Network Analysis of Turbine and Feedwater Systems of the Fugen Nuclear Power Plant

Journal of Nuclear Science and Technology ISSN: 00-33 (Print) 88-48 (Online) Journal homepage: http://www.tandfonline.com/loi/tnst Network Analysis of Turbine and Feedwater Systems of the Fugen Nuclear Power Plant Hiroyasu MOCHIZUKI & Takateru TSUKAMOTO To cite this article: Hiroyasu MOCHIZUKI & Takateru TSUKAMOTO () Network Analysis of Turbine and Feedwater Systems of the Fugen Nuclear Power Plant, Journal of Nuclear Science and Technology, 48:, 786-796 To link to this article: https://doi.org/0.080/8848..9776 Published online: 0 Jan. Submit your article to this journal Article views: 8 View related articles Citing articles: View citing articles Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalinformation?journalcode=tnst

Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 48, No., p. 786 796 () ARTICLE Network Analysis of Turbine and Feedwater Systems of the Fugen Nuclear Power Plant Hiroyasu MOCHIZUKI ; and Takateru TSUKAMOTO Research Institute of Nuclear Engineering, University of Fukui, 3-9- Bunkyo, Fukui 90-807, Japan Faculty of Mechanical Engineering, University of Fukui, 3-9- Bunkyo, Fukui 90-807, Japan (Received September 4, 0 and accepted in revised form November 9, 0) The present study describes the thermal-hydraulic network analysis of the turbine and feedwater systems of the Fugen reactor. Turbines, feedwater heaters, and corresponding piping systems are modeled using the network calculation code NETFLOW++ and thermal-hydraulic conditions are calculated using the coupled numerical model. As a result of the calculation, distributions of important characteristics of the single-phase flow and two-phase flow in the piping such as pressure and void fraction are clarified. Flow patterns in the piping were investigated using the calculated result. It was found that the state of the coolant in the drainpipe changes from saturated liquid at the inlet to a two-phase flow with a large void fraction at the connection to the feedwater heaters. This is attributed to the pressure difference between the inlet and outlet of the drainpipes. Even the drainpipe from the moisture separator to the shell of feedwater heater #4 shows a similar behavior, and the flow pattern changes from single phase to slug flow. The steam quality in the extraction line is very high, although a large number of droplets are contained in the flow. Contrary to expectation, these droplets do not completely evaporate in spite of the low-pressure conditions. KEYWORDS: turbine and feedwater systems, balance of plant, feedwater heater, plant dynamics, network analysis, flashing, two-phase flow, flow regime I. Introduction The Fugen reactor is a boiling-water cooled heavy-water moderated-pressure-tube-type reactor. It has been operated for years as a plutonium burner. The reactor is loaded with 77 MOX fuel assemblies and is waiting its complete dismantling. During this period, the piping in the feedwater (FW) system is sampled because it has a low contamination. Pipe geometries especially wall thicknesses are measured by the plant owner in order to inspect for corrosion or erosion of the inner surface. This inspection is motivated by the FW pipe break accident at the Mihama Unit-3 PWR on 9 August 04. A very large rupture occurred in an FW pipe upstream of a deaerator. Five workers were killed and six workers were seriously wounded by the high-temperature coolant discharged in the working area. The wall of the piping was corroded by a turbulence generated downstream of an orifice for the flowmeter. The pipe wall with 0 mm thickness at the initial condition was corroded to 0.4 mm at the thinnest location when the accident occurred. The cause of the rupture was estimated as flow-accelerated corrosion (FAC) enhanced by the turbulence of the orifice. Therefore, wall thicknesses around bends and regions where flow areas Corresponding author, E-mail: mochizki@u-fukui.ac.jp Ó Atomic Energy Society of Japan, All Rights Reserved. 