BOILING FLOW SIMULATION IN NEPTUNE_CFD AND FLUENT CODES. L. Vyskocil, J. Macek

Transcription

1 BOILING FLOW SIMULATION IN NEPTUNE_CFD AND FLUENT CODES L. Vyskoci, J. Macek Nucear Research Institute Rez (NRI), Dept. of Therma Hydrauic Anayses, Rez, Czech Repubic Abstract This paper presents simuations of the conectie boiing fow performed with NEPTUNE_CFD and FLUENT codes. The DEBORA experiments carried out at CEA Grenobe were used as an experimenta data set. In these experiments, freon R12 fows upwards inside a ertica pipe. Radia profies of the fow ariabes are measured at the end of the heated section. Seen DEBORA cases were seected for simuation. NEPTUNE_CFD code was used without modifications because it contains a necessary modes. In FLUENT, an important part of the modes has been impemented by programming in User Defined Functions. The comparison of the radia profies of oid fraction, iquid temperature, gas eocity and mean bubbe diameter at the end of the heated section shows that both codes can proide reasonabe resuts in boiing conditions. The presented work was carried out within the 6 th Framework EC NURESIM project. NEPTUNE_CFD code is impemented in the NURESIM patform. 1. INTRODUCTION The conectie subcooed boiing occurs when the heated was are superheated whie the iquid buk is subcooed at a gien operating pressure. Such a regime may occur in Pressurized Water and Boiing Water Reactors. This phenomenon can be predicted by the mechanistic boiing mode of Kuru and Podowski (1990) deeoped at Rensseaer Poytechnic Institute. This mode is impemented in NEPTUNE CFD code (Laieie, 2005a,b). A simiar boiing mode was impemented in CFD code FLUENT 6 (ref. FLUENT, 2003) by programming in User Defined Functions. These two codes were used to simuate the two-phase boiing fow. The DEBORA experiments (Manon, 2000; Garnier, 2001; Bestion 2006) carried out at CEA Grenobe were used as an experimenta data set. This paper is organized as foows: chapter 2 deas with the boiing mode, as impemented in FLUENT; in chapter 3, seected DEBORA experimenta cases are presented; chapter 4 describes soer settings used in NEPTUNE_CFD and FLUENT cacuations. The numerica resuts and a comparison with the experimenta data are shown in Chapter NUCLEATE BOILING MODEL This chapter describes the boiing mode, which was impemented in FLUENT 6 code using User Defined Functions. The aim of the presented mode is to simuate the onset of nuceate boiing, partitioning of wa heat fux and interfacia iquid-apour heat, momentum and mass transfer. A ery simiar boiing mode is incuded in NEPTUNE_CFD code. The nuceate boiing mode was deeoped for the appication in the Euerian mutiphase mode. Two phases are modeed: the primary phase is iquid and the secondary is apour bubbes. The same pressure is shared by the two phases. Continuity, momentum and energy equations are soed for each phase. The reaizabe k-ε turbuence modes appy to the indiidua phases. The distribution of the mean bubbe diameter in the fow is modeed using a one-group interfacia area transport equation. 2.1 Onset of Nuceate Boiing When the wa becomes superheated, apour bubbes can form een when the core iquid is sti subcooed. The position where the first bubbes occur at the wa is denoted as the onset of nuceate boiing. In our cacuations, Hsu s criterion is used to determine this position (Laieie, 2005b). 1

