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validation of the cfd code neptune for a full scale simulator for decay

1. output type each n t step Iteration freq of chrono outputs 50 i Chrono outputs at the MED format NEPTUNE CFD V1 0 8 i chrono output of nucleate boiling model madin output type each n t step iteration freq of histo output 50 Special modules Input output control N saving frequency 50 definition of probes defined in Edamox Fhuid amp flow prop Generalities mmber of probes 5 x_prob y_prob z_prob 4 95 2 195 0 05 4 95 1 195 0 05 3 54 2 695 0 05 3 54 2 195 0 05 3 54 0 055 0 05 iteration freq of listing output 50 averages _ time averages _ restart with tine averages 4 listing output chrono output J average deviations Close Cancel Help apts tex f pata bash unor 3 snaps G N ES aoaea Figure 5 8 Input Output control X X amp GENERALITIES k File Options Headings variable physical properties call usphyv i Mass transfer call ustrnv i User defined head losses call uskpdc NEPTUNE CFD 1 0 8 4 Porosity call uspors fi Isolated cells call usetan i Momentum sources call ustsns Special modules Input output control _ WALL TRANSFER
2. Overall Pool water discharge closure 4840 HX Pool level 2 07 m 4840 Triggering valve closure 4887 closed in 93 s Maximum level in the HX Pool 3 4m 11050 Maximum exchanged power 21 5 MW End of the test 7708 Table 3 8 Chronology of main events of test 9 ia F_POOL kgs a z g 60 40 20 0 1 Figure 3 19 Water flowrate between the pools Like in Test n 7 the Test n 9 foresees the system actuation with total HX Pool fill up followed by reaching of boiling conditions and pool level decreasing Table 3 7 shows the main test parameters This test is aimed at demonstrating the correct system behavior during long term accidental transient under reduced primary side pressure 4 1 M Pa It is performed to investigate the system actuation consequent to the HX Pool fill up and reaching of the thermal regime in both the pools the effectiveness of the Injector in mixing the Overall Pool water the power and flow regime variation after the Overall Pool level decreases THE PERSEO FACILITY 95 LvVQm LVPm 1000 2000 3000 4000 5000 6000 7000 8000 Time s Figure 3 20 HX Pool and Overall Pool water level 5000 7 3500 4500 4000 N semnncumteneennmenmesitiiiinnn Ss Ss t vy o a a S Pressure kPa P B001A kPa P 1001 kPa
3. 79 3 2 PERSEO experimental data aaa fhe gt Sep keldins ead Midi By 80 3 3 Experimental text MATRIX 2 send aaa ps BGod shih ae ded Ga 2 5 80 3 91 TESZ me ee ha ae hee BE oS See Chee GOA dee a 84 Sol TCSP Oe hata ds Wi hint Seth we eek ai Era el cee alte ee de eee Stee bg 93 CATHARE Modeling of PERSEO facility 99 41 The CATHARE model oare 05 5 a hacete nag ead eae eS 99 4 2 Analysis of the PERSEO Tests aaa ak eo hae eS eG BIS we eS 100 4 2 1 Testn Z Phase l ady atua Biante be awe a le wae a ee 100 422 Testn 7 Phase 2 saii eels 2064 Glee Be A ak AS 104 ADe TESIRI 5 eee se SBM e can Ben ape Ry See BN te ents OS Rees tee seed Oe Ge Cee Sasori ae h 108 4 3 3D Overall Pool modeling sacs ba va aks BE eR OS EOE Se OO 111 4 3 1 Testni 7 Phase reg Oates fe Bede en ke PL dk aes 113 ASD TESTEI o eke RN e he ae ho AO a A ANS RE ee seme eGo ate h 115 NEPTUNE_CFD modeling of PERSEO facility 119 Hal Introduction si 2 2 tH aoa g iaat el ae ee ines dhe Be d d 119 5 2 CATHARE NEPTUNE coupled simulation 0 119 5 3 The two dimensional model 0 00000 cee ee ees 122 5 3 1 Geometry and Boundary conditions for the Test9 122 5 3 2 Physical properties and models set in the param file 124 5 3 3 Results obtained for the test9 0 131 5 3 4 Steam injection on boiling pool 5 4 o 3 2 85 0ik a aoa d 4 138 5 3 5 Injection above water level naana aa 140
4. 500 650 time s Figure 5 43 Comparison between experimental and numerical water temperature data for different probes are considered The first couple TP006 and T P008 are positioned below the injector while the second one T P023 and T P025 are located towards the pool center The two probes T P006 and T P023 positioned at 2 195 m from the pool bottom the other two at 1 195m There is clearly a temperature difference between the two probes located be low which is not present in the records of the two probes positioned at the pool center at least in the first part of the transient It should also be noted that the probes below the injector undergo a very fast temperature rise at the beginning of the transient while the temperature rise is much more gradual for the probes in the pool center A consistent temperature stratification seems to be present for t gt 2000 s when both the probes at the higher level register temperature values higher than the lower probe ones In Figure 5 43 the comparison between numerical and experimental data is shown The experimental data refer to probes T P006 T P023 and TP025 The numerical data are taken at the same position of T P006 T P6 num and below the injector at the same vertical level as TP006 and T P023 P23_N_num The exact position for the latter numerical probe is given in the simulation frame of reference by the following coor dinates x 2 815m y 2 7355m z 2 1
5. 0 00 00 0000 105 4 9 Overall Pool collapsed water level 0000 106 4 10 HX Pool relative pressure 5 as te Ge te ee weet eee wet Sa gk 106 LIST OF FIGURES 165 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 4 26 4 27 4 28 5 1 BZ 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 HX exchanged power secesia a o o ala Go Era E ee AER le 107 Overall Pool temperatures ooa 4 OB ae Saw ey 107 HX tube wall temperatures ce hs tg BESS ee ee eae eS 108 HX Pool collapsed water level Ywig ave Oye PASSES 4 109 Overall Pool collapsed water level 00056 64s heed ee PRN 109 HX Pool relative pressure oe engok Sil de aati ee G8 ete HS 110 HX exchanged power 2 242 22 25 ee PERS Brie a e ES 110 Overall Pool temperatures 0 icy oleate we aie Sa Bite Bag da 8 111 HX tube wall temperatures 2 5 222 8S OS eS eee 111 3D volume Overall Pool modeling scheme 112 HX Pool relative pressure e Gate oe LSe ced pra hye eae ede we 113 HX Pool collapsed water level sisi wate ek ed See aS 4 114 HX exchanged pow r c sosai tens ax Oty ores ioan i alte niin cbc ations a 114 Overall Pool collapsed water level cc 2 i sew ere die ele es 115 Overall Pool collapsed water level 0000004 115 HX Pool relative pressure k otis eS Ee ck So ae ee Se ele F 116 HX Pool collapsed water leveled a s vows 26a SS ed SAS Rue es 1
6. Nbr of naysto sub cycles 1 Max Nbr of alpha pressure cycles 50 Max 1 Sum alpha 1e 06 W Printing of Max 1 Sum alphal restart time step if not converged stop if no convergence after last rstart Nbr of P sub iter reconstr implicit 2 Implicitatiom coef for fraction convection 1 pressure solver gradco _ symetrisation of pressure matrix gradco multigrid solver fraction solver jacobi pressure relaxation p0 during n iterations n 0 Min pressure 1e 15 Max pressure 1e 15 computation of potential state at first time step cell gradient of P mass ponderation density update compressible thermo laws usphyv Implicitation coef of thermo derivatives 1 E upwinding of density ininas inplicitation coef of water steam source terms 1 W Diffusion fluxes set to zero for inlet conditions ALGORITHMS Close Cancel Help Figure 2 11 Numerical Scheme panel 72 THE NEPTUNE CFD CODE 1 front 2 behind H Symmetries 1 front 2 behind E Adiabatic wall 5 F Heated wall 6 l Inlet 3 N Outlet 4 G os 3A inlet Figure 2 13 Boundary conditions applied on the boiling channel steam energy transfer for the two phases is specified For the water and steam phases the standard bubble models for liquid and vapor are chosen respectively In the Numerical Scheme
7. o 4 Time s Figure 3 21 Primary side pressure T T T T T T T 1000 2000 3000 4000 5000 6000 7000 8000 below the Injector outlet and the trend of power as a function of the water level in the pools decreasing for the loss off mass through the boil off The chronology of main events characterizing the conduct of the test is shown in Table 3 8 The described transient begins with the primary side pressure at about 4 1 M Pa and the HX Pool water level of 1 2 m The triggering valve begins to be opened at time 142 s and it is completely opened at 163 s 21 s opening time The water flowrate between the pools derived by the HX Pool level is reported in Figure 3 19 After full opening of the 96 THE PERSEO FACILITY 25000 7 20000 W_IC kw 15000 Power kW 10000 5000 7 0 1000 2000 3000 4000 5000 6000 7000 8000 Time s Figure 3 22 HX exchanged power T Q023 C T Q030 C 250 T Q032 C T Q016 C T Q007 c T Q006 C T Q031 C T Q024 C T Q009 C T Q013 C T Q015 C T Q034 C T Q036 C T Q022 C T Q033 C T Q010 C T Q008 C T Q037 C Temperature C r r r 0 1000 2000 3000 4000 5000 6000 7000 8000 Time s Figure 3 23 HX Pool temperatures triggering valve the collapsed water level in the HX Pool quickly increases stabilizing close to the top
8. 1 ai gt Acrit gt fo 1 zerp 20 a1 Qcrit l 2 69 1 Q 20a crit a1 lt Aerit gt for 5 l 2 70 crit We will notice that the classical choice fa 1 is also available The diffusive contribution part given to the vapor phase namely 2 is predicted by a classical law of single phase flow heat transfer at the wall p2 hy Twat Ta 2 71 As concerns the liquid diffusive part y is divided into two terms Yi Yot va 2 72 The mass transfer by nucleation is expressed as Pe for f Vop2 2 2 73 w gt 1 The vaporization heat flux yp is related to the mass transfer and is connected to the 46 THE NEPTUNE CFD CODE total heat flux Ywa by Pwall fa PC pQ PE 1 far Y2 2 74 When Ts tends towards Tsat b tends to towards 0 and the bubble diameter tends towards infinity To avoid this problem the Stanton number is used and it is defined by Pwall St 2 75 piCpi T sat T5 Us If St lt Stum the last definition of b is considered If St gt Stum the b definition is replaced by Pwall b 2 76 2 1 3 x Stim x prCpiUs a with Stum 0 0065 This theory has been dedicated to boiling flows in tubes which provide small values of U5 2 1 5 Turbulent modeling For each phase k the Reynolds stress tensor is closed using a Boussinesq like hypoth esis au ne lt y y ahs k i kj PkUkiUk j Ok Lp On TF De Uk m i orak nk 2 77
9. hi if hy gt hit 2 44 The correlation for COEF takes into account a delay to saturation s 2 UZ VW COEF FLASH x 1 210 x pj a ae x exp 4 5a2 Vo 4 2 45 S Q2 2 hi eet 2 c E h a _ psat CC 0 00 5h 1500 exp 1 253 107 h1 2 47 Default gt FLASH 1 lt 1 gt FLASH CC 1 lt lt 2 FLASH CC 1 CC 5 12 9 7 2 Steam phase In this phase the constant time scales and the sub cooled model must be defined The constant time scale return to saturation is defined as w s paC p2 I F a2 Tsat T 2 48 2 T is the time constant s given by the user f a is a pondering function which can takes different values 1 a1 2 or a a In this CATHARE1D like model a strong return to saturation is enforced if the steam temperature remains lower than the satu ration temperature Te Ty I fla 4 108 BaD 2 49 w s C To gt Toat gt Thy f a2 Tout T 2 50 In this numerical model the constant time scale is replaced by the local time step w s C ny a2 Toat T 2 51 42 THE NEPTUNE CFD CODE 2 1 4 Nucleate boiling model Basic computation of the flux heat In the lack of any global understanding of the processes involved in the heat transfer at the wall a first model for the wall heat transfer mechanisms is implemented in the NEPTUNE_CFD code Closures involving the parameters namely the mean bubble fre
10. 10 THE CATHARE CODE Figure 1 2 AXIAL 1D element be connected to all the other modules and to all the sub modules An example of Axial element is shown in Figure 1 2 Figure 1 3 VOLUME 0D element The VOLUME 0D module is a two node module used to describe large size plena with several connections such as the pressurizer the accumulator the steam generator dome the upper and lower plenum and the dome of the vessel of a PWR The volume predicts swell level total or partial fluid stratification and phase separation phenom ena at the junctions Main assumptions are considered for 0D module all thermal hydraulic quantities are assumed uniform in horizontal planes and inertial forces are assumed to be negligible compared to gravity forces Consequently the momentum equations are simplified and the pressure field is hydrostatic The stratification is rep resented by a two node model with two sub volumes The interface between the sub volumes has a variable level In each sub volume enthalpies and void fractions are assumed to be uniform but not the pressure which has a hydrostatic gradient It is as sumed that there is liquid in the lower sub volume possibly with gas rising towards the interface In the upper sub volume there is mainly gas possibly with liquid drops or falling jets Scalar variables are calculated inside the volume in front of each junction Flow distribution between sub volumes and the phase sorting phenomena are m
11. The water flowrate between the pools derived by the HX Pool level is reported in Figure 3 13 and it is valid only for the first phase of the water injection 300 s to 500 s THE PERSEO FACILITY 91 T T T T T 4 0 1000 2000 3000 4000 5000 6000 Time s Figure 3 14 HX Pool and Overall Pool water level 2 Phase 8000 7000 6000 5000 P B001A kPa P 1001 kPa 4000 e kPa essu Pr 3000 2000 1000 or T T T T T T T T T 10000 10500 11000 11500 12000 12500 13000 13500 14000 14500 15000 Time s Figure 3 15 Primary side pressure 2 Phase The HX Pool level begins to increase at time 310 s At time 531 s the HX Pool reaches the maximum level of 3 25 m then oscillations follows until about 1500 s Figure 3 14 The Overall Pool level is reported in the same figure After the early level decreasing for the water pouring off to the HX Pool strong and fast oscillations are observed due to the condensation of steam produced in the HX Pool and flowing through the Steam Duct At time 1150 s when the Overall Pool temperature is between 80 C and 90 C the level decreasing in the pools is accelerated by opening the discharge valve When the Overall Pool level is around 2 8 m about 3230 s the discharge valve is closed At this point the Injector outlet is uncovered and the steam flows directly outside through 92 THE P
12. introducing u and g the turbulent viscosity and the turbulent kinetic energy of the phase 2 1 1 qk lt Uk iUk j gt k 2 Basically the code uses two main turbulence models the q ex and the local equilib rium model The q ep model is an extension of the classical k model used on single phase flows It can be chosen to describe the turbulence of a continuous phase coupled with dispersed phases such as bubbles or droplets or with an other continuous phase strat ified two phase flows The transport equations system on the turbulent energy and the turbulent viscous dissipation is written in the following non conservative form Og Og 1 f Og P II 2 78 E Urkiza FP font SE on rod Gk k Ia 2 78 oek Oek 1 pt Oek pce 2 79 Pk a Uk Ox l Qk OX la Oc Sul px Ca Prod C max Gz 0 Cesk Cou oH k k THE NEPTUNE CFD CODE 47 where uj is the turbulent dynamic viscosity defined as qj ie Cupk ae C 0 09 2 80 k Prod represents the positive production contribution due to the mean velocity gra dients 1 1 U i Prod lt UU ns gt Ox 5 2 81 and G is a stratification attenuation term modeling the correlation between fluctuating density and velocity The closure form assumes a gravity equilibrium w Led GS a2 U8 oath Pr a 00 2 82 Prt Pk Ox Notice that this contribution can only be positive in the dissipation
13. P 1 P day at a and MY the inverse of the velocity coupling matrix The pressure gradient correction represents the basis of the elliptic scheme so the exact formulation has to be kept The fraction gradient correction is not essential but can introduce some numerical diffusion i e numerical stabilization in the mass balance equation Nevertheless the diagonal and isotropic contribution in only kept that is to say the diffusion contribution of the fraction in the equation the local spatial variation of the Da coefficients are neglected These remarks lead to the simple formulation P 1 aak Ung Uia Ces 2 110 ki ki ki Ox k Ok Pk Ax with CE and C two positive parameters defined as nphas _ At Chi D MN u ae 2 111 l 1 PI Ck MN lon AtDax i 2 112 2 2 2 Mass Energy equations the Alpha Pressure Energy cycle The next fractional step solves a coupled system of mass and total enthalpy in order to ensure a perfect conservation of these quantities The algorithm is called the Alpha Pressure Energy cycle since the final main variables are ait P H and UP 54 THE NEPTUNE CFD CODE Full implicit non linear system The mass energy system in its implicit form nphas oe ae 2 113 k 1 apt ptt Phe 1 1 1 Ay tap oe Uki TR 2 114 HH He 1 p p Sl ORRU HR Bet akekURT Pk At a Lox Ti 1 0 Goose O fla an Ox ai Ox
14. eises SAT Cae ee 61 Suggested parameter order o lt Oe aaa ano Gee Bel ee Pontes aes oan st 63 Geometry and mesh of the channel 0 000045 66 Fluid and Flow Properties panel o s sie Raed Go Saco 67 Inter phase forces for liquid and vapor phases 68 Tp Ue OMe OU Control panels es cs Bikey tol Ge yh gs oe ee heat Beales 69 Generale y pales v4 eani aay ia aaa WEAR ee ewes 70 Numerical Scheme panel s sp ee ae win as eR aE ee BAS eS 71 Scatarpanel sarisi set arie ae ate od a A a AG 72 164 LIST OF FIGURES 2 13 Boundary conditions applied on the boiling channel 72 2714 Boundary conde Ons panel gt sares ecko bBo ewok Gale ee eS 73 2 19 R mp nel snem diera iane ae ete iu pei sn erie E AAE ie EA E AANE 74 3 1 Scheme of the PERSEO facility aaa aaa Cole ee ey 75 3 2 PERSEO facility scheme of the primary side and main elevations 77 3 3 PERSEO facility Steam Duct and Liquid Line between the pools 78 3 4 Hx Pool temperature measurement position oaoa 81 3 5 Overall Pool temperature measurement position 82 3 6 Water flowrate between the pools partial HX Pool fill up 86 3 7 Water flowrate between the pools total HX Pool fill up 86 3 8 HX Pool and Overall Pool levels 0 0 0 0 0 0000 87 3 9 HX exchanged power 2 033 beam Bisel bee Se eS 87 3 10 Primary side pressure Awe 2 ard DER SRA SAS BS REDEEM 88 311 HX Pool tem peranir
15. Event Time s Beginning of the test 0 Triggering valve opening 300 opened in 26 s Overall Pool water discharge opening 1150 Onset of the Overall Pool water boiling 1400 Overall Pool water discharge closure 3230 Triggering valve closure 3338 closed in 123 s Primary side depressurization beginning for end of test 4685 End of the test 5736 Table 4 2 Chronology of main events of Phase 2 eal m eal _ l HX E pipes F D 0 1000 2000 3000 4000 5000 6000 Time s Figure 4 8 HX Pool collapsed water level the main events better described in section 3 3 1 is shown in Table 4 2 The comparison between the experimental results and the calculated ones is shown from Figure 4 8 to Figure 4 13 Water Level behavior After full opening of the triggering valve at t 326 s the water level in the HX Pool quickly increases When boiling is reached in the pool at t 500 s the collapsed water level decreases stabilizing around 0 25 m In the Overall Pool a progressive water level decrease begins at t 1150 s by water discharge valve opening at the pool bottom After 1400 s the Overall Pool reaches the boiling conditions and the water level decreases more quickly due to mass loss through the boil off pipe Around t 3400s the triggering valve is closed and the HX Pool level begins to rapidly de crease until boiling is finished and the HX tube bundle is fully uncovered The initial water level i
16. Gas phase a z Ava zz arava AT SG 5 Si 1 2 i 1 Non condensable transport equation sia EE T Si 1 3 Ot Oz with JA Api Xc Le 4Ge ET 1 4 Hy H e Ki T T is the interfacial mass transfer kg m s and T is the residual value use to have Amin SAS Amax o paga when a lt Qmin Vaporization Ir 40 amin lt Q lt Omar 1 5 pr ear eee when amar lt a Condensation Momentum equations Liquid phase v OVL OP l a AU o p1 a A ae dz a Oz Ovg Our va OvL ABa l a om Ge Spe tee Ge Be OA AT w vz At xsCr vrlo A 1 a pL9z RIP SMz 1 6 THE CATHARE CODE 17 Gas phase va va OP a Aapa Ot UG H nO MeT Ovg Our Ovg Ov Af all 0 0m Ge Be tee se Ge 1 OA AT wi va Ati xa f valva Aapag Rl J a 5z 7 SMe 1 7 with Pm apg 1 a pL 1 8 Energy equations Liquid phase 42 o o Za oma E OP A 1 a Aqre Xeon AT H A 1 a prvLgz SE 1 9 ot Gas phase ap one to 2 Aoncrete 2 oP Aa Adce Xe o AP He Aapevag SEa 1 10 State equations for the gas mixture Four non condensable gases can be calculated p Xpa Pi pihiTa 4 po gt pit pv To Hv for i 1 4 i 1 4 P S R Py i 1 Hg 1 ass i Hv ag Sx il hus7 cp Te Ts7 1 11 i l 18 THE CA
17. The turbulent contribution of the interface momentum trans fer depends on the turbulence modeling of each phase It will only be activated if the turbulence of the continuous phase phase 1 is k model and the turbulence of the THE NEPTUNE CFD CODE 39 dispersed phase p gt 1 are given by the Tchens local equilibrium model leading to an algebraic closure for the particles turbulent energy q2 0 5 lt U iUpi gt and the fluid particles covariance q p lt U1 Up gt l a Ear ap Volp 2 35 pi ae 3 turb Ipyrl tee aap Fp Va The first contribution is the part of the drag effect due to drifting velocity with vi given by t T1pQ1p Vap v 2 36 3 A1Ap Tip being the fluid particle turbulent time scale The second contribution is the fluctuating part of the added mass force The last contribution is the fluctuating pressure term due to the correlation between the particles distribution and the carrier phase constraint tensor Using extension of the classical model used for bubbly flows it is written using the added mass coefficient apC e eae Vie 2 Ap Vo1 p a Op Oy 2 37 Developing all these terms and neglecting the gradients of turbulence one can show that a simplified form of this turbulent contribution can be re written as a turbulent dispersive term Nee CPT Vay 2 38 Notice that such a modeling is possible in the code and does not require any a
18. au Pk In 1 1 a 1 eee moot THE HET sy At i ar ar ne p k with pit p P h 1 calculated from external tables or analytic user laws Te Telap apt Pett ape APM aU Te Te P he op Ae H fa a7 given by formula 2 69 Na e Gt ee Pt ya ae eet or given by a user routine U i updated from Uf and anti The system is now solved using sub cycles each containing sub steps solving se quentially total enthalpies volumetric fractions and pressure Density and velocities are actualized at the end of each sub cycle Before starting the cycles the variables must be initialized see Table 2 1 Initialization a Of Hp Hp Pulp op See UEU Table 2 1 Variable initialization Enthalpy j sub step H gt H b In order to get a simpler formulation the enthalpy jump and local enthalpy are sup posed to be equal ie HZ H The full balance is obtained after decomposition in THE NEPTUNE CFD CODE 55 fractional steps the explicit balance the source coupling balance the implicit balance and the extra diagonal source coupling actualization jt Enthalpy explicit balance HR gt H This equation is solved for each phase 1 j 7 a p A ar lan akeeugs HE Mak aneeogs 2 3 4 Tora OY BACIO a eae opt Fali Jog ap Mo 2 116 a Ox ar The first term represents the sum of explicit convection and mass accumulation part arly g p The handling ma
19. this configuration scheme the 0D two node module volume is chosen to represent the primary vessel the HX collectors the HX Pool lower and upper plenum and the Overall Pool complete mixing The volumes are interconnected by axial elements pipe representing the HX tube bundle the water lines and the steam lines Axial elements with cross flow junctions are used to best simulate 2D recirculation within the HX Pool Empirical correlations specifically derived at atmospheric pressure are implemented in the code for this specific case study The main correlations are EPICE correlation for boiling heat transfer in the HX Pool and SUPERCLAUDIA correlation for direct contact condensation in the Overall Pool 28 The last correlation is implemented in order to 100 CATHARE MODELING OF PERSEO FACILITY Overall Pool Water Line Figure 4 1 CATHARE nodalization scheme overcome some deficiencies evidenced using CATHARE standard models and better reproduce the experimental data 4 2 Analysis of the PERSEO Tests A test campaign on the PERSEO facility has been conducted in order to verify the cor rectness of the proposal and the effectiveness of heat removal section 3 3 explains in detail the PERSEO tests features In the present work the Test n 7 Phase 1 and Phase 2 and the Test n 9 have been performed with CATHARE V2 5 mod8 1 and the results are compared with the experimental data for code validation purposes In the com parison
20. 137 alpha_s alpha_s 4 999994 0 75 Figure 5 20 Steam entering the injector right and injection of steam into water left alpha_s alpha_s 999994 Figure 5 21 Steam and water mixing right and inverse flow left 138 NEPTUNE_CFD MODELING OF PERSEO FACILITY 308 Temp_probe1 Heated phase 307 5 i i We ih 4 Direct flow data_ExP dat u 1 4 data_EXP dat u 1 5 Temp_probe1 Temp_probe2 j 315 Inverse flow 310 305 300 295 Figure 5 22 Temperature of the probes TP6 red and TP8 green from experiment and NEPTUNE computation blue and violet and zoom of the temperature oscillations geometry these two flows may be added to define the boundary condition for the water line The NEPTUNE simulation shows a great mixing with no temperature stratifica tion The mixing is generated by the cyclic behavior of the injector The injector is periodically filled with steam The steam cannot enter the pool and condensates near the injector outlet The steam pressure pushes the water down till the level goes below the injector The steam mixes with water and the water enters the injector again The steam condensates and the water is sucked until it fills the injector almost completely Then the cycle repeats again This can be seen in Figures 5 20 5 21 On the top of Figure 5 20 the injector is filling with steam which
21. 2x107 1006 Table 5 2 Fluid and flow properties selected for PERSEO test 9 The param file is the dataset file in which physical properties models and boundary conditions are imposed to the case study section 2 3 2 gives a detail description the file As shown in Figure 5 4 in the OP injector system three fluids are present water NEPTUNE_CFD MODELING OF PERSEO FACILITY 125 steam and air The main physical properties of the fluids are reported in Table 5 2 In this simulation the special module water steam which allows the use of Cathare table for water steam systems is enable X File Options Headings n Link FLUID amp FLOW prop lt slipknot gt Ss Help NEPTUNE CFD V1 0 8 param Number of phases 3 GENERALITIES HgO Gn A fluid state liquid gas gas adin mm J o density 1000 a0 3 5 Special modules Inputoutputcoi Temp Tref 297 65 297 65 1e 10 Dyn visc 0 002 1e 05 0 0002 be e Dianeter 0 003 0 001 0 001 Fhuid amp flow prop Generalities Heat cap Cp 4183 1400 1005 alpha init 0 o 0 elast coef 0 9 0 9 0 9 rad transf 4 d 4 muinn nant n a a A TURBUL ENCE model _Rij eps none mix length mix length o o 0 1 TURBULENT REVERSE COUPLING on phase 1 influence gt 1 none Large inc Large inc PARTICLE PARTICULE INTERACTIONS ph
22. 885 lt t lt 15 18s Under these severe conditions the stability limit on the CF La condition had to be kept in the range 0 15 0 2 This is probably due to the fact that the phase front moves suddenly and at a high velocity and the time step must be tailored on this key feature of the flow As the mass flowrate at the inlet is increased the steam velocity is higher and the water front never comes back inside the injector as shown in Figure 5 38 Steam condensation mostly takes place at the exit of the injection system 150 NEPTUNE_CFD MODELING OF PERSEO FACILITY ay edd re mR 3 me i i NAT Figure 5 37 Water volume fraction top and condensation rate bottom for the ge ometry with a straight injector and a modified position of the injector nozzle at times t 12 88 14 15 15 18 s left to right or outside of it At the same time the high steam velocity at the exit and the small grid dimension below the injector wall require a very small time step If the stability limit is left at CF La 0 2 the time step is excessively small and the calculation diverges in the a P H loop For this reason the stability limits have been set to CFL CF La 0 5 and Fourier 1 0 The velocity field for t 200 6 s is shown in Figure 5 39 From the vertical component of the steam velocity it can be seen that the steam flowing out of the injector can reach the velocity Uj 188 m s while the maximum velocit
