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7.18.17 Hildebrand

Topic: 90th NIA CFD Seminar: Stability and Sensitivity Analysis for the Control of Shock-Driven Flows

Date: Tuesday, July 18, 2017

Time: 11:00am-noon (EST)

Room: NIA, Rm141

Speaker: Nathaniel Hildebrand, PhD Candidate, University of Minnesota


Abstract: A linear global mode approach using direct and adjoint equations has been used in the past to study the dynamics of mixing layers, free jets, wakes, boundary layers, and other open flows. This talk presents the results from applying a similar analysis to a transitional, hypersonic Oblique Shock Wave/Boundary Layer Interaction (OSWBLI) and a supersonic impinging jet. These complex flows are connected because they are both compressible and have multiple influential shock waves. They also happen to be globally unstable at certain flow conditions.

The OSWBLI at Mach 5.92 bifurcates from its original laminar state at a critical shock wave angle of 12.9 degrees according to Direct Numerical Simulation (DNS) and Global Stability Analysis (GSA). At bifurcation, the least stable global mode is non-oscillatory, and it selects a spanwise wavenumber of 0.25. This value agrees well with the DNS results. Examination of the critical global mode reveals it to be the result of interactions between small spanwise corrugations at the base of the incident shock, streamwise vortices inside the recirculation bubble, and spanwise modulation of the bubble strength. Furthermore, we compute the wavemaker, which is defined as the sensitivity of an eigenvalue to base flow modification. The wavemaker indicates that streamwise vortices inside the recirculation bubble are crucial to instability further verifying our physical interpretation.

Multi-block GSA about an ideally expanded round impinging jet at Mach 1.5 revealed several unstable modes with frequencies that matched experimentally measured impingement tones from the Florida State University. Both Large Eddy Simulations (LES) and the Reynolds-Averaged Navier-Stokes (RANS) equations were used to create the base flows. Using an adjoint stability solver, we show that the supersonic impinging jet is most sensitive to base flow modification in the downstream shear layer.

Speaker Bio: Nathaniel Hildebrand is a Ph.D. candidate in the Aerospace Engineering and Mechanics Department at the University of Minnesota – Twin Cities. He earned his Bachelor of Science in Physics and Applied Mathematics from the University of Wisconsin – La Crosse. After his time as an undergraduate student, he decided to pursue graduate level research at the University of Minnesota under Joseph Nichols. He obtained his Masters of Science in Aerospace Engineering and Mechanics near the end of 2016. Recently, he started working as a Pathways Intern in the Computational AeroSciences Branch at NASA LaRC. His research interests include aeroacoustics, transition to turbulence, hydrodynamic stability, and DNS/LES of high-speed flows. More specifically, he is applying multi-block global stability analysis to better understand the physics of supersonic impinging jets. He is also using stability and sensitivity analysis to study the interaction of an oblique shock wave impinging on a Mach 5.92 laminar boundary layer at a transitional Reynolds number.


Additional information, including the webcast link, can be found at the NIA CFD Seminar website:



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