- Email: [email protected]
Startup transient simulation for natural circulation boiling water reactors in PUMA facility
Nuclear Engineering and Design 236 (2006) 2365–2375
Startup transient simulation for natural circulation boiling water reactors in PUMA facility S. Kuran a , Y. Xu a , X. Sun a,1 , L. Cheng a , H.J. Yoon a , S.T. Revankar a , M. Ishii a,∗ , W. Wang b a
School of Nuclear Engineering, Purdue University, 400 Central Drive, West Lafayette, IN 47907, USA b U.S. Nuclear Regulatory Commission, Mail Stop T10K8, Washington, DC 20555, USA Received 19 July 2004; received in revised form 10 November 2005; accepted 10 November 2005
Abstract In view of the importance of instabilities that may occur at low-pressure and -flow conditions during the startup of natural circulation boiling water reactors, startup simulation experiments were performed in the Purdue University Multi-Dimensional Integral Test Assembly (PUMA) facility. The simulations used pressure scaling and followed the startup procedure of a typical natural circulation boiling water reactor. Two simulation experiments were performed for the reactor dome pressures ranging from 55 kPa to 1 MPa, where the instabilities may occur. The experimental results show the signature of condensation-induced oscillations during the single-phase-to-two-phase natural circulation transition. The results also suggest that a rational startup procedure is needed to overcome the startup instabilities in natural circulation boiling water reactor designs. © 2006 Elsevier B.V. All rights reserved.
1. Introduction Recently, vendors have proposed passive boiling water reactor (BWR) designs such as general electric’s simplified boiling water reactor (SBWR-600) (Duncan, 1988) and economic simplified boiling water reactor (ESBWR), Siemens’ small boiling water reactor(SBWR-200) (Goetzmann and Grüner, 1992), and the advanced heavy water reactor (AHWR) design in India (Sinha and Kakaodkar, 1990), the Dodewaard reactor in the Netherlands (Nissen et al., 1993) and the 5-MWt heating reactor in China (Wang et al., 1990). One of the most distinctive features of the passive BWR designs is the elimination of recirculation pumps and other active components which require ac power. Obviously, the simplifications based on the elimination of the recirculation pumps and associated piping systems enhance the safety and reduce the overall cost. However, the elimination of the recirculation pumps has certain disadvantages with respect to reactor control and the establishment of a rational startup procedure (Aritomi et al., 1990).
∗
Corresponding author. Tel.: +1 765 4944587; fax: +1 765 4949570. E-mail address: [email protected] (M. Ishii). 1 Present address: Department of Mechanical Engineering, Ohio State, University, 650 Ackerman Rd. Columbus, OH 43220, USA 0029-5493/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2005.11.002
The instability problem in the current BWRs has been investigated over several decades. Extensive experimental and analytical studies have been carried out for the coupled flow/power oscillations in conventional BWRs (Lahey and Drew, 1980; March-Leuba and Rey, 1993), but the instability problem in BWRs remains an issue during the startup transient in natural circulation BWRs (Chiang et al., 1994; Aritomi et al., 1993; Nissen et al., 1992). Shiralkar et al. (1993) described the main issues related to the thermal-hydraulics of the SBWR design, and the instabilities during the startup transient are considered an issue that needs to be resolved. The possibility of condensation-induced oscillations (geysering) during the startup is a concern for natural circulation BWR designs (Abe et al., 1994; Lin et al., 1993; Shiralkar et al., 1993). The geysering instability may occurs in a vertical subcooled liquid column which is heated at the bottom. The vapor generated near the exit of the heated section is condensed at the unheated section inlet by the subcooled liquid. The rapid decrease in the pressure due to the condensation causes the subcooled liquid to re-enter the heated section and restore the non-boiling conditions. The vapor generation and condensation cycles show the distinctive signature of geysering. Aritomi et al. (1990) investigated the geysering phenomenon in a single vertical channel during natural circulation BWR startup. They verified that the instabilities are pronounced when the subcooling at the inlet
2366
S. Kuran et al. / Nuclear Engineering and Design 236 (2006) 2365–2375
Nomenclature A cp D g G i ids k K l m ˙ N Nd NFr NPe Nsub NZu s ˙ Q qw q t t1φ V Vgj
flow area [m2 ] specific heat [kJ/kg] diameter [m] gravitational acceleration [kg/m s2 ] mass flux [kg/m2 s] enthalpy [J/kg] departure enthalpy [J/kg] thermal conductivity [W/m K] flow loss coefficient [−] length [m] mass flow rate [kg/s] dimensionless number [−] drift number [−] froude number [−] peclet number [−] subcooling number [−] zuber number [−] complex number [1/s] power [W] wall heat flux [W/m2 ] volumetric heat generation rate [W/m3 ] time [s] time at which Phase II starts [s] volume [m3 ] drift velocity [m/s]
Greek letters α void fraction [−] β volumetric thermal expansion coefficient [1/K] δ perturbation ifg latent heat [J/kg] ρ density difference between liquid and gas [kg/m3 ] icore core enthalpy rise [J/kg] P pressure drop [Pa] ξ perimeter [m] ρ density [kg/m3 ] τ time scale [s] υ velocity [m/s] Ψ property Subscripts and superscripts e equivalent f liquid g gas M model o reference value P prototype s saturation 1φ single-phase 2φ two-phase w wall or wetted
of the unheated section is high and the system pressure is low. Later, Aritomi et al. (1993) extended this study for the parallel channel system operating under forced and natural circulation conditions. They found that there is a strong correlation between the attained natural circulation flow rate and the condensation rate at the unheated section inlet in the occurrence of the geysering oscillations. Since the flow rate in a natural circulation BWR is a result of the density differential between the downcomer annulus and the inside of the shroud (core and chimney), the void distribution inside the core and chimney plays an important role in the flow dynamics. Void generation due to flashing inside the chimney greatly affects the attained natural circulation flow inside the reactor pressure vessel (RPV). Instabilities governed by the flashing in the chimney are also pronounced during the startup of natural circulation BWR designs. Fukuda and Kobori (1979) have demonstrated that the gravitational pressure drop perturbations are important in natural circulation systems at low-pressure and -quality conditions, even without flashing. However, the existence of flashing inside the chimney amplifies the importance of the gravitational pressure drop in the chimney and has additional non-linear effects on the system dynamics (Bragt et al., 2002; Inada et al., 2000; Tanimoto et al., 1998). Dodewaard reactor is a natural circulation reactor located in the Netherlands. Since the reactor is conceptually very similar to the proposed advanced BWR designs utilizing natural circulation, the experimental data from the operation of this reactor has been used to assess some of the key phenomena for natural circulation BWR designs (Nissen et al., 1993; Shiralkar et al., 1993). No startup instabilities were experienced during the February 1992 startup. However, the experiences gained from Dodewaard reactor may not be applied to some natural circulation BWR designs because of the differences in the geometry and operational parameters. Fukuda and Kobori (1979) classified several types of thermalhydraulic instabilities in a system with an unheated riser section. They described two different types of density wave oscillations: Type-I instability, which is dominated by the gravitational pressure drop perturbations in the unheated riser and Type-II instability, which is dominated by the frictional pressure drop in the heated section. Bragt and Hagen (1997a,b) investigated the nuclear-coupled instabilities in a natural circulation system by considering both Type-I and -II instabilities described by Fukuda and Kobori (1979). Hagen et al. (1997, 2000) reported the results of the experiments performed in the Dodewaard reactor with application to Type-I and -II instabilities. Hagen et al. (1997) has demonstrated that flashing in the chimney section is important for the Type-I oscillations. In view of the importance of flashing in natural circulation systems, Bragt et al. (2002) developed an analytical model for the dynamics of a natural circulation BWR under low-pressure conditions. The model was applied for the Dodewaard reactor to determine its stability characteristics at low-pressure. A 5-MW heating reactor developed by the Institute of Nuclear Energy and Technology at Tsinghua University has been in operation since 1989 (Wang, 1993; Wang et al., 1990). The reactor operates at low-pressure (1.5 MPa) and
S. Kuran et al. / Nuclear Engineering and Design 236 (2006) 2365–2375
2367
low-quality conditions. A series of experiments have been performed in an experimental facility to simulate the behavior of the reactor at low-flow and -pressure conditions (Jiang et al., 1995). Based on the experimental results, there are three kinds of flow instabilities observed in their experiments: geysering, flashing instability, and low-quality density wave oscillations. Jiang et al. (1995) proposed a startup procedure which includes the pressurization of the pressure vessel through the injection of a non-condensable gas into the steam dome. The transition phase from single- to two-phase natural circulation during startup is important for the geysering instability. Jiang et al. (1998) reported experimental results from the test loop which is used to simulate the 5-MW heating reactor. They showed that the steam space inside the pressure vessel has a significant effect on the oscillation amplitude. The startup transient in a typical natural circulation BWR design has been studied in the Purdue University MultiDimensional Test Assembly (PUMA) facility for the instabilities that may occur at low-pressure and -flow conditions. In this paper, the experiments performed for the prototypical value of the inlet flow loss coefficient are described. First, a brief description of the PUMA RPV and the instrumentation system is presented in the following section. Then, the startup procedure for a typical natural circulation BWR design is discussed with an emphasis on the possibility of instabilities. The investigation strategy developed based on the scaling criteria for single- and two-phase natural circulation systems is presented, and finally, the experimental results are discussed. 2. Experimental setup The PUMA facility was designed and built for a typical natural circulation BWR design to simulate the transient response following various loss-of-coolant-accident (LOCA) scenarios (Ishii et al., 1996). The facility has 1/4 height and 1/100 area ratio scaling, which corresponds to a volume scale of 1/400. It is designed to simulate transients where pressure is below 1.03 MPa (150 psia) following the initial blowdown. The reactor pressure vessel (RPV) component, which has been used to simulate the startup transient, and its major components are shown in Fig. 1. The lower plenum houses the non-heated portion of the fuelsimulating electrical heater rods. The perforated section on the shroud wall provides the lateral flow from the downcomer section. A new core inlet plate was designed and installed for the startup simulation experiments. Another plate was installed below the core inlet plate to adjust the core inlet flow loss coefficient without disassembling the RPV. Fig. 2 shows the loss coefficient adjustment mechanism and the top view of the core inlet plate. Cone-shaped cylinders attached to the lower plate enable to change the orifice flow area on the core inlet plate via moving the lower plate up and down. A position indicator was installed to indicate the position of the lower plate and thus the orifice flow area on the core plate. The PUMA core consists of four parallel channels: inner bypass, inner core (18 heater rods), outer bypass, and outer core
Fig. 1. PUMA RPV and its internals.
