Modeling of the Thermal Behavior of an Electric-Vehicle Battery

HWAHAK KONGHAK Vol. 38, No. 5, October, 2, pp. 63-68 (Journal of the Korean Institute of Chemical Engineers) * * S. V. Berezhnoj ** * **on leave from Physical Technical Department, St. Petersburg State Technical University, Russia (2 2 22, 2 7 3 ) Modeling of the Thermal Behavior of an Electric-Vehicle Battery Chang-Yeon Yun, Chee Burm Shin, Cheol-Nam Yang*, Seong-Yong Park* and S. V. Berezhnoj** Dept. of Chem. Eng., Ajou University *Institute for Advanced Engineering **on leave from Physical Technical Department, St. Petersburg State Technical University, Russia (Received 22 February 2; accepted 3 July 2),!"# $%& ' 3( )*+#,-&.. // 1 2345 /67 89 :9; <=>?@; A &.@B, CDE FG&H IJ&?@; KL&M N3# OP&.. QR ST U/V WXY@;Z K U/ [' DE \, ] V ^_\, ]/` &.. a, N Lbc deu/v %L&?f@; Db Sg U/ $%# Kh&H Y@;Z V Wi\, ] jk; l\, ]H &.. m <2 =n S op q ri sn@; tu, ]. Abstract A three-dimensional modeling was carried out to investigate the effects of operating conditions, ambient conditions, and design factors on the thermal behavior of an electric-vehicle(ev) battery. Thermal conductivities of various compartments of the battery were estimated based on the equivalent network of parallel/series thermal resistances of battery components. Heat generation rate was assumed to be uniform throughout battery electrodes. The maximal temperatures within the battery at various operating conditions were calculated in order to check whether the operating temperature of the battery is within acceptable range. In addition, the relation between the surface temperature of the specific region and the maximal temperature of the battery interior was obtained so that the measurement of the surface temperature may be used to predict the maximal temperature of the interior. The results of this study may be useful for the optimal design of the thermal management system of an EV battery. Key words: Modeling, Electric-Vehicle Battery, Thermal Behavior, Finite Element Method E-mail: cbshin@madang.ajou.ac.kr 1.! "# $%&'. ( )* +, HC, NO x, CO -+. / &( # LEV, ULEV1 2! "! 34 California 56 23 789# 3 :-;+ 1%1 <= +(zero emission vehicle) >(?@A '# B5 CD[1]. EF# G HI J# H 2. KL4# <! "# $% &'. M EV(electric vehicle)# lead-acid NH OP QR S>T energy density U35 Wh/kg>( VWP U 1-15 km %X D # YZ. [\! ]^# nickel/metal hydride(ni/ MH) NH OP QR! "'. Ni/MH NH energy density 67 Wh/kg %(VWP 2-3 km)( )* + 1/4-1/3 %X # D E Li-polymer NH1 EV QR# _` abc Z& d e 27 M fgh EV# Ni/MH NH ir h j>( kl! "'[2]. EV# mn =o dn p NH1 qa e?r sh tf # u vg& '. NH wxn y8z {. }>~, z %li>( v h 56 t ƒn z n 8v n 8v>( H, ; && tf '. &ˆ 56 Yi>(# H ŠP Œ wxž 63

