Entrained Liquid Fraction Research Articles

A Gaussian process embedded feature selection method based on automatic relevance determination

In Gaussian Process, feature importance is inversely proportional to the corresponding length scale when applying the Automatic Relevance Determination (ARD) structured kernel function. Features can be selected by ranking them according to their importance. Among the ARD-based feature selection methods, no uniform score exists for quantifying the output variation explained by feature subsets. This study proposes two feature selection approaches using two cumulative feature importance scores, one titled derivative decomposition ratio and the other normalized sensitivity, to determine the optimal feature subset. The performance of the approaches is assessed to test if irrelevant features are accurately identified and if the feature rankings are correct. The approaches are applied to identify relevant dimensionless inputs for a hybrid model estimating liquid entrainment fraction in two-phase flow. The results reveal that the proposed methods can identify the optimal feature subset for the hybrid model without significantly worsening its Root Mean Squared Error.

Liquid entrainment in annular gas–liquid two-phase flow: A critical assessment of experimental data and prediction methods

Annular flow is one of the most frequently observed flow patterns with gas–liquid two-phase flows in tubes or channels. In the annular flow pattern, a thin liquid film flows along the channel wall, while the gas flows in the center of the channel carrying liquid droplets in suspension. The fraction of the liquid flow rate that is transported as suspended droplets is quantified using the entrained liquid fraction (ELF), which is a key flow parameter in the analysis and modeling of annular flows. This review provides a critical assessment of ELF experimental data available in the open literature and of ELF prediction methods proposed to date. The experimental data assessment is carried out by means of a large ELF data bank collected from the literature (4175 data points from 53 literature studies; 10 fluids combinations; operating pressures from atmospheric to 20 MPa; experiments carried out with adiabatic, evaporating, and condensing flows through circular tubes, and non-circular channels with diameters from 3.02 to 155.7 mm), which is critically analyzed devoting special attention to important aspects not adequately addressed in previous studies, such as a cross-comparison between different ELF measuring techniques, and the analysis of flow development and gravity effects. The assessment of the ELF prediction methods focuses on 15 widely quoted methods, which are critically analyzed and whose prediction performance is evaluated against the measured data. The curated ELF experimental data bank is provided in full and usable form. Research gaps for further investigations are identified and discussed.

Void fraction and pressure gradient model for an adiabatic symmetric annular developed flow with entrainment

This paper presents a new method for the evaluation of the pressure gradient during annular two-phase flow in the presence of entrainment, based on the momentum balance on the liquid film trapped between the wall and the vapor core. The entrained liquid fraction, together with the atomization/deposition rates and shear stresses, are considered with the use of closure equations, in which the interfacial shear stress is calibrated by means of an experimental database. Through the resolution of a simple iterative procedure, the outcomes of the method are both pressure gradient and void fraction. The accuracy of the present model is tested with independent experimental databases from the literature, showing a very good agreement also with respect to existing available methods for pressure gradient and void fraction.

A hybrid modeling approach to estimate liquid entrainment fraction and its uncertainty

Liquid entrainment fraction is a key parameter for designing and optimizing downstream oil and gas production equipment and needs to be reliably estimated. In this study, a hybrid modeling approach, which combines semi-mechanistic and data-driven models, is introduced to estimate entrainment fraction and its uncertainty. The hybrid model incorporates three data-driven models developed using Gaussian Process Modeling trained with 1,662 experimental data. The performance of three different Gaussian Process Models (GPMs), GPM with known noise, GPM with estimated noise, and bagging GPM, is studied in the hybrid model to obtain a more robust and accurate result. The performance metrics used are the root mean square error (RMSE), area metric (AM), and calibration score (CS). The results reveal that the RMSE of the hybrid model is about 70% lower than the RMSE of the semi-mechanistic models. Bagging GPM gives the best result considering RMSE, AM, and CS.

