Reconstruction and forecasting of the unsteady flow around a surface-mounted obstacle from sparse measurements
File(s)
Author(s)
Lu, Shengqi
Type
Thesis
Abstract
A data-driven algorithm is proposed for flow reconstruction and forecasting around a surface-mounted obstacle from sparse velocity and/or scalar measurements. More specifically, the algorithm is applied to the flow around a wall-mounted, two-dimensional, square prism and a three-dimensional, cube. To reduce the dimensionality of the problem, snapshots of flow and scalar fields are processed to derive POD modes and their time coefficients. Then a system identification algorithm is employed to build a reduced-order, linear, dynamical system for the flow and scalar dynamics. Optimal estimation theory is subsequently applied to derive a Kalman estimator to reconstruct the time coefficients of the POD modes from sparse measurements. An accurate estimation method is also developed using a time-delayed Hankel matrix. This new framework is effective not only at reconstructing the flow concurrent with the measurements, but also forecasting the future evolution of the flow from current sparse measurements.
Analysis of the flow and scalar spectra demonstrate that the flow field leaves its footprint on the scalar, thus extracting velocity from scalar concentration measurements is meaningful. The results show that remarkably good reconstruction of the flow statistics (Reynolds stresses) and instantaneous flow patterns can be obtained for the two-dimensional case using a very small number of scalar sensors (even a single sensor yields very satisfactory results). However, more scalar sensors are needed for the three-dimensional turbulent flow reconstruction around a cube. The Kalman estimator derived at one condition can also reconstruct with acceptable accuracy the unsteady flow fields at two nearby off-design conditions.
Analysis of the flow and scalar spectra demonstrate that the flow field leaves its footprint on the scalar, thus extracting velocity from scalar concentration measurements is meaningful. The results show that remarkably good reconstruction of the flow statistics (Reynolds stresses) and instantaneous flow patterns can be obtained for the two-dimensional case using a very small number of scalar sensors (even a single sensor yields very satisfactory results). However, more scalar sensors are needed for the three-dimensional turbulent flow reconstruction around a cube. The Kalman estimator derived at one condition can also reconstruct with acceptable accuracy the unsteady flow fields at two nearby off-design conditions.
Version
Open Access
Date Issued
2024-12-04
Date Awarded
2025-06-01
Copyright Statement
Attribution-NonCommercial 4.0 International Licence (CC BY-NC)
License URL
Advisor
Papadakis, Georgios
Publisher Department
Department of Aeronautics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)