EnKF-Based Dynamic Estimation of Separated Flows with a Low-Order Vortex Model

Abstract

A data-driven vortex model of the unsteady aerodynamics of a two-dimensional separated flow is constructed. The vortex model relies on a standard collection of regularized vortex elements that interact mutually and with an infinitely-thin flat plate. In order to maintain a low-dimensional representation, with fewer than O(100) degrees of freedom, a novel aggregation procedure is developed and utilized in which vortex elements are coalesced at each time step. A flow state vector, composed of vortex elements properties as well as the critical leading-edge suction parameter of Ramesh and Gopalarathnam (J. Fluid Mech., 2014), is advanced within an ensemble Kalman filter (EnKF) framework. In this framework, surface pressure measurements, sampled from a truth case, are used to correct the states of an ensemble of randomly-initiated vortex element models. The estimation algorithm is applied to several scenarios of a flat plate impulsively started at 20 degrees angle of attack at Reynolds number 500, in which the truth case comprises a high-fidelity Navier–Stokes simulation. The algorithm provides a good estimate of the flow as well as the aerodynamic force in both the baseline undisturbed case (a separated flow) as well as in the presence of one or more incident gusts, despite lack of a priori knowledge of the incident gust character.