Liquid-film thickness and disturbance-wave characterization in a vertical, upward, two-phase annular flow of saturated R245fa inside a rectangular channel
Introduction
The co-current flow of vapor and liquid phases in a closed channel follows very different regimes depending on experimental conditions (Collier and Thome, 1994). Among these two-phase flow regimes, annular flow shows the greatest heat transfer coefficient values and it is commonly observed in refrigeration applications (Chu and Dukler, 1974; Schubring et al. 2010a; Zadrazil et al., 2014; Ju et al., 2015). In two-phase annular flow, a core of vapor flows at the center of the channel surrounded by a thin liquid film that is in contact with the wall. Liquid droplets are also entrained within the vapor core. These droplets flow with the same velocity as the vapor and they continuously interact with the liquid film via detachment and impingement (Schubring and Shedd, 2011; Cioncolini and Thome, 2012a).
The interface between the liquid film and the vapor core is not smooth. Different types of waves are observed at the interface, which are created and controlled by the interfacial shear between the vapor and the liquid as well as interactions with entrained droplets (Hewitt et al., 1990; Schubring and Shedd, 2008; Zadrazil et al., 2014; Ju et al. 2015; Vasques et al. 2018; Moreira and Ribatski, 2019). These waves are usually classified into two main categories: ripples and disturbance waves. Ripples have relatively short amplitude and life time, and they are not periodic. They are related to local perturbations of the liquid film/vapor core interface. Ripples may be generated by droplet impingement and detachment that occur at the liquid film/vapor core interface. In comparison, disturbance waves have a larger amplitude than ripples and they show some degree of periodicity. More recently, Moreira and Ribatski (2019) observed a third type of wave during the convective condensation of R134a in a horizontal round channel at vapor qualities near the transition from annular to intermittent or wavy flow patterns, with a larger amplitude than disturbance waves but a smaller velocity. However, these waves of the third type are not expected to be seen under the conditions of the present study.
Most of the work from the literature has focused on characterizing disturbance waves (Hewitt and Hall-Taylor, 1970; Hazuku et al., 2008; Zhao et al., 2013; Vasques et al. 2018; Wang et al. 2018). Disturbance waves are linked to the interfacial shear and therefore they relate to important flow features such as the frictional pressure gradient and the heat transfer coefficient (Vasques et al. 2018). In contrast, ripples and the larger waves described previously have practically no influence on these parameters (Sawant et al., 2008). However, the relationship between interfacial shear and disturbance waves is not direct and simple. For example, the interfacial shear and disturbance waves also depend on the fraction of entrained liquid in the vapor core and the liquid-film thickness. As a result of the complexity of the problem and the large number of variables involved there is no general theory available to describe disturbance waves. More experimental studies are necessary to shed light on the mechanisms by which disturbance waves affect two-phase annular flow.
To the exception of a few studies performed with pure water (Barbosa et al., 2003; Su, 2018), there is, to the authors’ knowledge, no experimental study of disturbance waves in vertical annular flow for single species halogenated refrigerants (e. g. R245fa) under saturated conditions available in the literature. Some studies were performed in fluid mixtures such as helium-water and C4F8-water (Damsohn, 2011), but most previous work was focused on air-water flows (Sawant et al., 2008; Schubring and Shedd, 2008; Damsohn and Prasser, 2009; Schubring et al., 2010a, 2010b; Vasques et al., 2018; Wang et al., 2018). The relative properties of the liquid and vapor phases in an air-water mixture are different from those in a two-phase single-species flow (see Table 1). While air-water studies are useful, correlations derived from air-water databases only may not be accurate for single-species flows. A general conclusion of these previous studies is that the velocity of the disturbance waves, u, increases with increasing superficial gas velocity and liquid Reynolds number. Schubring and Shedd (2008) also observed that the wave velocity increases with increasing tube diameter, all other experimental conditions being equal. These authors proposed a correlation based on their own database to estimate the disturbance-wave velocity. Sawant et al. (2008) and Wang et al. (2018) evaluated the effect of the system pressure, p, on the disturbance waves. They observed that the wave velocity increases with increasing pressure at constant superficial gas velocity and liquid Reynolds number. As the system pressure increases, the density increases and, consequently, so do the momentum of the vapor core, the interfacial shear and the disturbance waves. Damsohn (2011) observed similar trends of increasing disturbance-wave velocity and height as gas density increases. They also found that, in a C4F8-water mixture, whose relative properties are closer to a single-species liquid-vapor mixture than air-water, the disturbance-wave velocity is practically independent of mass flux. In contrast, in air-water flows, they observed that the disturbance-wave velocity is independent of mass flux only at high liquid loads, near the transition from annular to churn flow.