786 are changed in the Fugen reactor are measured using a laser method. Because the measurement over all the pipe lines is difficult, the owner, Japan Atomic Energy Agency (JAEA), wanted to investigate the important pipe regions in terms of the FAC. Since the author is going to establish a combined calculation model of the nuclear steam supply system (NSSS) and the turbine and feedwater (FW) systems, so-called balance of plant (BOP) of a fast reactor, this is a good opportunity to model precisely the BOP of Fugen. Therefore, the major objective of the present study is to create a practical BOP model that is applicable to Fast Breeder Reactors (FBRs) and light water reactors. However, FAC-related issues are discussed along the way in the present approach. An analysis has been conducted for the whole turbine and FW systems using the network analysis code NETFLOW++ developed by Mochizuki. ) Since the system pressure in the BOP has a very wide range, from 7 to 0.004 MPa, and condensed water in the shell of one FW heater (FWH) is sent to its upstream neighbor FWH, the real flow regime cannot be known without connecting all the FWHs by piping. Moreover, the calculation is usually unstable due to the phase change inside the component and piping such as condensation and flashing. Therefore, it is very seldom that the whole turbine and FW systems are calculated simultaneously using the network model. Teyssedow et al. ) calculated the turbine

Network Analysis of Turbine and Feedwater Systems of the Fugen Nuclear Power Plant 787 Low-pressure turbines Complex feedwater heaters #&# Demineralizer High-pressure turbine Moisture separators Condensate pumps Steam control valve Feedwater heater #3 Feedwater heater # Feedwater heater #4 Feedwater pumps Fig. Schematic of BOP of Fugen NPP and FW systems of the Gentilly- reactor in Canada with a model similar to the model reported by Mochizuki ) in order to evaluate the efficiency of the systems. Since they do not consider the momentum equation, two-phase flow characteristics cannot be solved. Zerkak et al. 3) calculated the behavior of the FW system of the Leibstadt power plant in order to solve the operational problems using the TRAC-BF and TRACE codes. Although the network of the shell side of the FWHs is not clear, these calculations are similar to those in the present study. Numerical models of a high-pressure turbine (HPT), a low-pressure turbine (LPT), a moisture separator, low-pressure FWHs, high-pressure FWHs, and an FW pump were constructed at first based on a heat-balance diagram of the Fugen plant. Then, these components were connected using a model of piping. Time marching calculation without any perturbation has been conducted to obtain the average operating condition of the plant. Because of the calculation, various flow regimes in piping have been clarified. This result is used to select regions where more precise 3D CFD calculations will be done. In terms of droplet corrosion of the FWH, Ferng 4) studied the wear of the wall in combination with a droplet impaction analysis on the wall using a CFD code and a droplet impingement wear model. II. BOP of Fugen Plant Figure shows the BOP of the Fugen plant that uses a direct cycle with two loops, i.e., steam produced in the core is supplied to the turbine system. It consists of one HPT, four LPTs, two moisture separators, a condenser, three condensate pumps including one standby pump, three FW pumps including one standby pump, three low-pressure FWHs, two high-pressure FWHs, and two FW flow control valves to deliver FW to individual loops. The moisture separator of the Fugen plant has no function of reheating. A drainpipe at the bottom of the moisture separator is connected to FWH #4. FWHs # and # consist of a complex-type FWH that separates two FWHs with a wall inside the heater. Two complex-type FWHs in terms of FWHs # and # are provided, and penetrate the housing of the condenser. Figure illustrates the heat balance used for the design of the BOP. Steam at 6. MPa is supplied to the steam flow control valve. A pressure drop of approximately MPa occurs at the valve, and a pressure of MPa is supplied to the HPT. Liquid droplets generated during expansion are separated by the moisture separator. Dried steam is supplied to the LPTs although reheating is not taken. The pressure at the inlet of the LPT is approximately MPa. In order to warm up the feedwater, extracted steam from the HPT is supplied to the shell of the high-pressure FWH #. Saturated