64 S. V. Berezhnoj 1 k : "'. Ni/MH NH 56 lead-acid NH tu+& d e [' i u P &! "'[3]. # H R NH ui šw. œ ž : "# simulation program Ÿt. œ( %!, Y ( cell module # 3. Ni/MH NH y 8 z v 1 k : i ª. «'. C ^W Hg Q1 :V«!, H 8v NH ]!z o l 1 ±>(² H 8v z1 % # je>( NH ]! z1 k : "³ «'. 2. # 9Ah Ni/MH( w battery pack y zv 1 Q±>(² =o y u vg. ] : "# ]i Œ. µ_ : " # i& "'. Y ( single cell module# %ll¹ aº zv 1»w³ # ¼_[½'. : i ª ir i %n '¾ '. NH uh# À w uhžá& ` à Ä Šj>( o '. H y u& Ædz tf'. Module 56 su su È!b S'. Fig. 2. Schematic of multilayer casing. Fig. 1n Hg Q l>( Én 9 Ah Ni/MH cell ŸÊ&'. Casingn uh1 ˳ SUS( a "! œ# YÌ(ÍÎ). s yrï8 œ& Ð( ÑÒ & a "'. P! y8# Fig. 1 ÓÔ [Õ& ˆ Ö p ¾ &, & a "! Q&# ŠP vp a "'. &Ø ÙÚ 1 :q Q # & u H šw. TÛ : "# sc 2& Ü'. # H ŽÁ GÝ. &R uh &Þ. QR NH uišw. C ^W e QR# Š(mesh) (element) :1 žç : "S'. u Hßn z à uh Fig. 3. Equivalent thermal resistance networks (a) for the serial resistances and (b) for the parallel resistances. %á! âã äáå( ŽÁ&Þ. &R H æ( à n sý>( : "'[4, 5]. Casing 561 k( ça[ Fig. 2à & uh N s èé 'ê'# j. ¼ : "'. Fig. 3 TÛë j & X, ZN 56# H Ž Á& ÄÂ( Å j>(!b : "!, YN 56# `Â( Å a "# j>( o! g '¾ n Ý>( Ns uh1 g : "'. užá Hg Q Ü 8 v ;wìçn Table 1 TÛyS'. <` ŽÁ 56: k Y > R=R A +R B +R C (1) x ---- = ---- + ---- +----- k Y x A k A x B k B x C k C ( x k A + x B + x C )k A k B k C Y = -------------------------------------------------------------------------------- x A k B k C + x B k C k A + x C k A k B (2) (3) Fig. 1. Schematic diagram of a cell. 38 5 2 1 <Ä ŽÁ 56: k X, k Z > --- 1 ----- 1 1 = ----- R R A R B A k X ( or k Z ) ----------------------------- L 1 + +------ R C A A k A A B k B A C k C = --------------- + --------------- +--------------- L L L (4) (5)

Table 1. Parameters used in calculations ρ --------- g C cm 3 P --------- J k -------------- W g K Tab 8.91.465 Ni electrode 3.97 1.559 MH electrode 4.8 3.199 Vent(Al) 2.7.925 H 2 (1 atm) 8.9741 5 14.34 Separator 1.17 3.161 Casing(SUS).93 2.31 Interior coating 1.35 1.674 Exterior coating 8.27.52 k X ( or k Z ) A A k A + A B k B + A C k = --------------------------------------------------------- C A cm K 7.931 1 1 2.28 1 2 1.634 1 2 2.73 1.722 1 2 5.323 1 3 3.287 1 3 2.77 1 3 1.63 1 1 '¾n cell à module zv 1 QR s %Ý&'. 65 References 9, 12 2, 9 9 1, 11 2, 9 (6) 8v uh# à! užá GÝ>(89 al ì. QR«'. 3. Fig. 5à 6 Hg Q l>( Én 9 Ah Ni/MH cell module C QR finite element mesh1 TÛ ys'. s%ý 5 Œç. E# 1 Galerkin C& QR S![8] cell 56 QR trilinear hexahedral element :# 2,968Ÿ&~ node :# 3,726Ÿ&'. Module 56# symmetry1 &R 5 cell. Q! >T 9 memory R+ ( 3 cell. Q«'. Module QR element :# 1,8Ÿ&~ node :# 11,586Ÿ&'. [# ùà & œ&t,o l& ù# 8v & z j&é! kl # 8vn mesh1 ñ³, n {þ# mesh1 w³ «'. cell cellq& ò T ρc p ------ = ( k T) + Q t Ý (7) uh1 TÛy# matrix kà H y8 Y 8í@ tu+. TÛy# Q # '¾ & Ý>( œ '[6]. k = k X k Y k Z Q = ---------- 1 a a i a U a dv+ a c i c U c dv V cell Va a cell i app V H rxn r Vc Cell. ˆ Ÿ1 `Â( Å 12 V1 : " Eî j. module&é 8ê# Fig. 4 ŸÊ1 TÛyS'. Module QR s%ýn cell 56à Ç'. Fig. 4 [Õ& u È i vg. module p ï# su & ðq a "! cell cellq&# 4Ÿ ñ(( # òéó. ôõ ö¾>( ². Eça ø½'. èé & 8v lr,r binding 8v# uh ì. ùúa û>(² È 1?vü TÛ T³ «'. &e òéó f# ý = n ý& 1mm( l@ü m e & 8v uh# laminar {þ "'# %>( g ì. QR«'[7]. Tÿ (7) (8) (9) Fig. 5. Finite element mesh of a cell. Fig. 4. Schematic diagram of a module. Fig. 6. Finite element mesh of a module. HWAHAK KONGHAK Vol. 38, No. 5, October, 2

