Input-Output analysis prediction of hypersonic laminar-turbulent transition over slender sphere-cones

The transition between laminar-turbulent flow is important to hypersonic re-entry vehicle design due to the associated rise in heat flux and shear stress. In particular, the location along the surface of the vehicle at which transition occurs is critical to know to mitigate large heating loads using thermal protective systems to prevent structural damage. Moreover, if the flow over the vehicle is turbulent, the heating rate can be 4x larger than that of laminar flow. Numerical simulations are unable to reliably predict the transition location a priori. Instead, boundary layer transition predictions are traditionally made using empirical correlations calibrated against historical flight data. But these correlations may be inaccurate when changes to the vehicle geometry or trajectory are made. In this work, we utilize computational fluid dynamics with input-output (IO) analysis to predict the transition location of hypersonic flow over both a sharp and blunt cone. We accomplish this goal by linearizing the compressible Navier-Stokes equations around a baseflow and applying the IO method to extract out the frequency that produces the largest disturbance. We find that slow acoustic waves reproduce the transition to turbulence on the sharp cone. Whereas, for the blunt cone, an optimized disturbance is the trigger to turbulence. Finally, we compare the results we find to those in the literature and experimental wind tunnel data.

This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.