VALIDATION OF A TRANSIENT THERMAL-FLUID SYSTEMS CFD MODEL FOR A PACKED BED HIGH TEMPERATURE GAS-COOLED NUCLEAR REACTOR

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1 2nd Internatinal Tical Meeting n HIGH TEMPERATURE REACTOR TECHNOLOGY Beijing, CHINA, Setember 22-24, 2004 #Paer C07 VALIDATION OF A TRANSIENT THERMAL-FLUID SYSTEMS CFD MODEL FOR A PACKED BED HIGH TEMPERATURE GAS-COOLED NUCLEAR REACTOR PG Russeau 1, CG du Tit 1 and WA Landman 2 1 Energy Systems Research, Faculty f Engineering, Nrth-West University, Private Bag X6001, Ptchefstrm 2520, Suth Africa 2 M-Tech Industrial (Pty) Ltd, 5 Luke Street, Ptchefstrm, Suth Africa Crresnding authr - PG Russeau: Fax: mgigr@uk.ac.za ABSTRACT: This aer rvides an verview f the theretical basis fr a new thermal-fluid systems CFD simulatin mdel fr high temerature gas-cled reactrs, cntained in the Flwnex sftware cde. Flwnex rvides fr detailed steady state and transient thermal-fluid simulatins f the cmlete wer lant, fully integrated with cre neutrnics and cntrller algrithms. The reactr mdel is funded n a fundamental arach fr the cnservatin f mass, mmentum and energy fr the cmressible fluid flwing thrugh a fixed bed, as well as the heat transfer in the ebbles and cre structures. The time-wise integratin f the resulting differential equatins is based n an imlicit ressure crrectin algrithm. This allws fr the use f rather large time stes making it very suitable fr simulating the slw transients that can be exected t fllw incidents like reactr shutdwns. The aer als cmares the Flwnex results fr fur transient tests with the measured results frm the SANA test facility as well as t the results f simulatins with the Thermix/DIREKT cde that were dne at the Research Centre Jülich. The Flwnex results cmare well with the Thermix/DIREKT results fr all the cases resented here. Gd cmarisn was als btained between the simulated and measured results, excet at tw ints within the ebble bed near the inner wall. The fact that quick cmuter simulatin times were btained indicates that the new mdel indeed achieves a fine balance between accuracy and simlicity. Hwever, the discreancies btained at the tw ints near the inner wall, tgether with the fact that additinal uncertainty was intrduced in the riginal SANA test set-u by nt being able t cntrl the temerature f the uter wall, highlight the need fr additinal systematic tests t be erfrmed in rder t better validate the new mdel. 0. INTRODUCTION The Pebble Bed Mdular Reactr (PBMR) wer lant is currently being develed by PBMR (Pty) Ltd in Suth Africa in assciatin with ESKOM and ther industrial artners. This high temerature gas cled reactr (HTGR) lant is based n a Braytn gas turbine cycle with helium gas as clant. The cmlexity assciated with the thermal-fluid design f the cycle requires the use f a variety f analysis techniques and simulatin tls. These range frm simle ne-dimensinal mdels that d nt cature all the significant hysical henmena t large-scale three-dimensinal CFD cdes that, fr ractical reasns, can nt simulate the entire lant as a single integrated mdel. One f the mst rminent cdes that rvide a suitable cmrmise is the thermal-fluid systems CFD r netwrk simulatin cde Flwnex [1]. Flwnex allws detailed steady state and transient thermalfluid simulatins f the cmlete wer lant, fully integrated with cre neutrnics and cntrller algrithms. The reactr mdel cntained in the cde is based n the fundamental equatins fr the cnservatin f mass, mmentum and energy fr the cmressible fluid flwing thrugh a fixed bed, as well as the equatins fr the cnservatin f energy fr the ebbles and cre structures. Detailed cmarisns f results btained with the reactr mdel and measured results btained frm the 1996 SANA test facility [2],[3], have recently been resented [4]. These included varius steady-state tests, cvering a range f temeratures as well as tw different fluids and different heating cnfiguratins

