Numerical Investigation of Sodium-Water Reaction Phenomenon in a Tube Bundle Configuration

Transcription

1 Proceedings of CAPP 2007 Numerical nvestigation of Sodium-Water Reaction Phenomenon in a Tube Bundle Configuration Takashi Takata 1, Akira Yamaguchi 1, Akihiro Uchibori 2 and Hiroyuki Ohshima 2 1 Osaka University, 2-1, Yamada, Suita, Osaka, apan 2 apan Atomic Energy Agency, 4002, Narita, O-arai, Higashi-baraki, baraki, apan Tel: , Fax: , takata_t@see.eng.osaka-u.ac.jp Abstract A numerical investigation of sodium-water reaction (SWR) phenomenon under a tube bundle configuration was carried out in order to evaluate characteristics of the reacting zone in an area nearby the leakage, such as distributions of the gas volume fraction, the temperature and the concentration of the sodium compounds, as well as to evaluate an applicability of the numerical methodology that has been developed in the previous authors work to a complicated flow path.swat-1r experiment, in which 43 tubes were placed in a zigzag alignment and water vapor leaked vertically upward from the bottom center of the bundle, was chosen as a benchmark problem. As a result of the numerical investigation, it was demonstrated that one can predict the SWR phenomenon with a complicated pin bundle configuration numerically. n addition, it was also demonstrated that numerical quantification of a secondary failure possibility due to over-heating rupture was to be achieved using the present result.. NTRODUCTON n a steam generator of sodium cooled fast reactor (SFR), a sodium-water reaction (SWR) will take place when a heat transfer tube fails and water and/or water vapor leaks into liquid sodium in the shell side. The SWR phenomena are roughly separated into four categories 1 according to the leakage rate. When the leakage rate is too small (less than 10-4 kg/s, designated as micro-leak ), the reacting zone due to the SWR only affects the failure tube itself. As a result, it was found in the previous experimental works 2 that some of the leakages were self-plugged because of the sodium compound. n the other cases, the leakage enlarges eventually by an erosion and corrosion (called selfwastage ) resulting in a transition to a larger leakage category. n the categories of small leak (10-4 to 10-2 kg/s) and intermediate leak (10-2 to a few kg/s), the reacting zone attaches directly to neighbor heat transfer tubes. Therefore, the neighbor tubes might be damaged by two occasions. One is the erosion and corrosion in a strong alkali condition (wastage) and the other is a deterioration of material due to high temperature (over-heating rupture). The difference between small leak and intermediate leak is the magnitude of the reacting zone. n other words, a single tube adjacent to the leakage is affected in small leak (one says target wastage ) and the reacting zone affects multiple tubes in intermediate leak. t is apparent that small leak and intermediate leak lead to another category of large leak (more than a few kg/s) because of a secondary failure and failure propagation mentioned above. t is commonly said that the SWR with a small leakage such as micro-leak and small leak has a relatively high probability of occurrence 3. n addition, the leakage rate can enlarge eventually in these categories. From the viewpoint of steam generator safety in SFR, it is clear that the leakage should be detected and the liquid sodium be isolated from the water immediately before it reaches to large leak category. Consequently, the secondary failure and the failure propagation have been paid much attention. Since the SWR is a complicated thermal-hydraulic phenomenon coupled with a chemical reaction and the measurement techniques in the SWR experiment is not matured well, a numerical investigation is an alternative way to deal with the characteristics of the reacting zone

