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Magnetohydrodynamics (MHD)

Branch of physics studying the interaction of electrically conducting fluids with magnetic fields, through electromagnetic forces called "Lorentz forces". The inventor of the basic concepts is the famous british scientist Michael Faraday. MHD has a very large field of investigation from astrophysics to leading-edge technologies, which covers two engineering aspects:

  1. MHD POWER GENERATION: The kinetic energy of a fluid, its enthalpy, can be converted into electric power. This refers to MHD generators. In such devices, when a ionized gas flow with a velocity V crosses a transverse magnetic field B, an induced electric field V × B separates the charged particules (free electrons and ions) which can be harnessed through electrodes or by inductive means.  
  2. MHD PROPULSION: On the other one, fluids can be accelerated through Lorentz force J × B. This refers to MHD accelerators.

Electrically conducting fluids can be a liquid (as salt water or liquid metal) or a ionized gas (a plasma). For MHD devices, the latter often refers in litterature to MHD-gas, MPD (magnetoplasmadynamics) or MAD (magnetoaerodynamics) in the case of ionized air.

 


 

I have a personal experience in MHD since 1964. From 1964 to 1972 I worked at the Marseille Institute of Fluid Mechanics (IMFM) in France. Then I shifted to astrophysics and theoretical cosmology at the Marseille Observatory. During the sixties I built pulsed power MHD generators, based on "shock tube" driven supersonic hot wind tunnels. These devices could produce short duration flows, high temperature and high velocity, with quite high pressures. They are not low pressure wind tunnels. Their typical parameters are:

  • Gas: argon
  • Velocity: 2,500 to 2,700 m/s
  • Temperature: 10,000 K
  • Pressure : one bar
  • Electrical conductivity: 3,500 to 4,000 mhos/m
  • Magnetic field: 2 teslas

These MHD shock tubes produced several megawatts of electric power. In 1967 I managed to make such generators work with non-equilibrium ionized gases and high Hall parameter by controlling the electrothermal instability.1,2,3,4,5,6,7,8,

In early 1972 I passed my Sc.D thesis defense, written about kinetic theory of gases applied to technological and astrophysical plasmas.10

  • The first part presented the basis for the first kinetic theory of gases with non-equilibrium ionization, starting from the Chapman-Enskog method for the transport phenomena and extending it to a biparametric expansion in series.11,12
  • The second part was an application of the kinetic theory of gases to galactic dynamics, where I worked on the calculation done by Subrahmanyan Chandrasekhar, rewriting them into a more compact matrix form.

Then from 1975 to 1987, I worked on new MHD propulsors.

  • Classical MHD plasma propulsors (often called MPD thrusters) are no more than electromagnetic rockets, where a hot ionized gas is accelerated internally, inside an electromagnetic rocket engine, then expelled through a nozzle, reaching high velocities greater than chemical propelled rockets. They are primary studied for future space propulsion systems. My coworkers at IMFM turned one of our MHD shock tubes into an MPD thruster in 1970, by injecting electrical power in it. The incoming hot gas had an initial velocity of 2'700 m/s, and was accelerated by Lorentz forces to more than 8'000 m/s, along an interaction length (the length of the electrodes in the MHD reactor) of only ten centimeters.9 This is an example among others showing that MHD forces can be very powerful. Imagine a current density J of 1 ampere per square centimeter combined with a 1-tesla magnetic field B. This gives a Lorentz force field J×B of 10'000 newtons per cubic meter: one ton per cubic meter.
  • MHD converters have no moving part. In 1975 I imagined MHD propulsors where "the engine would be put outside of the vehicle". Such an MHD accelerator would ionize the surrounding air (for example with microwaves), transforming it into a cold plasma, then accelerating it by electromagnetic fields around the external hull. I called that MHD propulsor with external airflow and ionization control an "MHD aerodyne". Such devices are shaped to make use of the Coanda effect in order to suck upstream air and create a partial vacuum area above or in front of them. Moreover the air could be locally accelerated or decelerated by MHD forces all over the surface of the body, eliminating the skin friction and wake turbulence (laminar flow) and even the wave drag. MHD flow control can make completely silent supersonic (and hypersonic) flight possible, even in dense air, because those force fields are powerful enough to suck the flow at the stagnation regions, where the shock waves take place. No sonic boom, no sound barrier. But more interesting: classically the temperature rises very quickly behind shock waves, so the thermal ablation of materials at hypersonic velocities is a big problem. But since the sound barrier and the heat barrier can be cancelled thanks to MHD, the hypersonic flight is written in our technological future.