2 VALIDATION OF A TRANSIENT THERMAL-FLUID SYSTEMS CFD MODEL FOR A PACKED BED HIGH TEMPERATURE GAS- COOLED NUCLEAR REACTOR #C07 The gd cmarisn btained between the simulated and measured results shwed that the systems CFD arach sufficiently accunts fr all f the imrtant henmena encuntered in the quasisteady natural cnvectin driven flws that will revail after critical events in a reactr. Hwever, results have nt yet been resented fr transient events. The urse f this aer is t rvide an verview f the theretical basis and resent the simulated results fr transient tests that were als carried ut n the SANA test facility. The Flwnex results are nce again cmared t the measured results as well as t the results f simulatins carried ut at Frschungszentrum Jülich as art f the SANA rject. 1. THEORETICAL OVERVIEW Reactr gemetry. Figure 1 shws a simlified sectin thrugh a art f what can tyically be exected in the reactr gemetry. The fuel ebbles are lcated in the annular vlume frmed between the central reflectr and the cre structures. The gas is fed int a ring-shaed inlet manifld. Frm there it flws u thrugh vertical riser channels situated at discrete intervals arund the circumference. The riser channels are intersected at the t by hrizntal inlet slts that feeds the gas inward and int the ebble bed at the t. Besides the riser channels and inlet slts, the cre structures can als cntain vertical cntrl rd channels. The cntrl rd channels are als situated at discrete intervals arund the circumference, but alternating with the riser channels. Nte that the gas flwing in the riser channels des nt mix with the gas cntained in the cntrl rd channels. The main cre structures are tyically surrunded by an annular gas-filled cavity cntained within the cre barrel. The cre barrel in turn is cntained within the reactr ressure vessel (RPV). Cntrl rd channels Hrizntal inlet slts Central reflectr Vertical riser channels Pebble bed Cre structures Gas inlet manifld Cre barrel annulus Cre barrel Figure 1 Sectin thrugh art f a tyical reactr gemetry. Simulatin methdlgy. The simulatin hilshy n which the mdel is based is t achieve a fine balance between accuracy and simlicity and t guard against simly develing anther detailed

3 HTR2004 Beijing, CHINA, CFD cde that des nt allw quick integrated lant simulatins. This means that the simlest ssible mdel was derived that can sufficiently accunt fr all f the imrtant henmena. The first simlificatin is that the mdel is based n a tw-dimensinal axi-symmetric crdinate system rather than a full three-dimensinal cylindrical crdinate system. This imlies that all variatins in gemetry r material rerties arund the erimeter f the reactr will be sread evenly arund the circumference t frm a material with cnstant rerties at each given height and radius. Fr instance, the inlet slts situated at discrete intervals arund the erimeter is reresented by a material with reresentative unidirectinal radial flw ermeability. Similarly the discrete vertical cntrl rd channels are reresented by a material with reresentative unidirectinal axial flw ermeability. The ebble bed in turn is reresented by a rus medium with multidirectinal rsity rather than a unidirectinal ermeability. Nte hwever, that the magnitude f the ermeability r rsity may vary between cntrl vlumes in bth the radial and axial directins. By emlying this tw-dimensinal arach with reresentative ermeability r rsity, all f the desired henmena may be simulated, althugh in less detail than wuld be the case in a traditinal CFD cde. Hwever, the reductin in the size f the required cmutatinal grid is substantial thus resulting is much faster simulatin times. Pebble bed flw resistance elements Pebble bed vid vlumes Cnvective heat transfer elements between slid and gas Inlet slt flw resistance elements Riser channel flw resistance elements Pebble surface temerature Effective cnductin and radiatin in ebble bed Inlet manifld Cre structure Slid mass temeratures Cnductin elements Pebble internal slid mass temeratures Cntrl rd channel flw resistance elements Figure 2 Integrated netwrk reresentatin f the ebble-bed and cre structure slids and flw aths Gverning differential equatins. The reactr mdel is based n the fundamental equatins fr the cnservatin f mass, mmentum and energy fr the cmressible fluid flw, as well as the equatins fr the cnservatin f energy fr a ebble, energy transfer between the surfaces f adjacent ebbles, and the slid materials cmrising the cre structure. Thrugh a rigrus analysis [4] the equatins can be reduced and recast in a frm that is suitable fr incrratin in a netwrk cde. This frmulatin f the equatins results in a cllectin f ne-dimensinal ndes (cntrl vlumes) and elements (mdels) that can be used t cnstruct a cmrehensive multi-dimensinal mdel f the reactr. The elements accunt fr the ressure dr thrugh the reactr; the cnvective heat transrt by the gas; the cnvectin heat transfer between the gas and the slids; the radiative, cntact and