(20 heater rods). Several dummy rods were installed in the outer bypass and core channels to reduce the flow area and decrease the hydraulic diameter for the startup simulation experiments. The chimney section extends from the top of the core to the bottom of the steam separator assembly. Three quarters of the chimney height is in the partitioned section. The perforated steam separator support skirt provides a path for the liquid flowing downward through the downcomer section. The PUMA facility has a detailed instrumentation system to measure key thermal-hydraulic parameters such as temperature, local pressure, water-level, and local void fraction. Seventy thermocouples, three pressure cells, 16 differential pressure cell, and 20 conductivity probes were used in the startup simulation experiments. Twelve conductivity probes were installed in the core section at three different axial locations. The local void fraction was measured at four different axial locations inside the chimney section.
2368
S. Kuran et al. / Nuclear Engineering and Design 236 (2006) 2365–2375
Fig. 2. Flow loss coefficient adjustment mechanism and top view of the core inlet plate
3. Normal startup procedure for a typical natural circulation BWR design The normal startup procedure for a natural circulation BWR design such as the one given byLin et al. (1993) is discussed in this section regarding the instabilities at low-pressure and -flow conditions. The reactor startup starts from very low-pressure at the steam dome (55 kPa) following the deaeration process. Initially the steam dome is saturated at 80 ◦ C, and nuclear heating starts when certain control rods are withdrawn. The reactor water cleanup system (RWCU) is used for water-level control and to reduce the thermal stratification at the lower plenum. The reactor power is ramped from zero to a value which will heat up the water in the core at a maximum rate of 55 K/h. A phenomenon identification and ranking table (PIRT) has been developed at Brookhaven National Laboratory for the startup transient (Rohatgi et al., 1997). According to the PIRT, the startup transient can be divided into four distinct phases as far as the instabilities are concerned. Each phase is characterized by specific thermal-hydraulic conditions of the reactor. The phenomenon identification for the startup transient determines the simulation strategy in the PUMA facility. The four phases are described below. • Phase I — Single-phase core heat-up: At the beginning, the dome is saturated at 55 kPa. However, due to the large hydrostatic head in the downcomer, there is some subcooling in the lower plenum. The length of the single-phase core heat up phase depends on the heat-up rate and the amount of subcooling present at the core inlet. Since the single-phase flow is generally more stable than the twophase flow, there is no stability concern during this phase. However, the temperature distribution inside the RPV following this phase plays a very important role in the geysering instability. This phase is terminated when the net vapor generation starts at the core exit. The vapor generation due to flashing in the upper part of the chimney (around chimney– separator interface) is observed before net vapor generation in the core. However, the major thermal-hydraulic conditions are described as single-phase natural circulation in the RPV.
• Phase II — Net vapor generation in the core: This phase is the most important phase with respect to instabilities. The subcooled boiling at the core exit at low-pressure may generate large slug bubbles. When the net vapor generation starts, the chimney inlet is subcooled. The bubbles generated in the core are condensed at the chimney inlet during this phase. The amount of subcooling and the void fraction at the core exit determine the condensation rate. During this phase, condensation-induced geysering oscillations may take place. Depending on the established natural circulation flow, flow reversal may occur, leading to large-amplitude void oscillations. Therefore, the transition from Phases I to II is particularly important for determining a rational startup procedure. • Phase III — Saturated chimney: The condensation at the chimney inlet reduces the subcooling. However, due to the decreasing hydrostatic head from the inlet to the exit of the chimney, the local saturation temperature decreases. Flashing in the chimney plays an important role in this phase. The void generation due to the flashing greatly changes the gravitational pressure drop along the chimney and affects the natural circulation flow rate. Flashing-induced loop-type oscillations may occur during this phase. The propagation of void waves and the thermal non-equilibrium between the liquid and vapor along the chimney determines the dynamic characteristics of the flow. • Phase IV — Power ascension at full pressure: Starting from Phase II, the RPV pressure increases due to the significant void generation. The increase in the dome pressure causes void collapse and suppresses the possible oscillation at the latter stage of Phase III. The pressurization phase lasts until the full-pressure condition is reached. At the full pressure, the reactor power is increased to full power by adjusting the control rods. Since the power level is low and the system pressure is high, the stability margin of the reactor is quite high. 4. Scaling strategy The simulation strategy for the startup transient in natural circulation BWR designs was prepared based on single- and
S. Kuran et al. / Nuclear Engineering and Design 236 (2006) 2365–2375
two-phase similarity parameters. A detailed scaling strategy for single- and two-phase natural circulation systems with application to the PUMA facility design was developed by Ishii et al. (1998). The intention here is not to reproduce the strategy used in the PUMA facility design. However, the startup simulation strategy based on the startup procedure discussed previously is highlighted here. The scaling criteria for natural circulation systems are quite complicated due to the strong coupling of fluid flow and heat transfer. For single-phase natural circulation systems, the scaling laws were derived from area-averaged forms of continuity, integral momentum, and energy equations (Heisler, 1982; Heisler and Singer, 1981). The important dimensionless numbers characterizing geometric, kinematic, dynamic, and energy similarity are given by Kocamustafaogullari and Ishii (1983), Yadigaroglu and Zeller (1994) and Ishii et al. (1998). The single-phase natural circulation is not primarily important in stability of the system. However, temperature distribution inside the vessel and the power level prior to the two-phase natural circulation (initiation of Phase II) are particulary important for the condensationinduced oscillations. Therefore, the determination of the time at which single-phase-to-two-phase natural circulation occurs is the key for developing the simulation strategy for the startup transient. The time scale for a single-phase natural circulation system is given by (Kocamustafaogullari and Ishii, 1983): τR
oR
1/3 ,
βqo 2o /(ρf cpf )
(1)
R
qo
where is the power density, o , the reference length (heated section height), β, the liquid expansion coefficient, ρf cpf , the volumetric heat capacity of the liquid, and ΨR = ΨΨMP ; ΨM and ΨP stand for the variable Ψ of the model and prototype, respectively. From Eq. (1), it is obvious that the power and time scales are interrelated. Therefore, real-time simulation is possible by adjusting the power scale. For systems where both single- and two-phase natural circulation exist, achieving same time scale for the whole transient is a difficult task. A detailed discussion on the problem is presented following the introduction of the two-phase scaling parameters. Ishii (1971) derived the scaling criteria for two-phase flow systems by using the one-dimensional drift-flux model. This study was extended by Ishii and Jones (1976) for integral system scaling. Ishii (1971) analyzed the dynamic behavior and stability of a boiling flow system by using the one-dimensional drift-flux model and a first-order perturbation analysis. A perturbation of inlet flow (e.g. at the core inlet) is introduced in the following form: δυ(s, t) = est ,
(2)
where s = a + jω is a complex number. The real part, a, gives the amplification coefficient and the imaginary part, ω, represents the angular frequency. By integrating the governing field equations, several transfer functions can be derived relevant to major variables such as the velocity, void fraction, density, enthalpy, and pressure drop. It has been shown that both the steady-state and the transient responses of the system are gov-
2369
erned by the transfer function between the internal pressure drop and the inlet flow (Ishii, 1971). Therefore, 1 δυ = , δP Q(s)
(3)
where Q(s) is the characteristic equation for the system. The characteristic equation can be non-dimensionalized by introducing proper scales (Ishii, 1971, 1976; Ishii and Zuber, 1970). Thus Q∗ (s∗ ) = Q∗ (s∗ , N1 , . . . , Nm ),
(4)
where N1 , . . . , Nm represent the dimensionless groups that characterize the kinematic, dynamic, and energy similarities. The core inlet orificing and the other localized flow resistances are important geometrical parameters and appear as a part of the geometrical similarity group and should be kept prototypical for two-phase similarity requirements. The other important dimensionless groups related to the system operational conditions such as flow rate, reactor power level, and pressure are given as follows: • Zuber number (or previously known as phase change number) NZu =
ξ ˙ c ρ qw ρ Q h o = , Aυo ifg ρf ρg mi ˙ fg ρg ρg
(5)
where υo is the core inlet velocity, which is the reference velocity and o denotes the reference length, which is the core heated length. As it is clear from the definition given by Eq. (5), the Zuber number scales the phase change due to heat transfer to the system. Since it includes the total heat input ˙ c , the number also scales the power under both to the flow, Q single- and two-phase natural circulation conditions. • Subcooling number Nsub
isub ρ ifg ρg
(6)
The subcooling number takes into account the time-lag effects in the single-phase heated section due to the subcooling of the coolant entering the heated section (core). At low-pressure conditions, the hydrostatic head above the core inlet determines the amount of subcooling. Both Nsub and NZu are significant not only for the stability of a given two-phase flow system, but also for the description of steady-state conditions. Pressure-dependent property group in both Eqs. (5) and (6), ρ/ifg ρg , provides the basis of the pressure scaling. • Drift number Vgj or void-quality relation (7) Nd υo The drift number takes the relative motion between the phases into account. It characterizes the flow pattern through the vapor drift velocity, Vgj . The drift number is particulary important when Nd NZu , where the change of the density and velocity are controlled by the drift. • Density number ρg Nρ (8) ρf
2370
S. Kuran et al. / Nuclear Engineering and Design 236 (2006) 2365–2375
The density number or the density ratio number explicitly appears in the drift stress term in the mixture momentum equation (Ishii, 1971). It also appears in the two-phase friction term, depending on the constitutive equation used for twophase friction factor. The density ratio number, Nρ , scales the system pressure. However, when Nρ Nd 1 and the twophase friction factor is not a strong function of Nρ , the density ratio appearing in the Zuber and the subcooling numbers controls the pressure scaling. • Froude number NFr
υo2 ρf , g o αo ρ
(9)
where αo is the reference void fraction which can be determined from the kinematic similarity parameters (Ishii and Kataoka, 1984). The Froude number is particularly important for a natural circulation system. It represents the relative importance of the gravity with respect to the inertia. The similarity laws for the two-phase flow can be derived from the given dimensionless groups (Ishii et al., 1998). For the similarity of void generation, the Zuber and subcooling numbers are the important dimensionless groups that need to be conserved in both the model and prototype systems. It can be shown that the time scale under two-phase natural circulation condition is given by τR = loR , (10) where loR is the height scale. The time scale given by Eq. (10) is purely geometrical. Therefore, real-time simulation cannot be achieved in reduced-height facilities. The startup simulation strategy for natural circulation BWRs involves the transformation of the prototypical power/pressure transient into the model power transient. Fig. 3 demonstrates the reactor power and the steam dome pressure during the startup transient. The power transient given by Lin et al. (1993) was used as a boundary condition for RAMONA-4B calculations to calculate the steam dome pressure in the prototype. The RAMONA-4B code (Rohatgi et al., 1996) is extensively used for the BWR stability evaluation. The reactor steam dome pressure is about 55 kPa during the initial phase of the startup transient. There is no significant increase in the pressure during the singlephase natural circulation part of the startup (Phase I). When the reactor power is increased beyond a certain value, void generation starts in the core and two-phase natural circulation prevails inside the RPV. However, flashing at the upper part of the chimney can be observed before significant void generation in the core, since the steam dome is always saturated during the transient. Based on the different phases of the startup transient given in the previous section, the reactor steam dome pressures ranging from 55 kPa to 1 MPa were considered with respect to the instabilities. Considering the difficulties associated with the vacuum conditions during the early part of the startup transient, two pressure-scaling windows were considered and simulation experiments were performed to cover the aforementioned prototypical conditions:
Fig. 3. Power and pressure transient during the startup transient.