23. CODE 27 Operator WALL Operator CCFL Operator SINK Figure 1 16 Examples of sub modules or gadget associated with an AXIAL element three pipes has two tee branches connected on its third scalar mesh Building the geometry to study For each circuit in the study system the following steps are recommended Step 1 Each element one after the other has to be completely defined as well as the belonging to sub modules thermal sub modules PWR sub modules or gadgets The steps for an AXIAL module and the sub modules and or gadgets associated with this element are summarized in Figures 1 15 and 1 16 Step 2 Definition of the components other than water in the circuit with NONCOND or RADCHEMI operator NONCOND is the key word to define the list of non condensable gases to use in the calculation see the Section 1 3 4 for more details of non condensable gases and RADCHEMI is the key word used to define for each circuit the acquisition of radio chemical component characteristics see the Section 1 3 5 for more details of radio chemical component Steps 1 and 2 must be repeated as many times as there are circuits in the reactor Step 3 Definition of the modules which belong to several CIRCUIT modules heat exchangers EXCHANGER SGTR special links between elements of different circuits EXHYLINK Step 4 Definition of circuits CIRCUIT Steps 1 to 4 must be repeated as many for each system i
24. Figures shown in the next sections the numerical and the measured values are reported with a different thickness line the thicker lines represent the code results while the thinner ones represent the test measurements 4 2 1 Test n 7 Phase 1 The Phase 1 of Test n 7 is aimed to verify the system behavior during start up In this phase the system actuation with partial HX Pool fill up without boiling conditions in the Overall Pool is performed In section 3 3 1 a detailed explanation of the test n 7 is CATHARE MODELING OF PERSEO FACILITY 101 Event Time s Beginning of the test 0 1 partial triggering valve opening and closure 300 433 2 partial triggering valve re opening and re closure 446 480 3 partial triggering valve opening and closure 864 1085 Primary side depressurization 900 1400 End of the test 4609 Table 4 1 Chronology of main events of Phase 1 3 5 L_ VQ 0 195 3 COLLVHX m SS TT E v 2 7 15 1 0 5 0 1000 2000 3000 4000 5000 Time s Figure 4 2 HX Pool collapsed water level 5 4 Injector level B 3 g el VP 4 v 2 MIXLEVCP COLLEVCP l 0 0 1000 2000 3000 4000 5000 Time s Figure 4 3 Overall Pool collapsed water level 102 CATHARE MODELING OF PERSEO FACILITY A L x ri N Saturation at pool F a P Q001 0 fe DP por 0 1000 2000 3000 4000 5000 Time s F
25. INTRODUCTION 3 5 4 The OP injector three dimensional model 142 5 4 1 Results obtained forthe test9 0 0 0048 142 Conclusions 156 Bibliography 163 Introduction Simulations of multi physics and multi scale systems have a fundamental impact on engineering sciences The study of multi physics systems deals with simulations that involve multiple physical models and multiple simultaneous physical phenomena The multi scale modeling is aimed to evaluated material properties or system behavior on one scale using information or models from different scales Various mathematical models may be used for the description of the system on each different scale Multi scale modeling is very important in complex systems where a direct simulation is not possible since the time and length scales of the individual processes involved differ by orders of magnitude However numerical simulations of these multi physics and multi scale problems require a strong development of sophisticated models both with efficient numerical algorithms and advanced computational techniques In order to study complex thermal hydraulic problems a multi scale analysis can be used to take advantage of increased computer power and improved simulation tools including Direct Numerical Simulation DNS Computational Fluid Dynamics CFD and system thermal hydraulic codes Furthermore this multi scale analysis is often developed with four scales correspondi
26. MODEL Wall transfer model Nucleate boiling Fhuid amp flow prop Generalities Wall function model for boiling flow Standard single phase wall function poe TES Fluid wall heat transfer model 4 flux model Max radius of cavities n 0 0001 Max detachnent bubble diameter m 0 003 Max oversaturation control A 1 _1 Fluid properties at ac acon Thermal cond W n K 17 Density kg n3 8000 ce G tkg K 531 SCALARS interfacial water steam energy transfer Fater stean model liquid phase Water steam model vapour phase yi Close Cancel Help Om E i erna Reto DQ crepes tex i oara bash ae gt Unie Hover 3 snaps GA RM S E S osan Figure 5 9 Physical models was only present with small traces Actually the numerical method allows a phase to appear below a given tolerance even where they are not physically expected to be The conserved quantities of these spurious phases must be kept under control through NEPTUNE_CFD MODELING OF PERSEO FACILITY 127 2I ksnapshoti l MM 7 S 5B soa6am Figure 5 10 Scalars proper source terms in order to prevent the calculation from diverging To consider these source terms the user defined routines usth12 F and ustsns F are adjoint in the simulation for a detail description see the n
27. P 1 where P and A n are the pressure at the inlet section and its area respectively With this correction the simulation was run up to t 60 s even if it was not possible to have a perfect control on the mass injected in the system therefore an intermediate stage was considered In Figures 5 34 5 35 the evolution of water volume fraction pressure and steam vertical velocity is presented on a section passing through the injector at times in the interval 50 6804 s lt t lt 55 9895 s A part of the mesh is also shown It can be seen the oscillatory behavior of the flow close to the injector with the pressure decreasing when the highest velocities are reached at the injector nozzle and the water is pushed away from that position Then the velocity decreases the water comes back closer to the nozzle and the pressure inside the injector increases again It should be observed that the pressure field presents spurious oscillations at time t 51 8309 s which are probably caused by the jump in the grid size in that region along the two horizontal directions The observer should also be aware that the software PARAVIEW which is used for data visualization reconstructs the field on triangles when performing a cut The wiggles along the lines that cut the squared cells with triangles may be in part due to the software itself With the correction in the mass flowrate the simulation run up to time t 60s but finally diverged However th
28. _ on 4 a a ak WES nuc s k bo BOR yr yelp ae gt pre ae 2 131 p k with J abr all c ve is a lt 0 y ise 2 132 xi o a a a 2 133 i e ap l yil Yok of if T k lt 0 pel a7 else Yig Vip 2 134 and the definition a maz at le7 jt mass convection balance a gt al Making the difference between equations 2 114 and 2 131 and neglecting transfer terms increments and density increments the mass convection balance is written 3 Cl a 1 OR Ok i mzrnt1 _ l aR a o 2 135 Using re actualization formula 2 110 of the velocity the convection diffusion equation obtained is the following 7 9 C 19k k 2 Unf per eP 2 ipi prl Pk At aa pk UE ag E k dal o aN 7 o 2 136 Ox ce In the end all the fractions are positive but they don t ensure the volume conservation defined in 2 113 2 2 3 Volume conservation and pressure projection The pressure step is the basis of the elliptic solver It can be obtained first by making the combination between mass equations 2 114 2 131 2 136 n 1 n l l j 1 Qk Pk Ok Pk A TE ly _ At e A big re 1 2 THE NEPTUNE CFD CODE 59 n l j Ce day Qk rk ath pan OEN Ga Trk al P Y ae sd 2 137 da Ox l i _ _ Se SS 4 3 Then each contribution in terms of the pressure increment is linearized The first term represents the unsteady
29. a very low efficiency of the calculation In addition very small time steps may induce instabilities on the calculation because of the time derivative terms in the pressure equation It should be noted that the grid has been constructed by taking advantage of the NEPTUNE capability to deal with non conforming grids As a matter of fact the first mesh is given by the union of different parts the upper half of the pool the lower half of the pool the injector the boil off and the water line sections All the junctions are non conforming It must be emphasized that the code proved to be very sensible to sharp changes in the cell dimensions even across the grid junction Therefore a great attention must be given to this aspect while constructing new grids Since the steam mass flowrate is approximately zero up to the time t 153s the simulation is shifted in time by the quantity to so that the real time is t t to where t is the simulation time In Figure 5 31 the pressure and water volume fraction fields are shown on a vertical section passing through the injector axis at time t 9 08398 s It can be observed that the steam condenses right at the injector nozzle and that the cell deformation near the 144 NEPTUNE_CFD MODELING OF PERSEO FACILITY pressure 44985 140000 130000 120000 110000 101250 a pressure 44985 140000 130000 120000 110000 101250 a pressure 44985 140000 130000 120000 1100
30. amp D INCKA Society CEA France January 2006 17 Y Y Hsu On the size range of active nucleation cavities on a heating surface J of Heat Transfer No 84 pp 207 216 1962 18 N Kurul M Z Podowski Multidimensional effects in forced convection subcooled boil ing Conference on heat and mass transfer Jerusalem 1991 19 H C Unal Maximum bubble diameter maximum bubble growth time and bubble growth rate during subcooled nucleate flow boiling of water up to 17 7MW m2 Int J Heat Mass Transfer No 19 pp 643 649 1976 20 E Deutsch O Simonin Large Eddy Simulation applied to the motion of particles in sta tionary homogeneous fluid turbulence Turbulence Modification in Multiphase Flows ASME FED 1991 Vol 110 pp 35 42 21 G T C Sanady Turbulent diffusion of heavy particles in the atmosphere J Atm Sc 1963 Vol 20 pp 201 208 22 R Ferri A Achilli S Gandolfi PERSEO PROJECT Experimetal Data Report SIET 01 014 RP 02 Piacenza Italy December 20 2002 23 P Meloni J F Pignatel Simulation of the PANDA Isolation Condenser Using CATARE and RELAP ENEA QT SBA 00006 Bologna Italy May 25 1999 24 M Rigamonti PERSEO project nodalisation for the Relap5 Mod 3 2 code and calcula tion results SIET 00 945 RF 02 Piacenza Italy February 28 2002 25 A Achilli Nuovo sistema di emergenza a scambiatore di calore immerso New emergency system with immersed heat exchanger SIET 00 915 ST 01
31. and is described by the nucleate boiling model It takes into account bubble creation and agrees with nphase 5 Y wall gt k Pwal With Pway the total flux imposed 2 14 k 1 II is the bulk interface heat transfer sum of the interface transfer between phase p and phase k which complies with conservation relation Ty Ipo with Ig Usp 0 2 15 pFk Square bracket terms are not taken into account in the code but could be quite easily coded in the future The interface heat transfer between two phases are divided into two contributions one related to mass transfer term the second independent of the mass transfer aE oes De E ea 2 16 36 THE NEPTUNE CFD CODE In order to verify the conservation relation two choices are possible for the jump of en thalpy for the two phases it may be the same or independent If the jumps of enthalpy is the same for the two phases then HZ Hg H so that the following relation must be verified Ip g Hj_ 0 if the the j jen of enthalpy are independent then in this case the following relation between heat and mass transfers must be verified i II a 2 17 Hik yap Notice that in the case of two phase water steam flows this last model is generally used with AZ M1 Hy Ae 2 18 and introducing independent models for heat transfers for each phase we have 21 te 192 i 2 19 so the condensation rate is simply given by Tee H H r
32. connection The second concept concerns the Weight notion This is used to simplify the data file avoiding to repeat identical parts of the reactor Junction notion __g __ e o fo fo fe Figure 1 13 junction between two AXIAL elements A junction is a topological notion used to link two elements Refer to Section 1 3 2 for an introduction to the notion of junction A junction is either upstream or down THE CATHARE CODE 25 stream of the element This choice is of no importance in terms of flow and is a topolog ical control for the element and the circuit In an element except boundary condition at least one upstream and one downstream junction should be defined In a circuit each junction should appear in two and only two different element definitions each with a different direction key word For each element a junction consists of an assem bly vector node and a scalar node which is a copy of the adjacent module node Figure 1 13 shows a junction between two AXIAL elements Weight notion volume 1 PT axial 2 3535959 5555555 Bo bb2h35sb353 55359595555 5955 55 bobsbodo bed bed3 59 ies sree volume Actual Plant CATHARE schematisation volume 1 Figure 1 14 weight notion in a hydraulic circuit description Weight for hydraulic elements In CATHARE the notion of weight appears twice in connections between elements and in a volume or a 3D element concerning
33. dispersed gas bubbles in a continuous liquid flow or dispersed 38 THE NEPTUNE CFD CODE liquid droplets in a continuous gas flow with regard to the volumetric fraction 1 bubbles ap lt 0 3 FIP F ap 2 2 26 Q1 Tp _ plp _ pdr pl droplets ap gt 0 7 Fp Fp ap F gt 2 27 Qp Ti pee 1 0 7 a bb Qp 0 3 dr mixing 0 3 lt ap lt 0 7 FR Ta 0 3 oae 0 7 2 28 limits 0 3 and 0 7 being arbitrary Ishii correlation used in the case of bubbly flow with automatic calculation of the drag coefficient based on the local regime Added mass closure law The closure law for the added mass coefficient C A is not general and has to be adapted to the simulated flow Different choices are proposed Standard EDF model implemented for isolated diluted spherical inclusions 1 OF n with aj maz a1 0 1 2 29 2 a Melt model i CP 5 AI QpPp 2 30 Separated phase model generalization of the standard model inspired by the drag coefficient form used for separated phase flows 1 bubbles ap lt 0 3 C C 2 31 1 1 droplets a lt 0 3 GH SOIS 2 32 p stl 1 0 7 a Ap 0 3 ap mixing 0 3 lt ap lt 0 7 C OF ga 03 apg 0 7 2 33 limits 0 3 and 0 7 being arbitrary Standard CEA Zuber model implemented for two phases bubbly flows any regime ne 2 a with aj maz ay 0 1 a min dap 0 1 2 34 ai Turbulent contribution
34. f 30 Dp fg 2 61 for the time tg the time of bubble growth is neglected The frequency is tg 1 f 2 62 The bubble diameter is Dm 2 421075 p0 709_ 4 2 63 vb wi ara DTA Toat Te wall T 4sat AS sat apa ace 2 64 2p2Hiat TaS 2 1 z G and ae i if Uc gt Uo o 9 2 65 1 if Ug lt Uo where Uo 0 61m s and s refers to the solid wall This correlation has been determined in subcooled water flows 19 Generalization of the heat flux decomposition model In order to account for the wall burning out phenomenon in this section a phenomeno logical function fa is proposed by introducing the different contributions on phases 1 THE NEPTUNE CFD CODE 45 water and 2 steam and defined as Pwall Pwalls1 Pwall2 5 Pwallo1 foi g ro Hi 2 66 Pwall gt 2 fao p2 r H3 where g is the energy part given to the phase 1 water and 2 is the energy part given to the phase 2 steam These fluxes are of diffusive nature I is the mass transfer by wall nucleation T i iy HY and Hg are the enthalpy jumps related to the mass transfer see 2 1 1 H7 H _ H7 H _ fa only depends on a fos 1 fo and must satisfy to Jai a1 lif Q1 gt 1 Soh a1 0 if Q1 gt 0 2 67 and 1 1 fou on gt 0if a 0 fou 1 04 Q1 Q O0ifa 7 1 2 68 The choice selected in NEPTUNE CFD is amp crit 0 2 and then fa is
35. fraction top and condensation rate bottom for the ge ometry with a straight injector and a modified position of the injector nozzle at times t 12 88 14 15 15 18 s left to right 5 38 Water volume fraction top and condensation rate bottom for the ge ometry with a straight injector and a modified position of the injector nozzle at times t 200 6 202 97 205 52 s left to right 5 39 Vertical left and radial right steam velocity components on the vertical section through the injector axis at x 2 75m and time t 200 6 s for the geometry with a straight injector and a modified position of the INjectot NOZZE ey fda kt ae BS os WR RO SS See eS G 5 40 Water temperature left and volume fraction right on the vertical sec tions through the injector axis at x 2 75m and y 2 75m and times in the range 200 65 lt t lt 243 36 s for the geometry with a straight injector and a modified position of the injector nozzle 5 41 Water streamlines and velocity vectors lower part only on plane x 2 75 m for t 213 28 s Contours for water volume fraction 5 42 Experimental water temperature evolution for different probes 5 43 Comparison between experimental and numerical water temperature data for different probes ss ssc ete ae ule a NEN aa BOA Sa a List of Tables 2 1 2 2 2 3 24 3 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8 4 1 4 2 4 3 5 1 5 2 5 3 5 4
36. in HX Pool and Overall Pool level decrease in the pools down to Injector outlet uncovering level decrease accelerated down to about 3 m from the pool bottom by water dis charge triggering valve closure and HX Pool boil off depressurization of the primary circuit 84 THE PERSEO FACILITY Moreover the main steps of the stability test procedure are the following 1 HX pool full of air 2 pressurization of the primary circuit to the required pressure 3 opening of the triggering valve 4 closure of the triggering valve when HX Pool water level reaches the heat ex changer pipe bottom 5 wait for steam production and check for condensation and instabilities 6 re opening of the triggering valve 7 check for condensation and instabilities with cold water inlet into the HX pool in presence of steam The tests confirmed the effectiveness of the PERSEO innovative system the heat trans fer from the primary to the pool side is soon actuated after the triggering valve opening it is stable and decreases according to the HX Pool level The Steam generated in the HX Pool and accelerated into the Overall Pool by the Injector promotes the water cir culation and avoids the thermal stratification in the Overall Pool Instabilities due to sudden steam condensation evidenced after an early interruption of the heat transfer and during the HX Pool re flooding to restart the heat removal are dumped very soon by means of the vacuum breake
37. particles thermodynamic phases of the same component liquid water and its vapor THE NEPTUNE CFD CODE 33 distinct physical components where some of which may be split into different groups water and several groups of different diameter bubbles different forms of the same physical components a continuous liquid field a dispersed liquid field a continuous vapor field a dispersed vapor field The classical two fluid model is in fact a two field formulation for modeling two phase flows The several multi fluid balance equa tions are obtained from the fundamentals conservation laws of physics restricted to Newtonian mechanics mass conservation momentum conservation and energy con servation The second law of thermodynamics is not represented through a transport equation in the NEPTUNE CFD module The above three conservation laws are writ ten in a classical integro differential form that is valid for arbitrary time and location within the continuum except across the interfaces between two physical phases At the interfaces jump conditions derived from the continuous equations are written If one wants to avoid the direct simulation in time and space of all the interfaces an averag ing procedure is needed Equations for m fields that can be a physical phase or a model field of a physical phase are written in a symbolic coordinate free notation Mass balance equations The multi field mass balance equation for the field k is wr
38. phases a 0 The last term represents the pressure gradient contribution In single phase or dispersed phase zones it is calculated as a simple finite volume gradient with mass weighted adaptation S 0 Y PY nija 2 97 JEVI with P77 the pressure calculated at the boundary of the cells using 1 1 Be PI atin ata M anp 2 98 k In order to take into account the non uniformity of the pressure gradient in cells where one detects a perfect phase separation a different contribution for each present phase is applied The weight is taken consistent with the assumption of gravity equilibrium 7 po o Pk oP a AkPkUk i e k Oe QkPRGi 2 99 ot i yea Appp Oi Implicit balance Uj gt U tI Making the difference between equations 2 88 and THE NEPTUNE CFD CODE 51 2 89 the implicit part of the balance is Ue Oo ass ISk ORAE conv Uka diff 6Uka J Sota SU At i ok U OU P UF 1 1 pr k D 60 21 Ox Pk Nt a Ox Pie OP Eia 2100 with dU U U 6UF UF U and P prt pr The convective and diffusive operators conv and diff are linear positive and defined as follow e conv Ar div lan ogtip C div af pg nue e diff div of ue VO The dispersive contribution form ar a Pr Da da Can be obtained after decomposition of the weighted gradient like contributions contained in momentum closure laws ex pression such as t
39. pre processing operations on the mesh of the parallelism and of the post processing files Neptune is organized in modules as shown in Figure 2 1 Edamox is the graphical user interface of NEPTUNE and the user Fortran mod ule allows to define user function within the code The kernel of the calculation is implemented in the NEPTUNE CFD module In version 1 0 8 NEPTUNE CED is in terfaced with the Enveloppe module of Code Saturne 15 a component managing the pre processing and post processing of the calculation component also referred to as the kernel Enveloppe also nicknamed ECS can communicate directly with the kernel or be run separately for example to test a mesh The kernel can also be used alone but with reduced functions i e in non standard mesh format mesh merging impossible parallel mode forbidden 2 1 Two fluid model in NEPTUNE code In this section the mathematical model of the flows that can be simulated with the NEPTUNE_CFD module is presented This includes the mass momentum and energy balance equations in a general multi field form the interface transfer closure laws the constitutive relations and the turbulence modeling 16 2 1 1 Multi field balance equations The behavior of a fluid made of several physical phases or components can be modeled using the general Eulerian multi field balance equations These fields can represent many kinds of multiphase flow distinct physical components gas liquid and solid
40. safety valves check valves flow limiters sub modules the CCFL sub module which may be connected at any junctions or at any vector node of the 1 D or 3 D modules in order to predict counter current flow limitation in complex geometries such as the upper core plate and the inlet of Steam Generator tubes 14 THE CATHARE CODE 1 1 4 Non condensable gases and radio chemical components More than the main fluid used for PWR or BWR reactors steam and liquid water CATHARE can define other main fluids or other elements in the circuit fluid Figure junction BCONDIT AXIAL VOLUME AXIAL Figure 1 8 Assembly of modules 1 8 shows an assembly of modules These elements are described through the following three components non condensable gases radio chemical elements and other fluids Transport of one to four non condensable gases by a circuit can be modeled by CATHARE These gases are assumed to be in thermal and mechanical equilibrium with steam Non condensable gas concentration has an impact on the standard calculation because it changes the vapor pressure which becomes a partial pressure with respect to the gas phase total pressure and the condensation correlations condensation is reduced in the presence of non condensable gases The radioactive radio chemical element module is used to follow boron concentration and or fission components in the primary circuit CATHARE includes a mass continuity equation for a solute
41. solution provides a unique scalar value the velocity profile is assumed to be constant During the interval t 0 143 s all the boundary mass flow rates are set to zero so that the system can reach a stable condition At t 150 s the water level of the simu lation is almost everywhere uniform as one can see in Figure 5 15 During the interval t 143 204 s a water level adjustment occurs The resulting level in the Overall Pool is shown in Figure 5 16 The water levels in the injector and in the Overall Pool are dif ferent due to the steam pressure In the final interval t 204 500 s the steam enters the injector with a significant mass flowrate and the Overall Pool temperature increases in an appreciable manner One can see this from the temperature probes in Figure 5 17 In this Figure the temperature values in probes TP6 called 1 and TP8 called 2 com puted by NEPTUNE are reported as a function of time along with the experimental measurements It is important to remark that the agreement between computed and measured temperature profiles is not very good The computed temperatures increase jointly and no temperature stratification that is no temperature difference between the two probes takes place The CATHARE simulation of this facility does not exhibit a temperature stratification as well due to the mono dimensional nature of the model The NEPTUNE computations are two dimensional and therefore the code should be ab
42. sre Ani SN SAAN RANN S VHT nts raan terii anena rare AEAN asats ya oe cae rou ra DN aN Sane SON Ty a mann N X A i att TG a c et Wi oa AAA i TT i Ait Wi HT th SS S Ss SS ER n ERS cannae Sama me SSS SSO Sos SSS Figure 5 30 PERSEO 3D hexahedral grid left and a detail of the injector and boil off region right for the real geometry NEPTUNE_CFD MODELING OF PERSEO FACILITY 143 pressure 44985 i A a vol frac 1 40000 130000 0 75 120000 05 cee os 101250 P Figure 5 31 Pressure Pa left and water volume fraction right at a x 3 12 m section for t 9 08398 s In a first analysis the OP injector model has been constructed on the real geometry of the overall pool and of the injector In Figure 5 30 the external part of the mesh and a detail of the injector and boil off zone are shown The grid is composed by 85041 hexahedral cells It can be seen how the most refined zones are close the injector nozzle and below the injector bend The dimensions of the small cells below the injector bend are determined by the high curvature of the injector wall and by the proximity to the pool wall In these cells the local Courant number has its highest values The time step is then determined by the field values in these cells while the Courant number in the rest of the computational domain is much lower This results in
43. the CATHARE so lution Figures 5 5 and 5 6 In particular Figure 5 5 shows the steam mass flowrate NEPTUNE_CFD MODELING OF PERSEO FACILITY 123 t Boil off Steam Inlet S r Air Water l Water to HX pool and discarge Figure 5 4 2D geometry and mesh of OP injector system through the main duct connecting the HX to the OP pool On the right of Figure 5 6 the CATHARE solution for the mass flowrate through the water discharge WD line is reported This line allows a faster water removal to accelerate the decrease of the water level in the OP pool On the left of the same figure the mass flowrate of water from the overall pool to the water to HX pool WL line is presented 124 NEPTUNE_CFD MODELING OF PERSEO FACILITY Steam_to_OP 0 1000 2000 3000 4000 5000 6000 7000 8000 Figure 5 5 Steam Mass flowrate to OP pool Water_to_HXPool 0 1000 2000 3000 4000 5000 6000 7000 8000 Water_discarge 0 1000 2000 3000 4000 5000 6000 7000 8000 Figure 5 6 Water Mass flowrate to HX pool left and water discharge Mass flowrate right 5 3 2 Physical properties and models set in the paran file The paranm file Fluid T K p Kg m u Pas Cp W m K steam 297 75 Cathare table Cathare table Cathare table water 297 75 Cathare table Cathare table Cathare table air gas law 2
44. the NEPTUNE CFD code have been derived In a first analysis a two dimensional model with a simplified geometry of the Overall Pool injector system has been adopted The numerical results obtained with this model are slightly different respect to the experimental data This may be due to a wrong modeling of the injector for which the hypothesis of adiabatic walls is made In order to better investigate the water steam behaviour inside the pool and the injector a three dimensional solution with different geometries has been obtained for the first part of transient evolution of the PERSEO Test 9 Three different configurations have been investigated by means of three dimensional simulations The results of this analisys are briefly recalled below The 3D OP system simulation with the real geometry diverges This is due to the pres sure fluctuations inside the injector and because of the small cells below the injector bend These cells are determined by the high curvature of the injector wall and by the proximity to the pool wall Here the local Courant number has its highest values The time step is then determined by the field values in these cells while the Courant number in the rest of the computational domain is much lower This leads to in a very low effi ciency of the calculation In addition very small time steps may induce instabilities on the calculation because of the time derivative terms in the pressure equation In order to avoid the insta