4 VALIDATION OF A TRANSIENT THERMAL-FLUID SYSTEMS CFD MODEL FOR A PACKED BED HIGH TEMPERATURE GAS- COOLED NUCLEAR REACTOR #C07 cnvectin heat transfer between the ebbles and the heat cnductin in the ebble and cre structure materials. A greatly simlified netwrk resentatin is shwn schematically in Figure 2. Du Tit et al. [4] have shwn that the equatins fr the cnservatin f mass, mmentum and energy (ttal secific enthaly) fr the fluid can be exressed in axi-symmetric cylindrical crdinates as 1 ( ερ ) + ( ερrur) + ( ερuz) = 0 t r r z 2 ur ρv T y ερ = ε ε ερg ρεβu t 2T r r r 2 uz ρv T y ερ = ε ε ερg ρεβu t 2T z z z 1 1 T T ( ερh) + ( ε rρhur) + ( ερhuz) = ( ε ) + ε rk + ε k t r r z t r r r z z + ερ gu + gu + q ( ) r r z z sf Three energy equatins can be distinguished in the case f the slids, i.e., the cnductin in the cre structures, cnductin in the ebbles and the heat transfer between the surfaces f the ebbles due t cntact, radiatin and cnvectin. Du Tit et al. [4] have shwn that the resective energy cnservatin equatins can be exressed in axi-cylindrical crdinates as 1 T T = t r r r z z ( 1 ε) ρse ( 1 ε) r ks ( 1 ε) ks ( 1 ε)( q fs q s) 1 2 T ( ρct v ) = k 2 r + q t r r r 1 0 T T rk eff k = + eff r r r z z The variatin in the rsity in the radial directin due t the influence f the walls is taken int accunt by the crrelatin f Hunt and Tien [5], whilst the resistance cefficient β due t the ebbles is determined using the KTA Ergun equatin [6]. The mdified Zehner-Schlünder crrelatin [4] is emlyed t determine the effective cnductivity k eff, whilst the heat transfer between the ebbles and the fluid is mdelled with the aid f the effectiveness-ntu methd [4]. Integrated equatins. Integrating equatins (1) t (4) fr the fluid ver a cntrl vlume and ver a discrete time ste leads t the fllwing algebraic equatins. Integratin f the equatin fr the cnservatin f mass gives ( ) ε ρ ρ V + α ( ερur) Ae ( ερur) Aw + ( ερuz) An ( ερuz) A e w n s s + t ( 1 α) ( ερur) Ae ( ερur) Aw + ( ερuz) An ( ερuz) A s = 0 e w n s r z (1) (2) (3) (4) (5) (6) (7) (8)

5 HTR2004 Beijing, CHINA, Integrating the equatins fr the cnservatin f mmentum leads t ( ) ( ) 2 ur u r ρ V Ar r + Ar ( T) ( T) + Ar ( ) ( ) e w e w t 2( T) ( ) ε ρ α ε ε 2 ρ V + ε ρgar[ ye yw] + ε ρβ( ur) Ar r} + ( 1 α) Ar ( T) ( T) ε e w 2( T ) + ε A r ( ) ( ) ε ρgar[ ye yw] ε ρβ( ur) Ar r 0 e w ( ) + + = ( ) ( ) 2 uz u z ρ V Az z + Az ( T) ( T) + Az ( ) ( ) n s n s t 2( T) ε ρ α ε ε 2 ρ V + ε ρgaz[ yn ys] + ε ρβ( uz) Az z} + ( 1 α) ε A z ( T) ( T) n s 2( T ) + ε A z ( ) ( ) + ε ρgaz[ yn ys] + ε ρβ( uz) Az z 0 n s = The integratin f the equatin fr the cnservatin f energy fr the fluid gives ( h ) ( h ) ( ) ε ρ ε ρ ε V V {( h u ) A ( h u ) A t t T + ( ερhu ) A ( ερhu ) A + ( ερhu ) A ( ερhu ) A ε k A + α ερ r e e ερ r w w r e e r w w z n n z s s e r e T T T + εk A εk A + εk A ε ρ ( g u + g u ) V r z z { w n s r r z z w n s + ( 1 α) ( ερhu ) A ( ερhu ) + ( ερ ) ( ερ ) + ( ερ ) r e e r w ( ) } w r e e r w w z n n z s s e w n s r e r w z n z s r r z z sf A h u A h u A h u A T T T T ( ερhu ) A ε k A + ε k A ε k A + ε k A ε ρ gu + gu V = q V (9) (10) (11) Terms with the suerscrit refer t the revius time ste, whilst terms withut a suerscrit refer t the current time ste. α is weighting factr between the revius and the current time stes and can vary between 0 and 1. When α = 0 the scheme becmes fully exlicit, with α = 1 it becmes fully imlicit and when α = 0.5 the time integratin is equivalent t that f the s-called Crank-Nichlsn methd. Fr α = 1 the methd is first-rder accurate in time, whilst fr α = 0.5 it is secnd-rder accurate. Fr α -values clse t 0.5 the scheme smetimes becmes unstable and an α -value f 0.6 ffers a gd cmrmise between accuracy and stability [7]. Integrating equatins (5) t (7) fr the slids and the ebbles als leads t the fllwing algebraic equatins