In heated two-phase annular flow of water, Su (2018) observed an increase in the disturbance-wave velocity and frequency with increasing vapor quality and mass flux. Su's study focused on the important role disturbance waves play in the bubble nucleation mechanism (see also Barbose et al., 2003).
Wang et al. (2018) compared their experimental disturbance wave velocity data against existing prediction methods developed by Kumar et al. (2002), Omebere-Iyari (2007), Schubring et al. (2010a) and Al-Sarkhi et al. (2012). Among those, the best predictions were obtained by the correlation proposed by Kumar et al. (2002) although the data was constantly underpredicted. Wang et al. (2018) adjusted the correlation of Kumar et al. (2002) based on their own database. Through such procedure the authors obtained a mean standard deviation of 5.4%, predicting all the data within an error range of ±30%. These correlations have never been verified for two-phase flows of single species.
Another parameter of importance in two-phase annular flow is the liquid-film thickness, LFT. The main thermal resistance to heat transfer in the annular flow regime is due to thermal conduction through the liquid film, which depends directly on the liquid-film thickness (Collier and Thome, 1994). The liquid-film thickness also affects the characteristics of the disturbance waves, the liquid entrainment ratio and the pressure drop (Cioncolini et al., 2009; Cioncolini and Thome, 2010; Cioncolini and Thome 2012a; Zadrazil et al., 2014; Wang et al., 2018).
Again, to the authors’ knowledge, there is no study in the literature concerning the liquid-film thickness in two-phase annular flow for a single species halogenated refrigerant (e. g. R245fa) under saturated conditions. Although a few studies were performed for pure water (Su, 2018) and chloroform (Bolesch, 2019) during flow boiling, most experiments in the literature were performed in air-water two-phase flows. These studies include works by Shedd and Newell (1998), Sawant et al. (2008), Schubring and Shedd (2008), Damsohn and Prasser (2009), Schubring et al. (2010a, 2010b), Alamu and Azzopardi (2011), Zadrazil and Markides (2014), Han et al. (2015), Ju et al. (2015) and Vasques et al. (2018). Damsohn (2011) also performed liquid-film thickness measurements in fluid mixtures of helium-water and C4F8-water. As expected, these authors found that the liquid-film thickness increases with increasing liquid and decreasing gas superficial velocities (i.e. with decreasing quality). However, the liquid-film thickness also depends on other parameters. Damsohn (2011), Han et al. (2015) and Su (2018) observed a reduction of the liquid-film thickness with increasing mass velocity. Su (2018) pointed out that as mass velocity and, consequently, the interfacial shear increases, the entrainment ratio also increases, thus reducing the liquid-film thickness. Sawant et al. (2008) evaluated the effect of the pressure on the liquid-film thickness at constant superficial gas and liquid velocities. The liquid-film thickness decreased with increasing pressure because of the increased gas density and associated inertial force of the gas. Several empirical models are available to predict the liquid-film thickness, as summarized by Ju et al. (2015). However, these models are all based on data for air-water flows and they have not been validated for single-species saturated flow.
The current work presents an experimental investigation of the liquid-film thickness and disturbance wave velocity under saturated conditions. Experimental data for the frequency of the disturbance waves are also presented. Section 2 presents the experimental setup and the measurement techniques. Wave velocity is measured using a novel approach based on the optical liquid-film thickness method introduced by Shedd and Newell (1998). Results are presented in Section 3. The effects of mass velocity and vapor quality on the disturbance-wave velocity and the liquid-film thickness are evaluated. The interconnection between disturbance waves, liquid-film thickness and frictional pressure drop is also studied. Finally, the measured liquid-film thickness and disturbance wave-velocity data are compared with prediction methods available in the literature.
Section snippets
Experimental facility
A schematic diagram of the two-phase annular flow facility is presented in Fig. 1. All the tests are performed with saturated R245fa (pentafluoropropane), a low-pressure refrigerant. More details about the experimental setup may be found in Fehring et al. (2020) and Dressler (2018). Saturated R245fa is stored in the storage tank where pressure (Omega PX409, 0–344.74 kPa) and temperature of the fluid are monitored. The liquid in the storage tank is constantly re-circulated by centrifugal pumps
Experimental results
All the experiments presented in this section were performed using saturated R245fa as working fluid. The saturation temperature of the fluid at the outlet of the test section was measured to be 23±1 °C. Mass velocities ranged from 95 to 130 kg/m2s and vapor qualities from 0.63 to 0.9. Ambient temperature outside of the test section was constant at 20 °C.
