School of Mechanical Engineering Seminar
Monday, June 3, 2019 at 14:00
Wolfson Building of Mechanical Engineering, Room 206
Data-Driven Modeling of Pitching and Plunging Wings in Single and Tandem Configurations in Hovering Flight
Victor Troshin
Academic Advisor:
Prof. Avi Seifert
The presented work addresses the challenges related to the low order dynamic modeling of the fluid domain with immersed moving solid bodies in it. In this work mathematical tools were developed and tested on numerical and experimental data. The ultimate goal of this work was to develop a methodology which enables a real-time flow field estimation based on a small number of sensors. As an example of such a problem, modeling of pitching and plunging wings in single and tandem configurations was chosen. In order to achieve the defined goal, the presented research was carried out in the three following stages:
In the first stage of the research, a proper orthogonal decomposition (POD) methodology for a flow field in a domain with moving boundaries was developed. In the standard POD approach, the properties of the region of the domain which alternatingly occupied by fluid and solid are not defined. Thus, here, prior to the decomposition, the domain with moving or deforming boundaries was mapped to a stationary domain using volume preserving mapping. This mapping was created by combining a transfinite interpolation and volume adjustment algorithm. The algorithm is based on an iterative solution of the Laplace equation with respect to the displacement potential of the grid points. At this stage of the research, the method was validated on CFD simulation of pitching and plunging ellipse in a still fluid.
The main goal of the second stage of the research was to develop a low order model of a heaving airfoil in a still fluid using experimental measurements. This was achieved by modifying and applying the tools developed in the first stage of the study. The modified POD approach together with a time delay neural network (TDNN) was used to model and predict the flow field evolution using only a couple of low profile load sensors. The neural network estimated the amplitudes of the most energetic modes using four sensory inputs. The modes were calculated using the proper orthogonal decomposition of the flow field data obtained experimentally by time-resolved, phase-locked particle imaging velocimetry (TRPIV). The model showed good estimation quality.
In the final stage of this study, a modeling methodology was implemented on measured flow field data of pitching and plunging wings in a tandem configuration. Here, the velocity field associated with the wings’ flapping motion was mapped and modeled using the previously developed POD approach. The flow field dynamics was approximated by a linear model based on only four POD modes. Since the state of the low order model (i.e. the amplitudes of the modes) is physically impossible to measure, a Kalman filter was implemented. The Kalman filter used the signals from two low-profile strain gauge sensors located at the root of the hindwing to evaluate the reduced-order state of the system. Then, the full state of the system was estimated using the POD approximation. Therefore, by using only two strain sensors’ signals, the complex vortex dynamics associated with the tandem wings motion was successfully modeled.