2 According to this criterion, a bubbe wi grow from a apour embryo occupying a caity in the wa if the iquid temperature at the tip of the embryo is at east equa to the saturation temperature corresponding to the bubbe pressure. 2.2 Wa Heat Fux Partitioning Mode The heat fux partitioning mode of Kuru and Podowski (1990) (see aso Yao, More 2004) has the foowing structure: Downstream of the onset of nuceate boiing, the wa heat fux q wa is spit into three parts: 2 q = q + q q W / m (1) wa f q + e [ ] The first part is the singe-phase heat transfer (conectie heat fux): q f = A 1 α wafcn ( Twa T ) (2) A1 = 1 A 2 (3) A 1 is the fraction of the wa surface infuenced by iquid, fraction A 2 is infuenced by apour bubbes formed on the wa, T is the iquid temperature at the centre of the wa adjacent ce, α wafcn is the wa heat transfer coefficient cacuated from the temperature wa function. The quenching part q q of the heat fux q wa is transported by the transient conduction during the time period between the bubbe departure and the next bubbe formation at the same nuceation site. qq = A 2 α quench ( Twa T ) (4) α quench is the quenching heat transfer coefficient (17). The heat fux q e is spent for eaporation of the iquid: q e = m& eh at (5) m& e is the eaporation mass transfer per unit wa area (15), H at is atent heat. The mode assumes that the diameter of the area infuenced by a singe bubbe is as arge as the bubbe departure diameter d w : 2 π d w n A = 2 min, 1 (6) 4 n is the actie nuceation site density. Actie nuceation site density is correated to the wa superheat: n = ( 210 ( Twa Tsat )) 2 m (7) Bubbe departure diameter d w is cacuated from Üna correation (Üna, 1976): a d w = p [ m] (8) bφ where p is pressure [Pa], ( Tw Tsat ) λs a = (9) 2ρ H πa at s a s is therma diffusiity and λ s is the therma conductiity of the soid wa Tsat T b = for St < ρ ρ ( ) ( ρ ρ ) = qwa b for ρ c U St where: p (10) (11) 2

3 St wa = (Stanton number) (12) ρ c p U q ( T T ) sat U is the iquid eocity magnitude at the wa adjacent ce 0.47 U φ = max 1, (13) 0.61 When T >T sat, buk boiing is initiated. In order to cacuate the eaporation rate m& e, the bubbe detachment frequency f is determined from the foowing equation: 4 g ( ρ ρ ) 1 f = 3 d s (14) w ρ The eaporation rate is the product of bubbe mass, detachment frequency and the actie nuceation site density: 3 π d w kg m& e = ρ f n 2 6 m s (15) The quenching heat transfer coefficient α quench depends on the waiting time between the bubbe departure and the next bubbe formation. This waiting time t w is fixed to the bubbe detachment period: 1 t w = [ s] (16) f tw W α quench = 2 λ f a 2 π m K (17) where a is the therma diffusiity of the iquid. The presented system of equations (1) (17) is cosed, but it cannot be soed expicity. The numerica method of bisectors (Neustupa, 1995) is used to soe this system. 2.3 Interfacia Momentum Transfer The interfacia momentum transfer can be diided into four parts: drag, irtua mass force, ift and turbuent dispersion (Lance, Lopez de Bertodano, 1994, Yao, More 2002, 2004). The interfacia drag force is cacuated as: r D r D α r r r r M = M = 0.75 ρcd V V ( V V ) (18) db d b is the Sauter mean bubbe diameter cacuated from the interfacia area transport equation, the drag coefficient c D is gien by Ishii (1979). The ift force is cacuated as: r L r L r r r M = M = clα ρ ( V V ) ( V ) (19) The ift coefficient c L is cacuated from the correation proposed by Moraga (1999). In this correation, the ift coefficient is cacuated from the product of the bubbe Reynods number and the bubbe shear Reynods number. The ift coefficient combines the action of the two opposing forces: 1. the cassica aerodynamic ift force that resuts from interaction between the bubbe and the iquid shear positie infuence on c L. 2. the interaction between the bubbe and ortices shed by the bubbe wake negatie infuence on c L 3

