Boundary Backstepping Control of Flow-Induced Vibrations of a Membrane at High Mach Numbers

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Aziz Sezgin ◽  
Miroslav Krstic
Keyword(s):  
Wave Equation ◽  
Original System ◽  
Target System ◽  
Spanwise Direction ◽  
Infinite Length ◽  
Flow Induced Vibration ◽  
Trailing Edge ◽  
Flow Induced Vibrations ◽  
Mach Numbers ◽  
High Mach

We design a controller for flow-induced vibrations of an infinite-band membrane, with flow running across the band and only above it, and with actuation only on the trailing edge of the membrane. Due to the infinite length of the membrane, the dynamics of the membrane in the spanwise direction are neglected, namely, we employ a one-dimensional (1D) model that focuses on streamwise vibrations. This framework is inspired by a flow along an airplane wing with actuation on the trailing edge. The model of the flow-induced vibration is given by a wave partial differential equation (PDE) with an antidamping term throughout the 1D domain. Such a model is based on linear aeroelastic theory for Mach numbers above 0.8. To design a controller, we introduce a three-stage backstepping transformation. The first stage gets the system to a critically antidamped wave equation, changing the stiffness coefficient's value but not its sign. The second stage changes the system from a critically antidamped to a critically damped equation with an arbitrary damping coefficient. The third stage adjusts stiffness arbitrarily. The controller and backstepping transformation map the original system into a target system given by a wave equation with arbitrary positive damping and stiffness.

scholarly journals Prediction of noise from serrated trailing edges

2016 ◽  
Vol 793 ◽  
pp. 556-588 ◽  
Author(s):  
B. Lyu ◽  
M. Azarpeyvand ◽  
S. Sinayoko
Keyword(s):  
Noise Reduction ◽  
Analytical Model ◽  
Leading Edge ◽  
Experimental Investigations ◽  
Destructive Interference ◽  
Trailing Edge ◽  
Trailing Edges ◽  
Mach Numbers ◽  
Trailing Edge Serrations ◽  
High Mach

A new analytical model is developed for the prediction of noise from serrated trailing edges. The model generalizes Amiet’s trailing-edge noise theory to sawtooth trailing edges, resulting in a complicated partial differential equation. The equation is then solved by means of a Fourier expansion technique combined with an iterative procedure. The solution is validated through comparison with the finite element method for a variety of serrations at different Mach numbers. The results obtained using the new model predict noise reduction of up to 10 dB at 90$^{\circ }$ above the trailing edge, which is more realistic than predictions based on Howe’s model and also more consistent with experimental observations. A thorough analytical and numerical analysis of the physical mechanism is carried out and suggests that the noise reduction due to serration originates primarily from interference effects near the trailing edge. A closer inspection of the proposed mathematical model has led to the development of two criteria for the effectiveness of the trailing-edge serrations, consistent but more general than those proposed by Howe. While experimental investigations often focus on noise reduction at 90$^{\circ }$ above the trailing edge, the new analytical model shows that the destructive interference scattering effects due to the serrations cause significant noise reduction at large polar angles, near the leading edge. It has also been observed that serrations can significantly change the directivity characteristics of the aerofoil at high frequencies and even lead to noise increase at high Mach numbers.

The aerodynamic resistance to a sphere rotating at high Mach numbers in the rarefied transition régime

1966 ◽  
Vol 293 (1433) ◽  
pp. 156-168 ◽  
Keyword(s):  
Experimental Study ◽  
Aerodynamic Resistance ◽  
Pressure Gauge ◽  
Transition Regime ◽  
Drag Torque ◽  
Free Molecule ◽  
Rotating Sphere ◽  
Mach Numbers ◽  
High Mach ◽  
Molecule Flow

An experimental study has been made of the gaseous drag torque on an isolated sphere rotating at high Mach numbers. The sphere was suspended electromagnetically and spun by induction. The drag torque has been measured through the transition régime from continuum to free molecule flow at Mach numbers (based on equatorial speed) of up to about five. These high Mach numbers were achieved in heavy vapours (diiodomethane, germanium tetrabromide and stannic bromide) with sonic speed as little as a quarter of that in air. To measure the pressure in the vapour a second (smaller) rotating sphere was used as a pressure gauge. The results agree well with those previously obtained and show an unexpected Mach number dependence in the transition régime.

Error feedback regulation for 1D anti-stable wave equation

2021 ◽  
pp. 014233122110592
Author(s):  
Zhiyuan Li ◽  
Feng-Fei Jin
Keyword(s):  
Wave Equation ◽  
Tracking Error ◽  
Feedback Regulation ◽  
Original System ◽  
Well Posedness ◽  
Error Feedback ◽  
One Dimensional ◽  
Internal Loop ◽  
Finite Dimensional ◽  
Uniformly Bounded

This paper is concerned with the boundary error feedback regulation for a one-dimensional anti-stable wave equation with distributed disturbance generated by a finite-dimensional exogenous system. Transport equation and regulator equation are introduced first to deal with the anti-damping on boundary and the distributed disturbance of the original system. Then, the tracking error and its derivative are measured to design an observer for both exosystem and auxiliary partial differential equation (PDE) system to recover the state. After proving the well-posedness of the regulator equations, we propose an observer-based controller to regulate the tracking error to zero exponentially and keep the states of all the internal loop uniformly bounded. Finally, some numerical simulations are presented to validate the effectiveness of the proposed controller.

Development of a MEMS-Based Active Control System for Flow Separation in the Transonic Regime

2000 ◽  
Author(s):  
Steve Tung ◽  
Brant Maines ◽  
Fukang Jiang ◽  
Tom Tsao
Keyword(s):  
Shear Stress ◽  
Control System ◽  
Wind Tunnel ◽  
Flow Separation ◽  
Control Flow ◽  
Separation Control ◽  
Sensors And Actuators ◽  
Trailing Edge ◽  
Flow Separation Control ◽  
Mach Numbers

Abstract A MEMS-based active system is currently under development for flow separation control in the transonic regime. The system consists of micro shear stress sensors for flow sensing and micro balloon actuators for separation control. We have successfully completed the first phase of the program in which the micro sensors and actuators were fabricated and tested in a wind tunnel facility. In the test, the sensors and actuators were flush mounted on a 3D model, which is representative of the upper surface of a wing with a deflected trailing edge flap. The model was installed in the wind tunnel and tested at a series of Mach numbers between 0.2 and 0.6. For all Mach numbers, the sensor output indicates that flow separates over the trailing edge when the micro balloons are in the ‘down’ position. When the micro balloons are inflated, the shear stress level on the trailing edge increases substantially, indicating an improvement of the separation characteristics. This result demonstrates the feasibility of using MEMS sensors and actuators to control flow separation. It is the first step toward the development of a revolutionary closed loop flow control system applicable to existing and future aircraft to enhance aerodynamic performance.

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