6 VALIDATION OF A TRANSIENT THERMAL-FLUID SYSTEMS CFD MODEL FOR A PACKED BED HIGH TEMPERATURE GAS- COOLED NUCLEAR REACTOR #C07 The equatin fr the cnservatin f energy fr the slids gives ( ) [ ρe ] [ ρe ] T T V 1 ε + α ( 1 ε) ks Ae + ( 1 ε) ks Aw t r r e w T T T ( 1 ε) ks An ( 1 ε) ks As ( 1 α) ( 1 ε) ks A z + z + r n s e T T T + ( 1 ε) ks Aw ( 1 ε) ks r z An + ( 1 ε ) ks As w z n s = 1 ε q + q V ( )( ) fs s The integratin f the equatin fr the cnservatin f energy fr a ebble results in ρe ρe T T + α e + w t r e r w V k A k A T T + ( 1 α ) k Ae k Aw q V r + = e r w and finally the equatin fr the transfer f heat between adjacent ebbles becmes T T T T keff Ae keff Aw + keff An keff As = 0 r r z z e w n s The numerical frmulatin f the equatins is based n a staggered grid arach with the ressures, densities and temeratures defined at cell (cntrl vlume) centers (ndes) and the velcities are defined at cell bundaries (elements). A cmutatinally effective segregated imlicit ressure crrectin methd [7] is emlyed t slve the resulting equatins. (12) (13) (14) 2. SANA TEST FACILITY AND COMPUTATIONAL MODEL Having develed the theretical basis fr the new systems CFD mdel, it is imrtant t rve its validity by cmaring the numerical results with that f exeriments. Of articular imrtance is the redictin f the ebble temeratures btained in the case f wer transients. Althugh limited, such data des exist in the frm f the exerimental results btained frm the SANA test facility [2],[3]. The SANA test facility was installed at the Research Centre Jülich in Germany secifically t investigate the heat transrt mechanisms inside the cre f a high temerature gas cled reactr (HTGR). Besides the hysical tests, simulatins were als cnducted at Jülich with tw sftware mdels namely TINTE and Thermix/DIREKT, bth f which allw bth steady state and transient simulatins. Results f these simulatins cmared well with measurements. SANA test facility. The test facility cnsisted f a heated ebble bed inside a furnace t simulate the thermal cnditins f such a HTGR-cre. Different heater cnfiguratins were ssible but Figure 3 shws a schematic f the test facility with a single central heating element. The diameter f the ebble bed is 1.5 m and the height is 1.0 m. The verall height f the facility is 3.2 m and the maximum heating caacity f the single central heating element is 35 kw. The t and bttm f the facility was well-insulated while the utside f the furnace was en t atmshere. Mre than 50 steady-state as well as sme transient tests were carried ut n the facility. In these exeriments all the main arameters f a ebble bed were varied, such as ebble material, ebble diameter, gas tye, heating wer and heating gemetry

