Experimental and numerical investigations of transition in a pressure-gradient-induced laminar separation bubble

A pressure-gradient-induced laminar separation bubble (LSB) was examined using wind-tunnel experiments, direct numerical simulations (DNS) and linear local/global stability analysis. The LSB was experimentally generated on a flat plate using the favourable-to-adverse pressure gradient imposed by an inverted modified NACA $64_3-618$ airfoil. Direct numerical simulation was performed using boundary conditions extracted from a steady precursor simulation of the entire flow field. Despite good agreement in the upstream boundary layer with the experiment, DNS exhibited an approximately 25 % longer mean separation bubble, attributed to an earlier onset of transition due to the free-stream turbulence (FST) in the experiment. Introducing a very low level of isotropic FST in the DNS, similar to that measured in the experiment, caused earlier transition, decreased the mean bubble length and led to a remarkably good agreement between the DNS and experiments. Differences were observed for the dominant frequencies in the experiment and DNS, but both were within the band of most amplified frequencies predicted by LST. Proper orthogonal decomposition confirmed that dominant coherent structures from DNS and experiments are related to the inviscid Kelvin–Helmholtz instability and have similar characteristics despite slight differences in frequency. Local and global stability and dynamic mode decomposition analysis corroborated the convective nature of the dominant two-dimensional (2-D) instability and showed that the LSB is globally unstable to a range of 3-D wavenumbers, in agreement with 3-D structures observed in experiments. Results confirmed the strong impact of very low FST levels on the LSB and indicate a close agreement of the time-averaged and instability characteristics between the experiments and DNS.