Numerical modelling of plasmas formed and magnetically controlled in hypersonic flows
In high enthalpy hypersonic flows, the pressures and temperatures in the shock layer can become so extreme that dissociation and ionisation reactions produce a weakly ionised plasma. Owing to its elevated electrical conductivity, the plasma can be actively manipulated via magnetohydrodynamic (MHD) effect when a magnetic field is imposed upon the flow. The concept is of current research interest for its applications in spacecraft reentry, hypersonic flight control, and emerging aerospace plasma technologies. However, many challenges prevail in the numerical modelling of the complex and multiscale flow physics arising in a compressible, electrically conductive, magnetically influenced fluid. This work makes advances in numerical modelling methodologies, combined with an advanced air-plasma equation of state, to permit the realistic and efficient simulation of hypersonically formed plasmas with imposed MHD effects. The dissertation wholly encompasses: the regime-specific mathematical modelling, the direct implementation and development of numerical algorithms within a high performance computing framework, and application of the numerical model to study the physics of hypersonic flows with imposed MHD effects. A modularised approach is derived with problem-specific mathematical sub-models offering a high degree of generality (many types of fluid and plasma problems can be simulated) without compromising on efficiency. Key extensions are made to an advanced 19-species equilibrium air-plasma equation of state (EoS), meaning the EoS can be newly applied to the regime of hypersonically generated equilibrium air-plasmas, and makes improvements in the prediction of electric properties which underpin MHD forcing dynamics. A unique combination of numerical methods is employed. This includes: an original hypersonically stabilised numerical solver paired with a rigid body Ghost Fluid Method (GFM) for embedded geometries, with stable Lorentz forcing integration. The model is directly implemented within the AMReX framework, which facilitates block-structured parallelism and hierarchical adaptive mesh refinement (AMR). The numerical methodology, combined with advanced EoS, is validated across a wide range of test problems. Quantitative agreement between simulation and experiment is achieved for the first time for a hypersonic flow over a double-cone geometry with multiple shock interactions, augmented by an imposed magnetic field. Extended numerical studies of this problem configuration reveal insights into the detailed and coupled magneto-dynamic flow physics. The numerical studies demonstrate how an applied magnetic field not only influences shock position, but conditions are identified which predict a topological adaptation to the fundamental flow structure. Such predictions have technological consequence for emerging MHD control technologies. The generality of the approach, as well as its specific advantages in simulating air-plasmas in compressible flows with complex shock interactions, means the developed numerical model can be applied to a wide set of problems. Application of the model to plasma generation via remote energy deposition is used as an example demonstration of extended model capabilities, and opens the door to future possibilities in aerospace plasma research.