Citation
Joe, Won Tae (2010) Optimized feedback control of vortex shedding on an inclined flat plate. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:06072010131025711
Abstract
This thesis examines flow control and the potentially favorable effects of feedback, associated with unsteady actuation in separated flows over airfoils. The objective of the flow control is to enhance lift at poststall angles of attack by changing the dynamics of the wake vortices. We present results from a numerical study of unsteady actuation on a twodimensional flat plate at poststall angles of attack at Reynolds number (Re) of 300 and 3000. At Re=300, the control waveform is optimized and a feedback strategy is developed to optimize the phase of the control relative to the lift with either a sinusoidal or the optimized waveform, resulting in a highlift limit cycle of vortex shedding. Also at Re=3000, we show that certain frequencies and actuator waveforms lead to stabl(highlift) limit cycles, in which the flow is phase locked to the actuation. First, a twodimensional flat plate model at a high angle of attack at a Re of 300 is considered. We design the feedback to slightly adjust the frequency and/or phase of actuation to lock it to a particular phase of the lift, thus achieving a phaselocked flow with the maximal periodaveraged lift over every cycle of acutation. With the sinusoidal forcing and feedback, we show that it is possible to optimize the phase of the control relative to the lift in order to achieve the highest possible periodaveraged lift in a consistent fashion. However, continuous sinusoidal forcing could be adding circulation when it is unnecessary, or undesirable. Thus we employ an adjointbased optimization in order to find the waveform (time history of the jet velocty) that maximizes the lift for a given actuation amplitude. The adjoint of the linearized perturbed equations is solved backwards in time to obtain the gradient of the lift to changes in actuation (the jet velocity), and this information is used to iteratively improve the controls. Optimal control provides a periodic control waveform, resulting in high lift shedding cycle with minimal control input. However, if applied in open loop, the flow fails to phase lock onto the optimal waveform, degrading the lift performance. Thus, the optimized waveform is also implemented in a closedloop controller where the control signal is shifted or deformed periodically to adjust to the (instantaneous) frequency of the lift fluctuations. The feedback utilizes a narrowband filter and an Extended Kalman Filter to robustly estimate the phase of vortex shedding and achieve phaselocked, high lift flow states. Feedback control of the optimized waveform is able to reproduce the highlift limit cycle from the optimization, but starting from an arbitrary phase of the baseline limit cycle. Finally, we apply the tools developed and knowledge gained at Re=300 to a Re of 3000 on a thin airfoil with a thicknesstochord ratio of 4%, which were chosen to match the experimental studies of Greenblatt et al. (2008). We consider more detailed timedependent aspects of the lift and corresponding flow fields, particularly the flow structures at the minimum and maximum lift, and the phase of pulses relative to the lift, in order to more precisely compare different actuated flow fields and distinguish the differences responsible for higher or lower instantaneous lift, along with identifying different vortex evolutions. We consider two representative angles of attack, 10 and 20 degrees, and investigate the lift enhancement and which combinations of forcing frequency and duty cycle lead to phaselocked flow. Finally, we show that for certain frequencies and actuator waveforms, there occur stable limit cycles in which the flow is phase locked to the actuation.
Item Type:  Thesis (Dissertation (Ph.D.))  

Subject Keywords:  flow control, feedback control, vortex shedding, optimization  
Degree Grantor:  California Institute of Technology  
Division:  Engineering and Applied Science  
Major Option:  Mechanical Engineering  
Thesis Availability:  Public (worldwide access)  
Research Advisor(s): 
 
Thesis Committee: 
 
Defense Date:  21 May 2010  
Funders: 
 
Record Number:  CaltechTHESIS:06072010131025711  
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:06072010131025711  
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  5928  
Collection:  CaltechTHESIS  
Deposited By:  Won Joe  
Deposited On:  04 Aug 2010 17:20  
Last Modified:  26 Dec 2012 04:28 
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