Mechanisms of transition and heat transfer in a separation bubble

Abstract

The laminar boundary layer on a flat surface is made to separate by way of aspiration through an opposite boundary, causing approximately a 25% deceleration. The detached shear layer transitions to turbulence, reattaches, and evolves towards a normal turbulent boundary layer. We performed the direct numerical simulation (DNS) of this flow, and believe that a precise experimental repeat is possible. The pressure distribution and the Reynolds number based on bubble length are close to those on airfoils; numerous features are in agreement with Gaster's and other experiments and correlations. At transition a large negative surge in skin friction is seen, following weak negative values and a brief contact with zero; this could be described as a turbulent re-separation. Temperature is treated as a passive scalar, first with uniform wall temperature and then with uniform wall heat flux. The transition mechanism involves the wavering of the shear layer and then Kelvin–Helmholtz vortices, which instantly become three-dimensional without pairing, but not primary Görtler vortices. The possible dependence of the DNS solution on the residual incoming disturbances, which we keep well below 0.1%, and on the presence of a ‘hard’ opposite boundary, are discussed. We argue that this flow, unlike the many transitional flows which hinge on a convective instability, is fully specified by just three parameters: the amount of aspiration, and the streamwise and the depth Reynolds numbers (heat transfer adds the Prandtl number). This makes comparisons meaningful, and relevant to separation bubbles on airfoils in low-disturbance environments. We obtained Reynolds-averaged Navier–Stokes (RANS) results with simple turbulence models and spontaneous transition. The agreement on skin friction, displacement thickness, and pressure is rather good, which we attribute to the simple nature of ‘transition by contact’ due to flow reversal. In contrast, a surge of the heat-transfer coefficient violates the Reynolds analogy, and is greatly under-predicted by the models.