A THERMAL-HYDRAULICS MODEL NUMERICAL ANALYSIS OF BWR INSTABILITY PREDICTIONS USING THE DYNOBOSS CODE Mauricio A. Pinheiro Rosa* and Michael Z. Podowski** *Instituto de Estudos Avançados – IEAv Centro Técnico Aeroespacial – CTA 12931-970 Sâo José dos Campos, SP, Brasil **Rensselaer Polytechnic Institute – RPI 12181 Troy, New York, USA ABSTRACT This paper is concerned with the analysis of the effects of various modeling and computational concepts applied to the main system components of a BWR loop on the accuracy of the predicted system response for natural circulation operating conditions near the marginal stability boundary. Both stable and unstable loop operating conditions have been considered in the analysis using the DYNOBOSS (DYnamics of NOnlinear BOiling SystemS) computer code. The overall loop response has shown to be more sensitive to the numerics of the reactor core and downcomer than the others components of the loop. Keywords: boiling water reactor, numerical methods, two-phase flow, reactor dynamics, reactor instabilities. I. INTRODUCTION A brief description of the models and numerical methods in DYNOBOSS is given below, followed by a The dynamics of boiling water nuclear reactors sensitivity study of this code`s predictions. (BWR) is governed by several complex physical phenomena, such as coolant thermal-hydraulics, heat transfer in reactor fuel element and core neutronics. The II. OVERVIEW OF THE DYNOBOSS CODE nonlinear nature of most phenomena involved and the coupling effects between them make the overall predictions DYNOBOSS (DYnamics of NOnliner BOiling of BWR stability very sensitive to the modeling SystemS) is a computer code for the analysis of transient assumptions and numerical methodologies used in the and instabilities in boiling systems in general and in boiling analysis. water nuclear reactors (BWR), in particular. The code has The objective of this paper is to study the effects of two options: a system parallel boiling channels, and a selected modeling and computational concepts applied to a boiling loop model. a BWR recirculation loop, in particular the reactor core and The BWR model in DYNOBOSS accounts for all downcomer, on the accuracy of the predicted system major components of the BWR nuclear steam supply system response for natural circulation operating conditions near as shown in Figs. 1 and 2. These components are the reactor the marginal stability boundary. The DYNOBOSS core, upper plenum, steam riser, steam separator and steam model/computer code [1-4] has been used in this analysis. dome in the boiling (two-phase) region of the loop and the An important feature of DYNOBOSS is the inclusion of downcomers and lower plenum in the nonboiling (single- various two-phase flow modeling assumptions and phase) part of the loop. The reactor thermal-hydraulics is numerical parameters in the integration scheme which based on a one-dimensional (1-D) modeling framework. In readily allow for numerical testing of the various this approach, both kinematics (phasic slip) and components of the loop and validation of the overall BWR thermodynamic (subcooled boilng) nonequilibrium are loop model against measured data such as of the LaSalle-2 accounted for using a four-equation model of two-phase BWR instability event [3]. flow. The equations governing two-phase/single phase flows in the various components of the loop are: Volumetric Flux Equation parameters, and either position-and-time-dependent or average parameters. ¶ ¶ r j g = Gv f g - vg a (1) ¶ z ¶ t STEAM DOME Void Propagation Equation STEAM STEAM DRYER ¶ a ¶ jg ¶r g + = vg (G - a ) (2) ¶ t ¶ z ¶ t STEAM SEPARATOR L SW FEEDWATER with G , the volumetric evaporation rate, given by RISER DOWM- COMER dh dh f g dp UPPER PLENUM , [1 - r (1 - a) - r a ] q f dp g dp dt G = + (3) h AXS h fg fg CORE JET PUMP Mixture Energy Conservation Equation LOWER PLENUM ¶ ¶ [r f hl (1 - a) + r h a] + [r j h + r j h ] = ¶ t g g ¶ z f l l g g g q, ¶ p = + , (4) A ¶ t Figure 1. Schematic of a BWR Nuclear Steam Supply xs System. Mixture Momentum Conservation Equation r j 2 2 ¶ G ¶ f f r g jg ¶ p + [ + ]+ + F + F = 0 , (5) ¶ t ¶ z 1-a a ¶ z f g , where G is the mass flux, q is the linear heat rate and F f and Fg are, respectively, the wall friction and gravity forces per unit area. All flow parameters are averaged over the flow cross sectional area, and the remaining notation in Eqs (1) – (5) is as in Lahey & Moody [5]. The governing equations for single-phase liquid flow can be derived from the two-phase flow equations, Eqs. (1) - (5), by setting a , G and jg to zero. In this case, Eqs. (1) and (2) reduce to the condition j = jl (z, t) = jin (t) . These equations can be used in the calculations for the single- phase region of the channels as well as for the