Subject: Testor's S4 Disk and MHD Propulsion
From: pstowe@ix.netcom.com (Paul Stowe)
Date: 8 Sep 1995 16:31:56 GMT
Message-ID: <42pr5s$13o@ixnews7.ix.netcom.com>
Below I am including an updated (cleaned up copy of an earlier post).
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MAGNETO-HYDRODYNAMIC (MHD) AERODYNES
Based on an article written by
Jean-Pierre Petit
Claude Poher
Maurice Viton
Magneto-Hydrodynamics
Magneto-Hydrodynamic (MHD) devices have been studied
extensively during the last 15 years (as of 1974). Such devices can
function either as a generator or as an accelerator. The MHD
generators are known to deliver high power densities. With MHD
generators one can obtain high specific impulses. But there are
very difficult basic problems connected with MHD processes.
First, the low electrical conductivity of gases requires either
seeding or the use of quite a large electronic temperature.
Secondly, strong interactions require a high magnetic field. These
two factors create severe technological difficulties. At present,
magnets of several Teslas strength can be built, using the
techniques of superconductivity. Another problem is the
production of electrodes which can carry large current densities.
In the following discourse we will assume that such technological
problems can be solved.
Suppose now that very powerful electrical generators are available;
could MHD flight be possible?
General MHD Propulsion
Faraday-type MHD accelerators are well-known. In such devices
a linear channel is combined with a magnet and a series of
electrodes, segmented in order to obtain a more homogeneous
electric discharge in the channel. In such accelerators, air is moved
through the channel by Lorentz forces. Thus it would be possible
to substitute MHD accelerators for the four engines of the
supersonic "Concorde". This would require a total electric power
of 200 megawatts. If one can design light but powerful electrical
generators, then MHD flight becomes possible. Let us suppose that
an electrical generator weighing 10 tons and generating 490 to
4000 megawatts is available.
The Cylindrical MHD Aerodyne
If a large amount of energy is available, Lorentz forces can be used
to produce both thrust and lift. Consider a cylinder, made of an
insulating material, in which a solenoid produces a dipolar
magnetic field. Pairs of electrodes are located on each side of the
cylinder and connected to the electrical generator, creating a glow
discharge in the surrounding air. The current intensity vector J is
perpendicular to the magnetic field B. Hence, in the vicinity of the
electrodes, where the current density is greatest, the Lorentz force
is tangential. This in turn induces a flow in the surrounding
medium. We have obtained experimental verification of these
effects using a model of 35 mm. diameter in an electrolytic
solution of water and HCl, with a 200 Gauss magnetic field and a
0.8 ampere electric current. The Lorentz forces tend to produce a
realignment of the flow behind the cylinder. As a matter of fact,
there is no wake and the flow appears to be laminar everywhere.
Since there is no disturbance behind the cylinder, we see that the
trihedra (J, E, and J X B ) rotates so as to maintain the
tangential force in the desired direction.
Spherical MHD Aerodyne
Now it seems logical to shift to a spherical aerodyne. We shall use
a pair of electrodes and again, a dipolar magnetic field. Here again
the Lorentz forces produce a lift. If we use a more symmetrical
system, we can place the electrodes in a circular belt around the
sphere, each half of a pair being placed diametrically opposite the
other half. The electric generator is connected to only one pair of
electrodes at a time, in sequence. To complete this sequential
operation, an internal series of solenoids provides a rotating
magnetic Enter name of file to field.
It is highly probable that the flow of the surrounding medium will
be similar to the flow associated with the cylindrical version. The
air flow pattern modifies the distribution of the static pressure on
the surface of the sphere resulting in lift. We know that the
Lorentz forces can act very powerfully in a fluid. Experiments
have been carried out in which these forces have produced very
strong shock waves. With sufficient magnetic field and electric
current, one can expect a very large amount of lift. Lorentz forces
depend upon both J (the current density) and B (the magnetic field)
and the following equations show that creation of a glow discharge
in air requires high voltages and high current densities, resulting in
high losses from the Joule effect and radiation. If we try to
increase the magnetic field we approach a critical value at which
the hall effect becomes important
The Hall Effect
The gyrofrequency is defined as:
W_e = eB/m_e Where e = elemental charge
B = intensity of the magnetic field
m_e = mass of the electron
The collision frequency for the electron species can be defined as:
V_e = SUM(s <> e) n_s Q_es T
Where N-e = density number of a heavy species, ions or
neutral
Q_es = collision cross section e X s
T = sqrt(8kT_e/pi m_e)
k = Boltzmann's constant
T_e = electronic temperature
The electric field E acts on electrons. If the gyrofrequency is small
compared to the collision frequency, the average movement of the
electron will be linear and parallel to E. In e X s collisions we can
consider that all the drift velocity of the electron is annihilated.
In
effect, in such collisions the velocity of the electrons is randomly
distributed over all directions of space.
If the gyrofrequency reaches the order of magnitude of the collision
frequency, there is a transverse drift motion of the electrons. The
preceding is very well described in Sutton and Sherman,
ENGINEERING MHD, 1967.
Proceeding, we can now define a critical non-dimensional
parameter, called the "Hall Parameter", as follows:
b = W_e/V_e = TAN (theta) Where theta is the angle
between J and E
The relationship between J and the field E is no longer scalar:
J = sigma dot E
The electrical conductivity becomes tensorial, as shown in the
matrix below;
| A -C 0 | A = eta/(eta + b^2)
| |
sigma = | C A 0 | C = b/(eta + b^2)
| |
| 0 0 eta |
sigma is the "scalar" electrical conductivity (i.e. with zero
magnetic field)
Let us return to the cylindrical and spherical aerodynes. These are
no longer practical. As a matter of fact, a component of the
Lorentz force, normal to the surface, appears in the vicinity of the
electrodes. We must seek other configurations for our model,
NAMELY, A DISC.
==== Updated Data (NOT VERBATIM ORIGINAL TEXT) ====
In a disc shaped aerodyne, made of insulating material, with two
belts of electrodes, one around the top, the other around the
bottom. An electric discharge is produced in the surrounding air
and upper and lower equatorial solenoid magnets produces an axial
magnetic field.
As a starting simplification, consider a disc shaped like two Fedora
hats one inverted and placed below (centered) the other. The
electrodes consist of rectangular sections ringed around the center
of the main rising section (Not the brim) of both sections. The
flow of electricity (Plasma) goes from the bottom electrodes to the
top electrode radially around the disc brim. During night time
operations the resulting plasma exhibits a glow out to about two
radii of the disc. The luminosity is strongest at the electrodes,
where the current density is greatest, and the electrodes can take on
the appearance of windows. The color of the glow is directly
related to temperature of the plasma generated. When the magnetic
field is introduced, we get a spiral current pattern. The electric
current lines are twisted as actual experiments have confirmed.
A check of the Lorentz forces demonstrate that if the Hall Effect
is strong, the resulting Lorentz will tend to straighten "make radial"
the twists mentioned above. The twist is reversed on the bottom
section of the disc.
The induced flow of air/plasma is very similar to that around a
helicopter. Such MHD craft operations are very similar to those of
a helicopter.
In atmospheric air, the value of the main solenoidal magnetic field
required to produce the Hall effect is quite high (Greater that
500,000 Gauss) necessitating a superconducting coil.
To obtain proper operation in a air (dielectric) medium requires a
high electron density in the plasma. Saha's law can be used to
compute the required thermodynamic conditions. This law can
produce very good results for electron temperatures greater than
4000 degrees K, when total particle density exceeds 10^14/cc, and
plasma dimensions are greater than 1 centimeter. Utilizing it is
possible to compute electron density.
Due to these high electron density values, these type of craft are
operated in a pulse mode. This pulse mode generates electrical
pulses of .between 10^11 and 10^13 watts. Typical operating
parameters are listed below:
Volts: 450,000 to 800,000
Amps: 10^7 to 10^9 Peak and 10^4 to 10^6
Averaged
Magnetic Flux (B): 500,000 to 600,000 sustained in main ring
Magnetic Flux (B): 600,000 to 800,000 Pulsed in steering
assemblies (3 units, equilateral spaced
straddling the craft's centerline)
The current generating voltage pulses are of one microsecond
duration with an operational frequency of 5 to 1 milliseconds. with
sustained power requirement of 75 MW. To obtain the proper
current carrying capacity in air, the air in the local vicinity of the
craft's surface must be ionized. To accomplish this required
ionization, a torodial "cyclotron" soft X-Ray emitter is provided on
both the upper and lower surfaces at the interface (brim and hat)
surface.
If the above configuration sounds familiar it should. It is exactly
the configuration of the Testor S4 disk Model. The "Black" areas
on the upper deck are the ablative resistant main electrodes
(positive pole). The re-written section simply took the original
author's data (obtained in actual scale model experiments) and their
extrapolations to full size craft, and just describe the full size
craft.
An actual hard copy of the article is available (which includes
many actual operational graphs and photos of the models in
operation) for only the cost of reproduction (20 pages)and mailing
(about $2.50).
Paul