Simulation and validation of a spatially evolving turbulent boundary layers up to Re_\theta = 8300

Authors: Eitel-Amor, G., Örlü, R., Schlatter, P.
Document Type: Article
Pubstate: Published
Journal: Int. J. Heat and Fluid Flow
Volume: 47   57-69
Year: 2014


Results of a finely resolved large-eddy simulation (LES) of a spatially developing zero-pressure-gradient turbulent boundary layer up to a Reynolds number of Re_\theta=8300 are presented. The very long computational domain provides substantial assessment for suggested high Reynolds number (Re) trends. Statistics, integral quantities and spectral data are validated using high quality direct numerical simulation (DNS) ranging up to Re_\theta=4300 and hot-wire measurements covering the remaining Re-range. The mean velocity, turbulent fluctuations, skin friction, and shape factor show excellent agreement with the reference data. Through utilisation of filtered DNS, subtle differences between the LES and DNS could to a large extent be explained by the reduced spanwise resolution of the LES. Spectra and correlations for the streamwise velocity and the wall-shear stress evidence a clear scale-separation and a footprint of large outer scales on the near-wall small scales. While the inner peak decreases in importance and reduces to 4% of the total energy at the end of the domain, the energy of the outer peak scales in outer units. In the near-wall region a clear k^-1 region emerges. Consideration of the two-dimensional spectra in time and spanwise space reveals that an outer time scale \lambda_t \approx 10 \delta_99/U_\infty, with the boundary layer thickness \delta_99 and free-stream velocity U_\infty, is the correct scale throughout the boundary layer rather than the transformed streamwise wavelength multiplied by a (scale independent) convection velocity. Maps for the covariance of small scale energy and large scale motions exhibit a stronger linear Re dependence for the amplitude of the off-diagonal peak compared to the diagonal one, thereby indicating that the strength of the amplitude modulation can only qualitatively be assessed through the diagonal peak. In addition, the magnitude of the wall-pressure fluctuations confirms mixed scaling, and pressure spectra at the highest Re give a first indication of a -7/3 wave number dependence.