Studies on Nuclear Fuel Rod Thermal Performance

Transcription

1 Avilble online t Energy Procedi 1 (1) 1 17 Studies on Nucler Fuel od herml Performnce Eskndri, M.1; Bvndi, A ; Mihndoost, A3* 1 Deprtment of Physics, Islmic Azd University, Shirz Brnch, Shirz, Irn Deprtments of Physics, University of Shirz, Shirz, Irn 3 Deprtments of Physics, University of Ark, Ark, Irn Abstrct In this rticle we used ABAQUS softwre to study temperture nd het flux chnges in nucler fuel rod. his softwre is bsed on finite element method. For this cse, it divides nucler fuel rod to series of elements nd then investigtes the chnges in ech element. During this study, we divide nucler fuel rod to 1 elements. Since the therml conductivity depends on temperture nd temperture is different in one nodl point to other point (in rdil direction), ech element hs different therml conductivity. During this rticle, the temperture distribution is investigted in ech nodl point nd finlly we represent the generl expression for the temperture nd het flux chnges in rdil direction 11 Published by Elsevier Ltd. Selection nd/or peer-review under responsibility of the orgnizing committee of nd 11 Interntionl Published by Conference Elsevier Ltd. on Advnces Selection in nd/or Energy peer-review Engineering under (ICAEE). responsibility Open ccess of under [nme CC BY-NC-ND orgnizer] license. Keywords: ABAQUS code, Finite element nlysis, Nucler fuel rod, herml performnce 1. Introduction Energy is relesed by fission within the fuel rod nd is trnsferred by het conduction to the surfce of the fuel nd through the cldding [1]. From the surfce of the cldding het is trnsferred by convection to the coolnt, which psses from the core to the externl het exchngers in which stem is generted to operte on power cycle. A nucler fuel rod is used s the source of nucler energy in rector. Most nucler rectors re powered by fuel rods tht contin two isotopes of urnium: urnium-38 nd urnium-35. he power genertion process in nucler core is directly proportionl to the fission rte of the fuel nd the present therml neutron flux. he therml power produced by rector is directly relted to the mss flow rte of the rector coolnt nd the temperture difference cross the core []. he fuel elements re usully long cylindricl rods or rectngulr pltes of urnium (or thorium) enclosed by cldding. he urnium my be in the pure metllic form, in the form of compound such s urnium * Corresponding uthor. el.: ; fx: E-mil ddress: Eskndri@physics.susc.c.ir Published by Elsevier Ltd. Selection nd/or peer-review under responsibility of the orgnizing committee of nd Interntionl Conference on Advnces in Energy Engineering (ICAEE). Open ccess under CC BY-NC-ND license. doi:1.116/j.egypro

2 Eskndri et l.\ / Energy Procedi 1 (1) oxide, U, or in the form of n lloy with nother metl such s luminum or zirconium []. he desirble properties of fuel, which must be fissionble, re high therml conductivity, good corrosion resistnce, good mechnicl strength t high tempertures nd high limiting temperture for opertion. he numericl method of solution is used extensively in prcticl pplictions to determine the temperture distribution nd het flow in solids hving complicted geometries, boundry conditions, nd temperture-dependent therml properties [3]. In this pper the finite-difference method is used. he problem is then discretized nd the numericl method of solutions is plyed out using finite difference method. Finlly, we simulte nucler fuel rod using commercil finite element code ABAQUS/Stndrd 9 nd investigte therml performnce of nucler fuel rod. Nucler energy t non-uniform rte of (w/m 3 ) is generted in the rod. Surrounding coolnt temperture is, nd the het trnsfer coefficient h is lrge Internl het genertion he het genertion due to fission within nucler fuel rod is not uniform, nd for cylindricl fuel rod the het genertion is generlly given by [] (1 ( ) ) g = r (1) Where is the het genertion rte per unit volume t the centre (r = ) nd is the outer rdius of the solid fuel rod. Evidently g is function of position r, i.e., the rdil distnce from the xis of the rod [1]. For stedy stte one-dimensionl het conduction in the rdil direction we hve: d (. r ) + g. = dr dr K () Substituting g from E. (1) we hve: d d ( r. ) + (1 ( r ) ). r dr dr K = (3) Upon twice integrtion ( r ( r )) 16 + = C1ln( r) + C. K () Invoking the boundry conditions, t r = (d / dr) =, = mx, then C 1 = & C = mx herefore E. () becomes, ( r ( r )) 16 mx = K. (5) If w is the temperture t the outer surfce (wll) of the rod i.e., t r =, then mx 3 w = 16K (6) he het flow t the surfce of the fuel rod is [], Q = KA d dr (t r= ) A Q =. (7) Under stedy stte conditions, this het would be converted from the outside surfce of the rod. ( A ) = ha ( ) w

