Analysis of Disk AC MHD Generator Performance by Finite Element Method

Transcription

1 J. Plaa Fuion Re. SERIES, Vol. 9 () Analyi o Dik AC MHD Generator Perorance by Finite Eleent Method Pattana INTANI, Toru SASAKI, Takahi KIKCHI and Nob.HARADA Departent o Electrical Engineering, Nagaoka niverity o Technology, 63-, Kaitoiokaachi, Nagaoka, Niigata 94-88, Japan (Received: Noveber 9 / Accepted: 6 March ) Thi paper tudie the poibility to generate alternating current (AC) electrical power by uing dik MHD generator. It phenoenon i perored by the inite eleent ethod (FEM). The coniguration o generator conit o a channel, an inulator and tator. The hape o channel i a lat dik, the liquid etal ued a conductor low inide the channel. A a channel wall, an inulator i ued to eparate the etal luid and tator. The tator winding i deigned a the coil on top and botto o a channel. nder thi condition, it can produce a agnetic ield by ean o tie haronic unction. The interaction between the etal luid and the electroagnetic wave can be explained by Maxwell equation and Oh law. A a reult, the ditribution o agnetic lux denity throughout the channel i evidently hown in two-dienional pace. The active power i liited by lip value and electrical conductivity. The optiized value o active and reactive power i uggeted by all lip value a lip -.. In addition, echanical power and power diipation in the generator are reported in ter o - and repectively. Electrical eiciency i explained in ter o /(-). Keyword: MHD Generator an AC MHD Generator MHD induction generator. Introduction Recently, Magnetohydrodynaic (MHD) generator i eectively utilized to generate electrical energy becaue o it iple tructure and could directly convert theral energy into electrical energy. An MHD generator can produce high power denity with low environental iue. On the other hand, an AC MHD generator i one type o MHD generator that generate an AC power without an inverter. It peror under the interaction between traveling wave and electrically conducting luid. The tator winding i erved a a tep-up tranorer by increaing terinal voltage and alo reducing arature current. A a reult, operating characteritic and deign conideration o an AC MHD generator have been propoed by W.D. Jackon and E.S. Pieron in 965 [,]. An annular and a linear type o the generator are conidered under the condition o etal luid and agnetic ield. The etal luid i eutectic odiu potaiu (Nak). It ha high electrical conductivity. W.D. Jackon and E.S. Pieron uggeted that the perorance o an AC MHD generator depend on agnetic Reynold nuber baed on the wavelength and the value o lip. Aterward, the theory and experient o a linear AC MHD generator uing liquid etal ha been propoed by T.C. Wang and S.J. Dudzinky in 967 [3,4]. with dierent approach or calculate. However, ot o all tructure are conidered with double-ide exciting winding to generate AC power. In addition, the quai-one-dienional technique alo applied to invetigate it. Thi paper propoe the ethod to generate AC power by the dik MHD generator. The perorance o the generator i explained by inite eleent ethod. A ingle-ide exciting winding o MHD generator i conidered. It coniguration contain a channel, an inulator and tator. The hape o channel i a lat dik. The liquid etal i acted a a conductor lowing inide the channel. Channel wall acted a an inulator eparate etal luid and tator coil. The tator winding i deigned a the coil on top and botto o channel. In thi condition, top tator winding can produce a agnetic ield by ean o tie haronic unction in the ae direction with etal luid. On the contrary, botto tator winding i ued a an inductive coil. The behavior o interaction between the etal luid and electroagnetic wave can be explained by Maxwell equation and Oh law baed on the ethod o inite-eleent. The econd order o triangular inite eleent i utilized to calculate the agnetic vector potential. The ditribution o agnetic vector potential and agnetic lux denity throughout channel i evidently hown in two-dienion pace. Active power on top and the botto o tator urace i real part o the urace integrating Poynting e-ail:intani@tn.nagaokaut.ac.jp 58 by The Japan Society o Plaa Science and Nuclear Fuion Reearch

