Start of MHD3
..The dashed line is intended to represent the region where the fluid begins to move away to make room for the object.
...In supersonic flow, these sound waves can no longer "inform" the fluid before the object arrives. The gas is thus "taken by surprise," and its reaction is to form shock waves. The idea was therefore to find a way to act remotely, upstream of the object, to manipulate the gas by encouraging it to make room.
..A first solution involves inserting an airfoil profile into air at supersonic speed. It is known that the impact of this object on the air causes abrupt deceleration. It therefore seemed logical to facilitate the flow of gas along the profile near the leading edge while initiating the gas deceleration upstream. This can be achieved by applying a magnetic field perpendicular to the plane of the figure, with two wall-mounted electrodes placed as indicated. The lines of electric current flowing through the gas are shown. This results in a Laplace force (Lorentz force, for Anglo-Saxons), which follows the "three-finger rule."
..Below is the general appearance of the electromagnetic force field, perpendicular to the lines of electric current.
..This approach thus provides three advantages:
..- Upstream of the vehicle, we begin to decelerate the fluid in advance.
..- We initiate a displacement of the fluid away from the object.
...- We facilitate its flow along the surface.
...The electromagnetic force per unit volume is J × B, where B is the magnetic field intensity, expressed in teslas (one tesla equals ten thousand gauss), and J is the electric current density, in amperes per square meter. The force is then expressed in newtons per cubic meter.
..An intensity of just one ampere per square centimeter (ten thousand amperes per square meter), combined with a field of 10 teslas, would produce a force of ten tons per cubic meter of gas—sufficient to impose the desired effects on the flow.
..The force is strongest near the electrodes, where the current concentrates and the current density is highest.
..The problem, of course, is passing such an electric current through a medium that is initially an excellent insulator at normal temperature: air. We will address this issue later.
..Initially, in 1976, we opted for simulations based on hydraulic experiments. The fluid was acidified water (to make it more electrically conductive). The next step was to scale the experiment. We have a magnetic field installation capable of producing one tesla within a few cubic centimeters. The flow velocity was 8 cm per second. Given that water has a density of 1000 kg/m³, it is possible to calculate the minimum value of J such that the interaction parameter:
where L is a characteristic dimension of the model.
...The bow wave was eliminated in the first test (1976). We conducted experiments on lens-shaped models, but the initial tests were performed on a cylindrical model, which produced a bow wave simulating a detached shock wave forming at a distance from a cylindrical obstacle:
..With a magnetic field perpendicular to the plane of the figure, the elimination of the bow wave was achieved using two electrodes arranged as shown in the figure. The positioning of the pole pieces of the electromagnet is also illustrated. Model diameter: 7 mm. Electrode width embedded in the wall: 2 mm.
...The figure above shows the waves in the absence of electromagnetic forces, and the following figure shows the result after annihilation of the front wave.
...The Laplace forces, resulting from the current passing through the acidified water combined with the transverse magnetic field, correspond to the figure below:
..These forces are particularly intense near the electrodes, where the current concentrates (maximum current density J). Upstream, they produce a deceleration of the fluid. However, this force field is not sufficient to completely eliminate the wave system. In experiments conducted with a cylindrical obstacle equipped with only one pair of electrodes, these waves were simply concentrated downstream of the model. Nevertheless, as shown in the figure, this was enough to create a depression at the "stagnation point," demonstrating that such a system could additionally be used for MHD propulsion.
...Complete suppression of the entire wave system can be achieved, as verified through these hydraulic simulations, around a lens-shaped model, using three pairs of electrodes this time. Indeed, referring back to a previous figure, one sees that the appearance of Mach waves results from the overlapping of Mach waves in two regions—upstream and downstream.
...We were the first (Ph.D. thesis by Bertrand Lebrun) to introduce the key concept of regularizing a supersonic flow using Laplace forces by imposing around a model a system of parallel Mach waves:
..The second family of characteristics, the Mach waves, has not been represented.
...Three actions are therefore required:
...- Prevent Mach waves from reorienting near the model’s leading edge by accelerating the fluid in this region.
...- Prevent them from lying down (in the "expansion fan") along its side.
..- Finally, re-accelerate the flow again near the trailing edge.
..This leads to a system of three wall-mounted electrodes:
...The magnetic field was perpendicular to the plane of the figure, but to create the appropriate force field, it was necessary (in computer simulations) to "shape" it—something that could be achieved using multiple coupled solenoids. Near the electrodes, the Laplace forces were schematically arranged as follows:
...Lebrun’s thesis (published at the 7th International MHD Conference in Tsukuba, Japan, and the 8th International MHD Conference in Beijing, 1990, as well as in The European Journal of Physics) demonstrated the theoretical feasibility of the operation. This result is significant on multiple counts. Indeed, when we accelerate the fluid, we supply it with energy, whereas when we decelerate it, it supplies energy. Why? Because the flow of fluid along the model at velocity V induces an electromotive force V × B. This tends to create a current density J = σ (V × B), where σ is the electrical conductivity, which, combined with the magnetic field according to the Laplace force J × B = σ (V × B) × B
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