High speed plasma flow about probes
Date
1971
Authors
Allen, Gregory Hamilton
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Abstract
A method for evaluation of the interaction between a uniform
magnetic field and a compressible inviscid, electrically conducting
ideal gas flow past a blunt body is presented. An experiment using a
double diaphragm shock tube to produce a slug of gas with high electrical
conductivity is performed to confirm the theoretical results.
The theoretical problem is considered in two parts.
Firstly, the flow field around a hemispherical cap in a
supersonic flow is evaluated using the method of integral relations.
The difficulty associated with the mathematical saddle point singularity
in this scheme is seen to be the instability of the integral
solution curves to small perturbations. This sensitivity is used to
advantage by applying small parameter perturbations to extend the
integral curves near the singularity, an innovation due to South
[1969] . In this way, the extrapolation error across the sonic line is
decreased while at the same time the computational effort expended in
determining the integral curve is reduced.
Secondly, the solution for the perturbed magnetic field is
obtained using the Biot-Savart relation and solution of the resulting
integral equations. The advantage of this approach, for problems in
which the boundary conditions are asymptotic to the undisturbed values
at infinity, lies in the simple way in which these conditions are
satisfied. The problem is reduced to the solution of a Fredholm
integral equation and this is solved numerically.
The large magnetic Reynolds number limit to the application
of this method is determined.
The analysis is applied to the determination of the induced
magnetic field near the nose of a magnetic probe in a supersonic stream
with an applied uniform magnetic field. The magnetic flux density
measured by the probe is significantly reduced when the magnetic
Reynolds number is greater than unity.
The experimental results show reasonable agreement with the
predicted values and differences are explained in terms of the short
test gas duration and the assumption of ideal gas behaviour for the
theoretical computations.
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