2 P. Intani et al., Analyi o Dik AC MHD Generator Perorance by Finite Eleent Method vector over the luid urace. While reactive power i deined by iaginary part o integrating Poynting vector over the luid urace. Finally, echanical power, power diipation and electrical eiciency are conidered by induction achine equation.. Baic o an AC MHD generation The principle o an AC MHD generator operation i the ae a that o a polyphae induction generator. In an induction generator, a rotating agnetic ield (B) i generated by a ditributed polyphae winding. The rotating ield induce a voltage (E) in conductor ibedded in the periphery o the cylindrical rotor. Hence, the current denity in the conductor depend on electrical conductivity () o the conductor in ter o E. In addition, induced voltage in conductor can be changed with varying velocity () o conductor. Conequently, the induced voltage in the conductor i explained by cro product o velocity o rotor and agnetic lux denity ( B). The current denity in conductor i replaced in ter o ( B). Thereore, the induced voltage in the conductor due to oving conductor in tie varied ield i replaced by E ind =E+ B. The current denity in conductor i explained by Oh law in ter o J ind =(E+ B). The energy in the conductor i tranerred into electrical load by connecting the conductor. ield in ter o tie haronic unction. Alo, energy ro the interaction between agnetic ield and etal luid can be extracted by inductive coil. 3. Analyi odel The MHD cheatic o the ingle-ide dik AC MHD generator i hown in Fig.. The coniguration o dik channel i yetry. Alo, right hand ide o dik channel i invetigated and applied to ake the odel o AC MHD generator. The odel ued or nuerical iulation i illutrated in Fig.3. The area o etal luid (I), channel wall (II) and tator (III) i deigned in the Cylindrical coordinate yte. The etal luid low along r-direction with contant velocity ( ). Beide, the electrical conductivity and pereability are replaced by conductivity = and pereability =, repectively. Channel wall act a inulator eparate the etal luid and the tator. Alo, the electrical conductivity and pereability are replaced by conductivity = i and pereability = i, repectively. Electrical conductivity and pereability o tator are deined by = c and = c, repectively. The top tator winding i connected with three phae yte which produce traveling wave velocity ( ) along r-direction. In thi paper, the top tator winding i replaced by urace current denity. On the other hand, energy ro interaction between agnetic ield and etal luid i tranerred to electrical load by inductive coil that intalled at botto tator. E ind E B Z r B B E ind E B E ind E B B Fig. Baic o AC MHD generation. Figure how the baic o linear AC MHD generator. The tator o AC MHD generator iilarly act a in the general induction generator. However, it winding are ditributed in a lat agnetic tructure. Thereore, the otion o the ield i a traight line rather than rotating a in a generator. The rotor i replaced by a layer o etal luid conined in an envelope o rectangular cro ection o the channel. Induced current in the etal luid depend on the current denity in ter o J ind =(E+ B). Thereore, the induced current generate the agnetic Fig. Coniguration o the dik AC MHD generator. J jt J e z Fig.3 The odel o an AC MHD generator. r, c c, i i,, c c 58

3 P. Intani et al., Analyi o Dik AC MHD Generator Perorance by Finite Eleent Method The phenoenon o AC MHD generator i explained by Maxwell equation. It can be evaluated by the ollowing orula, while a diplaceent current denity i neglected: E B / t () H J () B (3) J (4) where E i electric ield intenity H i agnetic ield intenity B i agnetic lux denity J i current denity By Oh law neglecting Hall eect, the current denity equation i given by J E B. (5) The relationhip between agnetic lux denity and vector agnetic potential i explained by B A. (6) The coponent o agnetic lux denity (B) in the Cylindrical coordinate, are replaced by B r =-A/z, B z =-(ra)/rr and B =. Alo, the electric ield intenity i expreed a A E, (7) t where A i agnetic vector potential. Subtituting (6) and (7) into (5), then a current denity i deined by Oh law a ollow A A. (8) t Fro (8), D i diplaceent current a zero when D, and ( A)=, i obtained that A(r,z,t)=rA (z)exp(j t)a where r i radiu o dik generator. A i agnitude o agnetic vector potential, a i unit vector along -direction, i angular velocity. In addition, an electroagnetic ource generating by the tator winding i replaced in ter o J =J exp(j t)a. Alo, equation (9) can be decribed by A j r r A r A J, () where =, i the electroagnetic wave requency, j i iaginary part o coplex nuber and J i an aplitude current denity at tator winding. The relationhip between angular velocity and wave velocity i deined a. () where i wavelength. Alo, the relationhip between wave velocity ( ) and etal luid velocity ( ) i repreented by the lip value () a. () The appearance o dierent requencie in exciting winding and etal luid i explained by =. Alo, ubtituting () and () into (), then a agnetic vector potential i deined by A - j A r r - J. A r (3) Fro (3), the agnetic vector potential i a unction o the lip value. The tandard algorith [5] o inite eleent analyi i reerred in thi paper. A A A. (9) t 4. Finite eleent orulation The AC MHD equation i evaluated in inite eleent ethod. The agnetic vector potential (A) i deined by 5. Power low in AC MHD generator The power low in AC MHD generator i evaluated by uing electrical power. The echanical power i the preure gradient through the channel by applying electroagnetic orce. Furtherore, an electrical power i calculated by integrating Poynting vector over the luid urace (). The active power i evaluated by 58

