Crbon fom impregnted with Phse Chnge Mteril (PCM) s therml brrier Osm Meslhy 1, Khlid Lfdi 1,2, nd Ahmed Elgfy 1 1 University of Dyton Reserch Institute, 300 College Prk, Dyton OH. 45469 USA 2 AFRL/MLBC, WPAFB, OH 45433 USA Corresponding uthor e-mil ddress: meslhom@notes.udyton.edu Introduction Control of temperture nd/or het trnsfer is of crucil importnce in numerous technicl processes nd nturl occurrences. This cn be chieved by using therml brrier to protect bounding surfces of system of interest. A therml brrier utilizing solid liquid phse chnge mteril PCM is one of the pssive therml mngement techniques receiving gret interest due to its inherent dvntge of simplicity nd relibility. Vrious geometric configurtions hve been considered for the phse chnge therml mngement devices. The configurtion of PCM-filled rectngulr cvity ws considered for spcecrft therml control [1]. The use of finned rectngulr PCM-filled cvities ws nlyzed for therml control of electronic equipment [2]. A numericl nlysis ws presented for therml protection chrcteristics of verticl rectngulr cell filled with solid-liquid PCM nd ir lyer [3,4]. In this work, the buoyncy induced flows developed in both the ir filled lyer nd the molten PCM zone were modeled s two-dimensionl lminr Newtonin flow. Although PCMs like prffin wxes exhibit desirble properties s PCMs, they present low therml conductivity. This property reduces the therml response of the therml protection system nd thereby my cuse system overheting. Different techniques to offset this low therml conductivity re studied minly experimentlly. These techniques include dding mtrix structure [5], dding crbon fibers or crbon fiber brushes [6,7]. It ws found tht using these techniques hs gret effect on enhncing the PCM therml conductivity. Melting nd solidifiction of PCM inside porous mtrix is very complicted phenomenon. This is becuse there will be the solid phse of the porous mtrix nd the PCM which my be in solid, liquid or mushy stte. Due to this complicted structure most of the works, which hs been done in this field re bsed on volume verging of the microscopic conservtion equtions to ccount for the complex interfcil structures of ech constituents. This model offers the dvntge tht the entire domin cn be treted s single region governed by one set of conservtion equtions. In other words, the sme equtions cn be used for the melt s for the fully solidified regions. Freezing nd melting of wter in sturted porous medi contined in vrious enclosures hve been studied experimentlly nd numericlly by Wever nd Visknt [8]. Their freezing experiments in rectngulr cvity clerly showed the influence of nturl convection on the solid/liquid interfce shpe nd motion. Beckermnn nd Visknt [9] combined numericl nd experimentl studies for solid/liquid phse chnge in porous medi with nturl convection in the molten region. Their model is bsed on
volume verged trnsport equtions, while phse chnge is ssumed to occur over smll temperture rnge. Experiments re performed in verticl, squre enclosure using gllium nd glss beds s the PCM nd the porous mtrix respectively. In this work different crbon foms with different therml conductivities nd porosities filled with prffin wx re introduced s therml brrier or crrier to protect bounding surfces of system of interest. The therml chrcteristics of the therml brrier re investigted experimentlly nd numericlly in simulted environment. The composite is introduced into cylindricl enclosure while it experiences its het from het source setting on the top of the enclosure. Due to the complexity of the porous medi, the numericl simultion is performed using volume verging technique. Finite volume technique is used to discretize the het diffusion eqution nd the enthlpy porosity method is used to model the phse chnge process. A fully implicit formultion is used for the time-dependent terms, nd the diffusion coefficients re evluted using centrl difference scheme. A line-by-line solver bsed on TDMA is used to itertively solve the lgebric discretiztion equtions. Experimentl Four types of crbon fom cylindricl disks with different porosities nd therml conductivities re fbricted to be introduced s the solid mtrix of the new composites. The crbon fom solid mtrix hs 51 mm dimeter nd 10 mm thickness nd the therml conductivities of ll types re mesured experimentlly. Ech one of the crbon fom mtrices is heted under vcuum in molten prffin wx to chieve mximum wx bsorption. All specifictions of these smples re illustrted tble (1). The composite is introduced into verticl cylindricl Teflon enclosure, which hs inside dimeter of 51 mm nd outside dimeter of 102 mm. An electricl heter is introduced into cylindricl copper disk of 51 mm dimeter nd 13 mm thickness. The cylindricl copper disk is instlled on the top of the enclosure to provide the required heting rte. The cylindricl enclosure is well insulted from its top side while the other sides re subjected to mbient ir. To ttin vrible heting rte, voltge regultor is used to supply the electricl heter with vrible voltge rtes. The experimentl set up is shown in Fig. (1) nd the therml protection cell is shown in Fig. (2). Thermocouples of J-type re used to detect temperture t vrious loctions inside the system. The heter surfce temperture is detected by two thermocouples, one thermocouple is instlled on its top surfce nd the other is instlled on its lower surfce. To detect the smple temperture history, six thermocouples re instlled t different xil nd rdil loctions in the crbon fom prffin wx composite s shown in Fig, (3). One of these thermocouples is instlled on the inner surfce of the Teflon enclosure, while nother one is instlled on its outer surfce. The thermocouples re ttched to multimeter which is connected to PC through stndrd RS-232 synchronous seril communiction port.