This idea seemed foolish at that time, but I published various papers about it.13,14,15,16,17,18,19,20

In 1975, with my colleague Maurice Viton, we built an hydraulic experiment with a one-tesla electromagnet. Such a B-field was necessary to modify an acidulated water flow around a tiny model, in a free-surface flow (8 cm/s). The model was a cylinder (7 mm diameter). The experience was a success and the front wave was completely cancelled. I presented these results at the 1983 international MHD meeting in Moscow.18 Fluids mechanics specialists know that the wave created by a ship in water is very similar to shock waves in air, because the laws in all fluids are the same (the Navier-Stokes equations). Incidentally before the advent of computers, hydraulic analogies in water tanks for aerodynamic simulations were common in aeronautical high schools.

In 1987, the student engineer Bertrand Lebrun from the French Engineering institute ENSAM defended his Doctor of Engineering thesis under my direction.22 The subject was the mathematical calculation of shock wave cancellation around a profile in a supersonic gas flow at 10'000 K, where we developed a method to solve the Navier-Stokes equations within an MHD force field, with the method of characteristics. This work was presented in several international MHD meetings and published through peer review.21,23,24,25

Nowadays we have new ideas and we are presently building a new lab, LAMBDA (Laboratory for Applications of MHD in Bitemperature Discharges to Aerodynamics), with private funding and a new young team around ageing but harden MHD specialists. The activity will cover different fields:

  • Numerical experiments
  • Hydraulic experiments (hydraulic analogies and high velocity submarines models)
  • Low pressure gaz experiments (magnetized plasma simulations).
  • Hot gas experiments (experimental achievement of Lebrun's thesis)
  • Cold gas experiments (supersonic flows of air at high altitude pressure)

We have published three new papers in an international MHD conference and an academic journal in 2008.26,27,28 In 2009, this work has been summed up in a long paper presented at AIAA "HyTASP" (international conference on hypersonic flight techniques).29

This web site, MHD Prospects, is for us the place to present analysis, popularized papers, course subjects and scientific publications focused exclusively on MHD. Please see the Documents section for available downloads.

 

  Jean-Pierre Petit

 

 
     
 

About Jean-Pierre Petit

Jean-Pierre Petit is a French scientist, senior researcher at National Scientific Research Center (CNRS) now retired. Gratuated from Supaero (French National Higher School of Aeronautics and Space) in 1961, Sc.D. in 1972, he is astrophysicist, fluid mechanician, plasma physicist, magnetohydrodynamics specialist. His carrier in the field of MHD is well-know: 1st method of eletrothermal instability control and 1st usable MHD generator with non-equilibrium ionized gas (1967); kinetic theory of non-equilibrium plasmas (1972); MHD aerodynes with ionization control (1975); Shock wave cancellation by MHD force field around a cylindrical profile imbedded in a liquid flow (1976); 2nd method of electrothermal instability control by magnetic pressure gradient in an MHD accelerator (1981); Thesis director about shock wave annihilation around a flat wing in a hot supersonic gas flow: Resolution of Navier-Stokes equations within an MHD force field by the method of characteristics (1987).

 

References

1 J.P. Petit; J. Valensi, J.P. Caressa (24–30 July 1968). "Theoretical and experimental study in shock tube of non-equilibrium phenomena in a closed-cycle MHD generator" in International Symposium on MHD Electrical Power Generation. International Atomic Energy Agency, Warsaw, Poland. Proceedings 2: 745–750.