45. then pushes the water level down Figure 5 20 on the bottom On the top of Figure 5 21 the water level drops down and wa ter and steam mix quickly to fill again the injector completely as shown on the bottom of Figure 5 21 The resulting temperatures at the probes is shown in Figure 5 22 The experiment exhibits the temperature stratification while the simulation shows a strong turbulent mixing Figure 5 22 on the right shows a zoom over a temperature oscillation During the initial part of the injection the temperature increases when the injector fills with steam The maximum temperature heated phase is obtained after the steam is injected into the pool Then the temperature decreases since the cold water is sucked into the injector The surrounding water temperature remains at the mixing pool tem perature This temperature is lower than the corresponding experimental temperature showing a high rate of mixing 5 3 4 Steam injection on boiling pool Around t 3200 s the pool starts boiling During the interval t 3200 4200 s the steam is injected directly into a boiling pool In Figure 5 23 the steam mass flowrate NEPTUNE_CFD MODELING OF PERSEO FACILITY 139 68 r T Steam_to_OP 6 75 L 67 4 6 65 4 oa 6 6 f 6 55 65 f 6 45 4 r 1 1 3200 3400 3600 3800 4000 4200 Figure 5 23 Steam mass flowrate to overall pool over the time interval 3200 4200 s defined from CA
46. to a dispersed flow Co current and counter current flows are modeled with prediction of the Counter Current Flow Lim itation CCFL The Figure 1 9 shows a map of motion regimes treated by CATHARE Heat transfer with wall structures and with fuel rods are calculated taking into ac count all heat transfer processes In Figure 1 9 one can see the appropriate zone for natural forced convection with liquid in both laminar and turbulent regimes natu ral forced convection with gas in both laminar and turbulent regimes subcooled sat urated nucleate boiling with criteria for onset of nucleate boiling critical heat flux dry out criterion rewetting temperature and transition boiling film boiling for in verted annular inverted slug and dispersed flows film condensation for effects of non condensable gases and finally radiation to vapor and to liquid 1 2 2 Mass momentum and energy equations Mass momentum and energy equations are established for any CATHARE module They are written for each phase and derived from exact local instantaneous equations 16 THE CATHARE CODE using some simplification through physical assumptions and using time and space av eraging procedures In this section the model for axial 1D module is presented to the 3D and 0D modules One up to four transport equations can be added when non con densable gases are present Mass balance equations Liquid phase o o BAG ver gA opro AT Sz 1 1
47. using an harmonic mean 2 a F art ny lJ k NOR aI ey Nes 2 93 CD apy apy Then the ratio is bounded Dy a 22 mI lt 2 Finally we can simply limit a with a numerical parameter and the default value is 10 6 The second term is the explicit convective contribution 1 01 ar Fay ee OR UR AU gO art a app OR OL naw 120 k 7 JEVI 50 THE NEPTUNE CFD CODE ap ap The ratio is determined as explained before The terms from 3 to 6 represent the diffusive contributions The different parts are the di agonal part of the deformation tensor laminar and turbulent the transposed gradient contribution laminar and turbulent the turbulence gradient and the second viscosity contribution The diagonal part of the deformation tensor laminar and turbulent is defined as UR UR OUR 1 y ar yt Q ar IJ u IJ U IJ n any Say i Hk an 7 ary 2 k Hw IJ Uka Inrs 2 95 is determined as explained before for the convective part but the limit IJ az The ratio any fraction used here a min value remains equal to 10 Expressions 4 to 6 are called weighted gradient contribu can be set to an other numerical value by the user The default tions such as the turbulence gradient 1 a2 3 Laon Zarpa 2 96 They are treated using a weighted mean square gradient method which presents the advantage to avoid problems due to the residual
48. while the water level in the vessel is maintained at the specified value for the test by discharge of water through the condensate discharge line at the vessel bottom Moreover at the initial state the heat exchanger is full of saturated steam the Overall Pool is full of cold water the HX Pool is full of air or steam depending on the specified test and the trig gering valve is closed Once reached a steady state condition according to the test matrix the triggering valve is opened and the HX Pool is flooded by cold water leading to steam condensation inside the HX tubes with power transfer from the primary side to the pool side As soon as pool water boiling starts the steam produced in the HX Pool is driven to the Overall Pool through the steam duct The injector flowing about 1 3 m below the water level contributes to mix the Overall Pool water thus limiting temperature stratification within the pool The condensation of steam inside the Overall Pool leads to progressive cold water heat up until reaching the boiling point The steam produced in the Overall 80 THE PERSEO FACILITY Pool flows outside at atmospheric pressure through the boil off pipe When the injector is uncover the Overall Pool level decreases according to the heat transfer rate since no condensation is present anymore and the steam flows outside directly through the boil off pipe and the water reserve line of the HX Pool During the system operation the natural circu
49. 0 40 Triggering valve opening 20 L g p 4 20 b 40 b 60 4 80 Figure 5 13 Water mass flowrate to HX pool over the time interval 0 500 s computed from CATHARE simulation 1 6 Water_discarge Steam_to OP Figure 5 14 Water discharge mass flowrate and steam mass flowrate to overall pool over the time interval 0 500 s computed from CATHARE simulation two flows are set as boundary conditions over the boundary that defines the water line In order to do this the CATHARE values are interpolated at the time nodes and the 134 NEPTUNE_CFD MODELING OF PERSEO FACILITY alpha_w 0 75 0 5 0 25 0 Figure 5 15 Water level at t 150 s alpha_w 0 75 0 5 0 25 0 resulting interpolating functions are reported on the file usclim F as described in the Figure 5 16 Water level at t 204s NEPTUNE_CFD MODELING OF PERSEO FACILITY 135 304 data_ExP dat u 1 4 data_ExP dat u 1 5 Temp_probe1 oe Temp_probe2 302 301 300 299 298 200 250 300 350 400 450 500 Figure 5 17 Computational and experimental temperature profiles in probes TP6 1 and TP8 2 as a function of time previous section The steam mass flowrate from the HX pool to the Overall Pool is reported on the right of Figure 5 14 This mass flow generates the velocity at the steam inlet Since the CATHARE
50. 0 ore K Joug BU Uk PRG 2 104 source term reactualisation sub step UP UP IUk Pky spror pr op pr pr OSk i oo pr Pk Soat lUi U bD 605i dU U i E At At OU 4 p k p k l i UR pk apo pri Ski gp rprl phe DO ap FB A suet gg AUR 2105 p k 5 This last system is local for each cell and each i space direction and can be written using matrix formalism sur sure MI m 2 106 t rl U phasi U phasi MY is a nphas x nphas positive definite matrix called the velocity coupling matrix in the 74 direction Its inversion is made either by a direct method for nphas lt 5 or by a conjugated gradient method M 9 is the diagonal part of the matrix The general form of the coefficient is OpFRAt apC At Sx MY for k 2 107 M kp pr pr pr Wp pF k k oe ey e one i k k l p Pk pk Uki l pZk k pk k i Final velocity U hi gt U ee Making the difference between equations 2 88 and 2 101 i and using 2 89 and neglecting the convective and diffusive increment contribution one THE NEPTUNE CFD CODE 53 can obtain the final velocity for each i space direction In this step final velocity U is solution of a linear system introducing the pressure and fraction increments UT Uis 1 pr U hass nphas i At At ot Bai 6P aot Bx P1Do 501 p SM i At 0 At 0 Pa Ox 5P GnphaaPe nas Dr PnphasDanpnas 90nphas 2 109 with P
51. 0 12500 13000 13500 14000 14500 15000 Time s Figure 3 12 Overall Pool temperatures is about 2 5 MW After the triggering valve is opened for the second injection and power begins to be exchanged heavily from the primary to the pool side the primary side pressure decreases rapidly so it is manually increased in order to compensate the pressure decreasing due to the heat removal After about 550 s the pressure average value returns to 7 MPa Figure 3 10 The HX Pool temperatures are shown in Figure 3 11 Before the water injection the air contained in the pool is hot due to the HX radiation Then after the first step of the water injection temperature decreases slowly for the steam production Successively after the second step of water injection the Temperature decreases more rapidly The saturation is reached early and temperature stabilizes around 104 C corresponding to the saturation at the pressure in the pool The Overall Pool temperatures are shown in Figure 3 12 In this condition even if the steam is not sufficient to circulate water in the Overall Pool no depressurization strike is observed because the water temperature at the steam water interface in the Injector is high around 70 C Test 7 phase 2 The Phase 2 of Test n 7 foresees the system actuation with total HX Pool fill up followed by reaching of boiling in the OP and water level decreasing This phase of the test is aimed at demonstrating the correct syste
52. 0 4000 5000 6000 Time s Figure 4 12 Overall Pool temperatures opening at t 300s is roughly estimated Figure 4 10 The large pressure underes timation after onset of HX Pool boiling associated to Overall Pool level oscillations produces the HX Pool level error shown in Figure 4 8 time between t 500 1400 s For the same reason the relative pressure over prediction between t 1400 3200s causes the discrepancy in HX Pool level during the same period of time The 20 MW power extracted by the HX is well predicted by the code until t 1600 s Figure 4 11 Temperature profiles Starting from temperature stratified phenomena reached at the 108 CATHARE MODELING OF PERSEO FACILITY 300 ary a O Pipe mip TW CO006 C 200 TW C007 C TW C008 C m WALLT10 Temperature C 150 0 1000 2000 3000 4000 5000 6000 Time s Figure 4 13 HX tube wall temperatures end of Phase 1 the Overall Pool temperatures are mixed by the injector until onset of boiling around 1600 s Figure 4 12 The calculated saturation temperature is higher than the measured value of 100 C at atmospheric pressure since the Overall Pool pres sure and corresponding saturation temperature are calculated by CATHARE at the middle of water pool height where the pressure is up to 20 kPa above the atmospheric value HX Temperature at the middle tube plane is very well predicted by the code Fig ure 4 13 Furthermor
53. 00 101250 a velocityU2 Z 07789 velocityU2 Z 789 4 75159 A velocityU2 Z 789 4 75159 a Figure 5 32 Pressure Pa left and z component of steam velocity m s right at a x 3 12m section for t 9 09419 s top t 9 09833 s middle and t 9 10886 s bottom free surface causes some distortion in the surface reconstruction itself In Figure 5 32 a sequence of pressure and steam vertical velocity distributions are presented in the time interval 9 09419 s lt t lt 9 10886 s At this early stage of the experiment the steam mass NEPTUNE_CFD MODELING OF PERSEO FACILITY 145 flowrate is very low Qsteam 0 157 kg s and its velocity does not exceeds 5 m s This is the reason for the prompt steam condensation right at the injector nozzle As it can be seen from the pressure field the steam condensation causes a pressure drop near the nozzle which then extends to the region between the injector and the pool wall These pressure fluctuations are also caused by the fact that the volume occupied by the steam inside the injector is too small to compensate the volume lost during the condensation and in a low mach number formulation of the problem the boundary conditions do not react to such a loss in volume This pressure fluctuations propagate inside the injector until the simulation finally does not converge However many sources of instability overlap in this simulation For this reason it has bee
54. 1 5 29 Steam injection above the water level 2 0000 142 5 30 PERSEO 3D hexahedral grid left and a detail of the injector and boil off region right for the real geometry be oe oS ee ee ee 142 5 31 Pressure Pa left and water volume fraction right at a x 3 12 m sec tion for ty 908398 S sees Sea Reed bye ed Swe 2 Oe ee See 143 5 32 Pressure Pa left and z component of steam velocity m s right at a x 3 12m section for t 9 09419 s top t 9 09833 s middle and t 9108865 DOOM cs a oh ce a e Boe Se ak eet oe Pe eS 144 5 33 PERSEO 3D hexahedral grid left and a detail of the injector and boil off region right for the geometry with straight injector and real position of LHC ANMECIOLERIG Toresa ak Soe Bhd Bee Oe he ele Ae ee aS 145 5 34 Water volume fraction top pressure middle and vertical component of steam velocity bottom for t 50 6804 s left and t 51 8309 s right on a section at x 3 312 i555 Bh gee ie ye sel got ee 146 FIGURES 167 5 35 Water volume fraction top pressure middle and vertical component of steam velocity bottom for t 53 7734 s left and t 55 9895 s right on a section at x 3 312 oth oe ork ON elo ities a 5 36 PERSEO 3D hexahedral grid left and a detail of the injector region right for the geometry with a straight injector and a modified position of the injector nozzle 4b gre ey ee ke a OS Oe ee we BS 4 5 37 Water volume
55. 15000 112000 F 108000 108000 F 104000 101325 N yyy ANNA ASASAN ASSAN NNN SES Mi peh EERE SSSSSS SENN NENSITERE N SA Figure 5 35 Water volume fraction top pressure middle and vertical component of steam velocity bottom for t 53 7734 s left and t 55 9895 s right on a section at x 3 312 a lt 2 107 in order to prevent the water velocity to diverge in the region of the domain where water is not actually present However the pressure fluctuations due to the prompt steam condensation were still present inside the injector and the routine usclim F was modified in order to reduce this effect From the available experimental data it is found that the pressure inside the HX pool is almost constant with a value close to P 113000 Pa Thus a correction for the steam mass flowrate Q steam has 148 NEPTUNE_CFD MODELING OF PERSEO FACILITY been introduced in such a way that Qsteam iS set to zero when the pressure at the inlet section exceeds P 115560 Pa on the other hand it is increased when it drops below P 109250 Pa The correction for this second case is Q steam gt vI APA Qadj 5 6 Qagj P P pA 5 7 an plow pi min pos PY
56. 16 HX exchanged powers lt 7 ca i Da paws Oe Gs ee ee let eect 117 Coupling CATHARE NEPTUNE et sioe toile heey ileal ected 4 120 Overall pool temperature measurement positions 121 Overall pool temperatures for different probes 122 2D geometry and mesh of OP injector system 123 Steam Mass flowrate to OP pool 4 4 2u0g Mewid eb eS ae Begs 124 Water Mass flowrate to HX pool left and water discharge Mass flowrate Aight gt vad bo a Na lie a gta Ml BR SMe oe Siac Baa aE Ga eas 124 Piysical pr peftti s 5 soerat d aiie Bt ok ot 8 Be Ga Sh ones ae 125 Input Output control 5 o 20 we Pa Nae a ED weeds DEA 126 Physical models 5 isn ee ee Sag We ce ge oe poate RS eect genie hs 126 SCalats scsi ch Base Goal i ee Seite BibT aa Beal a 127 Bo ndary c nditions os sp enea be Pk eS A ewan rede ae ten 128 Chronology of the temperature main events for the probe TP6 132 Water mass flowrate to HX pool over the time interval 0 500 s com puted from CATHARE simulation 2 06 Se peed ore Ges 133 Water discharge mass flowrate and steam mass flowrate to overall pool over the time interval 0 500 s computed from CATHARE simulation 133 Water level at t 1505 ii r ip ace ae wie ah ee inte ak ae 134 Water level att 204 si4 n tiranit home Bie Sopra hee We Ga Seals cg 134 166 LIST OF FIGURES 5 17 Computational and experimental temperature profiles in probes TP6 1 and TP8 2 asa func
57. 95m It can be seen how the numerical data follow quite closely the experimental data taken from the probes at the pool center T P023 and T P025 The fact that the experimental data for T P006 show a completely different behavior with a sudden temperature rise up to T 315 K seems to confirm the coupled effect of the injection and wall effects The comparison between the two numerical series with T P6 num always above TP23_N_num shows the presence of a wall effect It should be considered that in the real case the injector is close to the lateral wall the hot water below the injector moves immediately downwards before it can exchange heat with the surrounding colder water This may explain the steep rise NEPTUNE_CFD MODELING OF PERSEO FACILITY 155 in temperature evolution at T P006 which can be seen in the experimental data Conclusions In the present work a coupled CATHARE NEPTUNE CFD simulation has been per formed The main objective is to simulate the behaviour of an innovative heat removal system with in pool heat exchangers and in particular to explain through a CFD sim ulation the temperature stratification present in the experimental data taken from the probes below the injector system As a first step a reference solution for the system evolution by using the system code CATHARE has been obtained From this solution proper boundary conditions to simulate the Overall Pool OP and the injection system components by using
58. ALMA MATER STUDIORUM UNIVERSITA DI BOLOGNA Dottorato di Ricerca in Ingegneria Energetica Nucleare e del Controllo Ambientale Ciclo XXV Settore concorsuale di afferenza 09 C3 Settore scientifico disciplinare ING IND 19 VALIDATION OF THE CFD CODE NEPTUNE FOR A FULL SCALE SIMULATOR FOR DECAY HEAT REMOVAL SYSTEMS WITH IN POOL HEAT EXCHANGERS Presentata da FEDERICA BASSENGHI Coordinatore di Dottorato Relatore Prof ANTONIO BARLETTA Dott Ing SANDRO MANSERVISI Esame finale anno 2013 Contents Introduction 1 The CATHARE Code 1 1 CATHARE object oriented structure and system modeling 1 2 1 3 1 4 1 1 1 The assembly modules amp naaa SP Gre ooe eEe 1 1 2 Themain modules 3 22 etl aeee N e as Gata ts 14 3 The sub modules 22 02 2 Teda uua a Tee ae Poe eS 1 1 4 Non condensable gases and radio chemical components The two fluid model 0 a 1 2 1 The two phase flow regimes Soto Sd Go He Se 1 2 2 Mass momentum and energy equations 1 2 3 Closure relations o oo epee ee 1 2 4 Wall and interfacial transfers ooa CATHARE solution procedure 2 pe 8 Be ee ee ae ee 3 1 Introduction ose oe xin wee bsg est apy dead Blane Bivaled de gl as 1 3 2 Computation scheme ete gw oid ho Soak els eee amp 1 3 3 Post processing data specification 05 CATHARE Input deck sgn ate unig alee a id eo Ba ae Bad 14 1 The DATA block z 2go8 Sob Ae y a
59. EO facility Steam Duct and Liquid Line between the pools The pressure vessel can operate at the thermal hydraulic conditions typical of a BWR or the secondary side of a PWR steam generator Its volume is 43 m3 the height is 13 m and it is partially filled with saturated water with a nominal level 7 04 m It is pro vided with an internal vertical riser a steam separator and dryer The Heat Exchanger consists of two inconel 600 cylindrical headers and 120 vertical pipes The header inter nal diameter is 0 63 m and thickness 0 06 m the length is 2 48 m covers included and the volume is 0 732m The pipe outer diameter is 0 0508 m and thickness 0 0023 m average length 1 8m The Heat Exchanger is located in the HX Pool The Steam Line is a 10inch sch 80 pipe connecting the pressure vessel to the heat exchanger inlet The Drain Line is a 6 inch sch 80 pipe connecting the heat exchanger outlet to the pressure vessel The HX Pool has a volume of 28 7 m with a basis area of 5 04m and a height of 5 7m The HX Pool bottom is 0 1 m over the Overall Pool bottom It consists of stainless steel sheets reinforced by iron beams A diaphragm is located slightly inclined over the heat exchanger and contributes to the steam water separation during the system operation The Overall Pool has a volume of 173 m with a basis area of 29 84 m and a height of 5 8 m It contains the old heat exchanger of the Panthers PCC facility not used in these tests It consists
60. ERSEO FACILITY T T T 1000 2000 3000 Time s Figure 3 16 HX exchanged power 2 Phase T Q023 C 250 T Q030 C T Q032 C T 2016 C T Q007 C T Q006 C T Q031 C T Q024 C T Q009 C T Q013 C T Q015 C T Q034 C T Q036 C T Q022 C T Q033 C T Q010 C T Q008 C T 0037 C Temperature C T T T T T 1 0 1000 2000 3000 4000 5000 6000 Time s Figure 3 17 HX Pool temperatures 2 Phase the boil off pipe In order to compensate the pressure decreasing due to the heat removal the primary side pressure is manually increased After some oscillations the pressure average value returns to 7 M Pa remaining stable until the depressurization of the plant is started at 4685s Figure 3 15 The exchanged power is shown in Figure 3 16 After the triggering valve between the two pools is closed the HX Pool level decreases more rapidly and consequently the exchanged power The condensed steam flowrate at the maximum exchanged power is about 13 kg s THE PERSEO FACILITY 93 120 100 T P028 C T P023 C Temperature C T P030 C T P008 C T P025 C T P022 C l T P021 C T N001 C 0 1000 2000 3000 4000 5000 6000 Time s Figure 3 18 Overall Pool temperatures 2 Phase The HX Pool temperatu
61. I O88 p k In this sub step the explicit contributions are considered 1 2 E n 4 7 ki kya n n a n 1 0 n 1 n nrn n Pk Ai Pk Mt Ugi a Ox Aa akPkUkj an ap Oa OePRU RUE g THE NEPTUNE CFD CODE 49 7 8 A ee oP p eee oF pz oR Tkis Dis OE pegi 5 ET t SE io 2 89 k J p k with 3 4 aU Co a r ag Daj Eku t oe at bay OOM Hk On i ah ut hil a i 5 6 a n 2 n n n2 2 ny t OU km 3 i Ak PR Tk 3 bij Ue Uk uk Jz 2 90 Also we have In 1 In J I 2 91 p gt k i ar pk i with S S a1 UF P with 1 1 number of phases and p px P hz given by the thermodynamic table or analytic law The first term is so called explicit mass accumulation part i o a Ox non n n 1 n n n n akPkUkj UkiQI T S aR OR Uhm nia Uk s 2 92 ak JEVI with the values on the cell number J 7 the o at the interface of the cells J and J or on the boundary of the cell J n77 m the mt h component of the surface vector m Vr the neighboring of the cell J and Ny the volume of the cell J The main problem in this expression is the term ate a r Which is not bounded In order to bound this term one may set a gt at gt a r with a 7 equal to the interface fraction calculated by the conservative mass solver It is also possible set a lt a and in this case the interface fraction is re calculated
62. N Number of Integers 1000000 Number of Reals 10000000 GEOMETRY FILE Use of ENVELOPPE module YES l Face joining Other options Mesh file name s prisme des Nbr of tine steps Restart from previous rm Absolute max time 1 Ref Tine step dt0 0 001 Saving frequency of restart file suiava 0 Dt mode time dep Syrthes tine step Neptume dt dt dt0 min 1e 06 dt dt0 max 1000000 max dt variation increase 0 1 max dt variation decrease 0 5 CFL FOURIER LIMITS USER aber of usor arrays POST PROCESS output type each n t step Iteration freq of chrono outputs 10 i Chrono outputs at the MED format chrono output of nucleate boiling model output type each n t step iteration freq of histo output 1 saving frequency 1000 definition of probes defined in Edamox number of probes 2 x_prob y_prob z_prob 0 006 0 5 o Glose Cancel Help Figure 2 9 Input output control panel 70 THE NEPTUNE CFD CODE X amp GENERALITIES lt pool gt 2 NEPTUNE CFD 1 0 8 param GRAVITY X axis component Y axis component Z axis component DOMAIN LENGTH SCALE maximum eddy length scale domain length scale m 0 1 SEPARATE PHASES gradP correction separate phases Interface locating methods No interface locating _ Turbulenc
63. Pool The shake down tests matrix and a short description of tests are reported in Table 3 2 Two different kinds of PERSEO actual tests are suitable for the system concept demon stration Integral tests and Stability tests The integral tests aimed at demonstrating the behavior of the system following a request of operation and during all phases of a long accidental transient These tests are executed at two different primary side pressures 4 and 7 M Pa The stability tests are finalized to study particular critical problems happening in case of sudden condensation at the steam water interface in the Injector or in case of triggering valve re opening with cold water inlet in presence of steam These tests are performed at 7 M Pa primary side pressure The PERSEO tests matrix the main conditions and a short description of tests are shown in Table 3 3 THE PERSEO FACILITY 5800 se 5140 m7 3860 ma 3420 m4 2900 ess 2535 7a 13 1440 i et 485 Z 100 es ied x G f S g ni N a 50 815 R J TD O 1580 ig N S i qe A To 06 10 2080 f TO 13 16 5 g amp 2 a FE 2750 ie EA ile x8 g M a 3 s Be aa 4015 a E a 4780 Figure 3 4 Hx Pool temperature measurement position THE PERSEO FACILITY 82 Figur
64. Pref BC 0 101325 0 0 o Special modules Inputo a prop Genera Figure 5 11 Boundary conditions let boil off water line injector wall top pool wall pool wall and symmetry boundary region The names are self describing the steam inlet is the inlet of the steam in the injector and the boil off is the outlet boundary at the top of the pool The injector wall top pool wall and pool wall appear in Figure 5 11 as a unique column since all these regions can be considered as standard walls with the same kind of boundary condi tions The mesh is three dimensional with unitary thickness Since in finite volume discretization fields are constant in the cell and located at the center of the cell The symmetry boundary conditions are needed to simulate two dimensional geometries with three dimensional meshes For details see 29 On the steam inlet region only steam can enter with direction normal to the surface and mass flowrate is defined in the appropriate file usclim F user routine as a function of time by the previously solved CATHARE solution The temperature condition is set to Tgat option which de notes the saturation temperature at the corresponding pressure The boil off boundary condition is the standard outflow condition at atmospheric pressure for air while wa NEPTUNE_CFD MODELING OF PERSEO FACILITY 129 ter and steam are
65. Rev 1 Piacenza Italy Jan uary 21 2002 BIBLIOGRAPHY 161 26 P Meloni CATHARE2 V1 4 Capability to simulate the performance of Isolation Con denser Systems with Thermal Valve Proc International Conference Nuclear Energy in Central Europe Portoroz Slovenia 2001 27 P Meloni A Achilli R Ferri F Bianchi Experimental campaign and numerical anal ysis for the in pool energy removal system for emergency operation 13th International Conference on Nuclear Engineering Beijing China May 16 20 2005 28 F Bianchi et al Assessment of RELAP5 MOD3 3 and CATHARE 2 V1 5a against a Full Scale Test of PERSEO Device Proc 12th International Conference on Nuclear Engineering ICONE12 Arlington Virginia USA April 25 29 2004 29 R F Kulak and C Fiala NEPTUNE A System of Finite Element Programs for Three Dimensional Nonlinear Analysis Nuclear Engineering and Design 106 pp 47 68 1988 17 65 30 F Bassenghi G Bornia L Deon and S Manservisi P Meloni and M Polidori IM PLEMENTATION AND VALIDATION OF THE NURISP PLATFORM DIENCA University of bologna Via dei Colli 16 40136 Bologna Italy ENEA Via Martiri di Monte Sole 4 40129 Bologna Italy CERSE UNIBO RL1308 2011 31 F Bassenghi G Bornia S Manservisi R Scardovelli F Donato C Lombardo M Polidori OPTIMIZATION AND VALIDATION OF THE CFD MODULES IN THE NURISP PLATFORM CIRTEN UniversitA di Bologna DIENCA ENEA Via Mar tiri di Mont
66. THARE CODE with Hy Hy Py Tea 7 hus7 Ay sat 7bar y 2766430J kg and T7 Tsat Tbar xX 164 93 C The value of transport properties used during calculation depends on the mixture model chosen by user By default the following standard models are used for the gas mixture viscosity and conductivity computation hasy u AG Do wr 1 12 i i where y and u respectively A stands for the molar fraction and for the pure gas vis cosity respectively pure gas conductivity of each species SL Sa 5 are the source terms of mass for liquid steam and non condensable gases kg ms X is the specific fraction of the non condensable gas i 3 is the added mass coefficient w is the interface velocity m s x y is the friction perimeter m Cz and Cg are the wall fiction coefficient for the liquid and the gas and R is the rate of strati fication SMg and SM are the source terms of momentum for gas and liquid qze and qGe are the interface to liquid and to gas heat fluxes W m Xe is the heating perimeter m qp and qrg are the the wall to liquid and to gas heat fluxes W m The main variables are six pressure liquid enthalpy gas enthalpy void fraction liq uid velocity and gas velocity P Hz HG a v va and if it exists X i 1 4 non condensable mass fraction with related transport equations The model of the 1D module is extended to the 3D and 0D modules In the 3D module 10 X main vari ables are considered with th
