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Input-output analysis of receptivity and instability of hypersonic boundary layers

Event Type: 
Date and Time: 
Friday, May 21, 2021 - 06:30
Event Sponsor: 
Parviz Moin, Director of Center for Turbulence Research
Prof. Joseph Nichols

Spatial amplification owing to modal instability plays a significant role in determining when and how a hypersonic boundary layer transitions from a laminar state to turbulence. Traditional stability analysis methods rely on the strong assumption of a slowly-varying baseflow, which limits their predictive power. Such methods can calculate downstream amplification only relative to upstream points where the flow has already passed through shock waves (such as a vehicle’s bow shock) and that are far away from complex geometry (such as a blunt nose tip). The estimation of perturbation amplitudes at these upstream points from freestream disturbance levels then requires empirical formulae, calibrated for different geometries on a case-by-case basis. As a further complication, hypersonic boundary layers also support non-modal amplification mechanisms not captured by traditional stability analysis.

We instead investigate this problem using Input/Output (I/O) analysis which directly relates freestream perturbations to the total system response through the resolvent operator, eliminating the need for a slowly-varying base flow. As a global method, I/O analysis simultaneously incorporates receptivity, modal amplification, and non-modal amplification mechanisms. Furthermore, as a decomposition method, I/O analysis provides a technique to distinguish between different mechanisms competing in a single flow. Crucial to the accurate representation of receptivity, our method employs a linear model for the transmission and reflection of small perturbations through a shock wave. We validate our method through comparison to schlieren measurements of hypersonic instabilities over ogive-cylinders taken in the AFRL Mach-6 Ludwieg Tube. In addition to the expected Mack 2nd mode instability, I/O analysis predicts a new type of modal instability, as well as non-modal entropy-layer instability, in good agreement with experimental observations. The interaction between these different mechanisms may explain the phenomenon of “transition reversal” with increasing nose-tip bluntness.

Professor Joseph Nichols’ current interests are in the areas of stability and sensitivity analysis of hypersonic flows and the aeroacoustics of high-speed jets. He has performed some of the largest computational fluid dynamics simulations in the world, involving massively parallel high-fidelity Large Eddy Simulation of tactical aircraft engine exhausts, running on more than a million computer processors simultaneously. He is currently developing novel and scalable stability and transition analysis tools for hypersonic flow over complex geometry. Before joining the faculty at the University of Minnesota, he held postdoctoral research positions at the Laboratory d’Hydrodynamique (LadHyX) at the École Polytechnique in France, and at the Center for Turbulence Research (CTR) at Stanford University. At the University of Minnesota, Nichols teaches a number of courses in Fluid Mechanics, Computational Fluid Mechanics, and Hydrodynamic Stability Analysis.