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• ' ' ' ' '. . ' I • " ' ' \' \ l I ' ' ' ., 1 ' ' ' .. i , I, 14 ' r ' 1 ,1 ' I ( ,t l l • ,'I.;; , , , 1 ' I ri !' '') • , ' '' ' ' ,,, I , ,:'-·! ' ' I ' ' f,' ' I 11 ,, ' 'J ty '' ' I' I ' , l I '• 1,j 1,~fl ~ • ,. , J' ' •.. 1 , ' I I • 1 \ ,~r,.,. , • .Ji:'fi I ' i ~ '1· ' J • ~ · ·SPE':.t lllc:POWER ·01~ MHD-rGENEM.To· \'I 1 . \ I I '· ' I ' ' ' ' ' '' ' ' .' ' ( I' Wtrr.II'MOVING MAGNETIC FIELD I• "•· ft\ 1 °J' (L:o¢ul tli'eoky ofMagnetic. Turbine) . f :~ 11' t ' •· i ' ' 1:. This docunzent ·:&escribe.L~ a proce·s&:,..patentecf byr A•nclr~w 1-Cazantsev a,., '.f4d is protected under all laws applicable. }>]~ase cpmmunicate·Via SC1N, Inc. representing the' inte~est of the pqtent holder. ' ~ ' ' ,• ' In this article I i' , consider resolving €} MH~:· ·~q~'l:l;tion system for a two~djrnension,tflow of an ionized ... working medium (for e~~~~~; '.!;~·g~.·:, temp*ra~tire gas or plasma) intera'cting with ·moving magnetic ' fiela·: · L·et's .ust~· :a . :~andatd : eqillltl6n ·system lnc;luding .the morr1~n~~m .. equatio~ the continuity \ equation,.the Ofiln's laW: ·' · I I , 1 p(liV/qr) +·grad P = f == ]x B (1) pv:r.F =canst I ] = o{~x B+ E)-(_qJf)!Jx BJ \ . . r. \ ' ' ' (2) " (3) i· \. ·' } where: p v t p I I I !I I l l I \" t • v.~ F a E t ' Ez' - current density, - magnetic ind·u ction, , . - flow speed projection on "x" coordmate, _duct cross-section area, - flow conductivitt,, - electric iritynsity, · · Wx, Vx, Ux, Jx z Wz, Vz, Uz, Jz = fl · _I-Iall's parameter . ())r • By - flow velocity, - time, - pressure, - specific electromagnetic force, J B r" i y - n1ass density, : ;' ~ .. · , , ,, t fields and velocities, which are shown on the Let's use as positive direction5 ·thQs:e .o·f curren s, , , .' t k and assume that flow parameters figtlre. L~t's resolve a stationary (8/ot :;=:: ~) two-dimens10; t:~ential coordinate) because a du ti don't change (oli)z ,- 0) a1011g th~ "'z" ?oord~at~s(t~ar:;;~~al ring duct with.a constant cross- ecti n infinite along Pz" coordinate (for example, if thi _ ) ly the following condition result fr m . . ib·Ie flow (p - const on ' area F). lf to consider an mcompress1 . tI l<