A Boiling Water Reactor (BWR) circulates water past nuclear fuel in a large pressure vessel at 6.9 MPa. The nuclear fuel is configured as cylindrical pellets contained within long metallic tubes, referred to as fuel rods. The fuel rods are combined in various arrangements within flow channels to create fuel assemblies. Several hundred such fuel assemblies are connected in parallel between inlet and outlet plena. These parallel fuel assemblies are referred to as the core of a BWR. During passage of water along the nuclear fuel, significant boiling and vapor formation occur — typically producing 10% to 20% vapor flow that exits into the outlet plenum. The resultant vapor is separated and directed to steam turbines for electrical generation. The remaining liquid is circulated back, along with condensate liquid returning from the turbines, to the inlet plenum. Key components of a jet-pump BWR steam supply system are illustrated in Figure 1.
Normal operation of a BWR depends upon accurate prediction of several key thermal hydraulic parameters in the fuel assemblies. In particular, vapor void fractions, transition boiling limits and fuel assembly pressure drops must be accurately predicted to support BWR design and operation. Prediction methods must address the range of two-phase flow regimes from subcooled liquid at the fuel assembly inlet to annular flow at the outlet. (See Forced Convective Boiling.)
The surrounding channels on BWR fuel assemblies effectively isolate flows within each fuel assembly. This allows the necessary two-phase flow characteristics to be evaluated by reproducing realistic thermal hydraulic conditions in isolated fuel assembly simulation tests. Such simulations require large experimental facilities that can reproduce the power and flows of full-scale BWR fuel assemblies, using electrically heated fuel rod simulators. Data from such full-scale experiments are used to provide very accurate empirical relationships for the two-phase flow parameters required for BWR design analyses.
The vapor Void Fraction is the fraction of the flow area that is occupied by vapor. This is directly related to the average velocity of the vapor. In a BWR, the circulating water serves both as cooling medium and neutronic moderator for the nuclear fuel. This produces close coupling between power generation and two-phase flow conditions in the fuel assemblies. The primary coupling parameter is the density of the steam-water mixture surrounding the nuclear fuel. Predicting the two-phase density requires accurate prediction of the void fraction.
Fuel assembly Pressure Drop is one of the most important parameters determining conditions in the BWR core. Fuel assembly power and flows can differ significantly due to mechanical and nuclear design differences, as well as locations within the core. To assure appropriate flow distribution to all of the fuel assemblies, it is important to have accurate predictions of pressure drops over the entire range of fuel assembly operating conditions. (See Pressure Drop, Two-Phase.)
Boiling transition refers to conditions where typical boiling heat transfer starts to deteriorate. This has also been referred to as critical heat flux (see Burnout). The boiling transition limit for BWR operation is usually associated with deterioration of the liquid film flowing on a fuel rod under annular flow conditions. The fuel rods of a BWR fuel assembly utilize zirconium alloy, which minimizes parasitic capture of neutrons, for the outer metallic tubes. This material has good corrosion resistance for temperatures existing under typical boiling conditions. However, if boiling transition conditions are exceeded, the deteriorated heat transfer causes higher temperatures in the fuel. If such conditions persist for an extended period of time, the increased corrosion rate of the metallic tubes can cause fuel failures. Therefore, accurate predictions of boiling transition limits are very important for reliable BWR operation.
The elimination of crossflows between BWR fuel assemblies allows for both realistic experimental simulations of fuel assembly thermal hydraulics and simplified analyses methods. BWR analyses methods typically utilize either one dimensional representations of fuel assemblies or subchannel representations. One-dimensional analyses utilize correlations based on cross-sectional averaged flow quantities, with empirical parameters to account for radial variations where necessary. Nuclear coupling based upon one-dimensional values is usually sufficiently accurate for typical BWR fuel assemblies. Representative solution techniques and correlations are discussed by Collier (1980) and Lahey (1993). Subchannel analyses icorporate more detailed mechanistic descriptions of two-phase flow phenomena to predict crossflows and local parameters within fuel assemblies. Subchannel methods are summarized by Shiralkar (1992).
One-dimensional void fraction predictions are often based on the Drift Flux concept of Zuber (1965). Average vapor velocity is characterized by the average of local vapor drift velocities and the volumetric flux adjusted by a distribution parameter. The distribution parameter incorporates radial phase and velocity distribution effects. These parameters are determined from experimental void fraction data. While the original drift flux work anticipated discrete values of these parameters for various flow regimes, considerable success has been achieved by Dix (1971) and Chexal (1991) with continuous correlation relations which implicitly reflect the effects of flow regimes. These correlations are usually assumed to be insensitive to power distribution changes across the fuel assemblies. It has been confirmed by recent data from Yagi (1992) which demonstrated that average void fraction results were unchanged even when large variations were imposed in local void fractions within a typical BWR fuel assembly.