(1) scaled-up pressure test: this test covers the reactor dome pressures ranging from 55 to 500 kPa. This part of the transient is simulated by PUMA RPV dome pressures from 110 kPa to 1 MPa. (2) equal pressure test: in this test, the reactor steam dome pressures ranging from 110 kPa to 1 MPa were simulated in the PUMA RPV such that the dome pressure in the PUMA RPV becomes prototypical. Part of this test covers a certain part of the conditions simulated in the scaled-up pressure test. The simulation of the startup transient requires a calculation of the corresponding power transient in the PUMA facility by pressure scaling. To achieve the proper simulation, following factors were considered: • Core inlet subcooling is significantly affected by the hydrostatic head in the downcomer section. Since PUMA is 1/4 height scale facility, the core inlet subcooling in the PUMA is smaller. The subcooling number ratio between the prototype and the model can be approximated by means of the
Fig. 4. Pressure-dependent property group in Eq. (11).
S. Kuran et al. / Nuclear Engineering and Design 236 (2006) 2365–2375
Clasius-clapeyron relation such that, (Nsub )R ≈ (cpf Ts )R
ρ oR , ρg ifg R
(11)
where Ts is the saturation temperature at given pressure. During Phase I, the subcooling at the core inlet continiously decreases as the reactor power increases. The singlephase-to-two-phase transition can be considered as the time at which core inlet subcooling is removed. In this respect, the subcooling ratio, which is around 1/16, is close to the time scale during Phase I of the startup transient. The time scale in Phase I is particularly important for the similarity of the temperature distribution inside the vessel prior to Phase II. As shown in Fig. 3, the reactor power increases linearly with time during Phase I. For a kwown power transient, the time at which net vapor generation at the core exit can be calculated by using the following equation for both prototype and model: t1φ ˙ 1φ t1φ , m(t)i ˙ (12) core (t)dt = Q 2 0 where m ˙ is the natural circulation flow rate, which is calculated from the loop momentum integral for the singe-phase natural circulation rate, icore , the core enthalpy rise, t1φ , the time at which net vapor generation at the core exit starts, ˙ 1φ is the power level at the single-phase-to-two-phase and Q natural circulation transition occurs or the net vapor generation starts at the core exit. Since there is no external heat sink during the single-phase natural circulation, the core inlet temperature also increases due to heat addition in the core and it is also a function of the core flow rate. Therefore, a simple numerical algorithm is employed to calculate the core enthalpy rise and the natural circulation flow rate for a given core heat-up rate during single-phase core heat-up. For a more accurate treatment, subcooled boiling is taken into account through the departure enthalpy at which net vapor generation starts given by Saha and Zuber (1974): ⎧ ⎨ 0.0022 q De cpf N < 70000 Pe kf ids = ifs − (13) ⎩ q NPe ≥ 70000 154 G where ifs is the local saturated liquid enthalpy, G, the mass , the wall heat flux, and k is the liquid thermal conflux, qw f ductivity. The Peclet number, NPe is defined as NPe
Gcpf kf
(14)
where cpf is the liquid specific heat. Eq. (12) can be solved for t1φ numerically to calculate the time scale during Phase I. The calculations for both model and prototype yield τR = 1/17.2 for single-phase natural circulation. The time scale for the single-phase natural circulation is very small compared to 1/2 for the two-phase natural circulation. In other words, the single-phase natural circulation is terminated quickly in the model due to hydrostatic head difference.
2371
• The difference in solid structure heat capacity between the model and the prototype needs to be considered when determining the power transient. A certain portion of the total power increases the solid structure temperature. Therefore, ˙ ˙ ˙ c (t) + the total power, Q(t), is partitioned such that Q(t) =Q ˙ ˙ Qs (t). Qc (t) represents the power that goes to the coolant, ˙ s (t) denotes the portion of the total power which whereas Q increases the solid heat structure temperature. This power can be estimated from the following relation: ˙ s (t) = ρs cps Vs dTs , Q (15) dt where Ts is the volume-averaged heat structure temperature and Vs is the total solid structure volume. • The coolant power is scaled through Zuber number during the two-phase natural circulation. Therefore, the coolant power scale can be determined from ˙ c )R = AR υR ρf ρg ifg , (Q (16) ρ R
where AR is the area ratio, which is 1/100 in the PUMA facility and υR is the velocity ratio, which is related to the length scale during two-phase natural circulation. The last term in Eq. (16) represents the pressure-dependent property group which determines the pressure scaling. Since the inlet subcooling cannot be controlled independently, the effect of the core inlet subcooling was taken into account by evaluating the properties at lower plenum pressure. This is particularly important during the early phase of two-phase natural circulation or Phase II, which is covered by scaled-up pressure test. As the dome pressure increases, the relative importance of the hydrostatic head difference becomes less. The power level at the transition from single-phase-to-two-phase natural circulation (Phase I-to-II) is determined by using Eq. (16), since the power transient is a continious function (Fig. 4). Based on the above considerations, the PUMA heater power was scaled from the given reactor power transient. Fig. 5 presents the PUMA heater power during the scaled-up pressure test. Up to 350 s of the transient, the power linearly increases in time due to single-phase natural circulation. After 350 s, the property group ratio given in Eq. (16) determines the power transient through pressure scaling. The power transient calculated for the equal pressure test is shown in Fig. 6. The transient starts from relatively high power since the starting point of this test corresponds to a later stage of the startup transient where the reactor power is relatively higher. 5. Experimental results This section presents experimental results for the two different pressure-scaling tests where the core inlet loss coefficient is prototypical. 5.1. Scaled-up pressure test Fig. 7 compares the measured steam dome pressure in the PUMA and the calculated steam dome pressure in the reactor.
2372
S. Kuran et al. / Nuclear Engineering and Design 236 (2006) 2365–2375
Fig. 5. PUMA total power for the scaled-up pressure test.
Fig. 7. Steam dome pressure in scaled-up pressure test.
The experimental data is scaled up to the prototype conditions considering the pressure and time scales. From the figure, it can be clearly seen that reasonably accurate pressure transient can be reproduced in the PUMA facility by using the scaling strategy discussed in the previous section. The downcomer velocity measurement through the pitot tube is shown in Fig. 8. The signature of geysering oscillations is evident during the initial phase of the two-phase natural circulation. Fast Frouier transformation (FFT) analysis on the velocity data shown in Fig. 9 demonstrates that the oscillation has no well-defined dominant frequency, owing to its chaotic nature. However, oscillations with periods around 10–12 s can be distinguished. The void fraction at the exit of the core section was determined through averaging of the data from the four conductivity probes. The averaged void fraction at the core exit is shown in Fig. 10. The single-phase-to-two-phase natural circulation transition can be clearly observed in this figure. From Eq. (12), the duration of single-phase natural circulation was
Fig. 8. Downcomer velocity transient in scaled-up pressure test.
Fig. 6. PUMA total power for the equal pressure test.
Fig. 9. Power spectrum of downcomer velocity data for scaled-up pressure test.
S. Kuran et al. / Nuclear Engineering and Design 236 (2006) 2365–2375
Fig. 10. Area-averaged core exit void fraction in scaled-up pressure test.
estimated to be around 350 s. The void fraction data validates this estimate. Fig. 11 shows the conductivity probe measurement at the chimney inlet and exit in the scaled-up pressure test. A significant amount of flashing occurs in the chimney section. Due to the condensation at the chimney inlet, no void fraction developed in this section before about 1400 s. However, as the subcooling at the chimney inlet diminishes due to the condensation, bubbles tend to appear. Fig. 12 shows the variation of the subcooling at the chimney inlet. The subcooling decreases as the bubbles generated in the core section are condensed.
2373
Fig. 12. Subcooling at the chimney inlet for scaled-up pressure test.
As discussed in the previous section, the equal pressure test simulates the reactor dome pressures ranging from 110 kPa to 1 MPa. Therefore, the test includes the early part of the
two-phase natural circulation. Fig. 13 shows the steam dome pressure comparison. The figure clearly shows that the pressurescaling strategy yields a very similar steam dome pressure transient. The downcomer velocity measurement shown in Fig. 14 demonstrates the signature of the condensation-induced oscillations. As can be seen from the power spectrum in Fig. 15, similar to the scaled-up pressure test, it is difficult to identify the dominant period for the oscillations. However, it can be concluded that the oscillations have periods around 10–15 s. Figs. 16 and 17 show the void fraction at the core exit and the inlet and exit of the chimney, respectively. The flashing in the chimney is significant in this test and causes longer period oscillations because of the wave propagation phenomenon in this section of the RPV. As shown in Fig. 17, most of the voids appear to be at the chimney exit, showing the importance of flashing in the equal pressure test.
Fig. 11. Void fraction at the chimnet inlet and exit for scaled-up pressure test
Fig. 13. Steam dome pressure comparison in equal pressure test.
