The thickness of an ion shock embedded in a collisional shock propagating in an electron proton gas is calculated, using both the kinetic theory and the continuum approach, for the free stream Mach numbers M=3 to M→∞. It is found that the shock thickness predicted by the kinetic theory is 2–4 times the thickness obtained from the continuum approach. It is also found that the electric field, via which the electrons are compressed across the ion shock, although representing considerable dissipation of the ion kinetic energy, has very little effect on the ion shock broadening.
An approach to compute three-dimensional flows using two stream functions is presented. The independent variables used are χ, a spatial coordinate, and ξ and η, values of stream functions along two sets of suitably chosen intersecting stream surfaces. The dependent variables used are the streamwise velocity, and two functions that describe the stream surfaces. Since the value of a stream function is constant along the solid boundaries, this choice of variables makes it easy to satisfy the boundary conditions. To illustrate the approach, computations of incompressible potential flow through a circular-to-rectangular transition duct are also presented.
The effect of initially unequal electron and ion temperatures on the structure of a collisional shock wave propagating through a fully ionized gas is investigated and is found to be restricted to a small region at the beginning of the shock.
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