3 1 Eskndri et l.\ / Energy Procedi 1 (1) 1 17 ( A w = + ) (8) Where h is the convective het trnsfer coefficient nd is the mbient temperture. From Es. (6) nd (8), we get 3 1 mx ( ) ( = ) ( ) (9) h he governing non-dimensionl energy eution for the stedy stte one dimensionl rdil het conduction with non-uniform internl het genertion for cylindricl nucler fuel rod is given s [5] ( θ θ ) ( ) = (1) ( ) Where, θ = 1 3 ( ) ( ) ( ) h temperture nd non-dimensionl rdius respectively. nd = ( r ) re non-dimensionl 1.. Boundry conditions he non-dimensionl boundry conditions re t = θ/ = & t = 1 θ = Eution 1 is discretized using centrl difference for ( θ/ ) nd ( θ/ ) t ny interior grid point i s follows, ( θi+ 1 θi + θi 1)( ) + ( θi+ 1 θi 1) Δ + ( Δ ) = (11) he second term on the right hnd side of the governing differentil eution cn be written s ( θ/ )/. At =, θ/ = from the second boundry condition. herefore the term ( θ/ )/ will give rise to / condition. However, this difficulty cn be llevited by mking use of the L Hopitl s rule. hen we hve: ( θ i + 1 θ i + θ i 1) + 1 = (1) ( Δ ) At the centre, i =1, i-1=, i+1=. Using mirror-imge techniue (Fig. 1) t the centre =, i-1= i=1 i+1= Fig. 1: mirror imge techniue therefore E. (1) becomes, ( θ θ 1) + ( Δ ) = (13) he outer boundry is mintined t temperture, the temperture of the surrounding fluid, ssuming lrge het trnsfer coefficient h (i.e.) w =. At =1, θ =, tht is due to second boundry condition. Let us consider n exmple in which Δ = (1/9). herefore, the number of nodl points is ten (i.e. from 1 to 1) nd the numbers of unknown tempertures re nine (i.e. from 1 to 9). Since = t the outer boundry, the vlue of θ is zero t the nodl point 1 [5]. At Nodl Point 1 = & i = 1 ( θ 1 1 θ ) 9

4 Eskndri et l.\ / Energy Procedi 1 (1) At Nodl Point = (1/9) & i = θ θ1 θ3 9 At Nodl Point 3 = (/9) & i = 3 θ θ θ 9 At Nodl Point = (3/9) & i = θ θ3 θ At Nodl Point 5 = (/9) & i = 5 θ θ θ At Nodl Point 6 = (5/9) & i = 6 θ θ5 θ At Nodl Point 7 = (6/9) & i = 7 θ θ6 θ At Nodl Point 8 = (7/9) & i = 8 θ θ7 θ At Nodl Point 9 = (8/9) & i = 9 θ θ8 θ At Nodl Point 1 = (9/9) = 1 & i = 1 eclling the second boundry condition At = 1 θ = θ 1 =. hese re the 9 eutions to be solved to find the 9 unknown tempertures. hese 9 eutions cn be written in the mtrix form nd cn be solved through vrious methods like Gussin elimintion, Gussseidel itertion, etc. As those nlyticl pproches re too lengthy if the nodl points re more, computer progrmming is mostly preferred. Here mtlb progrm is used to solve the bove mtrix. he results thus obtined re shown in Fig..

5 16 Eskndri et l.\ / Energy Procedi 1 (1) Non-Dimensionl emperture Nodl Points Fig. : Non-dimensionl temperture distribution long the nodl points from the center 1.3. emperture chnges in nucler fuel rod Meshing of nucler fuel rod is shown in Fig. 3. In this model we lso consider the pellet-cldding gp which hs different therml conductivity from nucler fuel rod. he prmeters re used in this nlysis re: distnce of nodl points from ech other, therml conductivity of ech element, therml conductivity of pellet-cldding gp, temperture of coolnt. Obtined results from simultion of nucler fuel rod using ABAQUS/Stndrd 9 re shown in Fig.. Fig. 3: meshing of nucler fuel rod Fig. : temperture chnges of nucler fuel rod over time 1.. Het flux chnges in nucler fuel rod Het flux cn be expressed ccording to E. 7. Obtined results indicte liner increse in het flux through the outer surfce of fuel rod during the time. Attined result is shown in Fig. 5.

6 Eskndri et l.\ / Energy Procedi 1 (1) Fig. 5: het flux chnges through the outer surfce of rod over time 1.5. Conclusions he grphicl representtion between the non-dimensionl temperture nd the rdil distnce from the center of the nucler fuel rod unveils tht s expected the temperture is mximum t the center nd minimum t the outer dimeter. his mens tht temperture reduces over distnce from the centerline nd our clcultions hs shown tht the temperture in ech nodl point increse linerly over the time. his shows the het is trnsferred from the nucler fuel rod to the surrounding coolnt ccording to the second lw of thermodynmics. hus from the surfce of the nucler fuel rod, het is trnsferred by convection to the coolnt, which psses from the core to the externl het exchngers in which stem is generted to operte on power cycle. In this pper the temperture distribution studies for the nucler fuel rod with cldding hs been performed. Since we should consider the direction of het flux flow, nd in the ABAQUS defults, the input flux to the medium is positive nd output flux is negtive, the negtive sign of het flux cn be explined. As the net het flux is emerging from the outer surfce of rod, its sign should be negtive but its vlue increse over the time becuse the het flux in nodl point i+1 is the sum of het flux from the point i nd the het flux from tht point itself. eferences [1] Ghoshdstidr PS. Computer simultion of flow & het trnsfer. t McGrw Hill. Edt [] Gupt GP, jendr Prksh. Engineering het trnsfer. NemChnd & Brothers. 6th Edt [3] Ng PK. Power Plnt Engineering. t McGrw Hill. Sixth reprint -. [] Pndey K.M, Mhesh M. Determintion of emperture Distribution in Cylindricl Nucler Fuel od Mthemticl Approch. Interntionl Journl of Innovtion, Mngement nd echnology, Vol. 1, No. 5, December 1. [5] Necti Ozisik M. Het rnsfer. t McGrw Hill interntionl Edt