7 HTR2004 Beijing, CHINA, Figure 3. Schematic f SANA test facility taken frm [2]. Fr the tests cnducted with the 60 mm diameter grahite ebbles, measurements were taken f the ebble temeratures at different radial sitins clse t the bttm f the ebble bed (height 90 mm) as well as at the center (height 500 mm) and t (height 910 mm) as shwn in Figure 4. Figure 4. Schematic f the temerature measuring ints n the SANA test facility taken frm [2]

8 VALIDATION OF A TRANSIENT THERMAL-FLUID SYSTEMS CFD MODEL FOR A PACKED BED HIGH TEMPERATURE GAS- COOLED NUCLEAR REACTOR #C07 Adiabatic bundary T Fixed heat inut bundary Centre Fixed ambient temerature bundary Bttm Adiabatic bundary Figure 5. Schematic f the discretizatin scheme used in all f the Flwnex simulatins. Cmutatinal grid. In all f the Flwnex simulatins the ebble bed was discretised int cntrl vlumes with equal heights f 100 mm and equal radial widths f 29.6 mm. Half cntrl vlumes were emlyed at all the bundaries as shwn in Figure 5. The bttm and t bundaries were assumed t be adiabatic since in ractice it was very well insulated. The heat inut t the heating element was distributed unifrmly at the inner bundary and n allwance was made fr cnductive heat transfer within the material f the heating element sheath. At the uter bundary a 5 mm thick stainless steel wall with heat cnductin and heat caacity was secified, cnnected t a fixed ambient temerature thrugh cnvective heat transfer elements. Due t the lack f detailed infrmatin frm the test rerts, the ambient temerature was simly fixed at 26 C fr all cases while values fr the cnvective heat transfer cefficient were fixed between 20 and 25 W/m 2 K. These values were estimated based n insectin f the steady-state test results. This highlighted a shrtcming in the riginal test set-u namely that the temerature f the uter wall culd nt be cntrlled and therefre additinal uncertainty is intrduced in all f the measured results. In all f the cases the simulatins were based n 60-secnd time-stes, which rvided a time-ste indeendent slutin. The cmuter simulatin time fr btaining the steady-state initial values were all in the regin f 4.5 secnds and the transient simulatins fr a sixty-hur erid tk in the rder f 450 secnds n a ntebk cmuter with a 1.6 GHz Centrin rcessr and 512 Megabytes f memry. 3. RESULTS This sectin will resent cmarisns between results rduced with Flwnex and measured results btained with SANA facility as well as cmarisns between the results f the Flwnex and Thermix/DIREKT cmutatinal mdels fr fur transient cases. In all fur cases the furnace

9 HTR2004 Beijing, CHINA, cntained grahite ebbles with 60 mm diameter, which is naturally f articular interest t the PBMR alicatin. Heating was dne within the central electrde alng the full height f the ebble bed. The first tw cases invlve a linear ram-dwn f the wer inut, ne with Helium as clant and the ther with Nitrgen. The ther tw cases invlve an instantaneus ste-u f the wer inut, again ne with Helium as clant and the ther with Nitrgen. In all cases the calculated r measured temerature distributin at different radial sitins at the center alng the height f the ebble bed (i.e. height 500 mm) is cmared. Ram-dwn f wer inut: The transient starts with a steady-state cnditin at a nminal wer inut f 30 kw. The wer inut is linearly ramed dwn t 10 kw ver a erid f 50 hurs, i.e. at 0.4 kw/h, after which it is ket cnstant t eventually again reach steady-state cnditins. Case 1. Ram-dwn f wer inut frm 30 kw t 10 kw in 50 hurs with Helium as clant. Figure 6 shws the cmarisn between the measured and simulated temeratures fr different radial sitins in the center alng the height f the ebble bed while Figure 7 shws the cmarisn between the simulated Thermix/DIREKT and Flwnex results. Frm Figure 6 it can be seen that the Flwnex results cmare well with the measurements excet fr tw ints alng the radius i.e. at radius = 10 cm and radius = 22 cm. Althugh the general trend ver time is crrect there seems t be an ffset f arximately 60 C thrughut. Nte that this ffset is nt nly bserved during transients but als at steady state cnditins at the start f the transient. This difference therefre des nt indicate a discreancy in the thermal mass calculatin r in the timedeendent numerical integratin, but rather in the calculatin f the effective thermal resistance in the radial crdinate directin. Hwever, the Flwnex results cmare very well with the Thermix/DIREKT results at all f the ints, including the tw ints mentined abve. This raises the susicin that the measuring ints may erhas have been sitined differently in the test facility, fr instance ne ball diameter t the inside f where it was sused t be. Althugh it seems unlikely that such an errr culd have been made, there is unfrtunately n way t verify it at this time Temerature ( ) Time (h) Flwnex (6.5) Sana (6.5 ) Flwnex (22) Sana (22) Flwnex (34) Sana (34 ) Flwnex (46) Sana (46) Flwnex (58) Sana (58) Flwnex (70) Sana (70 ) Flwnex (75) Sana (75) Flwnex (10) Sana (10) Figure 6. Results f measured (SANA) and simulated (Flwnex) ebble temeratures fr Helium with a ram-dwn f wer inut frm 30 kw t 10 kw in 50 hurs