67. THARE simulation 11 7 m 7 water_discarge Water_to_HXPool 3200 3400 3600 3800 4000 4200 3200 3400 3600 3800 4000 4200 Figure 5 24 Water mass flowrate to the HX pool and water discharge mass flowrate over the time interval 3200 4200 s defined from CATHARE simulation injected into the overall pool is reported as a function in the considered time interval The steam mass flow has a steady value around 6 6 Kg s Figure 5 24 shows the water mass flowrate to the HX pool and the water discharge mass flowrate on the left and right computed by CATHARE and used as boundary conditions for NEPTUNE simu lation The water discharge mass flowrate is kept to a constant value of 18 kg s so as to rapidly decrease the water level in the overall pool In Figure 5 25 the water tempera ture distribution at t 4000 s is shown All the water is boiling The temperature field is extended from the water region to the whole pool region even if in these parts there is only steam or air The top of Figure 5 26 shows the injection of steam into the boiling pool when the water level is below the injector outlet In this case the condensation is 140 NEPTUNE_CFD MODELING OF PERSEO FACILITY OP_Temp 76 7932 370 360 350 340 330 325 017 Figure 5 25 Extended water temperature distribution in boiling pool alpha_w 0 75 0 5 0 25 7 672e 14 7 672e 14 Figure 5 26 Steam injection on boi
68. Temperature C T NO001 C 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Time s Figure 5 3 Overall pool temperatures for different probes Position X Y Z Code Overall pool under the Injector 500 3400 2195 TP006 Overall pool under the Injector 500 3400 1795 TP007 Overall pool under the Injector 500 3400 1195 TP008 Overall pool central area 1910 3745 2695 TP021 Overall pool central area 1910 3745 2195 TP023 Overall pool central area 1910 3745 1195 TP025 Overall pool central area 1910 3745 50 TP028 Overall pool central area 3540 3745 2695 TP030 Overall pool central area 1910 3745 2495 TP022 Table 5 1 Exact locations in mm of the probes for temperature measurements with respect to the reference frame indicated in Figure 5 2 5 3 The two dimensional model 5 3 1 Geometry and Boundary conditions for the Test 9 The two dimensional geometry and mesh modeling of the OP injector system are shown in Figure 5 4 The mesh consists of three dimensional hexahedral cells with unitary thickness and is refined near the injector outlet The water to HX pool line and the water discharge line are considered as an unique line The injector is positioned out side the pool to simplify the simulation 30 As described in the previously section the boundary conditions for the NEPTUNE code are obtained from
69. Variable initialization 0 ee A 54 NEPTUNE modules are eaa a E E E Ean E rE EN 62 Scalar equation options o oo Dee Dee Res 64 User routines 6 298 645 ea 28 tale eae e e ae e alee a To hd 65 PERSEO facility design features 2 444 oven Ge bom ae ea So ew 4 79 PERSEO shake down test matrix 2 0 en 83 PERSEO test matrix Daae a e e eara a irel a i 83 Main PERSEO test 7 parameters in phase 1 nananana aaa aaa 84 Chronology of main events of Phase 1 anaa 85 Chronology of main events of Phase 2 nanana aaa 90 Main PERSEO test 9 parameters oaa By ee ee 93 Chronology of main events oftest9 2 2 ee ee 94 Chronology of main events of Phase anana 101 Chronology of main events of Phase 2 anana 105 Chronology of main events of test9 2 2 0 eee ee ee 112 Exact locations in mm of the probes for temperature measurements with respect to the reference frame indicated in Figure 5 2 122 Fluid and flow properties selected for PERSEO test9 124 Chronology of the Temperature main events 132 Initial conditions of Overall Pool and HX pool 133
70. a surement Figure 4 22 Moreover the small HX Pool level difference better predict the exchanged power diminution curve observed in the test Figure 4 23 during the Over all Pool level decreasing phase In the time t 1600 3500s due to a greater HX power with corresponding increase of Overall Pool boiling rate the recalculated Overall Pool collapsed water level is very similar to the measure one Figure 4 24 CATHARE MODELING OF PERSEO FACILITY 115 5 T UF a ee 4 PRS ieee g 3 Ea 1 0 0 1000 2000 3000 4000 5000 6000 Time s Figure 4 24 Overall Pool collapsed water level 4 3 2 Test n 9 6 tae ane J PeT Na a pe ite 2 aa _ m 1 74 0 0 1000 2000 3000 4000 5000 6000 7000 8000 Time s Level m Ww Figure 4 25 Overall Pool collapsed water level The new code results for the Test n 9 regarding the water level in the two pools the HX Pool relative pressure and the HX exchanged power are shown from Figure 4 25 to Figure 4 28 in comparison with the test measurements As expected the differences with previous results become significant only after on 116 CATHARE MODELING OF PERSEO FACILITY aa SE P Q001 kPa yA i oe oOo T a a Q 0 1000 2000 3000 4000 5000 6000 7000 8000 Time s Figure 4 26 HX Pool relative pressure 3 5 Miela 3 H y kai A E 2 H E H T ben m a a 0 5 eo 0 sy 1000 2000 3000 4000 5000 6000 7000 8000 Time s Fi
71. ameter model for a monodispersed approach valid for bubbly flows GTD Generalized Dispersion Turbulent model valid for bubbly flows No wall force is considered Figure 2 8 Inter phase forces for liquid and vapor phases In the Input output control panel the meshes the numerical settings and the post processing outputs are defined Figure 2 9 shows the panel In the simulation two probes are inserted close to the end of the test section One user array is introduced for the post processing of the steam bubbles diameter The Generality panel as shown in Figure 2 10 contains the physical settings of the simulation For this case the gravity is set to the standard value of 9 81m s along y axis and the domain length scale is set to 0 01m Since the water steam module is defined in the Special module panel the CATHARE table containing the physical properties of the water and steam phases are automatically activated In the boiling pa rameter section the Extended Kurul Podovsky model is chosen as heat transfer model from wall to fluid The fluid properties are calculated at y 250 where y is defined ypU as y where yp is the distance to the wall U defines the friction velocity and v stands for the cinematic molecular viscosity In the Scalar section the interface water THE NEPTUNE CFD CODE 69 X mo INPUT OUTPUT CONTROL lt pool gt 2 NEPTUNE CFD V1 0 8 param CONTROLED MEMORY ALLOCATIO
72. and above the water only air is present The FORTRAN routine is the following DO IEL 1 NCEL IF XYZCEN 1 IEL GT 4 5 THEN RTP IEL IALPR 2 1 D0 RTP IEL IALPR 1 0 DO RTP IEL IALPR 3 0 DO0 ELSE 130 NEPTUNE_CFD MODELING OF PERSEO FACILITY RTP IEL IALPR 1 1 D0 RTP IEL IALPR 2 0 DO RTP IEL IALPR 3 0 DO0 ENDIF ENDDO The RTP e a function gives the value of the volume fraction in the element e with phase a The physical laws and properties must be added in the file usphyv F For the air the gas law is applied and the FORTRAN routine is the following DO ITEL 1 NCEL H3 RTPA IEL IENTHT 3 amp 0 5 RTPA IEL IU 3 2 amp RTPA IEL IV 3 2 amp RTPA IEL IW 3 2 GAM 1 4 ROPHY IEL IROM 3 GAM GAM 1 RTPA IEL IPR H3 ROPHY IEL ITEMPK 3 H3 PROPHY IEL ICP 3 ENDDO as x T las where the air temperature is defined as T h cp Details can be found in 31 The enthalpy source term in the steam enthalpy equation due to direct contact with the air has been coded in the user defined routine usth12 F and is given by Qo3 10 a203 T3 To 5 3 The routine is the following ZET12 Q DO IF IPHAS2 EQ 3 THEN ZET12 RTPA ICEL IALPR IPHAS1 RTPA ICEL IALPR 3 1 D6 ENDIF This term is added i
73. and secondary loops THE PERSEO FACILITY 77 Heat Exchanger Test Section Steam Pressure Vessel 10 SCH 8D Steam supply lins le SCHOO Vessel bypass Condensate retum fine Figure 3 2 PERSEO facility scheme of the primary side and main elevations The primary side of the facility mainly consists of a pressure vessel and a full scale module of the SBWR IC heat exchanger Vessel and exchanger are connected by the Feed Line steam side and the Drain Line liquid side The pool side of the facility con sists of the HX Pool containing the heat exchanger and the Overall Pool representing the water reservoir HX Pool and overall pool are connected at the bottom by means of the liquid line including the triggering valve and at the top by means of the steam duct ending into the overall pool with an injector about one meter below the water level A boil off pipe is connected at the top of the overall pool 78 THE PERSEO FACILITY ap on 4 ep A i AL TRIGGERING VALVE j T j ji STEAM DUCT iN int 1100 lt j BOIL OFF int 1000 hl OVERALL POOL View from 4935 y A fer tculor of the liquid Line POOL Figure 3 3 PERS
74. ases gt 1 frict model none none none gran nodel none none none kine model none none none maximum particle compaction 0 64 WALL Be Wall BC friction dvR dn 0 friction INTER PHASE FORCES drag lt gt 1 none Ishii none Added mass none Zuber none lift none none none turb disp none none none wall force none none none Figure 5 7 Physical properties The label Cathare table refers to an internal database that correlates pressure and temperature of water and steam to other physical properties The reference and initial pressure is set to p latm Figure 5 7 shows the Fluid and flow properties module of the param file for this specific test case The turbulence model in water is the Rij model recommended by NEP TUNE Mixing length model for air is set while no turbulence model is set in the steam component The Separated Phases drag model and the Large interface model have been used for steam water and air water interactions respectively Simple source terms for enthalpy and momentum between air and steam have to be included in order to pre vent these quantities to diverge during the calculation in the regions where each phase 126 NEPTUNE_CFD MODELING OF PERSEO FACILITY X File Options Headings X O INPUT OUTPUT CONTROL Y 2 NEPTUNE cro v1 0 8 param
75. bilities due to the bend injector of the real three dimensional geom etry simulations with the straight injector entering the pool from the top at the same position respects to the real geometry has been performed The pressure fluctuations which do no allow temperature stratification are still present These are mainly due to the high rate of steam condensation inside the injector Though corrections have been 158 CONCLUSIONS implemented in the model through the boundary conditions that improved the code stability for the first part of the transient no stable solution could be obtained Another critical issue was the interaction of non conforming grid junctions with the described obscillations The last tree dimensional model locates the injector in central position surrounded by an additional volume simulating a portion of HX pool to prevent the pressure oscillations inside the injector The grid adopted for this configuration is fully conforming With this new configuration the simulation is stable although the tem perature results are slightly different respect to the experimental data since the real position of the injector is not preserve It should be noted that temperature stratifi cation is not predicted below the injector by the model Wall effect is therefore to be considered a key issue for the setting of the stratification In order to improve the re sults obtained a new model concerning the only injector system can be real
76. ble the variables to be tracked in the listing i e textual output The probes number fields are used to track the values of variables at the probes The values given for this case mean that results are wanted at all the probes The run module allows to run the code and save the results Before running the code it is necessary to save the param file In the module Run it is possible to set the number of processors for a parallel run and to launch the code on line with the button Run on line The NEPTUNE GUI generates a paran file as Headings SPECIAL MODULES 1 MODULE SPECIFIQUE 1 FLUID amp FLOW prop 1 NPHAS 2 GENERALITIES 2 NOM FLUIDE eau vapeur ETAT FLUIDE 0 1 THERMO 2 ASSE VOLUMIQUE 1000 1000 TEMPERATURE REFERENCE 610 293 14 THE NEPTUNE CFD CODE 65 VISCOSITE DYN 0 001 0 001 G Zo wW Gq Z Q 2 ITURB 2 1 CNUTLO 0 0 FLUID 1 2 UENT CONDL1 0 0 0 0 0 This file can also be generated directly by editing the file The file is subdivided in various sections with characteristic key words The same keys on the NEPTUNE GUI interface 2 3 3 User routines routine description usinil F initialization from settings read from EDAMOX usclim F boundary conditions at boundary faces usphyv F calculation of physical properties usini
77. cally The word contain should be understood literally in the physical sense but also with re spect to the structure of CATHARE software modules inherit properties from assembly modules similarly gadgets or sub modules inherit properties from their parent mod ules Non condensable gases for example can consequently be defined as belonging to an assembly module and are not need to be defined for each element making up the hydraulic circuit Now the different modules are briefly described 1 1 1 The assembly modules The assembly modules are used to group basic modules There are three assembly ele ments REACTOR CIRCUIT and ZONE The REACTOR element consists of CIRCUIT elements Circuits connected in this way may be physically connected by heat exchangers Several reactor elements can be de fined in the same input deck but from the calculation point of view is separated from one another This module is used to control thermal hydraulic computation It may also be used to launch specific calculations or initializations THE CATHARE CODE 9 The CIRCUIT element consists of all the basic elements making up the hydraulic circuit Some parts of the circuit can be isolated from the circulating fluid zone with valves But as the fluid is the same in the entire circuit non condensable gases and ra diochemical components are defined for a circuit element obviously the concentration or radioactivity of fluid components are not nec
78. changers This project is a joint research and development program between EDF French utility CEA French Atomic Energy Commission IRSN French Nu clear Safety Institute and AREVA NP for nuclear reactor simulation tools Based on a fully unstructured finite volume solver and on state of the art physical modeling the NEPTUNE_CFD code is currently being developed and validated against numerous 32 THE NEPTUNE CFD CODE experimental data NEPTUNE_CFD has also been chosen as a basis for the develop ment of CFD tools within the European Project NURISM and NURISP which aims at building an international shared software platform for nuclear thermal hydraulics NEPTUNE can process from 1 to 20 fluid fields or phases 14 In particular it can process water steam flows with actual thermodynamic laws The code can be used with meshes with all types of cell element and non conforming connections with quality constraints The code is cell center type finite volume with calculation of co localized gradients with reconstruction methods and distributed memory parallelism by domain splitting There are several physical models implemented in the code such as interface momentum transfer interface energy transfer turbulence head losses and porosity NEPTUNE coded in Fortran 77 the majority and C ANSI 1989 procedural programming is ported on LINUX and UNIX systems and it can be interfaced with the Code Saturne Enveloppe module for management of the
79. de Figure 4 2 and Figure 4 3 Oscillations of the Overall Pool level observed in 104 CATHARE MODELING OF PERSEO FACILITY the test produced by free surface fluctuations cannot be taken into account by the code Relative Pressure and Power profiles The injector differential pressure calibration al lows a good representation of the HX Pool relative pressure Figure 4 4 At the be ginning of the test the injector is full of water and the HX relative pressure respect to the Overall Pool pressure is close to zero Around t 400s the injector empties and the HX relative pressure stabilizes at 12 kPa according to the Overall Pool water level The largest discrepancy is observed at t 1200 s when the saturation conditions are reached at the HX pool bottom due to water recirculation As result the sudden vaporization calculated at the bottom shows a pressure peak in the pool steam duct and through the injector since the triggering valve is closed On the other hand the experimental results shows that the transition to boiling at the HX Pool bottom is more smooth respect to the numerical results and the peak pressure is not observed The 2kPa deviation around t 2000s is in accordance with the extracted power under estimation leading to a reduced steam flowrate through the injector during the same period of time t 1800 2200s At the end of the test the injector is full of satu rated steam and the differential pressure of 12 4 kPa
80. del mass transfers directly depend on heat transfers Different models are available for T and II Water Phase In this phase the constant time scales and the different models must be defined The Constant time scale return to saturation is defined by w s piCpi i flor Psat T 2 40 T is the time constant s given by the user f a1 is a pondering function which can takes different values 1 a1 a2 or ay a2 The Bulk model ASTRID like model for diluted bubbly flows is set to 6a2gNur wi SS 1 2 Tsat Ti 2 41 with Nusselt number definition Nu 2 0 6 Re Pr Re pel Pr me 2 42 and relative velocity V calculated for laminar or turbulent velocity fields The Hugues Duffey model for turbulent stratified flows is given by T1 ai 1 Toot Ti 2 43 with a being the interface area m supposed to be equal to Va1 in stratified areas and 1 the heat transfer coefficient calculated from DOG oo B a PEP r VS m r V0 0 V min Ui C2 y a THE NEPTUNE CFD CODE 41 Since this model only takes into account condensation effect at the water steam in terface it has been completed by a residual droplet term in the upper zone where a lt 0 1 taken as a return to saturation term with a constant time scale 7 arbitrary equal to 1s and the pondering function f a equal to az The Flashing model CATHARE1D like model is defined as M COEF hi
81. del including non condensable gas 8 THE CATHARE CODE equations and additional equations for transporting radio chemical components The most recent version of the code V2 5 CATHARE is provided with new modules suit able for gas reactors HTR High Temperature Reactor Gas Turbine Modular Helium Reactor GT MHR for the simulation of gas turbines or compressors for the repre sentation of the containment building and its interaction with the primary circuit etc 1 1 1 CATHARE object oriented structure and system modeling In the CATHARE code each element of the reactor hydraulic circuits must be defined Each element is described by a CATHARE module or CATHARE object type 2 De pending on their function nature and similarity these modules may be assembly mod ules main or basic modules sub modules and non condensable gases together with radio chemical components For each module if not already predefined by CATHARE users must provide a topological definition a nodalization definition a geometrical definition object size for example and a hydraulic definition kind of flow singular pressure drops The term object oriented structure is used because modules are hierarchically orga nized assembly modules contain modules that contain gadgets and or sub modules Sub modules are distinguished from gadgets because they may interfere with several modules whereas gadgets only modify the behavior of a single module lo
82. e 2 20 The non conservative form is obtained after decomposition of the unsteady term with respect to the mass balance equation and after division by the volumetric fraction 1 1 H H Cg H Up Pra He ke ax RPE bi Oy Dany OP kUk j 1 OP Pwall gt k Uaioe ae e das an Qkj Be PRU Rg me T Ay e gt m pk T r gt k pk 2 21 Notice that in the standard case where H k is taken equal to H and where nucleate transfer does not exist gt T5 Ix the mass transfer terms do not appear in the equation 2 1 2 Interface transfer closure laws The interface momentum transfer between phases k and p is written as a symmetric ex tension of the closure obtained for fluid inclusions bubbles drops or solid particles It can be split into laminar and turbulent contributions THE NEPTUNE CFD CODE 37 Laminar contribution The laminar part is the sum of the drag force the added mass force the lift force and additional user forces Drag added mass and lift are inde pendently usable in the code and must be understood as forces between the first phase k 1 chosen as the carrier fluid or continuous phase and other phases The general form is 1 Ns 3 2 22 LE aiap FPV a1ap C T l1 gt p a1ap L Up U1 A rot U1 with F the drag coefficient between phases 1 and p V U U V is the av eraged value of the local relative
83. e the same discrepancy is verified in the calculation of external wall temperature of HX tubes 4 2 3 Testn 9 The Test n 9 provides the system actuation with total HX Pool fill up and the reaching of boiling conditions in the Overall Pool This test is performed to verify the correct system behavior during long term accidental transient under reduced primary pres sure 4 M Pa The chronology of main events is shown in Table 4 3 The comparison between the experimental results and the calculated ones is shown from Figure 4 14 to Figure 4 19 Water Level behavior After full opening of the triggering valve at t 163s the collapsed water level in the HX Pool quickly increases stabilizing close to the top of the tube bundle The progressive decrease of the Overall Pool level is started by wa ter discharge from the bottom at t 2790s The water discharge valve is closed at t 4840s From this time the Overall Pool level decrease is terminated and the ex tracted power tends to zero according to the full uncover of HX tube bundle reached at CATHARE MODELING OF PERSEO FACILITY 109 E D gt o l O 1000 2000 3000 4000 5000 6000 7000 8000 Time s Figure 4 14 HX Pool collapsed water level 6 5 4 Aa oN E M X ET BE v i 2 Pm LV ser T TT 1 COLLEVCP eee 0 1000 2000 3000 4000 5000 6000 7000 8000 Time s Figure 4 15 Overall Pool collapsed water level the end of test The initial wat
84. e 1 14 SECT is section of one elementary element PERI is wall friction perimeter of one elementary element SIZE represents the size of one elemen tary element Operator AXIAL Directive MESH Operator XAXIS Operator SEGMENT Directive GEOM Directive HYDR Directive SINGULAR Figure 1 15 Description of an AXIAL element Weight for sub modules and gadgets The WEIGHT is a property that is inherited between a module and its connected sub modules or gadgets Example an AXIAL element is defined with a weight 3 A sink gadget is connected to the third scalar mesh of this axial element Each of the 3 pipes has a sink connected to its third scalar mesh If this sink is activated it will be activated for the three pipes Consequently there is no way of imposing a different extracted flow rate for one of these three sinks because in fact for CATHARE there is only one AXIAL element and one SINK gadget This is the same for all gadgets and sub modules The TEE is the only gadget or sub module on which a particular weight may be defined with respect to the main AXIAL module This is due to the special correlations used for flow rate distribution and stratification making it possible to define several tee branches connected to the same scalar mesh For example an AXIAL element can be defined with a weight 3 A tee branch gadget with a weight 2 is connected to the third scalar mesh of this axial element Each of the THE CATHARE
85. e 3 5 Overall Pool temperature measurement position THE PERSEO FACILITY 83 Test Test conditions Description 1 Atmospheric pressure Pool side check cold water poor off cold conditions from Overall Pool to HX Pool with HX Pool uncovered 2 Atmospheric pressure Pool side check cold water poor off cold conditions from Overall Pool to HX Pool with HX Pool covered 3 Primary side pressure Adiabatic test pressurization and heat up up to 6 M Pa in of the primary side with HX Pool empty saturation conditions 4 Primary side pressure 4M Pa Integral test 5 Primary side pressure Primary side pressurization up to 9 M Pa Cold conditions Table 3 2 PERSEO shake down test matrix Test Test conditions Description 6 Primary side pressure 7 M Pa Integral test interrupted at the beginning of the pool level decreasing 7 Primary side pressure 7 M Pa Stability and integral test Partial and subsequent HX Pool filling with reaching of boiling conditions and level decreasing 8 Primary side pressure 7 M Pa Stability test Partial HX Pool filling with reaching of boiling conditions 9 Primary side pressure 4 M Pa Integral test Table 3 3 PERSEO test matrix The main steps of the integral test procedure are the following 1 2 pressurization of the primary circuit to the required pressure opening of the triggering valve reaching of saturation conditions
86. e Sole 4 40129 Bologna Italy NNFISS LP2 089 List of Figures 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 1 11 1 12 1 13 1 14 1 15 1 16 2 1 2 2 2 3 24 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 Juction between two modules 0 0 00 eee eee es 9 AXIAL ID elemente hcg Be Bee ie He neck Rho EE ew ech CaS Se Ri 10 VOLUME 0D elements 23 8425 Peete ete Me sleet 4 10 SDmod les pa e Beet Peace ASE GO IE ad ed DG Ge Sad a ai 11 Boundary condition module i 2 594 2 6 areca gw BEY SOE ee 12 RUPTURE element e 00 ope te ity See ne alee ep ete ete dy aes ite 2 12 TEE seh me kojac Br aldo ete Bhat ee AOE aE Meare her a RSS 13 Assembly OfMmOd Mes an By PPG tee he PS ere ga ae i 8 14 Map of the motion regimes in CATHARE code 15 Spatial discretization of the AXIAL module 21 Spatial discretization of the standard VOLUME module 22 Spatial discretization of the 3D module 0 22 junction between two AXIAL elements 004 24 weight notion in a hydraulic circuit description 25 Description of an AXIAL element oaa hired ne ange 26 Examples of sub modules or gadget associated with an AXIAL element 27 Modules of the NEPTUNE CFD 2 acc eeue 2b Bowes SES Res a 31 Boiling heat flux at the wall 2 62 See Se ls ee ee hee poets 4 44 Tree structure OF a case study b sods ge Ros pode Bh eaten Rea 60 NEPTUNE GUlinterface Edainox s 2 e lt 8
87. e additive terms ide view Tee branch o Tee branch Pipe Figure 1 7 TEE scheme Two kinds of sub modules exist and are listed below Extended sub modules having a wide interaction with the module the multi layer WALL sub module in which radial conduction is calculated the heat exchangers sub module that can be used between two circuits or between two elements of a circuit the fuel pin thermo mechanics sub module which can predict fuel cladding deformation creep rupture clad oxidation and thermal exchanges the reflooding sub module with a 2 D heat conduction model in the wall or in fuel rod for predicting the quench front progression Two kind of reflooding sub modules can be used the bottom up reflood ing Finaly the top down reflooding and the point neutronics sub module a 3 D neutronics code can also be coupled to CATHARE Sub modules or gadgets connected to one mesh the TEE sub module used to represent a lateral branch tee branch on a 1D module This sub module predicts phase separation phenomena and a specific modeling effort has been paid for cases where the flow is stratified in the main pipe Figure 1 7 shown an example of TEE scheme The ac cumulator sub module sources fill and sink loss injection mass sub modules including break and Steam Generator Tube Rupture the 1 node pump sub module the PRZ pres surizer sub module based on the 0D module with specific features valves
88. e effect on waves height Interfacial friction function of wawe roughness SECTION AVERAGING Definition of sections No section Reference and initial pressure 15000000 Default Surface tension 0 059 i call THETIS tables W call CATHARE fictions Fluid WATER Std rev6 extended W Enthalpy pressure clipping physical values 1 Non condensable gas imber of non condensable gases 0 SPECIAL PHYSICS USER DESIG Variable physical properties call usphyv J Mass transfer call ustrmv i User defined head losses call uskpdc Porosity call uspors J Isolated cells call usetan _j Momentum sources call ustsns WALL TRANSFER MODEL Wall transfer model Nucleate boiling Wall fimetim wodel ifar hailing flout Standard feindle nhace wall fimetim Close Cancel Help Figure 2 10 Generality panel THE NEPTUNE CFD CODE 71 A b NUMERICAL SCHEMES lt pool gt 2 NEPTUNE CFD 1 0 8 Velocity update end of time step by the pressure gradient increment Velocity update alpha P cycle by the pressure gradient increment Boundary faces color for RTO update all Velocity predictor algorithm standard difvit W velocity mass flux filter coefficient gt 1 001 2 transposed gradient amp second viscosity W isotropic coupling of velocities ENERGY ALPHA PRESSURE COUPLING