liquid from the moisture separator is supplied to FWH #4, as well as steam extracted from the main steam and the LPT. Extracted steam from the LPTs containing a large amount of liquid droplets is supplied to the low-pressure FWHs from # to #3. Condensed water on the shell side of each of the FWH is supplied to the neighboring FWH one after another, and finally drained to the condenser. The condenser is cooled by seawater. The coolant is supplied to the FW system by the condensate pumps. Before the coolant is supplied to FWH #, it is demineralized by ion-exchanger towers. The FW at 6 C is warmed by the FWHs up to 80 C. Since the Fugen NPP consists of two loops, the FW is delivered to each loop via the FW flow control valve. III. Modeling of BOP Two complex-type feedwater heaters are provided in the VOL. 48, NO., MAY

788 H. MOCHIZUKI and T. TSUKAMOTO High-pressure turbine 6.P 3.0G 774.6H 0.6G 0.07G 4.8H 0.4G 0.3G 3.G 4.8H.0P 709.7H.G 0.44G Steam control valve Moisture Separator 37.4G.9G 793.0H 3.3G 674.9H.09P 4.G 744.0H 0.78G 46.4H 0.93G 464.4H.04P.0P 0.43G 39.7H 4.4G 30.i.G 373.0H 7.84G 398.H Low-pressure turbines.83g 7.H.8G 38.4H G 6.0G 38.3H 0.37G 6 C 0.6G 774.6H 0.097P Condenser 83.3 C 99. C # #4 #3 # # to steam drum.08p 0.63P 0.6P 0.09P 0.04P 9.33P 80 C 8 C C 83.0 C 9.0 C 3.6G 767.9H P: Pressure MPa G: Flow rate kg/s H: Enthalpy kj/kg 697.H 33.8H 368.H 3.7G 7.3H 3.8G Bank of feedwater heaters 0.G 7.8 C 4.6G 33.3 C Fig. Heat balance diagram of Fugen Modeling # feedwater heater # feedwater heater # feedwater heater # feedwater heater Fig. 3 Modeling of complex-type feedwater heaters # and # system. These are heat exchangers that have two kinds of feedwater heaters working under 4 and 9 kpa in one shell. They are separated right and left by a plate. Therefore, FWHs # and # are modeled as shown in Fig. 3, i.e., FWHs # and # are separated as two independent FWHs. In the modeling, data of volume, number of heat transfer tubes, flow area, length and so forth are consistent with the original FWHs. Therefore, this modeling is reasonable. Figure 4 shows an example of modeling of the high-pressure FWH #4. This heater is the most complicated one, and has three feeding pipes and one drainpipe in the shell. The shell is divided into 3 volumes (numbered circled 3, 4, and in Fig. 4), and each volume is subdivided into several nodes. The precise model is described in the paper by Mochizuki. ) The FW pipe is sectioned with the same number of nodes as that of the shell. The extraction line from the turbine, the drainpipe from the moisture separator, and the drainpipe to the downstream FWH is sectioned into 0 nodes. A negative number indicates the pressure boundary condition where an arbitrary pressure can be given in general as a function of time. In the present single model, the constant pressures close to the real conditions are given as a function of time. The number in a circle indicates volumes; other italic numbers indicate the identification numbers of piping. Heat transfer of the U-tube-type heat exchanger is treated using a countercurrent heat exchanger model incorporated in the code. The length of the heat transfer tubes in the model should be equivalent to the effective heat transfer length of the shell side. Therefore, the number of heat transfer tubes on the shell side is doubled in order to obtain the correct heat transfer area. But the number and length of heat transfer tubes on the tube-side calculation are the actual numbers. Boundary conditions of flow rates for the tube and shell sides are given, and pressure boundary conditions are given in order to calculate those for the individual heat exchanger. Italic numbers in the figures indicate links that represent flow passages. If this numerical model cannot be solved stably, connection of the individual model to the network model is impossible. Figures (a) and (b) show the model for the HPT and LPT, respectively. Although there are 4 LPT units, they are numerically approximated by one LPT for the sake of simplicity. The volumes, indicated by circles in the turbine model, are the locations of the extraction or exhaust pipes. The flow passage between two volumes is sectioned by JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

