High-Order Simulation of Turbulent Hypersonic Flows

Paolo Scuderi^∗,1,2 , Thierry Magin^1,2 , Georg May¹ , Olivier Chazot¹

¹Aeronautics and Aerospace Department, von Karman Institute for Fluid Dynamics, Belgium

²Aéro-Thermo-Mécanique Department, Université Libre de Bruxelles, Belgium

^∗paolo.scuderi@vki.ac.be (corresponding author)
thierry.magin@ulb.be, georg.may@vki.ac.be, olivier.chazot@vki.ac.be

 

Although impending space programs, one of the unexplored frontiers of fluid dynamics still remains the planetary re-entry/entry phase. The latter, known as hypersonic, was coined in 1946 by Tsien from the union of the Greek hyper (over) and Latin sonus (sound) to describe ”flow fields in which the fluid velocity is much greater than the propagation velocity of small disturbances”. Nowadays, hypersonic is recognized as a unique flight regime in which several complex phenomena mutually interact, such as turbulence, chemistry, and thermodynamic non-equilibrium.

In this regard, for the current era of technological progress, intensive studies are needed to design innovative spacecraft for future space missions. Ground testing is essential for this research, therefore, in 2015, a novel freestream rebuilding method, generally applicable to any Hypersonic Wind Tunnel (HWT), has been implemented in the VKI Longshot Wind Tunnel. Theoretically consistent with a more conventional rebuilding methodology, this strategy provided deviations in terms of the Mach number, close to 11 rather than the predicted value of 14.

Since then, several hypotheses have been tested: nozzle design inaccuracy, flow condensation, dense gas effects, and high-temperature effects combined with thermal non-equilibrium phenomena, such as vibrational freezing. Most of these failed to replicate the mismatch observed.

Standing on these grounds, the discrepancies are still unexplained. At least one key feature remains to be addressed: the influence of disturbances radiated from the turbulent boundary layer in the expansion nozzle. Indeed, HWTs are subject to free-stream fluctuations typically one or two orders of magnitude larger than the ideal real flight. It is expected that the non-isentropic phenomenon can be explained in terms of weak but numerous shock waves, called shocklets, through this process. Even though this physical mechanism has been theorized, neither numerical nor experimental evidence are available to date.

In this scientific framework, this work aims to present a state-of-the-art approach to high-order numerical simulations for hypersonic flows. An embryonic view of our scientific formulation of the above problem will be preset. In more detail, challenges of the complex aspects of high-speed boundary-layer aerothermodynamics will be coupled with critical aspects of the Discontinuous Galerkin numerical method, providing a perspective of its future abilities in the physical understanding of acoustic-hypersonic interaction.