89. e momentum equations being written in all three direc tions P HL HG a Vix VGz VLy VGy VLz VGz The 0D modules is divided in two sub volumes The main variables are pressure liquid enthalpy gas enthalpy void fraction and non condensable mass fraction with related transport equations for each sub vol ume and the separation level elevation between the two sub volumes Two energy and mass balance equations are written for each sub volume For the volume a total pres sure equation is written The system always has six equations even in single phase computations a residual phase treatment is used To simplify the balance equation some terms such as the axial component of the vis cous stress tensor and its work the axial heat conduction the axial mass diffusion in case of non condensable gas transport the work of the interface forces and the pressure distribution forces in the energy equation are negligible Moreover in the averaging process all correlation coefficients are assumed equal to one and the phase kinetic en ergy is assumed to be due to the axial motion Finaly the water and gas properties which are valid for local instantaneous variables are assumed also valid for averaged variables and they are calculated with the mean pressure P and not the phase pressure Simplify assumptions are applied also on the interface balance equations In partic THE CATHARE CODE 19 ular it has been assumed that the interface
90. eak coupling between the OP injector system and the rest of the PERSEO facility are the mass flow rates through the water discharge and the water to HX pool lines Atmospheric pressure is imposed at the boil off section for the outgoing gas flow while at the inlet section of the injector both temperatures and mass flowrate or steam velocity are required The boundary velocities for the NEPTUNE _CFD code can be computed from the mass flowrate predicted by the CATHARE code Since the state variables in CATHARE are 1D along the axis uniform fields across each boundary section have been considered The aim of this simulation is to reproduce the correct temperature behavior from PERSEO test 9 Figure 5 2 shows the layout of the overall pool temperature measure ment positions while the experimental results are reported in Figure 5 3 The computed temperatures at the probe positions denoted by TP6 TP8 TP23 and TP25 are chosen for this case study and are listed in the Input Output Control module The exact location of the probes can be found in Table 5 1 121 NEPTUNE_CFD MODELING OF PERSEO FACILITY Figure 5 2 Overall pool temperature measurement positions 122 NEPTUNE_CFD MODELING OF PERSEO FACILITY 120 7 T P006 C T P028 C T P023 C T P030 C T P008 C _ T P025 C T P022 C T P021 C
91. eate the tree structure of the current case Then the mesh file m1 unv of the geometry is copied in the MESH folder and the Edamox GUI is opened by launching the command edam from the DATA folder The expert level for this case is set in the menu Options that provide access to a larger number of numerical settings In order to activate the two phase option of the code the Water steam module in the Special Modules panel is defined The fluid and flow properties panel is opened to setting the number of flu ids involved in the simulation the flow properties the turbulence models the wall THE NEPTUNE CFD CODE 67 X amp FLUID amp FLOW prop lt pool gt 9 oO Figure 2 7 Fluid and Flow Properties panel boundary conditions and the inter phase forces Figure 2 7 shows the fluid and flow properties panel For this simulation two phases water and steam are de fined The turbulent model chosen for the liquid phase is the Rij epsilon turbulence model No turbulence model is set for the vapor phase Friction wall boundary condi tions are chosen for the liquid phase and zero flux on the relative velocity conditions for the vapor phase The inter phase forces are shown in Figure 2 8 68 THE NEPTUNE CFD CODE INTER PHASE FORCES Ishii model derived from the CATHARE code valid for bubbly flows Zuber model derived from the CATHARE code valid for bubbly flows Tomiyama SMD Sauter Min Di
92. ection panel The selection panel for the data structure is composed by 9 modules Special modules Fluid amp flow properties Input output control Generalities Numerical schemes Boundary conditions Scalars Variable output control and Run In order to insert the parameters of the case it is preferable to follow the order shown in Figure 2 5 In the menu Options it is possible to set the level of the users There are three differ ent level User Expert Programmer The standard level is the user level and it contains less parameters respect to the other levels the expert and programmer levels provide access to a larger number of settings whose modification requires deeper knowledge of the numerical method Now we illustrate briefly the NEPTUNE modules shown in Table 2 2 The module Special Modules allows to enable special features of the two phase flow The options are the option none for the separate phases the option water steam mod ule and the option water non condensable module In the Fluid amp flow properties module one can find the number of fluids and the fluid name options All the physical properties and the turbulence models are defined in this module The input output control module allows to set memory allocation the mesh file the time step and all input output parameters The Generality module contains the general physical settings gravity pressure etc and controls the calling of many user routines To compile these subr
93. ector outlet and the trend of power as a function of the water level in the pools decreasing for the loss off mass through the boil off Test 7 phase 1 Event and phenomena Time s Quantity HX Pool partial flooding 1 partial triggering valve opening and closure 300 433 2 partial triggering valve re opening and re closure 446 480 Maximum level in the HX Pool 1 41 m 508 Maximum exchanged power 3 5 MW Minimum level in the HX Pool 1 40 m 874 Overall Pool average temperature 17 C Instabilities for steam condensation in the Injector 755 1115 HX Pool total flooding 3 partial triggering valve opening and closure 864 1085 Maximum level in the HX Pool 3 4m 875 Maximum exchanged power 21 5 MW HX Pool minimum level 1 25 m 4625 Overall Pool average temperature 70 C Table 3 5 Chronology of main events of Phase 1 The Phase 1 of Test n 7 foresees the system actuation with partial HX Pool fill up without reaching of boiling conditions in the Overall Pool This test phase is aimed at verifying the system behavior during start up The chronology of main events charac terizing the conduct of the test is shown in Table 3 5 In the initial status the Overall Pool is full of cold water at 4 62 m level from the pool bottom the HX Pool is empty and covered and the primary side is active The triggering valve begins to be opened slowly at time 300 s then it is complete
94. ed file for analysis The input files are FORT21 result file containing saved values the file containing the cho THE CATHARE CODE 21 sen definitions of variables for post processing and files containing the variables corre sponding to experimental values to be compared to calculated values may be used for post processing The output file is FORTO7 formatted file with the chosen variables 1 3 2 Computation scheme integration volume for momentum equation vector node Vi Vg nmail 1 1 _ n scalar mesh f i i i nmail nmail 2 O lt O lt vector mesh nvect volume for scalar node mass amp energy equations P H Hy a Xi Figure 1 10 Spatial discretization of the AXIAL module The numerical method in the CATHARE code uses for the spatial discretization a first order finite volume mass energy equations and finite difference momentum equation scheme with structured and staggered nodalization Figure 1 10 1 11 and 1 12 show the spatial discretization of scalar and vector variables for 1D AXIAL module 0D VOLUME module and 3D module respectively The scalar properties of the fluid such as pressure enthalpy and density are represented by average conditions of the fluid and are valued in the center of a mesh scalar point Vector properties of the fluid such as speed are valued in internal points points between two meshes of an axial element poi
95. equals the hydraulic head of the water column between the injection level and the pool free surface The Overall Pool level which increases after triggering valve closure at t 1085 s due to water ther mal expansion is well predicted by the code As a consequence the HX Pool relative pressure is well predicted too The power extracted by the HX reaching a maximum of about 20 MW when the HX tubes are fully submerged by water steam mixture is well simulated Figure 4 5 and the temporary power reduction during primary side depressurization between t 900 1400 s is captured Temperature profiles Figure 4 6 shows that the mean Overall Pool temperature in crease is well predicted by the code while there is a large gap in the temperature stratification calculation The HX pool Temperature at the middle plane of HX tube bundle is well simulated as shown in Figure 4 7 Under the wet side the external wall temperature of HX tubes is over predicted about 20 C over the experimental data However this discrepancy is probably caused by uncertainties in the thermocouple measurements 4 2 2 Test n 7 Phase 2 The Phase 2 of Test n 7 is aimed to verify the correct system behavior during long term accidental transient In this phase the system actuation with total HX Pool fill up and the boiling conditions reached in the Overall Pool are performed The chronology of CATHARE MODELING OF PERSEO FACILITY 105
96. equation Ce 1 44 and Ce 1 92 are the two classical constants taken from the single phase flow model II represents the production or destruction influence of the nphas 1 other phases i e the turbulent contribution of combined drag and added mass terms Hg Macs 2 83 pFk p Nok apF EP 2 dkp 2ak TAV Ups UK Vir 2 84 D Pp Qk ce with vie the drifting velocity already defined qkp lt Ux iUp gt the covariance of the fluctuating velocities of phases k and p that will be either modeled or neglected The multiplicative constant Ce used in the dissipation equation is equal to 1 2 The Local equilibrium model extended Tchen s theory assumption is an algebraic model developed in the framework of Tchens theory 20 and used for dilute dispersed phase i e bubbles or droplets transported by a continuous phase The main assump tion here is that the continuous phase is the first one p 1 and its turbulence is given by a k e model With this assumption the turbulent kinetic energy q and the covari ance qix of the dispersed phase k gt 1 are calculated from the turbulent kinetic energy qi b 7 b 2 2 r 2 r 2 85 dk q 1 Nr dik q 1 Nr 2 where b and m are functions of drag and added mass coefficient and two specific time scales p a T b ai t ah 2 86 Pk T Q104 Tik 48 THE NEPTUNE CFD CODE Th is the characteristic time scale of the momentu
97. equired wall superheat is higher Pwall 20T sat r 2 54 At ad HiatPLsat emar Twall Tsat Terit2 In a first simplified approach and following the analysis of Kurul and Podowski 18 the boiling heat flux splits into three terms a single phase flow convective heat flux at the fraction of the wall area unaffected by the presence of bubbles a quenching heat flux where bubble departures bring cold water in contact with the wall periodically and a vaporization heat flux needed to form the vapor phase THE NEPTUNE CFD CODE 43 The wall surface unit is split into two parts an area influenced by bubble departure Ag and a single phase area Ac with the relation Ag Ac 1 Ag is the sum of the areas of influence of each bubble over the unit surface Neglecting the overlapping areas of influence between adjacent bubbles Ag is written Ag min 1 7D n 4 2 55 where n is the active site density and Dm is the bubble diameter departure A classical law of single phase flow heat transfer at the wall is used to predict the flux gc Achiog Twal T5 2 56 where refers to a pointin the fluid turbulent sub layer hrog represents the heat transfer within the thermal boundary layer The quenching heat flux is modeled as the mean value of a transient conductive heat flux supplied to a semi infinite medium at external temperature Ts during the waiting period tg between the departure of a bubble and the beginning of grow
98. er level increase in the HX Pool is very well captured by CATHARE Figure 4 14 while the level is overestimated in the first part of the transient t 900 2100 s and then largely underestimated from t 2900 s until the triggering valve is closed The decrease of the HX Pool level during the last phase of the transient is well reproduced until the end of the test The Overall Pool collapsed water level be havior is well predicted by CATHARE during the whole transient Figure 4 15 The oscillatory behavior observed in the test before Overall Pool water boiling might be produced by sudden steam condensation at the injector outlet inducing fluctuations at the pool free surface 110 CATHARE MODELING OF PERSEO FACILITY 0 1000 2000 3000 4000 5000 6000 7000 8000 Time s Figure 4 16 HX Pool relative pressure 18000 15000 12000 9000 Power kW 6000 3000 0 1000 2000 3000 4000 5000 6000 7000 8000 Time s Figure 4 17 HX exchanged power Relative Pressure and Power profiles The HX Pool relative pressure overestimation between t 2700 5000s see Figure 4 16 is consistent with the corresponding HX Pool level underestimation The calculated extracted power in Figure 4 17 is 15 MW slightly higher than the measured one 14 MW The power diminution predicted by the code after triggering valve closure at about t 5000s is slightly more accelerated than the one observed in the test Temperature prof
99. es susy nls toe Ge Glee Gael E EALS e B 88 3 12 Overall Pool temperatures ead sya cote pow arson Be weg ye te Se eS 89 3 13 Water flowrate between the pools 2 Phase 90 3 14 HX Pool and Overall Pool water level 2 Phase 91 3 15 Primary side pressure 2 Phase 5 eve tke kOe Ee Se ES 91 3 16 HX exchanged power 2 Phase 0 2 ie ys ge Srp vial dap ads Ree ed 92 3 17 HX Pool temperatures 2 Phase cwravsvicct Oe Bee eR ee Wed ee hk 92 3 18 Overall Pool temperatures 2 Phase 0 2a 5 eos ee ke Ya ta eG 93 3 19 Water flowrate between the pools i ina se bide es Be eS HC 94 3 20 HX Pool and Overall Pool water level 0 0040 95 3 21 Primary sid pr ss res n ceas aota i he e eh ee Olt ame dee ere 95 3 22 HX exchanged DOWEL sinesme Gord a ia pa a a E Be a R ye Bk 96 3 23 HX Pool temperatures eie 2 Mec pon e ta e Bee A years amp baie 96 3 24 Overall Pool and pool connecting line temperatures 97 4 1 CATHARE nodalization scheme aoaaa aa 100 4 2 HX Pool collapsed water level naa aaa eRe AY Ree os 101 4 3 Overall Pool collapsed water level onnaa aa 101 4 4 HX Pool relative pressure aaa aaa SE Se re ee His 102 AD HX ex ha ged powers n i ub te So e wi yee Eee gs ex Oty amet aE any 102 4 6 Overall Pool temperatures 444 404 24 ba ed edhe eed wes A 103 4 7 HX tube wall temperatures bares ea eh Be A AO Bone XOaK 103 4 8 HX Pool collapsed water level
100. essarily the same in the entire circuit The ZONE element is designed to help CATHARE users process calculation results It enables several elements of the same circuit to be combined in an assembly on which CATHARE performs mass and energy balance calculations 1 1 2 The main modules Several main modules can be assembled to represent the primary and secondary cir cuits of any reactor and of any separate effect test or integral effect test facility The main modules are the following the AXIAL element 1D module the VOLUME element OD module the 3D module the BOUNDARY CONDITION module and the RUPTURE module Modules are connected by JUNCTIONS as shown in Figure 1 1 element i 4 element j junctiona junction element i element j Figure 1 1 Juction between two modules A JUNCTION is represented by a physical vector point and by two scalar points which are all shared by the two connected elements The vector point specifications geometrical parameters flow area gravity etc are provided adopting the point of view of each adjacent element both sets of specifications must be consistent with each other and should satisfy CATHARE reader controls The AXIAL element 1D module is used to describe parts of the plant in which the re frigerant flow is predominantly one dimensional such as hot and cold legs SG U tubes expansion line core channels core bypass downcomer SG rise SG vapor line It may
101. ext section On the wall friction boundary conditions for water and air and zero velocity normal derivative for steam are used The Ishii drag model and the Zuber added masses model for the steam phase are used In Figure 5 8 is shown the Input Output Control module Here the mesh the post processing saving frequency and the probes location are set In the Generalities module shown in Figure 5 9 the gravity force is set The wall trans fer model chosen is the Nucleate Boiling model with a standard wall function and the interfacial water steam energy transfer model chosen is the Standard model both for the steam and the water Three scalars are set in the module shown in Figure 5 10 the total enthalpies for each fluid Two of these are enable automatically when the steam water module is selected in the Special modules the total enthalpies for water and steam phases The third scalar is adjoint to consider the air phase and the initial value of this scalar is defined as As shown in Figure 5 11 the boundary conditions consists of seven regions steam in 128 NEPTUNE_CFD MODELING OF PERSEO FACILITY X X BOUNDAR IwITION lipkn y o x File Options Headings _2 NEPTUNE CFD 1 0 8 paran Help GENERAL x Mber of zones 5 E a m a zone name steam inlet boil off water line wall_injector symmetry Le dt zme refs ry 2 3 456 7 et met __ BC type inlet outlet inlet vall symmetry SSS
102. files necessary for the case The next step is to open the directory SCRIPT and to launch the command file runcase From this moment the NEPTUNE calculation starts and the temporary files of this simulation appears in the directory tmp NEPTUNE In this directory is possible to supervise the calculation through the file listing in which are reported the the main information of the run At the end of the calculation the results are copied to the directory RESU It is also possible to change the temporary directory name and use for example a specific local disk name 2 3 2 The NEPTUNE param file Module description Special enable special modules Fluid amp flow properties Fluid properties input output control input and output control Generality general physical settings Numerical schemes numerical schemes Scalar set scalar equations Variable output control output control Run run the code Table 2 2 NEPTUNE modules The param file is an input file create by the user to set the data for the simulations and it is contained in the DATA directory see 2 3 1 There are two different ways to generate this dataset file Using the NEPTUNE Edamox GUI or by editing the param file directly The paran file consists of several sections As shown in Figure 2 4 the NEPTUNE GUI opens a window which is divided into two main panels the menu bar and the THE NEPTUNE CFD CODE 63 Figure 2 5 Suggested parameter order sel
103. ge a aoe Be al eee 14 2 Ex cutable block peaini damea ead ee eh ee eee f 2 The Neptune CFD code Two fluid model in NEPTUNE code 2h 4 6 66 bce Oe ae es 2 1 2 2 2 1 1 2 1 2 2 1 3 2 1 4 2 1 5 Multi field balance equations 004 Interface transfer closure laws 0 0 0 0 000 eee Bulk interface heat and mass transfer 0 Nucleate boiling model 0 00 00 000 Turbulent modeling 40 2 2450 8 sreterene sha Bae Se he ete Numerical discretization 0 0 00000 eee eee eens O ON 12 14 14 15 15 19 19 20 20 21 23 23 23 28 CONTENTS 2 2 1 Momentum equations 5 628 6 kad wre Nee Bak a 48 2 2 2 Mass Energy equations the Alpha Pressure Energy cycle 53 2 2 3 Volume conservation and pressure projection 58 2 3 The NEPTUNE data param file and user routines 60 2 3 1 NEPTUNE data structure of the code 60 2 3 2 The NEPTUNE param file 229i ah ee tee te ee Sa 62 2 393 User roules eea e ae ete noe Bae ak be a we ae 65 2 4 Aparam file for standard boiling flow in a rectangular channel with con stant bubbles diameter o coen er enaa dAn a 000 eee eee eee 66 The PERSEO Facility 75 3 1 The main features of the PERSEO test facility 75 Sid An troductions lt emad Sh Pk we oe Se Ded eh ed Be es 75 O42 West facility geometry 2 3 earns at EMSS ORS Be SG OS 76 3 1 3 Circuit configuration and operation
104. gure 4 27 HX Pool collapsed water level CATHARE MODELING OF PERSEO FACILITY 117 18000 eee 15000 T Une 12000 A Pee tt 9000 soot Pl Sees Ve AL oS 1000 2000 3000 4000 5000 6000 7000 8000 Time s Power kW Figure 4 28 HX exchanged power set of Overall Pool water boiling around t 3200s After this time due to significant reduction of the calculated Overall Pool swollen level Figure 4 25 the HX Pool rela tive pressure is much better predicted Figure 4 26 Moreover the right pressure trend reflects in more accurate calculation of the HX Pool collapsed level Figure 4 27 No significant changes are shown in the HX exchanged power Figure 4 28 Chapter 5 NEPTUNE CFD modeling of PERSEO facility components 5 1 Introduction In the previous chapter the CATHARE code has been employed for the analysis of two main tests of the PERSEO facility This system code does not reproduce a detailed simulation of a specific component Therefore a CFD simulation of this component by means of the NEPTUNE CFD code has been performed in order to analyze carefully the system transient in the Overall Pool and in the injector This should allow us to give an evaluation of the non homogeneous distribution of the void fraction in the pool In the next sections a two dimensional model of the overall pool and the injector also called OP injector system and the results as well obtained by the simulati
105. has no thickness and no mass the superficial tension in the momentum balance is neglected the contribution of superficial tension in the energy balance is neglected and both phases have the same velocity at the interface supposed uniform 1 2 3 Closure relations The solution of the system of differential equations implemented in the CATHARE code requires closure equations that take into account the physical model and heat mass and momentum transfer phenomena between a phase and the other and between the fluid and the walls These closure equations are developed according to some considerations First as far as possible physical closure laws are developed on an experimental basis A set of a separate effect experiments were performed and analyzed Original correlations are developed when existing models are not satisfactory The degree of empiricism depends on the comprehension of the physical mechanisms involved In the domain where experimental and theoretical knowledge are missing it needs to extrapolate the data by making simple assumptions depending of the case studied Also it needs to consider that thermal and mechanical transfers are interconnected So it is assumed in a first approximation that mechanical interactions do not strongly depend on thermal exchanges Mechanical terms are first derived from experiments where thermal non equilibrium is negligible Interfacial heat transfer terms are then derived Then wall to fluid heat fluxe
106. he gradient of turbulence the drift contribution or the turbulent added mass term For instance if we only retain the gradient of turbulence the dis persive coefficient will remain equal to Da Zak Prediction velocity step U U In this sub step we solve the momentum equa tion neglecting the volumetric fractions and pressure variations da 0 and P 0 oUi Josi ISk 3UE phe conv SUf diffu J SUP o SUR R 2101 with UP UP Up This system of equations cannot be solved easily since phases are strongly coupled by the implicit nature of the momentum source terms interface ones J and external pk ones Sp The linearization of these contributions with respect to the definition of drag and added mass terms lead to the following expression pr Pk AP conv diff 5U oy OSki oor UE S aF sur our Y a U SUE DO Sour pA p k p k Cir 2 102 There is only one condition to obtain an invertible system The external source term 52 THE NEPTUNE CFD CODE derivatives must verify Ski Ski 2 f 2 1 Ue lt 0 and aU gt 0 for l k 2 103 The system is then split in two sub steps which guarantee the conservative property of the interface transfer terms convection diffusion sub step U gt UP so solved by a Jacobi process pri pk SUE nV ki r1 k pCa ri Ski arrpri _ nU ki Py conv diff 6
107. he primary circuit in order to supply boundary conditions to a three dimensional CFD code for the investigation of the ther mal hydraulic of a specific component In the present work a multi physics simulation concerning an innovative safety system for light water nuclear reactor is studied with the aim to increase the reliability of its main decay heat removal system In particular the system studied is able to re move the decay power from the primary side of the light water nuclear reactor through a heat suppression pool In previous works two examples of energy removal systems utilizing in pool heat exchangers have been proposed to be installed in the GE SBWR and in the Westinghouse AP 600 the isolation condenser and the passive residual heat removal system respectively In both systems the heat transfer was actuated by open ing of a valve installed on the primary side of the reactor The first proposal of moving the primary side valve to the pool side was analized by CEA and ENEA in the thermal valve concept project In this case the valve was located steam side at the top of a bell covering the pool immersed heat exchanger During normal operation the valve is closed to prevent the heat transfer due to the formation of steam under the bell while in emergency conditions the valve opening caused the discharge of the insulating steam and the beginning of heat transfer from the primary side to the pool The PERSEO in Pool Energy Removal Sy
108. he real transient scenario Some regulation tools can be used but are not actually available in reactor plants or facility plants For example it is possible to regulate loop mass flow rates or flow distribution by changing pressure loss coefficients at volume junctions It is also possible to regulate the temperature differ ence between a primary and a secondary circuit by introducing a fouling factor in the heat exchanger In both cases after convergence the final values of the pressure loss coefficients or fouling factor have to be checked Realistic values may be used The Transient scenario of the executable block is used to represent the actual reactor or experiment transients Available directives may be sorted into different categories such as the RESETIME directive that is used to reinitialize the CATHARE calculation time as well as the time input deck local variable to zero Chapter 2 The Neptune CFD code peoeeeresteetenas e lt a es mis ne O wae g LETT a The kernel ee eer tessepaneentt Figure 2 1 Modules of the NEPTUNE CFD NEPTUNE CED is a three dimensional two fluid code for calculating multiphase or multifield flows at the local scale and in geometries that may be complex It is de veloped for nuclear reactor applications in particular for three dimensional computa tions of the main components of the reactors cores steam generators condensers and heat ex
109. hich is described in the User manual of CATHARE code 1 and the syntax of each commands is developed in the dictionary 13 1 4 1 The DATA block The data block has a modular structure and consists of the description of the reactor in particular the definition of all module specifications topological connections between modules geometrical length high diameter angle etc numerical mesh hydraulic type of flow hydraulic diameter flow section etc the definition of all sub modules and gadgets connected to these main modules the choice of chemical elements and non condensable gas the assembling of circuit s and reactor In the Input deck there are two kinds of instruction OPERATOR instruction is a declaration of a variable or an object and it is character ized by symbol 24 THE CATHARE CODE Example varl 12 5 eleml AXIAL ent USTREAM exit DSTREAM DIRECTIVE instruction acts upon calculation or objects properties In the data block key words for each element are utilized to define all module spec ifications For example to characterized an AXIAL element the following key words are needed AXIAL topological definition GEOM geometrical definition HYDR hydraulic definition MESH mesh definition SINGULAR optional singular pressure drop definition To describe the reactor geometry two concepts are then used The first is the Junc tion notion and concerns the object element