4 The irtua mass force is gien by: r r r VM r VM V r r V r r M = M = cvmα ρ + V V + V V (20) t t The irtua mass force coefficient is c VM = 0.5. The turbuent dispersion force is gien by: TD TD M = M = ctd ρ k α (21) The turbuent dispersion coefficient is set to c TD = 1 (Troshko 2003, 2007). k is the turbuence kinetic energy of the iquid. 2.4 Interfacia Heat Transfer Interface to iquid heat transfer (used from Yao 2002): 3 Qi = hi ai ( Tsat T ) [ W / m ] (22) The heat transfer coefficient h i is: λ W hi = Nu d m K (23) 2 b d b is the Sauter mean bubbe diameter. The oumetric interfacia area a i is gien by: 6α 1 ai = d m b (24) In the case of condensation (Ja<0), the Nusset number Nu is cacuated from: Nu = Re Pr (25) d b V Re = re ν (26) Pr is the Prandt number of the iquid, V re is the magnitude of the reatie eocity between phases, ν is the kinematic iscosity of the iquid. ρ cp, ( T Tsat ) Ja = (Jakob number) (27) ρ H at In the case of eaporation the Nusset number is gien by: 4Pe 12 Nu = max, Ja, 2 (28) π π db Vre Pe = (Pécet number) (29) a a is the iquid therma diffusiity. Interface to apour heat transfer: Interface to apour heat transfer is cacuated using the time-step return to saturation method. It is assumed that the apour retains the saturation temperature by rapid eaporation/condensation. α ρcp, W Qi = ( Tsat T ) 3 δt m (30) δt is the time step, c P, is the isobaric heat capacity of the apour. The interfacia mass transfer depends directy on the interfacia heat transfer. 4

5 2.5 Interfacia Area Transport The Sauter mean bubbe diameter distribution in fow was cacuated from the interfacia area concentration. One group interfacia area concentration equation with modes for coaescence and break-up (Yao and More, 2004; More, Yao, Bestion, 2003, More 2007) is used to describe the eoution of the interfacia area concentration. A user-defined scaar equation is used to mode the transport of the interfacia area in FLUENT. 3. SELECTED DEBORA TEST CASES The boiing mode was tested against DEBORA experiments carried out at the CEA (Manon, 2000; Garnier, 2001). The DEBORA experiment is a ertica heated pipe with Freon R12 fowing upwards. At the tube inet, R12 is a subcooed iquid. The refrigerant is heated as it fows upwards and apour bubbes are created on the wa surface. These bubbes break away from the wa and are dispersed in the turbuent fow. The bubbes condense party in the core region of the tube. The interna diameter of the pipe is 19.2mm. The whoe pipe can be diided into three sections: the inet adiabatic section 1m ong, the heated section 3.5m ong and the outet adiabatic section 0.5m ong. The oid fraction, apour eocity, the mean bubbe diameter and interfacia area profies were measured at the end of the heated section. Unfortunatey, in this test series iquid temperature profies were not measured. Tabe 1: Seected DEBORA test cases Case Test pressure mass fux q w T inet T sat x eq No. bar kg/m 2 /s W/m 2 C C G1P30W12Te52.7_ G1P30W12Te58.4_ G1P30W12Te63.6_ G1P30W12Te68.1_ G1P30W12Te70.4_ G1P30W12Te72.9_ G1P30W12Te74_ q w is the wa heat fux, x eq is the outet equiibrium apour quaity. 4. CALCULATIONS IN NEPTUNE AND FLUENT 4.1 NEPTUNE Soer Settings Turbuence: k-epsion iq mode for iquid, aminar fow of apour. Interface momentum transfer: drag by Ishii, added mass by Zuber, no ift (ift force caused conergence troubes) The turbuent dispersion force is based on the oid fraction gradient see eq. (21), the turbuent dispersion coefficient was set to c TD =2.5. This aue was taken from ref. Yao (2002), note that this is a different aue than that used in FLUENT cacuations (c DT = 1). If c DT = 2.5 is used in FLUENT it spois the resuts it oerestimates mixing. On the other hand, if c DT = 1 is used in NEPTUNE, it proides insufficient mixing. Wa-fuid heat transfer: Grenobe modes (no superheating of the apour, same modes as in chapter 2.2) Interface heat transfer: Grenobe modes for iquid and apour (same modes as in chapter 2.4) 5