Improved correlation of liquid entrainment fraction in horizontal pipes

New correlations to predict the entrainment fraction in horizontal pipes are proposed based on the Pan & Hanratty correlation. The Pan & Hanratty correlation cannot properly predict the entrainment fraction at low liquid flow rates, and this results from too high critical liquid Reynolds numbers for the calculation of the maximum entrainment fraction. To solve this problem, we suggest two new entrainment models by replacing the maximum entrainment model in the original equation with the one from Al-Sarkhi et al. (2012) or from Mantilla (2008). For the Mantilla model, we propose a minor modification so that the correlation can predict the maximum entrainment fraction better. We validate the proposed models with an extensive range of experimental data involving pressure from 1 to 70 bar, pipe diameter from 2.3 to 9.5 cm, and fluid type of air-water and N2-water. The proposed models show good agreement with the experimental measurements by improving the predictions at low liquid flow rates, and their performances are better or similar compared to the other entrainment models. In particular, the Pan & Hanratty correlation with the modified Mantilla model demonstrates satisfactory performance showing root mean square error of 10 % over all data.

Relative importance of entrained liquid fraction and mass transfer at the interface on pressure drop of annular flows

Fully developed adiabatic two-phase flows are commonly encountered in practice and their modeling is of primary importance for accurate, local calculations of pressure gradients and void fraction for the design of several industrial applications as heat exchangers and long fluid transfer piping. For large void fractions, the entrainment of liquid droplets into the vapor core can have a large effect on the pressure gradients. In this paper starting from theoretical considerations about the modeling of the pressure gradients in an annular two-phase flow, a numerical analysis as well as a discussion are proposed in order to quantify the relative importance of the entrainment on the calculations and to address further experimental studies and models on this topic.

A prediction method for entrained liquid fraction in adiabatic gas-liquid flow at high reduced pressure

A goal of the study is development of an approximate but well-grounded model of entrainment/deposition processes in annular two-phase flow at high reduced pressures (p/pcr>0.45). Nakazatomi and Sekoguchi (1996) have presented the unique experimental data on liquid distribution between the core and the film in air/water two-phase flow at high pressures, up to 20 MPa; at pressures higher 10 MPa the data feature with abnormally high fraction of entrained liquid and manifest very strong deviation from any known empirical correlations, including the recent one by Cioncolini and Thome (2012). In deducing the approximate model of droplets entrainment, we used the experimental observations, according to which a liquid film becomes thin and smooth at high reduced pressures. A plenty of tiny droplets detach from the liquid film surface at the points, which spacing is determined as a length scale in Weber number for gas flow. This spacing and the liquid film thickness are assumed being the parameters controlling a droplet departure diameter. These assumptions allow developing an equation for calculating entrainment intensity at high reduced pressures. A balance between the flows of droplets entrainment and deposition due to turbulent diffusion corresponds to the dynamic equilibrium. The equation based on this balance contains one unknown numerical factor and allows one to calculate liquid distribution in a channel cross section. Comparing the calculation results with the experimental data for the water–air flows at high reduced pressures (more than 0.45) has shown their good agreement at the universal value of the numerical constant.

A complete set of simple and optimized correlations for microchannel flow boiling and two-phase flow applications

In this work a complete set of simple and optimized correlations for flow boiling and two-phase flow conditions in microchannels were developed for prediction of the critical heat flux, flow pattern transition, heat transfer coefficient, frictional pressure drop, void fraction, slip ratio and liquid entrainment fraction in compact thermal applications. The goal was to identify and optimize a set of the dimensionless numbers associated with these parameters to obtain simple and easy to be implemented correlations but still with low prediction error. These simple correlations were characterized by three points: (i) just one continuous function with few dimensionless numbers, (ii) easily linearized and (iii) a equation format that makes possible to obtain analytically the inverse function of any of its independent parameters. These characteristics are important when developing models for simulations of compact thermo-hydraulic systems, where linear models and fast numerical codes are desired. The third characteristic simplifies solution and convergence of system of equations by use of explicit methods. The correlations were optimized using the dimensionless numbers which better correlated to the experimental data. The experimental database was carefully selected for each parameter to cover a wide range of flow conditions and fluids used in microchannels applications. This set of simple correlations could predict their database with a similar or better performance than more complex correlations presented in literature. In addition, the analysis of all these prediction parameters together allowed identification of similarities and relations among the predicted parameters.

Droplet entrainment analysis of three-phase low liquid loading flow

Most of the commonly used multiphase flow models neglect the amount of droplets entrained in stratified wavy flow. However, the experimental data presented in this study show high entrainment values, exceeding 50% in some cases. This shows that neglecting entrainment phenomenon can introduce a major source of discrepancy into multiphase flow modeling predictions. This study improves the entrainment fraction predictions in three-phase stratified flow.The droplet entrainment in three-phase stratified flow in horizontal pipelines is experimentally investigated using a 0.152-m ID facility. The experiments are conducted under low liquid loading conditions, which is very commonly observed in wet gas pipelines. The oil-aqueous-gas flow experiments are initially performed without mono-ethylene glycol (MEG), and then repeated with 50 wt% of MEG in the aqueous phase to analyze the effects of MEG presence on entrainment. MEG is a commonly used inhibitor in oil industry, applied to avoid hydrate formation in offshore systems. Its impacts on multiphase flow droplet entrainment are investigated.The experimental range of this study covers superficial gas velocity (vSg) values from 17 to 23m/s, superficial liquid velocity (vSL) values of 0.01 and 0.02m/s, and inlet liquid stream aqueous phase fraction (APFin) values between 0 to 100%. Similar test matrix is completed for both water and water and MEG solution as the aqueous phase. An isokinetic probe system is used to measure the entrained droplet flux at different vertical positions in the gas phase. Liquid entrainment fraction is then estimated by means of volumetric averaging. The trends of the data with respect to input parameters are investigated.The two and three-phase entrainment fraction data are used for a correlation evaluation study. Performances of ten correlations for two-phase entrainment fraction are compared to the experimental data, and best performing correlations are identified. The correlation of Pan and Hanratty (2002) is modified in an effort to improve the entrainment fraction estimations. The predictions of the modified correlation are compared with the acquired data and datasets from the literature. In addition, a simple empirical correlation is proposed to predict liquid phase entrainment fraction for three-phase flow systems.

Entrained liquid fraction calculation in adiabatic disperse-annular flows at low rate in film

In this work, we continue our study [1] and extend further an approach to low reduced pressures. An approximate model of droplets entrainment from the laminar film surface and an equation for calculating entrainment intensity are proposed. To carry out direct verification of this equation using experimental data is extremely difficult because the integral effect—liquid flow rate in a film at a dynamic equilibrium between entrainment and deposition—is usually measured in the experiments. The balance between flows of droplets entrainment and deposition corresponds to the dynamic equilibrium because of turbulent diffusion. The transcendental equation, which was obtained on the basis of this balance, contains one unknown numerical factor and allows one to calculate the liquid rate. Comparing calculation results with the experimental data for the water–air and water–helium flows at low reduced pressures (less than 0.03) has shown their good agreement at the universal value of a numerical constant, if an additional dimensionless parameter, a fourth root of vaporliquid densities ratio, is introduced. The criterion that determines the boundary of using methods of this work and that of [1] in calculations and that reflects effect of pressure and state of film surface on distribution of the liquid in the annular flow is proposed; the numerical value of this criterion has been determined.

Unified Modeling Suite for Two-Phase Flow, Convective Boiling, and Condensation in Macro- and Microchannels

This paper focuses on the unified modeling suite for annular flow that the authors have developed and continue to develop. The annular flow suite currently includes models to predict the void fraction, the entrained liquid fraction, and the wall shear stress and pressure gradient, and a turbulence model for momentum and heat transport inside the annular liquid film. The turbulence model, in particular, allows prediction of the local average liquid film thicknesses and the local heat transfer coefficients during convective evaporation and condensation. The benefit of a unified modeling suite is that all the included prediction methods are consistently formulated and are proven to work well together, and provide a platform for continued advancement based on the other models in the suite. First the unified suite of methods is presented, illustrating in particular the most recent updates. Then results for the pressure drop and the heat transfer coefficient during convective evaporation and condensation are presented and discussed, covering both water and refrigerants flowing through circular tubes and noncircular multi-microchannel configurations for microelectronics cooling.

Effects of grid spacer with mixing vane on entrainments and depositions in two-phase annular flows

The effects of mixing vanes (MVs) attached to a grid spacer on the characteristics of air ewater annular flows were experimentally investigated. To know the effects, a grid spacer with or without MV was inserted in a vertical circular pipe of 16-mm internal diameter. For three cases (i.e., no spacer, spacer without MV, and spacer with MV), the liquid film thickness, liquid entrainment fraction, and deposition rate were measured by the constant current method, single liquid film extraction method, and double liquid film extraction method, respectively. The MVs significantly promote the re-deposition of liquid droplets in the gas core flow into the liquid film on the channel walls. The deposition mass transfer coefficient is three times higher for the spacer with MV than for the spacer without MV, even for cases 0.3-m downstream from the spacer. The liquid film thickness becomes thicker upstream and downstream for the spacer with MV, compared with the thickness for the spacer without MV and for the case with no spacer.

Modified liquid entrainment fraction correlation for varying pipe orientation and system pressure

2015 Elsevier Ltd. All rights reserved. Review Cioncolini and Thome (2012) proposed a correlation to predict the liquid entrainment fraction in vertical upward gas–liquid annular two phase flow. Their correlation is based on a two-step method of predictor and corrector technique. This technique calculates an approximate value of liquid entrainment fraction in the first (predictor) step and then recalculates its corrected value in the second (corrector) step. In the predictor step, as shown in Eq. (1), the predicted value of gas core Weber number (Wec,p) is calculated using gas density (qG) [kg/m], superficial gas velocity (USG) [m/s], pipe diameter (D) [m] and the gas–liquid interface surface tension (r) [N/m]. Based on this predicted Weber number, the first estimate of liquid entrainment fraction (Ep) is calculated from Eq. (2) where the multiplying factor (n) of 279.6 and exponents of 0.8395 and 2.209 are determined from the experimental data for vertical upward flow by solving for a nonlinear regression problem and are based on least absolute residuals. Next, the gas core density (qc) [kg/m] based on two phase flow quality (x) and the gas and liquid phase density (qG and qL) is calculated using Ep in Eq. (3) and the corrected values of gas core Weber number (Wec) and liquid entrainment fraction (E) are calculated in Eqs. (4) and (5), respectively. Wec;p 1⁄4 DqGU 2 SG r ð1Þ Ep 1⁄4 ð1þ n We 0:8395 c;p Þ 2:209 where n 1⁄4 279:6 ð2Þ qc 1⁄4 xþ Epð1 xÞ ðx=qGÞ þ Epð1 xÞ=qL ð3Þ Wec 1⁄4 DqcU 2 SG r ð4Þ E 1⁄4 ð1þ n We 0:8395 c Þ 2:209 where n 1⁄4 279:6 ð5Þ The correlation of Cioncolini and Thome (2012) is based on the experimental data set consisting of 2293 data points for circular pipes and 71 data points for non-circular pipes in vertical upward flow. Their correlation also used 96 data points in horizontal two phase flow for preliminary comparison and to validate their correlation (based on data in vertical upward two phase flow). For horizontal flow, Cioncolini and Thome (2012) found a significant scatter between the measured data and the predicted values however; they concluded that the general trend of the liquid entrainment in horizontal flow was correctly captured by their correlation.

Entrained liquid fraction prediction in adiabatic and evaporating annular two-phase flow

A new method to predict the entrained liquid fraction in annular two-phase flow is presented. The underlying experimental database contains 2460 data points collected from 38 different literature studies for 8 different gas-liquid or vapor-liquid combinations (R12, R113, water-steam, water-air, genklene-air, ethanol-air, water-helium, silicon-air), tube diameters from 5.0 mm to 95.3 mm, pressures from 0.1 to 20.0 MPa and covers both adiabatic and evaporating flow conditions, circular and non-circular channels and vertical upflow, vertical downflow and horizontal flow conditions. Annular flows are regarded here as a special form of a liquid atomization process, where a high velocity confined spray, composed by the gas phase and entrained liquid droplets, flows in the center of the channel dragging and atomizing the annular liquid film that streams along the channel wall. Correspondingly, the liquid film flow is assumed to be shear-driven and the energy required to drive the liquid atomization is assumed to be provided in the form of kinetic energy of the droplet-laden gas core flow, so that the liquid film-gas core aerodynamic interaction is ultimately assumed to control the liquid disintegration process. As such, the new prediction method is based on the core flow Weber number, representing the ratio of the disrupting aerodynamic force to the surface tension retaining force, a single and physically plausible dimensionless group. The new prediction method is explicit, fully stand-alone and reproduces the available data better than existing empirical correlations, including in particular measurements carried out in evaporating flow conditions of relevance for boiling water nuclear reactor cooling. (C) 2011 Elsevier B.V. All rights reserved.

Algebraic turbulence modeling in adiabatic and evaporating annular two-phase flow

The study considers algebraic turbulence modeling in adiabatic and evaporating annular two-phase flow, focusing in particular on momentum and heat transfer (so-called ‘convective boiling’) through the annular liquid film. In contrast with single-phase wall-bounded flow theory, shear-driven annular liquid films are assumed here to behave as fluid-bounded flows, mostly interacting with the shearing gas-entrained droplets core flow. Besides providing velocity and temperature profiles through the liquid film, the turbulence model proposed here predicts key parameters such as the average liquid film thickness, the void fraction and the convective boiling heat transfer coefficient with accuracies comparable or better than those of leading design correlations. This turbulence model is part of a unified annular flow modeling suite that includes methods to predict the entrained liquid fraction and the axial frictional pressure gradient. The underlying heat transfer database covers nine fluids (water, two hydrocarbons and six refrigerants) for vertical and horizontal tubes of 1.03–14.4 mm diameter and pressures of 0.1–7.2 MPa. Importantly, this study shows that there appears to be no macro-to-microscale transition when it comes to annular flow. Simply better physical modeling is required to span this range.

Simultaneous Investigation of Entrained Liquid Fraction, Liquid Film Thickness and Pressure Drop in Vertical Annular Flow

The mechanism of atomization of part of the liquid film to form drops in annular two-phase flow is not entirely understood. It has been observed that drop creation only occurs when there are large disturbance waves present on the film interface. (Woodmansee and Harrantty, 1969, “Mechanisms for the Removal of Droplets From a Liquid Surface by a Parallel Air Flow,” Chem. Eng. Sci., 24, pp. 299–307) observed that ripples on these waves were precursors to drops. Though it has been reported that drops occur in bursts by (Azzopardi, Gas-Liquid Flows Begell House Inc., New York, 2006), all previous drop size or concentration measurements have always been time integrated to simplify data analysis. Dynamic time averaged drop size measurements are reported for the first time in annular flow. Experiments were carried out on a 19 mm internal diameter vertical pipe with air and water as fluids. Spraytec, a laser diffraction-based, drop size measurement instrument, was used in the drop related data acquisition. Simultaneous time-resolved measurements were carried out for drop, film thickness, and pressure drop. Film thickness has been measured using the conductance probes employing a pair of flush mounted rings as electrodes. Pressure drop was logged using differential pressure cell connected to two pressure taps located within the test section. The gas superficial velocity was varied systematically from 13 to 43 m/s at fixed liquid superficial velocities of 0.05 and 0.15 m/s, respectively. Additional tests were carried out with the gas velocity fixed at 14 m/s while the liquid superficial velocity was varied from 0.03 to 0.18 m/s. Signal acquired are presented in form of time series to permit data analysis at different levels. Based on signal analysis, interrelationships between liquid film where the drops are sourced and the contribution of the entrained liquid droplets to the overall pressure drop in the system has been elucidated. Though structures are not clearly visible in the signals acquired, the time series have been analyzed in amplitude space to yield probability density function (Pdf). Beyond gas superficial velocity of 30 m/s, Pdf of drop size distribution becomes monomodal or single-peaked marking transition to mist annular flow.

Void Fraction Prediction in Annular Two-Phase Flow Using an Algebraic Turbulence Model

The study considers the prediction of the main flow parameters of adiabatic annular two-phase flows, focusing in particular on the void fraction. Recently developed models to predict the entrained liquid fraction, the wall shear stress and the velocity profile in the annular liquid film are discussed and integrated to provide a unified annular flow model that is used to predict the void fraction. A comparison with experimental void fraction data shows that the unified annular flow model slightly outperforms some of the most accurate void fraction empirical correlations currently available.

Prediction of the entrained liquid fraction in vertical annular gas–liquid two-phase flow

The study considers the prediction of the entrained liquid fraction in adiabatic gas–liquid annular two-phase flow in vertical pipes. Nine empirical correlations have been tested against an experimental data bank drawn together in this study containing 1504 points for 8 different gas–liquid combinations and 19 different tube diameters from 5.00 mm to 57.1 mm. The correlation of Sawant, Ishii and Mishima and the one of Oliemans, Pots and Trompé were found to best reproduce the available data. A new correlating approach, derived from both physical intuition and dimensional analysis and capable of providing further physical insight into the liquid film atomization process, was proposed and worked better than any of the existing methods. This new correlation is based on the core flow Weber number that is also a controlling dimensionless group in determining the wall shear stress and associated frictional pressure gradient of annular flows.

A new method of entrainment fraction measurement in annular gas–liquid flow in a small diameter vertical tube

A new method was introduced to measure liquid entrainment fraction in gas–liquid two-phase upward annular flow in a vertical tube (i.d.=9.525 mm). In this method, a new liquid–gas separator was designed and the chemically-based titration method was used to effectively measure the entrainment fraction in real time. Experiments were conducted at low system pressure (∼1 atm), and relatively low gas and liquid superficial velocities ( V sg = 25.8 –45.5 m/s, and V sl = 0.15 –0.30 m/s). Data analysis shows that the results are repeatable and occupy the range commonly seen in annular flow. The entrainment fraction was found to be under 7% for all the experimental set points. The repeatability of the test results and comparisons with previous entrainment data indicate that the new technique can perform as well as the film removal technique.

Experimental Study of Low-Liquid-Loading Gas-Liquid Flow in Near-Horizontal Pipes

Summary Low-liquid-loading flow in wet-gas pipelines is a common occurrence in the transport of raw gas. The most important parameters governing the flow behavior are pipe geometry (inclination angle and diameter), operating conditions (flow rate, pressure, and temperature), and physical properties of the gas and liquid (density, viscosity, and surface tension). In this study, extensive experiments were conducted with a test loop made of 50.1 mm diameter acrylic pipe with inclination angles from the horizontal of −2°, −1°, 0°, 1°, and 2°. Gas and liquid superficial velocities ranged from 5 to 25 m/s and from 0.001 to 0.053 m/s, respectively. In-situ liquid loading ranged from 150 to 1800 m3. The flow patterns studied were stratified (smooth and wavy) and annular. Measured parameters included gas and liquid volumetric flow rates, liquid-film flow rate, pressure drop, temperature, liquid holdup, and droplet deposition rate. The experimental results show that there is a broad gas velocity range for the transition from stratified to intermittent flow at low liquid loading. Entrainment can occur in the gas core at relatively low velocities, and droplet deposition occurs simultaneously with entrainment. An increase in gas velocity did not increase the liquid entrainment fraction over a relatively broad range of velocities. However, an increase in the liquid flow rate did increase the liquid entrainment fraction. In the annular flow region, a new phenomenon was observed at certain superficial gas velocities; an increase in the liquid flow rate decreased the liquid-film flow rate and liquid holdup and increased the entrainment flow rate. This phenomenon may have a significant impact on operations to sweep liquids from wet-gas pipelines. Seven correlations of the liquid entrainment onset point and the entrainment fraction in the gas core are evaluated. The interfacial friction-factor closure relationship should be different for upward flow when compared to horizontal and downward stratified flow, owing to the existence of counter-current flow in upward-inclined pipes.