Speaker
Description
1. Introduction
Hypersonic aerothermodynamics (ATD) involves a plethora of complex physical phenomena. The harsh environment within the post-shock region produces a significant effect on the flow where fluid properties such as specific heat, viscosity and thermal conductivity can no longer be considered constant as in traditional aerodynamics. Instead they vary with temperature, pressure and chemical composition. Under these conditions, the space vehicle's TPS experiences high thermal loads due to among others an exothermic chemically reacting boundary layer around the re-entry vehicle.
The developed open-source high-order solver focuses on thermo-chemical nonequilibrium (TCNEQ) hypersonic viscous flows. The Flux Reconstruction (FR), or Correction Procedure via Reconstruction (CPR), formulation is used, coupled with a novel positivity preserving shock capturing scheme adapted to TCNEQ flows. The solver is part of the world-class open-source framework for multi-physics modeling and simulations COOLFluiD. More information on the development of this platform can be found in [1,2].
2. Flux Reconstruction Code
The FR formulation is a compact high-order method with a large computational efficiency as compared to traditional low-order methods. It was originally developed by Huynh in [3]. The FR approach is readily adaptable to high-performance parallel architectures and is capable to deal with complex unstructured geometries. Our high-order FR code, which is parallel and fully implicit, is able solve the Euler and Navier-Stokes equations in 2D and 3D. In addition, its structure is extremely modular and can be easily coupled to arbitrary sets of advection-diffusion-reaction PDEs. In particular, the FR solver is extended to solve TCNEQ flows by adapting the convective and diffusive flux schemes in order to deal with the extended set of governing equations, by interfacing the Mutation library for providing the physico-chemical properties, by adding the source term discretization to the FR method, by implementing boundary conditions and a novel shock capturing scheme. Robust shock capturing is the main pacing item for high-order finite element-type CFD methods. In the vicinity of discontinuities within the flow field, spurious oscillations appear due to the Gibbs phenomenon. This effect is more severe for higher orders, stronger shocks and more complex physical models. Several schemes to overcome this problem have been investigated in among others [4,5]. However these schemes have not been successfully applied in conjunction with FR to viscous hypersonic flows, let alone TCNEQ. The present solver incorporates a modified positivity-preserving Localized Laplacian Artificial Viscosity scheme adapted to TCNEQ flows.
3. Hypersonic Flow Simulations
The reference test case presented is the hypersonic flow around the QARMAN CubeSat. QARMAN is the QubeSat for Aerothermodynamic Research and Measurements on AblatioN of the von Karman Institute, developed in the framework of the QB50 project.
For the present results, dissociated air with five species is considered: $O, N, NO, O_2, N_2$. For the TCNEQ simulation a two-temperatures model is used. The wall has a constant temperature of 500K. The considered free stream conditions are:
- Mach = 8.46
- $p$ = 39.53 Pa
- $\rho$ = $1.970\cdot 10^{-4}\ \text{kg}/\text{m}^3$
- $T$ = 530.3 K
- $T_v$ = 2343.3 K
Using the FR solver, promising flow fields for second- and third-order of accuracy were found on a 2D mesh consisting of curved quadrilateral elements. The results were compared with the Finite Volume solver of COOLFluiD and a good agreement was found in terms of flow field and heat flux prediction.
References
[1] A. Lani. An object oriented and high performance platform for aerothermodynamics simulation. PhD thesis, von Karman Institute, Université libre de Bruxelles, page 268, 2009.
[2] T. Quintino. A component environment for high-performance scientific computing: design and implementation. PhD thesis, von Karman Institute, KU Leuven,
2008.
[3] HT. Huynh. A flux reconstruction approach to high-order schemes including discontinuous Galerkin methods. AIAA paper, 4079:2007, 2007.
[4] ML. Yu et al. Localized artificial viscosity stabilization of discontinuous Galerkin methods for nonhydrostatic mesoscale atmospheric modeling. Monthly
Weather Review, 143(12):4823–4845, 2015.
[5] Y. Li et al. A convergent and accuracy preserving limiter for the FR/CPR method. In 55th AIAA Aerospace Sciences Meeting, page 0756, 2017.
Summary
Numerical simulations of hypersonic flows around re-entry vehicles and space debris have traditionally been carried out with low-order Computational Fluid Dynamics (CFD) codes using a multi-temperature finite rate chemistry model. The vast majority of state-of-the-art codes rely on standard second-order schemes that are robust and relatively easy to implement. However, achieving accurate heat flux predictions and accurately capturing viscous effects such as shock wave-boundary layer interaction remains problematic even on simple geometries. This may potentially lead to an unoptimized design of the Thermal Protection System (TPS) of hypersonic vehicles. High-order finite element-type methods show great promise and are well-consolidated for certain classes of CFD applications such as turbulence, aero-acoustics, etc. These methods attain a much higher accuracy per degree of freedom as compared to traditional low-order methods. Additionally, they are very efficient in a massively parallel environment. However, these methods are still in their infancy for hypersonic applications due to the difficulty of robustly capturing shocks.
The present paper presents a novel high-order Flux Reconstruction solver that is capable of simulating hypersonic thermo-chemical nonequilibrium flows. The Flux Reconstruction method is coupled with a novel positivity-preserving shock capturing scheme in order to handle strong shocks. This solver is developed in the open-source COOLFluiD platform for multi-physics simulations. The applicability of the present solver to simulate the flow around the QARMAN CubeSat during re-entry is demonstrated.
