Correlation of Surface Pressure and Vortical Flow Structures in an Unsteady Separating Flow

Controlling flow in an unsteady separating flow requires accurate information about the surface forces and the effect that vortical structures in the flow field have on those surface forces. A correlation between vortex passage and surface pressure is defined to determine appropriate locations for sensors on the surface of a square cylinder for control feedback. Data are generated using a large eddy simulation of flow over a square cylinder at Reynolds number of 21,000. The flow is decomposed using proper orthogonal decomposition (POD) based on the frequency and energy content of the velocity and pressure fields around the square cylinder. Two data sets are reconstructed from the POD: (i) the first two modes containing approximately 75% of the energy of the flow and representing the large scale wake oscillation, and (ii) higher order modes containing the remainder of the energy of the flow representing smaller scale features in the flow, such as those shed from the leading edge. Vortex detection using the Γ∗ function is performed on both data sets, where the Γ∗ function is an area-averaged measure of the swirl around each point in the flow. Vortices in the data set composed of the first two modes tend to be large scale features and oscillate with the same frequency as the bluff body wake oscillation. The vortices detected in the higher order modes are smaller and tend to be the vortical structures shed from the leading edge of the square cylinder and convected downstream. In both data sets, the correlation values increase from the leading edge to the trailing edge, indicating that the downstream half of the square cylinder is most affected by vortical structures in the flow. Based on the correlation values, the segments of the square cylinder surface closest to the trailing edge would be best for sensor location to provide input for flow control.