Abstract
A closed-loop control algorithm for the reduction of turbulent flow separation over NACA 0015 airfoil equipped with leading-edge synthetic jet actuators (SJAs) is presented. A system identification approach based on Nonlinear Auto-Regressive Moving Average with eXogenous inputs (NARMAX) technique was used to predict nonlinear dynamics of the fluid flow and for the design of the controller system. Numerical simulations based on URANS equations are performed at Reynolds number of 106 for various airfoil incidences with and without closed-loop control. The NARMAX model for flow over an airfoil is based on the static pressure data, and the synthetic jet actuator is developed using an incompressible flow model. The corresponding NARMAX identification model developed for the pressure data is nonlinear; therefore, the describing function technique is used to linearize the system within its frequency range. Low-pass filtering is used to obtain quasi-linear state values, which assist in the application of linear control techniques. The reference signal signifies the condition of a fully re-attached flow, and it is determined based on the linearization of the original signal during open-loop control. The controller design follows the standard proportional-integral (PI) technique for the single-input single-output system. The resulting closed-loop response tracks the reference value and leads to significant improvements in the transient response over the open-loop system. The NARMAX controller enhances the lift coefficient from 0.787 for the uncontrolled case to 1.315 for the controlled case with an increase of 67.1%.
Highlights
Efficient and safe design of aircraft, missiles, propellers, turbines, compressors, automobiles, ships, trains, and civil engineering structures depend to a far extent on an understanding of the nature of flow around bodies (Gad-el-Hak [1])
The Nonlinear Auto-Regressive Moving Average with eXogenous inputs (NARMAX) approach is utilized to construct a feedback control subroutine for flow separation on NACA 0015 airfoil with leading-edge synthetic jet actuators (SJAs) mounted at 10% chord length
A NARMAX model for flow over airfoil based on the static pressure data and the synthetic jet actuator was developed using the data from the incompressible flow simulations results for cases with and without SJAs
Summary
Efficient and safe design of aircraft, missiles, propellers, turbines, compressors, automobiles, ships, trains, and civil engineering structures depend to a far extent on an understanding of the nature of flow around bodies (Gad-el-Hak [1]). For non-model based flow control, the well-known system identification (ID) schemes are utilized to model the system dynamics, including the actuator and unsteady surface pressure sensors. The NARMAX approach is utilized to construct a feedback control subroutine for flow separation on NACA 0015 airfoil with leading-edge SJA mounted at 10% chord length. A NARMAX model for flow over airfoil based on the static pressure data and the synthetic jet actuator was developed using the data from the incompressible flow simulations results for cases with and without SJAs. The describing function technique was used for linearization of the identified pressure signal within its frequency range, and a low pass filtering was used to provide quasi-linear state values (linear in plant/nonlinear in instrumentation), which was used in the application of the quasi-linear control techniques.
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