Bistable states and separation hysteresis in curved compression ramp flows

The separation hysteresis of the boundary layer induced by the variation of the angle of attack (AOA) is observed and investigated numerically in curved compression ramp (CCR) flows. The occurrence of this new phenomenon is based on the bistable states of CCR flows even for the same free-stream and boundary conditions, indicating that the boundary layer's state (attachment/separation) depends on its evolutionary history with AOA varying. Specifically, beginning with an attachment state, the boundary layer remains attached as AOA increases slowly and suddenly separates once AOA reaches a marginal angle alpha (s). However, if we decrease AOA back from this angle, the boundary layer will not attach and remain separated until AOA reaches a small enough angle alpha (a). The AOA extent [alpha (a), alpha (s)] is called the dual-solution region. Three characteristic adverse pressure gradients (APGs), I-sb, I-cw, and I-b, are proposed to explain the existence of this dual-solution region, where I-cw and I-sb (I-cw < I-sb) are induced by the curved wall and the separation bubble, respectively, and I-b is the maximum APG that the boundary layer can resist. (i) When I-b > I-sb, the flow must be attached, (ii) when I-b < I-cw, the flow must be separated, and (iii) when I-cw < I-b < I-sb, both of these two states are theoretically possible. Since AOA-variation can make (i), (ii), and (iii) occur alternately, it could induce the separation hysteresis of CCR flows, which has been observed in this paper.