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Feedback control of boundary layer Tollmien-Schlichting waves using a simple model-based controller

Chinese Journal of Aeronautics 2021年第3期34卷 25-38页

作者： Yong LI Zhengwu CHEN School of Mechanical and Electrical Engineering Wenzhou UniversityWenzhou 325035China Key Laboratory of Aerodynamic Noise Control China Aerodynamic Research and Development CenterMianyang 621000China

The attenuation of spatially evolving instability Tollmien-Schlichting(T-S)waves in the boundary layer of a flat plate with zero pressure gradients using an active feedback control scheme is theoretically and numerically investigated.The boundary layer is excited artificially by various perturbations to create a three-dimensional field of instability waves.Arrays of actuators and sensors are distributed locally at the wall surface and connected together via a feedback controller.The key elements of this feedback control are the determination of the dynamic model of the flat plate boundary layer between the actuators and the sensors,and the design of the model-based feedback controller.The dynamic model is established based on the linear stability calculation which simulates the three-dimensional input-output behaviour of the boundary layer.To simplify the control problem,an uncoupled control mode of the dynamic model is made to capture only those dynamics that have greatest influences on the input-output behaviour.A Proportional-Integral-Derivative(PID)controller,i.e.a lead-lag compensator,combining with a standard Smith predictor is designed based on the system stability criterion and the specifications using frequency-response methods.Good performance of the feedback control with the uncoupled control mode is demonstrated by the large reduction of the three-dimensional disturbances in the boundary layer.This simple feedback control is realistic and competitive in a practical implementation of T-S wave cancellation using a limited number of localised sensors and actuators.

关键词： boundary layer instability Control system Feedback control PID controller Tollmien-Schlichting waves

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Selective enhancement of oblique waves caused by finite amplitude second mode in supersonic boundary layer

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Applied Mathematics and Mechanics(English Edition) 2017年第8期38卷 1109-1126页

作者： Cunbo ZHANG Jisheng LUO Department of Mechanics Tianjin UniversityTianjin 300072China

Nonlinear interactions of the two-dimensional （2D） second mode with oblique modes are studied numerically in a Mach 6.0 fiat-plate boundary layer, focusing on its selective enhancement effect on amplification of different oblique waves. Evolution of oblique modes with various frequencies and spanwise wavenumbers in the presence of 2D second mode is simulated successively, using a modified parabolized stability equation （PSE） method, which is able to simulate interaction of two modes with different frequen- cies efficiently. Numerical results show that oblique modes in a broad band of frequencies and spanwise wavenumbers can be enhanced by the finite amplitude 2D second mode instability wave. The enhancement effect is accomplished by interaction of the 2D second mode, the oblique mode, and a forced mode with difference frequency. Two types of oblique modes are found to be more amplified, i.e., oblique modes with frequency close to that of the 2D second mode and low-frequency first mode oblique waves. Each of them may correspond to one type of transition routes found in transition experiments. The spanwise wavenumber of the oblique wave preferred by the nonlinear interaction is also determined by numerical simulations.

关键词： supersonic boundary layer boundary layer instability nonlinear mode interaction

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