Prologue to MHD and Applications to Thermofluids of Fusion Blankets .


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  Introduction to MHD and Applications to Thermofluids of Fusion Blankets. One of a number of lectures given at the Institute For Plasma Research (IPR) at Gandhinagar, India, January 2007 Mohamed Abdou (web: http://www.fusion.ucla.edu/abdou/ )
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Prologue to MHD and Applications to Thermofluids of Fusion Blankets One of various addresses given at the Institute For Plasma Research (IPR) at Gandhinagar, India, January 2007 Mohamed Abdou (web: http://www.fusion.ucla.edu/abdou/) Distinguished Professor of Engineering and Applied Science Director, Center for Energy Science and Technology(CESTAR) ( http://www.cestar.seas.ucla.edu/) Director, Fusion Science and Technology Center ( http://www.fusion.ucla.edu/) University of California, Los Angeles (UCLA) Abdou Lecture 4

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Introduction to MHD and Applications to Thermofluids of Fusion Blankets OUTLINE MHD* rudiments MHD and fluid covers UCLA exercises in thermofluid MHD * Our center is incompressible liquid MHD. Try not to blend with Plasma Physics. Abdou Lecture 4

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MHD nuts and bolts What is MHD ? MHD applications Magnetic fields Electrically directing liquids MHD conditions Scaling parameters Hartmann issue MHD stream in a rectangular channel MHD weight drop Electric protection Complex geometry/non-uniform B-field Numerical reproduction of MHD streams Abdou Lecture 4

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MHD covers marvels in electrically leading liquids, where the speed field V , and the attractive field B are coupled. Any development of a leading material in an attractive field creates electric streams j , which thus actuates an attractive field. Every unit volume of fluid having j and B encounters MHD constrain  j x B , known as the "Lorentz drive". What is MHD ? In MHD streams in cover channels, communication of the actuated electric ebbs and flows with the connected plasma-constrainment attractive field brings about the stream contradicting Lorentz drive that may prompt high MHD weight drop, turbulence adjustments, changes in warmth and mass exchange and other essential MHD wonders. Abdou Lecture 4

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Alfv é n was the first to present the expression "MAGNETOHYDRODYNAMICS". He portrayed astrophysical marvels as an autonomous logical teach. The official birth of incompressible liquid Magnetohydrodynamics is 1936-1937. Hartmann and Lazarus performed hypothetical and exploratory investigations of MHD streams in pipes. The most fitting name for the marvels would be " MagnetoFluidMechanics ," however the first name "Magnetohydrodynamics" is still for the most part utilized. A couple of certainties about MHD Hannes Alfvén (1908-1995), winning the Nobel Prize for his work on Magnetohydrodynamics. Abdou Lecture 4

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Astrophysics (planetary attractive field) MHD pumps (1907) MHD generators (1923) MHD stream meters (1935) Metallurgy (enlistment heater and throwing of Al and Fe) Dispersion (granulation) of metals Ship drive Crystal development MHD stream control (decrease of turbulent drag) Magnetic filtration and division Jet printers Fusion reactors (cover, divertor, limiter, FW) MHD applications, 1 GEODYNAMO A depiction of the 3-D attractive field structure reproduced with the Glatzmaier-Roberts geodynamo show . Attractive field lines are blue where the field is coordinated internal and yellow where coordinated outward. One year of calculations utilizing a supercomputer! Nature , 1999. Abdou Lecture 4

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In some MHD applications, the electric current is connected to make MHD impetus compel . An electric ebb and flow is gone through seawater within the sight of an exceptional attractive field. Practically, the seawater is then the moving, conductive part of an electric engine, pushing the water out the back quickens the vehicle. The primary working model, the Yamato 1 , was finished in Japan in 1991.The ship was first effectively impelled 1992. Yamato 1 is moved by two MHD thrusters that keep running with no moving parts. In the 1990s, Mitsubishi constructed a few models of boats moved by a MHD framework. These boats were just ready to achieve paces of 15km/h, notwithstanding higher projections. MHD applications, 2 A case of advantageous use of MHD: Ship Propulsion Generation of drive constrain by applying j and B in Jamato 1 (Mitsubishi, 1991). Abdou Lecture 4

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Earth – 0.5 10 - 4 T Sun – 10 - 4 T, up to 0.4 T at sunspots Jupiter – 10 - 2 T (most grounded planetary attractive field in the nearby planetary group) Permanent research center magnets with ~0.1 m crevice – around 1-2 T Electromagnets – 25-50 T Fusion Reactor (ARIES RS) – 12 T Experimental Fusion Reactor (NSTX) – 1.5 T Magnetic fields Supplying energy to the world\'s most grounded long-beat magnet at Los Alamos\' National High Magnetic Field Laboratory is a 1.4 billion-watt generator, itself the biggest among attractive power sources. It can create enough vitality to control the whole condition of New Mexico. Abdou Lecture 4

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Electrically leading liquids * , electrical conductivity (1/Ohm m), indicates capacity of fluid to interface with an attractive field Abdou Lecture 4

