Tracking the flapping motion of flow separation using pointwise measurement

In recent investigations of the unsteadiness of flow separation, time-resolved whole-field information, such as the temporal variation of reverse flow area and proper orthogonal decomposition modes, is commonly used to quantify the flapping motion of separation bubbles. In the present study, we explore the possibility of tracking the flapping motion of flow separation using only pointwise measurements. A generalized framework for designing the optimal number and positions of measurement points is presented and assessed using time-resolved particle image velocimetry measurement data for turbulent flow separations induced by a broad range of two- and three-dimensional surface-mounted bluff bodies. Two models are proposed to approximate the temporal variation of reverse flow area over the bluff bodies. These two models require only the mean reattachment length, mean velocity at the body height in the oncoming flow, and time-resolved single- or two-point measurements of streamwise velocity. The optimal location for the single-point model is in the rear part of the mean separation bubble around the highest elevation of the mean separating streamline. While the single-point model predicts the temporal variation of reverse flow area reasonably well, it consistently misidentifies the subdominant frequency of reverse flow area as the dominant one. For the two-point model, one measurement point is in the rear part of the mean separation bubble and the other measurement point is slightly downstream of the mean reattachment point. The two-point model reproduces the temporal variation as well as the dominant frequency of reverse flow area remarkably well. Overall, the present study proposes a simple and reliable method to track the temporal variation of reverse flow area and holds promise for the future development of active closed-loop flow control based on real-time flapping motion of separation bubbles.