2 Proceedings of CAPP 2007 such a distribution of temperature, gas volume fraction and chemical species near the neighbor tubes and to predict a possibility of secondary failure. For this purpose, the authors have developed the numerical methodology for the SWR 4,5 and investigated the characteristics of the heating zone with a simple configuration in which a free jet of water vapor leakage into liquid sodium has been considered 6. n the present paper, a numerical investigation of the SWR under a pin bundle configuration has been carried out in order to evaluate an applicability of the developed methodology to a complicated flow pass. SWAT-1R experiment 7 is chosen as a benchmark problem for this purpose. Additionally, the characteristics of the reacting zone near neighbor tubes have been also investigated.. SUMMARY OF NUMERCAL METHODOLOGY 4-6 The developed numerical methodology for the SWR is introduced briefly in the following. Liquid sodium, water and multi-component gas are taken into consideration as a working fluid. Multi-fluid and one pressure model are applied for a multi-phase thermal-hydraulic analysis. The HSMAC method is used for numerical solution and is extended to a compressible multi-phase flow analysis. Bubbly-flow-based constitutive equations are employed for the multi-fluid model from the aspect that a bubbly flow region represents a high contact area between the phases compared with the other flow region map and thus leads to a more intense chemical reaction. With regard to the SWR model, two models have been developed. One is the surface reaction model in which the water vapor reaches the liquid sodium surface directly. Hence, the SWR takes place at the surface between the liquid sodium and the water vapor. An analogy between a heat transfer and a mass transfer is assumed to estimate the reaction rate. When liquid sodium evaporates vigorously due to reaction heat, gas phase sodium reacts with water vapor. This is designated as the gas-phase reaction. The reaction rate of the gas-phase model is obtained base on the Arrhenius law.. SWAT-1R EXPERMENT 7 Figure 1 shows the test apparatus of the SWAT-1R. The test apparatus consists of a double cylindrical vessel. n the experiment, liquid sodium was fed from the bottom of the outer vessel and also fed into the inner vessel through three holes placed at the bottom of the inner vessel as shown in Fig. 1. Argon gas was put into the upper side of the test apparatus so as to suppress a pressure increase due to the SWR. During the experiment, no forced convection was embedded to the liquid sodium. The target leakage rate was set to 0.15kg/s ( intermediate leak category mentioned in the ntroduction). nside the inner vessel, a pin bundle of 43 straight tubes, which alignment was same as apanese prototype fast breeder reactor Monju but rotated by an angle of 24º, was implemented. Figure 2 depicts the test section of the pin bundle. An opening of 3.7mm was placed on the upper side of one tube located at the bottom end of the bundle (gray colored tube in Fig. 2) and water vapor of approximately 17.0MPa and 625 was blown down vertically upward from the leakage. Liquid sodium Water vapor feeding line (for leakage) Support 31.8 Liquid sodium feeding line (for dummy tube cooling) Test section (tube bundle) 1800 A A AA Openings º 630 Failed tube Dummy tube (with heat removing) Dummy tube Leak direction (unit: mm) 50 Fig. 1 Test apparatus of SWAT-1R Fig. 2 Pin bundle section

3 Proceedings of CAPP 2007 A dozen of thermocouples were installed at a certain place and temperature was measured mainly during the experiment in order to observe the temperature distribution in the reacting zone. n addition, some thermocouples were implanted into tubes adjacent to the leakage so that the heat transfer coefficients on the tube outer surface under the SWR configuration were evaluated. Liquid sodium was flown inside of one tube (hatched tube in Fig. 2) during the experiment in order to reproduce a heat exchange with water in the actual system. Both ends of the other tubes were opened and liquid sodium was filled through the openings. t is noted that the skewed bundle configuration was adopted in the experiment because of the spatial limitation in the test section. The angle of 24º was chosen so as to maximize the influence of the reacting zone on the neighbor tubes based on the previous observation 8. The actual image of leakage direction is indicated in Fig º Fig. 3 Actual image of leakage direction V. NUMERCAL NVESTGATON V.A. Computational Condition n the computation, the inside of the inner vessel from the bottom of the vessel including three holes to the liquid sodium surface is selected as an analytical region. Hence, the size of the analytical region is 400mm in diameter and 1800mm in height (see Fig. 1). The structural mesh with the Cartesian coordinates is adopted and is divided into Fig. 4 Analytical geometry 122() 63 () 172 () as shown in Fig. 4. The total number of mesh is approximately 1.3 million. As concerns the boundary condition, the constant pressure condition is applied to both the upper end boundary which corresponds to the liquid sodium surface and the leakage. Hence, the leakage rate is computed in the present study by solving the governing equations of the mass, the momentum and the energy at the boundary. Since the bottom end boundary (three holes) is placed comparatively near the leakage and it is expected that liquid sodium will flow into the analytical region through the boundary, a continuity of the pressure gradient ( 2 P/ z 2 =0) is assumed. With regard to the thermal boundary condition, an adiabatic condition is assumed for simplicity. Hence, the heat capacity of the inner structure and the heat removal from the tubes are ignored. n the previous studies 5,6, it has been found that sodium hydroxide (NaOH) be a dominant product in the SWR and that the latent heat for evaporation of sodium hydroxide is considerable comparing with the reaction heat. Therefore, both liquid and gas phase sodium hydroxide and hydrogen gas are assumed to be the SWR products in the present study. The proportion of the gas phase sodium hydroxide to the liquid phase is evaluated based on the saturated vapor pressure. n addition, only the surface reaction is considered in the computation. This is attributed the fact that the reaction rate of the gas-phase TABLE Computational condition nitial conditions [Water vapor] Temperature : 625 [] Pressure at the leakage : 17.0 [MPa] Leakage size : [mm] ( 3.7mm in experiment) [Sodium] Temperature : 743 [] nitial pressure : 0.2 [MPa] Constitutive equations [Area density] Nigmatulin model (N = ) [Phase friction] Autruffe model [Wall friction] Martinelli-Nelson model [Vaporization and condensation] Silver-Simpson model Analytical conditions Mesh arrangement : Time step : 1.0 [ s] Analysis time : 0.6 [s] Sodium compounds in the surface reaction : NaOH (g) and (l)

4 Proceedings of CAPP 2007 reaction is negligible small comparing with that of the surface reaction 5. The time step and the computation duration are set to 1.0 s and 0.6s respectively. The analytical conditions and the constitutive equations applied in the present study are summarized in TABLE. As in TABLE, the Nigmatulin model 9, in which a bubbly flow is taken into account, is adopted for an estimation of interfacial area density. n the Nigmatulin model, the bubble number density per unit volume (N) should be determined. n the present analysis, the number density of is selected based on the physical properties and the previous authors investigation 6. V.B. Results and Discussion The spatial distributions of the gas volume fraction (void fraction) and the gas temperature at (a) 10ms, (b) 0.1s (100ms) and (c) 0.6s (600ms) are shown in Figs. 5 and 6 respectively. t is noted that the region where the void fraction is larger than 0.1 is pictured as a colored contour in the following figures. As in Fig. 5(a), the gas region develops spherically at the beginning of the leakage. Then it develops along the inline and the axial directions as seen in Figs. 5(b) and (c). At the end of the analysis (at 0.6s, Fig. 5(c)), the gas region almost covers up the gap space of the bundle. At that time, the gas outflows from the bundle through the inline direction. t is because a flow resistance in the inline direction is lower than the others. The white colored region, seen just above the upper end of the bundle in Fig. 5(c), means that liquid sodium is not swept out well because of the gas flow pattern. t is noted that the leakage rate in the analysis becomes constant immediately because the pressure of 17.0MPa at the leakage is set to be constant during the computation. On the other hand, a long and narrow feeding tube was implemented in the experiment (see Fig. 2). Hence, the leakage rate developed gradually in the experiment and it took several seconds to obtain the constant value. However, the developed leakage rate has an excellent agreement between the analysis (0.162kg/s) and the experiment (0.158kg/s). As concerns the high temperature region (over 1000ºC), it reaches an adjoining tube even at early stage of the analysis and is surrounding the leakage as seen in Fig. 6(a). This corresponds to the fact that the high temperature region appear just near the interface between the water vapor and the liquid sodium due to the surface reaction. As seen in Fig. 6(b) and (c), the longitudinal coverage of the high temperature region in vertical axis seems not to be changed differently. Hence, it is said that the high temperature region will develop well within a short period of time. (3mm above from leakage) (a) 10ms (b) 0.1s (100ms) (c) 0.6s (600ms) Fig. 5 Analytical result of gas volume (void) fraction

5 Proceedings of CAPP 2007 (3mm above from leakage) (a) 10ms During the analysis, almost the maximum value of approximately 1300ºC, which value agrees with the previous experimental observations 3, is predicted constantly regardless of the gas region development. The reason why the constant maximum value is predicted can be explained in the following. Figure 7 shows the volume fractions of (a) water vapor and (b) hydrogen gas in the gas phase at 10ms. Comparing Fig. 7(a) with Fig. 6(a), it is again said that the high temperature region exists just near the interface between the water vapor and the liquid sodium. At the same time, hydrogen gas that is produced at the interface covers up the interface as in Fig. 7(b). As a result, the concentration of the water vapor is lowered at the interface and the chemical reaction is moderated resulting in the constant maximum value regardless of the transient. (b) 0.1s (100ms) (3mm above from leakage) (a) Water vapor (c) 0.6s (600ms) Fig. 6 Analytical result of gas temperature (b) Hydrogen gas Fig. 7 Volume fractions in gas phase at 10ms