110. igure 4 4 HX Pool relative pressure 25000 20000 15000 x 3 10000 5000 0 0 1000 2000 3000 4000 5000 Time s Figure 4 5 HX exchanged power described Table 4 1 shows the chronology of main events The comparison between the experimental results and the calculated ones is shown from Figure 4 2 to Figure 4 7 Water Level behavior After partial triggering valve openings the HX Pool water level increases producing a corresponding decrease of the Overall Pool level according to the pool area As soon as the HX tubes are covered by water after about 900 s from CATHARE MODELING OF PERSEO FACILITY 103 9 g g o a oa fe 0 1000 2000 3000 4000 5000 Time s Figure 4 6 Overall Pool temperatures 9 g 2 g o a E v 0 1000 2000 3000 4000 5000 Time s Figure 4 7 HX tube wall temperatures the beginning of the transient the power exchange becomes more significant leading to HX pool boiling conditions The steam produced flows to the Overall Pool through the steam duct and the injector with consequent Overall Pool water temperature pro gressive increase At time t 1085 s the triggering valve is closed and the HX water level decreases Moreover a temperature stratification phenomena is observed in the Overall Pool Unless of a small underestimation of level decrease in the second part of the transient the HX collapsed and the Overall Pool water level are well predicted by the co
111. iles The onset of boiling in the Overall Pool occurring around t 3200 s is very well captured by the code Figure 4 18 Figure 4 19 shows the HX Tem CATHARE MODELING OF PERSEO FACILITY 111 T P008 C T P021 C T P022 C T P023 C T P025 C T P028 C Temperature C 0 1000 2000 3000 4000 5000 6000 7000 8000 Time s Figure 4 18 Overall Pool temperatures TW C006 C TW C007 C TW C008 C WALLT10 Temperature C 0 1000 2000 3000 4000 5000 6000 7000 8000 Time s Figure 4 19 HX tube wall temperatures perature profile Once more the HX tube wall temperature is over predicted 4 3 3D Overall Pool modeling In the previous section the results obtained shown the general capability of CATHARE to evaluate main natural circulation and heat transfer phenomena occurring during the PERSEO tests Apart from temperature stratification and free level oscillation effects in the Overall Pool discrepancies have been found in the calculation of the HX Pool rela 112 CATHARE MODELING OF PERSEO FACILITY Event Time s Beginning of the test 0 Triggering valve opening 142 opened in 21 s Overall Pool water discharge opening 2790 Onset of the Overall Pool water boiling 3200 Overall Pool water discharge closure 4840 Triggering valve closure 4887 closed in 93 s End of the test 7708 Table 4 3 Chron
112. imum value of 1 3m The Overall Pool level decreasing is observed during the two water pouring off towards the HX Pool Figure 3 8 then level increases slowly due to the Overall Pool water heat up and 88 THE PERSEO FACILITY Pressure kPa P B001A kPa P 1001 kPa 3000 Time s Figure 3 10 Primary side pressure T Q023 T Q030 C T Q032 C T Q016 C T Q007 C T Q006 C T 0031 C T Q024 C T Q009 C T Q013 T Q015 C T Q034 C T Q036 C T Q022 C T Q033 C T Q010 T Q008 C T Q037 Temperature C 13000 16000 Time s Figure 3 11 HX Pool temperatures density diminution After the first step of water pouring off power exchanged from the primary to the pool side is quite low around 3 5 MW because of the low water level in the HX pool while it increases by increasing the level up to reaching the maximum value of about 21 MW Later power decreases following the trend of level in the HX Pool as shown in Figure 3 9 When level reaches the minimum value of 1 3m the exchanged power THE PERSEO FACILITY 89 o 4 T P006 C T P028 C T P007 C T P023 C T P030 C T P008 C T P025 C T P022 C T P021 C T N001 C i i a i Temperature C w 20 10000 10500 11000 11500 1200
113. ing rate within the Overall Pool The Phase 2 of the Test n 7 and the Test 9 in which boiling conditions are reached in the Overall Pool have been recalculated with the new modeling and the obtained results are presented in the following sections 4 3 1 Test n 7 Phase2 A T ENS 0 1000 2000 3000 4000 5000 6000 Time s Figure 4 21 HX Pool relative pressure The new code results for the Phase 2 of Test n 7 regarding the HX Pool relative pressure the water level in the two pools and the HX exchanged power are shown from Figure 4 21 to Figure 4 23 in comparison with the test measurements As expected the differences with previous results become significant only after the onset of Overall Pool boiling around t 1400s After this time the deviations from the experimental trend are in general reduced allowing the best simulation of all phenomena concerned in the test The HX Pool relative pressure is very well predicted after the onset of boiling Fig ure 4 21 The reduced pressure value reflects in a more accurate evaluation of the HX 114 CATHARE MODELING OF PERSEO FACILITY E v gt o ond 0 1000 2000 3000 4000 5000 6000 Time s Figure 4 22 HX Pool collapsed water level 25000 20000 j P POWERHX 15000 k J g amp 10000 5000 0 1000 2000 3000 4000 5000 6000 Time s Figure 4 23 HX exchanged power Pool collapsed level which slightly increases in better agreement with the test me
114. is simulation pointed out that one of the main reasons for the numerical instability of the run was the excessive stiffness of the boundary conditions together with a too small portion of the domain occupied by the steam Another critical aspect was identified in the junction of the grid blocks where the grid size undergoes a steep variation Case 3 Geometry with the injector in central position and an additional volume simulating a portion of the HX pool In order to further reduce the sources of numerical instabilities a third geometry has been considered In Figure 5 36 the discretized geometry is shown together with a local zoom of the injector region Furthermore to prevent the pressure oscillations inside the injector a larger cylindrical vessel has been added upstream The volume of such a vessel is approximately that occupied by the steam in the HX pool The inlet section where the boundary conditions from the CATHARE simulation are imposed is now NEPTUNE_CFD MODELING OF PERSEO FACILITY 149 Y E p PANNU N X x ES PASE y y se SI IZA SE OA A Sat KOS NK RY N OS Aiae Me A AH We OE ROS We SA SS OS x ESS i Ea Figure 5 36 PERSEO 3D hexahedral grid left and a detail of the injector region right for the geometry with a straight injector and a modified position of the injector noz
115. itten as ga 21r Fey Cr PrUk i T 2 1 with ak Pk Uk the volumetric fraction the density and the mean velocity of phase k respectively T is the interface mass transfer rate on phase k sum of all the other phases contributions De SOT oe T 2 2 p k T 18 the interface mass transfer from phase p to phase k bulk transfer TS r represents the mass transfer contribution to phase k induced by wall nucleate boiling In our model these terms are calculated near heated walls and only affect liquid and steam phases i e k 1 2 and verify wt T lwo 9 2 3 and nue gt 0 2 4 34 THE NEPTUNE CFD CODE since steam is produced by nucleation Conservation relations for mass and volume lead to Soop 1 2 5 k 5 oTi 0 since Thr T gt p 9 2 6 k Momentum equations The multi field momentum balance equation for the field k is first presented in its semi conservative form all the contributions are conservative except for the pressure gradi ent one gg owe U bi Bay CPrUki Ung o OP Ban CT DRS ak Be AkPkIi gt pst TU 0p 55 2 7 pFk with P the mean pressure and g acceleration due to gravity The viscous stress tensor is defined by OU OU 2 Tk ij melar H Da 3 div U dig 2 8 where juz is the dynamic viscosity oR QkPk lt Up Uk j gt is the turbulent stress tensor that has to be modeled or neglected when the flo
116. ized to investigate the heat exchange between the steam and the liquid phases at the interface and to reproduce the condensation ebollition phenomena inside the injector Then an overall pool system can be modeled by considering as boundary conditions the results obtained from the injector simulations The multi scale and multi physics computation coupling monodimensional and three dimensional codes is still in a developement stage but it should be considered the unique way to define the behaviour of systems where the time and length scales of individual processes involved differ by orders of magnitude Bibliography 1 G Lavialle Cathare V2 5_1 USER S MANUAL Laboratoire de developpement des applications pour les systemes CEA Grenoble France Mars 2006 2 www cathare cea fr 3 D Bestion G Geffraye The Cathare Code Laboratoire de developpement des ap plications pour les systemes CEA Grenoble France Avril 2002 4 D Bestion Interfacial friction determination for the 1 D 6 equation 2 fluid model used in the CATHARE code European Two Phase Flow Meeting Marchwood 1985 5 D Bestion The physical closure laws in the CATHARE code Nuclear Engineering and design Vol 124 pp 229 245 1990 6 J Bartak T Haapalehto Simultaneous bottom a n d Top down rewetting calculalions with the CATHARE codc Nuclear Technology Vol 106 pp 46 59 1994 7 J Kelly J Bartak A Janicol Reflood modelling under oscillato
117. jector and a modified position of the injector nozzle NEPTUNE_CFD MODELING OF PERSEO FACILITY 153 Figure 5 41 Water streamlines and velocity vectors lower part only on plane x 2 75 m for t 213 28 s Contours for water volume fraction TP006 K TP008 K TP023 k TP025 K 1000 2000 3000 4000 JOU time s Figure 5 42 Experimental water temperature evolution for different probes to the presence of the wall can be observed near the pool lateral boundary The reason may become clear by looking at Figure 5 41 There is a net transfer of vertical momen tum to the water in the upward direction due to buoyancy effects because of the heated water and to friction on the steam upflow near the external wall of the injector A circu lation is therefore setup inside the pool with the fluid moving upwards in the central part and downwards close to the lateral walls However in the real configuration the injector is positioned close to the wall and buoyancy and wall effects will then overlap Because of this consideration we should reconsider the experimental data and verify if the assumption that the temperature stratification at least in this first part of the tran sient is mainly due to a wall effect With reference to Figure 5 42 two couples of probes 154 NEPTUNE_CFD MODELING OF PERSEO FACILITY TP23_N num TP6 num _ TP025 K AM y 1P023 k 315 hai Y TPOO6 K
118. junctions The weight of an element is the number of identical elements simulated by this element For example for a reactor with three loops the broken loop is simulated by elements with weight 1 and the intact loops can be described with a single loop and weight 2 in each element Inside a capacity or a VOLUME or 3D element the weight notion for each junction is used to connect several identical elements or assembly of elements to the module The introduction of weights is a way of simplifying the model but has a drawback the user loses the possibility of representing asymmetric effects Moreover the weight has to be taken into account to ensure flow section gravity and friction perimeter continuity at junctions In VOLUME elements the junction data SECT and PERI are those of an elementary junction linked to an elementary axial element The Figure 1 14 illustrates how to use the weight notion to simplify a hydraulic circuit description In particular SECT is the section of one elementary axial element and PERI is the wall friction perimeter of one 26 THE CATHARE CODE axial element The SIZE data should be equal to the total size because it is used to determine flow distribution in sub volumes The weight value n is then attributed to the junction connected with n elementary elements modeled by an axial element with weight n In the AXIAL element all geometrical data are those of an elementary axial element With reference with Figur
119. kes appear unbounded terms ai r The solution is once again to k adapt the value of face fractions choosing either geometric or harmonic interpolation for a 7 The second term represents the diffusive thermal contribution For practical reasons it is evaluated as 1 ap Ox a Qk tee Bk k pa accounting for turbulent diffusion 2 117 Cbn Os The third term represents the wall heating diffusive contribution The weighting by fa function is only available for phases 1 and 2 in water steam regime The term 4 represents the temporal variation of pressure that remains explicit The term 5 represents the source contributions that can be decomposed into user defined sources and water steam model sources see 2 1 3 el gt n oA ene 2 118 Prk p k user defined water or steam i e k 1 2 The explicit part of IT w s is kept with regard to the enthalpy and a linear development in terms of the pressure increment is used w s ou s an n j meran re gor Tg 7 P 1 p 2 119 Moreover division by volumetric fraction is controlled in order to avoid residual phase problems 1 _ 1 _ k 56 THE NEPTUNE CFD CODE Finally non dimensional coefficient ul value is close to one It is solution of the mass source step and ensures the exact conservation of the mass energy system j Enthalpy source coupling balance H H y C Neglecting convective and diffu sive incremen
120. lation which stabilizes on both primary and secondary sides determines the power evacuated by the system 3 2 PERSEO experimental data A set of instruments for conventional thermal hydraulic measures is provided in the PERSEO facility Direct measures of pressure differential pressure temperature and strain are performed Hence some of these quantities are utilized to obtain derived quantities like levels flow rates and energies Figures 3 4 3 5 shows the probes position in the two pools For the protection of the plant a pressure indicator is installed on the Main supply line to switching off the main steam valve in case of overpressure All the instruments are calibrated in the SIET metro logical laboratory The nominal accuracy of the Differential Pressure Transmitters is 0 1 of the instrument full scale The nominal accuracy of the Pressure Transmitters is 0 25 of the instrument full scale while the nominal accuracy of the Differential Pressure Transducers is 0 25 of the instrument full scale The nominal accuracy of the thermocouples and the nominal accuracy of the Resistor Thermal Detector are respectively 1 05 C and 1 5 C 3 3 Experimental text MATRIX The PERSEO facility set up was conducted by executing a series of shake down tests suitable to verify the correct plant operation and to characterize the main parameters of the facility in particular the water pouring off from the Overall Pool to the HX
121. le to capture the stratification phenomenon This means that either the initial or the boundary conditions or the modeling equations are not correctly implemented Never theless many attempts have been made with different conditions and different physical 136 NEPTUNE_CFD MODELING OF PERSEO FACILITY models with the purpose of reproducing stratification but none of them has been suc cessful This may be due to a wrong modeling of the injector for which the hypothesis of adiabatic walls is made Temperature stratification Steam_to OP 65 f 55 500 1000 1500 2000 2500 3000 Figure 5 18 Steam mass flowrate to overall pool over the time interval 500 3000 s defined from CATHARE simulation Water_to_HxPool Water_discarge Water discarge opening 50 500 1000 1500 2000 2500 3000 500 1000 1500 2000 2500 3000 Figure 5 19 Water mass flowrate to HX pool and water discharge mass flowrate over the time interval 500 3000 s defined from CATHARE simulation During the interval t 500 3200 s the pool temperature increases until it reaches boiling For the time interval under study the steam mass flowrate to the overall pool is shown in Figure 5 18 the water mass flow rates to the HX pool and to the discharge line are reported in Figure 5 19 on the left and right respectively In two dimensional NEPTUNE_CFD MODELING OF PERSEO FACILITY
122. ling pool right and steam release to the water sur face left minimal and all the steam goes above the level of the water pool as shown in Figure 5 26 on the bottom Condensation may take place in some areas of the pool especially near the boil off where the cold air may condensate the saturated steam 5 3 5 Injection above water level During the interval t 4200 7700 s the pool level decreases until it is below the injector outlet Figure 5 27 shows the evolution of the steam mass flowrate entering the overall pool in this last time interval The temperature of this flow is the saturation temperature In a similar way in Figure 5 28 the water mass flowrate to the HX pool and the water discharge mass flowrate are shown on the left and right respectively The NEPTUNE_CFD MODELING OF PERSEO FACILITY 141 Steam_to OP 1 1 L 4 L 1 1 4500 5000 5500 6000 6500 7000 7500 Figure 5 27 Steam mass flowrate to overall pool over the time interval 4200 7700 s defined from CATHARE simulation Water_to_HXPool a 20 Water_discarge 2 Water discarge closing o 0 4500 5000 5500 6000 6500 7000 7500 4500 5000 5500 6000 6500 7000 7500 Figure 5 28 Water mass flowrate to the HX pool and water discharge mass flowrate over the time interval 4200 7700 s defined from CATHARE simulation water discharge mass flowra
123. ly 86 THE PERSEO FACILITY F_POOL kg s j7 Flowrate kg s T T 10500 10550 Time s Figure 3 6 Water flowrate between the pools partial HX Pool fill up F_POOL kgis Flowrate kg s 11150 Time s Figure 3 7 Water flowrate between the pools total HX Pool fill up closed at 433 s At time 446 s a further opening is actuated and the valve is completely closed at 480 s This sequence valve opening and closure represents the first step of water injection The second step of water injection occurs when the valve is opened at 864 s and completely closed at 1085 s The water flowrate between the pools derived by the HX Pool level for the first and second phase of injection is reported in Figures 3 6 and 3 7 THE PERSEO FACILITY 87 10000 10500 11000 11500 12000 12500 13000 13500 14000 14500 15000 Time s Figure 3 8 HX Pool and Overall Pool levels Power kW ot T T T T T T T T T 10000 10500 11000 11500 12000 12500 13000 13500 14000 14500 15000 Time s Figure 3 9 HX exchanged power respectively The HX Pool level begins to increase at time 308 s At time 508 s the HX Pool reaches the level of about 1 41 m then it decreases slowly down to about 1 40 m Figure 3 8 At time 905 s level increases again up to 3 4 m following the second water injection Then level decreases down to the min
124. m behavior during long term accidental tran sient The chronology of main events characterizing the conduct of the test is shown in 90 THE PERSEO FACILITY Event and phenomena Time s Quantity HX Pool partial flooding Triggering valve opening 326 opened in 26 s Maximum level in the HX Pool 3 25 m 531 Maximum exchanged power 21 MW Overall Pool average temperature 85 C Overall Pool water discharge opening 1150 Onset of the Overall Pool water boiling 1400 Overall Pool water discharge closure 3230 HX Pool level 2 07 m 3230 Triggering valve closure 3338 closed in 123 s Maximum level in the HX Pool 3 4 m 11050 Maximum exchanged power 21 5 MW Primary side depressurization beginning for end of test 4685 Table 3 6 Chronology of main events of Phase 2 F_POOL kg s Flowrate kg s 20 T TA L 250 300 Time s Figure 3 13 Water flowrate between the pools 2 Phase Table 3 6 The second part of the test starts with the HX Pool water level of 1 2 m in saturation conditions the Overall Pool full of warm water and the primary side pressure at 7 M Pa The triggering valve begins to be opened at time 300 s and it is completely open at 326 s Then it is closed at 3338 s in 123 s in order to isolate the two pools and investigate the trend of power as a function of the HX Pool level
125. m transfer rate between 1 and k i e the particle relaxation time scale Tik E ob 2 87 at 2 87 Ti represents the time scale of the continuous phase turbulence viewed by the dis persed phase or the fluid particle turbulent time scale that takes into account crossing trajectories effect 20 21 Ti a 3 g gt 3 3 4 T E E t 5G amp Vr i Vi Q Cg is the crossing trajectory coefficient taken equal to 1 8 2 2 Numerical discretization In this section an overview of the numerical algorithm used in NEPTUNE CFD code to solve conservation equations on mass momentum and energy is given 16 The main idea is a fractional step method that leads either to use linear solvers or direct nphas x nphas matrix inversion The main interest of the method is the so called alpha pressure energy cycle that ensures conservative of mass and energy and allows strong interface source term coupling The algorithm is compressible and allows variation of density in function of pressure and enthalpy during a time step Moreover all the variables are locates at the center of the cells 2 2 1 Momentum equations Basic equation The momentum equations are solved using the implicit for as possible The final equation is the following one that will be split in fractional steps SUr Te ki 1 1 prt n U eae E ngnti Al ki a Ox akPrUkj an Ox z ak ki kj 1 0 pn 1 Rertt oprtl af Bay REG EES Gt a othe SE
126. ment into four parts e Beginning e Temperature stratification pool heating 132 NEPTUNE_CFD MODELING OF PERSEO FACILITY tempEXP _ 290 1 1 1 1 1 1 1 O 1000 2000 3000 4000 5000 6000 7000 8000 Figure 5 12 Chronology of the temperature main events for the probe T P6 e Steam injection pool boiling e Injection above water level The time interval of each part is summarized in Table 5 3 n Description Time s 1 Beginning of the test 0 500 2 Pool heating 500 3200 3 Pool boiling 3200 4200 4 Low water level 4200 7700 Table 5 3 Chronology of the Temperature main events Beginning of the test During the initial part of the simulation the pool temperature is low Table 5 4 shows the initial conditions of the system t 0 and the boundary conditions for NEPTUNE during the time interval 0 500 s as computed by CATHARE are shown in Figures 5 13 5 14 In Figure 5 13 and on the left of Figure 5 14 the water mass flowrate from Overall Pool to HX pool and the water discharge mass flowrate are shown respectively These NEPTUNE_CFD MODELING OF PERSEO FACILITY 133 Parameter Unit Value OP water level m 4 50 OP water temperature C 24 5 HX pool water level m 1 222 HX pool water temperature C 47 Table 5 4 Initial conditions of Overall Pool and HX pool Water_to_HXPool 80 6
127. moving with the liquid field for a gas moving with the gas phase and also allows dissolution and evaporation of the component In case of radioactive products the decay period is taken into account to calculate the activity 1 2 The two fluid model The CATHARE code describes properly the different of phase regimes the interface behavior and the transport of the state variable by using well defined physical models All modules use the two fluid model to describe steam water flows and four non con densable gases Both thermal and mechanical non equilibrium of the two phases may THE CATHARE CODE 15 be taken into account 3 1 2 1 The two phase flow regimes ANNULUS ROD BUNDLE 0 0 lt E lt 1 PIPE R 0 BUBBLY ANNULAR ANNULAR CHURN DROPLETS SLUG 0 lt R lt 1 TRANSITION R 1 STRATIFIED Figure 1 9 Map of the motion regimes in CATHARE code The two phase flow patterns are modeled in the CATHARE code but only two transitions are explicitly written and used in several closure terms of CATHARE the transition between stratified and no stratified flow This transition depends on two criteria a first criterion is based on Kelvin Helmholtz instability threshold and the sec ond depends on the relative effects of bubble sedimentation and of bubble turbulent mixing The second transition is between annular and droplets flows These two tran sitions describe the change from a separate flow
128. n decided to generate new grids starting from a simplified geometry in order to isolate and correct the most important factors that lead the simulation to divergence Case 2 Geometry with straight injector at the real position Figure 5 33 PERSEO 3D hexahedral grid left and a detail of the injector and boil off region right for the geometry with straight injector and real position of the injector exit In order to reduce the possible sources of numerical instabilities a new geometry has been generated by introducing a straight injector entering the pool from the top of the domain The injector nozzle is in the same position and with the same area The grid is still composed by different blocks lower half of the pool upper half of the pool block around the injector boil off injector WD and WL water lines With respect to the first mesh a block of cells in the part of the pool around the injector as been added This block has conforming junctions with the remaining part of the upper pool even though the grid size in the normal direction of the connecting surfaces undergoes a steep variation especially in the upper part of the injector again the short distance from the pool wall requires small cells and near the injector nozzle The junctions between the grid in the lower half of the pool and the other blocks are non co
129. n particular in the adiabatic wall number 5 no sliding condition is applied and a Neumann condition is imposed on the two enthalpies The wall number 6 is heated with an heat flux of 10 W m The inlet conditions are applied on the wall number 3 For the liquid phase the velocity is imposed along the y direction the mass flow rate is set to 0 2 kg s and the enthalpy is imposed for a temperature of 610 K For the steam phase the properties are taken at the enthalpy saturation point The outlet conditions are applied on the wall number 4 In this wall the reference pressure is im posed and a Neumann condition is applied on the two enthalpies Figure 2 14 shows the structure of the Boundary Condition panel Finally in the variable output control panel the probe numbers for each variable and the post processing visualization are set In this case the probes are lo cated with the purpose to measure pressure and temperature Before running the simulation it is necessary to save the param file The number of processors is set in the Run panel and the simulation is started with the button Run on line Figure 2 15 shows this Run panel Chapter 3 The PERSEO Facility 3 1 The main features of the PERSEO test facility 3 1 1 Introduction HEAT 47 EXCHANGER Water discharge VESSEL Steam supply Condensate discharge line Figure 3 1 Scheme of the PERSEO facility Within the frame of a research activity on inn
130. n the data block Step 5 Definition of the modules which belong to several REACTOR modules special links between elements of different reactors EXHYLINK Step 6 Definition of reactors REACTOR 28 THE CATHARE CODE 1 4 2 Executable block The executable block manages the actions that are carried out on the reactor This ac tions can be of two types internal and external The internal actions are refer to the numerical solution of the problem in question recalling gradually appropriate solvers and proceeding in steps of calculation External actions are implemented by the user through directives With these actions it is possible to manage the output information but also act on the objects described in the DATA BLOCK to modify these characteris tics for example by closing a valve which in the data block was initialized open or to modify the boundary conditions etc The command block consist of the initialization of the thermal hydraulic state for the entire reactor the achievement of the initial steady state and the transient scenario The initialization is a mandatory step for any CATHARE calculation because any time step calculation requires the knowledge of the initial values of all the variables To minimize the amount of data to enter and to facilitate this first calculation this ini tialization step aims at reaching a plant steady step The initialization order for each hydraulic circuit is defined with the PERMINIT di
131. n the enthalpy equation in order to prevent the calculation from diverging NEPTUNE_CFD MODELING OF PERSEO FACILITY 131 The source term in the steam momentum equation for the k th direction due to direct contact interaction with the air is coded in the user routine ust sns F is given by Q M aapa Fda3 v Us 5 4 with Fdo3 10 1 V Ea 5 5 and Vp is the module of the relative velocity between phases The FORTRAN routine is reported here IF IPHAS EQ 2 OR IPHAS EQ 3 THEN ALP2 RTPA IEL IALPR 2 ALP3 RTPA IEL IALPR 3 ROM2 PROPHY IEL IROM 2 ROM3 PROPHY IEL IROM 3 VR23 RTPA IEL 1U 3 RTPA IEL 1U 2 x 2 amp RTPA IEL IV 3 RTPA IEL IV 2 2 amp RTPA IEL IW 3 RTPA IEL IW 2 2 FD23 1 D5x 1 VR23 IF IPHAS EQ 2 THEN T T T TSA 2 TSA 2 ALP3 FD23 ROM2 TSA 3 TSA 3 ALP3 FD23 ROM2 ENDIF IF IPHAS EQ 3 THEN TSA 2 TSA 2 ALP2 FD23 ROM3 TSA 3 TSA 3 ALP2 FD23 ROM3 ENDIF ENDIF The drag coefficient in the momentum equation is calculated in the user routine usdrag F 5 3 3 Results obtained for the test 9 In this section the results of the two dimensional OP injector system simulations are described in detail In order to consider temperature evolution for test 9 as reported in Figure 5 12 it is possible to divide the experi