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MHD conditions Navier-Stokes conditions with the Lorentz compel (1) Continuity (2) Energy condition with the Joule warming (3) Ampere\'s law (4) Faraday\'s law (5) Ohm\'s law* (6) *Eqs.(4-6) are generally assembled together to give either a vector acceptance condition or a scalar condition for electric potential Abdou Lecture 4

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Basic scaling parameters Reynolds number Magnetic Reynolds number Hartmann number Alfven number Stuart number (association parameter) Batchelor number (attractive Prandtl number) Abdou Lecture 4

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Z 2a 2b Y X (stream course) B 0 Hartmann issue, 1 J. Hartmann , Theory of the laminar stream of electrically conductive fluid in a homogeneous attractive field , Hg-Dynamics, Kgl. Danske Videnskab. Selskab. Tangle.- fus. Medd., 15, No 6, 1937. Major MHD issue. MHD simple of plane Poiseuielle stream. Exemplary detailing (J.Hartmann, 1937) tended to completely created stream in a rectangular conduit with an expansive angle proportion, a/b>>1. Scientifically, the issue decreases to two coupled 2-d arrange ODEs, understood diagnostically. Abdou Lecture 4

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Hartmann layer  Ha  b/Ha Z +b X 0 - B 0 Hartmann issue, 2 If Ha develops, the speed profile turns out to be increasingly smoothed. This impact is known as the "Hartmann impact" . The thin layer close to the divider where the stream speed changes from zero to U m is known as the "Hartmann layer" . The Hatmann impact is created by the Lorentz constrain, which quickens the liquid in the Hartmann layers and backs it off in the mass. Abdou Lecture 4

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t w Y B 0 2a Z 2b  MHD stream in a rectangular channel, 1 Formulation of the issue Dimensionless parameters: J.C.R.Hunt, " Magnetohydrodynamic Flow in Rectangular Ducts ," J.Fluid Mech., Vol.21, p.4. 577-590 (1965) ( Hartmann number ) ( divider conductance proportion ) ( viewpoint proportion ) Fully created stream conditions (dimensionless): Boundary conditions: Abdou Lecture 4

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MHD stream in a rectangular conduit, 2 Duct with protecting dividers ( c w =0). Instigated attractive field Ha=600, c w =0,  =2,  =0 Hartmann layers B 0 Electric streams prompted in the stream mass close their circuit in the thin Hartmann layers at the channel dividers opposite to the connected attractive field. Abdou Lecture 4

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The speed profile is straightened in the mass. High speed angles show up close to the dividers. At the dividers opposite to the B-field, two MHD limit layers with the thickness ~1/Ha are framed, called "Hartmann layers". At the dividers parallel to the attractive field, there are two optional MHD limit layers with the thickness ~ 1/Ha 0.5 , called "side layers". Side layer Hartmann layer MHD stream in a rectangular conduit, 3 Duct with protecting dividers ( c w =0). Speed Abdou Lecture 4

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MHD stream in a rectangular conduit, 4 Duct with leading dividers ( c w >0). Prompted attractive field Ha=600, c w =0.1,  =2,  =0 B 0 Much more grounded electric streams are incited contrasted with the non-leading conduit. The streams close their circuit through the dividers. Abdou Lecture 4

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High-speed planes show up close to the dividers parallel to the B-field. The speed profile is called "M-molded". The fly development happens because of high stream contradicting vortical Lorentz compel in the mass, while no constrain shows up close to the parallel dividers. The M-molded profile has expression focuses. Under specific conditions, the stream gets to be precarious. MHD stream in a rectangular pipe, 5 Duct with directing dividers ( c w >0). Speed Abdou Lecture 4

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Hartmann layer  Ha  b/Ha Z +b X 0 - B 0 MHD weight drop Hartmann stream  is the weight drop coefficient If Ha  0,  0 =24/Re. I. Non-directing dividers (c w =0), Ha>>1: II. Leading dividers (c w >0), Ha>>1: Conclusion: In electrically directing channels in a solid attractive field, the MHD weight drop is ~ Ha 2 , while it is ~ Ha in non-leading pipes. LM cover: Ha~10 4 ! Abdou Lecture 4

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Either protecting coatings or stream additions can be utilized for decoupling the fluid metal from the electrically directing dividers to diminish the MHD weight drop. Indeed, even minuscule imperfections in the protection will bring about electrical streams shutting through the dividers. Challenge: Development of stable coatings with great protection attributes. Divider Coating Liquid metal R ins Emf R w R Ha Electrical protection Current spillage through an infinitesimal break in a 50 m protecting covering Electro-circuit relationship Abdou Lecture 4

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Complex geometry and non-uniform attractive field MHD streams are comparative in nature. The particular component is 3-D (hub) streams , which are in charge of additional MHD weight drop and M-formed speed profiles. Such issues are extremely troublesome for diagnostic studies. Test and numerical information are accessible, indicating N Flow S Complex geometry/non-uniform attractive field Fringing B-field US-BCSS Cross-sectional and hub streams in MHD stream in a non-uniform B-field Abdou Lecture 4

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