4 P. Intani et al., Analyi o Dik AC MHD Generator Perorance by Finite Eleent Method P Re E z H d, (4) where d i channel urace and H i coplex conjugate o agnetic ield intenity. The reactive power o generator i deined by iaginary part o integrating Poynting vector over the luid urace a paraeter in the iulation odel are lited in Table. Thi odel i divided into 79 eleent and 665 triangular eleent node. The econd-order i conidered in thi paper. In cae o boundary condition, the agnetic vector potential at the edge o botto and top tator i deined by zero (A=) A Q I E z H d. (5) 6 J. 5 e j t, c The echanical power i the relationhip between electrical power and lip. It i calculated by, A 6 i, i P Re E z H d ( ). (6) Moreover, the power diipation ro generator can be deined by d Re E z H d P, (7) where P i the echanical power in luid baed on electroagnetic orce. P d i the power diipation in the generator. Thu, electrical eiciency o induction generator i given by P. (8) P Thereore, the electrical eiciency () i deterined by only the luid electrical loe in channel. 6. Nuerical reult and dicuion The AC MHD generator coniguration i deigned by condition o contant luid velocity throughout the channel illutrated in Fig. 4. The electrical conductivity and pereability are replaced by electrical conductivity o a eutectic odiu potaiu a = 6 S/ and a pereability o ree pace a =4-7 H/, repectively. The channel wall are electrical inulator, conductivity and pereability are deined by i = and i, repectively. Electrical conductivity and pereability o tator a lainated teel are deined by c = and c repectively. The tator on top i an exciting winding with traveling wave J =.5exp(j t) A/ along r-direction with =.54. Phyical Fig.4 Coniguration o AC MHD generator conideration. Table. Paraeter or conideration. Paraeter Value Power line requency (Hz) 5 Pereability o etal luid (H/) 4-7 Pereability o iron core (H/) 4-7 Pereability o inulator (H/) 4-7 Electrical conductivity o etal luid (S/) 6 Current denity (A/ ).5x 6 Wave length ().54 Wave velocity (/) 7.7 Magnetic Reynold nuber.4 The nuerical iulation i invetigated the odel o AC MHD generator which i produced AC power ro interaction between traveling wave and etal luid. The power low in AC MHD generator i evaluated under the ratio o the etal luid velocity and the electroagnetic wave velocity which i the lip value in ter o =( - )/. In thi paper, the range o the lip value i deined by -. In cae o the negative lip value, the velocity o etal luid i higher than two tie o the velocity o electroagnetic wave. The axiu active power o -.54kW at =-.6 with = 6 S/ i hown in Fig.5. The negative active power i expreed by generating electrical power in the MHD channel. On the contrary, i the velocity o traveling wave i higher than etal luid velocity, the lip value i poitive. Thi phenoenon act a an accelerator. The etal luid i accelerated by electroagnetic orce. The axiu power ued or propulion i.77kw at lip =.7 with electrical conductivity = 6 S/. Neverthele, in the range o the lip value -.., thi area ha low active power; the generator i acted a accelerator. A a reult, the AC MHD generator i deigned with all lip 583

5 P. Intani et al., Analyi o Dik AC MHD Generator Perorance by Finite Eleent Method value.. In the ae way, i generator i acted a an accelerator. It i deigned with high lip value.. Active power [kw] kW Fig.5 The relationhip between active power and lip Figure 6 and 7 how agnetic lux denity ditribution at =-.6 and =.7, repectively. The agnetic ield not only ditribute in the channel but alo induce high agnetic lux denity at the etal urace. lip.7kw ro the reactive power in application. A a reult, the axiu reactive power a 39kVAR i around the lip value at the origin. Thi lip value hould not be ued generator and accelerator. For axiu active power, axiu reactive power in cae o generator and accelerator i 4.kVAR and 9.3kVAR, repectively. Alo, the reactive power hould be copenated by connecting a capacitor at the input terinal. Reactive power [kvar] 4.kVAR kVAR lip Fig.8 The relationhip between reactive power and lip. Fig.6 Magnetic lux denity ditribution at =-.6. Figure 9 how the relationhip between echanical power and lip. The power ued to oving the etal luid into the channel i deined by echanical power. It i calculated by the induction achine equation baed on the lip. In cae o poitive echanical power, the phenoenon act a generator, the echanical power i increae with - tie o the active power. The echanical power i 4kW with =.6. However, In cae o negative echanical power, the phenoenon act a an accelerator. Metal luid i alo accelerated by the electroagnetic orce. The echanical power i reduce with - tie o the active power. The power i -.5kW with =.7. It ugget that the echanical power o the generator i higher than the accelerator with contant active power at etal urace. Mechanical power [kw] 4kW kW Slip Fig.7 Magnetic lux denity ditribution at =.7. Figure 8 how the relationhip between reactive power and lip. The optiized range o lip i evaluated Fig.9 The relationhip between echanical power and lip. Lo in the generator i explained by the power diipation and lip in Fig.. The power diipation i evaluated by product o lip value with an active power. In cae o generator, the axiu power diipation increae 584