5.2. Equal pressure test
2374
S. Kuran et al. / Nuclear Engineering and Design 236 (2006) 2365–2375
Fig. 14. Downcomer velocity transient in equal pressure test.
Fig. 17. Void fraction at the chimney inlet and exit for equal pressure test.
6. Conclusions
Fig. 15. Power spectrum of the downcomer velocity data in equal pressure test.
An experimental investigation of the startup transient in a typical natural circulation BWR design was performed in the PUMA facility to study the startup instabilities. By using the pressure scaling, two sets of experiments were performed to simulate the startup transient for the reactor steam dome pressures ranging from 55 kPa to 1 MPa. The signatures of condensationand flashing-induced oscillations were observed in the simulation results. This clearly demonstrates the significance of the startup instabilities for natural circulation BWR designs. However, the inclusion of nuclear feedback such as void-reactivity feedback is indispensable to draw more realistic conclusions about the startup instabilities. Since the PUMA facility is a reduced-height facility, the flashing cannot be scaled unless pressure scaling is carried out to conserve the void generation due to flashing in the chimney. In the experiments described in this paper, the void generation in the core section was considered the pressure-scaling basis. The flashing is more pronounced in the reactor geometry due to its longer chimney section. The subcooling at the chimney inlet is also higher in the reactor and this yields to higher condensation rate. Based on the PUMA startup simulation tests, it can be concluded that oscillations (either induced by flashing or by condensation) would be more significant in the prototype design. Acknowledgments
Fig. 16. Average core exit void fraction in equal pressure test.
This study was carried out under the auspices of the U.S. Nuclear Regulatory Commission (NRC). The authors would like to thank F. Eltawila, J. Rosenthal, J. Kelly, S. Bajorek and J. Staudenmeier of the U.S. NRC for their support on the project. Authors also appreciate the valuable discussion on the subject with U.S. Rohatgi from Brookhaven National Laboratory (BNL).
S. Kuran et al. / Nuclear Engineering and Design 236 (2006) 2365–2375
References Abe, N., Yokobori, S., Nagasaka, H., Tsunoyama, S., 1994. Two-phase flow natural circulation characteristics inside BWR vessels. Nucl. Eng. Des. 146, 253. Aritomi, M., Chiang, J., Mori, M., 1993. Geysering in parallel boiling channels. Nucl. Eng. Des. 141, 111. Aritomi, M., Nagahashi, T., Chiang, J.H., Wataru, M., Mori, M., 1990. Transient behaviour of natural circulation for boiling two-phase flow (experimental results). In: Proceedings of the 6th Nuclear Thermal-Hydraulic, ANS Winter Meeting, Washington, DC. Bragt, D.D.B.V., Hagen, T.H.J.J.V.D., 1997a. Stability of natural circulation boiling water reactors. Part I. Description stability model and theoretical analysis in terms of dimensionless groups. Nucl. Technol. 121, 40–51. Bragt, D.D.B.V., Hagen, T.H.J.J.V.D., 1997b. Stability of natural circulation boiling water reactors. Part II. Parametric study of coupled neutronicthermohydraulic stability. Nucl. Technol. 121, 52–62. Bragt, D.D.B.V., Kruijf, W.J.M.D., Manera, A., Hagen, T.H.J.J.V.D., Dam, H.V., 2002. Analytical modeling of flashing-induced instabilities in a natural circulation cooled boiling water reactor. Nucl. Eng. Des. 215, 87–98. Chiang, J., Aritomi, M., Inoue, R., Mori, M., 1994. Thermo-hydraulics during startup in natural circulation boiling water reactors. Nucl. Eng. Des. 146, 241. Duncan, J.D., 1988. SBWR, a simplified boiling water reactor. Nucl. Eng. Des. 109, 73–77. Fukuda, K., Kobori, T., 1979. Classification of two-phase flow instability by density wave oscillation model. J. Nucl. Sci. Technol. 16, 95–108. Goetzmann, C.A., Grüner, W., 1992. SBWR-200, a low-cost NPP with high inherent safety features. Nucl. Eng. Des. 136, 65–72. Hagen, T.H.J.J.V.D., Bragt, D.D.B.V., Kaa, F.J.V.D., Karuza, J., Killian, D., Nissen, W.H.M., Stekelenburg, A.J.C., Woters, J.A.A., 1997. Exploring the Dodewaard type-I and type-II stability; from startup to shutdown, from stable to unstable. Ann. Nucl. Energy 24, 8. Hagen, T.H.J.J.V.D., Stekelenburg, A.J.C., Bragt, D.D.B.V., 2000. Reactor experiments on type-I and type-II BWR stability. Nucl. Eng. Des. 200, 177– 185. Heisler, M.P., 1982. Development of scaling requirements for natural convection liquid-metal fast breeder reactor shutdown heat removal test facility. Nucl. Eng. Des. 80, 347. Heisler, M.P., Singer, R.M., 1981. Facility Requirements for Natural Convection Shutdown Heat Removal System Testing. Hemisphere, Washington, DC, p. 113. Inada, F., Furuya, M., Yasuo, A., 2000. Thermo-hydraulic instability of boiling natural circulation loop induced by flashing (analytical consideration). Nucl. Eng. Des. 200, 187–199. Ishii, M., 1971. Flow instabilities in two-phase mixtures in thermal equilibrium. Ph.D. thesis, Georgia Institute of Technology. Ishii, M., 1976. Study on flow instabilities in two-phase mixtures. Tech. Re ANL-76–23, Argonne National Laboratory. Ishii, M., Jones, O.C., 1976. Derivation and application of scaling criteria for two-phase flows. In: Two-phase Flows and Heat Transfer, vol. 1. NATO Advanced Studies Institute, Istanbul, Turkey, p. 163. Ishii, M., Kataoka, I., 1984. Scaling laws for thermal-hydraulic system under single-phase and two-phase natural circulation. Nucl. Eng. Des. 81, 411– 425. Ishii, M., Zuber, N., 1970. Thermally induced flow instabilities in two-phase mixtures in thermal equilibrium. In: Proceedings of the 4th International Heat Transfer Conference, vol. V. Tokyo. B5.11.
2375
Ishii, M., Revankar, S. T., Dowlati, R., Bertodano, M. L., Babelli, I., Wang, W., Pokharna, H., Ransom, V. H., Viskanta, R., Wilmarth, T., Han, J. T., 1996. Scientific design of Purdue University Multi-Dimensional Integral Test Assembly (PUMA) for GE SBWR. Tech. Rep. NUREG/CR-6309, U.S. Nuclear Regulatory Commission. Ishii, M., Revankar, S.T., Leonardi, T., Dowlati, R., Bertadano, M.L., Babelli, I., Wang, W., Pokharna, H., Ransom, V.H., Viskanta, R., Han, J.T., 1998. The three-level scaling approach with application to the Purdue University Multi-Dimensional Integral Test Assembly (PUMA). Nucl. Eng. Des. 186, 177–211. Jiang, S., Zhang, Y., Bo, J., Wang, F., 1998. Conversion from single to two-phase operation in a natural circulation nuclear reactor. Kerntechnik 63, 132. Jiang, S.Y., Yao, M.S., Bo, J.H., Wu, S.R., 1995. Experimental simulation study on startup of the 5 MW nuclear heating reactor. Nucl. Eng. Des. 158, 111– 123. Kocamustafaogullari, G., Ishii, M., 1983. Scaling criteria for two-phase flow loops and their application to conceptual 2x4 simulation loop design. Nucl. Technol. 65, 146–160. Lahey, R. T., Drew, D. A., 1980. An assessment of literature related to LWR instability modes. Tech. Rep. NUREG/CR-1414, U.S. Nuclear Regulatory Commission. Lin, J.H., Huang, R.L., Dawyer, C.D., 1993. SBWR core thermal-hydraulic analysis during startup. In: Proceedings of the ASME, JSME Nuclear Engineering Conference, vol. 1. 281–285. March-Leuba, J., Rey, J.M., 1993. Coupled thermohydraulics-neutronic instabilities in boiling water nuclear reactors: a review of the state of the art. Nucl. Eng. Des. 145, 97–111. Nissen, W., Voet, J.V.D., Karuza, J., 1992. The startup of the dodewaard natural circulation BWR-experiences. In: Proceedings of the International Confernce on Design and Safety of Advanced Nuclear Power Plants, vol. II. Tokyo. 25.2. Nissen, W.H.M., Voet, J.V.D., Karuza, J., 1993. The startup of the Dodewaard natural circulation boiling water reactor-experiences. Nucl. Technol. 107, 93–102. Rohatgi, U., Cheng, H., Khan, H., Slovik, G., 1996. RAMONA-4B: A computer code with three-dimensional neutron kinetics for BWR system transientsmodification assessment application. Tech. Rep. NUREC/CR-6359, BNL. Rohatgi, U.S., Cheng, H.S., Khan, H.J., Wulff, W., 1997. Preliminary phenomena identification and ranking tables (PIRT) for SBWR startup instability. Tech. Rep. NUREG/CR-6474, U.S. Nuclear Regulatory Commission. Saha, P., Zuber, N., 1974. Point of net vapor generation and vapor void fraction in subcooled boiling. In: Proceedings of the 5th International Heat Transfer Conference. Shiralkar, B.S., Alamgir, M., Andersen, J.G.M., 1993. Thermal-hydraulic aspects of the SBWR design. Nucl. Eng. Des. 144, 213–222. Sinha, R.K., Kakaodkar, A., 1990. Requirements for the design of the advanced heavy water reactor. In: IAEA TCM Workshop for Next Generation Water Cooled Reactors. Beijing, China. Tanimoto, K., Ishii, M., Lee, S.Y., 1998. Examination of transient characteristics of two-phase natural circulation within a freon-113 boiling/condensation loop. Nucl. Eng. Des. 183, 77–95. Wang, D., 1993. The design characteristics and construction experiences of the 5 MWt nuclear heating reactor. Nucl. Eng. Des. 143, 19–24. Wang, D., Ma, C., Dong, D., Ling, J., 1990. A 5 MW nuclear heating reactor. In: Proceedings of the Transactions of the American Nuclear Society 468– 481. Yadigaroglu, G., Zeller, M., 1994. Fluid-to-fluid scaling for a gravity- and flashing-driven natural circulation loop. Nucl. Eng. Des. 151, 49–64.
