Ph.D Thesis

Ph.D StudentFriedman Aaron Joseph
SubjectReduced System Order and Sensing/Actuation Resolution for
Estimation and Control of Transition to Turbulence
DepartmentDepartment of Aerospace Engineering
Supervisors PROF. Yaakov Oshman
PROF. Jacob Cohen
Full Thesis textFull thesis text - English Version


Skin drag in shear flows can be reduced by half in some cases by maintaining laminar versus turbulent flow, rendering the control or delay of transition to turbulence of engineering interest. Controlling transition from laminar to turbulent plane Poiseuille flow serves as a model problem for more geometrically complex or realistic shear flows, such as boundary layers or pipes. In previous numerical studies, application of a linear systems approach to controlling transition to turbulence in plane Poiseuille flow has been shown to increase transition thresholds by at least several factors, depending on the type of flow perturbation assumed. Generally speaking, these studies have two primary shortcomings: large model order and assuming a continuum or near continuum of wall-mounted sensors and actuators.

            This research takes a new approach toward overall model order reduction, and subsequently sensor and actuator resolution reduction, by utilizing insights regarding the physical mechanisms of transition to turbulence in plane Poiseuille flow. We propose that peak transition threshold improvement can still be obtained both by controlling only a narrow range of wave-number pairs and using sparsely distributed discrete actuators. We thereby also establish the foundation for the use of sparsely distributed discrete sensors, which relies upon the assumption that only a narrow range of wave-number pairs is of interest for state estimation and control.

            The results of a state estimator designed using an aliased wave-number pair augmentation approach are promising, significantly improving performance when using low-resolution measurements relative to an un-augmented estimator. The methodology is extended and refined to accommodate process noise, actuator input for use with a controller, and further model order reduction. Combining the estimation strategy with the reduced resolution actuation results (and loop transfer recovery for improved closed-loop robustness) demonstrates the ability to improve transition to turbulence thresholds relative to un-augmented system models when using a sensor and actuator simulation paradigm more physically realistic than a continuum, approaching the results obtainable with a compensator using full resolution sensing and actuation.