet are recycled back and used as the inflow after re-scaling based on inner and outer length scales. The inner length scale is based on the viscous length scale (for smooth walls) or surface specific scales (for rough walls). Prior recycling methods for smooth and rough boundary layers typically use δ₉₉ as the outer length-scale. Since δ₉₉ is a threshold based quantity, it is strongly dependent on the mean velocity profile and can have large undesired fluctuations, particularly if the profile shape is atypical or unsteady. Here the use of profile integrated quantities such as the displacement thickness (δ₁) to obtain a’ surrogate’ for δ₉₉ is proposed, in order to mitigate the adverse effects of having to determine the outer scale from a point-wise measurement of the mean velocity profile. The outer length scale at downstream plane is determined based on the local displacement thickness and higher-order moments of the integrated velocity profile. The inlet displacement thickness is fixed at a desired value and the outer length scale at the inlet is determined through iterations. The use of high-order moments of the velocity profile is tested a-priori on DNS of developing boundary layer data. Also, an initial application to LES over a surface with roughness elements is presented.