The effects of surface tension on flooding in counter-current two-phase flow in an inclined tube

Abstract

The purpose of the present study is to investigate the effects of surface tension on flooding phenomena in counter-current two-phase flow in an inclined tube. Previous studies by other researchers have shown that surface tension has a stabilizing effect on the falling liquid film under certain conditions and a destabilizing or unclear trend under other conditions. Experimental results are reported herein for air–water systems in which a surfactant has been added to vary the liquid surface tension without altering other liquid properties. The flooding section is a tube of 16 mm in inner diameter and 1.1 m length, inclined at 30–60° from horizontal. The flooding mechanisms were observed by using two high-speed video cameras and by measuring the time variation of liquid hold-up along the test tube. The results show that effects of surface tension are significant. The gas velocity needed to induce flooding is lower for a lower surface tension. There was no upward motion of the air–water interfacial waves upon flooding occurrence, even for lower a surface tension. Observations on the liquid film behavior after flooding occurred suggest that the entrainment of liquid droplets plays an important role in the upward transport of liquid. Finally, an empirical correlation for flooding velocities is proposed that includes functional dependencies on surface tension and tube inclination.

Introduction

The current work focuses on the dependence of flooding on surface tension for counter-current liquid–gas flow in tubes of various inclinations. Flooding can be defined as the onset of flow reversal of the liquid component which results in an upward co-current flow. While studies by other researchers have indicated significant surface tension effects on the conditions for flooding occurrence, the results have not been consistent. The current work aims to extend the understanding of the physics of the relationship between surface tension and flooding phenomena by clarifying the flooding mechanisms under various values of surface tension for a range of tube inclinations. Such understanding is important because the surface tension varies in applications from that of air–water at room temperature. Industrial applications employ various fluids that have different thermophysical properties. Steam and water in nuclear reactors at higher temperature and pressure will also have a greatly different surface tension. A mechanistic understanding of the role of surface tension will allow for more accurate analysis techniques to promote extended operation and improved safety.

Counter-current two-phase flow in vertical tubes has many applications in a diverse range of process industries. The phenomenon of flooding is of considerable technological importance, as flooding can be a limiting factor in the operation of equipment. For example, in a pressurized water reactor (PWR), the counter-current flow of steam (upward) and cold water (downward) may take place in vertical channels when the emergency core cooling (ECC) water is injected into the reactor vessel. This leads to complex processes including the condensation of steam due to the introduction of cold water into the reactor core. Most importantly, upward steam flow may prevent sufficient cooling of reactor components by the ECC water.

Flooding in inclined channels can also potentially occur in a variety of situations, such as the pressurizer surge line of a PWR. The pressurizer surge line is typically comprised of several sections with various inclination angles. Under certain accident conditions, counter-current flow takes place in the surge line with liquid flowing down from the pressurizer vessel and steam flowing up from the hot leg of the reactor pressure vessel. The steam venting rate as well as the liquid draining rate may affect the ECC actuation [20].

Chung et al. [3] reported that the surface tension had a stabilizing effect on flooding, i.e. the flooding gas velocity was lower for a lower surface tension. English et al. [7] found the same trend. However, Kamei et al. [10] found the opposite trend. On the other hand, Suzuki and Ueda [19] reported that the effect of surface tension was complicated and the flooding gas velocity took its maximum value at a surface tension close to 5.0 × 10⁻² N/m.

While the above studies were performed in vertical tubes, little work has been reported on the effects of surface tension in inclined tubes. Barnea et al. [1] studied air–water counter-current two-phase flow in an inclined tube for a wide range of inclinations (1–90° from horizontal). They reported that the gas velocities upon flooding occurrence increase and then decrease as the tube inclination is changed from horizontal to vertical. Zapke and Kroger [23] investigated the effect of gas and liquid properties upon flooding in inclined tubes, but they only examined a tube inclination of 60°. Next Mouza et al. [15] examined the incipient flooding in inclined tubes of small diameter. In the conclusion of their study, it is suggested that additional data is needed in order to explain the effects of liquids and gases properties on flooding and to assess the significance of dimensionless numbers employed for general correlations. A more detailed survey of the literature for flooding in inclined tubes was performed and a simplified analytical model to predict the optimum channel inclination angle for gas venting has been proposed by Liao and Vierow [12].

Recently, a subset of the authors [6] observed the liquid film behavior upon flooding of an adiabatic counter-current two-phase flow in an inclined tube by using the combination of time variation measurements of liquid hold-up taken along the tube and visual observation. The liquid hold-up is the fraction of the tube cross sectional area occupied by liquid. This work provides the basis for studies of the effects of surface tension in inclined tubes. They reported that there are two prevalent locations of flooding in an inclined tube which are associated with distinct conditions: “lower flooding” and “upper flooding”, respectively. The terms lower flooding and upper flooding indicate whether flooding is initiated at the lower or the upper locus of the test section.

Lower flooding occurred at lower liquid flow rate and high tube inclination angle, and the breakdown of the waves at the air–liquid interface occurred in the lower part of the tube (x/L ranged from 0.0 to 0.5). Here, L is the total tube length and x is the distance from liquid outlet. The breakdown of waves is considered as the point of flooding because all the liquid supplied cannot flow down smoothly. It is initiated by the increase of the wave height, in which the wave formation is begun from the upper part of the test tube (x/L ≅ unity). The wave height increases with the downward movement. It is disrupted by the air flow when the wave height reaches a certain height in counter-current flow. Liquid droplets arise at nearly the same time of the breakdown of the wave and there is no upward motion in the liquid film.

On the other hand, upper flooding occurred at higher liquid flow rate and low tube inclination. It is initiated by the formation of low void fraction region in the upper part of the test tube (x/L ≅ unity), in which the maximum of liquid hold-up is 1.0. For small tube diameters, the liquid slug can completely bridge the cross sectional area of the test tube. It moves downward for a short distance and is broken up by air flow in the upper part of the test tube (x/L from 0.5 to 1.0). Furthermore, it was noticed that there was no reverse motion of the liquid film at the point of flooding during the occurrence of either lower flooding or upper flooding.

The objective of the current work is to carry out a series of flooding measurements for different surface tension values, making detailed observations in each case, to clarify the governing phenomena for flooding and the post-flooding conditions of partial liquid delivery and zero penetration. In this paper, the experimental results of instantaneous liquid hold-up at the point of flooding and afterwards, under a single liquid flow rate, will be presented first for a range of surface tension values. This data will reveal information on the wave growth and the propagation direction of the liquid film. The philosophy of upper flooding and lower flooding, as proposed in the previous papers, will be extended. Next, the effect of surface tension on the gas velocity at flooding and possible explanations will be presented. The effect of surface tension on flow patterns occurring after flooding, namely partial liquid delivery and zero penetration, are also experimentally examined. Finally, an empirical correlation for the onset of flooding gas velocity that incorporates the effect of liquid surface tension is proposed.