Conclusions
The liquid-film flow in a vertical and upward two-phase annular flow of saturated R245fa in a rectangular channel has been characterized under adiabatic conditions. The liquid-film thickness, and disturbance-wave velocity and frequency, are measured optically using an extended version of the method introduced by Shedd and Newell (1998). Based on the experimental results, the following conclusions can be drawn:
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The time-averaged liquid-film thickness decreases linearly with quality and it tends
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors acknowledge the CNPq (National Council for Scientific and Technological Development, Brazil) for the grant given under Contract Number 305673/2017–3, FAPESP (São Paulo Research Foundation, Brazil) for the scholarships under Contract Numbers 2016/16849–3 and 2018/06057–4 and CAPES (Coordination for the Improvement of Higher Level Personal, Brazil).
The authors also thank Prof. Gregory Nellis for his advice and encouragement throughout this work.
References (66)
Drops in annular two-phase flow
Int. J. Multiph. Flow
(1997)- et al.
High speed visualization of nucleate boiling in vertical annular flow
Int. J. Heat Mass Transf.
(2003) A comparison of some void-fraction relationships for cu-current gas-liquid flow
Int. J. Multiph. Flow
(1975)- et al.
Prediction of the entrained liquid fraction in vertical annular gas–liquid two-phase flow
Int. J. Multiph. Flow
(2010) - et al.
Algebraic turbulence modeling in adiabatic and evaporating annular two-phase flow
Int. J. Heat Fluid Flow
(2011) - et al.
Entrained liquid fraction prediction in adiabatic and evaporating annular two-phase flow
Nucl. Eng. Des.
(2012) - et al.
Void fraction prediction in annular two-phase flow
Int. J. Multiph. Flow
(2012) - et al.
Unified macro-to-microscale method to predict two-phase frictional pressure drops of annular flows
Int. J. Multiph. Flow
(2009) - et al.
High-speed liquid film sensor for two-phase flows with high spatial resolution based on electrical conductance
Flow Meas. Instrum.
(2009) - et al.
Condensation n horizontal tubes, part 1: two-phase flow pattern map
Int. J. Heat Mass Transf.
(2003)
Measurement of liquid film thickness in micro tube annular flow
Int. J. Multiph. Flow
Experimental study on axial development of liquid film in vertical upward annular two-phase flow
Int. J. Multiph. Flow
Structure of thin liquid films in gas-liquid horizontal flow
Int. J. Multiph. Flow
Film thickness of vertical upward co-current adiabatic flow in pipes
Int. J. Heat Mass Transf.
Prediction of interfacial shear stress of vertical upward adiabatic annular flow in pipes
Int. J. Heat Mass Transf.
Flow pattern based two-phase frictional pressure drop model for horizontal tubes. Part I: diabatic and adiabatic experimental study
Int. J. Heat Fluid Flow
Properties of the liquid layer in horizontal annular flow
Int. J. Multiph. Flow
Calculation of void volume fraction in the subcooled and quality boiling regions
Int. J. Heat Mass Transf.
Properties of disturbance waves in vertical annular two-phase flow
Nucl. Eng. Des.
A Prediction of wall shear for horizontal annular air-water flow
Int. J. Heat Mass Transf.
A model for pressure loss, film thickness, and entrained fraction for gas-liquid annular flow
Int. J. Heat Fluid Flow
Wave behavior in horizontal annular air-water flow
Int. J. Multiph. Flow
Planar laser-induced fluorescence (PLIF) measurements of liquid film thickness in annular flow. Part II: analysis and comparison to models
Int. J. Multiph. Flow
Studying disturbance waves in vertical annular flow with high-speed video
Int. J. Multiph. Flow
Comparison of disturbance wave parameters with flow orientation in vertical annular gas-liquid flows in a small pipe
Exp. Therm. Fluid Sci.
Interfacial wave velocity of vertical gas-liquid annular flow at different system pressures
Exp. Therm. Fluid Sci.
Downwards co-current annular flow
Int. J. Multiph. Flow
An experimental characterization of liquid films in downwards co-current gas-liquid annular flow by particle image and tracking velocimetry
Int. J. Multiph. Flow
An experimental characterization of downwards gas-liquid annular flow by laser-induced fluorescence: flow regimes and film statistics
Int. J. Multiph. Flow
Disturbance wave development in two-phase gas-liquid upwards vertical annular flow
Int. J. Multiph. flow
Handbook of uncertainty in gas turbine measurements
National Technical Information Service
Simultaneous investigation of entrained liquid fraction, liquid film thickness and pressure drop in vertical annular flow
J. Energy Resour. Technol.
Inclination effects on wave characteristics in annular gas-liquid flows
AIChE J.
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