Transition on a flat plate with a semi-circular leading edge under uniform and positive shear free-stream flow

Abstract

The effect of the free-stream velocity profile on the transition from laminar to turbulent flow on a flat plate was studied experimentally and numerically and it is presented in this paper. The flows investigated are based on the T3L test case of the ERCOFTAC Special Investigation Group for transition. According to this test case, the boundary layer development on a flat plate with a semi-circular leading edge is examined by means of transition due to separation, under various free-stream conditions concerning the turbulence intensity and velocity magnitude. In the present work, two free-stream velocity distributions were studied. The first was a uniform velocity one and the second, with a mean shear velocity profile with positive gradient, ∂ U/ ∂y=27.7 s −1. Measurements using hot-wire anemometry were taken in two primary regions: far upstream of the flat plate to observe the velocity and turbulence distributions and near the flat plate to capture the boundary layer development and the transition phenomenon. The effect of the two free-stream velocity distributions was studied and it was shown that for both velocity distributions a recirculation region of the flow occurred near the flat plate wall that led to transition dominated by the boundary layer separation. For the positive velocity gradient the separation region was smaller compared to the case of uniform free-stream profile. Both cases were also studied computationally. Two widely used linear eddy-viscosity turbulence models, the k– ε and the k– ω with specific low Reynolds formulations were applied and in addition, a non-linear eddy-viscosity based on the k– ε model has been implemented. In general, all the k– ε models gave satisfactory predictions for both flow cases regarding the predicted velocity distributions, while the k– ω model gave poor results. Concerning the longitudinal Reynolds stress distributions in the near-wall region, the non-linear k– ε model gave the best predictions inside the separation zone but it over predicted the corresponding values beyond the reattachment point while beyond the separation the linear models predicted the longitudinal stresses in a more satisfactory way.