Input / Output Analysis of Complex Hypersonic Boundary Layers
Abstract
Over the past decade or so, great progress has been made in the understanding and prediction of hypersonic boundary layer transition. It is now possible to correlate experimental data for certain classes of flows that are dominated by a single instability mechanism. These advances were made through the use of mechanism-based stability analysis methods rather than relying on empirical correlations. There remain several outstanding issues in the prediction of instability growth and transition. For example, it is not known how modal disturbances interact and compete with one another on complex geometries. Similarly, if modal interactions lead to transient growth and ultimately to transition, standard stability analysis methods will fail. Furthermore, it is not possible to study how realistic disturbance environments trigger transition because standard approaches can only analyze single disturbances, rather than an arbitrary disturbance field that may cause earlier transition. For these reasons, we propose to generalize stability analysis using results from the linear systems literature. Such an approach has the potential to revolutionize hypersonic boundary layer stability analysis and make it possible to perform full-vehicle flow field stability analyses on realistic flight geometries. For canonical flow configurations such as flows over sharp cones, linear stability analysis offers insight into how small fluctuations amplify and cause transition. Instability modes, such as the second Mack mode, play a dominant role in such cases. For more complicated flows created by realistic vehicle geometries, the physical mechanisms leading to transition are much less well understood. In particular, classical stability analysis (e.g. parabolized stability equations (PSE)) provides no information about the receptivity of hypersonic boundary layers to the external disturbance environment. Furthermore, by focusing on individual stability modes, PSE-based transition prediction methods do not capture multi-modal or non-modal effects which are known to become increasingly important as the flow geometry becomes more complicated. We have recently initiated the development of theoretical methods and numerical techniques that will revolutionize the prediction of hypersonic boundary layer transition to turbulence. Our theory provides insight into flow physics and our algorithms handle complex geometries and incorporate information about realistic disturbance environments. Our new algorithms are based upon well-established methods from linear systems theory which identify optimal disturbances that maximize the response of a flow system. The maximal response of the system can be thought of as a “path of least resistance” to transition to turbulence. This is because forcing the system with the optimal disturbance produces the most output for the least input (these methods are called Input/Output (I/O) analysis in the controls literature). The question remains, however, whether such optimal disturbances are realized in wind tunnel experiments and flight, and answering this question will be the primary focus of the research. We will quantify the meaning of optimal disturbances in increasingly complicated flow configurations and make comparisons with direct numerical simulations and experimental observations. The novel I/O approach will be implemented in the University of Minnesota US3D code so that it can be transitioned to the user community. We expect that I/O analysis will have a major impact on simulations and analyses at many research and development facilities, and will ultimately make it possible to link measureable free-stream disturbances directly to instability growth and transition to turbulence.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Dec 17, 2018
- Source ID
- N000141912037
Entities
People
- Graham Vardy Candler
Organizations
- Office of Naval Research
- Regents of the University of Minnesota
- United States Navy