132. ncrease in the HX Pool is well captured by CATHARE Figure 4 8 How 106 CATHARE MODELING OF PERSEO FACILITY LVPm MIXLEVCP COLLEVCP Oooo Injector T POSIN peee Ta a 1 16 2 kale 0 ees ee ey 0 1000 2000 3000 4000 5000 6000 Time s Level m Figure 4 9 Overall Pool collapsed water level DP kPa 0 1000 2000 3000 4000 5000 6000 Time s Figure 4 10 HX Pool relative pressure ever the level is initially overestimated until t 1400 s and then underestimated until triggering valve closure t 3338 s Finaly at the end of the transient the level is slightly overestimated Large oscillations of the Overall Pool level are observed in the test after the steam injection at t 500 s These oscillations are produced by free surface fluctuations and cannot be reproduced by the 0 D module used to represent the Overall Pool Figure 4 9 Relative Pressure and Power profiles Starting from the initial value of 12k Pa with water empty injector the HX Pool relative pressure decrease after triggering valve CATHARE MODELING OF PERSEO FACILITY 107 w_Ic kw i w T POWERHX N 20000 15000 10000 Power kW 5000 _ m taaan 0 1000 2000 3000 4000 5000 6000 Time s Figure 4 11 HX exchanged power 120 100 i T P021 80 d T P022 T P023 T P025 60 T P028 TEMPWAT Temperature C 40 0 1000 2000 300
133. nforming but the grid size in the direction normal to the common surfaces are kept constant on 146 NEPTUNE_CFD MODELING OF PERSEO FACILITY ANW JTN NNNN 0 5 li SANSS AANA AR ARRARAS SA A Ni DDS SSS ER ih 1 137e 06 pressure Pa 115000 112000 112000 F 108000 F 108000 F 104000 F 104000 101325 101325 SASSER ANN NNNNA AN ANN NANNAN i SSIS AN N IN N N N SES TS ANN NN RA ROR ARANAANNI NNN ANE ANN AA AA TZ Figure 5 34 Water volume fraction top pressure middle and vertical component of steam velocity bottom for t 50 6804 s left and t 51 8309 s right on a section at x 3 312 both sides The mesh has now 129338 hexahedral cells With the second mesh the simulation starts at time t 451 s that is before the increase of the steam mass flow at the inlet takes place The simulation appears to be more stable than with the first mesh but a few changes were required in the user defined functions in order to run the simulation up to t 60s More particularly in the drag model usdrag F the water characteristic diameter was set to d 5 1075 when the water volume fraction NEPTUNE_CFD MODELING OF PERSEO FACILITY 147 ANAN AAAA aaa st pressure Pa 1
134. ng the local effects of the injection jet has been developed 10 The non condensable gas effect The modeling of mass diffusion effects is based on a classical heat and mass transfer analogy An original procedure was developed in order to avoid the calculation of the interface temperature 11 12 1 3 CATHARE solution procedure 1 3 1 Introduction A CATHARE computation consists of three stages corresponding to three separate exe cutables pre processing computation and post processing Each of them requires and generates some files containing data CATHARE pre processing READER exe involves a user input deck These data con tain a description of the hydraulic circuit s to be simulated the events occurring during the simulation and how calculation is managed The input file is the Input deck The output files are V25 INIT file containing the image of the input deck data block and FORTRAN file PILOT f translation of input deck execution block CATHARE calculation CATHAR exe is the stage where one execute the simulation de scribed in the input deck i e basically the thermal hydraulic computation The input files are DICO Dictionary of key words used by CATHARE FAST H and FASTSIZE f CATHARE memory dimensioning files The Output files are the Listing file and the FORT21 Result file In the CATHARE post processing stage POSTPRO exe users may process CATHARE binary output files to output useful information to a formatt
135. ng to four topologies of simulation software the system scale the component scale the CFD scale meso scale and the DNS scale micro scale The system scale is dedicated to the overall description of the circuits of a nuclear plant The component scale is made for the design safety and operation studies of reactor cores and heat exchangers steam generators condensers auxiliary exchangers The meso scale requires a CFD type software to be solved in an open three dimensional medium The average scale one millimeter or less goes beyond the limits of the component scale for a finer description of the flows This scale includes turbulence modeling using the RANS or URANS approach This is also the only scale able to predict the fluid temperature field to analyze thermal shocks or thermal fatigue of the reactor structures The micro scale corresponds to the DNS or pseudo DNS ap proaches and may also include some LES like approaches This characteristic length may focus on very small domains e g containing a few bubbles or droplets In order to better investigate a component of the system or when detailed information on a spe 6 INTRODUCTION cific part of the domain is required as when there is a particular interest in small scale phenomena taking place in a limited part of the domain a coupling between two or more scales may be used For example it is possible to conceive a monodimensional system code which can predict the behavior of t
136. nlet junction conditions are not given by ele ments that have already been calculated then additional real constraint points have to be defined Boundary conditions are not calculated during this step The second step allows the user to reach an overall coherent state THE CATHARE CODE 29 This is the stabilized solution of the standard transient calculation of ten time steps for the entire reactor i e a calculation with time set to zero During this step contrary to the previous one the boundary conditions and then their models as defined in the data block and the real exchanged power between circuits are taken into account The purpose of the Stabilized transient is to obtain a system at equilibrium with the required initial conditions P at pressurizer flowrate at secondary side pump rotation speed etc Usually this part of the input deck consists of a transient loop with regulations and with outlet condition tests set on a time step value to ensure the stability of the physi cal state obtained and its agreement with the imposed reference state tests on physical variable values with respect to imposed values This transient block may be performed with time set constant to 0 or not Performing this phase with running time may be advantageous in order to post treat the regulation results in order to check reactor con vergence towards the desired state Then the RESETIME directive can be used to reset time to 0 before beginning t
137. not allowed to exit Concerning the water line boundary condition temperature is fixed to reference Temperature and mass flow is imposed through the usclim F user file as a function of time At the wall standard turbulent boundary conditions for water and air are imposed User routines In this simulation some user files are modified by introducing specific subroutines Boundary conditions are imposed by using the CATHARE solution In order to im pose the boundary conditions as a function of time one must modify the file usclim F On the injector inlet boundary the mass flow function m t for phase 1 steam over the interval t 1 43E 02 1 68E 02 is given by 5952 98 74 3234 t 0 228571 m t 547 5 2 The FORTRAN language is the following IF TTCABS GE 1 43E 02 amp AND TTCABS LT 1 68E 02 THEN DEBCL 1 2 FACT_Wx 5952 98 74 3234 xTTCABS 0 228571 amp TTCABS TTCABS ENDIF Here DEBCL j amp is the mass flowrate on boundary j steam inlet boundary is de noted by 1 in order for phase a steam is phase 2 Time is denoted in this file by TTCABS The same procedure is used to set the steam boundary conditions on all the simulation time and the water boundary conditions in which the mass flowrate on boundary is denoted by DEBCL 3 1 Initial conditions must be defined in the file usiniv F The water level in the Overall Pool is set by 4 5 m
138. nts located in the middle of each mesh cell face for a 3D element or at the junctions between two elements The time discretization varies from the fully implicit discretization used in the OD and 1D modules to the semi implicit scheme used in the 3D module These methods are known for their robustness in a wide range of flow configurations An hyperbolic system of equations is used to ensure the well posedness of the problem Mass and energy equations use a conservative form and are discretized in order to keep a very 22 THE CATHARE CODE amp Junction external scalar point defined by the next element X upper sub volume Potj X amp O 2 lower sub volune Figure 1 11 Spatial discretization of the standard VOLUME module Scalar node located in the center of the mesh cell X Vector node located in the middle of each mesh cell face Figure 1 12 Spatial discretization of the 3D module good mass and energy conservation The phase appearing and disappearing problem is properly solved using some residual volume fractions and an appropriate conditioning of interfacial mass and energy transfers The wall conduction is implicitly coupled to hydraulic calculations The non linear system of equations is solved by a Newton Raphson iterative method following several steps At each iteration e increments of internal variables of each element are eliminated as function of in crements of junction va
139. od THE CATHARE CODE 11 eled at each junction taking into account the two phase jet effect pull through process Mass and energy transfer between the two sub volumes bubble rise fall of droplets condensation evaporation are modeled For the one phase liquid case the upper sub volume is residual height 1 cm Respectively the lower sub volume is residual for one phase gas fluid height 1 mm In Figure 1 3 it is shown a OD volume structure where Zc is the variable separation level Figure 1 4 3D module The 3D module is created to represent large scale thermal hydraulic 3D effects in nu clear power plants One of the main applications is the modeling of a PWR vessel Figure 1 4 shows an example of 3D module The 3D module has been only validated for PWR vessel modeling The use of the 3D module can be extended to other ge ometries but the validation of such geometries has to be performed by users The main phenomena to be addressed are the three main phases of a large break LOCA i e blow down downcomer refill and core reflooding phases for which turbulent phenomena are not dominant Therefore the turbulent model is dedicated to very specific applica tions where the model is applied to a single phase The BOUNDARY CONDITION module is an element which can be placed at the ex tremity of a pipe a volume a tee or a 3D module Figure 1 5 shows an example of boundary condition module It is used to impose one or mo
140. of fiberglass walls reinforced by iron beams The liquid line connecting the Overall Pool bottom to the HX Pool bottom is an 8 inch sch 40 pipe It contains the triggering valve 8 inch diameter manual valve The Steam Duct is an horizontal fiberglass pipe OD 1 13 m ID 1 1m connecting the HX THE PERSEO FACILITY 79 Pool to the Overall Pool The terminal part of the Steam Duct ending into the Overall Pool is a conical injector built in stainless steel 3 1 3 Circuit configuration and operation The PERSEO facility design features are listed in table 3 1 Description Unit Value Power 20 MW Vessel Pressure 10 MPa Vessel temperature 310 C Heat exchanger pressure 8 62 MPa Heat exchanger temperature 302 C Superheated steam flowrate 12 kg s De superheating water flowrate 3 kg s Pool side pressure 0 15 MPa HX Pool temperature 300 C Overall Pool temperature 130 C Pool side make up water flowrate 25 kg s Table 3 1 PERSEO facility design features In order to simulate the execution tests initial conditions are imposed to the facil ity In particular for the primary side the pressure vessel is maintained in saturation conditions typical for BWRs or secondary side of PWR steam generators P 7 MPa This is done by supplying properly de superheated steam coming from a nearby power station The pressure is kept constant by controlling the steam supply valve
141. of tube bundle see Figure 3 20 The Overall Pool level is reported in the same figure The progressive decrease of the Overall Pool level is started by water discharge from the bottom at 2790 s approximately 400 s before the onset of boiling The water discharge is stopped at 4840 s that is 140 s before complete triggering valve closure At this point the Injector outlet is uncovered and steam flows directly outside through the boil off pipe After the triggering valve is opened and power begins to be exchanged from the pri mary to the pool side the primary side pressure is manually increased in order to com THE PERSEO FACILITY 97 T P006 C T P028 C T P023 C T P030 C T P008 C T P025 C T P022 C T P021 C T NO001 C 5 e a g a 2000 3000 4000 5000 6000 7000 8000 9000 Time s Figure 3 24 Overall Pool and pool connecting line temperatures pensate the pressure decreasing due to the heat removal After some oscillations the pressure average value returns to 4 1 M Pa remaining stable until the end of test see Figure 3 21 The exchanged power is shown in Figure 3 22 After the triggering valve between the two pools is closed from 4887 s to 4980 s the HX Pool level decreases more rapidly and consequently the exchanged power The HX Pool temperatures are shown in Figure 3 23 Before the water injection s
142. ology of main events of test 9 p 9 1 Overall Pool i i t iL Water Line Figure 4 20 3D volume Overall Pool modeling scheme tive pressure and collapsed water level behavior after boiling is reached in the Overall Pool The HX Pool relative pressure against the Overall Pool pressure atmospheric value strongly depends on the hydraulic head of the water column above the steam injector outlet in the Overall Pool This hydraulic head increases under Overall Pool boiling conditions depending on void formation in the pool and swollen level effect see Figure 4 9 and Figure 4 15 Likely this swollen level effect is overestimated by the OD module of CATHARE representing the Overall Pool because of homogeneous dis tribution of voids considered in the boiling water pool which could be in contrast with non uniform radial and axial distribution of voids expected in the tests The use of a CATHARE MODELING OF PERSEO FACILITY 113 3D volume Overall Pool modeling has been evaluated in this study in order to verify the Overall Pool swollen level effect and try to reduce the discrepancies with the test measurements The implementation of the new Overall Pool modeling in the original nodalization scheme is shown in Figure 4 20 The height of the Overall Pool bottom volume is different for the two tests according to the respective extracted power value and then different boil
143. ons Then the linear system is solved for each cell Hol yt HEC _ HUA MM u 2 127 oF m ss E HEN BES z Ho with M the extra diagonal part of the coupling matrix One can remark that in the simple case of a two phase steam water flow the coupling matrix is diagonal so the re actualization reduces for each phase to H b I H Ly 1 Mass j sub step a gt al The mass balance equations are solved in terms of vol umetric fractions The full balance is obtained after decomposition in two fractional steps the mass source coupling balance and the convection balance iC jt mass PESTE balance aj all w s contributions T Tp Tobe pAr PG on Mass transfer terms have 3 possible The first term is the mass transfer that in the water steam bulk model is deduced from energy transfer nes Ws pes pen aO Ta w o fork gt 3 2 128 1 2 Hg He k 1 1 w s n with I IP Pr hg or TP 2 The second term is the nucleate boiling at heated wall A ee ar e s n 7 PU aa Cae O mesmes nE SOT 0 oaa 2 129 w gt 2 w 1 ith Dee Dene pr TP ora N pull pr wi w w Doe OP Jo The third term is the user define transfer term SS a 2 130 p k To ensure the positivity of all the volumetric fractions the sub step must includes a 58 THE NEPTUNE CFD CODE numerical treatment introducing weighted coefficients l 1 WC
144. ons will be analyzed Then a three dimensional model of the components will be presented All the simulations are obtained considering the test n 9 of the PERSEO tests in section 3 3 2 this test is analyzed in detail 5 2 CATHARE NEPTUNE coupled simulation A simple scheme of OP injector system and the coupling with CATHARE results is shown in Figure 5 1 The water discharge WD is a line that allows water removal in order to accelerate the decrease of the water level in the Overall Pool The water to HX pool line WL is the feed line that joins the Overall Pool to the HX pool The steam line allows the steam to flow from the HX pool to the injector while both steam and air flow out the system through the boil off section In order to analyze the Overall pool and the injector of the PERSEO facility it is necessary to impose specific boundary conditions of the case study To do this a weak 120 NEPTUNE_CFD MODELING OF PERSEO FACILITY Steam L Boiloff aa Input data CATHARE OVERALL POOL discharge To HX pool Figure 5 1 Coupling CATHARE NEPTUNE coupling between CATHARE code and NEPTUNE_CFD code is performed This cou pling allows first the solution of the CATHARE code over all the domain and then the solution of the overall pool and injector components with the NEPTUNE_CFD code using the previously results obtained as boundary conditions The boundary condi tions required for the w
145. or providing real time calculation The code is nowdays mainly used to perform safety analysis with best estimate calculations of thermalhydraulic transients of PWR for de signed accidents such us LBLOCAs and to quantify the conservative analysis in SBLO CAS SGTR Loss of RHR Secondary breaks and Loss of Feed water accidents The CATHARE code is also used to define plant operating procedures and for research and development In this case the code is integrated with training simulators providing real time calculation In fact a simplified version of CATHARE is implemented in the SIPA simulator presently used at EDF Also the standard CATHARE version is implemented in the next generation simulator family under the SCAR project On the recent version of the CATHARE code specific modules have been implemented to allow modeling of other reactors like boiling water reactor or gas cooled reactors The CATHARE code includes several independent modules that take into account any two phase flow behavior such as mechanical non equilibrium vertical co or counter current flow flooding counter current flow limitation and horizontal stratified flow critical or not critical flow co or counter current flow thermal non equilibrium criti cal flow cold water injection super heated steam reflooding and all flow regimes and all heat transfer regimes In order to take into account these phenomena the CATHARE code is based on a two fluid and six equation mo
146. or Emergency Operation project is an evolution of the Thermal Valve concept where the triggering valve is installed liquid side on a line connecting two pools at the bottom The valve is closed during normal operation and the pool containing the heat exchanger HX Pool is empty The other pool Overall Pool is full of cold water In emergency conditions the valve is opened the heat exchanger is flooded with consequent heat transfer from the primary side to the pool Moreover the pools are connected at the top by means of a pipe ending with an injector accelerating the produced steam under water from the HX Pool to the Overall Pool in order to promote the circulation and the homogenization of water and to delay the boiling and steam release in the containment A new experimental facility was designed and the system was simulated with the Relap5 code in order to optimize the dimensions of the HX Pool 24 25 The PERSEO facility was built at SIET labo ratories by modifying the existing PANTHERS IC PCC facility Performance Analysis and Testing of Heat Removal System Isolation Condenser Passive Containment Con denser utilized in the past for testing a full scale module of the GE SBWR in pool heat exchanger 3 1 2 Test facility geometry The PERSEO facility mainly consists of two main facilities the primary side and the pool side Figure 3 1 shows the scheme of the PERSEO facility Figures 3 2 and 3 3 show the specific schemes of primary
147. outines it is nec essary to copy them from the USERS directory in the SRC directory The numerical schemes module contains the options that coupled the different equa 64 THE NEPTUNE CFD CODE tions and lead to the iterative solution of each system In the Scalar section one can set the scalars In particular there are two scalars that are enabled automatically when the water steam module is selected in Special mod ules the two total enthalpies for each phase water and steam Other scalars must be defined by specifying total number of scalars The possible option that define a scalar equation are shown in Table 2 3 routine description Convection selection of the convection phase of the scalar T dep time dependent term in the scalar equation Effective Diffusion diffusion term in the scalar equation Laminar Dynamic Coefficient reference diffusion coefficient Turbulent Schmidt turbulent Schmidt number Initialization Choice scalar initialization choice Type passive scalar or total enthalpy Initialization value and limit Table 2 3 Scalar equation options In general the Boundary Conditions module has several options to define Dirichlet or Neumann boundary conditions over the different boundary regions For a complete explanation see Section 2 4 In the Variable output control section the chrono buttons select the output of vari ables in the chronological post processing files The listing buttons ena
148. ovative safety systems for Light Water Reactors at SIET laboratories Piacenza and in collaboration with ENEA particular 76 THE PERSEO FACILITY attention is addressed to increase the reliability of Decay Heat Removal Systems that implement in pool heat exchangers In particular a system able to remove the decay power from the primary side of a LWR is studied able to be actuated without installing any mechanical device valve on the primary loop 22 In the past two examples of energy removal systems utilizing in pool heat exchangers were proposed to be installed in the GE SBWR and in the Westinghouse AP 600 the IC Isolation Condenser and the PRHR Passive Residual Heat Removal respectively In both of these systems the heat transfer was actuated by opening a valve installed on the primary side of the reactor 23 The first proposal of moving the primary side valve high pressure to the pool side low pressure was studied by CEA and ENEA in the Thermal Valve concept In this case the valve was located steam side at the top of a bell covering the pool immersed heat exchanger Closed during normal operation the valve prevented the heat transfer due to the formation of steam under the bell while in emergency conditions e g primary circuit high pressure the valve opening caused the discharge of the insulating steam and the beginning of heat transfer from the primary side to the pool The PERSEO in Pool Energy Removal System f
149. panel shown in Figure 2 11 the numerical options are setting For this case the pressure is bounded between two values 1500000 Pa and 3000000 Pa This approach is preferred when thermodynamics tables are used The THE NEPTUNE CFD CODE 73 vy A souiARY eCONuirois 2 NEPTUNE CFD 1 0 8 extra extra_extra Neptume FORMATION NEPTUNE BOIL ING_CHANNEL CASE1 DATA param orig Number of zones E zone name adia wall heated wall inlet outlet 2symn zone ref s 5 6 3 4 12 BC type wall wall inlet outlet symmetry Pref BC 0 0 0 15000000 0 BC type flux flux m Timp K flux flux m EntHall o 1000000 610 0 o BC type flux i flux Hsat P a flux al flux i EntHal2 jo o 0 0 jo tose Cancel exp Figure 2 14 boundary conditions panel restart time step and the upwinding of the density are set In the Scalar panel the enthalpies of phase 1 and 2 are initialized respectively at the reference pressure and temperature and at the enthalpy saturation depending on the reference pressure Po The Figure 2 4 shows the Scalar panel The Boundary Conditions panel is used to set the specific boundary conditions of the case Figure 2 13 shows a simplify scheme of the boundary conditions applied 74 THE NEPTUNE CFD CODE Figure 2 15 Run panel on each wall I
150. part The linearization leads to all At 1 ie 0 n n j Fs P _ pli 1 ale th 1 _ pb 1 ST azt al 2 138 The enthalpy increment is supposed proportional to the pressure increment one can derive a simplified equation from 2 115 that only takes into account the pressure varia tion and energy source terms increments development see 2 121 o a i areas Ca RO nll E FAP Y iga ze 1_ pl 2 139 p k amp One may remark that in a flow without any energy transfer term the first part of the unsteady contribution remains classical introducing the celerity c 1 OPK pr Oh Opr OP OPK Oh OPK OP 1 In P poh list oP P 2 140 Ck In the general case a modified celerity og is used solution of equations 2 139 and 2 140 The first term becomes j j 1 az prt pil Pk art a 2 141 cy At Ag E k The second term represents the diffusive called elliptic contribution The third term is ignored in the sub step The fourth term represents the mass transfer increment Only pressure increment of water steam and nucleate boiling contributions are considered see 2 131 and that leads to the simple expression P w s arre Oi n 1 j 1 wp Tk _ pork ahlil w gt k SEP PUN with SE yp E Hye 2 142 Pressure equation PUY Pl The pressure equation applies to the increment 5 Pl Pll PU l It is obtained after combining the nphas equa
151. quency the mean waiting time between bubble departures the mean bubble maxi mum equivalent diameter and the active site spatial density should be provided The two steps of this model are presented below the condition for on setting boiling and the heat flux calculation In order to obtain satisfactory results the incipient boiling point in forced convec tion has to be determined accurately To do this the widely used Hsus criterion is cho sen 17 According to this criterion a bubble will grow from a vapor embryo occupying a cavity if the liquid temperature at tip of the embryo is at least equal to the saturation temperature corresponding to the bubble pressure The single phase temperature pro file in the viscous sub layer allows to obtain the relations described as follow If cavities of all sizes containing vapor embryo are available which means that even the largest cavities contain vapor embryo the wall superheat at boiling incipience Twa Tsat and the wall heat flux wau are related by 80T 1 2 Twatt Tsat Terit H wa 2 52 latPsatA1 while the activated cavity radius r is M Tori ra oo 2 53 2Pwall When the wall temperature reaches the critical value the cavities of radius equal to ra are activated Then as the temperature still increases smaller cavities are activated too If the radius remax of the largest cavity available allowed to contain vapor embryo on the surface is smaller than ra the r
152. r valve at HX Pool top or on the Steam Duct In the present work the stability Phase 1 and integral Phase 2 Test n 7 and the in tegral Test n 9 have been analyzed and studied with CATHARE code and Neptune_CFD code 3 3 1 Test n 7 Parameter Unit Test n 7 Primary side Pressure MPa 7 Primary side Temperature C 285 Primary steam flowrate kg s 13 HX extracted Power MW 20 HX Pool side Pressure MPa 0 12 HX Pool side Temperature C 105 HX Pool Steam flowrate kg s 9 Table 3 4 Main PERSEO test 7 parameters in phase 1 THE PERSEO FACILITY 85 The test n 7 foresees the system actuation with partial HX Pool fill up Phase 1 fol lowed by the HX Pool total fill up with reaching of boiling conditions and pool level decreasing Phase 2 with the primary side pressure of 7 M Pa The main Test parame ters at full power operation during the transient phase are listed in Table 3 4 This test is defined to investigate the system actuation and the trend of power with a low HX Pool level the presence of instabilities due to steam condensation at the interface between water and steam in the Injector Moreover this test verifies the system re actuation con sequent to the HX Pool filling up and reaching of the thermal regime in both the pools the effectiveness of the Injector in mixing the Overall Pool water the power and flow regime variation after the Overall Pool level decreases below the Inj