One-dimensional pressure drop predictions typically use average values for void fraction and flow quality in combination with standard two-phase flow formulations and correlations. Single-phase pressure drop data associated with wall friction and local losses are necessary to provide the reference bases for each specific fuel assembly design.
Boiling transition limits reflect local liquid film disruptions on individual fuel rods. Those limits are dependent upon both local film flow characteristics and local power distributions across fuel assemblies. Mechanical spacers, which maintain fuel rod spacing along their axial lengths, have important effects on boiling transition limits. Detrimental thinning of the fuel rod liquid films can be caused just upstream of the spacers, while favorable deposition of droplets into the liquid films can be caused just downstream of the spacers. The detrimental upstream effects are usually sufficient to cause initial boiling transitions to occur just upstream of spacers. However, the favorable downstream effects usually dominate, such that boiling transition improves with closer axial pitch of the spacers. Boiling transition limits can vary by 10% due to mechanical features of the spacers.
Predictions of boiling transition are often based on one dimensional averaged parameters, such as critical quality and boiling length, with empirical treatments of local effects. Such correlations can provide very accurate predictions but require extensive calibration with full scale test results for each specific fuel assembly design and radial power distribution range. This extensive testing requirement is one of the major motivations for more general subchannel analyses methods.
Subchannel analyses methods are based upon radial solution meshes within the fuel assemblies. Subchannel methods divide fuel assemblies into a number of interacting flow regions for analyses. The models then track liquid films, core vapor and core entrained droplets as separate fields for each of the subchannel regions. The goals for subchannel methods are to provide predictions which are mechanistically-based and less dependent upon full-scale calibration experiments, particularly for the development of new fuel designs.
Since BWR boiling transition limits are related to the deterioration of annular liquid films flowing on fuel rod surfaces, the subchannel methods incorporate mechanisms to predict and track the net liquid flows in those films, as well as criteria for the minimum film flows corresponding to film disruption and boiling transition. Key aspects for these film predictions are liquid evaporation, entrainment of liquid from the film to the vapor/droplet core and deposition of droplets from the core onto the surface films. Flow distributions among the subchannel regions usually require empirical mechanisms such as ‘void drift’ to achieve the overall flow distributions observed in BWR fuel assembly experiments.
The effects of fuel rod spacers are very important in determining boiling transition limits of BWR fuel assemblies, as previously discussed. Current subchannel methods incorporate various modeling assumptions to describe these spacer effects, including empirical parameters which must be calibrated with full scale boiling transition data for the specific spacer to be analyzed. General modeling of these spacer effects in subchannel analyses will require a further level of detail and mechanistic understanding which is not yet available.
Current subchannel modeling methods provide excellent predictions of boiling transition for limited variations from their calibration bases. Void fraction distributions are also predicted quite well by these methods, except for highly heterogeneous conditions across fuel assemblies. In general, subchannel methods are appropriate tools for BWR analyses, but further developments are necessary to significantly reduce dependence on full-scale testing for final design applications.
Parallel flow channels and close coupling between neutronic power and two-phase flow conditions can cause instability conditions in a BWR. Accurate predictions and avoidance of potentially unstable conditions are important for reliable BWR operation. Two types of instability can occur. Density wave oscillations can be driven by the two-phase hydraulics in individual fuel assemblies, with only minor effects from neutronic coupling. Alternatively, core-wide neutronic coupling can cause instabilities in many or all of the fuel assemblies. The fuel assemblies can all have oscillations in-phase, or local regions can oscillate. Accurate predictions of these oscillation conditions require coupled solutions of neutronics and two-phase flow equations. The same basic one-dimensional formulations for two-phase flow parameters are also applied in stability predictions. Both frequency domain and time domain solution techniques are used successfully for these analyses, as discussed by Lahey (1993). (See Instability, Two-phase.)
One of the most challenging and well-researched areas of BWR analyses is the prediction of safety system and fuel cooling responses to a wide range of accidents that might result in the loss of coolant water from the core. Postulated breakage of pipes connected to the pressure vessel are the primary bases for these accident evaluations. BWR designs include emergency systems to distribute coolant above the core, as well as systems to refill the pressure vessel and reflood the core if it does become uncovered during an accident. Modern BWR designs also include recirculation pumps within the pressure vessel (rotary or jet pumps) to minimize the size of potential breaks to pressure vessel connections.
Predictions of fuel cooling under these postulated loss of coolant accident (LOCA) conditions require detailed system simulation methods to analyze the transient two-phase fluid conditions adjacent to the fuel as the postulated accident proceeds. Accurate predictions require modeling of flow and heat transfer of flow and heat transfer with surface temperatures well above Leidenfrost conditions. Elements include falling liquid films, reflooding from below and countercurrent flows of the two phases. Modeling requirements for accurate BWR/LOCA predictions are summarized by Andersen (1985).