Startup transient simulation for natural circulation boiling water reactors in PUMA facility S. Kuran a , Y. Xu a , X. Sun a,1 , L. Cheng a , H.J. Yoon a , S.T. Revankar a , M. Ishii a,∗ , W. Wang b a
School of Nuclear Engineering, Purdue University, 400 Central Drive, West Lafayette, IN 47907, USA b U.S. Nuclear Regulatory Commission, Mail Stop T10K8, Washington, DC 20555, USA Received 19 July 2004; received in revised form 10 November 2005; accepted 10 November 2005
Abstract In view of the importance of instabilities that may occur at low-pressure and -flow conditions during the startup of natural circulation boiling water reactors, startup simulation experiments were performed in the Purdue University Multi-Dimensional Integral Test Assembly (PUMA) facility. The simulations used pressure scaling and followed the startup procedure of a typical natural circulation boiling water reactor. Two simulation experiments were performed for the reactor dome pressures ranging from 55 kPa to 1 MPa, where the instabilities may occur. The experimental results show the signature of condensation-induced oscillations during the single-phase-to-two-phase natural circulation transition. The results also suggest that a rational startup procedure is needed to overcome the startup instabilities in natural circulation boiling water reactor designs. © 2006 Elsevier B.V. All rights reserved.
1. Introduction Recently, vendors have proposed passive boiling water reactor (BWR) designs such as general electric’s simplified boiling water reactor (SBWR-600) (Duncan, 1988) and economic simplified boiling water reactor (ESBWR), Siemens’ small boiling water reactor(SBWR-200) (Goetzmann and Grüner, 1992), and the advanced heavy water reactor (AHWR) design in India (Sinha and Kakaodkar, 1990), the Dodewaard reactor in the Netherlands (Nissen et al., 1993) and the 5-MWt heating reactor in China (Wang et al., 1990). One of the most distinctive features of the passive BWR designs is the elimination of recirculation pumps and other active components which require ac power. Obviously, the simplifications based on the elimination of the recirculation pumps and associated piping systems enhance the safety and reduce the overall cost. However, the elimination of the recirculation pumps has certain disadvantages with respect to reactor control and the establishment of a rational startup procedure (Aritomi et al., 1990).
∗
Corresponding author. Tel.: +1 765 4944587; fax: +1 765 4949570. E-mail address: [email protected] (M. Ishii). 1 Present address: Department of Mechanical Engineering, Ohio State, University, 650 Ackerman Rd. Columbus, OH 43220, USA 0029-5493/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2005.11.002
The instability problem in the current BWRs has been investigated over several decades. Extensive experimental and analytical studies have been carried out for the coupled flow/power oscillations in conventional BWRs (Lahey and Drew, 1980; March-Leuba and Rey, 1993), but the instability problem in BWRs remains an issue during the startup transient in natural circulation BWRs (Chiang et al., 1994; Aritomi et al., 1993; Nissen et al., 1992). Shiralkar et al. (1993) described the main issues related to the thermal-hydraulics of the SBWR design, and the instabilities during the startup transient are considered an issue that needs to be resolved. The possibility of condensation-induced oscillations (geysering) during the startup is a concern for natural circulation BWR designs (Abe et al., 1994; Lin et al., 1993; Shiralkar et al., 1993). The geysering instability may occurs in a vertical subcooled liquid column which is heated at the bottom. The vapor generated near the exit of the heated section is condensed at the unheated section inlet by the subcooled liquid. The rapid decrease in the pressure due to the condensation causes the subcooled liquid to re-enter the heated section and restore the non-boiling conditions. The vapor generation and condensation cycles show the distinctive signature of geysering. Aritomi et al. (1990) investigated the geysering phenomenon in a single vertical channel during natural circulation BWR startup. They verified that the instabilities are pronounced when the subcooling at the inlet
2366
S. Kuran et al. / Nuclear Engineering and Design 236 (2006) 2365–2375
Nomenclature A cp D g G i ids k K l m ˙ N Nd NFr NPe Nsub NZu s ˙ Q qw q t t1φ V Vgj
flow area [m2 ] specific heat [kJ/kg] diameter [m] gravitational acceleration [kg/m s2 ] mass flux [kg/m2 s] enthalpy [J/kg] departure enthalpy [J/kg] thermal conductivity [W/m K] flow loss coefficient [−] length [m] mass flow rate [kg/s] dimensionless number [−] drift number [−] froude number [−] peclet number [−] subcooling number [−] zuber number [−] complex number [1/s] power [W] wall heat flux [W/m2 ] volumetric heat generation rate [W/m3 ] time [s] time at which Phase II starts [s] volume [m3 ] drift velocity [m/s]
Greek letters α void fraction [−] β volumetric thermal expansion coefficient [1/K] δ perturbation ifg latent heat [J/kg] ρ density difference between liquid and gas [kg/m3 ] icore core enthalpy rise [J/kg] P pressure drop [Pa] ξ perimeter [m] ρ density [kg/m3 ] τ time scale [s] υ velocity [m/s] Ψ property Subscripts and superscripts e equivalent f liquid g gas M model o reference value P prototype s saturation 1φ single-phase 2φ two-phase w wall or wetted
of the unheated section is high and the system pressure is low. Later, Aritomi et al. (1993) extended this study for the parallel channel system operating under forced and natural circulation conditions. They found that there is a strong correlation between the attained natural circulation flow rate and the condensation rate at the unheated section inlet in the occurrence of the geysering oscillations. Since the flow rate in a natural circulation BWR is a result of the density differential between the downcomer annulus and the inside of the shroud (core and chimney), the void distribution inside the core and chimney plays an important role in the flow dynamics. Void generation due to flashing inside the chimney greatly affects the attained natural circulation flow inside the reactor pressure vessel (RPV). Instabilities governed by the flashing in the chimney are also pronounced during the startup of natural circulation BWR designs. Fukuda and Kobori (1979) have demonstrated that the gravitational pressure drop perturbations are important in natural circulation systems at low-pressure and -quality conditions, even without flashing. However, the existence of flashing inside the chimney amplifies the importance of the gravitational pressure drop in the chimney and has additional non-linear effects on the system dynamics (Bragt et al., 2002; Inada et al., 2000; Tanimoto et al., 1998). Dodewaard reactor is a natural circulation reactor located in the Netherlands. Since the reactor is conceptually very similar to the proposed advanced BWR designs utilizing natural circulation, the experimental data from the operation of this reactor has been used to assess some of the key phenomena for natural circulation BWR designs (Nissen et al., 1993; Shiralkar et al., 1993). No startup instabilities were experienced during the February 1992 startup. However, the experiences gained from Dodewaard reactor may not be applied to some natural circulation BWR designs because of the differences in the geometry and operational parameters. Fukuda and Kobori (1979) classified several types of thermalhydraulic instabilities in a system with an unheated riser section. They described two different types of density wave oscillations: Type-I instability, which is dominated by the gravitational pressure drop perturbations in the unheated riser and Type-II instability, which is dominated by the frictional pressure drop in the heated section. Bragt and Hagen (1997a,b) investigated the nuclear-coupled instabilities in a natural circulation system by considering both Type-I and -II instabilities described by Fukuda and Kobori (1979). Hagen et al. (1997, 2000) reported the results of the experiments performed in the Dodewaard reactor with application to Type-I and -II instabilities. Hagen et al. (1997) has demonstrated that flashing in the chimney section is important for the Type-I oscillations. In view of the importance of flashing in natural circulation systems, Bragt et al. (2002) developed an analytical model for the dynamics of a natural circulation BWR under low-pressure conditions. The model was applied for the Dodewaard reactor to determine its stability characteristics at low-pressure. A 5-MW heating reactor developed by the Institute of Nuclear Energy and Technology at Tsinghua University has been in operation since 1989 (Wang, 1993; Wang et al., 1990). The reactor operates at low-pressure (1.5 MPa) and
S. Kuran et al. / Nuclear Engineering and Design 236 (2006) 2365–2375
2367
low-quality conditions. A series of experiments have been performed in an experimental facility to simulate the behavior of the reactor at low-flow and -pressure conditions (Jiang et al., 1995). Based on the experimental results, there are three kinds of flow instabilities observed in their experiments: geysering, flashing instability, and low-quality density wave oscillations. Jiang et al. (1995) proposed a startup procedure which includes the pressurization of the pressure vessel through the injection of a non-condensable gas into the steam dome. The transition phase from single- to two-phase natural circulation during startup is important for the geysering instability. Jiang et al. (1998) reported experimental results from the test loop which is used to simulate the 5-MW heating reactor. They showed that the steam space inside the pressure vessel has a significant effect on the oscillation amplitude. The startup transient in a typical natural circulation BWR design has been studied in the Purdue University MultiDimensional Test Assembly (PUMA) facility for the instabilities that may occur at low-pressure and -flow conditions. In this paper, the experiments performed for the prototypical value of the inlet flow loss coefficient are described. First, a brief description of the PUMA RPV and the instrumentation system is presented in the following section. Then, the startup procedure for a typical natural circulation BWR design is discussed with an emphasis on the possibility of instabilities. The investigation strategy developed based on the scaling criteria for single- and two-phase natural circulation systems is presented, and finally, the experimental results are discussed. 2. Experimental setup The PUMA facility was designed and built for a typical natural circulation BWR design to simulate the transient response following various loss-of-coolant-accident (LOCA) scenarios (Ishii et al., 1996). The facility has 1/4 height and 1/100 area ratio scaling, which corresponds to a volume scale of 1/400. It is designed to simulate transients where pressure is below 1.03 MPa (150 psia) following the initial blowdown. The reactor pressure vessel (RPV) component, which has been used to simulate the startup transient, and its major components are shown in Fig. 1. The lower plenum houses the non-heated portion of the fuelsimulating electrical heater rods. The perforated section on the shroud wall provides the lateral flow from the downcomer section. A new core inlet plate was designed and installed for the startup simulation experiments. Another plate was installed below the core inlet plate to adjust the core inlet flow loss coefficient without disassembling the RPV. Fig. 2 shows the loss coefficient adjustment mechanism and the top view of the core inlet plate. Cone-shaped cylinders attached to the lower plate enable to change the orifice flow area on the core inlet plate via moving the lower plate up and down. A position indicator was installed to indicate the position of the lower plate and thus the orifice flow area on the core plate. The PUMA core consists of four parallel channels: inner bypass, inner core (18 heater rods), outer bypass, and outer core
Fig. 1. PUMA RPV and its internals.
