A quasi-one-dimensional model for the stagnation streamline in hypersonic magnetohydrodynamic flows

The flow near the stagnation streamline of a blunt body is often attracted and analyzed by using the approximation of local similarity, which reduces the equations of motion to a system of ordinary differential equations. To efficiently calculate the stagnation-streamline parameters in hypersonic magnetohydrodynamic (MHD) flows, an improved quasi-one-dimensional model for MHD flows is developed in the present paper. The Lorentz force is first incorporated into the original dimensionally reduced Navier-Stokes equations to compensate for its effect. Detailed comparisons about the shock standoff distance and the stagnation point heat flux are conducted with the two-dimensional Navier-Stokes calculations for flows around the orbital reentry experiment model, including gas flows in thermochemical nonequilibrium under different magnetic field strengths. Results show that the shock curvature should be considered in the quasi-one-dimensional model to prevent accuracy reduction due to the deviation from the local similarity assumption, particularly for hypersonic MHD flows, where the shock standoff distance will increase with larger magnetic strength. Then, the shock curvature parameter is introduced to compensate for the shock curvature effect. A good agreement between the improved quasi-one-dimensional and the two-dimensional full-field simulations is achieved, indicating that the proposed model enables an efficient and reliable evaluation of stagnation-streamline quantities under hypersonic MHD flows.