AAWSAP DIRD, MHD Air Breathing Propulsion and Power for Aerospace Applications, November 2010

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the shock or boundary layer with a modest amount of alkali metal vapor helps in
getting the conductivity close to the maximum achievable level of ~3,000
mho/m. At this level of conductivity, a modest magnetic field, B~0.1-0.3 Tesla,
is sufficient for substantial MHD effects (power generation, flow acceleration, or
aerodynamic control). However, at gas temperatures of "only" 1,500-2,000K or
so typical for scramjet combustors, even seeding the flow with alkali vapor
results in conductivities no higher than 10-30 mho/m, in which case the strength
of magnetic field required for substantial MHD performance at L= 1 meter or less
is quite high: 8=3-10 Tesla. The weight, volume, and complexity associated with
such a strong magnetic field that must be created in such a large volume make
this application very problematic.
NONEQUILIBRIUM MHD IN COLD AIR FLOWS
The situation becomes worse in relatively cold air. Indeed, static gas
temperatures at Mach number less than about 12 are quite low (<1,S00K) even
in shock and boundary layers. At these temperatures, the electrical conductivity
of air, even if seeded with alkali metals, is negligible. For MHD devices to operate
in such conditions, conductivity (ionization) has to be created in a nonthermal
(nonequilibrium) way. Nonequilibrium (i.e., with cold gas and hot electrons)
plasmas are routinely sustained in glow and RF discharges such as those in
fluorescent light tubes and devices used in microchip fabrication. The principal
differences between those devices and the MHD systems for aeronautics follow :
•
Pressures of interest in aeronautics (>10-100 Torr) are much higher than
those in typical glow discharges (1 Torr or less) resulting in much higher
power required to sustain plasmas and to severe problems with arcing
instabilities.
•
The ionization fraction needed for a good electrical conductivity and
acceptable MHD performance is much higher than that required for a
fluorescent light, again resulting in high power budget and overheating.
For cold nonequilibrium plasmas, the power budget is determined by the average
energy cost (usually expressed in eV), W;, of ionization (i.e., of producing an
electron-ion pair), and the rate at which the electron-ion pairs must be
generated in order to compensate for electron losses in recombination,
attachment, and other processes. The recombination is the dominant loss
mechanism at reasonably high electron densities, and its rate is proportional to
the product of electron and ion number densities. Since in quasineutral plasmas
the number densities of electrons and ions are close to each other, the
recombination rate (per unit volume) is equal to kdrne2 , where kdr is the
dissociative recombination rate coefficient and ne is the electron number density.
Note that the characteristic plasma decay time due to recombination is almost
always very short, typically ~1-10 microseconds, so that the flow moves only a
very short ( ~1 cm) distance during the decay time. This is why schemes with
pre-ionization upstream of the MHD region with no ionization in the MHD reg ion
itself are not viable; the ionization must be done continuously throughout the
MHD region.
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