(20 heater rods). Several dummy rods were installed in the outer bypass and core channels to reduce the flow area and decrease the hydraulic diameter for the startup simulation experiments. The chimney section extends from the top of the core to the bottom of the steam separator assembly. Three quarters of the chimney height is in the partitioned section. The perforated steam separator support skirt provides a path for the liquid flowing downward through the downcomer section. The PUMA facility has a detailed instrumentation system to measure key thermal-hydraulic parameters such as temperature, local pressure, water-level, and local void fraction. Seventy thermocouples, three pressure cells, 16 differential pressure cell, and 20 conductivity probes were used in the startup simulation experiments. Twelve conductivity probes were installed in the core section at three different axial locations. The local void fraction was measured at four different axial locations inside the chimney section.
2368
S. Kuran et al. / Nuclear Engineering and Design 236 (2006) 2365–2375
Fig. 2. Flow loss coefficient adjustment mechanism and top view of the core inlet plate
3. Normal startup procedure for a typical natural circulation BWR design The normal startup procedure for a natural circulation BWR design such as the one given byLin et al. (1993) is discussed in this section regarding the instabilities at low-pressure and -flow conditions. The reactor startup starts from very low-pressure at the steam dome (55 kPa) following the deaeration process. Initially the steam dome is saturated at 80 ◦ C, and nuclear heating starts when certain control rods are withdrawn. The reactor water cleanup system (RWCU) is used for water-level control and to reduce the thermal stratification at the lower plenum. The reactor power is ramped from zero to a value which will heat up the water in the core at a maximum rate of 55 K/h. A phenomenon identification and ranking table (PIRT) has been developed at Brookhaven National Laboratory for the startup transient (Rohatgi et al., 1997). According to the PIRT, the startup transient can be divided into four distinct phases as far as the instabilities are concerned. Each phase is characterized by specific thermal-hydraulic conditions of the reactor. The phenomenon identification for the startup transient determines the simulation strategy in the PUMA facility. The four phases are described below. • Phase I — Single-phase core heat-up: At the beginning, the dome is saturated at 55 kPa. However, due to the large hydrostatic head in the downcomer, there is some subcooling in the lower plenum. The length of the single-phase core heat up phase depends on the heat-up rate and the amount of subcooling present at the core inlet. Since the single-phase flow is generally more stable than the twophase flow, there is no stability concern during this phase. However, the temperature distribution inside the RPV following this phase plays a very important role in the geysering instability. This phase is terminated when the net vapor generation starts at the core exit. The vapor generation due to flashing in the upper part of the chimney (around chimney– separator interface) is observed before net vapor generation in the core. However, the major thermal-hydraulic conditions are described as single-phase natural circulation in the RPV.
• Phase II — Net vapor generation in the core: This phase is the most important phase with respect to instabilities. The subcooled boiling at the core exit at low-pressure may generate large slug bubbles. When the net vapor generation starts, the chimney inlet is subcooled. The bubbles generated in the core are condensed at the chimney inlet during this phase. The amount of subcooling and the void fraction at the core exit determine the condensation rate. During this phase, condensation-induced geysering oscillations may take place. Depending on the established natural circulation flow, flow reversal may occur, leading to large-amplitude void oscillations. Therefore, the transition from Phases I to II is particularly important for determining a rational startup procedure. • Phase III — Saturated chimney: The condensation at the chimney inlet reduces the subcooling. However, due to the decreasing hydrostatic head from the inlet to the exit of the chimney, the local saturation temperature decreases. Flashing in the chimney plays an important role in this phase. The void generation due to the flashing greatly changes the gravitational pressure drop along the chimney and affects the natural circulation flow rate. Flashing-induced loop-type oscillations may occur during this phase. The propagation of void waves and the thermal non-equilibrium between the liquid and vapor along the chimney determines the dynamic characteristics of the flow. • Phase IV — Power ascension at full pressure: Starting from Phase II, the RPV pressure increases due to the significant void generation. The increase in the dome pressure causes void collapse and suppresses the possible oscillation at the latter stage of Phase III. The pressurization phase lasts until the full-pressure condition is reached. At the full pressure, the reactor power is increased to full power by adjusting the control rods. Since the power level is low and the system pressure is high, the stability margin of the reactor is quite high. 4. Scaling strategy The simulation strategy for the startup transient in natural circulation BWR designs was prepared based on single- and
S. Kuran et al. / Nuclear Engineering and Design 236 (2006) 2365–2375
two-phase similarity parameters. A detailed scaling strategy for single- and two-phase natural circulation systems with application to the PUMA facility design was developed by Ishii et al. (1998). The intention here is not to reproduce the strategy used in the PUMA facility design. However, the startup simulation strategy based on the startup procedure discussed previously is highlighted here. The scaling criteria for natural circulation systems are quite complicated due to the strong coupling of fluid flow and heat transfer. For single-phase natural circulation systems, the scaling laws were derived from area-averaged forms of continuity, integral momentum, and energy equations (Heisler, 1982; Heisler and Singer, 1981). The important dimensionless numbers characterizing geometric, kinematic, dynamic, and energy similarity are given by Kocamustafaogullari and Ishii (1983), Yadigaroglu and Zeller (1994) and Ishii et al. (1998). The single-phase natural circulation is not primarily important in stability of the system. However, temperature distribution inside the vessel and the power level prior to the two-phase natural circulation (initiation of Phase II) are particulary important for the condensationinduced oscillations. Therefore, the determination of the time at which single-phase-to-two-phase natural circulation occurs is the key for developing the simulation strategy for the startup transient. The time scale for a single-phase natural circulation system is given by (Kocamustafaogullari and Ishii, 1983): τR
oR
1/3 ,
βqo 2o /(ρf cpf )
(1)
R
qo
where is the power density, o , the reference length (heated section height), β, the liquid expansion coefficient, ρf cpf , the volumetric heat capacity of the liquid, and ΨR = ΨΨMP ; ΨM and ΨP stand for the variable Ψ of the model and prototype, respectively. From Eq. (1), it is obvious that the power and time scales are interrelated. Therefore, real-time simulation is possible by adjusting the power scale. For systems where both single- and two-phase natural circulation exist, achieving same time scale for the whole transient is a difficult task. A detailed discussion on the problem is presented following the introduction of the two-phase scaling parameters. Ishii (1971) derived the scaling criteria for two-phase flow systems by using the one-dimensional drift-flux model. This study was extended by Ishii and Jones (1976) for integral system scaling. Ishii (1971) analyzed the dynamic behavior and stability of a boiling flow system by using the one-dimensional drift-flux model and a first-order perturbation analysis. A perturbation of inlet flow (e.g. at the core inlet) is introduced in the following form: δυ(s, t) = est ,
(2)
where s = a + jω is a complex number. The real part, a, gives the amplification coefficient and the imaginary part, ω, represents the angular frequency. By integrating the governing field equations, several transfer functions can be derived relevant to major variables such as the velocity, void fraction, density, enthalpy, and pressure drop. It has been shown that both the steady-state and the transient responses of the system are gov-
2369
erned by the transfer function between the internal pressure drop and the inlet flow (Ishii, 1971). Therefore, 1 δυ = , δP Q(s)
(3)
where Q(s) is the characteristic equation for the system. The characteristic equation can be non-dimensionalized by introducing proper scales (Ishii, 1971, 1976; Ishii and Zuber, 1970). Thus Q∗ (s∗ ) = Q∗ (s∗ , N1 , . . . , Nm ),
(4)
where N1 , . . . , Nm represent the dimensionless groups that characterize the kinematic, dynamic, and energy similarities. The core inlet orificing and the other localized flow resistances are important geometrical parameters and appear as a part of the geometrical similarity group and should be kept prototypical for two-phase similarity requirements. The other important dimensionless groups related to the system operational conditions such as flow rate, reactor power level, and pressure are given as follows: • Zuber number (or previously known as phase change number) NZu =
ξ ˙ c ρ qw ρ Q h o = , Aυo ifg ρf ρg mi ˙ fg ρg ρg
(5)
where υo is the core inlet velocity, which is the reference velocity and o denotes the reference length, which is the core heated length. As it is clear from the definition given by Eq. (5), the Zuber number scales the phase change due to heat transfer to the system. Since it includes the total heat input ˙ c , the number also scales the power under both to the flow, Q single- and two-phase natural circulation conditions. • Subcooling number Nsub
isub ρ ifg ρg
(6)
The subcooling number takes into account the time-lag effects in the single-phase heated section due to the subcooling of the coolant entering the heated section (core). At low-pressure conditions, the hydrostatic head above the core inlet determines the amount of subcooling. Both Nsub and NZu are significant not only for the stability of a given two-phase flow system, but also for the description of steady-state conditions. Pressure-dependent property group in both Eqs. (5) and (6), ρ/ifg ρg , provides the basis of the pressure scaling. • Drift number Vgj or void-quality relation (7) Nd υo The drift number takes the relative motion between the phases into account. It characterizes the flow pattern through the vapor drift velocity, Vgj . The drift number is particulary important when Nd NZu , where the change of the density and velocity are controlled by the drift. • Density number ρg Nρ (8) ρf
2370
S. Kuran et al. / Nuclear Engineering and Design 236 (2006) 2365–2375
The density number or the density ratio number explicitly appears in the drift stress term in the mixture momentum equation (Ishii, 1971). It also appears in the two-phase friction term, depending on the constitutive equation used for twophase friction factor. The density ratio number, Nρ , scales the system pressure. However, when Nρ Nd 1 and the twophase friction factor is not a strong function of Nρ , the density ratio appearing in the Zuber and the subcooling numbers controls the pressure scaling. • Froude number NFr
υo2 ρf , g o αo ρ
(9)
where αo is the reference void fraction which can be determined from the kinematic similarity parameters (Ishii and Kataoka, 1984). The Froude number is particularly important for a natural circulation system. It represents the relative importance of the gravity with respect to the inertia. The similarity laws for the two-phase flow can be derived from the given dimensionless groups (Ishii et al., 1998). For the similarity of void generation, the Zuber and subcooling numbers are the important dimensionless groups that need to be conserved in both the model and prototype systems. It can be shown that the time scale under two-phase natural circulation condition is given by τR = loR , (10) where loR is the height scale. The time scale given by Eq. (10) is purely geometrical. Therefore, real-time simulation cannot be achieved in reduced-height facilities. The startup simulation strategy for natural circulation BWRs involves the transformation of the prototypical power/pressure transient into the model power transient. Fig. 3 demonstrates the reactor power and the steam dome pressure during the startup transient. The power transient given by Lin et al. (1993) was used as a boundary condition for RAMONA-4B calculations to calculate the steam dome pressure in the prototype. The RAMONA-4B code (Rohatgi et al., 1996) is extensively used for the BWR stability evaluation. The reactor steam dome pressure is about 55 kPa during the initial phase of the startup transient. There is no significant increase in the pressure during the singlephase natural circulation part of the startup (Phase I). When the reactor power is increased beyond a certain value, void generation starts in the core and two-phase natural circulation prevails inside the RPV. However, flashing at the upper part of the chimney can be observed before significant void generation in the core, since the steam dome is always saturated during the transient. Based on the different phases of the startup transient given in the previous section, the reactor steam dome pressures ranging from 55 kPa to 1 MPa were considered with respect to the instabilities. Considering the difficulties associated with the vacuum conditions during the early part of the startup transient, two pressure-scaling windows were considered and simulation experiments were performed to cover the aforementioned prototypical conditions:
Fig. 3. Power and pressure transient during the startup transient.