6 Proceedings of CAPP 2007 Another important factor for the maximum temperature is the evaporation of sodium hydroxide. Based on the thermo-chemical properties 10, the reaction heat of the surface reaction where liquid sodium reacts with water vapor and sodium hydroxide in liquid phase and hydrogen gas are produced and the latent heat for sodium hydroxide evaporation are calculated as; Na( l) H 2O( g) NaOH ( l) 1/ 2 H2, (1) 298 H k/mol. NaOH ( l) NaOH ( g), (2) 298 H k/mol. Here, (l) and (g) denote the liquid and the gas phase respectively. H 298 is the standard enthalpy change of formation and the negative value means the exothermic. As in Eqs. (1) and (2), the latent heat is considerably large and it is expected that a small amount of sodium hydroxide evaporation affects the maximum temperature. The volume fraction of the gas phase sodium hydroxide at 10ms is depicted in Fig. 8. The gas phase sodium hydroxide appears at the high temperature region (see Fig. 6(a)). t is apparent that the total heat generation is reduced by the latent heat resulting in a decrease of the maximum temperature. Figure 9 shows the comparison of the temperature distribution at the center of the bundle between the computation and the experiment. n the experiment, the average of thermocouples was taken during three seconds after the leakage rate was almost kept to be constant. On the other hand, the mass weighted mean temperature of the gas and the liquid sodium at 0.6s is drawn in case of the computational result. t is noted that the red symbols in the right side of Fig. 9 represents the locations of the thermocouples. The high temperature region develops along the inline direction both in the analysis and the experiment. The maximum value in the analysis agrees with the experimental result, whereas, the high temperature region is overestimated in the analysis. n the experiment, the reaction heat was removed from one tube (see Fig. 2) and the other tubes have a large heat capacity because liquid sodium exists inside of the tubes. On the contrary, the tubes are treated as an adiabatic in the analysis. Therefore, the overestimation of the high temperature region is obtained generally in the analysis. Consequently, it can be said that the developed methodology has an applicability to investigate a SWR phenomenon under a pin bundle configuration. With regard to the experimental results, it is also the fact that the thermocouples placed in the test section are not sufficient to depict the temperature distribution in detail. Moreover, it is difficult to estimate a temperature exactly from a thermocouple under a non-equilibrium state. As mentioned in the ntroduction, the characteristics of the reacting zone near neighbor tubes play an important role for the secondary failure caused by the over-heating rupture and the wastage. Let us discuss the transient of the characteristics near the neighbor tubes. Two locations near the outer surface of surrounding tubes are chosen for example and are placed directly above the leakage as shown in Fig. 10. Figure 11 shows the time transient of the temperature and the gas volume fraction. The red colored solid and dashed lines indicate the temperature of the gas phase and the liquid sodium respectively, whereas the blue line shows the gas volume fraction. At the position (a), the high temperature gas reaches the neighbor tube continuously in a short period of time. The liquid sodium acts as a dispread phases and a thermal non-equilibrium state is investigated in almost all of the Thermocouple (3mm above from leakage) Fig. 8 Volume fraction of gas phase sodium hydroxide at 10ms (a) Present analysis (b) Experiment Fig. 9 Comparison of mean temperature at the center of the bundle

7 Proceedings of CAPP Fig. 10 Evaluation points Failed tube computational duration. On the other hand, the gas region fully develops after approximately 0.2s at the position (b). n addition, a thermal equilibrium state is almost achieved and comparative lower temperature is predicted than that in the position (a). t might be said that the thermal equilibrium state is achieved quickly in the SWR phenomenon. t is noted that the upper limitation of the liquid sodium temperature seen at the position (a) indicates the boiling point of liquid sodium at that pressure (approximately 0.2MPa). When one takes the over-heating rupture into consideration, the quantification of heat transfer to a tube is essential rather than the evaluation of the maximum temperature near the tube. The authors have developed the quantification method of the heat transfer using onedimensional thermal-hydraulic and structural analyses based on the boundary layer approximation 11. Appling the present results shown in Fig. 11 to the quantification of the heat transfer, the possibility of the over-heating rupture is to be evaluated in a future work. Figure 12 shows the mass concentration of sodium hydroxide at each location. As concerns the tube failure due to the wastage, a caustics environment in the reacting zone is of important as well as the temperature and the velocity profiles. As in Fig. 12, the mass concentration of sodium hydroxide at the position (b) is larger compared with that at the position (a). This is because the gas density increases in accordance with the decrease of the temperature. Hence, it might be said that the higher erosive action occurs at the position (a). On the contrary, the corrosive effect will be more intense at the position (a) than (b) because of the higher temperature and the existence of the gas phase sodium hydroxide. Unfortunately, theoretical and mechanistic modeling of the wastage, in which local characteristics of the reacting zone is considered, has not been matured well. This is attributed the fact that the measurements, such as the temperature, the velocity and the mass concentration of the product, is quite difficult in an actual SWR phenomenon. Accordingly, it is said that the numerical (b) (a) Temperature [ºC] Temperature [ºC] Gas Liquid sodium Time [s] Position (a) Volume fraction of gas [-] Time [s] Position (b) Fig. 11 Transient of gas volume fraction and temperature 3.0 Concentration of NaOH [kg/m 3 ] Concentration of NaOH [kg/m 3 ] Liquid phase Gas phase Time [s] Position (a) Liquid phase Gas phase Volume fraction of gas [-] Time [s] Position (b) Fig. 12 Transient of sodium hydroxide concentration