153. re hydraulic conditions for each phase pressure enthalpies or temperatures velocities or mass flow rates for gas or liquid the void fraction or the mass fraction of non condensable gases or radio chemical components These boundary conditions can be defined at the inlet or the 12 THE CATHARE CODE next module BCONDIT O mK L 2 Figure 1 5 Boundary condition module outlet of an element The choice of the type and number of boundary conditions to impose takes account of the characteristic velocities For example when liquid enters liquid enthalpy and void fraction are imposed when gas enters gas enthalpy and non condensable gas qualities are imposed The RUPTURE module The RUPTURE element is used to model a double ended pipe break with scope for critical flow rate conditions An example of RUPTURE elements is shown in Figure 1 6 This object can only be connected to two AXIAL elements because critical flow can only be calculated on meshed elements The RUPTURE element may be seen as the combination of two outlet boundary conditions each one attached to an AXIAL element Pipe 1 RUPTURE Pipe 2 e O L 2 L 2 L 0 Figure 1 6 RUPTURE element 1 1 3 The sub modules A sub module is a group of subroutines connected locally to a module that calculates additive terms for the equations of the module A sub module may have internal vari THE CATHARE CODE 13 ables and internal equations to calculate th
154. rective This directive reads the or der of the elements of each circuit used to compute the initial state of the system Then the imposed thermal hydraulic state has to be defined To perform this operation the code needs to know the values of the main variables for at least one junction in each fluid zone of the circuit from which the initialization will be propagated to the entire zone This corresponds in the input deck to the definition of a real constraint point REALC operator When the definition is complete the initialization calculation can be launched using the GOPERM directive This directive is used to trigger steady state computation of a reactor The initialization procedure is performed in two steps The first step following the initialization order given by PERMINIT calculates in each ele ment the variable values which satisfy the stationary condition The inlet conditions are propagated along the element taking into account an hydrostatic pressure correction If there are walls a conduction calculation will be done taking into account generating power or heat loss flux All connected gadgets are taken into account during this cal culation The calculation is done to obtain a thermal hydraulic stationary state with the inlet junction calculated pressures being monitored with respect to the imposed values REALC Knowledge of the thermal hydraulic variables for all the inlet junctions is thus required This implies that if the i
155. res are shown in Figure 3 17 Before the water injection superheated steam due to the HX radiation is contained in the upper part and sub cooled water in the lower one After the HX Pool flooding and water boiling all tem perature stabilize around 104 C corresponding to the saturation at the pressure in the pool Steam accelerated into the Overall Pool by the Injector promotes the water cir culation and mixing until the Overall Pool decreasing is accelerated and the Injector outlet uncovered The Overall Pool temperatures are shown in Figure 3 18 The peaks observed around 650 and 1040 s are due to level oscillations between the pools and water transfer from the HX to the Overall Pool through the water line 3 3 2 Testn 9 Parameter Unit Test n 9 Primary side Pressure MPa 4 Primary side Temperature C 250 Primary steam flowrate kg s 8 HX extracted Power MW 14 HX Pool side Pressure MPa 0 12 HX Pool side Temperature C 105 HX Pool Steam flowrate kg s 6 5 Table 3 7 Main PERSEO test 9 parameters 94 THE PERSEO FACILITY Event and phenomena Time s Quantity HX Pool partial flooding Triggering valve opening 142 opened in 21 s Maximum level in the HX Pool 3 33 m 416 Maximum exchanged power 21 MW Overall Pool average temperature 85 C Overall Pool water discharge opening 2790 Onset of the Overall Pool water boiling 3200
156. riables e increments of all junction variables are calculated THE CATHARE CODE 23 e all variable increments are regenerated and convergence tests are performed In the last versions of CATHARE since V2 5 1 and V2 5 2 versions the solution can be distributed over several processors in order to reduce the CPU time by parallel computing OPEN MP This will allow real time calculation of reactor transients for the simulator application speed up of 5 on 8 processors for most of the reactor plant safety studies 1 3 3 Post processing data specification In CATHARE code a post processing tool is available also called postpro executable This program processes the result binary file FORT21 following user postpro input deck directives and creates a formatted file FORTO7 suitable for simple graphic representa tions XY plots The default format of this file is not a column format and thus cannot be easily visualized But an option XMGROP can be used in the user postpro input deck to generate two column formatted files which can be read by most standard soft ware packages 14 CATHARE Input deck The CATHARE input deck is composed by two parts the data block part which deals with the spatial reactor description and the command block or exec block part which deals with the simulated scenario steady state and time transient To be understood by CATHARE pre processing data acquisition has to use a specific language w
157. ry flow conditions with CATHARE New Trends in Nuclear System Thermalhydraulics Pisa Italy Mai June 1994 8 I Bartak D Bestion T Haapalehto The top down reflooding model in the CATHARE code NURETH6 Grenoble France October 1993 9 T Maciaszek J C Micaelli D Bestion Modelisation de I autovaporisation d a n s le cadre d un modele 4 deux fluides II La houille blanche Vo1 2 pp129 2133 1988 10 A Janicot D Bestion Condensation for ECC injection Nuclear Engineering and De sign VOL 2 pp 129 133 1993 11 D Bestion P Coste Study on condensation modelling in the CATHARE code with and without non condensable gases New Trends in Nuclear System Thermalhydraulics Pisa Italy May June 1994 160 BIBLIOGRAPHY 12 P Coste D Bestion A simple modelling of mass diffusion effects on condensation with non condensable gases for a 1 D 2 fluid code Second international Conference on Mul tiphase Flow Kyoto Japan April 1995 13 CSSI A Fouquet CATHARE 2 V2 5_1 Dictionary of operators and directives Lab oratoire de developpement des applications pour les systemes CEA Grenoble France Avril 2008 14 User Guide of NEPTUNE_CFD 1 0 8 EDF R amp D CEA France 2010 15 Y Fournier Code_Saturne version 1 1 guide pratique et theorique du module Enveloppe EDF R amp D report HI 83 03 007 16 Lavieville J Quemerais E Mimouni S Boucker M Mechitoua N NEPTUNE CFD V1 0 theory manual EDF R
158. s are correlated Finaly it should be known that each closure law is unique No choice between several correlations is proposed to the users in order to reduce the user effect Also it should be emphasized that the user does not have the possibility of choosing between the various correlations used by the code in order to minimize the influence of the choices of the user on the results provided from the code 1 2 4 Wall and interfacial transfers These terms are calculated by the code through the application of many correlations The main ones are mention below The interfacial friction correlations for bubbly slug churn flows This correlations were developed from an extensive database and validated for tube annular and rod bundles geometries 4 The wall friction It is mainly derived from a modified Lockhardt Martinelli cor relation An empirical phase distribution consistent with limit cases and with the CATHARE experimental basis has been developed 5 20 THE CATHARE CODE The wall heat transfer for dry wall situation A semi empirical approach has been fol lowed starting from bibliography correlations for inverted annular and droplet flow regimes Models parameters have been adjusted to fit reflooding data 6 7 8 The flashing The correlation is mainly empirical and derived from the analysis of critical flow tests 9 The direct contact condensation at safety injection A semi empirical correlation ac counti
159. ssump tion on the dispersed phase turbulence Nevertheless the turbulence of the continuous phase has to be described by a k e model 2 1 3 Bulk interface heat and mass transfer General user case It has been seen in the previous section that interface heat and mass transfer can be either independent or dependent depending on the choice of the enthalpy jump in the heat and mass transfers formulation In the first case three user FORTRAN files can be implemented The first regards the heat transfer between phase p and k which agree with IT 4 Wasp temperature difference between two phases 0 The standard form implemented is written in terms of the pk Skp Zp Tk with Ckp Gok 0 the heat transfer coefficient 2 39 40 THE NEPTUNE CFD CODE pk third concerns the mass transfer between phase p and k verifying T p T kp 0 The second is related to the jump of enthalpy verifying H Hyp and finally the In this form one can have some mass transfer without heat transfer and some heat transfer without mass transfer The case of dependent heat and mass transfer corre sponds to the Water Steam transfer models In this frame one can separate direct heat transfer at liquid vapor interface and wall heat transfer with nucleate boiling Interface Steam Water transfers In this part a two phase liquid vapor flow is supposed The liquid phase is located by index 1 and the vapor phase by index 2 In this mo
160. stem for Emergency Operation project is an evolution of the Thermal Valve concept project where the triggering valve is installed liquid side on a line connecting two pools at the bottom The valve is closed during normal operation In emergency conditions the valve is opened the heat exchanger is flooded with con sequent heat transfer from the primary side to the pool side In this work two main experimental PERSEO tests are studied computationally by coupling the monodimen sional system code CATHARE which reproduces the system scale behaviour with a three dimensional CFD code NEPTUNE _CFD allowing a full investigation of the pools and the injector and for code validation purposes The coupling between the two codes is realized through the boundary conditions Chapter 1 The CATHARE Code The Code for Analysis of Thermal Hydraulics during an Accident of Reactor and Safety Evaluation CATHARE is a system code developed to perform best estimate calcula tions of a pressurized water reactor PWR This code is the result of a joint effort of the main French reactor commercial industry for nuclear power AREVA NP the French Atomic Energy Commission CEA the French electric utility EDF and the French Nuclear Safety Institute IRSN The CATHARE team in charge of the development the assessment and the maintenance of the code is located at CEA in GRENOBLE The main objectives of the code are to perform safety analysis and analyze plant behavi
161. t contributions the system can be set in a linear and conservative form involving source written as follows P Pe Nn At ore k CPp C Pk jC A A HOI He _ Gi H H Hp c a H yet ie aE H OL wey 2 121 Qk Making sure that the derivative of water steam sources terms are negative ae lt 0 2 122 The system can be written using a matrix formalism oH SHP ai o a with SHPO al e and SHP SP e nphas nphas 2 123 M is anphas nphas positive definite matrix called the enthalpy coupling matrix Its inversion is made either by a direct method for nphas lt 5 or by a conjugated gradient method The general form of the coefficient is At M ep Sek SoC forp k 2 124 M k 1 o ae np At 2 125 Wapa OH a pk j Enthalpy implicit balance H H y 1 The following step accounts for implicit contributions of convection and diffusion and is obtained by making the difference between 2 115 and 2 121 and using 2 116 Diagonal part of source coupling is kept A a LO T ae ite a U O f n nrl o O a lom RAUK H H ar R 10 7 HP PRIM ikk lc a ait Ap SHE 2 126 THE NEPTUNE CFD CODE 57 with SH Al He Extra diagonal source coupling actualization H gt H b l The last step is obtained by making the difference between 2 115 and 2 126 and neglecting convective and diffusive double increment contributi
162. te is kept constant to 18 8 kg s till about t 4700 s and then it is set to zero when the water discharge line is closed The temperature on this boundary region is room temperature With these boundary conditions the velocity and temperature profiles of all the phases can be computed The top of Figure 5 29 shows the steam injection into the water pool In Figure 5 29 on the bottom the steam is injected above the water level There is no mixing with water and the energy is released directly to the pool surface From the pool surface the steam mixes with the air and then it goes out of the system through the boil off boundary In this case the NEPTUNE code simulates pretty well the heat exchange between the different phases 142 NEPTUNE_CFD MODELING OF PERSEO FACILITY alpha_w alpha_w 0 25 7 672e 14 7 672e 14 Figure 5 29 Steam injection above the water level 5 4 The OP injector three dimensional model In order to improve the investigation within the Overall Pool and to better understand what happens inside the injector and the pool a 3D simulation of the system is per formed 31 In the next sections the results obtained by simulating the Overall Pool and the injector system on three hexahedral meshes with different geometry are pre sented 5 4 1 Results obtained for the test 9 Case 1 Real geometry Be v wane an AE i HAH RENN Eps geal nitty TH lt UA AWW WAN SANG
163. th of the following one 2a Leal 15 pQ Agtof Jraitg where a is the liquid thermal diffusivity f is the bubble departure frequency tg 2 57 1 fq is the time fraction during which quenching occurs The use of a pure convective process to model quenching is not well established since the external convective heat flux often has a time scale comparable to it The vaporization heat flux is assumed to be proportional to the volume V of the bubble pe fVopo H3 H7 n 2 58 where H7 and Hf are the enthalpy jumps defined in 2 1 1 H7 Hgo H3 He _42 The volume of a bubble is D3 V 2 o 2 59 It means that the net heat flux used to form vapor is supposed to arise from the wall This approximation is well adapted for subcooled boiling while for saturated boiling energy is also received at the upper part of the bubbles Figure 2 2 shows the boiling heat flux scheme of Kurul amp Podowski Provided coherent closure relations for n Dm f and tg are given and the radius remax is estimated we have a closed model of the on off boiling conditions associated with a given heat flux The density of active sites 44 THE NEPTUNE CFD CODE Single Phase Evaporative Quenching Heat Flux Heat Flux Heat Flux Qi Qi Q yes se ah oae I Ae Nees Na Ps a Fi a YL VEEL EEE AA hea Figure 2 2 Boiling heat flux at the wall is nm 210 Twatt N T 2 60 4g p1 p2 1 e 2 61
164. the trace ability of the calculations the files and directories placed in the directory RESU are given a suffix identifying the calculation start date and time by a ten digit number two digits each for year month day hours minutes In the standard cases RESU directory contains the files suiava for the calculation restart compil log giving a compilation report resume giving information including machine type and code version list ing reporting on the kernel run listenv pre reporting on the Enveloppe run during 62 THE NEPTUNE CFD CODE pre processing listenv post reporting on the Enveloppe run during post processing param copy of the settings file param used for the calculation and runcase copy of the launch script Finally the RESU directory contains the following directories CHR ENSIGHT containing the post processing files in EnSight format default op tion MED containing the post processing files in MED format if requested by the user SRC containing the user routines taken into account and HIST containing individual log files These files record the monitoring over time of certain certain vari ables at certain points defined by the user called probes The SCRIPT Directory contains the calculation launch script runcase Before running the case it is necessary to copy the meshes to the directory MESH to generate the settings file param using the EDAMOxX interface and to adapt the User Fortran
165. tion of time oaoa aa 135 5 18 Steam mass flowrate to overall pool over the time interval 500 3000 s defined from CATHARE simulation 0 0 136 5 19 Water mass flowrate to HX pool and water discharge mass flowrate over the time interval 500 3000 s defined from CATHARE simulation 136 5 20 Steam entering the injector right and injection of steam into water left 137 5 21 Steam and water mixing right and inverse flow left 137 5 22 Temperature of the probes TP6 red and TP8 green from experiment and NEPTUNE computation blue and violet and zoom of the tempera CULE OSciMABONS Sesi k Giese Geto Pana whe ne ane BR Wee dha a ee 138 5 23 Steam mass flowrate to overall pool over the time interval 3200 4200 s defined from CATHARE simulation 500500 139 5 24 Water mass flowrate to the HX pool and water discharge mass flowrate over the time interval 3200 4200 s defined from CATHARE simulation 139 5 25 Extended water temperature distribution in boiling pool 140 5 26 Steam injection on boiling pool right and steam release to the water Surtace left he iea whe A wee aaa ee Rg Ae a op ov 140 5 27 Steam mass flowrate to overall pool over the time interval 4200 7700 s defined from CATHARE simulation 0 0 141 5 28 Water mass flowrate to the HX pool and water discharge mass flowrate over the time interval 4200 7700 s defined from CATHARE simulation 14
166. tions 2 137 so as to make appear the volume conservation criterion nphas j ij nphas l al At ary SPU 1 9 tl mop splil 32 142 rape eee eres r ef Pk Oka gr OP k 1 Pk k Pk k 1 Pk 60 THE NEPTUNE CFD CODE 1 nphas l nphas mal Yat of 2 143 k 1 k 1 equal to 1 The Alpha Pressure Energy cycle stops after the mass conservation sub step when the volume conservation holds It is possible to adapt the criterion parameter but this one remains very severe aS it applies toa maximum value over the whole domain j m 1 I 2 144 IENCEL 7 ak D lt Svor The standard value of eyo is 107 2 3 The NEPTUNE data param file and user routines 2 3 1 NEPTUNE data structure of the code StudyName x POST REPORT Case1 CaseN pnm tmp directory Figure 2 3 Tree structure of a case study NEPTUNE requires a specific structure for the configuration and input files Figure 2 3 shows this structure Each simulation is denoted as case It is possible to create a studyName directory where all the NEPTUNE simulations are performed Inside this directory each case will have its own directory for example case1 case2 and there must be a MESH directory where all the meshes are stored Also inside each case direc tory four sub directories are required to run the code The utility buildcase_nept is used to b
167. uild the tree structure of the study The syntax of the command line is buildcase_nept study casel This generates the correct directory structure as shown in Figure 2 3 THE NEPTUNE CFD CODE 61 edamox Figure 2 4 NEPTUNE GUI interface Edamox When the study has been generated new cases can be added by running the follow ing command from the study base directory buildcase_nept case casel During the execution NEPTUNE will generate some temporary files that are by de fault stored in the tmp_NEPTUNE directory in the user directory This directory must be periodically cleaned by hands there is no automatic procedure The MESH directory contains the mesh es necessary for the study The mesh formats accepted with the use of Enveloppe module are the DEAK Universal extension unv and the MED 2 3 extension med If Enveloppe is not used only binary or ASCII Common Solver format is accepted The POST directory contains any post processing programs The REPORT directory is intended to contain a spreadsheet or a report on the study The SRC directory contains a sub directory USERS in which there are all the user Fortran routines necessary for the case and it is possible to create other routines The DATA directory contains the data file param generated by the EDAMOxX graphic user interface and also any file suiamo used for calculation restart The RESU directory contains the results of the NEPTUNE_CFD runs To aid
168. uperheated steam due to the HX radiation is contained in the upper part and sub cooled water in the lower one After the HX Pool flooding and water boiling all tem perature stabilize around 103 5 C corresponding to the saturation at the pressure in the pool Steam accelerated into the Overall Pool by the Injector promotes the water circulation and mixing until the Overall Pool decreasing is accelerated and the Injector outlet uncovered The Overall Pool temperatures are shown in Figure 3 24 Chapter 4 CATHARE Modeling of PERSEO facility A complete assessment of the reliability and efficiency of the PERSEO innovative sys tem requires a numerical analysis of the overall plant response to selected accidental scenarios Industrial system codes like CATHARE are suitable to this purpose Within the frame of the research program a benchmark approach has been adopted for the numerical analysis detailed models of the PERSEO facility have been developed with the the last V2 5 mod8 1 version of CATHARE code and widely utilized for the design support and the pre test analysis Finally the post test analysis has allowed an accurate assessment of such models verification of the set of closure relationships heat trans fer in condensation and pool boiling conditions direct contact condensation etc and qualification of the nodalization 27 4 1 The CATHARE model The Figure 4 1 shows the CATHARE nodalization scheme of the PERSEO facility In
169. v F definition of initial conditions usdrag F drag coefficient calculation ustsht F water and steam total enthalpy source uslift F lift coefficient calculation ustsns F generic momentum source terms ustssp F passive scalar source terms ustrmv F mass source terms transfer or not usth12 F source terms for energy transfer between two phases usmaaj F added mass force ushsig F interface enthalpy model uskpdc F head losses zones uspors F zones of porosity Table 2 4 User routines During the definition of the param file it is possible to add user Fortran routines to specify laws boundary conditions or property of the case study that are missing in the param file These user routines are contained in the USERS folder within the SRC directory When a user wants to modify a routine it must to copy this routine in the directory SRC The available user routines are the defined in Table 2 4 66 THE NEPTUNE CFD CODE 2 4 Aparan file for standard boiling flow in a rectangular chan nel with constant bubbles diameter 0 01 m gt 4 ro o 3 QZ 4ApmMmMI 9g Figure 2 6 Geometry and mesh of the channel In this section an example of param file is presented step by step The case analyzed is the standard boiling flow with constant bubble diameter The geometry and the mesh chosen are shown in Figure 2 6 First it is necessary to cr
170. velocity between phases 1 and p expressed in terms of the total relative mean velocity and a drifting velocity v due to the correlation between the instantaneous distribution of dispersed particles and the turbulence struc ture of the carrier fluid Note that the laminar contribution only takes the laminar part of the relative velocity Up U1 CZ is the added mass coefficient between phases 1 and p and dV dt the relative acceleration symmetrically handled as avi u Bis e 2 23 a dt dt de dt Lj dx j Finally L is the lift coefficient Drag closure law The closure law for the drag coefficient F is not general and has to be adapted to the simulated flow Several choices are however proposed In the case of isolated diluted spherical inclusions such as bubbles droplets or solid particles p represents the dispersed phase and 1 the continuous phase The drag coef ficient is written in terms of the particle drag relaxation time scale 24 1 1 P1 3Cp pip Pe lt V gt Cp J1 0 15Re 687 24 a1 a TE Pp4 dp Tr Pp D Ree T p The particulate Reynolds number is based on the particle diameter and on the relative velocity modulus that takes into account turbulence and fluctuating velocities covari ance Ve d Rep je 1 Sa ee by 1 2 0 0 0 20 ap 28 225 In the case of separated phases used for liquid gas separated flows this Simmer like model considers either
171. w is considered lami nar Sk Skla Ui P with 1 number of phases is the external source terms such as head losses for instance resistance forces due to porous medium and Us is the interface velocity between phases p and k I p 1 a k i T PU represents the average interface momentum transfer rate from phase p to phase k that accounts for mass transfer drag force added mass force lift etc and complies with the local balance equations Lip sk Lin p 0 2 9 T is the part of the interface momentum transfer rate that remains after substitution of the mass transfer contribution The non conservative form is obtained after decomposition of the non stationary term with respect to the mass balance equation and dividing by the volumetric fraction The result is the following an PKU KR Uk j 1 Uki Uki k ki Qk Ox Pk oe THE NEPTUNE CFD CODE 35 1 OP a Dns ORT 2g DES ary PRG y a Ski 2 10 J p k with eae Tooni Wg 2 11 Energy equations For the total enthalpy variable 1 P Hy ek a 2 12 2 Pk The energy equations in conservative form is written anpe Hr oror HUn Bp Or khk Bn QkPklikUk j OP Laps OUT Dn CHES Ok T ak PkUk igi Mk Pwall gt k D Leah Ukil 2 13 pFk with Qk AkxTk and Ax the thermal conductivity containing both molecular and tur bulent contributions Y wat represents the heat exchanges with boundaries
172. y of the flow going up outside the injector is U2 74 55 m s As a consequence the radial component of the velocity reaches its highest value right below the end of the injector wall The water temperature field evolution in the time interval 200 6 s lt t lt 243 36 s is presented in Figure 5 40 together with the corresponding water volume fraction It can be seen how the high temperature region below the injector does not extend far be low the water steam front On the contrary a possible temperature stratification due NEPTUNE_CFD MODELING OF PERSEO FACILITY 151 a f TTE Figure 5 38 DANY PIANTAN W TURN ahh NAY fit PH i E ii liii tapos Water volume fraction top and condensation rate bottom for the ge ometry with a straight injector and a modified position of the injector nozzle at times t 200 6 202 97 205 52 s left to right U2Z m 9 74 652 188 135 i Figure 5 39 Vertical left and radial right steam velocity components on the vertical section through the injector axis at x 2 75m and time t 200 6 s for the geometry with a straight injector and a modified position of the injector nozzle 152 NEPTUNE_CFD MODELING OF PERSEO FACILITY Figure 5 40 Water temperature left and volume fraction right on the vertical sections through the injector axis at x 2 75 m and y 2 75 m and times in the range 200 6 s lt t lt 243 36 s for the geometry with a straight in
173. zle the upper surface of this volume With this modification the pressure fluctuations in side the injector which are due to the prompt condensation of the steam are greatly reduced With the repositioning of the injector in the center of the domain the change in the geometry is not negligible and this has an impact on the comparability between numerical and experimental data but it allows to create a single mesh inside the pool without non conforming junctions or sudden changes in the grid size Furthermore it removes the presence of small size cells and the smaller grid dimension is now the in jector wall thickness The grid has now 32250 hexahedral cells and with these changes larger time steps are now possible removing in this way a possible source of insta bility The simulation has been performed with a variable time step which is deter mined by several stability coefficients CFL CF La Fourier It should be remarked that the stability limit of these coefficients was not constant during the simulation At the very beginning when the steam mass flowrate at the inlet Qsteam lt 3 kg s the sys tem undergoes very large fluctuations the steam condensation takes place inside the injector until the pressure in the injection system is high enough to push the water out of the injector This fluctuating behavior can be seen in Figure 5 37 where the water volume fraction and the steam condensation rate are both shown in the time interval 12

validation of the cfd code neptune for a full scale simulator for decay

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