Separation angle for flow past a circular cylinder in the subcritical regime

Instantaneous and time-Averaged flow separation locations for the canonical case of flow past a circular cylinder are investigated through direct numerical simulations. It is found that the instantaneous movement of the upper/lower separation point on the cylinder surface is governed by a dynamic balance between the upper/lower separating shear layer and a shear layer generated at the back of the cylinder due to wake recirculation. It is also found that flow three-dimensionality contributes to an upstream movement of the time-Averaged separation point through the effect of the separating shear layer. For the three-dimensional flow, the disordered mode B flow structures developed in the separating shear layer (which is directly responsible for the flow three-dimensionality) would result in turbulent energy dissipation and, therefore, the separating shear layer is less rolled-up in the cross-flow direction, which weakens the effect of the separating shear layer in pushing the separation point downstream. The time-Averaged separation angle vs the Reynolds number (θs̄-Re) relationship is not monotonic over the three-dimensional wake transition regimes of Re = 190-270 since there is a transition sequence of different wake flow patterns with different levels of flow three-dimensionality. For Re ≥ 270, on the physical basis that the increasingly disordered mode B flow becomes the sole wake flow pattern, an empirical formula is proposed for the θs̄-Re relationship, i.e., θs̄=78.8+505Re-1/2 (270 ≤ Re â 10⁵).