Ensemble Kalman filter for vortex models of disturbed aerodynamic flows

Abstract

The task of dynamic flow estimation is to construct an instantaneous approximation of an evolving flow, and particularly its response to disturbances, using measurements from available sensors. Building from previous work by Darakananda et al. [ Phys. Rev. Fluids 3, 124701 (2018)], we further develop an ensemble Kalman filter (EnKF) framework for aerodynamic flows based on an ensemble of randomly perturbed inviscid vortex models of flow about an infinitely thin plate. In the forecast step, vortex elements in each ensemble member are advected by the flow and new elements are released from each edge of the plate; the elements are modestly aggregated to maintain an efficient representation. The vortex elements and leading-edge constraint are corrected in the analysis step by assimilating the surface pressure differences across the plate measured from the truth system. We show that the overall framework can be physically interpreted as a series of adjustments to the position and shape of an elliptical region of uncertainty associated with each vortex element. In this work, we compare the previously used stochastic EnKF with the ensemble transform Kalman filter (ETKF), which uses a deterministic analysis step. We examine the response of the flat plate at ${20}^{\circ }$ in two perturbed flows, with truth data obtained from high-fidelity Navier-Stokes simulation at Reynolds number 500. In the first case, we apply a sequence of large-amplitude pulses near the leading edge of the plate to mimic flow actuation. In the second, we place the plate in a vortex street wake behind a cylinder. In both cases, we show that the vortex-based framework accurately estimates the pressure distribution and normal force, with no a priori knowledge of the perturbations or their structure. We show that, in each case, the ETKF is consistently more robust than the stochastic EnKF and is qualitatively better at representing the coherent structures of the true flow. Finally, we examine the mapping from measurements to state update in the analysis step through singular value decomposition of the Kalman gain.