Network Analysis of Turbine and Feedwater Systems of the Fugen Nuclear Power Plant 789 from moisture separator 6.9 kg/s 793.0 kj/kg.09 MPa 3.6 kg/s 677.3 kj/kg from turbine 6 #4 feedwater heater 3 4 3 4 - from feedwater pump - 3.6 kg/s 3.6 kg/s C 8.0 C 4. kj/kg 67.0 kj/kg 9.7MPa 9. MPa 3.09 kg/s 6 C 697. kj/kg Fig. 4 Modeling of feedwater heater #4 0.89 kg/s 7.0 C 33.8 kj/kg 0.6 MPa 3 3 9-9 0.88 P 4.3 G (kg/s) 744.0 H (kj/kg).0 P (MPa).4 G (kg/s) 774.6 H (kj/kg).0 P (MPa) 8 30 30-3 0. G.0 P (a) 3 3 33 34 3 37 38 39 4 36 4 0.0 G - -.7 G -4-3.3 G 4.90 G -3 8.63 G 0.0034 P 0.883 P 0.6 P 0.044 P.7 G 0.0686 P (b) Fig. 43 (a) Modeling of high-pressure turbine (b) Modeling of low-pressure turbine several nodes. For the single turbine model, boundary conditions about flow rate and pressure are given in order to solve this model. The steam expansion in the turbine is calculated using Stodola s empirical correlation ) taking into account the efficiency of the turbine and the pressure loss at the fixed nozzles and rotors to enable the calculation of the thermal-hydraulic conditions at the volumes. However, because of a lack of details in the specification of the turbine, the model parameters such as efficiency and pressure loss coefficient for each stage of the turbine blade and nozzle are chosen such that the designed steady state-conditions are reproduced. Heat exchange between the coolant inside the pipe and the surrounding air is calculated treating the pipe as a heat exchanger. The moisture separator is modeled using a separator model that separates liquid and vapor spontaneously. The drain line from the bottom of the separator is designated as a line that discharges only liquid phase. Precise mathematical models relevant to these models are described in the paper by Mochizuki. ) These individual models are calculated setting boundary conditions of the neighboring components in order to survey the flow resistance and heat transfer coefficient and/or effective heated surface. The boundary conditions are set based on the heat balance diagram. After all the individual components are modeled numerically and stable numerical solutions are obtained, they are connected one by one as shown in Fig. 6. The steam flow control valves are not modeled because of the steady-state calculation. Furthermore, two small heat exchangers between the condenser and FWH # are neglected because they have a small influence on the overall system. A couple of drainpipes of condensed water used for sealing a rotor shaft are also neglected for the same reason mentioned above. Since the lengths of most pipes connecting two components are more than 30 m, the pipes are sectioned by approximately 0 nodes. The flow regime of two-phase flow in each node is calculated using lumped parameters. The FW flow rate and enthalpy are given to the code as boundary conditions at volume-. In reality, a condensate pump and associated piping are neglected because they are not very important in terms of corrosion. Steam flow rates and enthalpies are given to the code as boundary conditions at volume-7 and volume-8. Boundary conditions relating pressure are set downstream of the FW (circled-) and at the condenser (circled-). An example of the meshing is shown in Fig. 7 for extraction line #. The mesh positions are provided at the bends. The input data distinguishes horizontal and vertical portions in order to consider static head. VOL. 48, NO., MAY

790 H. MOCHIZUKI and T. TSUKAMOTO Flow rate boundary - 7 7 # #4 #3 # # 3 4 4 7 3 3 33 7 High-pressure 9 8 30 turbine 8 9 30 3 8 9 Feedwater 8 pump 6 Moisture separator 3 3 4 6 9 6 4 7 9 6 6 0 Bank of feedwater heaters 3 36 34 37 38 39 40 8 9 8 0 Joint - Pressure boundary Low-pressure turbine 3 3 33 34 3 7 4 4 43 44 3 4 3 6 4 Condenser - Fig. 6 Modeling of BOP using the NETFLOW++ code Fig. 7 An example of segments of extraction line # The shell side of the FWH is sectioned by 8 nodes. The node length of the FW pipe should be equal to the above node length of the shell side because of a consistent heat transfer calculation. The pressure distribution is calculated using the pipe friction factor and local loss coefficients. The local loss coefficients are estimated at first based on the pressure difference between equipment, such as the turbine and shell of the FWH. Since valves are usually provided in the line, the loss coefficient includes the value of the valves. The local loss coefficient at a bend is taken into account at the node where the bend exists. JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

