Magneto-gasdynamic flow over solid bodies

Swan, George W (1966) Magneto-gasdynamic flow over solid bodies. PhD thesis, University of Glasgow.

Abstract

The Method of Gharaoterlatics is applied to the study of the non-linear partial differential equations which govern the two-dimensional steady motion of a fully ionised gas which is idealised as a perfect fluid of infinite electrical conductivity in the presence of a magnetic field. Certain results are derived for the flow over slender wedges. For the steady flow over a convex corner of infinitesimal angle (of Prandtl-Meyer type in ordinary gas dynamics) it is shown that no steady state solution exists. The reasons for the breakdown of this type of flow are investigated via the propagation of magnetic disturbances in the non-conducting solid wall and the disturbances in the gas. Reflected and transmitted waves are given as solutions of a singular integral equation. A solution is now presented to the non-linear problem of the attached shock-wave configuration which appears when a non-conducting symmetric wedge of finite angle travels through the gas. The applied magnetic field is oblique to and is in the same plane as the incident stream. The presence of the magnetic field non-aligned with the stream renders the shock-wave pattern on the upper half-plane different from that in the lower half-plane. There is no symmetry in the flow. From the jump conditions appropriate to these plane magneto-gasdynamic shock waves expressions for the unknown parameters downstream of the shocks are given in expressions of the known (in general) quantities upstream. Direct analytic solution is not feasible. Perturbations are made from the known solution for the case when the magnetic field is aligned with the stream and depends on the solution of 24 equations in 26 unknowns. To obtain sufficient equations it is required to watch the solution for the flow with that found in the wedge. The effect of the coupling of the flows above and below the wedge via the boundary conditions 0x1 the magnetic field is demonstrated. These equations are solved numerically and solutions are presented for angles of inclination of the magnetic field to the stream up to 12

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Additional Information: Adviser: D C Pack
• Keywords: Electromagnetics, Thermodynamics
• Date of Award: 1966
• Depositing User: Enlighten Team
• Unique ID: glathesis:1966-72731
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 11 Jun 2019 11:06
• Last Modified: 11 Jun 2019 11:06
• URI: https://theses.gla.ac.uk/id/eprint/72731