Large scale experiments have demonstrated that condensation of vapor by subcooled liquid and three-dimensional distribution effects are important aspects determining the progression of emergency coolant to the fuel. A significant effect for BWR/LOCA is the accumulation and drainage of coolant water in the plenum region above the core. Countercurrent flow limitation (CCFL) conditions at the top of fuel assemblies cause accumulation of emergency coolant water in a pool above the core. Some fuel assemblies then experience downward flow of subcooled liquid, while others experience counter-current flows. The results of this complex pattern are rapid reflooding and cooling of BWR core. These effects and other LOCA studies are summarized by Dix (1983). (See also Flooding and Flow Reversal.)
The Simplified Boiling Water Reactor (SBWR) is a new reactor design which incorporates passive safety features rather than active safety systems used previously. This design includes a gravity drain pool inside the containment to provide liquid to the core in case of a LOCA. Heat exchangers submerged in large water pools outside the containment absorb energy from within the reactor containment and transport it to the atmosphere. The latter energy transport occurs without any activation in case of a LOCA. The water pools have sufficient capacity to transport decay heat for several days and can be replenished from outside the containment.
Since the SBWR is designed to maintain the core covered during a LOCA, the primary design limit is containment structure pressure capability. Prediction of containment pressure responses for such events requires computer programs that address the entire coupled system. Condensation on the containment concrete walls and structure, as well as interaction effects between steam and other noncondensable gases, are particularly important for accurate predictions of these slow transient responses.
Andersen, J. G. M., Chu, K. H., Cheung, Y. K., and Shaung, J. C. (1985) BWR Full Integral Simulation Test (FIST) Program, TRAC-BWR Model Development Volume 2 — Models, GEAP-30875-2,NUREG/CR-4127-2, EPRI NP-3987-2.
Chexal, B., Lellouche, G., Horowitz, J., Healzer, J., and Oh, S. (1991) The Chexal-Lellouche Void Fraction Correlation for Generalized Applications, NSAC Report-139.
Collier, J. G. (1980) Convective Boiling and Condensation, McGraw Hill.
Dix, G. E. (1971) Vapor Void Fractions for Forced Convection with Subcooled Boiling at Low Flow Rates, General Electric NEDO-10491 (PhD Thesis, University of California Berkeley).
Dix, G. E. (1983) BWR Loss of Coolant Technology Review, Proceedings ANS Symposium Thermal Hydraulics of Nuclear Reactors, Volume 1.
Lahey, R. T. and Moody, F. J. (1993) The Thermal Hydraulics of a Boiling Water Reactor, ANS Monograph.
Shiralkar, B. S. (1992) Recent Trends in Subchannel Analysis, Proceedings of the International Seminar on Subchannel Analysis, Tokyo.
Yagi, M., Mitsutake, T., Morooka, S., and Inoue, A. (1992) Void Fraction in BWR Fuel Assembly and Evaluation of Subchannel Code, Proceedings of the International Seminar on Subchannel Analysis, Tokyo.
Zuber, N. and Findlay, J. (1965) Average Volumetric Concentration in Two-Phase Flow Systems, Transactions of ASME, Volume 87, Series C.
- Andersen, J. G. M., Chu, K. H., Cheung, Y. K., and Shaung, J. C. (1985) BWR Full Integral Simulation Test (FIST) Program, TRAC-BWR Model Development Volume 2 â€” Models, GEAP-30875-2,NUREG/CR-4127-2, EPRI NP-3987-2.
- Chexal, B., Lellouche, G., Horowitz, J., Healzer, J., and Oh, S. (1991) The Chexal-Lellouche Void Fraction Correlation for Generalized Applications, NSAC Report-139.
- Collier, J. G. (1980) Convective Boiling and Condensation, McGraw Hill.
- Dix, G. E. (1971) Vapor Void Fractions for Forced Convection with Subcooled Boiling at Low Flow Rates, General Electric NEDO-10491 (PhD Thesis, University of California Berkeley).
- Dix, G. E. (1983) BWR Loss of Coolant Technology Review, Proceedings ANS Symposium Thermal Hydraulics of Nuclear Reactors, Volume 1.
- Lahey, R. T. and Moody, F. J. (1993) The Thermal Hydraulics of a Boiling Water Reactor, ANS Monograph.
- Shiralkar, B. S. (1992) Recent Trends in Subchannel Analysis, Proceedings of the International Seminar on Subchannel Analysis, Tokyo.
- Yagi, M., Mitsutake, T., Morooka, S., and Inoue, A. (1992) Void Fraction in BWR Fuel Assembly and Evaluation of Subchannel Code, Proceedings of the International Seminar on Subchannel Analysis, Tokyo.
- Zuber, N. and Findlay, J. (1965) Average Volumetric Concentration in Two-Phase Flow Systems, Transactions of ASME, Volume 87, Series C.