Network Analysis of Turbine and Feedwater Systems of the Fugen Nuclear Power Plant 79 3 [] [37] [38] 4 [36] 4 3 [48] -3 6 8 [] Loop-B [9] [8] - Upper plenum [46] 6 [30] [3] [9] [8] 3 Loop-A 7 Air cooler [4] Pump [7] [3] 8 9 [3] [33] [47] - 0 [] to turbine [] [4] [43] [] [4] [39] [40] 7 9 Loop-C [4] [] [7] [8] 4 [] High pressure plenum [9] [] [0] Pump IHX to Loop-B to Loop-C [3] [34] Evaporator [6] from Loop-B, C 3 Super-heater 3 [6] [49] -4 4 [7] [44] [4] 3 [3] Link -Link 6: st to 6 th layer (Inner driver) Link 7: 7 th & 8 th layer (Outer driver) Link 8: 9 th to th layer (Blanket) Link 9: Center CR Link 0: CRs Link : Bypass No. feed water heater Low-pressure turbine Condenser (Pressure boundary) Extraction No. feed Feed water water heater pump (Flow boundary) Deaerator Drain Drain Fig. 8 Analytical model of FBR Monju Pressure loss in the turbine is evaluated without considering the geometric shape using the following old but simple correlation based on the study by Stodola: ) pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pin W ¼ P out p ffiffiffiffiffiffi ; ðþ T in where W stands for flow rate (kg/s) and P in and P out stand for inlet and outlet pressures in Pascal, respectively. T in stands for inlet temperature in Kelvin, a kind of constant that has unit. From the above equation, pressure loss in the turbine can be calculated using the following equation. p in p out ¼ IV. Calculation T in ðp in þ p out Þ W ¼ jwjw. Validation of the NETFLOW++ Code Validation of the NETFLOW++ code in terms of the FW system with high-pressure components was conducted by Mochizuki ) using data measured at the fast breeder reactor Monju. However, the existence of specific data taken at 4% thermal power at the Monju prototype fast breeder reactor, reported by Miyakawa et al., 6) was brought to our attention, and validation of the NETFLOW++ code including the primary, secondary, and tertiary systems of Monju was conducted again. The calculation was conducted by a null-transient method that is a kind of transient calculation without any perturbation to obtain the steady-state condition using the analytical model illustrated in Fig. 8. Solid lines show the piping system in terms of liquid sodium for the primary and secondary heat transport systems with three loops. Dashed lines show the piping system in terms of the ðþ turbine and FW systems. Steam is generated by three sets of steam generators and is sent to the steam pipe. FW is returned to the steam generators via three FW control valves. In the analytical model, the low-pressure systems consisting of the LPTs and low-pressure FWHs were eliminated. FW flow rate and temperature, and pressure at the inlet of the LPTs were given to the code as boundary conditions of the NETFLOW++ code. Table shows the comparison of plant parameters between a thermal power confirmation test at Monju and the calculated result using the NETFLOW++ code. Temperatures in the heat transport systems including the water system are predicted within 0 C error. Since the turbine and FW systems of the Fugen reactor are almost the same as that of the Monju reactor even though the nuclear types are different, it is expected that the main parameters in the BOP of the Fugen plant can be calculated with similar accuracy.. Network Calculation Result Flow regimes in the BOP of Fugen are calculated using the network calculation model shown in Fig. 6. The plant parameters in the BOP listed in Table are obtained as a result of the time marching calculation. Although there is a discrepancy between the calculated and designed temperatures at the outlet of FWH #, the temperature at the outlet of FWH # is predicted with a small error. This is because the steam pressure in the shell of FWH # is only 4 kpa; thermal-hydraulic calculation is usually difficult and not very accurate. Moreover, the method of obtaining the design value is not clear although it is assumed that the design values were calculated based on a simple heat balance. Therefore, the comparison in Table indicates the relative errors between design values and calculated results. If the VOL. 48, NO., MAY

