Comparison of experiments and simulations for zero pressure gradient turbulent boundary layers at moderate Reynolds numbers

Abstract

A detailed comparison between recent direct numerical simulation (DNS) and experiments of a turbulent boundary layer under zero pressure gradient at Re θ = 2,500 and 4,000 (based on the free-stream velocity and momentum-loss thickness) is presented. The well-resolved DNS is computed in a long spatial domain (Schlatter and Orlu in J Fluid Mech 659:116, 2010a), including the disturbance strip, while the experiments consist of single hot-wire probe and oil-film interferometry measurements. Remarkably, good agreement is obtained for integral quantities such as skin friction and shape factor, as well as mean and fluctuating streamwise velocity profiles, higher-order moments and probability density distributions. The agreement also extends to spectral/structural quantities such as the amplitude modulation of the small scales by the large-scale motion and temporal spectral maps throughout the boundary layer. Differences within the inner layer observed for statistical and spectral quantities could entirely be removed by spatially averaging the DNS to match the viscous-scaled length of the hot-wire sensor, thereby explaining observed differences solely by insufficient spatial resolution of the hot-wire sensor. For the highest Reynolds number, Re θ = 4,000, the experimental data exhibit a more pronounced secondary spectral peak in the outer region (y/δ 99 = 0.1) related to structures with length on the order of 5–7 boundary layer thicknesses, which is weaker and slightly moved towards lower temporal periods in the DNS. The cause is thought to be related to the limited spanwise box size which constrains the growth of the very large structures. In the light of the difficulty to obtain “canonical” flow conditions, both in DNS and the wind tunnel where effects such as boundary treatment, pressure gradient and turbulence tripping need to be considered, the present cross-validation of the data sets, at least for the present Re θ -range, provides important reference data for future studies and highlights the importance of taking spatial resolution effects into account when comparing experiment and DNS. For the considered flow, the present data also provide quantitative guidelines on what level of accuracy can be expected for the agreement between DNS and experiments.