Analysis of Low-frequency Unsteadiness in Separated Flows Using Vorticity Variants

Separated flows exhibit low-frequency unsteadiness (LFU), characterized by oscillationsat time scales much longer than the primary flow dynamics (such as vortex shedding and convection in the boundary layer). Despite secondary in amplitudes and frequencies, the LFU is practically important since it is usually manifested as long-time modulation in integral quantities, such as heat transfer, drag force, pressure loading, all of which have significant implications for the performance and robustness of the underlying flow device/system. The physical mechanism responsible for LFU is still not fully understood. Existing theories, models, and descriptions are often qualitative and heuristic, leading to ongoing debates among them. In this dissertation work, a reduced-order analysis framework is developed to characterizethe LFU of separated flows. The framework interprets LFU as a consequence of kinetic energy imbalance in the separation bubble. The rotational form of the Navier–Stokes equations, which involves several terms derived from vorticity (hence vorticity variants), is used to formulate the kinetic energy evolution in separation bubble, motivated by their connections to vorticity transport and vortical motions. Temporal low-pass filter is employed so that LFU much weaker in amplitude and lower in frequency than the primary flow dynamics can be extracted from the background flow for analysis. The developed framework is applied to four different separated flow cases, includingtwo- and three-dimensional laminar wake past a zero-thickness plate at a 90  angle of attack, oblique shock/turbulent boundary layer interaction, and supersonic transitional flow over a backward-facing step. Strong correlations are observed between the LFU and the filtered kinetic energy evolution in the separation bubble. Detailed analysis of the dynamics of kinetic energy evolution is conducted. Unsteadiness frequency is estimated quantitatively using a dimensional argument. A reduced-order model is extract from the time series data using a data-driven model discovery algorithm for the two-dimensional laminar wake case.