10 VALIDATION OF A TRANSIENT THERMAL-FLUID SYSTEMS CFD MODEL FOR A PACKED BED HIGH TEMPERATURE GAS- COOLED NUCLEAR REACTOR #C Temerature ( ) Time (h) Flwnex (6.5) Thermix (6.5 ) Flwnex (22) Thermix (22) Flwnex (34) Thermix (34 ) Flwnex (46) Thermix (46) Flwnex (58) Thermix (58) Flwnex (70) Thermix (70 ) Flwnex (75) Thermix (75) Flwnex (10) Thermix (10) Figure 7. Results f ebble temeratures simulated with Thermix/DIREKT and Flwnex resectively fr Helium with a ram-dwn f wer inut frm 30 kw t 10 kw in 50 hurs. Case 2. Ram-dwn f wer inut frm 30 kw t 10 kw in 50 hurs with Nitrgen as clant. Figure 8 shws the cmarisn between the measured and simulated temeratures fr different radial sitins at the center alng the height f the ebble bed while Figure 9 shws the cmarisn between the simulated Thermix/DIREKT and Flwnex results. Figure 8 shws that the initial temeratures are n average higher in the case f Nitrgen than in the case f Helium. Once again the Flwnex results cmare well with the measurements excet at the tw ints mentined earlier. In this case the Thermix/DIREKT results are much clser t the measured values at these tw ints. Hwever, fr all f the ther ints t the utside f radius = 34 cm, the Flwnex results cmare better with the measurements than the Thermix/DIREKT results

11 HTR2004 Beijing, CHINA, Temerature ( ) Time (h) Flwnex (6.5) Sana (6.5 ) Flwnex (22) Sana (22) Flwnex (34) Sana (34 ) Flwnex (46) Sana (46) Flwnex (58) Sana (58) Flwnex (70) Sana (70 ) Flwnex (75) Sana (75) Flwnex (10) Sana (10) Figure 8. Results f measured (SANA) and simulated (Flwnex) ebble temeratures fr Nitrgen with a ram-dwn f wer inut frm 30 kw t 10 kw in 50 hurs Temerature ( ) Time (h) Flwnex (6.5) Thermix (6.5 ) Flwnex (22) Thermix (22) Flwnex (34) Thermix (34 ) Flwnex (46) Thermix (46) Flwnex (58) Thermix (58) Flwnex (70) Thermix (70 ) Flwnex (75) Thermix (75) Flwnex (10) Thermix (10) Figure 9. Results f ebble temeratures simulated with Thermix/DIREKT and Nitrgen resectively fr Helium with a ram-dwn f wer inut frm 30 kw t 10 kw in 50 hurs. Ste-u f wer inut: In the fllwing cases the transient starts with a steady-state cnditin at a nminal wer inut f 10 kw, which is then instantaneusly steed u t 25 kw. Case 3. Instantaneus ste-u f wer inut frm 10 kw t 25 kw with Helium as clant. Figure 10 shws the cmarisn between the measured and simulated temeratures fr different radial sitins at the center alng the height f the ebble bed while Figure 11 shws the cmarisn between the simulated Thermix/DIREKT and Flwnex results

