Generating wall-bounded turbulent inflows at high Reynolds numbers

One of the main challenges in simulating high Reynolds number (

) turbulent boundary layers (TBLs) is the long streamwise distance required for large-scale outer-layer structures to develop, making such simulations prohibitively expensive. We propose an inflow generation method for high

italic Re Re ${\textit{Re}}$

wall turbulence that leverages the known structure and scaling laws of TBLs. Pre-multiplied spectra of streamwise velocity show that with an increase in

italic Re Re ${\textit{Re}}$

the outer region grows and occupies more of the spanwise wavenumber space in proportion to the increase in

italic Re Re ${\textit{Re}}$

, while the inner region remains approximately the same. Exploiting this behaviour, we generate inflow conditions for a target

italic Re Re ${\textit{Re}}$

by starting from cross-stream velocity slices at a lower base

italic Re Re ${\textit{Re}}$

. In spectral space, we identify the inner- and outer-region wavenumbers, and shift the outer-region components proportionally to the desired

italic Re Re ${\textit{Re}}$

increase. We examine the capability of this method by scaling velocity slices at

italic Re Subscript theta Baseline equals 2240 Re θ = 2240 ${\textit{Re}}_\theta =2240$

and 4430 to

italic Re Subscript theta Baseline equals 8000 Re θ = 8000 ${\textit{Re}}_\theta =8000$

, and using them as inflow conditions for direct numerical simulations of TBLs growing in the range

italic Re Subscript theta Baseline equals 8000 minus 9000 Re θ = 8000 − 9000 $ {\textit{Re}}_\theta =8000-9000$

, with

italic Re Subscript theta Re θ ${\textit{Re}}_\theta$

being the Reynolds number based on the momentum-loss thickness

theta θ $\theta$

. The predicted skin friction coefficient and shape factor, regardless of the base

italic Re Subscript theta Re θ $ {\textit{Re}}_\theta$

tested, lie within

plus or minus 3.5 percent sign ± 3.5 % $\pm 3.5\,\%$

and

plus or minus 0.5 percent sign ± 0.5 % $\pm 0.5\,\%$

, respectively, of that of a precursor simulation right from the inlet. Reynolds stresses match very well after approximately

8 delta Subscript 99 Sub Subscript 0 8 δ 99 0 $8\,\delta _{99_0}$

. The development length in terms of the Reynolds stresses is approximately

8 delta Subscript 99 Sub Subscript 0 8 δ 99 0 $8\delta _{99_0}$

, where

delta Subscript 99 Sub Subscript 0 δ 99 0 $\delta _{99_0}$

is the boundary layer thickness at the inlet. This gives an order of magnitude reduction in development length compared with other methods proposed in the literature.