The focus of the present work is on the use of magneto hydrodynamics as a flow control device for supersonic and hypersonic vehicles. A three dimensional parabolized Navier Stokes solver was developed to take into account the effects of magnetic fields , by incorporating two magneto-hydrodynamic models. The modified solver was then used to study the effects of magneto-hydrodynamics on a variety of configurations, one study of which involved surrogate model based optimisation procedures. The first component of research involved validation of the low magnetic Reynolds number model model against well documented test cases. Good agreement with the nu- merical test cases for flows past a blunt body and a flat plate boundary layer flow, both in the presence of a magnetic field, was found. A novel application of the method of man- ufactured solutions to the simplified mapeto-hydrodynamic model was made to ensure its Accuracy. Assessment of the procedures used for numerical optimisation, were made against known closed-form solutions, and a theoretical axisymmetric body of revolution. An investigation for an optimal magnetic field configuration, for an over-sped Ram- jet intake was made. It was found that for a suitable choice of magnetic field strength, shock on lip could be achieved. Furthermore, for a suitable choice for the position of the magnetic field source, the design condition can also be satisfied using a weaker mag- netic field. Finally a study examining the use of magnetic fields for flows past a slender body were was performed. Given a suitably orientated dipole source, it was shown that the magnetic field can introduce asymmetries, for an otherwise symmetric flowfield, and thereby introduce side form on the missile
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