Improving vortex models via optimal control theory

Maziar S. Hemati, Jeff D. Eldredge, Jason L. Speyer

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


Low-order inviscid point vortex models have demonstrated success in capturing the qualitative behavior of aerodynamic forces resulting from unsteady lifting surface maneuvers. However, the quantitative agreement is often lacking for separated flows as a result of the ambiguity in the edge conditions in this fundamentally unsteady process. In this work, we develop a model reduction framework in which such models can be systematically improved with empirical results. We consider the low-order impulse matching vortex model in which, in its original form, Kutta conditions are applied at both edges to determine the strengths of single point vortices shed from each edge. Here, we relax the Kutta condition imposed at the plate[U+05F3]s edges and instead seek the time rate of change of the vortex strengths that minimize the discrepancy between the model-predicted and high-fidelity simulation force histories, while the vortex positions adhere to the dynamics of the low-order model. A constrained minimization problem is constructed within an optimal control framework and solved by means of variational principles. The optimization approach is demonstrated on several unsteady wing maneuvers, including pitch-up and impulsive translation at a fixed angle of attack. Additionally, a stitching technique is introduced for extending the time interval over which the model is optimized.

Original languageEnglish (US)
Pages (from-to)91-111
Number of pages21
JournalJournal of Fluids and Structures
StatePublished - Aug 2014

Bibliographical note

Funding Information:
The authors gratefully acknowledge the support for this work from the Air Force Office of Scientific Research , Grant FA9550-11-1-0098 monitored by Dr. Douglas Smith. A previous version of this work, Hemati et al. (2013) , was presented at the 51st AIAA Aerospace Sciences Meeting (AIAA Paper 2013-0351). Appendix A


  • Model optimization
  • Optimal control
  • Point vortex
  • Unsteady aerodynamics


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