Blunt body paradox and improved application of transient growth framework

The "Reshotko-Tumin transition criterion" based on optimal transient growth successfully correlates laboratory measurements of roughness induced transition over blunt body configurations. Even though transient growth has not been conclusively linked to the measured onset of transition, the above correlation denotes the only available physics-based model for subcritical transition in blunt body flows, since the latter do not support any modal instabilities at typical experimental conditions. Unlike other established models based on empirical curve fits that are valid for a specific subclass of datasets, the optimal-growth-based transition criterion appears to provide a reasonable correlation with measurements in various wind tunnel and ballistic range facilities and for a broad range of surface temperature ratios. This paper is focused on optimal growth calculations that improve upon significant shortcomings of the computations underlying the Reshotko-Tumin correlation. The improved framework is applied to leeward transition over a spherical section forebody that was tested in the Mach 6 Adjustable Contour Expansion wind tunnel at Texas A&M University. The computed results highlight the significance of nonparallel basic state evolution, curvature terms, and an optimization procedure that varies both inflow and outflow locations of the transient growth interval. More important, the results indicate that the modified correlation is very close to its original form, and hence, that the accuracy of the transient-growth-based transition criterion is not compromised by using a more thorough theoretical framework. Yet the results also show that the optimal energy gain up to the predicted transition onset location can be rather small, highlighting the need to further investigate the optimal growth criterion for additional experimental configurations and to also uncover the in-depth physics underlying blunt body transition.