Development and numerical investigation of magneto-fluid-dynamics formulations
Magnetofluiddynamics (MFD) is the branch of fluid dynamics that involves mutual interaction of electrically conducting non-magnetic fluids and magnetic fields. MFD offers promising advances in flow control and propulsion of future hypersonic vehicles. With the advent of computational fluid dynamics (CFD), the numerical study of inherently complicated fluid dynamics problems, such as flows at high velocities, high-temperature re-entry bodies, and mixed subsonic-supersonic flows, has become an interesting area of research. Further advancement in high-speed cluster machines and development of efficient algorithms has made it possible to explore MFD problems numerically. In this work, development and validation of numerical algorithms for the simulation of MFD problems of supersonic and hypersonic flows have been conducted. Validity of low magnetic Reynolds number approximation has been checked with respect to the results obtained from full MFD equations. In addition to the two commonly used formulations for MFD, a third formulation based on the decomposition of a magnetic field for solving full MFD equations was explored. The governing equations were transformed to a generalized computational domain and discretized using a finite difference technique. A time-explicit multistage Runge-Kutta scheme augmented with total variation diminishing (TVD) limiters for time integration was implemented. The developed codes were validated with the existing closed form solution of the magnetic Rayleigh problem for both two- and threedimensional cases. The results obtained from decomposed full MFD equations compare well with the results obtained by solving low magnetic Reynolds number approximation and classical full MFD equations for a wide range of magnetic Reynolds numbers. It is shown that the decomposed full MFD technique requires substantially less computation time compare to classical full MFD equations for the solution of flow fields with strong imposed magnetic fields. Finally, high-speed flows over a backward-facing step that is subject to an applied magnetic field were numerically simulated. The global domain of computation was vii decomposed into upstream and downstream domains from the step location. The low magnetic Reynolds number approximation under a multiblock grid approach was used for modeling the backstep flow. Pressure distribution for the Navier-Stokes analysis was found to be in good agreement with the experimental data. Different types of magnetic field distributions were investigated. Both uniform and variable electrical conductivity distributions were considered. It was observed that an increase in the separation zone and displacement of oblique shock wave towards the exit section occurs subsequent to application of the magnetic field. A comparison of results obtained with uniform and variable electrical conductivities showed a reduction in magnetic interaction for variable electrical conductivity.
Thesis (Ph.D.)--Wichita State University, College of Engineering, Dept. of Aerospace Engineering