Numerical simulation of hypersonic magnetofluid control based on non-linear coupling constitutive relation

To address the complex nonlinear flow mechanisms of high-speed plasma in magnetic fields, the conventional‌ Navier-Stokes (N-S) equations based on continuum theory fail to provide accurate predictions. Therefore, a novel framework was developed by‌ coupling the nonlinear coupling constitutive relations (NCCR) with Maxwell's electromagnetic field governing equations, augmented with the Park's TTv two-temperature model and the Park 11-component chemical reaction model. This integration established‌ a numerical simulation method and code for hypersonic magnetohydrodynamic (MHD) thermochemical non-equilibrium under‌ low magnetic Reynolds numbers conditions‌. Numerical simulations of high-speed plasma flow past a spherical body were conducted to investigate the influence mechanism of a dipole magnetic field on high-speed MHD control, with particular focus on‌ the effects of magnetic field existence‌ and its induction strength on plasma flow field structures. The results show that the presence of a magnetic field significantly alters high-speed plasma flow structures, with stronger magnetic fields inducing greater Lorentz forces on charged particles and consequently increasing bow shock detachment distances (e.g., a 452.38% increment observed at B₀ = 3.0 T). Stagnation point heat flux variations exhibit dependence on multiple factors including magnetic induction strength, inflow altitude, and Mach number, showing a notable 45.55% reduction at H = 80 km after magnetic field introduction. Furthermore, the magnetic field induces prominent thermochemical non-equilibrium effects, primarily enhancing N₂ dissociation in post-shock regions while modifying recombination reactions near walls, yet exerting minimal influence on O₂ dissociation dynamics.