Massively Parallel and Robust High-Order Methods for Transitional Hypersonic Flow Modelling on Unstructured Grids: Application to Reusable Launcher Stages

During their ascent and descent trajectories, reusable space vehicles travel primarily in the hypersonic regime (5 < Mach < 25) which is characterized by high speeds, strong shock waves, chemical dissociation, radiation, viscous interaction, etc. Additionally, the flow experiences various changes in regimes, i.e. laminar, transitional and turbulent, along the trajectory. Prediction of the onset and extent of the transition from laminar to turbulent regime is particularly challenging and a main subject of ongoing research activities.

Furthermore, resolving the thermal and aerodynamic loads acting on such vehicles requires high-accuracy Computational Fluid Dynamics (CFD) methods that can handle complex geometries and are well suited to massively parallel high-performance computing. High-order finite element-type methods show great promise in accurately and efficiently resolving such flows. However, they are in their infancy for high-speed flows with strong shocks, as well as for laminar-turbulent transition modelling.

In the present work a fast and robust parallel flow solver based on high-order finite element-type methods is developed. Such methods exhibit a much higher accuracy per degree of freedom in the computational mesh as compared to traditional low-order methods and allow for calculating more accurate solutions on relatively coarser computational grids.

A novel shock capturing scheme for the high-order finite element-type Flux Reconstruction (FR) method is developed in order to accurately resolve flows with strong shocks in a robust way. This scheme is based on localized Laplacian artificial viscosity, while alleviating the need for fine-tuning the shock capturing parameters for different cases and ensuring positivity of the pressure and density.

The core of the developed code, solving the Navier-Stokes equations with explicit time marching, is ported to Graphical Processing Units (GPUs) in order to speed up convergence and take advantage of the compact nature of high-order finite element-type methods. Two parallelization schemes are investigated for the FR method and their performance is compared.

In order to demonstrate the generality of the developed solver and its applicability to more complex Partial Differential Equations (PDEs) with strong source term formulations, a novel Local Correlation-Based Transition Model (LCTM) for the Reynolds-Averaged Navier Stokes equations (RANS) to predict laminar-turbulent transition is incorporated. This LCTM is based on the Langtry-Menter model, while having a more physics-based transport equation for the intermittency. Additionally, the present LCTM has been verified in several hypersonic cases.

The accuracy and performance of the solver is investigated for several verification cases. Furthermore, the FR code is successfully applied to several hypersonic reference cases. Good agreement is shown both with numerical and experimental data. The RANS solver is also applied to the flow around a representative reusable launcher stage, i.e. the HIFiRE-5 vehicle. The results are compared to numerical and flight data. As such, the applicability of high-order finite element-type methods to fully-3D complex high-speed cases is demonstrated.

The final result provides the first open-source high-order finite element-type solver able to simulate transitional hypersonic flows for complex 3D cases.