Precursors for Partially Observed Systems and Applications to Unsteady Flow Separation Events
Abstract
The goal of this project is the derivation of precursors for the prediction of flow instabilities leading to separation around airfoils using partially observed states. This is a challenging problem due to the inherent nonlinearity of the separation process, the uncertainty of the inflow conditions and the angle of attack, and also the limited sources of information/measurements. The goal of the proposed research and the development of a rigorous framework for the prediction of extreme events for speci fie quantities of interest, using partially observed states, i.e. without having access to the full state of the system. This is a proposed advancement at a fundamental level, but it is motivated by the real-world problem of flow separation around an airfoil. In this case, the only available information about the flow state can be acquired only through a very small number of points on the boundary of the airfoil. We aim to address this challenge using two independent approaches. The first approach will utilize the equations of motion for the flow. while the second one will be fully data-driven. In particular, the first method will rely on a constrained variational framework, developed previously, with stochastic time-space representations of the fluid flow that we will obtain using machine-learning ideas. A major milestone for this effort is the representation of the fluid flow using sparse information on the boundary of the airfoil. The second approach will be fully data-driven and will rely on several long simulations or experiments containing extreme events. Given a particular quantity of interest, exhibiting extreme events and a set of other observable features. the question is to identify the function of the observables and their history that best predicts the quantity of interest. This is a search problem that can be seen in the context of binary classification. However, standard statistical metrics like total accuracy are poor fits for wildly unbalanced data sets and those associated with intermittent events. An objective of this proposal is to develop statistical metrics appropriate for the problem of intermittent rare events which will accelerate the optimization process, resulting efficient predictors of extremes with minimal data. The canonical problem for our efforts will be the airfoil in a configuration where the inflow is stochastic, having mean that is slightly below the critical Re number and undergoing fluctuations that sporadically lead to separation. We plan to begin with the 2D problem and in the later stages of the project apply the approach in the 3D version. A successful implementation of the proposed plan will pave the way for prediction of extreme events in even more realistic settings, beyond the proposed application. In the context of flow separation it will allow for the derivation of practical precursors that can be directly employed for experiments and practical applications.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 09, 2020
- Source ID
- W911NF2010100
Entities
People
- Themistoklis Sapsis
Organizations
- Army Contracting Command
- Massachusetts Institute of Technology
- United States Army