8 Proceedings of CAPP 2007 investigation near the surface of neighbor tube is useful and helpful for the modeling of the wastage. V. CONCLUSONS A multi-dimensional numerical investigation of sodium-water reaction (SWR) under a pin bundle configuration has been carried out in order to evaluate the characteristics of reacting zone, such as the volume fraction of gas, the temperature and the concentration of the product, nearby the leakage. For this purpose, the SWAT-1R experiment, in which the SWR under the pin bundle of 43 heat transfer tubes was observed, is chosen as a benchmark analysis. As a result of the analysis, it is demonstrated that good agreements are obtained in terms of the leakage rate and the mass weighted average temperature although the high temperature region (> 1000ºC) is overestimated in the computation because of the adiabatic conditions of the inner structure. Hence, it is concluded that the present numerical methodology is applicable to investigate the SWR with a complicated structural configuration. The maximum temperature of approximately 1300ºC is predicted constantly during the analysis because hydrogen gas covers over the interface between the water vapor and the liquid sodium where the SWR is most intense. Furthermore, an evaporation of sodium hydroxide suppresses the increase of the maximum temperature. The characteristics of the reacting zone near the neighbor tubes are also investigated in the present paper. From the viewpoint of the structural integrity in a steam generator of sodium cooled fast reactor, a secondary failure due to the over-heating rupture and the wastage is of great concern. t is concluded that the present methodology is promising to evaluate a heat transfer to neighbor tube and a possibility of the over-heating rupture. The numerical quantification of the heat transfer and the possibility of the over-heating rupture are to be carried out in a future work. t is also said that the present methodology is useful and helpful to develop the theoretical and mechanistic modeling of the wastage phenomena. NOMENCLATURE N Number density [1/m 3 ] P Total pressure [Pa] H 298 Standard enthalpy change of formation [k/mol] Proc. of AEA/WGFR Specialists Meeting on Steam Generator Failure and Failure Propagation, p , Aix-en Provence, France (1990). 2. H. H. Neely and C. E. Boadman, Status of U. S. Studies of Failures and Failure Propagation in Steam Generator, Proc. of AEA/WGFR Specialists Meeting on Steam Generator Failure and Failure Propagation, p , Aix-en Provence, France (1990). 3. AEA TECDOC, Fast reactor fuel failures and steam generator leaks: transient and accident analysis approaches, AEA-TECDOC-908, p. 156 (1996). 4. T. Takata and A. Yamaguchi, Numerical Approach to the Safety of Evaluation of Sodium-Water Reaction,. Nucl. Sci. Tech., 40, 10, p (2003). 5. T. Takata and A. Yamaguchi, et al., Numerical Methodology of Sodium-Water Reaction with Multiphase Flow Analysis, Nucl. Sci. and Eng., 150, p (2005). 6. T. Takata and A. Yamaguchi, et al., Computational Sensitivity Study on Sodium-Water Reaction Phenomenon,. Nucl. Sci. Tech., 43, 5, p (2006). 7. M. Nishimura and. Shimoyama, et al., Sodium- Water Reaction Test to Confirm Thermal nfluence on Heat Transfer Tubes, NC Technical report, NC TN (2003) [in apanese]. 8. H. Tanabe and T. Watanabe, Results of Failure Propagation Tests in the Steam Generator Safety Facility (SWAT-3) Report No. 5, PNC Technical report, PNC SN (1986) [in apanese]. 9. H. Ninokata and T. Okano, SABENA: An Advanced Subchannel Code for Sodium Boiling Analysis, Proc. 3rd nt. Mtg. on Reactor Thermal Hydraulics, 16., Newport. U. S. A. (1985). 10. Malcolm W. and Chase,r., NST-ANAF Thermochemical Tables Fourth Edition Part, Cr- Zr,. of Physical and Chemical Reference Data, Monograph No.9, National nstitute of Standards and Technology, Gaithersburg, Maryland A. Yamaguchi and Y. Tajima et al., Numerical Simulation Study on Sodium Water Reaction (11) Evaluation of Sodium-Tube Heat Transfer Coefficient based on Numerical Simulation and Experiment, 2004 Annual Meeting of AES, M14 (2004) [in apanese]. REFERENCES 1. H. Tanabe and E. Wachi, Review on Steam Generator Tube Failure Propagation Study in apan,