AER Benchmark Specification Sheet

Transcription

1 AER Bechmark Specificatio Sheet. Test ID: AER-DYN Short Descriptio: A three-dimesioal hexagoal dyamic bechmark describig the ejectio of a peripheral cotrol rod i a VVER-440 core with eutro kietics ad simple adiabatic Doppler feedback. The iitially critical reactor experieces a power excursio without ay reactor scram. The power of the reactor is limited by the cotiuous accumulatio of heat i the fuel. 3. Submitted by: Ulrich Grudma, FZ Rossedorf, Istitute of Safety Research, Germay Date: Reviewed by: Pertti Siltae, Fortum Egieerig Ltd Filad Date: Accepted by: (ame) Date: 6. Objective: Compariso of three-dimesioal eutro kietic codes for a rod ejectio accidet with a simple Doppler feedback mechaism which is the most importat feedback mechaism for this type of trasiets []. The assumptio of adiabatic fuel temperature heatig do ot require a detailed thermohydraulic model i the eutro kietic code. 7. Ratioale for Test Setup: Three-dimesioal aalysis of trasiets avoids coservative assumptios required for the applicatio of simpler models. Cosiderig the speed of computatio ad the size of memories of the available computers three-dimesioal aalysis of accidets i uclear reactors ca be performed with acceptable computatio time. Due to cosequeces of most trasiets experimets are ot available for code validatio. Compared with the pure eutro kietic problem of the previous bechmark (AER-DYN-00) [2] this bechmark ca be cosidered as a step further to the verificatio of best estimate codes for trasiet calculatios. The geeratio of a mathematical referece solutio was ot possible so far by usig fie mesh calculatios with the help of fiite differece or fiite elemet codes. of 2

2 8. Iput: a, Reactor Core Geometry ad Compositio The iitial cofiguratio of the cosidered VVER-440 reactor is close to the stadard cofiguratio with fresh fuel. The positio of the lower ed of the absorber of the cotrol rod bak K6 is 50 cm from the bottom of core. Fig. shows the distributio of the three fuel types, 2 ad 3 to the homogeeous assemblies. The absorber material is of type 4. The absorber rods are situated i the hexagos surrouded by thick lies. The cotrol assemblies cosist of absorber type 4 i the upper part ad fuel of type 2 i the lower part. The positio of the ejected rod is i the hexago filled with lies. The axial positio of the absorber rods i the lowest horizotal row of fig. ca be see i fig. 2. Axial ad radial reflector is described by give boudary coditios. The stadard mesh for the odal calculatio is oe ode/assembly ad directio. Solutios performed with a fier mesh are also welcome. z = 25 cm i axial Fig. : Core map with the fuel types. Absorbers of bak K6 at positios of types 4/2. 2 of 2

3 Fig. 2: Axial scheme of core alog the lowest row of core map i fig. Table : Mai fuel parameters Parameter Value Distace betwee parallel sides of hexagos 4.7 cm Height of core 250 cm Number of pis per fuel assembly 26 Outer diameter of fuel pellet 0.76 cm Ier diameter of fuel pellet 0.4 cm Desity of fuel 0.4 g/cm 3 Heat capacity of fuel 0.3 J/(g o C) 3 of 2