12 VALIDATION OF A TRANSIENT THERMAL-FLUID SYSTEMS CFD MODEL FOR A PACKED BED HIGH TEMPERATURE GAS- COOLED NUCLEAR REACTOR #C Temerature ( ) Time (h) Flwnex (6.5) Sana (6.5 ) Flwnex (22) Sana (22) Flwnex (34) Sana (34 ) Flwnex (46) Sana (46) Flwnex (58) Sana (58) Flwnex (70) Sana (70 ) Flwnex (75) Sana (75) Flwnex (10) Sana (10) Figure 10. Results f measured (SANA) and simulated (Flwnex) ebble temeratures fr Helium with an instantaneus ste-u f wer inut frm 10 kw t 25 kw Temerature ( ) Time (h) Flwnex (6.5) Thermix (6.5 ) Flwnex (22) Thermix (22) Flwnex (34) Thermix (34 ) Flwnex (46) Thermix (46) Flwnex (58) Thermix (58) Flwnex (70) Thermix (70 ) Flwnex (75) Thermix (75) Flwnex (10) Thermix (10) Figure 11. Results f ebble temeratures simulated with Thermix/DIREKT and Flwnex resectively fr Helium with an instantaneus ste-u f wer inut frm 10 kw t 25 kw. In this case the results fr the innermst ints cmares excetinally well with the measured values. Discreancies f as much as 100 C are again bserved at radius = 10 cm and radius = 22 cm. Frtunately, in almst all cases Flwnex rvides cnservative results frm the viewint f accident analyses, i.e. where the redicted ebble temeratures are higher than the measured values. The Flwnex and Thermix/DIREKT results cmare excetinally well fr all cases, excet the inner wall temerature, where the Flwnex results are much clser t thse f the measured values. Case 4. Instantaneus ste-u f wer inut frm 10 kw t 25 kw with Nitrgen as clant. Figure 10 shws the cmarisn between the measured and simulated temeratures fr different radial

13 HTR2004 Beijing, CHINA, sitins at the center alng the height f the ebble bed while Figure 11 shws the cmarisn between the simulated Thermix/DIREKT and Flwnex results. These results shw very much the same trends as thse btained fr Helium with very gd crrelatin between the tw numerical mdels and Flwnex rviding cnservative results cmared t the measurements. Hwever, in this case the Thermix/DIREKT results fr the inner wall crrelate better with the measured values. Fr all f the cases resented abve, there seem t be systematic errrs between the simulated and measured values at tw secific ints alng the radius. This either indicates that the effective thermal resistance is nt mdelled crrectly in the regin near the inner wall, which may be related t an incrrect redictin f the rsity distributin near the wall, r erhas that the measuring rbes may have been sitined incrrectly in the test facility. Hwever, besides these tw ints, the Flwnex results cmare well with the measured values and generally rvide cnservative results frm the int f view f safety analyses. The temerature gradients with resect t time are mdelled crrectly in all cases which indicates that the thermal strage effects are crrectly accunted fr and als rvides cnfidence in the time-wise numerical integratin scheme. In almst all cases the Flwnex results cmare well with that f the Thermix/DIREKT simulatins Temerature ( ) Time (h) Flwnex (6.5) Sana (6.5 ) Flwnex (22) Sana (22) Flwnex (34) Sana (34 ) Flwnex (46) Sana (46) Flwnex (58) Sana (58) Flwnex (70) Sana (70 ) Flwnex (75) Sana (75) Flwnex (10) Sana (10) Figure 12. Results f measured (SANA) and simulated (Flwnex) ebble temeratures fr Nitrgen with an instantaneus ste-u f wer inut frm 10 kw t 25 kw

