Modelling of the droplet entrainment phenomena for the simulation of - PDF document

Transactions of the Korean Nuclear Society Virtual Spring Meeting July 9-10, 2020 Modelling of the droplet entrainment phenomena for the simulation of reflood phase during a large-break loss-of-coolant accident in a pressurized water reactor Jee Min Yoo, Byong Jo Yun, Jae Jun Jeong* School of Mechanical Engineering, Pusan National University (PNU) *Corresponding author: jjjeong@pusan.ac.kr 1. Introduction amount of droplets generated at the QF using Kelvin- Helmholz instability analysis and data of vertical pipe The droplet has a large surface area per unit volume reflood experiments. However, it remains to be and so it has excellent heat transfer characteristics. In a questioned whether the assumptions and experimental large-break loss-of-coolant (LOCA) in a pressurized data used in the model development adequately water reactor (PWR), droplet behavior in the reactor reflected the droplet entrainment phenomena of the rod core is very important. In particular, the droplets bundle condition. downstream of the quench front (QF) during the reflood phase greatly affect the thermal-hydraulic phenomena Table I: Existing droplet entrainment correlations inside the reactor core. The droplets reduce the Correlations     temperature of the superheated vapor through interfacial       min 1.0,5.0 max 0.0, max 0.0, m m m 1 ,   E l E d i heat transfer and evaporate near the fuel to increase wall  2  heat transfer. That is, the droplet behavior downstream   u   g  1.5min 2.5,   m m 1   of the QF is closely related to the prediction of fuel E   g  u  COBRA-TF crit   temperature. The droplets entrained into the U-tubes 0.25 induce the so-called steam binding effect, which also 0.25        4 We g   affects the core heat removal.   d  u crit   2 3    C Downstream of the QF, a post-dryout regime D   g (inverted flow) is formed. To observe the thermal- 0.25     hydraulic behavior under this flow condition,    3.57 g   1/6    u N  crit  g visualization experiments have been conducted[1-5].  2    C D l  g Through the experiments, various droplet entrainment Yonomoto  mechanisms in the post-dryout regime were identified. g  N  g 0.5 However, a few studies have been conducted to develop        the droplet entrainment model using the experimental   g    g  observation results. And there are still insufficient    6 0.625     4 10 experimental and theoretical researches related to the m Ai u u We E l l g l droplet entrainment phenomena downstream of the QF.   CATHARE3 2   u u D In this paper, a droplet entrainment model was g g l h  We proposed based on the results of the experiments  observing the droplet entrainment phenomena in post-   0.5 2 2    P u u dryout regime. The proposed model and the existing , , crit l h g crit g bqf  8 1.83 Holowach   1.46 10 Re m , E g gen models[6-9] were implemented into the CUPID code A f [10], in which the 3-field model is applied. And they were evaluated using reflood heat transfer experiments, 3. Modelling of the droplet entrainment phenomena such as FLECHT SEASET [11] and FEBA [12]. 3.1. Droplet entrainment phenomena in the post-dryout 2. Existing droplet entrainment models regime The COBRA-TF, a subchannel analysis code, has Ishii[2-4], Jarlais[1], Babbelli[5] performed the used a droplet entrainment model in which the gas mass visualization experiments to understand the thermal- flow rate is multiplied by several engineering hydraulic behavior in the post-dryout regime. They factors(Table I). This model has been applied in the observed the post-dryout flow under adiabatic and reflood analysis for a long time. In the study of Valette diabatic conditions using Freon-113. As a results of the et al.[9], reflood heat transfer experiments were experiments, the post-dryout flow was divided into an simulated using the CATHARE3 code, in which the inverted annular flow, agitated regime, and dispersed entrainment model based on relative velocity of gas and droplet regime. Under the inverted annular flow liquid was applied. The models used in both codes conditions, droplets were produced on the core liquid contain several engineering factors(Table I), but the jet through varicose jet breakup, sinuous jet problem is that the basis of these factors is not clear. breakup(Fig. 1) and roll-wave entrainment. In the Holowach et al.[8] developed a model to predict the agitated region formed downstream of the inverted

Transactions of the Korean Nuclear Society Virtual Spring Meeting July 9-10, 2020 annular flow, droplets were generated from the core L   B . (3) liquid jet and the liquid sheet located near the heating w u l surface (Fig. 1). The dispersed droplet regime consisted  and in Eqs. 2 and 3 are calculated using the L B of multiple droplets and a small amount of liquid correlations proposed by Ishii and Jarlais[2]. Table II ligament. Through these, it can be seen that droplets are shows the correlations for the varicose jet and the mainly entrained from the core liquid jet and liquid sinuous jet. sheet in the post-dryout regime. The experimental result that the liquid sheet is generated from the crest of the roll wave[2] and the result of instability analysis for the liquid sheet of Senecal[13] were introduced to derive the droplet entrainment on the liquid sheet. It is assumed that the (a) Varicose jet liquid sheet is uniformly located near the heating surface. The correlations for the liquid sheet breakup are summarized in Table III. The droplet entrainment model was applied as shown in Table IV based on the post-dryout regime map of TRACE code[14]. The study of Ishii and Denten [4] showed that the agitated region existed up to about 0.85 void fraction. Based on this, conditions of void fraction (b) Sinuous jet from 0.6, which is the transition criteria for the inverted slug, to 0.85 are considered as the agitated regime. When the void fraction is 0.85 or more, it is considered as a dispersed droplet flow. In this flow condition, the assumption that all the continuous liquid phases become droplets was applied, and so the droplet entrainment rate was defined as    . m u E l l l (c) Liquid sheet breakup Table II: Correlations for varicose and sinuous jet Fig. 1. Schematics of liquid jet and sheet Correlations for varicose jet   5.8 D 3.2. Modelling jet  4 sub l A A f  ,  D N In this study, based on the observation results of the jet jet  A sub visualization experiments, the droplet entrainment rate  0.53 0.5  480Re of the core liquid jet and the liquid sheet was modeled L We D B j j jet using some correlations[2] and instability analysis[13]. Correlations for sinuous jet The entrainment rate is defined as follows. 2   g V   7.6  entr l . (1) D jet m E We  , g rel A f w A where  and are liquid density and flow area,  4 sub l f A A  l f  N D jet jet  A , sub respectively. To obtain , the volume of entrained m E 0.645 droplets, entr , and the breakup time w  were modeled.  2   V  0.53 0.5   g  685Re L We D In the case of the core liquid jet breakup in the inverted B j j jet   We ,  g rel  annular flow, it is assumed that the droplets detached by the wavelength of the wave,  , based on the Table III: Correlations for the liquid sheet experiment of Ishii and Jarlais[2]. And, assuming that   there is a core liquid jet per subchannel, entr is defined  s rw V V P entr h 2 2 as follows. 2   3  2   . (2) g   [13],   V N D 7.6 D entr jet jet s rw jet 4 2  We , u g rel g r In the above equation, and are the number of N D jet jet   1 a [13]   ln   jets and the jet diameter, respectively. w  is defined as w   w a ,max 0 r the breakup length L divided by the velocity of the B 3 6  4    u liquid jet. a g r  , ln   12 w ,max r 2     27 a 0 l