6 P. Intani et al., Analyi o Dik AC MHD Generator Perorance by Finite Eleent Method with all lip value. Since, high agnetic lux denity appear at the urace o etal luid near exciting winding. Power diipation i.5kw with =-.6. In cae o an accelerator, the axiu power diipation i increae with increaingly value o lip. The axiu power diipation i.kw with =.7. Power diipation [kw].5kw kw Slip Fig. The relationhip between power diipation and lip. The electrical eiciency i evaluated only under the luid electrical loe. Figure how the electrical eiciency o AC MHD generator and accelerator depend on value o /(-) and (-), repectively. In cae o generator, the axiu active power with -.54kW at =-.6 and = 6 S/ i hown in Fig. 6. At thi point, electrical eiciency i 6.5%. In cae o accelerator, the axiu active power with.7kw at =.7 and = 6 S/ i hown in Fig. 5. At thi point, electrical eiciency i 3%. Eiciency [%] 6.5% Slip 3% Fig. The relationhip between electrical eiciency and lip. The relationhip between abolute axiu active power and electrical conductivity o the etal luid i hown in Fig.. The optiu value o the electrical conductivity i deined by =5 6 S/ or active power.7kw. However, electrical conductivity i le than =5 5 S/, a axiu active power decreae. A a reult, the generator ha high power diipation. Moreover, an electrical conductivity i higher than =5 7 S/, a axiu active power decreae. Thu, an electroagnetic induction appear on the etal urace. However, a axiu reactive power i contant Active power [kw] 3 Active power.e+4.e+5.e+6.e+7.e+8 Electrical conductivity(s/) Reactive power Reactive power [kvar] Fig. The relationhip between active power, reactive power and electrical conductivity. 7. Concluion Thi paper ha propoed the poibility to produce an AC power by dik MHD generator with a ingle-ide exciting. It perorance i evaluated by inite eleent ethod. The reult conir that the ditribution o agnetic ield appear at the etal urace and high agnetic lux denity. The active power o interaction between traveling agnetic ield and etal luid i liited by the lip value and electrical conductivity o the etal luid. The optiized value o an active and reactive power o the generator i uggeted by all lip value a -.. Maxiu power in thi yte i uggeted with active power (-.54kW), reactive power (4.kVAR), echanical power (4kW), power diipation (.5kW) and eiciency (6.5%). In addition, active power i unction o electrical conductivity. However, AC MHD generator i adjuted to accelerator by.. Maxiu power in thi yte i perored by active power (.7kW), reactive power (9.3kVAR), echanical power (-.5kW), power diipation (.kw) and eiciency (3%). 8. Reerence [] W. D. Jackon, and E. S. Pieron, "Operating characteritic o the.p.d. induction generator," Int. o Elec. Engr., London, Con. Rept., Ser. 4, pp (963). [] W. D. Jackon, E. S. Pieron, and R. P. Porter, "Deign conideration or MHD induction generator," Proc. Internat'l Syp. on Magnetohydrodynaic Electrical Power Generation.Pari: Organization or Econoic Cooperation and Developent, European Nuclear Energy Agency, pp (964). [3] T. C. Wang, and S. J. Dudzinky, "Theoretical and experiental tudy o a liquid etal MHD induction generator," AIAA J. vol. 5, pp. 7- (967). [4] T. C. Wang and S. J. Dudzinky, "Coparion o MHD induction generator analye," AIAA J., vol. 5, pp. 59-6(967). [5] Joao Pedro, A. Bato and Nelon Sadowki, " Electroagnetic odeling by inite eleent ethod," (3). 585