(1) scaled-up pressure test: this test covers the reactor dome pressures ranging from 55 to 500 kPa. This part of the transient is simulated by PUMA RPV dome pressures from 110 kPa to 1 MPa. (2) equal pressure test: in this test, the reactor steam dome pressures ranging from 110 kPa to 1 MPa were simulated in the PUMA RPV such that the dome pressure in the PUMA RPV becomes prototypical. Part of this test covers a certain part of the conditions simulated in the scaled-up pressure test. The simulation of the startup transient requires a calculation of the corresponding power transient in the PUMA facility by pressure scaling. To achieve the proper simulation, following factors were considered: • Core inlet subcooling is significantly affected by the hydrostatic head in the downcomer section. Since PUMA is 1/4 height scale facility, the core inlet subcooling in the PUMA is smaller. The subcooling number ratio between the prototype and the model can be approximated by means of the
Fig. 4. Pressure-dependent property group in Eq. (11).
S. Kuran et al. / Nuclear Engineering and Design 236 (2006) 2365–2375
Clasius-clapeyron relation such that, (Nsub )R ≈ (cpf Ts )R
ρ oR , ρg ifg R
(11)
where Ts is the saturation temperature at given pressure. During Phase I, the subcooling at the core inlet continiously decreases as the reactor power increases. The singlephase-to-two-phase transition can be considered as the time at which core inlet subcooling is removed. In this respect, the subcooling ratio, which is around 1/16, is close to the time scale during Phase I of the startup transient. The time scale in Phase I is particularly important for the similarity of the temperature distribution inside the vessel prior to Phase II. As shown in Fig. 3, the reactor power increases linearly with time during Phase I. For a kwown power transient, the time at which net vapor generation at the core exit can be calculated by using the following equation for both prototype and model: t1φ ˙ 1φ t1φ , m(t)i ˙ (12) core (t)dt = Q 2 0 where m ˙ is the natural circulation flow rate, which is calculated from the loop momentum integral for the singe-phase natural circulation rate, icore , the core enthalpy rise, t1φ , the time at which net vapor generation at the core exit starts, ˙ 1φ is the power level at the single-phase-to-two-phase and Q natural circulation transition occurs or the net vapor generation starts at the core exit. Since there is no external heat sink during the single-phase natural circulation, the core inlet temperature also increases due to heat addition in the core and it is also a function of the core flow rate. Therefore, a simple numerical algorithm is employed to calculate the core enthalpy rise and the natural circulation flow rate for a given core heat-up rate during single-phase core heat-up. For a more accurate treatment, subcooled boiling is taken into account through the departure enthalpy at which net vapor generation starts given by Saha and Zuber (1974): ⎧ ⎨ 0.0022 q De cpf N < 70000 Pe kf ids = ifs − (13) ⎩ q NPe ≥ 70000 154 G where ifs is the local saturated liquid enthalpy, G, the mass , the wall heat flux, and k is the liquid thermal conflux, qw f ductivity. The Peclet number, NPe is defined as NPe
Gcpf kf
(14)
where cpf is the liquid specific heat. Eq. (12) can be solved for t1φ numerically to calculate the time scale during Phase I. The calculations for both model and prototype yield τR = 1/17.2 for single-phase natural circulation. The time scale for the single-phase natural circulation is very small compared to 1/2 for the two-phase natural circulation. In other words, the single-phase natural circulation is terminated quickly in the model due to hydrostatic head difference.
2371
• The difference in solid structure heat capacity between the model and the prototype needs to be considered when determining the power transient. A certain portion of the total power increases the solid structure temperature. Therefore, ˙ ˙ ˙ c (t) + the total power, Q(t), is partitioned such that Q(t) =Q ˙ ˙ Qs (t). Qc (t) represents the power that goes to the coolant, ˙ s (t) denotes the portion of the total power which whereas Q increases the solid heat structure temperature. This power can be estimated from the following relation: ˙ s (t) = ρs cps Vs dTs , Q (15) dt where Ts is the volume-averaged heat structure temperature and Vs is the total solid structure volume. • The coolant power is scaled through Zuber number during the two-phase natural circulation. Therefore, the coolant power scale can be determined from ˙ c )R = AR υR ρf ρg ifg , (Q (16) ρ R
where AR is the area ratio, which is 1/100 in the PUMA facility and υR is the velocity ratio, which is related to the length scale during two-phase natural circulation. The last term in Eq. (16) represents the pressure-dependent property group which determines the pressure scaling. Since the inlet subcooling cannot be controlled independently, the effect of the core inlet subcooling was taken into account by evaluating the properties at lower plenum pressure. This is particularly important during the early phase of two-phase natural circulation or Phase II, which is covered by scaled-up pressure test. As the dome pressure increases, the relative importance of the hydrostatic head difference becomes less. The power level at the transition from single-phase-to-two-phase natural circulation (Phase I-to-II) is determined by using Eq. (16), since the power transient is a continious function (Fig. 4). Based on the above considerations, the PUMA heater power was scaled from the given reactor power transient. Fig. 5 presents the PUMA heater power during the scaled-up pressure test. Up to 350 s of the transient, the power linearly increases in time due to single-phase natural circulation. After 350 s, the property group ratio given in Eq. (16) determines the power transient through pressure scaling. The power transient calculated for the equal pressure test is shown in Fig. 6. The transient starts from relatively high power since the starting point of this test corresponds to a later stage of the startup transient where the reactor power is relatively higher. 5. Experimental results This section presents experimental results for the two different pressure-scaling tests where the core inlet loss coefficient is prototypical. 5.1. Scaled-up pressure test Fig. 7 compares the measured steam dome pressure in the PUMA and the calculated steam dome pressure in the reactor.
2372
S. Kuran et al. / Nuclear Engineering and Design 236 (2006) 2365–2375
Fig. 5. PUMA total power for the scaled-up pressure test.
Fig. 7. Steam dome pressure in scaled-up pressure test.
The experimental data is scaled up to the prototype conditions considering the pressure and time scales. From the figure, it can be clearly seen that reasonably accurate pressure transient can be reproduced in the PUMA facility by using the scaling strategy discussed in the previous section. The downcomer velocity measurement through the pitot tube is shown in Fig. 8. The signature of geysering oscillations is evident during the initial phase of the two-phase natural circulation. Fast Frouier transformation (FFT) analysis on the velocity data shown in Fig. 9 demonstrates that the oscillation has no well-defined dominant frequency, owing to its chaotic nature. However, oscillations with periods around 10–12 s can be distinguished. The void fraction at the exit of the core section was determined through averaging of the data from the four conductivity probes. The averaged void fraction at the core exit is shown in Fig. 10. The single-phase-to-two-phase natural circulation transition can be clearly observed in this figure. From Eq. (12), the duration of single-phase natural circulation was
Fig. 8. Downcomer velocity transient in scaled-up pressure test.
Fig. 6. PUMA total power for the equal pressure test.
Fig. 9. Power spectrum of downcomer velocity data for scaled-up pressure test.
S. Kuran et al. / Nuclear Engineering and Design 236 (2006) 2365–2375
Fig. 10. Area-averaged core exit void fraction in scaled-up pressure test.
estimated to be around 350 s. The void fraction data validates this estimate. Fig. 11 shows the conductivity probe measurement at the chimney inlet and exit in the scaled-up pressure test. A significant amount of flashing occurs in the chimney section. Due to the condensation at the chimney inlet, no void fraction developed in this section before about 1400 s. However, as the subcooling at the chimney inlet diminishes due to the condensation, bubbles tend to appear. Fig. 12 shows the variation of the subcooling at the chimney inlet. The subcooling decreases as the bubbles generated in the core section are condensed.
2373
Fig. 12. Subcooling at the chimney inlet for scaled-up pressure test.
As discussed in the previous section, the equal pressure test simulates the reactor dome pressures ranging from 110 kPa to 1 MPa. Therefore, the test includes the early part of the
two-phase natural circulation. Fig. 13 shows the steam dome pressure comparison. The figure clearly shows that the pressurescaling strategy yields a very similar steam dome pressure transient. The downcomer velocity measurement shown in Fig. 14 demonstrates the signature of the condensation-induced oscillations. As can be seen from the power spectrum in Fig. 15, similar to the scaled-up pressure test, it is difficult to identify the dominant period for the oscillations. However, it can be concluded that the oscillations have periods around 10–15 s. Figs. 16 and 17 show the void fraction at the core exit and the inlet and exit of the chimney, respectively. The flashing in the chimney is significant in this test and causes longer period oscillations because of the wave propagation phenomenon in this section of the RPV. As shown in Fig. 17, most of the voids appear to be at the chimney exit, showing the importance of flashing in the equal pressure test.
Fig. 11. Void fraction at the chimnet inlet and exit for scaled-up pressure test
Fig. 13. Steam dome pressure comparison in equal pressure test.