66 S. V. Berezhnoj éó»w # n ç { & >å( È 1?vü!b : " «'. gn SUN UltraSPARC 143 Workstation :V«>~, # CPU timen cell 56 1.5v, module 56 36v&S'. 4. Single cell. Hg Q# Ü i :# H t u+ NH1 Ï8 = z&'. H tu+n N H Àà Œ èé ßé³ '. èé # Ý (9)(89 1C( sh e tu+. /(.1[W/cm 3 ]) >( Œ tu+ ±ã :V«'. P! z# èé & å( 2 o C1 / z( 1 o C, 3 o C 56!b Hg Q1 $«'. &e QR NH Ï8œ uhß :ìn.5[w/cm 2 rk]&'[9]. Fig. 7# al Œ %ll¹ ß. e zv 1 TÛë j&'. [ ¼ : "Õ& NH ]!z# H & "#, Y8»w # j. : "'. P! cell l8# : {. }_ H Ën H. èé l8( u& Hß. ¼ : "'. Fig. 8# cell y Ns >( z a!³»w #1 TÛy /'. (a) 56# XN s >( z 1 TÛë j&'. "6 p ¾ ; & ( 'ê e : qi>(# Uo &1 [&T #. &$S! &# < E«'. YN s z 1 TÛë (b) 56# %%ü "6 #. &$S!, ZN s (c)# : {. }_ 5.5 cm 8^ ]! z1»w«! H & ït# Z 13.4 cm 8^ # l& ù z 1 [«'. Table 2# tu+&.1,.2,.4 W/cm 3 Ç e z 1, 2, 3 o C 56 cell y ]! ]Ž zì& a!³»w & #1 TÛë j&'. tu+& n 56#, & wxžj& QR : "E tu+& ' 56# single cell Çé (.!b > )'# j. *³ k : "'. Fig. 8. Isothermal surfaces and temperature distributions along x, y and z directions in a Ni/MH cell. Fig. 7. Isothermal surfaces distributions at steady state. 38 5 2 1 Module 56single cell 56à(.1[W/cm 3 ], 2 o C 1 />( zà tu+. ùúa ~ Hg Q1 :V«'. šü

Table 2. Maximal and minimal temperatures of a cell for various heat generation rates and air temperatures Heat generation rate[w/cm 3 ] Air temperature [ o C] Max. temperature of a cell[ o C] 67 Min. temperature of a cell[ o C] q=.1 T=1 32.3 17.2 T=2 41. 27.2 T=3 52.3 37.2 q=.2 T=1 54.6 24.3 T=2 64.6 34.3 T=3 74.6 44.3 q=.4 T=1 99.3 38.7 T=2 19.3 48.7 T=3 119.3 58.7 Fig. 1. Maximum temperature distributions along Y axis and corresponding temperature of tabs. Fig. 9. Surface temperature distribution of a module at steady state. module 56pÔ ï ß* su cell cellq& \?. QR # òéó e»w # & H zv a º {. 3q# +,[½'. Fig. 9# tu+&.1[w/cm 3 ], z 2 o C 56 %ll¹ zv 1 TÛë j&'. -Ž su È 1 +,[, Fig. 9 [# ùà & " 8. a "# su n â cell/ # z v l@ {. # j>( TÛ! ñ cell /# U³ {. 3qT 1 cell89# P {. 3q 2# j>( TÛ'. $ ( module ]! zzn '3, 3 cell TÛT# j.!b e su q# i 4 '# j. ¼ : "'. z ÆÇw. & # ( sc& 2 aa j>( Y'. '¾>( òéó»w # È 1 +,[, 1mm X D # n &E. - # u+n ¾. ¼ : "'. Fig. 9 6 & GzK&.»w! l@ü ç565 j. : "#, &# òéó # uhß& 7 ä # u& 89T e&'. Fig. 9 cell cellq& z»w # %1 [! È %1 ¼_ : "'. NH z z : 1 ;a ³ b NH y8 ]! z1 %A '. Ø <Vü ]! n z»w # Zn H y8,, Y8&'. & 8vn cell y8& e z %& W <x'. èé cell y8 z % = Ï8 š% 8v z1 thermistor1 &R %±>(² y8»w # ]!z1 > : " # j & Ü'. Ï8 z1 %# 8vn cell case, Y8 TH 8v& K%h : "'. # H 8v z à ]! z?@# Z YN s z v 1 Fig. 1 & ±>(² 8v zt š%8 œz1 %# je>( moduley ]! z v 1 k : " «'. & A# NH?H sh Yoy dn p tu( z : 1 ;að 56 NH :B Ž A NH1 a : "# MA( QRh : "'. 