CFD MODELLING OF MULTIPHASE SLUG FLOW IN A PRESSURIZED WATER REACTOR USING THE EULERIAN-EULERIAN MODEL AND ADAPTIVE INTERFACE SHARPENING SCHEME (ADIS) Dimitrios Papoulias1, Vinesh H. Gada2, and Mohit P. Tandon2 1 CD-adapco, A Siemens Business 200 Shepherds Bush Road, London W6 7NL, UK 2 CD-adapco, A Siemens Business Pune, Maharashtra 411001, India
[email protected],
[email protected],
[email protected] Simon Lo3 CD-adapco, A Siemens Business Trident House, Basil Hill Road, Didcot, OX11 7HJ, UK
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ABSTRACT In this study the flow operation of a scaled PWR replica is examined by means of computational fluid dynamic calculations (CFD), performed with the Eulerian-Eulerian Large-Scale Interface (LSI) model available in STAR-CCM+. The simulated transient scenarios considered different Counter-Current Flow Limitation conditions (CCFL), leading to water fluctuations in the Steam Generator (SG) compartment and in some cases flooding. To account for the effects of different multiphase morphologies coexisting in the flow regimes, the two-fluid model blends momentum-transfer phase interactions of dispersed bubbles and droplets as well as free-surfaces according to the local interfacial area density. The topology of separating LSI structures is reconstructed using the interface detection method suggested by Coste [1]. To preserve a sharp transition in the vicinity of the interface flow, the Adaptive Interface Sharpening Scheme (ADDIS) is used for the convective transport of the phasic volume-fraction. Moment-closures for the multiphase system of equations are formulated in terms of the k-ω turbulence model. Validation of the numerical predictions is performed against experimental measurements and high-speed flow visualizations reported in the work of Vallée [2]. KEYWORDS CCFL, LSI, ADIS, two-phase flow 1. INTRODUCTION The behavior and characteristics of two-phase flow regimes developing in PWR cooling systems are critical for the effective and safe operation of nuclear power plants. In the event of a sudden loss of coolant accident (LOCA), natural circulation trigged across the primary circuit allows the removal of the excess heat from the reactor cell. The cooling flow can potentially become unstable if the water level at the reactor pressure vessel (RPV) drops below the supply line. Under these conditions, the rate of steam generation at the RPV is amplified, causing the incoming liquid to deflect and flow upstream towards the steam generator (SG). This marks the onset of counter-current flow limitations (CCFL) across the hot-leg flow circuit, which undermine the natural cooling process.
To a great extent, experiments conducted in test channels and PWR replica models have provided useful results for understanding the multiphase dynamics developing in stratified free-surface flows as well as transitional two-phase regimes. A representative collection of experiments in this field is available in the work of Vellée [3]. The conducted laboratory tests documented in this thesis included co-current and counter current multiphase flows in transparent Horizontal Air/Water Channels (HAWAC) and scaled hotleg models, encountered at different operational envelopes. Using the experimental TOPFLOW facilities, the author of this work captured with the aid of high-speed cameras the transient evolution of stratified flows into different multiphase regimes, consisting of dispersed bubbles, droplets and liquid slugs, which coexisted and interacted at different parts of the flow channels. The Particle Image Velocimetry (PIV) and pressure measurements obtained in these parametric experiments, facilitated the derivation of scaling laws for the break-up occurrence of developing large-scale waves and the onset of limiting flood conditions, in terms of characteristic non-dimensional numbers. The kinematic behavior of fully-developed co-current stratified flows is described in the experiments of Fabre [4], based on PIV measurements for the turbulent shear-stress and mean phase velocities, acquired at different sections of the rectangular channel. Thermal and condensation effects due to Emergency Core Cooling (ECC) injection are analyzed in the scaled coldleg circuit tested by Janicot and Bestion [5]. In this case, temperature probes at various location across the pipe channel characterized the mass-transfer mechanism of different multiphase evaporating/condensing structures. Despite the valuable experimental results available in horizontal two-phase flows, the multiscale structures and multidisciplinary physical mechanisms involved in this type of regimes are difficult to model using a universal CFD approach. Most of the reported calculations in this field utilized the Eulerian two-fluid method and blending techniques for discriminating between dispersed phase regimes with bubbles and droplets, and areas where the fluids are segregated into different continua. Different variations of the Eulerian framework are proposed in the literature by Höhne et al. [6], Coste [1] and Gada et al. [7]. In each case, the methodologies assumed different drag models and blending functions for the interfacial momentum exchange across the spectrum of regimes. Surface tension effects in two-fluid models are expressed based on the Continuous Surface Force (CSF) approach [8], which in this framework is extended in order to account for the different fluids in the multiphase system [9]. For the advection of the interface, the suggested Eulerian models typically employed 2nd order upwind/central scheme, while a novel approach is developed in [10] for reconstructing a sharp interface between continuous phases using the HighResolution Interface-Capturing (HRIC) scheme. In some methods [11, 12], wall-type closures are modelled at the vicinity of fluid interfaces in order to resolve the shear-stress of the developing boundary layer. Egorov et al. [13] recommended a low Reynolds number (Re) treatment for modelling turbulence near large interfaces. In this approach, the specific dissipation rate is modified by incorporating a source-term proportional to the distance from the interface, which effectively leads to laminarization of the local flow. The results published using the aforementioned large interface models [14-16] appear to capture the morphology of different multiphase regimes in a more consistent manner, compared to traditional Eulerian techniques for continuous-dispersed flows. In the present work, an Eulerian multi-fluid approach is utilized for simulating CCFL effects in a PWR replica model. The two-fluid LSI model is supplemented with a detection algorithm for tracking the interface between separated continuous regimes as well as with a high-order adaptive sharpening scheme for preserving their topology. Momentum transfer between the coexisting interface and dispersed-phase regimes is modeled using a blended closure approach for the interaction forces.
2. EULERIAN LSI MULTIPHASE MODEL 2.1. Eulerian-Eulerian Two-Fluid Model In the context of the Eulerian multiphase approach the different phases are modelled as interpenetrating continua, coexisting in the flow domain. In that sense, a separate set of conservation equations is solved for each of the flow phase. Accordingly, each phase is characterized by its own velocity and temperature fields as well as physical properties, while sharing the same pressure. The flow phases are coupled by integrating momentum transfer-terms for the forces acting across the interfacial contact area. To account for the individual fluids at any location in the continuum, the flow variables are phase-averaged by means of the phasic volume fractions. By definition, the summation of the volume fractions of phases occupying the flow cells is equal to one. For incompressible and adiabatic flows, the continuity and momentum equations for phase k assume the following form: (
and, (
)+∇∙(
)+∇∙(
⨂
)−∇
(1)
)=0 +
,
=−
∇ +
+
(2)
where, αk, ρk and uk are the volume fraction, density and velocity vector of phase k, respectively. The remaining terms in Eq. 2 stand for the molecular τk and turbulent stresses τt,k, the pressure p and the sum of interfacial forces M. Typical closures for modelling the force-balance of dispersed flows with particles include effects due to drag, lift, virtual-mass as well as turbulent dispersion. For dispersed flow which also involve free surfaces, the momentum transfer term is supplemented with a surface-tension model [9], to account for the tangential tensile force of large-scale interfaces separating the fluids. In the current study, the interface drag law proposed by Ŝtrubelj and Tiselj [17] is blended with drag correlations for bubbles and droplets [18, 19], in order to couple the different flow regime (t): =
, ,
,
(3)
The summation in Eq. (3) is performed for the first regime (fr), the interface regime (ir) and the second regime (sr). The linearized drag in this expression is denoted as AD,t and ur stands for the slip velocity between the phases. The aforementioned drag model for the interface regime ensures that the slip between the phases is locally reduced and also assumes that the regime high the highest concentration imparts momentum to the surrounding phases. ,
=
1
(4)
where, tr is the relaxation time (=0.01 s), m stands for the mixture properties and p and s are the primary and secondary phases. The remaining term Wt in Eq. (3) corresponds to the blending weight of the different regimes, occupying each cell. For distinguishing between the dispersed and separated regimes, a volume-fraction based approach is employed similar to the techniques suggested in [1]. Accordingly, two user-defined thresholds are set for the volume-fraction of the secondary phase, which represent the terminus (αfr) and onset (αsr) of the dispersed regimes. In that sense three flow topologies are detected for a pair of primary (p) and secondary phases (s). For example, in a system where p and s phases are water and air respectively, the
regimes are classified as follows: i) dispersed bubbly flow in continuous liquid (0
