MHD and Shock Wave Cancellation

Appendix 1: MHD

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1 - Generalities on the Concept of Shock Wave Cancellation

This concept was introduced at the beginning of the 1970s. Later, the US government realized that MHD could play an important role in future military projects. At the same time, American scientists realized that MHD was related to hypersonic flight. They decided to misinform the public. Officially, in the US, MHD was abandoned. Civilian MHD was abandoned. Large industrial projects were abandoned. But in parallel, an intense effort began, in complete secrecy, on military MHD. This reality was discovered very recently (2001). The reader is free to believe or not to believe this information. We were informed about what happened in the US between 1970 and today by high-level American scientists involved in secret black programs, concentrated in Area 51. The only argument supporting this claim is based on scientific grounds. Even today, people still ignore many very important characteristics related to MHD applied to supersonic gas flows, which allowed a fantastic and fundamental breakthrough in the US in the middle of the 1970s. Thirty years after the US dominated the world with advanced technologies in many (military) fields, including long-duration hypersonic flight, up to Mach 12.

I don't know who will read this appendix, which requires advanced knowledge in supersonic fluid mechanics, characteristic theory, and MHD. A very good book was published in 1967, entitled "Engineering Magnetohydrodynamics"; Sutton and Sherman, Mac Graw Hill Books Company.

Let us now present some basic concepts.

In a supersonic flow, we can consider the "Mach lines":

Mach lines (or Mach surfaces) in a supersonic flow

The angle of these Mach lines depends on the local value of the velocity.

Effect of increasing velocity on the Mach angle

If we consider a supersonic flow, the Mach lines, or "characteristic lines," are real. They map the flow. Then, a 2D supersonic test nozzle (supersonic wind tunnel).

In the convergent section, the fluid is subsonic. From a mathematical point of view, the characteristic lines (the Mach surfaces) are imaginary. The speed of sound is reached at the throat of the nozzle. Then, the Mach surfaces become real. We can visualize them:

Evolution of Mach surfaces, or Mach lines, in a supersonic nozzle.

In the nozzle, the velocity increases continuously. At the same time, the Mach angle decreases (it is equal to 90° at the throat section). This corresponds to the "natural variation" of the Mach surfaces system, due to the expansion of a supersonic flow.

Now, consider a 2D supersonic flow around a flat wing. We can calculate the theoretical system of Mach lines, using characteristic theory:

Theoretical characteristic lines around a flat wing immersed in a supersonic gas flow.

This is not physical. It is "purely mathematical" (a solution of a "characteristic system"). It shows how the characteristic surfaces collide, accumulate in certain points. These are elementary pressure variation surfaces. In the middle of the flow, we see a classical expansion fan, where the pressure decreases and the gas is accelerated. But in other regions, we see how the Mach surfaces accumulate and tend to give attached shock waves. The following figure corresponds to a truly physical solution, with attached shock waves:

Physical conditions with attached oblique plane shock waves.

Next: these attached oblique shock waves.

Next: these flat waves, plus the flow lines.

If the leading edge is sharp, the front waves are attached. See detail:

Attached front shock wave near the leading edge of a flat wing

If the leading edge is rounded, the situation is somewhat different. The shock looks like a bow shock.

Shock wave at a blunt leading edge.

From a classical point of view, these shock waves cannot be avoided. They correspond to pressure and temperature jumps. When the Mach number exceeds 3, materials cannot withstand the heat flux and evaporate. In "scramjets," the leading edge is cooled with liquid hydrogen and oxygen, which allows achieving short-duration flights at Mach 5-6. But hypersonic flight (Mach 12) is considered impossible, from a technological point of view. In 1947, the UFO phenomenon raised a strange question: is it possible to achieve such high Mach numbers? At Roswell, the Americans recovered a crashed machine, which immediately proved two things:

• UFOs were definitely real

• They came from other planetary systems.

It was decided to keep a total secret about this. An intense and active policy of misinformation was established in the US, which is still in effect. For example, NASA explains on its official website that UFOs are nothing but an illusion, almost 50 years later. It took time for Americans to understand that MHD was the key, the master word of hypersonic (and silent) flight. The silent flight of UFOs showed that shock waves (and turbulence) were avoided. To illustrate this, we refer to the author's personal works (developed during the 1960s and 1970s). These researches were conducted with rather modest laboratory equipment, compared to the colossal American effort, hidden in underground factories in Area 51. But this will be enough to show the basic ideas. In the following figure, a "Faraday MHD linear converter" with its MHD channel and its two coils.

Faraday MHD converter

If we remove the two coils, we get this:

Faraday channel (the coils have been removed)

Here, the converter acts as an MHD generator. The supersonic flow enters the channel at velocity V, which causes an induced electric field E × B. This produces an electric current in the gas, which flows through external loads, as shown. Part of the kinetic energy of the gas can be converted into electricity. This results in a slowing down of the gas. The system composed of the velocity, the electric field, and the resulting Lorentz force is illustrated below:

Electric field and Lorentz force field in an MHD generator.