5. HR NH ui W. k cell à module. simulation program& Ÿt S'. Cell module 56 # 3 C& QR S>~, NH ui šw.?vü T Ûy g QR # :1 ž& À NH w uh ŽÁ& ` à ÄÂ( Å j>( o«'. &ˆ. NH?rsHC n Œ = zà n ç& NH ui W 3q# {. Q«'. # 'p Œ èó ]r] z1 ±> (² cell& z : y # 81 Y : " «>~, Ü èé ( Öq 8. 81!b : " ³ «'., % Dî H y8 ]!z1 8^EF %& R& Ï8 š%8v ze. %±>(² NH ]!z1 k : "³ z a Ü MA( &R : "³ «'. $) QR module su q# u. È i>( W# T ]!z module,8v»w # j>(!b e u vg# q i4 ¾. ¼ : "S'. & Å # H R NH ]i u P Ÿ t R MA( GRh :". j>( Y'. HWAHAK KONGHAK Vol. 38, No. 5, October, 2

68 S. V. Berezhnoj # g 8 G7 H ŸtQvA, + Ã H Ÿt Q>( SIJ'.Ž, S. V. Berezhnoj # '99 ˆ_ Ã K qq(99ˆ 6-16) _ L @1 }½IJ'. a : anode c : cathode x :x-direction y :y-direction z : z-direction A : heat-transfer area [m 2 ] a a : interfacial area of solid-phase particles per unit volume of porous anode [m 2 /m 3 ] a c : interfacial area of solid-phase particles per unit volume of porous cathode [m 2 /m 3 ] a cell : geometric electrode surface area per unit volume of cell [m 2 /m 3 ] C p : cell heat capacity at constant pressure [J/kg K] i a : local interfacial current per unit area of solid-phase particle for anode [A/m 2 ] i c : local interfacial current per unit area of solid-phase particle for cathode [A/m 2 ] i app : applied cell current per unit area of projected electrode [A/m 2 ] k i : thermal conductivity along i-direction(i=x, y, z) [W/m 2 K] Q : heat-generation rate per volume of the cell [J/m 3 s] r : reaction rate per unit volume of the cell [mol/m 3 s] U a : local enthalpy potential of anode [V] U c : local enthalpy potential of cathode [V] V : cell potential [V] V cell : volume of the cell [m 3 ] Η rxn : heat of reaction, 2.891 5 [J/mol] ρ : cell density [kg/m 3 ] 1. California Air Resource Board: Low-Emission Vehicles/Clean Fuels and New Gasoline Specifications-Progress Report, (1989). 2. Crompton, T. R.: Battery Reference Book, Butterworths, London(199). 3. Wu, M. S., Wang, Y. Y. and Wan, C. C.: J. of Power Sources, 74, 22 (1998). 4. Bennett, C. O. and Myers, J. E.: Momentum, Heat, and Mass Transfer, 3rd ed., McGraw-Hill, New York, NY(1982). 5. Bird, R. B., Stewart, W. E. and Lightfoot, E. N.: Transport Phenomena, John Wiley & Sons, Inc., New York(196). 6. Botte, G. G., Johnson, B. A. and White, R. E.: J. Electrochem. Soc., 146(3), 914(1999). 7. Gartling, D. K.: Comput. methods Appl. Mech. Engrg., 12, 365(1977). 8. Hughes, T. J. R.: The Finite Element Method, Prentice-Hall, New Jersey, NJ(1987). 9. Perry, R. H.: Perry s Chemical Engineers Handbook, 6th ed., Mc- Graw-Hill, New York, NY(1984). 1. Welty, J. R., Wicks, C. E. and Wilson, R. E.: Fundamentals of Momentum, Heat, and Mass Transfer, 3rd ed., John Wiley & Sons, New York, NY(1984). 11. Reid, R. C., Prausnitz, J. M. and Poling, R. E.: The Properties of Gases and Liquids, 4th ed., McGraw-Hill, New York, NY(1987). 12. Dean, J. A.: Lange s Handbook of Chemistry, 13th ed., McGraw- Hill, New York, NY(1973). 38 5 2 1