Tble (1) Properties of the crbon fom composites POCO-HP CF0514 POCO POCO-HT Smple Volume, m 3 2.03E-05 2.03E-05 2.03E-05 2.03E-05 Mss before sturtion, gm 7.10E+00 1.15E+01 1.03E+01 1.95E+01 Mss fter sturtion, gm 2.01E+01 2.06E+01 2.10E+01 2.64E+01 Wx Mss, gm 1.30E+01 9.14E+00 1.07E+01 6.89E+00 Solid Crbon Volume,m 3 3.94E-06 6.37E-06 5.72E-06 1.09E-05 Void Volume, m 3 1.64E-05 1.39E-05 1.46E-05 9.45E-06 Porosity 8.06E-01 6.86E-01 7.18E-01 4.66E-01 Wx Volume, m 3 1.46E-05 1.03E-05 1.20E-05 7.74E-06 Wx Active Porosity 7.20E-01 5.06E-01 5.92E-01 3.81E-01 Therml Conductivity, W/m.K 9.80E-01 7.00E-01 1.20E+01 1.40E+01 PC Power Supply Dt Acquisition System Therml Protection Cell Voltge Regultor Thermocouples Fig. (1) Experimentl setup φ102 mm φ 51 mm Insultion Copper Heter 4mm 6 5 2 Lower heter surfce 4mm 4 3 2mm 48 mm 13 mm 10 mm 7 6 5 2 4 3 Teflon Crbon Fom with PCM 8.46mm 8 16.9 mm Fig. (2) Therml protection cell Fig. (3) Thermocouple loctions
Numericl model The numericl nlysis is bsed on solving the het diffusion eqution in the pure solid mterils such s Teflon nd heting element. The volume verging energy eqution with phse chnge is used to model the het trnsfer process inside the porous composite with phse chnge. Due to the smll size of the crbon fom pores nd experiencing the het from the upper surfce, it ws found tht the convection motion of liquid phse is negligible. So, the conservtion of mss nd momentum re omitted from the governing equtions nd the problem is modeled in pure conduction mode. The contct between the different surfces such s Teflon, crbon composite, nd the heter is considered by ssuming certin vlue of contct resistnce. Becuse of the symmetry, the system is formulted in two-dimensionl xi-symmetric coordintes. The outer sides nd bottom surfce of the enclosure re ssumed to be subjected to free convection, while the upper surfce is insulted. The heting power is presented by introducing het genertion source in the heter mteril. Assumptions nd governing equtions The mthemticl formultions hve been done bsed on the following ssumptions: 1- The properties of ech mteril is isotropic 2- The thermo-physicl properties re constnt with temperture 3- The mechnicl energy for the volume chnge during phse chnge is ignored 4- The het genertion inside the heter is ssumed to be uniform Bsed on these ssumptions, the energy eqution for the heting element will tke the following form: Th ρ h c h =.(k h Th ) + q& (1) t Where, q& is the het genertion per unit volume inside the heting element nd the subscript h refers to the heter. The energy equtions for crbon fom nd PCM cn be written s: PCM Energy Eqution TPCM df ε ( ρc) PCM =.(k eff TPCM ) + h sf sf (Ts TPCM ) ρpcmlε (2) t dt Solid Energy Eqution Ts ( 1 ε)( ρc) s =.(k eff Ts ) h sf sf (Ts TPCM ) (3) t Where, ε is the crbon fom porosity. The subscripts PCM nd s stnd for the phse chnge mteril nd the crbon solid phses, respectively. While, k eff, sf, nd h sf re the effective therml conductivity, interfcil re per unit volume, nd the het trnsfer coefficient between the solid nd PCM, respectively. All of these prmeters depend on the structure of the porous medium nd the volume frctions of ech constituent. In the
cse of locl therml equilibrium, T PCM =T s =T, the two energy equtions for solid mtrix nd PCM cn be dded together to give, T df ( ρ c) eff =.(k eff T) ρpcmlε (4) t dt Where, ( ρ c) eff = ε( ρc) PCM + (1 ε)( ρc) s is the effective het cpcity. L is the het of fusion of the PCM, nd f is the liquid frction. The effective therml conductivity of the fom is mesured experimentlly for ll the smples nd the experimentl vlues hve been used in the numericl model. Numericl technique The het eqution is discretized using finite volume pproch. A typicl control volume is shown in Fig. (4). A fully implicit formultion ws used for the time-dependent terms, nd the diffusion coefficients re evluted using centrl difference scheme. A line-by-line solver bsed on TDMA is used to itertively solve the lgebric discretiztion equtions, [10]. The generl difference eqution tkes the form: o old ( p Sp) φp = nφn + pφp + Su (5) The vribles S P nd Su re used to linerize ny source term S such tht: SdV = Sp φ + p Su The subscript n stnds for the neighboring points E, W, S, nd N. Using the centrl difference scheme, the coefficients will tke the following forms: k ere k wrw k nrn r k srs r E = W = N = S = re rw n s ρc V o o P = P = W + E + S + N + P (6) t At ny contct between two different mterils, therml resistnce is introduced for clculting the het diffusion coefficient which ppers in eqution (6). The contct resistnce between the heting surfce, mtrix composite, nd the enclosure wlls is tking into considertion by pplying one dimensionl het conduction pproximtion. If the contct surfce coincides with the south surfce of the control volume, the vlue of het diffusion coefficient k s will be clculted s the inverse of the totl therml resistnce between points S nd P s shown in Fig.(5). k s = 1 2k m1 1 R + contct + 1 2k m2 Where, k m1 nd k m2 re the therml conductivities of the two contcting mterils. The therml resistnce is ssumed to be of the order of 0.001 (m 2 K/W).