6 Physica properties of fuid R12: CATHARE tabes. The partice diameter was cacuated from the interfacia area concentration, Yao (2002) mode was used for coaescence and fragmentation. NEPTUNE ersion: FLUENT Soer Settings Modes used in FLUENT cacuations were described in chapter 2. Soer: segregated, 1st order impicit unsteady formuation, Euerian mutiphase mode. Turbuence: reaizabe k-epsion mode soed per phase Discretisation: second-order upwind for conection terms in a equations except for the user defined scaar, user-defined scaar equation: first order upwind (used for cacuating the interfacia area) Physica properties of fuid R12: piecewise-inear profies based on NIST Chemistry WebBook. FLUENT ersion Main Differences Between NEPTUNE and FLUENT Cacuations turbuence modes ift force turbuent dispersion coefficient physica properties of fuid R Computationa Grid The case is axisymmetric, a 10 wedge confined with symmetry cutting panes is used to mode the pipe. Grid Resoution: radius: 14 interas axia direction: 200 interas - inet section (1m ong) 700 interas - heated section (3.5m ong) 100 interas - outet section (0.5m ong) Wedge ces in the centre of the pipe are incuded in the grid for FLUENT (Fig. 1), whie in NEPTUNE they had to be omitted and repaced with a sma symmetry cutting pane (because of conergence troubes). Fig. 1 Computationa Grid Note: A grid independence test was performed see chapter

7 5. RESULTS The foowing figures show the radia profies at the end of the heated section. Fig. 2 Resuts: Case 1 T in = C, x eq = Note: Diameter D g corresponds to an equiaent two-phase fow (keeping the bubbe centre density and the interfacia area density) where a the bubbes are assumed to hae the same diameter, see Manon (2000). Fig. 3 Resuts: Case 2 T in = C, x eq =

8 Fig. 4 Resuts: Case 3 T in = C, x eq = Fig. 5 Resuts: Case 4 T in = C, x eq =

9 Fig. 6 Resuts: Case 5 T in = C, x eq = Fig. 7 Resuts: Case 6 T in = C, x eq =

10 Fig. 8 Resuts: Case 7 T in = 73.7 C, x eq = (cose to DNB) 5.1 Probem oerestimated bubbe diameter in FLUENT cacuations The turbuence mode in FLUENT proides a ower epsion in the core of the fow than NEPTUNE. The coaescence and break-up terms in Yao s interfacia area transport mode depend on epsion. A ower epsion causes exaggerated coaescence and decrease of break-up in the duct centre, which in turn eads to oerestimated bubbe diameter. This probem can be seen in Fig. 5 - Fig. 8. Attempt to soe this probem in FLUENT: The coaescence and break-up terms use the function max(epsion,0.13m 2 /s 3 ) instead of epsion. The foowing figures compare the resuts obtained with this modification and without this modification. Fig. 9 Resuts - Case 7: modification of the coaescence and break-up mode in FLUENT can proide more reaistic aues of bubbe diameter in the duct centre The infuence of this modification on the iquid temperature and apour eocity profie is not so marked. 10

11 5.2 Grid Independence Test Fig. 10 Case 4 FLUENT: grid independence test From the aboe figure it can be seen that the origina grid is fine enough and grid refinement does not improe the resuts of FLUENT cacuations. Grid independence was aso tested in NEPTUNE with the same concusion. Note: The modified coaescence and break-up mode from the preious page was used in these cacuations. 6. CONCLUSIONS The capabiity of CFD codes to simuate conectie boiing fow in a ertica tube has been demonstrated. Seen DEBORA tests hae been simuated with NEPTUNE_CFD and FLUENT codes. In these cases, the equiibrium outet apour quaity ranges from to (cose to DNB). The interfacia area transport was modeed in both codes. The main differences in the modeing used with the two codes were as foows: turbuence modes, the turbuent dispersion coefficient, ift force and the physica properties of fuid R12. An important part of the modes has been impemented in FLUENT by programming in User Defined Functions. FLUENT and NEPTUNE CFD codes proided comparabe resuts. Reasonabe agreement with experimenta data was obtained. In tests with a higher inet temperature NEPTUNE oerestimates the oid fraction in the core of the fow whie Fuent oerestimates the oid fraction near the wa. NEPTUNE sighty underestimates the mean bubbe diameter. If Yao s interfacia area mode is used in FLUENT, it causes oerestimation of the bubbe diameter in the duct centre, this probem coud be soed by modifying the epsion aues used by Yao s mode. In the ast case cose to DNB, a sudden rise of a oid fraction cose to the wa was obsered in the experiment. Whie the maximum aue of the oid fraction at the wa was captured we by the two codes, the shape of the oid fraction peak near the wa was not reproduced in either of the codes. In the near-wa region, the cacuated oid fraction profies are more mixed than the experimenta profie. 11

