CFD Seminar: Adjoint-Based Optimization of Flapping-Wing Flows
Speaker: Dr. Nail Yamaleev
Biography: Dr. Nail Yamaleev is an Associate Professor in the Department of Mathematics at North Carolina A&T State University. He received his Ph.D. degree in Mathematical Modeling and Numerical Methods from the Moscow Institute of Physics and Technology in 1993. Prior to joining NCA&T, he held the senior research scientist position at the Institute of Mathematics (Ufa, Russia) from 1993 to 1997; the Humboldt research fellow position in the Institute of Mechanics at the Technical University (RWTH) in Aachen, Germany from 1997 to 1999; and the National Research Council senior research associate position at NASA Langley Research Center from 1999 to 2002.
Dr. Yamaleev’s current research interests include adjoint-based optimization of unsteady flows, high-order entropy/energy-stable methods, adjoint-based grid adaptation, and reduced-order modeling.
Abstract: In spite of the significant progress in modeling and analysis of micro air vehicle (MAV) flows, questions related to optimization of this type of flows have not been properly addressed especially in three dimensions because of the complex physical phenomena and computational cost involved. Experimental and numerical studies have revealed that there is an essentially nonlinear relationship between the major wing kinematic parameters (amplitude, frequency, phase shift angle, etc.) and shape parameters (wing platform, twist, thickness, etc.). Note, however, that the conventional parametric studies do not take into account this nonlinear relationship, thus indicating that mathematically rigorous optimization techniques should be used for solving this class of problems. In the present work, the wing thrust coefficient is considered as a functional which is maximized by using the optimal control theory. This time-dependent optimization problem is solved by the method of Lagrange multipliers which is used to enforce the flow and grid equations as constraints. The sensitivities of the Lagrangian to wing shape and kinematic parameters are computed using the time-dependent discrete adjoint formulation. The key advantage of this adjoint-based approach is its ability to compute the sensitivity derivatives with respect to all design variables at a cost comparable to that of a single flow solution. The unsteady discrete adjoint RANS equations are integrated backward in time. The gradient of the objective functional computed with the adjoint formulation is then used to update values of the design variables. The efficiency of this time-dependent optimization method is demonstrated by maximizing the thrust and propulsive efficiency of a wing undergoing
insect-based flapping motion. Our numerical results show that the highest improvement in the wing performance is achieved using the combined optimization of wing shape and its kinematics. Furthermore, we find that the optimal wing shape and kinematics closely resemble those observed in flying insects and hummingbirds.
Additional information, including the webcast link, can be found at the NIA CFD Seminar website, which is temporarily located at: