Experimental investigation and new void-fraction calculation method for gas–liquid two-phase flows in vertical downward pipe

https://doi.org/10.1016/j.expthermflusci.2020.110252Get rights and content

Highlights

  • Commonly used void fraction methods were analyzed.

  • Void fractionexperiment was carried out.

  • A new model was developed based on drift flux model.

  • The proposed method considers the flow pattern.

Abstract

The void fraction is a key parameter of the two-phase flow in vertical downward pipes, particularly for calculating the mixture density, mixture velocity, mixture viscosity, heat transfer coefficient, and pressure gradient of the flow. Studies on two-phase flows have focused primarily on vertical upward and horizontal pipe flows, while vertical downward pipe flows have been largely neglected. Compared with the flow characteristics of the gas–liquid two-phase flow in upward pipes, those of a downward pipe flow are more complex under the interaction of the gravity, buoyancy, and inertial forces. In this study, a detailed experimental analysis of the void fraction of the gas–liquid two-phase flow in a vertical downward pipe was conducted with a pipe having an inner diameter of 20 mm. A total of 171 void-fraction data points were measured using the quick-closing valve method, and the performances of 12 commonly used correlations that do not take into consideration the flow pattern were assessed based on experimental data points. Errors were obtained on using some of the correlations for calculating the void fraction of the gas–liquid two-phase.

flow in a vertical downward pipe at a low liquid superficial velocity. These models will regularly produce errors in the calculation of the void fraction, mainly because this problem is outside the scope of their application. In addition, a new model that takes into consideration the flow pattern was established based on the drift flux model; this new model overcomes the deficiencies of the conventional correlations in the calculation of the void fraction of the gas–liquid two-phase flow in vertical downward pipes at a low liquid superficial velocity. The reliability of the new method and 12 conventional correlations was assessed using 243 published data points. The mean relative errors of these correlations ranged from −21.65% to 8.65%, and the average absolute errors ranged from 8.57% to 23.17%. The results of the proposed method fit the experimental data in the literature better than those of the 12 existing correlations; the average relative error was −2.80%, and the average absolute error was 6.49%. The proposed model thus improves the prediction of void fractions of the gas–liquid two-phase flow in downward pipes.

Introduction

Gas–liquid two-phase flows in vertical downward pipes are prevalent in the fields of chemical engineering, nuclear engineering, boiler applications, refrigeration, and the power, petroleum, and natural gas industries. However, research on two-phase flows has been focused primarily on vertical upward and horizontal pipe flows, while that on two-phase vertical downward pipe flows has been largely neglected. The void fraction is a key parameter of a two-phase flow, particularly for calculating the mixture density, mixture velocity, mixture viscosity, heat transfer coefficient, and pressure gradient of the flow [1], [2], [3], [4]. Several correlations for predicting the void fraction of the gas–liquid two-phase flow in vertical upward pipes have been presented, for example, by Chen [5], Woldesemayat [6], Godbole [7], Parrales [8], and Guo [9]. However, because vertical downward pipes have not been studied thoroughly, a comprehensive method for determining the void fraction of the gas–liquid two-phase flow in vertical downward pipes has not yet been derived.

The void fraction of a two-phase flow is governed by the interaction between the buoyancy, gravity, inertia, and surface tension forces. The buoyancy force and inertia of the gas phase act in the same direction as the gas–liquid two-phase flow in the vertical upward pipe and in the opposite direction in the vertical downward pipe (Fig. 1). Therefore, methods for predicting the void fraction of a two-phase flow in a vertical downward pipe are more complex.

The majority of void-fraction correlations for the two-phase flow in vertical downward pipes have been studied and developed based on the two-phase flow in vertical upward or horizontal pipes [10], [11], [12], [13], [14], [15], [16]). However, models that employ the aforementioned correlations cannot be used in the absence of a void fraction in the two-phase upward and horizontal flow modes. The void fraction correlations of the gas–liquid two-phase flow in vertical downward pipes can be classified into five categories according to the research methods, and the following section provides an introduction into the relevant research progress.

The first model category takes into consideration the void fraction of the gas–liquid two-phase flow in vertical upward pipes. In the early stage of research on the gas–liquid two-phase flow in downward pipes, the calculation methods for the void fraction were developed based on the gas–liquid two-phase flow in upward pipes. For instance, Sokolov studied the void fraction of the gas–liquid two-phase flow in vertical downward pipes in detail and discovered that the void fraction of the gas–liquid two-phase flow in a vertical downward pipe is closely related to that of the upward flow. Accordingly, Sokolov proposed a method for calculating the void fraction of the gas–liquid two-phase flow in downward pipes according to the upward flow and fitted the relevant empirical relationship based on experimental data [11]. This correlation is presented below:αg-downward=2β-αg-upwardwhere αg-upward is the void fraction of the gas–liquid flow in a vertical upward pipe, β is the gas volumetric flow fraction (β = Qg/Ql), and Qg and Ql are the volumetric flow rates of the gas and liquid phases, respectively.

Based on the above method, Yijun experimentally studied the void fraction in a vertical co-current upward and downward two-phase gas–liquid flow in a transparent Plexiglas pipe (9.525 mm inner diameter). Moreover, an empirical correlation for describing the void fraction of the gas–liquid two-phase flow in downward pipes based on upward flow was provided. This concept is the equivalent of that used by Sokolov; however, Yijun's correlation expands the application field of this method and takes into consideration the influence of the Reynolds number [12], [13]:αg-downward=0.076+0.074Rel0.05αg-upwardRel<17400αg-downward=0.025+0.058Re10.05αg-upwardRel>17400

However, this method has a drawback: the selection of the void-fraction model of the gas–liquid two-phase flow in upward pipes directly affects the calculation results for the gas–liquid two-phase flow in downward pipes. If the void-fraction model of the gas–liquid two-phase flow in upward pipes is unsuitable, the errors in the calculation of the void fraction of the downward pipe flow become large.

A different model type was developed based on the void fraction of the gas–liquid two-phase flow in horizontal pipes. In 1973, Beggs and Brill analyzed the behavior of a gas–liquid two-phase flow at various inclination angles (−90° to 90°) in round pipes of inner diameter 25.4 and 38.1 mm [10]. The liquid holdup was measured using pneumatically actuated, quick-closing ball valves. Based on the plots of the liquid holdup versus the inclination angle for constant, Beggs and Brill discovered that the former is dependent on the latter, and they normalized the holdup by dividing its value at any inclination angle by the holdup at an inclination of 0°.αl(θ)αl(0)=ψ

It was found that ψ could be predicted for all conditions by using an equation of the form:ψ=1+C(sin(1.8θ)-13sin3(1.8θ))

Therefore, the void fraction of the gas–liquid two-phase flow in a vertical downward pipe can be calculated when θ is − 90°.

Subsequently, Mukherjee (1979) conducted an experimental investigation of the gas–liquid two-phase flow in a 38 mm inner diameter pipe at various inclinations and proposed a comprehensive and dependent empirical correlation for the downhill flow. Because the studied liquids were oil and kerosene [14], [15], [16], this correlation cannot be directly used for calculating the void fraction of the gas–water two-phase flow in downward pipes. The correlation has the following form:αg=1-exp(C1+C2sinθ+C3sin2θ+C4NL2)NgvC5NLvC6Ngv=vsg(ρLgσL)1/4NLv=vsL(ρLgσL)1/4NL=μL(1ρLσL3)1/4where ρL is the density of the liquid phase in g/cm3; σL is the interfacial tension between the gas and liquid phases in mN/m; υsl and υsg are the superficial velocities of the liquid and gas phases, respectively, in m/s; and Nl, Ngv, and Nlv represent the liquid viscosity, liquid velocity, and gas velocity numbers, respectively.

The third model category includes drift-flux-model-based correlations. The drift flux model was originally designed for predicting the void fraction of the gas–liquid two-phase flow in upward pipes. Subsequently, some researchers [6], [17], [18] applied the drift flux model to the prediction of the void fraction of the two-phase flow in vertical downward pipes by changing the sign of the drift velocity from positive to negative. Furthermore, Clark and Flemmer conducted a detailed experimental study of the void fraction of the gas–liquid two-phase flow in vertical downward pipes (round pipes having inner diameters of 52 and 100 mm) [19]. They concluded that the distribution coefficient was not a fixed constant and proposed an empirical calculation method for the downward-flow distribution coefficient.Co= 1.521(1 - 3.67ε)where Co is the Zuber and Findlay profile constant, and ε is the gas void fraction.

Furthermore, Hasan [20] analyzed the drift velocity (Vgj) based on the published literature data of the gas–liquid two-phase flow in downward pipes and discovered that the drift velocities (Vgj) of bubble and slug flow modes are similar to the drift velocity of upward flow proposed by Harmathy and Nicklin [21], [22]. In addition, Hasan reported that the distribution coefficient of the bubble flow is 1.2. Its drift velocity can be expressed as follows:Vgj-Bubble=1.53gσρL-ρgρL21/4Vgj-Slug=0.345gσρL-ρgρL21/4where Vgj-Bubble represents the drift velocities of bubble flow, and Vgj-Slug represents the drift velocities of the slug flow.

Moreover, Cai et al. [23] measured the void fraction of bubbly and slug flow modes in the horizontal and downward directions with oil and gas (pipes of 1.5 m length and 44 mm inner diameter). They focused on the distribution coefficients of the bubbly and slug flow modes and modified the distribution coefficient of the drift model according to the experimental data with Co = 1.185 for the bubbly flow and Co = 1.15 for the slug flow. The drift velocity follows the drift velocity of the bubbly and slug flow modes proposed by Hasan.

Based on the same theory, Kawanishi [24], Usui [25], and Goda [26] provided different correlations for describing the void fraction of the downward flow. Although these researchers proposed methods for calculating the void fractions of the bubble and slug flow modes, the applicability of their models to flow conditions beyond their experimental conditions is still questionable. The prediction accuracy of these models must be verified for the void-fraction calculations of other flow patterns.

Swanand [17] and Xue [27] demonstrated that some void-fraction correlations that have not been derived for downward flow can also be used for predicting the void fraction of the gas–liquid two-phase flow in downward pipes [22], [28], [29], [30]. The accuracy of these void fraction correlations was verified by Swanand and Xue using experimental data. The results show that some void fraction correlations of the two-phase flow in vertical upward pipes can also be used for vertical downward flows.

Nicklin (1962):αg=vsg1.2vsg+vsl±0.35gD

Bonnecaze (1971):αg=vsgvsg+vsL1.20+0.35(ρL-ρGρL)δvsg+vsLgD

Kokal (1989):αg=vsg1.17vsg+vsl±1.53(gσ(ρL-ρg)ρL2)0.25

Gomez (2000):αg=vsg1.15vsg+vsl+1.53(gσ(ρL-ρg)ρL2)1/4(1-αg)0.5sinθwhere D is the inner diameter of pipe, mm. vsg is the gas superficial velocity in m/s, vsl is the water superficial velocity in m/s, ρg is the density of gas in kg/m3, ρL is the density of fluid in kg/m3, and σ is the interfacial tension of the gas and liquid phases in N/m.

The last type of void-fraction model includes the function of the gas volumetric flow fraction. This model type is simple and empirical and comprises the consideration of fewer factors. The gas volumetric flow fraction is also referred to as the homogeneous void fraction with no assumed slip between the two phases.

Moreover, Yamazaki systematically studied the void fraction of the gas–water two-phase flow in vertical downward pipes (round pipes of 25 mm inner diameter) using the quick-closing-valve method [31]. According to the results, the void fraction increases as the volumetric gas flow increases. This correlation was verified using 560 data points, and the percentage error of this model was within ± 20%. In addition, the following empirical correlation was presented:αg(1-αg)(1-Kαg)=β1-βForβ0.2,K=2-0.4/βForβ0.2,K=-0.25+1.25ββ=vsgvsg+vslwhere υsl and υsg are the superficial velocities of the liquid and gas phases, respectively, in m/s.

Thus, the calculation processes of the first and second model types depend on the void fraction of the horizontal and vertical pipes, while their accuracy directly affects the calculation error of the downward flow; thus, their application is limited. The fourth correlation model type comprises the calculation of the void fraction by changing the plus sign (+) into the minus sign (−) in the denominator of the upward pipe drift flux model, which was designed for upward pipes. Unfortunately, this method is unsuitable because the distribution coefficient and drift velocity are not corrected. Some scholars have verified this type of model when calculating the void fraction of the gas–liquid two-phase flow in a vertical downward pipe. It was found that the calculated void-fraction value obtained with this type of model is larger than that obtained in an experiment. Moreover, errors are regularly observed with this type of model when it was used for calculating the void fraction of the gas–liquid two-phase flow in a vertical downward pipe at a low liquid superficial velocity, such as in the case of the Bonnecaze and Nicklin model, which was verified in Section 3.3. In the fifth method type, it is assumed that there is no slip effect between the gas and liquid, and fewer factors are taken into consideration. This is not consistent with the reality of gas–liquid two-phase flows. Compared with other empirical models, the third model type has made great progress in the theoretical field and will remain the focus of future research; however, its calculation accuracy requires further verification and improvement.

Therefore, a systematic and thorough study of the void fraction of the gas–liquid two-phase flow in vertical downward pipes and the development of a comprehensive correlation are crucial. In this study, a detailed experimental analysis of the gas–liquid two-phase flow in vertical downward pipes was conducted. The void fraction was determined using the quick-closing-valve method, and 171 experimental data points were recorded. In addition, 12 correlations, which have been developed for various pipe orientations and fluid combinations, were assessed based on the 171 data points. During the evaluation of the void-fraction model, certain new problems were observed. Meanwhile, a new and comprehensive model was proposed for predicting the void fraction of the gas–liquid two-phase flow in vertical downward pipes.

Section snippets

Experimental system

To study the void fraction of the gas–water two-phase flow in a vertical downward pipe, an experimental loop was built using a transparent Plexiglas pipe (inner diameter of 20 mm). This experiment was conducted at room temperature (20 ℃), and the pressure in the experimental pipe was below 0.8 MPa (gauge pressure). Fig. 2 presents the experimental setup. To eliminate the influence of the entrance and exit, a 2 m upstream stabilization segment and 0.5 m downstream stabilization segment were

Assessment of performance of correlations for predicting void fraction

In this section, the accuracy and reliability of the published correlations are assessed and analyzed using the experimental data. To find a suitable model for predicting the void fraction of the gas–liquid two-phase flow in a downward pipe, some researchers have analyzed void-fraction correlations that have been designed for two-phase flow in upward and horizontal pipes. Accordingly, the void-fraction models of a two-phase flow in upward and horizontal pipes are unsuitable for a two-phase flow

Development of new method

To overcome the deficiencies of the commonly used void fraction correlations for the gas–water two-phase flow in vertical downward pipes, a new method that takes into consideration the flow pattern was developed based on the drift flux model. The latter was proposed by Zuber and Findlay to calculate the void fraction of the gas–liquid two-phase flow in upward pipes; it takes into consideration the relative motion between the two phases rather than the motions of the individual phases [45]. The

Conclusions

From the experimental results and data analysis, the following conclusions can be reached:

  • (1)

    In this experiment, five flow patterns were analyzed: falling-film, bubbly, slug, transition, and annular flow modes. Compared with those of the gas–liquid two-phase flow in an upward pipe, the flow characteristics of a downward pipe are more complex under the interaction of the gravity, buoyancy, and inertia forces. The falling-film flow is a unique flow type and is observed only in vertical downward

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.

Acknowledgement

This work was supported by Laboratory evaluation of synergist for heavy oil thermal recovery and study on mechanism and reasonable process parameters of supercritical multi-element thermal fluid production (No.2016ZX05058-003-017). I am grateful to my wife (Su Wei) for her support and help over the past 10 years. Taking your hand, living to old age together.

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