2 J.P. Petit; J. Valensi, J.P. Caressa (24–30 July 1968). "Electrical characteristics of a converter using as a conversion fluid a binary mix of rare gases with non-equilibrium ionization" in International Symposium on MHD Electrical Power Generation. International Atomic Energy Agency, Warsaw, Poland. Proceedings 3.

3 J.P. Petit; J. Valensi, D. Dufresne, J.P. Caressa (January 27, 1969). "Caractéristiques d'un généateur linéaire de Faraday utilisant un mélange binaire de gaz rares, avec ionisation hors d'équilibre" (tr. Characteristics of a Faraday linear generator using a binary mix of rare gases, with non-equilibrium ionization). CRAS 268 (A): 245–247. Paris: French Academy of Sciences.

4 J. Valensi; J.P. Petit 15 mars 1969). Etude théorique et expérimentale des phénomènes accompagnant la mise hors d'équilibre dans un générateur à cycle fermé (tr. "Theoretical and experimental study of phenomena accompanying the non-equilibrium stage in a closed-cycle generator"), Compte rendu 66-00-115, Institut de Mécanique des fluides, Université d'Aix-Marseille, France.

5 J.P. Petit; J. Valensi (April 14, 1969). "Performances théoriques d'un générateur de type Faraday avec ionisation hors d'équilibre" (tr. "Theoretical performances of a Faraday generator with non-equilibrium ionization"). CRAS 268 (A): 245–247. Paris: French Academy of Sciences.

6 J.P. Petit (April 14, 1969). "Instabilité de régime dans un générateur de Hall avec ionisation hors d'équilibre" (tr. "Running instability in a Hall generator with non-equilibrium ionization"). CRAS 268: 906–909

7 J.P. Petit; J. Valensi, D. Duresne, J.P. Caressa (January 27, 1969). "Caractéristiques électriques d'un générateur linéaire de Faraday utilisant un mélange binaire de gaz rares, avec ionisation hors d'équilibre" (tr. "Electrical characteristics of a linear generator using a binary mix of rare gases, with non-equilibrium ionization"). CRAS 268: 245–247

8 J.P. Petit; J. Valensi (September 1, 1969). "Growth rate of electrothermal instability and critical Hall parameter in closed-cycle MHD generators when the electron mobility is variable". CRAS 269: 365–367. Paris: French Academy of Sciences.

9 B. Forestier; B. Fontaine, P. Bournot, P. Parraud (July 20, 1970). "Study of the variations in the aerodynamic flow parameters of ionized argon subjected to Laplacian accelerating forces". CRAS 271: 198–201. Paris: French Academy of Sciences.

10 J.P. Petit (March 10, 1972). "Applications de la théorie cinétique des gaz à la physique des plasmas et à la dynamique des galaxies" (tr. "Applications of the kinetic theory of gases to plasma physics and galactic dynamics"). Doctor of Science thesis, CNRS#6717, University of Provence, Aix-Marseille, France.

11 J.P. Petit; M. Larini (May 1974). "Transport phenomena in a nonequilibrium, partially ionized gas in a magnetic field". Journal of Engineering, Physics and Thermophysics 26 (5): 641–652.

12 J.P Petit; J.S. Darrozes (April 1975). "Une nouvelle formulation des équations du mouvement d'un gaz ionisé dans un régime dominé par les collisions" (tr. "New formulation of the equations of motion of an ionized gas in collision dominated regime"), Journal de Mécanique 14 (4): 745–759, France.

13 J.P. Petit (September 15, 1975). "Convertisseurs MHD d'un genre nouveau" (tr. "New MHD converters"). CRAS 281 (11): 157–160. Paris: French Academy of Sciences.

14 J.P. Petit; M. Viton (February 28, 1977). "Convertisseurs MHD d'un genre nouveau. Appareils à induction" (tr. New MHD converters: induction machines"). CRAS 284: 167–179. Paris: French Academy of Sciences.

