Pressure drop, void fraction and wave behavior in two-phase non-Newtonian churn flow
Introduction
Pressure drop is of great concern for industrial process design which in turn depends strongly on the better understanding of flow patterns. Extensive researches have been carried out in gas and Newtonian liquid systems and the characteristics of two-phase flow in horizontal, inclined and vertical pipes have been fully addressed (Wallis, 1969, Hewitt and Hall-Taylor, 1970, Omebere-Iyari and Azzopardi, 2007). However, many commonly used fluids (e.g., lacquers or polymer solutions) are non-Newtonian, i.e. their viscosity exhibits a non-linear relation between stress and rate of deformation. Remarkably, non-Newtonian viscosity has a dominant effect on flow structures and properties of gas and non-Newtonian liquid two-phase flow (Xu, 2010, Xu et al., 2010, Bar et al., 2010). Hence, how non-Newtonian fluid affects flow pattern and system pressure gradient is of great interest for industrial applications. As one of the least known flow patterns, churn flow is generally characterized by the presence of a very thick and unstable liquid film with liquid frequently oscillating up and down (Hewitt and Hall-Taylor, 1970, Jayanti and Hewitt, 1992). It occurs not only in Newtonian systems (Hewitt and Hall-Taylor, 1970, Jayanti and Hewitt, 1992, Barbosa et al., 2001, Wang et al., 2013) but also in non-Newtonian fluids (Dziubinski, 1986, Dziubinski et al., 2004) in vertical pipes. Essentially, the breakdown of slug flow and the existence of huge waves result in a drastic change in pressure gradient (Owen, 1986), which would cause damage to equipment in industrial processes where such a highly-disturbed flow pattern occurs. Cases in point include gas lift in chemical engineering, emergency cooling of reactor cores in case of loss of coolant, and potential flow pattern transition from severe slugging to churn flow in pipeline-riser systems, etc.
The pressure drop in two-phase flow is heavily influenced by gas-liquid interface roughness. Previous models for the impact of liquid viscosity on pressure drop and void fraction have focused on the annular flow of gas and non-Newtonian liquids on the assumption that the gas-liquid interface is smooth (Shedd and Newell, 2004, Shu, 1981, Li et al., 2013). Given that the gas-liquid interface in annular flow has been demonstrated to be not smooth but rather wavy and irregular (Hewitt and Hall-Taylor, 1970), the assumption is intended to provide a simplified approach to analysis since the amplitude of ripples and disturbance waves is relatively small compared to the pipe diameter. However, huge waves of large amplitude flow up and down throughout the churn flow regime, causing the liquid film to act as a very rough wall. Its roughness significantly affecting the frictional component of pressure drop (Parsi et al., 2015a, Parsi et al., 2015b, Sharaf et al., 2016, Wang et al., 2017a). Additionally, huge waves act as the main source of entrained droplets during their movement and are observed to have a noticeable effect on pressure drop of the system (Hewitt et al., 1985, Azzopardi and Wren, 2004, Sawai et al., 2004, Wang et al., 2017b). Some relevant experimental and theoretical analysis of the effect of viscosity on churn flow have been carried out. Parsi et al. (2015a) employed a dual wire mesh sensor to measure void fraction and two-phase interfacial structures in churn flow to study the effect of liquid viscosity on churn flow. They discussed the effect of liquid viscosity on the variation of mean void fraction and proposed that increasing liquid viscosity yielded a decrease in the frequencies of huge waves. Nevertheless, research findings regarding the pressure drop and void fraction in gas/non-Newtonian churn flow are lacking.
The present study investigates the flow characteristics with non-Newtonian fluids under the churn flow condition. We develop an analytical model for predicting pressure drop, void fraction and wave behavior in churn flow with both Newtonian and non-Newtonian fluids. We employ the power-law model to describe the non-Newtonian fluid and study the effect of liquid viscosity on film thickness, velocity profiles in both gas and liquid phase, and the effect of forces acting on the wave, wave growth and its movement on the falling film. Our predictions coincide with the published experimental results. Though the present model is based on the simplified condition of interface, this paper presents an insightful discussion on the effect of liquid viscosity on churn flow.
Section snippets
Mathematical model
Generally, huge waves are observed to travel co-currently with gas flow on the falling film between the waves (Hewitt et al., 1985, Barbosa et al., 2001, Wang et al., 2013). They receive liquid from the falling film above and grow in both the radial and axial direction. Meanwhile, some of the liquid is released into the film below and initially moves upwards (with respect to the wall) with a velocity lower than that of the wave. Owing to the influence of gravitational force, the released liquid
Model validation
To the best of our knowledge, no data are available for comparison study with non-Newtonian fluids in churn flow. Note that Newtonian liquid can be considered to be a power-law liquid with power law exponent , and consistency index (Shu, 1981). Fig. 8 shows the quantitative validation of the present model by comparing the experimental void fraction from Parsi et al. (2016) and the calculation results. Parsi et al. (2016) investigated the void fraction in a pipe with an internal diameter
Conclusions
A mechanical model for pressure gradient, void fraction and wave movement in gas-non-Newtonian churn flow is developed in this paper. For the sake of simplicity, non-Newtonian fluid is characterized by the power-law model and liquid entrainment and aeration are ignored. Since the liquid phase of churn flow is not homogeneous, one churn flow unit is delicately divided into two parts (the falling film region and the wave region) and analyzed separately. Compared with existing experimental data,
Acknowledgments
The authors gratefully acknowledge research support from the Agency for Science, Technology and Research (A∗STAR), Engineering Research Grant, SERC Grant No. 1021640147, the National Natural Science Foundation of China under Grant No. 51706245 and the Science Foundation of China University of Petroleum, Beijing No. 2462016YJRC029.
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