single-phase part of the recirculation loop (lower and upper downcomers and lower plenum). An important feature of the model is that it includes two options regarding the subcooled boiling phenomena: a profile-fit model [6] and a mechanistic model [5]. Another option is also available in which subcooled boiling is ignored. Similarly, the effects of phasic slip can be Figure 2. Reactor Pressure Vessel Components and Coolant accounted for using different modeling assumptions, such as Flow Diagram Modeled in the DYNOBOSS Code. the EPRI [7] correlation or user specified drift-flux The numerical method of solution of the governing Alternatively, Eq. (10) can be integrated along the equations is based on a two-parameter approach which characteristic, d y / d t = jin (t) , between instants tn-1 and allows for testing and quantifying the effects of both tn to yield temporal and spatial implicitness on the results of calculations. The governing equations are first discretized in t space: n y(zn , tn ) = y(zn-1, tn-1)+ S(t) d t (11) - ò d yi R( yi ) R( yi-1) t + = ci (6) n-1 d t D z where where the node-average variable, yi , is expressed as a zn = zn-1 + jin (tn ) D t (12) weighted average of the values at node boundaries By applying Eq. (11) to evaluate the energy of fluid yi = (1 - s ) yi-1 + s yi (7) particles entering the channel at time instants, tn , and tracking down their positions using Eq. (12), the time- where 0 < s £ 1. dependent fluid energy at the channel exit can be calculated. Taking Eq. (6) over all the nodes, after some Because the method of characteristics is based on an manipulations one obtains analytical solution, it does not suffer the problem of numerical dispersion and diffusion. d y = H y + d = g (8) Certain components of the BWR loop, typically d t those characterized by a low L / A ratio, can be modeled using a simplified lumped-parameter approach. Specifically, The, the finite-difference approximation of Eq. (8) is integrating Eq. (10) between the inlet (zin ) and the exit given as ( zex ) of a given control volume, yields y n - y n-1 = (1-q ) y n-1 +q y n D t (9) [ ] d y jin (t) + [yex (t) - yin (t)] = S(t) (13) d t L where 0 < q £ 1 is a measure of temporal implicitness of the scheme. z Depending on the values of q and s , various 1 ex where L = zex - zin and y(t) = y(z, t) d z . numerical schemes are obtained, from fully explicit for L ò zin q = 0 , through semi-implicit (Crank-Nicholson) for Assuming y = y in Eq. (13) yields a perfect q = 0.5 to fully implicit q = 1. ex The method described above has also been used for mixing model, the nonboiling portion of the BWR recirculation loop. In this case, however, another approach has also been d yex jin (t) jin (t) + yex (t) = S(t) + yin (t) (14) developed based on the method of characteristics. The d t L L advantage of applying this method to single-phase liquid flows (where the effects of local compressibility are Eq. (14) is solved for the variable y at the exit of negligible) is that it does not require spatial discretization the control volume using implicit/semi-implicit methods of and thus, is more accurate and faster than nodal methods. integration for ordinary differential equations. For a constant-area section of a nonboiling channel, Table 1 summarizes the methods and approaches the propagation of the thermal waves can be evaluated by used in the modeling and respective numerical solution of rewriting Eq. (4) as the main components of a BWR loop implemented in the DYNOBOSS code. ¶ ¶ y(z, t) + [ jin (t) y(z,t)] = S(z, t) (10) ¶ t ¶ z III. NUMERICAL ANALYSIS where y = r f hl . When Eq. (10) is applied to external As indicated in the previous section, the portions of the BWR loop, such as the downcomers, the DYNOBOSS code has been implemented in a way which source term, S , mainly accounts for heat transfer with the readily allows for testing the accuracy of predictions by reactor vessel wall and is normally small. comparing the effects of various modeling assumptions and Similarly as for the two-phase flow equations, the parameters in the solution scheme on the results of same finite difference approximation given by Eq. (9) which calculations. Several results of DYNOBOSS testing and uses the two-parameter approach can be applied to Eq. (10). validations have been reported before [1-4] against both experimental [8] and other models computer code [9]. TABLE 1. Methods and Approaches METHODS AND COMPONENTS OF APPROACHES THE LOOP Finite-difference method Reactor core, Steam with two interpolation riser and upper and parameters lower downcomers Lumped-parameter approach Upper and lower with implicit/semi-implicit plena, steam methods for ODEs separator and upper downcomer Method of characteristics Upper and lower (MOC) downcomers Figure 3.