15 J.P. Petit (1979). "Prospects on magnetohydrodynamics". Technical Report CNRS on behalf of CNES.

16 J.P. Petit; M. Billiotte, M. Viton, (October 6, 1980). "Accélérateur à courants spiraux" (tr. "Magnetohydrodynamics: Spiral-current accelerators"). CRAS 291 (5): 129–131. Paris: French Academy of Sciences.

17 J.P. Petit; M. Billiotte (May 4, 1981). "Méthode pour supprimer l'instabilité de Velikhov" (tr. "Method for eliminating the Velikhov instability"). CRAS 292 (II): 1115–1118. Paris: French Academy of Sciences.

18 J.P. Petit (September 1983). "Is supersonic flight without shock wave possible?" in 8th International Conference on MHD Electrical Power Generation. Proceedings, Moscow, Russia.

19 J.P. Petit (September 1983). "Cancellation of the Velikhov instability by magnetic confinment" in 8th International Conference on MHD Electrical Power Generation. Proceedings, Moscow, Russia.

20 J.P. Petit (September 1983). "Spiral electric currents with high appearent Hall parameter confinment" in 8th International Conference on MHD Electrical Power Generation. Proceedings, Moscow, Russia.

21 J.P. Petit; B. Lebrun (November 1986). "Shock wave cancellation in gas by Lorentz force action" in 9th International Conference on MHD Electrical Power Generation, Tsukuba, Japan. Proceedings III, Part. 14.E - MHD Flow, art.5: 1359–1368.

22 B. Lebrun [dir. J.P. Petit] (1987). "Approche théorique de la suppression des ondes de choc se formant autour d'un obstacle effilé placé dans un écoulement supersonique d'argon ionisé à l'aide de forces de Laplace" (tr. "Theoretical study of shock wave annihilation around a flat wing in hot supersonic argon flow with Lorentz forces". Engineer-Doctor thesis, Aix-Marseille University; & Journal of Mechanics, France.

23 J.P. Petit; B. Lebrun (1989). "Shock wave annihilation by MHD action in supersonic flow. Quasi one dimensional steady analysis and thermal blockage". European Journal of Mechanics B/Fluids 8 (2): 163–178.

24 J.P. Petit; B. Lebrun (1989). "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 (4): 307–326.

25 J.P. Petit; B. Lebrun (October 1992). "Theoretical analysis of shock wave anihilation with MHD force field" in 11th International Conference on MHD Electrical Power Generation. Beijing, China. Proceedings III, Part.9- Fluid dynamics, art.4: 748–753.

26 J.P. Petit; J. Geffray (22-26 September 2008). "MHD flow-control for hypersonic flight" in 2nd Euro-Asian Pulsed Power Conference (EAPPC2008), Vilnius, Lithuania; and in Acta Physica Polonica A 115 (6): 1149–11513 (June 2009).

27 J.P. Petit; J. Geffray (22-26 September 2008). "Wall confinement technique by magnetic gradient inversion. Accelerators combining induction effect and pulsed ionization. Applications." in 2nd Euro-Asian Pulsed Power Conference (EAPPC2008), Vilnius, Lithuania; and in Acta Physica Polonica A 115 (6): 1162–1163 (June 2009).

28 J.P. Petit; J. Geffray (22-26 September 2008). "Non equilibrium plasma instabilities" in 2nd Euro-Asian Pulsed Power Conference (EAPPC2008), Vilnius, Lithuania; and in Acta Physica Polonica A 115 (6): 1170–1173 (June 2009).

29 J.P. Petit; J. Geffray, F. David (19-22 October 2009). "MHD Hypersonic Flow Control for Aerospace Applications", AIAA-2009-7348, in 16th AIAA/DLR/DGLR International Space Planes and Hypersonic Systems and Technologies Conference (HyTASP), Bremen, Germany.

N.B.: To download some of these papers, please see the Documents section.