Certifiable Transition Prediction and Control
Abstract
The objective of the proposed research is to develop n framework to certify the efficacy, reliability and performance of feedback flow control laws without reliance upon resource intensive direct numerical simulations (DNS) or physical experiments. The focus will be on transition suppression within a channel flow configuration, which will be used to validate the analysis framework using an existing spectral DNS code. This problem is ideally suited for developing and investigating these techniques because nonlinear dynamics are essential to transition and a plethora of flow control literature exists for comparison, baselining, and validation. Nonlinear flow interactions are fundamental to the transition process. Yet, such interactions are rarely taken into account for stability analysis and transition prediction. The proposed effo1t is predicated in the fact that nonlinear flow interactions are dynamically constrained by the Navier-Stokes equations, both at a given time instant and across time instances. Mathematically, these physical constraints can be expressed as integral quadratic constraints (IQC), providing a convenient framework for modeling nonlinear flow interactions to conduct nonlinear stability analysis. The !QC framework can be viewed as an extension of passivity analysis, which has been successfully used in past studies on flow stability and control; however, IQCs provide a more precise characterization for systems modeled by linear dynamics interacting with nonlinearities. The proposed work seeks to determine how !QC-based representations of nonlinear flow interactions can be exploited to reliably predict transition-both with and without feedback control. To this end, three complementary objectives are proposed: Objective# I: Faithfully model nonlinear flow interactions. Formulate a complete description of nonlinear flow interactions using IQCs, then compare with DNS to determine which flow interactions are most important to the input-output dynamics. Objective #2: Reliably predict transition and characterize baseline stability. Use JQCs to precisely determine the critical Reynolds number Re*, above which global stability is lost. Formulate and apply IQCs to conduct region of attraction (local stability) analysis for Re Re*, then use this analysis to determine disturbance thresholds minimal seeds, and optimal disturbances for transition to turbulence. Further quantify flow sensitivity to nonlinear flow interactions and provide guidance on when linear analysis is justified. Objective #3: Certify transition control performance Extend Objectives #1 and #2 to the context of flow control, in order to assess the performance and reliability of feedback flow control laws in suppressing transition. Further, assess the impact of implementation effects (i.e., actuator, sensor, and processor dynamics) on transition control performance. The proposed effort will result in a reliable framework for assessing and certifying the performance of new candidate control strategies, without needing to resort to extensive DNS campaigns for validation. The effort will also lay the requisite groundwork for synthesizing reliable and certifiable feedback control laws for nonlinear transition control in the future
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 09, 2020
- Source ID
- W911NF2010156
Entities
People
- Maziar S. Hemati
Organizations
- Army Contracting Command
- United States Army
- University of Minnesota