79 H. MOCHIZUKI and T. TSUKAMOTO Table Comparison of plant parameters between thermal power confirmation test at Monju and calculated result using the NETFLOW++ code Items Test result Converged value by time marching calculation Difference (Calc. Test) Temperature at the inlet of the reactor vessel ( C) 364 37.8 7.8 Temperature at the outlet of the reactor vessel ( C) 486 490. 4. IHX outlet temperature (Primary) ( C) 367 37. 4. IHX inlet temperature (Secondary) ( C) 8 79. :8 IHX outlet temperature (Secondary) ( C) 486 489.8 3.8 Primary flow rate (kg/s) 70.4 707.0 4.6 Secondary flow rate (kg/s) 398.6 39.0 3:6 Feedwater temperature ( C) 96.9 94.0 :9 Evaporator outlet temperature ( C) 370 366.8 3: Superheater outlet temperature ( C) 483. 48.7.6 Table Plant parameters in BOP of Fugen Items Calculation Design value Difference (Calc. Design) Outlet temperature of # feedwater heater ( C) 66.8 9 7.8 Outlet temperature of # feedwater heater ( C) 87. 83 4. Outlet temperature of #3 feedwater heater ( C).3.3 Outlet temperature of #4 feedwater heater ( C) 6. 8 :8 Outlet temperature of # feedwater heater ( C) 80. 80 0. Drain flow rate in link # (kg/s).9 3. 0: Drain flow rate in link # (kg/s).0 49.6.4 Drain flow rate in link # (kg/s) 64.8 64. 0.3 Enthalpy of extraction in line # (kj/kg),69.0,47. 96. Enthalpy of extraction in line #7 (kj/kg),764.,67.0 9. Enthalpy of extraction in line # (kj/kg),4.0,4.8 3:8 Enthalpy of drain line #7 from moisture separator (kj/kg) 78.7 793.0 :3 errors are large, both results should be checked again. However, the comparison shows us that there is no problem in practical use. In general, the calculation around the LPT is less accurate than that of the high-pressure parts, e.g., the enthalpy of extraction line # from the LPT has a larger discrepancy against the design value than that of the extraction line from the HPT. The time mesh of the calculation is approximately 0.0 s. Figure 9 illustrates the distribution of steam quality in piping for the rated operating condition. As might be expected, the steam qualities are very high in the extraction lines from the turbines, and the steam qualities are very low in the drainpipes from the FWHs. Therefore, it seems that the flow regimes in these pipes are single-phase flow of steam and single-phase flow of liquid. However, when the void fraction distribution is illustrated as shown in Fig. 0, it is clear that all the drainpipes are voided by flashing caused by the pressure gradient of the drained water fed to the low-pressure FWHs. Although the drainpipe from FW heaters # to #4 seems to be single phase according to the color, the void fraction at the exit is approximately %. Because of the voiding mentioned above, the single-phase flow occurs only in the FW pipe where it is between volume () and (-). JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

Network Analysis of Turbine and Feedwater Systems of the Fugen Nuclear Power Plant 793 3 4 8 7 7 High-pressure turbine 8 9 30 7 9 30 3 3 Moisture separator 6 33 34 3 3 33 34 3 3 36 37 38 39 Low-pressure turbine # #4 #3 # 8 9 Feedwater 3 4 8 9 # pump 40 0 7 4 4 43 3 4 44 Condenser - Steam quality, x(-).0 0.9 0.8 0.7 0.6 0. 0.4 0.3 0. 0. 0.0-3 4 7 8 9 6 6 3 4 6 6 7 8 9 3 4 0 Bank of feedwater heaters 6 Fig. 9 Steam quality distribution in piping 3 4 8 7 High-pressure turbine 7 8 9 30 7 9 30 3 3 Moisture separator 6 33 34 3 3 33 34 3 3 36 Low-pressure turbine 37 38 39 # #4 #3 # 8 9 Feedwater 3 4 8 9 # pump 40 0 7 4 4 43 3 4 44 Condenser - Void fraction, α (-).0 0.9 0.8 0.7 0.6 0. 0.4 0.3 0. 0. 