The Lorentz force obeys the "three fingers' rule":

This first idea is very important. Indeed, we see that the MHD accelerator slows down a supersonic fluid. If properly managed, we can imagine that the fluid parameters can be modified in a "gentle way," without the birth of a shock wave. That is the key idea of the hypersonic flight concept, as we will see later. Next, we show the characteristic pattern of Mach lines in an MHD generator. The Mach angle changes continuously and no shock occurs.

Shockless modification of the Mach lines system, due to the action of the Lorentz force

This is a very simple idea, but it was considered top secret for a very long time around the world. On the other hand, an MHD converter can be used as an accelerator. To do that, it is sufficient to inject electric power in order to reverse the electric current and obtain accelerating Lorentz forces. Thus, we can modify the local value of the Mach angle. In my laboratory, in 1967, we obtained very impressive accelerations over very short distances.

The gas enters the channel from the left and the Lorentz forces accelerate it.

Let us show that this was not a dream. Here is my MHD laboratory from the 1960s at the Institute of Fluid Mechanics in Marseille, France.

My MHD laboratory from the 1960s. Front: electrodes. Left: an old Tektronix vacuum tube oscilloscope. Below: the Faraday converter with its suspended coils. In addition, an "ignitron" used to switch the 50,000 ampere electric current produced by a capacitor bank.

It was a "short duration wind tunnel" based on a "shock tube." A shock-driven argon flow (200 microseconds) was pushed into a 6-meter-long constant area wind tunnel. The gas was moved and compressed (pressure after compression: 1 bar). The gas was heated to 10,000 K, which provided a very good electrical conductivity (3000 mhos/m). The velocity of the gas at the entrance of the MHD channel was 2,750 m/s. This channel was 10 cm long. During acceleration experiments, the exhaust velocity reached 8,000 m/s, which demonstrated the extraordinary efficiency of the Lorentz forces to accelerate with a high magnetic field (2 teslas) and high electric current densities. Next, the classical MHD efficiency:

MHD efficiency. J is the electric current density, B is the magnetic field, L is a characteristic length, below: the mass density and v the velocity.

At the beginning of the 1980s, a French engineer, Bertrand Lebrun, started a PhD with me. I defined the basic idea of shockless supersonic flight. This was a civilian research, but we know that similar research was carried out in secret in the famous Lawrence Livermore Laboratory, California, at the same time. We have already presented the general pattern of Mach lines associated with the theoretical supersonic flow around a flat wing. We have seen that we could change the local value of the Mach angle by a suitable choice of the Lorentz force field. For example, we can accelerate the flow around the leading edge using a transverse magnetic field and two wall electrodes, as follows:

Accelerating electrodes, near the leading edge

Next, the corresponding Lorentz force field:

Lorentz force field

With such a device, it was possible to cancel the front shock wave near a sharp leading edge, which showed that a shock system could be avoided. This drastically changed the problem of hypersonic flight. The new goal was to cancel the shocks around a flat wing, which implied keeping the Mach lines parallel:

Lebrun's thesis: the goal

Three pairs of wall electrodes were arranged on the flat wing model:

Lebrun's PhD thesis (1987)

Top: the idealized pattern of characteristic lines (Mach lines or Mach surfaces). If a suitable Lorentz force field could be applied around the model, it was expected that a characteristic line focusing phenomenon could be avoided. This was shown through computer calculations and presented at several international MHD meetings (Tsukuba, Japan, Beijing, China, see bibliography and cited articles). The general pattern of Mach lines becomes the following:

Lebrun's thesis. Characteristic lines.

This work was carried out in a civilian laboratory, but we know that, at the same time, the Americans were doing the same thing in absolute secrecy. In France, the authorities were terrified at the idea that such results could reveal the extraterrestrial nature of UFOs, and they became furious. All civilian research was stopped. The military tried to continue this research in its secret laboratories, for its own purposes, but it failed due to its lack of knowledge. Meanwhile, the US projects experienced a very strong acceleration. Parallel research was intensively carried out on torpedoes and submarine propulsion. To avoid confusing the reader's mind, we will talk about that later.

Bibliography :

(1) J.P. Petit : "Is supersonic flight possible?" Eighth International Conference on MHD Electric Power Generation. Moscow, 1983.

(2) J.P. Petit & B. Lebrun : "Shock wave cancellation in a gas by the action of the Lorentz force". Ninth International Conference on MHD Electric Power Generation. Tsukuba, Japan, 1986.

(3) B. Lebrun & J.P. Petit : "Shock wave annihilation by MHD action in supersonic flows. Quasi-one-dimensional steady analysis and thermal blockage". European Journal of Mechanics, B/Fluids, 8, n°2, pp.163-178, 1989.

(4) B. Lebrun & J.P. Petit : "Shock wave annihilation by MHD action in supersonic flows. Two-dimensional steady non-isentropic analysis. Anti-shock criterion, and shock tube simulations for isentropic flows". European Journal of Mechanics, B/Fluids, 8, pp.307-326, 1989.

(5) B. Lebrun : "Theoretical approach to the suppression of shock waves forming around a sharp obstacle placed in an ionized argon flow". Thesis in Energy, n° 233. University of Poitiers, France, 1990.

(6) B. Lebrun & J.P. Petit : "Theoretical analysis of shock wave annihilation by a Lorentz force field". International MHD Symposium, Beijing, 1990.

Annex1 (MHD), next page