4 b, Neutroics Data The eutro kietics cosists of the solutio of the trasiet eutro diffusio equatio for two eergy groups which ca be described for the bechmark problem i the followig form ϕ ( r, t) v t ϕ ( r, t) D () t ϕ( r, t) + Σr () t ϕ( r, t) = ( ß g ) νσ f,g ( t) ϕg ( r, t) k eff 2 g= ( t) ϕ ( r, t) + Σ ( t) ϕ ( r, t) = Σ ( t) ϕ (, t) 2 D2 2 a 2 s r 2 t v + M j= λ j c j ( r, t) c j t ( r, t) = k eff 2 g= ß g,j νσ f,g ( t) ϕ ( r, t) λ c ( r, t) for j =,2,..., M g j j with ß g = M j= ß g, j It is assumed that the cross sectios i the odes do ot deped o space variable. The cross sectios ad eutro velocities of the 4 types of material are give i table 2. The boudary coditios at the core boudary describig the properties of radial ad axial reflectors are cotaied i table 3. The boudary coditios for treatig the absorber rods as ier holes are cotaied also i this Table. The equivalece with the cross sectios of type 4 is based o calculatios with the code KIKO3D [2]. The albedo values of a boudary i of a hexagoal ode describe the ratio of the et curret ad the flux averaged over the side i. The values deped oly o the type of boudary, but ot o space ad time. α i g = g D ϕ ϕ g g ( r, t) i i ( r, t) The umber of delayed eutro groups M = 6. There is oly oe set of costats for all odes. The costats of delayed eutros are give i Table 4. The total yield of delayed eutros is reduced to ß = which icreases the reactivity i relatio to ß ad stads also for the higher cotet of Plutoium i burt fuel. The reactivity worth of the absorbers was icreased by chage of cross sectios. It leads to a reactivity isertio of about 2ß by the rod ejectio. It was chose to cover ay cosidered trasiet of this type i the existig plats. 4 of 2

5 Table 2: Neutro group costats Mat. Mat. 2 Mat. 3 Mat. 4 Absorber D (cm) D 2 (cm) Σ r (cm - ) Σ s (cm - ) Σ a (cm - ) ν Σ f, (cm - ) ν Σ f,2 (cm - ) ν ν v (cm/s).25e+7.25e+7.25e+7.25e+7 v 2 (cm/s) 2.50E E E E+5 The value of 200 MeV is used for the eergy per fissio, idepedetly from material type ad eergy group. Table 3: Boudary coditios Radial Reflector Axial Reflector Absorber α α Table 4: Costats of delayed eutros Group j ß, j = ß2, j λ j (s - ) of 2

6 The adiabatic feedback is described by the followig depedece for the fissio cross sectio of the secod eutro eergy group o fuel temperature () t Σ + T () t T,0 Σ f,2 = f,2 γ f f,0 with f, 0,0 f,2 4 T = 260 C ad = ( C) 2 γ. Σ is the fissio cross sectio of the thermal eergy group give by the values i Table 2. It is assumed that the value of the Doppler costat γ ad the referece temperature T f, 0 is idepedet from the type of fuel. c, Iitial Coditios ad Sceario for the Trasiet The trasiet is iitiated by the ejectio of the eccetric rod of group K6 i 0.6 s at hot zero power (HZP). The costat speed of 2.5 m/s is assumed. The iitial reactor power is.375 kw. The feedback mechaism is based o the adiabatic icrease of fuel temperature from the iitial value of 260 C. No heat is removed from the fuel. If the code has problems to hadle the iitial power without ay heat trasport, the code has to be modified by the developer. The trasiet is simulated up to t = 2 s. 0. Output a, Expected Results (primary, secodary) The followig results are requested for comparisos of codes A) Steady State A) Eigevalue k eff of the iitial state. A2) Eigevalue k eff of the state with the ejected rod. B) Time fuctios B) reactor power i MW B2) itegral reactor power i MWs B3) maximum fuel temperature i deg C B4) odal power peakig factor [max. odal power/core average power] (if possible) B5) reactivity (if possible) i ß 6 of 2