0.0-3 4 7 8 9 6 6 3 4 6 6 7 8 9 3 4 0 Bank of feedwater heaters 6 Fig. 0 Void fraction distribution in piping In the case of drainpipe #7 from the moisture separator to FWH #4, liquid is voided by depressurization as illustrated in Fig.. At the inlet of the drainpipe, the void fraction is zero. However, the drained liquid is voided due to the low system pressure in the shell. The void fraction increases at the bend because of an additional local loss coefficient compared with the straight portion. The flashing causes a temperature reduction of the fluid, which is reflected in a change in the color of the drainpipes from FWHs #3, #, and # as illustrated in Fig.. V. Discussion In the present calculation model, four LPTs are modeled as one LPT for simplicity. This causes the large steam flow rate ratio at the higher pressure region compared with that of the plural turbine model. There is a possibility that the simplification affects the accuracy of the calculation of the turbine. However, this problem is limited in the very low temperature region. This sort of simplification has little problem in the present analysis because of the steady-state calculation. However, one has to confirm the effect of the VOL. 48, NO., MAY

794 H. MOCHIZUKI and T. TSUKAMOTO Void fraction (-). 0.8.3 Void fraction (-) 0.6. 0.4 0.9 0. 0.7 Pressure (MPa) 0 0. 0 0 30 40 0 60 Distance (m) Fig. Distribution of void fraction in the drainpipe from the moisture separator to FWH #4 Pressure (MPa) simplification on the accuracy when a transient calculation is conducted. The corrosion of piping is dependent on the flow regime such as the single-phase flow or two-phase flow. In the single-phase flow, existing experience tells us that the corrosion is likely to occur at around 0 C. Since the yellow color in Fig. indicates the temperature of around 0 C where the corrosion is likely to occur, the yellow-colored regions of single-phase flow of liquid are the areas where careful inspection should be done in terms of the FAC. As clarified in the previous result, the single-phase liquid flow exists only in the FW pipe, and the FAC-sensitive region is limited to the region from FWHs #3 to #. Therefore, this portion can be nominated as a careful inspection region. As for drainpipes, the flow regime map of steam/water system proposed by Mandhane et al. 7) is used to identify the flow regime because most parts of the drainpipes are horizontal. Superficial flow rates at the outlet of the drainpipes are plotted in Fig. 3 together with the flow regime map. The High-pressure turbine 8 7 8 9 30 9 30 3 3 Moisture separator 6 33 34 3 3 33 34 3 3 36 Low-pressure turbine 37 38 39 40 0 7 4 4 43 44 Condenser - Temperature, T ( C) 80 60 40 0 80 60 40-3 4 3 4 7 7 # #4 #3 # 8 9 Feedwater 3 4 8 9 # pump 7 8 9 6 6 3 4 3 4 6 6 7 8 9 3 4 00 80 60 40 Bank of feedwater heaters 0 6 Fig. Temperature distribution in piping 0 j l (m/s) 0. 0.0 Plug Slug Stratified Smooth Bubbly Stratified Wavy Annular ST-B W-S B,S-D ST,B-W,S W,S-A D-A # # # #0 # 0.00 0. 0 00 000 j g (m/s) Fig. 3 Flow regimes at the outlet of drainpipes (numbers in the legend indicate line numbers in Fig. 6) JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

Network Analysis of Turbine and Feedwater Systems of the Fugen Nuclear Power Plant 79 Steam quality x(-) 0.88 0.88 0.87 Extraction line #3 x (-) Pressure Extraction line #.3.....0 Pressure (MPa) terms of line #7, the droplet velocity is largest among the extraction lines but the droplet flow rate is small. Both parameters are relatively large in line #. Therefore, extraction lines # and # are nominated as lines for inspection. The calculation models of turbine and FWHs can be used for the BOP model of another type of nuclear reactor such as a fast breeder reactor. If the complete BOP model is connected to the NSSS of the FBR, the plant transient calculation of the whole plant is possible. This work is useful to establish the network model for the entire heat transport systems. 0.87 0 0 Distance (m) 40 Fig. 4 Distributions of steam quality and pressure along the extraction lines #3 and # Table 3 flow regimes change from single phase to plug flow for the drainpipe from FWH #, to slug flow for the drainpipe from FWH #4, and to annular flow for the drainpipes of FWHs #3, #, and #. The numbers in the legend show the identification numbers of drainpipes in Fig. 6. The flow regime in drain line #7 is single phase at the inlet. However, the pipe is connected to the shell of FWH #4, the void fraction in the water increases, and the flow regime transfers from single phase to the plug flow, then slug flow. For this and other drainpipes, the importance of inspection is low. In the case of two-phase flow, impingement of droplets on the pipe wall may cause erosion. Therefore, the dispersed annular region should be investigated. The void