Generating wall-bounded turbulent inflows at high Reynolds numbers

TL;DR

This paper introduces a novel inflow generation method for high Reynolds number turbulent boundary layers that reduces simulation costs by leveraging known spectral scaling laws, enabling accurate inflow conditions from lower Reynolds simulations.

Contribution

The authors develop a spectral scaling-based inflow generation technique that accurately predicts high-Reynolds turbulent boundary layers from lower-Reynolds data, significantly reducing simulation development length.

Findings

Skin friction coefficient within ±3.5% of precursor simulations.

Shape factor within ±0.5% of precursor simulations.

Order of magnitude reduction in development length.

Abstract

One of the main challenges in simulating high Reynolds number ($Re$) 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 $Re$ wall turbulence that leverages the known structure and scaling laws of TBLs, enabling shorter development lengths by providing rich input information. As observed from the inner-scaled pre-multiplied spectra of streamwise velocity, with an increase in $Re$ the outer region grows and occupies more of the spanwise wavenumber space in proportion to the increase in $Re$; while the inner region remains approximately the same. Exploiting this behavior, we generate high-$Re$ inflow conditions for a $\textit{target}$ $Re$ by starting from cross-stream velocity slices at a lower $\textit{base}$ $Re$. In spectral space, we identify the inner and outer region wavenumbers, and shift the outer-region components proportionally to the desired $Re$ increase. We closely examine the capability of this method by scaling a set of velocity slices at $Re_\theta=2240$ and $4430$ to $Re_\theta=8000$, and using them as inflow conditions for direct numerical simulations (DNS) of spatially developing TBLs growing from $Re_\theta=8000-9000$. The skin friction coefficient and shape factor predicted by the new method, regardless of the $\textit{base}$ $Re$ tested, is within $\pm3.5\%$ and $\pm0.5\%$, respectively, of that of a precursor simulation right from the inlet. Reynolds stresses match very well after approximately $8~\delta_{99_0}$. This gives an order of magnitude reduction in development length compared to other methods proposed in the literature.