When: Mar 13 2020 @ 4:00 PM
Where: 213 Hodson Hall
213 Hodson Hall

4:10 pm Presentation
“Effect of Axial Casing Groove Geometry on Rotor-Groove Interactions in the Tip Region of a Compressor”
Presented by SUBHRA SHANKHA KOLEY (Adviser: Prof. Katz)
The present experimental study expands an ongoing effort to characterize the interactions of axial casing grooves (ACGs) with the flow in the tip region of an axial turbomachine. In recent work, we have tested a series of grooves with the same inlet geometry but with different exit directions. Two geometries have stood out: The U grooves, which have an outflow in the negative circumferential direction (opposing the blade motion) are the most effective in suppressing stall, but cause a decrease in efficiency around the best efficiency point (BEP). In contrast, the S grooves, which have an outflow in the positive circumferential direction, achieve a milder improvement in stall suppression but do not degrade the performance near BEP. Stereo-Particle Image Velocimetry (SPIV) measurements is carried out at various planes to elucidate the flow in the tip region and within the U and S grooves. At low flow rates, the inflow into both grooves peaks periodically when the blade pressure side (PS) faces the entrance (downstream side) to the grooves. This inflow rolls up into a large vortex that remains and lingers within the groove long after the blade clears the groove. The outflow depends on the shape of the groove. For the S groove, the outflow exits at the upstream end of the groove in the positive circumferential direction, as designed. In contrast, for the U grooves, the fast radially and circumferentially negative outflow peaks at the base of the U. The resulting jet causes substantial periodic variations in the flow angle near the leading edge of the rotor blade. Close to the BEP, the chordwise location of primary blade loading moves downstream, as expected. The inflow into the grooves occurs for a small fraction of the blade passing period, and most of the tip leakage vortex remains in the main flow passage. For the S grooves, the rotor-groove interactions seem to be minimal, with little (but not zero) inflow or outflow at both ends, and minimal changes to the flow angle in the passage. In contrast, for the U groove, the inflow into and outflow from the groove reverses direction (compared to the low flowrate trends). The resulting entrainment of secondary flows from the groove into the passage are likely contributors to the reduced efficiency at BEP for the U grooves.

4:35 pm Presentation
“An Input-Output Inspired Method for Permissible Perturbation Amplitude of Transitional Wall-Bounded Shear Flows”
Presented by CHANG LIU (Adviser: Prof. Gayme)
Determining the permissible level of perturbation to maintain a laminar flow state is of critical importance in a wide range of applications. Historical approaches to this problem in wall-bounded shear flows focused on linear analysis that is only provably valid in a small neighborhood of the laminar solution and precludes the evaluation of the role of nonlinearity. Extensive simulations or experimental studies allow exploration of the full dynamics, but a finite set cannot provide a definitive bound. This work takes an input-output approach that partitions the dynamics into a feedback interconnection of the linear and nonlinear dynamics (i.e., a Luré system in which the nonlinearity is static feedback). We construct a model of the nonlinear term that is constrained by system physics to be energy conserving (passive) and to have bounded input-output energy. We then formulate computation of the region of attraction of the laminar state (set of safe perturbations) and permissible perturbation amplitude as Linear Matrix Inequalities (LMI), which allows a more computationally efficient solution than prevailing nonlinear approaches based on Sum of Squares (SOS) programming. We apply our approach to low dimensional nonlinear shear flow models for a range of Reynolds numbers. The results from our analytically derived bounds are consistent with the bounds identified through exhaustive simulations. However, our results are obtained at a much lower computational cost and have the benefit of providing a provable guarantee that a certain level of perturbation is permissible.