5.2. Equal pressure test
2374
S. Kuran et al. / Nuclear Engineering and Design 236 (2006) 2365–2375
Fig. 14. Downcomer velocity transient in equal pressure test.
Fig. 17. Void fraction at the chimney inlet and exit for equal pressure test.
6. Conclusions
Fig. 15. Power spectrum of the downcomer velocity data in equal pressure test.
An experimental investigation of the startup transient in a typical natural circulation BWR design was performed in the PUMA facility to study the startup instabilities. By using the pressure scaling, two sets of experiments were performed to simulate the startup transient for the reactor steam dome pressures ranging from 55 kPa to 1 MPa. The signatures of condensationand flashing-induced oscillations were observed in the simulation results. This clearly demonstrates the significance of the startup instabilities for natural circulation BWR designs. However, the inclusion of nuclear feedback such as void-reactivity feedback is indispensable to draw more realistic conclusions about the startup instabilities. Since the PUMA facility is a reduced-height facility, the flashing cannot be scaled unless pressure scaling is carried out to conserve the void generation due to flashing in the chimney. In the experiments described in this paper, the void generation in the core section was considered the pressure-scaling basis. The flashing is more pronounced in the reactor geometry due to its longer chimney section. The subcooling at the chimney inlet is also higher in the reactor and this yields to higher condensation rate. Based on the PUMA startup simulation tests, it can be concluded that oscillations (either induced by flashing or by condensation) would be more significant in the prototype design. Acknowledgments
Fig. 16. Average core exit void fraction in equal pressure test.
This study was carried out under the auspices of the U.S. Nuclear Regulatory Commission (NRC). The authors would like to thank F. Eltawila, J. Rosenthal, J. Kelly, S. Bajorek and J. Staudenmeier of the U.S. NRC for their support on the project. Authors also appreciate the valuable discussion on the subject with U.S. Rohatgi from Brookhaven National Laboratory (BNL).
S. Kuran et al. / Nuclear Engineering and Design 236 (2006) 2365–2375
References Abe, N., Yokobori, S., Nagasaka, H., Tsunoyama, S., 1994. Two-phase flow natural circulation characteristics inside BWR vessels. Nucl. Eng. Des. 146, 253. Aritomi, M., Chiang, J., Mori, M., 1993. Geysering in parallel boiling channels. Nucl. Eng. Des. 141, 111. Aritomi, M., Nagahashi, T., Chiang, J.H., Wataru, M., Mori, M., 1990. Transient behaviour of natural circulation for boiling two-phase flow (experimental results). In: Proceedings of the 6th Nuclear Thermal-Hydraulic, ANS Winter Meeting, Washington, DC. Bragt, D.D.B.V., Hagen, T.H.J.J.V.D., 1997a. Stability of natural circulation boiling water reactors. Part I. Description stability model and theoretical analysis in terms of dimensionless groups. Nucl. Technol. 121, 40–51. Bragt, D.D.B.V., Hagen, T.H.J.J.V.D., 1997b. Stability of natural circulation boiling water reactors. Part II. Parametric study of coupled neutronicthermohydraulic stability. Nucl. Technol. 121, 52–62. Bragt, D.D.B.V., Kruijf, W.J.M.D., Manera, A., Hagen, T.H.J.J.V.D., Dam, H.V., 2002. Analytical modeling of flashing-induced instabilities in a natural circulation cooled boiling water reactor. Nucl. Eng. Des. 215, 87–98. Chiang, J., Aritomi, M., Inoue, R., Mori, M., 1994. Thermo-hydraulics during startup in natural circulation boiling water reactors. Nucl. Eng. Des. 146, 241. Duncan, J.D., 1988. SBWR, a simplified boiling water reactor. Nucl. Eng. Des. 109, 73–77. Fukuda, K., Kobori, T., 1979. Classification of two-phase flow instability by density wave oscillation model. J. Nucl. Sci. Technol. 16, 95–108. Goetzmann, C.A., Grüner, W., 1992. SBWR-200, a low-cost NPP with high inherent safety features. Nucl. Eng. Des. 136, 65–72. Hagen, T.H.J.J.V.D., Bragt, D.D.B.V., Kaa, F.J.V.D., Karuza, J., Killian, D., Nissen, W.H.M., Stekelenburg, A.J.C., Woters, J.A.A., 1997. Exploring the Dodewaard type-I and type-II stability; from startup to shutdown, from stable to unstable. Ann. Nucl. Energy 24, 8. Hagen, T.H.J.J.V.D., Stekelenburg, A.J.C., Bragt, D.D.B.V., 2000. Reactor experiments on type-I and type-II BWR stability. Nucl. Eng. Des. 200, 177– 185. Heisler, M.P., 1982. Development of scaling requirements for natural convection liquid-metal fast breeder reactor shutdown heat removal test facility. Nucl. Eng. Des. 80, 347. Heisler, M.P., Singer, R.M., 1981. Facility Requirements for Natural Convection Shutdown Heat Removal System Testing. Hemisphere, Washington, DC, p. 113. Inada, F., Furuya, M., Yasuo, A., 2000. Thermo-hydraulic instability of boiling natural circulation loop induced by flashing (analytical consideration). Nucl. Eng. Des. 200, 187–199. Ishii, M., 1971. Flow instabilities in two-phase mixtures in thermal equilibrium. Ph.D. thesis, Georgia Institute of Technology. Ishii, M., 1976. Study on flow instabilities in two-phase mixtures. Tech. Re ANL-76–23, Argonne National Laboratory. Ishii, M., Jones, O.C., 1976. Derivation and application of scaling criteria for two-phase flows. In: Two-phase Flows and Heat Transfer, vol. 1. NATO Advanced Studies Institute, Istanbul, Turkey, p. 163. Ishii, M., Kataoka, I., 1984. Scaling laws for thermal-hydraulic system under single-phase and two-phase natural circulation. Nucl. Eng. Des. 81, 411– 425. Ishii, M., Zuber, N., 1970. Thermally induced flow instabilities in two-phase mixtures in thermal equilibrium. In: Proceedings of the 4th International Heat Transfer Conference, vol. V. Tokyo. B5.11.
2375
Ishii, M., Revankar, S. T., Dowlati, R., Bertodano, M. L., Babelli, I., Wang, W., Pokharna, H., Ransom, V. H., Viskanta, R., Wilmarth, T., Han, J. T., 1996. Scientific design of Purdue University Multi-Dimensional Integral Test Assembly (PUMA) for GE SBWR. Tech. Rep. NUREG/CR-6309, U.S. Nuclear Regulatory Commission. Ishii, M., Revankar, S.T., Leonardi, T., Dowlati, R., Bertadano, M.L., Babelli, I., Wang, W., Pokharna, H., Ransom, V.H., Viskanta, R., Han, J.T., 1998. The three-level scaling approach with application to the Purdue University Multi-Dimensional Integral Test Assembly (PUMA). Nucl. Eng. Des. 186, 177–211. Jiang, S., Zhang, Y., Bo, J., Wang, F., 1998. Conversion from single to two-phase operation in a natural circulation nuclear reactor. Kerntechnik 63, 132. Jiang, S.Y., Yao, M.S., Bo, J.H., Wu, S.R., 1995. Experimental simulation study on startup of the 5 MW nuclear heating reactor. Nucl. Eng. Des. 158, 111– 123. Kocamustafaogullari, G., Ishii, M., 1983. Scaling criteria for two-phase flow loops and their application to conceptual 2x4 simulation loop design. Nucl. Technol. 65, 146–160. Lahey, R. T., Drew, D. A., 1980. An assessment of literature related to LWR instability modes. Tech. Rep. NUREG/CR-1414, U.S. Nuclear Regulatory Commission. Lin, J.H., Huang, R.L., Dawyer, C.D., 1993. SBWR core thermal-hydraulic analysis during startup. In: Proceedings of the ASME, JSME Nuclear Engineering Conference, vol. 1. 281–285. March-Leuba, J., Rey, J.M., 1993. Coupled thermohydraulics-neutronic instabilities in boiling water nuclear reactors: a review of the state of the art. Nucl. Eng. Des. 145, 97–111. Nissen, W., Voet, J.V.D., Karuza, J., 1992. The startup of the dodewaard natural circulation BWR-experiences. In: Proceedings of the International Confernce on Design and Safety of Advanced Nuclear Power Plants, vol. II. Tokyo. 25.2. Nissen, W.H.M., Voet, J.V.D., Karuza, J., 1993. The startup of the Dodewaard natural circulation boiling water reactor-experiences. Nucl. Technol. 107, 93–102. Rohatgi, U., Cheng, H., Khan, H., Slovik, G., 1996. RAMONA-4B: A computer code with three-dimensional neutron kinetics for BWR system transientsmodification assessment application. Tech. Rep. NUREC/CR-6359, BNL. Rohatgi, U.S., Cheng, H.S., Khan, H.J., Wulff, W., 1997. Preliminary phenomena identification and ranking tables (PIRT) for SBWR startup instability. Tech. Rep. NUREG/CR-6474, U.S. Nuclear Regulatory Commission. Saha, P., Zuber, N., 1974. Point of net vapor generation and vapor void fraction in subcooled boiling. In: Proceedings of the 5th International Heat Transfer Conference. Shiralkar, B.S., Alamgir, M., Andersen, J.G.M., 1993. Thermal-hydraulic aspects of the SBWR design. Nucl. Eng. Des. 144, 213–222. Sinha, R.K., Kakaodkar, A., 1990. Requirements for the design of the advanced heavy water reactor. In: IAEA TCM Workshop for Next Generation Water Cooled Reactors. Beijing, China. Tanimoto, K., Ishii, M., Lee, S.Y., 1998. Examination of transient characteristics of two-phase natural circulation within a freon-113 boiling/condensation loop. Nucl. Eng. Des. 183, 77–95. Wang, D., 1993. The design characteristics and construction experiences of the 5 MWt nuclear heating reactor. Nucl. Eng. Des. 143, 19–24. Wang, D., Ma, C., Dong, D., Ling, J., 1990. A 5 MW nuclear heating reactor. In: Proceedings of the Transactions of the American Nuclear Society 468– 481. Yadigaroglu, G., Zeller, M., 1994. Fluid-to-fluid scaling for a gravity- and flashing-driven natural circulation loop. Nucl. Eng. Des. 151, 49–64.