7 The time tables are give as separate tables cosistig of pairs of time ad value. At least oe space is required betwee time ad value. The pairs have to be separated by oe ew lie. The FORTRAN formats Ew.d or Fw.d (with chagig w ad d) should be used for the data. C) Three-dimesioal distributios are requested at the followig times: C) t = 0.0 s C2) t = 0.6 s (ejectio time) C3) t = t(p max ) (time of power maximum) C4) t = 0.4 s C5) t = 2.0 s (defied ed of trasiet) For each time poit, the followig three distributios are give: - ormalized odal powers - odal fast flux values - odal thermal flux values The spatial distributios are give separately i the followig order: - i a cosidered layer the odes are umbered as show i core map of fig. from left to right begiig with the row at the top ad edig with the row at the bottom. - the values are give layer by layer startig with the lowest axial layer at the bottom of core. If a mesh differet from the stadard is used the results have to be coverted to the stadard mesh. Normalized distributios have to be ormalized to the core average value of (odes with absorber belogs to the core volume!). The recommeded format of the umbers is F7.4. At least oe space or a ew lie is required betwee the umbers. The preferred file form is ASCII (.txt) which ca be used directly for computer iput. All output is give i oe file. For more details, please refer to oe of the give outputs.. Refereces [] Grudma, U., Rohde, U.; Defiitio of the Secod Kietic Bechmark of AER, Proceedigs of the 3 rd Symposium of AER, KFKI Atomic Research Istitute, Budapest (993) 7 of 2

8 [2] Kereszturi, A., Telbisz M.; A Three-Dimesioal Hexagoal bechmark Problem, Proceedigs of the 2 d Symposium of AER, KFKI Atomic Research Istitute, Budapest (992) [3] M. P. Lizorki, V. N. Semeov, V. S. Ioov, V. I. Lebedev: "Time Depedet Spatial Neutro Kietic Algorithm for BIPR8 ad its Verificatio", Proceedigs of the 2 d Symposium of AER, KFKI Atomic Research Istitute, Budapest (992) [4] U. Grudma, U. Rohde: "/M2 - a Code for Calculatio of Reactivity Trasiets i Cores with Hexagoal Geometry", IAEA Techical Committee Meetig o Reactivity Iitiated Accidets, Wie 989Report ZfK - 690, Rossedorf 989 [5] R. Kyrki-Rajamäki: "VVER Reactor Dyamics Code for Three-Dimesioal Trasiets", Proceedigs of the st Symposium of AER, KFKI Atomic Research Istitute, Budapest (99). [6] A. Keresztúri, L. Jakab: "A Nodal Method for Solvig the Time-Depedig Diffusio Equatio i IQS Approximatio", Proceedigs of the st Symposium of AER, KFKI Atomic Research Istitute, Budapest (99) [7] U. Grudma, "Results of the Secod Kietic AER-Bechmark", Proceedigs of the 4 th Symposium of AER, KFKI Atomic Research Istitute, Budapest (994). 2. Recommeded Solutio No referece solutio is available so far. Therefore the compariso of the results of differet odal codes is cosidered as a importat step of code verificatio. 3. Summary of Available Solutios Results of the followig codes were obtaied ad aalyzed by comparisos: BIPR8 /M2 HEXTRAN KIKO3D Russia Research Ceter "Kurchatov Istitute", Moscow, (Russia) Code BIPR8 /3/ Forschugszetrum Rossedorf, Istitute of Safety Research, Rossedorf (Germay) Code /M2 /4/ VVT Eergy/ Nuclear Eergy, Espoo, (Filad) Code HEXTRAN /5/ KFKI Atomic Eergy Research Istitute, Budapest, (Hugary) Code KIKO3D /6/ 8 of 2

9 Absorber ad reflector ca be described by cross sectio data or albedos. The four codes describe the absorbers by usig albedos of table 3 or equivalet diffusio costats of table 2. KIKO3D is able to use both of them. Usig cross sectios i KIKO3D albedos were calculated givig early the same eigevalue i the iitial state ad the same reactivity effect for the ejected rod. HEXTRAN has used these albedos while ad BIPR8 have applied cross sectios for the absorbers. Table 5 shows the list of results which were provided for the comparisos. Some of comparisos show i the followig were preseted i /7/. Table 5: List of results result BIPR8 *) HEXTRAN KIKO3D A X X X X A2 X X X X B X X X X B2 X X X X B3 X X X X B4 X **) X X **) X **) B5 X X C X X X X C2 X X X X C3 X X X X C4 X X X X C5 X X X X *) The time history of the iverse period (result B6) ad the distributios of power ad fluxes at t = 5.0 s (results C6) are give as additioal results **) The power peak factors are give at time poits t = 0.0 s, 0.6 s, 0.25 s, 0.4 s ad 2.0 s (see table 7). a, itegral parameters ad time fuctios The ucertaities of the obtaied results have ot bee evaluated, sice o referece bechmark solutio exists. O the basis of selected calculatios a itercompariso of differet codes, i which the deviatios are referred to the results of, is preseted here. 9 of 2

