Science and Technology of Nuclear Installations

Volume 2018, Article ID 2153019, 10 pages

https://doi.org/10.1155/2018/2153019

## On the One-Dimensional Modeling of Vertical Upward Bubbly Flow

^{1}Department of Mechanical Engineering and Construction, Universitat Jaume I, Campus del Riu Sec, 12080 Castelló de la Plana, Spain^{2}Institute for Energy Engineering, Universitat Politècnica de València, Camí de Vera, s/n, 46022 València, Spain^{3}Research Institute for Industrial, Radiophysical and Environmental Safety, Universitat Politècnica de València, Camí de Vera, s/n, 46022 València, Spain

Correspondence should be addressed to S. Chiva; se.iju.cme@avihcs

Received 27 July 2017; Accepted 6 December 2017; Published 16 January 2018

Academic Editor: Tomasz Kozlowski

Copyright © 2018 C. Peña-Monferrer 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 one-dimensional two-fluid model approach has been traditionally used in thermal-hydraulics codes for the analysis of transients and accidents in water–cooled nuclear power plants. This paper investigates the performance of RELAP5/MOD3 predicting vertical upward bubbly flow at low velocity conditions. For bubbly flow and vertical pipes, this code applies the drift-velocity approach, showing important discrepancies with the experiments compared. Then, we use a classical formulation of the drag coefficient approach to evaluate the performance of both approaches. This is based on the critical Weber criteria and includes several assumptions for the calculation of the interfacial area and bubble size that are evaluated in this work. A more accurate drag coefficient approach is proposed and implemented in RELAP5/MOD3. Instead of using the Weber criteria, the bubble size distribution is directly considered. This allows the calculation of the interfacial area directly from the definition of Sauter mean diameter of a distribution. The results show that only the proposed approach was able to predict all the flow characteristics, in particular the bubble size and interfacial area concentration. Finally, the computational results are analyzed and validated with cross-section area average measurements of void fraction, dispersed phase velocity, bubble size, and interfacial area concentration.

#### 1. Introduction

Two-phase flow phenomena have been an object of study during several decades with a great impact in nuclear field. From the reactor to the turbines, one can find a wide variety of systems where two-phase flow plays a main role: BWR core, secondary loop, or reactor heat removal system (RHRS) are examples of two-phase flow components. In such cases, two-phase flow is present in normal operating conditions, but also in specific situations, like instabilities events, loss-of-coolant accidents, or refueling. The previous cases imply different conditions of pressure, temperature, or mass flow.

This broad range of situations is considered in one-dimensional thermal-hydraulics codes to set the appropriate flow regime in each situation. They are based on the two-fluid model [1], where averaged Navier-Stokes equations are solved for each phase including momentum, energy, and continuity equations. Then, one can account for the interaction terms between phases, to consider the mass transfer, momentum, and energy at the interface. The interfacial momentum term differs depending on which flow regime is working. The proper regime is selected according to a flow regime map and the velocities of each phase. Different flow regime maps have been proposed by different authors [2, 3]. This paper investigates the performance of RELAP5/MOD3 predicting the results of experiments in a vertical upward bubbly flow for low velocity conditions. Bubbly flow at those conditions can be found in pressurizers, reactor pools, or refueling operations. To investigate in depth the bubbly flow behavior and the one-dimensional modeling, we perform experiments in a vertical pipe of around 6 meters of length along which an air-water fluid in bubbly regime moves upwards in adiabatic conditions and atmospheric pressure.

In the one-dimensional two-fluid model (1D TFM) the drag term plays the main role in the interfacial momentum transfer. System codes use different approaches to model the interfacial drag force depending on the flow regime. Two approaches are usually used to define the interfacial drag force: the drift-velocity approach (DVA) and the drag coefficient approach (DCA).

RELAP5/MOD3 uses DVA for bubbly flow in vertical pipes and DCA was used in the previous version RELAP5/MOD2. The drift models, although simpler than the drag coefficient approach, are usually only valid in the range of applicability for which they were obtained as they depend on flow and geometry.

In this work we make use of DCA in RELAP5/MOD3, by modifying the code. The drag force calculated with DCA relies on correlations that are defined traditionally as a function of Reynolds and/or Eötvös numbers, making the calculation of the drag term more general than with the drift-velocity.

However, the use of DCA incorporates a set of assumptions to calculate the drag term. We propose a more rigorous version of the drag coefficient approach () that has been implemented to evaluate the influence of these assumptions, consisting of the following:(i)A drag coefficient correlation that takes into account the effect of the bubble shape through the Eötvös number and the effect of the contaminants present in the system used.(ii)Bubble size distribution (BSD) consideration by means of its statistical parameters including the axial evolution due to the gas expansion.(iii)Interfacial area calculated directly from the definition of the Sauter mean diameter of the BSD.

In summary, three drag coefficient approaches are used: a drift-velocity approach named DVA, an existing drag coefficient approach DCA, and the proposed drag coefficient approach (see Figure 1).