Science and Technology of Nuclear Installations

Volume 2018, Article ID 1426718, 11 pages

https://doi.org/10.1155/2018/1426718

## Effects of Diameters on Countercurrent Flow Limitation at a Square Top End in Vertical Pipes

^{1}Institute of Nuclear Technology, Institute of Nuclear Safety System, Inc., 64 Sata, Mihama-cho, Mikata-gun, Fukui 919-1205, Japan^{2}Graduate School of Engineering, Kobe University, 1-1 Rokkodai, Nada-ku, Kobe-shi, Hyogo 657-8501, Japan

Correspondence should be addressed to Michio Murase; pj.oc.ssni@esarum

Received 14 September 2018; Accepted 15 November 2018; Published 2 December 2018

Academic Editor: Tomoaki Kunugi

Copyright © 2018 Michio Murase et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The falling liquid flow rate under flooding conditions is limited at a square top end of a vertical pipe in the pressurizer surge line with the diameter of about 300 mm that consists of a vertical pipe, a vertical elbow, and a slightly inclined pipe with elbows. In this study, therefore, we evaluated effects of diameters on countercurrent flow limitation (CCFL) at the square top end in vertical pipes by using existing air-water data in the diameter range of* D* = 19-250 mm. As a result, we found that there was a strong relationship between the constant and the slope* m* in the Wallis-type correlation where the Kutateladze parameters were used for the dimensionless gas and liquid velocities. The constant and the slope* m* increased when the water level is increased in the upper tank* h*. CCFL at the square top end of the vertical pipes could be expressed by the Kutateladze parameters with = 1.53±0.11 and* m* = 0.97 for* D* ≥ 30 mm. The values were smaller for* D* = 19-25 mm than those for* D* ≥ 30 mm.

#### 1. Introduction

Under postulated accident conditions such as loss-of-coolant accidents (LOCAs) in pressurized water reactors (PWRs), steam and condensate water form countercurrent flows in a hot leg (consisting of a horizontal pipe, a 50-deg vertical elbow, and a short inclined pipe) and a pressurizer surge line (consisting of a slightly inclined pipe with elbows, a vertical elbow, and a vertical pipe), and flooding may occur. For transient and accident analyses of PWRs, characteristics of countercurrent flow limitation (CCFL) should be considered strictly, where CCFL is defined by the relationship between the time-averaged gas superficial velocity and falling liquid superficial velocity, and , under flooding conditions, because the falling liquid flow rate affects the water mass in the reactor core and cooling of the fuel rods.

Previously, we (Murase et al. [1]) developed a one-dimensional computation method with parameters adjusted from CCFL data in hot leg and pressurizer surge line models (Mayinger et al. [2]; Minami et al. [3]; Futatsugi et al. [4]), and we could predict CCFL in nearly horizontal pipes for the hot leg and pressurizer surge line within a practical uncertainty. There are only a few CCFL experiments simulating the pressurizer surge line with a diameter of about 300 mm. In available data (Takeuchi et al. [5]; Futatsugi et al. [4]; Yu et al. [6, 7]), the pipe diameters were* D* = 30-90 mm, so that the CCFL data were not sufficient to evaluate effects of the diameters. In the pressurizer surge line, the falling liquid flow rate is limited at the square top end of the vertical pipe, and so we (Yamamoto et al. [8]) derived a correlation for CCFL-U at the square top end for the pressurizer surge line by using existing data for* D* = 19-140 mm (Richter [9]; Doi et al. [10]). However, CCFL-U behavior is very complex and there are some disagreements among experimental data. Therefore, it is important to evaluate effects of the diameters on CCFL-U at the square top end of vertical pipes and to apply these results to the pressurizer surge line.

In this study, we evaluated effects of diameters on CCFL-U at the square top end in vertical pipes by using existing air-water data reported by Richter [9] for* D* = 19-140 mm, Doi et al. [10] for* D* = 30-60 mm, Wallis and Kuo [11] for* D* = 19-145 mm, Bharathan et al. [12] for* D* = 19-250 mm, and Matsumura and Kaminaga [13] for* D* = 20 mm. From data by Richter [9], Wallis and Kuo [11], and Bharathan et al. [12], CCFL-U for large diameters was evaluated. The effects of the water level in the upper tank were evaluated from data mainly by Doi et al. [10], and the difference between data by Richter [9] and Doi et al. [10] was discussed. From the results, CCFL-U characteristics were classified depending on the diameter, the shape of the top end, and the water level in the upper tank, and features of CCFL-U were summarized. All data used in this study were obtained under air-water conditions at atmospheric pressure.

#### 2. Previous Studies on CCFL at the Square Top End

##### 2.1. General Form of CCFL Correlation

For safety analyses during transients and accidents in nuclear power plants, the CCFL correlation by Wallis [15] has often been applied to evaluate the falling liquid flow rate. The general form of the Wallis correlation is given bywhere [m/s^{2}] is the gravitational acceleration,* J* [m/s] is the superficial velocity, [-] is the dimensionless velocity, [m] is the characteristic length, and* ρ* [kg/m

^{3}] is the density. The slope

*m*and the constant

*C*

_{i}are determined from experiments, where the subscripts K and W show the Kutateladze parameter and Wallis parameter for , respectively. Bankoff et al. [16] defined the characteristic length bywhere

*D*[m] is the diameter,

*L*[m] is the Laplace capillary length, and

*[N/m] is the surface tension. In (1), indicates the Wallis parameter at*

*σ**β*= 0, while is the Kutateladze parameter at

*β*= 1. and can be converted to each other by using , as follows:Equations (2) and (3) show primary parameters for the length scale (

*D*or

*L*) and fluid properties (

*and*

*ρ**). However, it is well known that in (3) changes depending on*

*σ**D*in vertical pipes (Wallis and Makkenchery [17]) and that the liquid viscosity (which is not included in (2) and (4)) affects CCFL in vertical pipes (Wallis [15]).

##### 2.2. CCFL Characteristics and Technical Issues

Figure 1 shows CCFL characteristics at the square top end in vertical pipes. CCFL data reported by Richter [9] and Doi et al. [10] are well expressed by the Kutateladze parameters. From the data of* D* =19-140 mm in Figure 1(a), the Wallis-type correlation (6) was derived using the least-square method (Yamamoto et al. [8]).Figure 1(b) shows the CCFL constant , which was obtained for each experimental case using the least-square method. Data by Wallis and Kuo [11] are not the CCFL constant but the zero water penetration (ZWP), which generally agrees with . Technical issues are disagreements between data by Richter [9] and Doi et al. [10] for* D* = about 30 mm, and data by Richter [9] and Wallis and Kuo [11] for* D* = about 140 mm. The values by Richter [9] and the ZWP values by Wallis and Kuo [11] suggest that CCFL characteristics might be expressed by the Wallis parameter ( = 0.7) for the region of small diameters of* D* < 40 mm, but this should be confirmed from CCFL data.