10 The itial eigevalue k eff,0 ad the eigevalue of the steady state with the ejected rod are give i table 6. The results of KIKO3D calculated with both albedoes ad diffusio costats for absorbers are the same i terms of eigevalues ad reactivities. The static reactivity values ad the deviatios from are give i the right colums. ad KIKO3D give approximately the same reactivity. The largest differece was obtaied by BIPR8, but reactivities of BIPR8 ad HEXTRAN differ i the same order as ad KIKO3D. Table 6: Static eigevalue i the iitial state ( k eff,0 ), i the state with ejected rod ( k eff, ) ad static reactivity worth of the ejected rod ( ρ ). Code k eff,0 k eff, Rod worth ρ ρ = ( k eff k eff,0 ), ( ρcode ) 00% ρ BIPR HEXTRAN KIKO3D KIKO3D KIKO3D : Absorbers were take ito accout by cross sectios KIKO3D 2. Equivalet albedos were used for descriptio of absorbers. A higher reactivity value results i a higher power peak, which ca be see i fig. 3. The higher reactivity gives a earlier peak also. The power peaks of KIKO3D ad have early the same maximum value. The peak of KIKO3D is about 0.0 s earlier, caused possibly by the 0.8 % higher reactivity or the differet time itegratio techique. The highest power peak is give i the result of HEXTRAN, but it is close to the result of BIPR8. Fig. 3 shows that BIPR8 ad HEXTRAN o the oe side ad ad KIKO3D o the other side should give differet values of itegral power which ca be see i fig. 4. The differeces i itegral power are caused maily by the differet peaks. This ca be see also i the curve of maximum fuel temperature versus time (fig. 5). Besides the specific eergy release i the fuel, the maximum fuel temperature is a importat safety parameter for reactivity iitiated accidets. The positio of the maximum fuel temperature after rod ejectio is the 5 th axial layer from the bottom of core i the fuel elemet which is situated i the lowest row of fig. at the secod positio from the left had side. This positio was obtaied by the results of. Cosiderig the power distributio calculated by the other codes the maximum seems to be at the same positio. 0 of 2

11 The % higher reactivity value of HEXTRAN ad BIPR8 i compariso to KIKO3D ad gives a maximum fuel temperature which is about 50 degrees higher. Cosiderig the differeces of maximum fuel temperature the cotributio of the global power peak ad the ifluece of the power peakig factor should be ivestigated. Fig. 6 shows the time behaviour of power peakig factor give by the calculatio. The maximum value of peakig factor occurs after ejectio of the rod. The Doppler feedback, beig maximal i the local power peak, reduces the power i the peak more tha i other parts of the reactor. The power peakig factor for the other codes were calculated from the spatial distributios give at several time poits (table 7). It ca be see that the results of all codes are close to each other except at the time of power maximum. The chages of power peakig factor at power maximum are very fast. Therefore the differeces do ot ifluece the other results. Later the deviatios of peakig factors are lower tha 0.5 %. b, spatial distributios Fig. 7 shows the assembly powers of ad the deviatios of the other codes at the iitial state. Besides the assemblies with iserted absorbers (hexagos with thick boudary) we see that the differeces betwee ad KIKO3D are lower tha.3%. The deviatios of the other codes are larger. BIPR8 gives deviatios of 6.2% ad HEXTRAN - 4.5%. The maximum deviatios betwee BIPR8 ad HEXTRAN are.8%. Aalyzig the agreemet of results we see that ad KIKO3D form oe group of codes ad BIPR8 ad HEXTRAN the other. That was suggested also by the results show i the previous chapter. Nevertheless, the deviatios betwee BIPR8 ad HEXTRAN seems to be sometwhat larger tha betwee ad KIKO3D. The maximal deviatios of the assembly powers betwee both code groups are observed at the boudary ad cetral core regios, but with the opposite sig. The assembly power distributio of ad the deviatios of the other results are show at ejectio time t = 0.6 s (fig. 8), at time of maximum power (fig. 9) ad at t = 2.0 s (fig. 0). Cosiderig the power distributio at the ejectio time t = 0.6 s i fig. 8 the higher flux values i the assembly No. 4 (positio of ejected rod) of the the codes BIPR8, HEXTRAN i compariso to ad KIKO3D are leadig to larger values of reactivity. Fig. shows the radial averaged axial powers of at the iitial state ad the deviatios of the other codes. We see a good agreemet of all results. BIPR8 gives a small deviatio i the secod layer which is the ext layer uder the lower ed of cotrol rods. The values of averaged power calculated by ad the relative deviatios of the other codes ca be see i table 8. The powers i the first ad last layer are small ad the relative deviatios are also larger betwee ad KIKO3D. Cosiderig these distributios at the ejectio time t = 0.6 s (table 9), at the time of the maximum power (table 0) ad after of 2

12 power peak at t = 2.0 s (table, fig. 2) the deviatio at upper ad lower layer are similar. Cosiderig the layer uder the lower ed of cotrol rods, the deviatio of BIPR8 is reduced from.9 % at t = 0.0 s to.3 % at t = 2.0 s, because we have a radial power peak at the positio of the ejected rod. If the deviatio is iflueced by the ed of absorbers, it should be reduced, because there is o ay absorber i the regio of power peak which gives a essetial cotributio to the radial averaged value. Table 7: Power peakig factors at differet time poits. Time (s) Power maximum (~ 0.25 s) BIPR HEXTRAN KIKO3D Table 8: Normalised axial (radially averaged) power distributio of ad the relative deviatios of the other codes for t = 0.0 s. LAYER KIKO3D - HEXTRAN - BIPR of 2

13 Table 9: Normalised axial (radially averaged) power distributio of ad the relative deviatios of the other codes for ejectio time t = 0.6 s. LAYER KIKO3D - HEXTRAN - BIPR Table 0: Normalised axial (radially averaged) power distributio of ad the relative deviatios of the other codes at maximum power. LAYER KIKO3D - HEXTRAN - BIPR of 2

14 Table : Normalised axial (radially averaged) power distributio of ad the relative deviatios of the other codes for ejectio time t = 2.0 s. LAYER KIKO3D - HEXTRAN - BIPR of 2

15 /M2 BIPR8 KIKO3D HEXTRAN N u c le a r Power (M W) Itegra l Power (M Ws) /M2 BIPR8 KIKO3D HEXTRAN Time (s) Time (s) Fig. 3: Nuclear power versus time Fig. 4: Itegral power versus time 5 of 2

16 F u e l Tempera tu re (d eg C ) /M2 BIPR8 KIKO3D HEXTRAN Power Peak Facto r (re l. u its ) Time (s) Time (s) Fig. 5: Maximum fuel temperature versus time Fig.6: /M2 Power peakig factor versus time 6 of 2

17 Fig. 7 : Assembly powers of with the deviatios of the results of the other codes at time t = 0.0 s. 7 of 2

18 Fig. 8 : Assembly powers of with the deviatios of the results of the other codes at time t = 0.6 s. 8 of 2

19 Fig. 9 : Assembly powers of with the deviatios of the results of the other codes at time of maximum power. 9 of 2

20 Fig. 0: Assembly powers of with the deviatios of the results of the other codes at time t = 2.0 s. 20 of 2

21 Power (relative uits) 0.8 Power (relative uits) 0.8 /M2 BIPR8 KIKO3D HEXTRAN /M2 BIPR8 KIKO3D HEXTRAN x (cm) x (cm) Fig. : Normalized axial (radially averaged) power distributio Fig. 2: Normalized axial (radially averaged) power distributio at t = 0.0 s. at t = 2.0 s. 2 of 2