12 It is interesting that to obtain the best resuts, different turbuent dispersion coefficients had to be used in the two codes. REFERENCES Bestion, D., Caraghiaur, D., Angart, H., Péturaud, P., Krepper, E., Prasser, H M., Lucas, D., Andreani M., Smith B., Mazzini D., Moretti F., Macek J.: Deierabe D2.2.1: Reiew of the Existing Data Basis for the Vaidation of Modes for CHF, NURESIM SP2 Deierabe (2006). Garnier J., Manon E., Cubizoes G.: Loca measurement on fow boiing of Refrigerant 12 in a ertica tube, Mutiphase Science and Technoogy, Vo.13, pp.1-58 (2001). Ishii, M., Zuber, N.: Drag coefficient and reatie eocity in bubby, dropet or particuate fows, AIChE Journa Vo.25, No.5, pp (1979) Kuru, N., Podowski, M.Z.: Mutidimensiona Effects in Forced Conection Subcooed Boiing, Proceedings of the 9 th Internationa Heat Transfer Conference, Jerusaem, Israe, August (1990) Lance M., Lopez de Bertodano M.: Phase distribution phenomena and wa effects in bubby two-phase fows, Mutiphase Science and Technoogy 8, pp (1994) Laieie, J., Quemerais, E., Boucker, M., Maas, L.: NEPTUNE CFD V1.0 User Guide (Draft), EDF (2005a). Laieie, J., Quemerais, E., Mimouni, S., Boucker, M., Mechitoua, N.: NEPTUNE CFD V1.0 Theory Manua, EDF (2005b). Manon, E.: Contribution a 'anayse et a a modéisation ocae des écouements bouiants soussaturés dans es conditions des réacteurs a eau sous pression. These de Doctorat. Ecoe Centrae Paris (2000). Moraga, F.J., Bonetto, F.J., Lahey, R.T.: Latera forces on spheres in turbuent uniform shear fow, Int. J. Mutiphase Fow 25, pp , (1999). More, C., Yao, W., Bestion, D.: Three Dimensiona Modeing of Boiing Fow for the NEPTUNE Code, NURETH-10, Seou, Korea, October 5-9 (2003). More C.: Deierabe D : Vaidation of NURESIM CFD against DEBORA tests cose to CHF conditions, NURESIM SP2 Deierabe (2007). Neustupa, J.: Matematika 1, Czech Technica Uniersity In Prague (1995). Troshko A.: Impementation and Testing of Subcooed Boiing Mode, Fuent Technica Notes, TN228, Fuent.Inc (2003). Troshko A., Schowater D., Guetari Ch.: CFD Vaidation Benchmark of Subcooed Nuceate Boiing Under Near Saturation Conditions, NURETH-12, Pittsburgh, PA, USA, Sept 30-Oct 4 (2007). Üna, H.C.: Maximum bubbe diameter, maximum bubbe growth time and bubbe growth rate during subcooed nuceate fow boiing of water up to 17.7MW/m 2, Int. J. Heat Mass Transfer 19, pp , (1976) Yao, W., More, C.: Prediction of Parameters Distribution of Upward Boiing Two-Phase Fow with Two-Fuid Modes, ICONE , Apri (2002). 12

13 Yao W., More C.: Voumetric interfacia area prediction in upward bubby two-phase fow, Int. J. Heat and Mass Transfer 47, pp (2004). FLUENT 6.1 User s Guide, Fuent Inc., Lebanon NH, USA (2003). NIST Chemistry WebBook, Thermophysica Properties of Dichorodifuoromethane (R12), Nationa Institute of Standards and Technoogy, 13