fractions in extraction lines #, #7, and # are almost unity, but the steam quality is around 0.9. Therefore, there is a possibility that many droplets impinge on the pipe wall or the FWH. Figure 4 shows the distributions of steam quality and pressure along extraction lines #3 and #. The steam quality increases slightly to around 0.88 as the pressure decreases. However, this value shows that a lot of droplets are still flowing in the steam. The liquid flow rate and velocity in line # are approximately.7 kg/s and 4 m/s, respectively. The droplet flow rates and velocities for all extraction lines are summarized in Table 3. The droplet flow rate in line # is largest and the droplet velocity is relatively high. In 30 3 Droplet flow in extraction lines Line No. Droplet flow rate (kg/s) Droplet velocity (m/s) #.7 44.8 #7 0.043 7.4 # 0.986 70.8 #7 0.7 7.7 # 0.63 60.3 VI. Conclusions The balance of plant of the Fugen reactor has been numerically modeled using the network analysis code NETFLOW++, and the thermal hydraulics of the BOP have been analyzed in order to clarify the flow regimes in piping. The following is clarified. ) Plant parameters such as temperatures, flow rates, and enthalpies are calculated with the developed network model that includes high-pressure and low-pressure components. Most parameters are predicted with good precision, except temperature at the outlet of feedwater heater #. ) The single-phase liquid flow occurred only in the feedwater pipe. From the standpoint of corrosion, the temperature of the coolant in the feedwater pipe around feedwater heater #4 is around 0 C, which enhances FCA. 3) It was found that the state of the coolant in the drainpipe changes from saturated liquid at the inlet to a two-phase flow with a large void fraction at the connection to the feedwater heaters. This is attributed to the pressure difference between the inlet and outlet of the drainpipes. Even the drainpipe from the moisture separator to the shell of feedwater heater #4 shows a similar behavior, and the flow pattern changes from single phase to slug flow. 4) The steam quality in the extraction line is very high, although a large amount of droplets is contained in the flow. Contrary to expectation, these droplets do not completely evaporate in spite of the low-pressure conditions. Therefore, the extraction line to feedwater heaters # and #3 should be inspected carefully because both the droplet flow rate and velocity are large. ) On the basis of this study, it is almost certain that the network model for the entire heat transport systems of an FBR will be created and used for the transient analysis relating to the water system. Acknowledgements The present analysis was requested by the Japan Atomic Energy Agency (JAEA) and was supported financially by the Japan Nuclear Energy Safety Organization (JNES). The authors express their gratitude to JAEA and JNES for giving the opportunity to present this work. VOL. 48, NO., MAY

796 H. MOCHIZUKI and T. TSUKAMOTO Abbreviations BOP: balance of plant CFD: computational fluid dynamics FAC: flow-accelerated corrosion FW: feedwater FWH: feedwater heater HPT: high-pressure turbine LPT: low-pressure turbine MOX: mixed oxide NSSS: nuclear steam supply system References ) H. Mochizuki, Development of the plant dynamics analysis code NETFLOW++, Nucl. Eng. Des., 40, 77 87 (0). ) A. Teyssedou et al., Modeling and optimization of a nuclear power plant secondary loop, Nucl. Eng. Des., 40, 403 46 (0). 3) O. Zerkak et al., Analysis of the Leibstadt power plant condensate and FW systems during selected operational transients, Nucl. Eng. Des., 37, 9 8 (07). 4) Y. H. Ferng, CFD investigating the influence of power upgrade on impingement wear sites for the feedwater heater in the nuclear power plant, Nucl. Eng. Des., 39, 3 38 (09). ) A. Stodola, Steam and Gas Turbine, McGraw-Hill, New York (97). 6) A. Miyakawa et al., The Prototype Fast Breeder Reactor Monju System Startup Test Report Summary Report of the System Startup Tests hcriticality Test Power Up Test (40% Power)i, JNC TN40 0-00 (0), [in Japanese]. 7) J. M. Mandhane et al., A flow pattern map for gas-liquid flow in horizontal pipes, Int. J. Multiphase Flow,, 37 3 (974). JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY