For example, if we immersed such a model, providing it with only a single pair of electrodes—the central pair—and short-circuited them, a current would pass through the gas, looping around, which would strongly slow down the gas:
Such an airfoil, immersed in a highly electrically conductive gas (or made conductive), behaves like a high-power "MHD generator." It is a "direct MHD converter." Where does the energy come from? It is simply the kinetic energy of the fluid, and the extracted power is accompanied by a loss of kinetic energy in the fluid, resulting in its natural deceleration.
In 1965, we implemented MHD electrical generators operating a direct conversion of the kinetic energy of a fluid into electricity through a "Faraday-type MHD channel." The geometry differs, but the principle remains the same. Below is a diagram of a Faraday MHD generator, with its square-section channel.
Next image, with solenoids removed, shows the arrangement of "segmented electrodes" (to achieve better current distribution within the channel).
In the experiments we conducted in the 1960s at the Institute of Fluid Mechanics in Marseille, we injected argon gas at 10,000 K, under one atmosphere, entering at a speed of 2,500 meters per second. With a magnetic field reaching 2 teslas, the electromotive field therefore amounted to:
2,500 × 2 = 5,000 volts per meter
Given that the distance between opposing electrode pairs was 5 cm, the voltage difference was 250 volts. Subtracting 40 volts (due to wall phenomena near the electrodes), this left 210 volts.
The electrical conductivity of argon at such a temperature being 3,500 mhos per meter, the current density was J = σE = σV × B = 735,000 amperes per square meter—equivalent to 73.5 amperes per square centimeter. For a channel length of 10 cm and width of 5 cm (50 cm²), this yielded a maximum current in short circuit of 3,675 amperes.
When the electrodes were short-circuited, the current was maximal, and the resulting Laplace force was intense enough, as the experiment demonstrated, to slow the gas to the point of generating a normal shock wave—achieved without any physical obstacle, solely through electromagnetic force.
Thus, a gas arriving at supersonic speed onto a lens-shaped airfoil carries its own energy, which can be exploited. The energy required to eliminate shock waves was therefore the energy used to accelerate the gas near the leading and trailing edges, minus the energy recovered through deceleration linked to the operation of the central electrode pair.
This result was extremely interesting, as it showed that the energy needed to eliminate these shocks was lower than one might have initially expected. The main loss occurred via Joule heating. In the case of a flying machine moving through cold air, one would need to add the energy required to ionize the gas using microwaves—energy which we had also quantified.
How do Laplace forces act on the slope of Mach waves?
It's very simple. When the MHD channel operates, for example, as a generator, thus decelerating the fluid, here is how the Mach waves evolve within the channel:
This represents a moderate fluid deceleration. The waves appear to compress, like the bellows of an accordion. The electrodes are "under load," which limits the current density. This also explains how a more intense deceleration can lead to a shock wave: when the speed drops to the point where the gas tends to become subsonic. The Mach waves then concentrate, like an accordion, accumulating pressure disturbances. The shock wave then forms and rapidly moves toward the channel inlet, stabilizing in front of the first "streamer" (a jet of electric current emerging from the first electrode pair), as if this streamer acted like an invisible obstacle.
On the other hand, if electrical power is injected into the system, the channel behaves like a Faraday MHD accelerator. The Mach waves tend to flatten:
This MHD acceleration was also demonstrated in the 1960s in the laboratory where I worked. It proved highly effective. With an inlet velocity of 2,500 m/s, we achieved outlet velocities exceeding 8,000 m/s—representing a speed gain of over five kilometers per second over a distance of barely ten centimeters.
These experiments demonstrate the extreme effectiveness of MHD action on a gas, provided the gas has sufficient ionization. For information, such electrical conductivity (3,500 mhos/m) in argon corresponds to an ionization rate of 10⁻³ (one atom per thousand ionized).
In cold air, artificial ionization would be required—for example, by exposing the surrounding gas to a microwave flux at three gigahertz, which would strip electrons from the most easily ionizable component: nitric oxide (NO). Alternatively, one could consider introducing an alkali metal with low ionization potential, such as cesium or sodium.
Thus, Lebrun and I performed all these calculations within the framework of a PhD thesis funded by the CNRS in the 1980s. Computer simulations yielded a completely "regularized" flow, free of shock waves. In the figure below, the two families of Mach waves are depicted.
This theoretical work was complemented by hydraulic analogy experiments, always using the three-electrode system. Bow and stern waves were successfully eliminated. Since the electrical conductivity of acidic water was too low, it was not feasible to use the fluid’s energy to improve the energy balance. The result was identical to that presented above: the flow remains "flat."
Interested readers may find some of these elements in my comic strip "The Wall of Silence" (see CD-ROM Lanturlu).
How to implement these research findings.
These ideas are compelling. They open the door to a new mechanics of supersonic fluids, where instead of enduring shock waves as inevitable phenomena, one can actually avoid them.
The challenge of MHD lies in working with a gas possessing sufficient electrical conductivity. Over twenty years of work...