r N W w n P e E n 2k m1 P s s R contct Contct S r w r e Fig. (4) Numericl control volume 2k m2 S Fig. (5) Contct resistnce The liquid frction for ech computtionl cell is updted using relible itertive method. At ny itertion, if the phse-chnge hppens, the temperture will be set t the melting temperture nd the liquid frction will be updted. o old ρlε V n+ 1 old ptm = ntn + ptp (f f ) t Subtrcting this eqution from the originl discretized energy eqution, this will give the following itertive formul: n 1 n p t f + = f + ( Tp Tm ) Lε ρ V For stbility purpose, the liquid frction is clculted from: n+ 1 n+ 1 n f = α f f + (1 α f )f Where α f is the under-relxtion fctor for updting the liquid-frction. The vlue of α is ssumed to be between 0.1 nd 0.2. f Convergence Criteri The convergence criteri for the numericl solution of the het eqution re bsed on the energy imblnce within the system. The unstedy energy imblnce ws clculted s the difference between the het generted by the heting element nd the sum of the het bsorbed by the mteril in the system s sensible or ltent het nd the het loss to the tmosphere ech time step. Q error = Q heter Q ltent Q sensible Q loss Convergence is ssumed to be chieved for energy imblnce equl to 0.001. Results nd discussion The experimentl nd numericl studies hve been crried out for four types of crbon fom s shown in tble (1) nd under vrible het inputs to perform the required prmetric study. Figure (6) shows the experimentl nd numericl results for the temperture time history t different loctions in the mtrix composite CF0415, which hs low therml conductivity nd medium porosity, under different het inputs. The
P=7.03 W P= 7.03 W P=11.63 W P= 11.63 W P=17.38 W P= 17.38 W Fig. (6) Temperture time history for the mtrix composite, 0514 t different power inputs Fig. (7) Temperture time history for the mtrix composite, POCO t different power inputs
experiments re performed under three input power levels, 7.04, 11.63, nd 17.38 Wtt. The numericl nd experimentl results show good greement. It is shown from the figure tht the mximum temperture is ttined on the heting element surfce, P(0,0), while the temperture decreses when we go down through the xil direction. The rte of increse of temperture decreses clerly inside the porous composite t temperture between 60 to 70 o C which is the melting temperture of the PCM. This temperture rte decrese is evident t high power input cses. In the cse of low het input the temperture increses slowly which cuses slow rte of the melting process of the PCM. Figure (7) shows the experimentl nd numericl results of the temperture time history for crbon mtrix composite POCO which hs higher therml conductivity. In the cse of high therml conductivity porous foms, the temperture difference between the xil loctions is very smll compred to those of the low therml conductivity. Figure (8) shows the numericl results of the temperture time history of the lower heting surfce for ll the smples t different het inputs. The figure shows tht the lowest temperture of the heting surfce is chieved ccording to this sequentil, POCO, POCO-HT, POCO-HP nd finlly CF0415. Out of this it cn be concluded tht controlling the surfce temperture depends minly on two prmeters. The first one is the therml conductivity of the crbon fom nd the second is the crbon fom porosity. The higher the therml conductivity nd the higher the porosity the lower of the heter surfce temperture. Figure (9) represents the het bsorption rte by the mtrix composite over the input het rte for ll cses. From the figure, one cn see tht for ll the cses, the het bsorption rte by the mtrix composite is incresed rpidly in the erly stge of heting process due to the temperture difference between the heting surfce nd the mtrix composite. After this period the het bsorption rte by the mtrix composite decreses until the PCM begins to melt. During the melting process of the PCM inside the mtrix pores, the het bsorption rte by the mtrix composite increses shrply to the mximum vlue due to the ltent het of the PCM then decreses gin but in this time to level higher thn tht of the erly stge. By performing comprtive study between ll the cses we cn conclude tht, the mount of the PCM inside the mtrix pores, which is depending minly upon the porosity of the solid mtrix, controls nd expnds the het bsorption durtion time during the heting process by direct proportionl reltion. On the other hnd, the therml conductivity of the mtrix composite plys n importnt role in the het bsorption rte. The highest the vlue of the therml conductivity of the mtrix composite, the highest the vlue of the het bsorption rte but through smll time intervl becuse this highest vlue of the therml conductivity cts to conduct the het rpidly nd so cts to bsorb het rpidly. So, we will hve compromise sitution ccording to the pplied ppliction. We cn lso conclude from the figure tht the het bsorption rte by the mtrix composites increses with the increse of the pplied het input.