14 VALIDATION OF A TRANSIENT THERMAL-FLUID SYSTEMS CFD MODEL FOR A PACKED BED HIGH TEMPERATURE GAS- COOLED NUCLEAR REACTOR #C Temerature ( ) Time (h) Flwnex (6.5) Thermix (6.5 ) Flwnex (22) Thermix (22) Flwnex (34) Thermix (34 ) Flwnex (46) Thermix (46) Flwnex (58) Thermix (58) Flwnex (70) Thermix (70 ) Flwnex (75) Thermix (75) Flwnex (10) Thermix (10) Figure 13. Results f ebble temeratures simulated with Thermix/DIREKT and Flwnex resectively fr Nitrgen with an instantaneus ste-u f wer inut frm 10 kw t 25 kw. 4. CONCLUSIONS An verview f the theretical basis and cncetual frmulatin f a cmrehensive reactr mdel t simulate the thermal-fluid henmena f the PBMR reactr cre and cre structures was given. Thrugh a rigrus analysis the fundamental equatins were recast in a frm that is suitable fr incrratin in a systems CFD cde. The frmulatin f the equatins resulted in a cllectin f nedimensinal elements (mdels) that can be used t cnstruct a cmrehensive multi-dimensinal netwrk mdel f the reactr. The time-wise integratin f the resulting differential equatins is based n an imlicit ressure crrectin algrithm that ffers a gd cmrmise between accuracy and stability. This allws fr the use f rather large time stes in the case f the slw transients that can be exected t fllw incidents like reactr shutdwns and ther imrtant transient events. The fact that cmuter simulatin times f less than 10 minutes were achieved n a standard ntebk cmuter fr all f the simulatins cvering a 60-hur lng transient als indicates that the new mdel indeed achieves a fine balance between accuracy and simlicity. Gd cmarisn was btained between the simulated and measured results fr all cases, excet at tw ints within the bed near the inner wall. This indicates a systematic errr but unfrtunately it is nt entirely ssible t inint the causes given the data available frm the riginal SANA tests. The Flwnex results cmared well with the Thermix/DIREKT results fr all the cases resented here. Hwever, the discreancy inted ut abve, tgether with the fact that additinal uncertainty was intrduced in the riginal test set-u by nt being able t cntrl the temerature f the uter wall, highlight the need fr additinal systematic tests t be erfrmed in rder t better validate the new mdel. 5. ACKNOWLEDGEMENTS The authrs wish t thank PBMR (Pty) Ltd. whse financial surt made this wrk ssible as well as M-Tech Industrial (Pty) Ltd., develers f the Flwnex sftware

15 HTR2004 Beijing, CHINA, NOMENCLATURE A c v g i h k L n r area secific heat caacity gravitatinal acceleratin cmnent secific ttal enthaly thermal cnductivity reresentative length utward inting vectr nrmal t surface static ressure ttal ressure q bf heat flux frm ebbles t clant q fb heat flux frm clant t ebbles q fs heat flux frm clant t slid r T T t u i radial crdinate static temerature ttal temerature time velcity cmnent V velcity magnitude V vlume z axial crdinate Greek Letters β resistance cefficient due t sheres ε ρ τ ij rsity f bed density f fluid shear stress cmnent REFERENCES [1] VAN DER MERWE, J. & VAN RAVENSWAAY, J.P., Flwnex Versin 6.4 User Manual, M-Tech Industrial, Ptchefstrm, Suth Africa. [2] NIESSEN, H-F. & STÖCKER, B., Data sets f SANA exeriment: , JUEL-3409, Frschungszentrum Jülich. [3] STÖCKER, B. 1998, Untersuchungen zur selbsttätigen Nachwärmeabfuhr bei Hchtemeraturreaktren unter besnderer Berücksichtigung der Naturknvektin, Jüll-3504, Frschungszentrum Jülich

16 VALIDATION OF A TRANSIENT THERMAL-FLUID SYSTEMS CFD MODEL FOR A PACKED BED HIGH TEMPERATURE GAS- COOLED NUCLEAR REACTOR #C07 [4] DU TOIT, C.G. ROUSSEAU, P.G. GREYVENSTEIN, G.P. & LANDMAN, W.A A systems CFD mdel f a acked bed high temerature gas-cled nuclear reactr. (In De Vahl Davis, G. & Lenardi, E. eds. CHT 04 Advances in Cmutatinal Heat Transfer III : Prceedings f 3rd Internatinal Symsium n Advances in Cmutatnal Heat Transfer held n MS Midnatsl, Nrway n Aril New Yrk : Begell Huse. [CD-ROM], Paer 157) [5] HUNT, M.L. & TIEN, C.L Nn-Darcian flw, heat and mass transfer in catalytic ackedbed reactrs. Chemical Engineering Science, 45, [6] KUGELER, K. & SCHULTEN, R Hchtemeraturreaktrtechnik, Heidelberg : Sringer- Verlag. [7] GREYVENSTEIN, G.P An imlicit methd fr the analysis f transient flws in ie netwrks. Int. J. Num. Meths. Engrng, 53,