Successful modeling and/or design of engineering systems often requires one to address the impact of multiple "design variables" on the prescribed outcome. There are often multiple, competing objectives based on which we assess the outcome of optimization. Since accurate, high fidelity models are typically time consuming and computationally expensive, comprehensive evaluations can be conducted only if an efficient framework is available. Furthermore, informed decisions of the model/hardware's overall performance rely on an adequate understanding of the global, not local, sensitivity of the individual design variables on the objectives. The surrogate-based approach, which involves approximating the objectives as continuous functions of design variables from limited data, offers a rational framework to reduce the number of important input variables, i.e., the dimension of a design or modeling space. In this paper, we review the fundamental issues that arise in surrogate-based analysis and optimization, highlighting concepts, methods, techniques, as well as modeling implications for mechanics problems. To aid the discussions of the issues involved, we summarize recent efforts in investigating cryogenic cavitating flows, active flow control based on dielectric barrier discharge concepts, and lithium (Li)-ion batteries. It is also stressed that many multi-scale mechanics problems can naturally benefit from the surrogate approach for "scale bridging."

The performance of micro air vehicles (MAVs) is sensitive to flow unsteadiness such as wind gusts, due to their low flight speed and light weight. We investigate the interplay of active flow control and stable flight performance. Specifically, a dielectric barrier discharge (DBD) actuator, characterized by fast response and non-moving parts, is used to control unsteady aerodynamics under fluctuating free-stream conditions on finite and infinite wings with the SD7003 airfoil geometry at chord Reynolds numbers between 300 and 1000. Feedback control is achieved using a retrospective cost adaptive controller, which adjusts control gains by minimizing a quadratic function of the retrospective performance and requires knowledge of nonminimum-phase (NMP) zeros (i.e., the complex numbers with magnitude greater than one where the transfer function equals zero) of the linearized flow-actuator model. The linearized flow-actuator system with lift as the performance has one real NMP zero, which approaches one as the distance between the actuator and the leading edge, Reynolds number, wing aspect ratio, or voltage increment decreases. At 15° angle-of-attack under modest free-stream fluctuation, DBD actuator commanded by the control law can stabilize lift by adjusting pressure and suction regions on the airfoil surface.

Retrospective cost adaptive control is applied to low Reynolds number aerodynamics around an SD7003 airfoil with a dielectric barrier discharge (DBD) actuator located near the leading edge. The adaptive control algorithm uses knowledge of Markov parameters to capture information about any nonminimum-phase zeros in the dynamics. In this paper, we explore the impact of the adaptive controller on the aerodynamics under the chord Reynolds numbers of 300 and 60,000, and with both steady and unsteady free-stream conditions. By varying the voltage to the DBD actuator, effective control of unsteady flow structure can be performed to decrease drag and increase lift. Nomenclature E Electric field vector F avg Quasi-steady body force from the DBD actuator F 1 , F 2 Body forces in the x 1 and x 2 directions q i Electric charge of a species n i Particle number density of a species ρ c Net charge density q c Unit electric charge (= 1.6 × 10 −19 C) c Chord length of airfoil U Free stream velocity C l Lift coefficient of an airfoil, which is the integral over the surface of the airfoil of the normalized pressure force in the direction of lift C d Drag coefficient of an airfoil, which is the integral over the surface of the airfoil of the normalized pressure force in the direction of drag V app Voltage applied to the DBD actuator U t/c Normalized time in the flow simulation Re Reynolds number * Graduate student, AIAA Student Member.

Successful modeling and/or design of thermo-fluid and energy systems often requires one to address the impact of multiple “design variables” on the prescribed outcome. There are often multiple, competing objectives based on which we assess the outcome of optimization. Since accurate, high fidelity models are typically time consuming and computationally expensive, comprehensive evaluations can be conducted only if an efficient framework is available. Furthermore, informed decisions of model/hardware’s overall performance rely on an adequate understanding of the global, not local, sensitivity of the individual design variables on the objectives. The surrogate-based approach, which involves approximating the objectives as continuous functions of design variables from limited data, offers a rational framework to reduce the number of important input variables, i.e., the dimension of a design or modeling space. In this paper, we discuss the fundamental issues that arise in surrogate-based analysis and optimization, highlighting concepts, methods, techniques, as well as practical implications. To aid the discussions of the issues involved, we will summarize recent efforts in investigating cryogenic cavitating flows, active flow control based on dielectric barrier discharge concepts, and Li-ion batteries.