Fig. (8) Temperture time history of the heting surfce t different power inputs Fig. (9) Het bsorption rte for ll smples t different power inputs
Conclusions The effect of the porosity nd therml properties of porous medium filled with PCM re studied numericlly nd experimentlly. Crbon fom mtrices with different porosities nd therml properties re introduced s the porous medium while prffin wx is introduced s the PCM occupies the mtrix pores. The mtrix composite is introduced into cylindricl enclosure while it experiences its het from het source setting on the top of the enclosure. The experimentl nd numericl results showed good greement which indictes tht the ssumptions nd numericl model proceedings re ccepted. The PCM ctive porosity nd therml conductivity of the mtrix composite ply importnt roles in their therml performnce. The highest the ctive porosity of the PCM inside the mtrix pores, the more stbility of the therml performnce of the mtrix composite. On the other hnd, the therml conductivity of the composite mtrix cts shrply to increse or decrese its het bsorption rte. According to these lst sttements we will hve compromise sitution between the therml stbility of the mtrix composite nd its bility to bsorb or conduct het. References [1] Bin, RL, Stermole, FJ, nd Golden, JO. Grvity induced free convection effects in melting phenomen for therml control. ASME Journl of Spcecrft, Vol. 8, 1971: 1000-1002. [2] Ismil, KAR, nd Trullenque, MRB. Finned rectngulr cvities filled with PCM for therml control of electronic equipments. Proceedings of the 6 th interntionl symposium on trnsport phenomen in therml engineering, Seoul, Kore, 1993: 237-242. [3] Ho, CJ, nd Chu, CH. Therml protection chrcteristics of verticl rectngulr cell filled with PCM/ir lyer. Het nd mss trnsfer, Vol. 31, 1996: 191-198. [4] Ho, CJ, nd Chu, CH. Numericl simultion of het penetrtion through verticl rectngulr phse chnge mteril/ir composite cell. Int. journl of het nd mss trnsfer, Vol.39, No. 9, 1996: 1785-1795. [5] Xvier Py, Regis Olives, nd Sylvin Murn. Prffin/Porous-grphite-mtrix composite s high nd constnt power therml storge mteril. Int. Journl of Het nd Mss Trnsfer, Vol. 44, 2001: 2727-2737. [6] Fuki, J, Knou, M, Kodm, Y nd Miytke, O. Therml conductivity enhncement of energy storge medi using crbon fibers. Energy Conversion & Mngement, Vol. 41, 2000: 1543-1556. [7] Fuki, J, Hmd, Y, Morozumi, Y, nd Miytke, O. Effect of crbon-fiber brushes on conductive het trnsfer in phse chnge mterils. Int. Journl of Het nd Mss Trnsfer, Vol. 45, 2002: 4781-4792. [8] Wever, JA, nd Visknt, R. Freezing of Wter Sturted Porous Medi in Rectngulr Cvity. Int. Commun. Het Mss Trnsfer, Vol. 13, 1986: 245-252. [9] Beckermnn, C, nd Visknt, R. Nturl Convection Solid/Liquid Phse Chnge in Porous Medi. Int. Journl of Het nd Mss Trnsfer, Vol. 31, No.1, 1988: 35-46. [10] Ptnkr, SV. Numericl Het Trnsfer nd Fluid Flow. Hemisphere, Wshington, DC 1980.