Interfacial Friction Factor Research Articles

Relationship Between Wavy Liquid Film Dynamics and Droplet Formation From Trailing Edge

Abstract Erosion of steam turbine blades due to coarse droplet impingement is a serious problem. The physical relationship is still elusive between the dynamics of wavy liquid film on a wall and the droplet dispersion from the trailing edge. In this study, we experimentally and theoretically investigate the liquid film subjected to the turbulent airflow and following fragmentation process under well-controlled flow conditions, where the airflow velocity is up to 100 m/s, and initial liquid film velocity is 0.06 and 0.10 m/s, and trailing edge thicknesses are 0.5, 1.0, and 2.0 mm. By applying the developed PLIF based method with no use of artificial threshold of brightness, we quantify the film thickness and interfacial friction factor. As the airflow velocity increases, the liquid film instability promotes and the interfacial friction factor increases, much exceeding the Blasius correlation. When the liquid film reaches the trailing edge, several liquid columns extend by the Rayleigh-Taylor instability. We identify that the interfacial friction factor to accelerate the ligament corresponds to the Blasius correlation, distinct from the one on the wavy liquid film upstream. Incorporating the identified two interfacial friction factors, we successfully formulate the diameter of ligament as the characteristic lengthscale of the spreading droplet downstream. Derived formulation for the droplet statistics is well validated by the experimental results of mean and maximum diameters and size distribution.

A new mechanistic model to predict liquid loading in inclined natural gas wells

Accurately predicting the critical gas velocity and inclination angle is crucial for gas field development. However, the mechanism of liquid loading remains elusive due to insufficient attention given to the multivaluedness of flow structures and phase non-uniformity. This paper theoretically studied the flow pattern and gas-liquid configuration in wellbore based on the minimum energy principle. The Kelvin-Helmholtz instability of liquid film was analyzed, and a new correlation for the interfacial friction factor was proposed based on wave properties. The results indicated that the flow pattern transitioned from stratified to annular flow as the inclination angle increased. The gas-liquid interface presented a curved shape, with the interface curvature being influenced by various factors such as fluid properties, tube diameter, inclination angle, and gas and liquid velocities. As the inclination angle increases, the critical gas velocity first increases and then decreases, reaching a peak between 44° and 59°, aligning well with experimental and conventional results. Larger tube diameter, higher liquid density, and viscosity result in a higher critical gas velocity. Waves are more prone to develop in inclined pipes, and capillary waves can break up liquid film due to instability, leading to a discontinuous flow in inclined tubes. Film instability is exacerbated by a smaller diameter, higher liquid holdup, or greater inclination angle. Finally, a new model was devised to predict liquid loading in inclined natural gas wells, demonstrating better performance than existing models. In practice, the present model can achieve real-time prediction of critical gas velocity and continuously monitor the location of liquid accumulation in gas wells over the lifespan.

Numerical and experimental investigation on droplet entrainment mechanism and closed equations of two-fluid model

As a clean and low-carbon energy source, natural gas is an important force in achieving carbon peaking and carbon neutrality goals. Affected by the strong force of gas and liquid during mining and transportation, it exhibits the phenomenon of droplet entrainment. Entrained droplets change the properties of gas and liquid phases, which is crucial for accurate measurement of liquid film thickness, gas holdup, pressure drop and flow rates in natural gas pipelines. The measurement of entrained droplets has always been a focus and difficulty in the two-phase flow research field. Therefore, numerical simulation combined with experimental measurement are presented to study the droplet entrainment mechanism and closed equations of two-fluid model. The specific parameter settings for simulating horizontal gas–liquid annular flow based on numerical method are discussed, and effective simulation of droplet entrainment and deposition in annular flow is achieved. By comparing liquid film thickness and wave velocity from the simulation results with the experimental results, the correctness of the simulation method is verified. Then, the mechanism and dynamic evolution process of entrained droplets in annular flow are revealed, and the generation and deposition characteristics of entrained droplets are studied. As a result, the closed equations of two-fluid model such as droplet velocity, gas–liquid interface velocity, and gas–liquid interface friction factor are established. The proposed two-fluid model is validated using dual mode ultrasound and differential pressure sensors, demonstrating its good applicability and extrapolation.

EFFECTS OF PIPE DIAMETER ON INTERFACIAL AND WALL FRICTION FACTORS OF SWIRLING ANNULAR FLOWS IN A VERTICAL PIPE

Interfacial and wall friction factors, <i>f<sub>i</sub></i> and <i>f<sub>w</sub></i>, of swirling annular flows in a vertical pipe of 20 mm in diameter D were measured for comparison with those in a vertical pipe of <i>D </i>= 30 mm. A three-fluid model was applied to evaluate the friction factors. Measurements were carried out in two sections, one near the swirler and the other far downstream the swirler. The swirl intensity of the flow was evaluated by the interfacial swirl number si defined by the ratio of the azimuthal to the axial components of interfacial wave velocity. The interfacial swirl numbers were smaller in the smaller pipe. The ratio of <i>f<sub>i</sub></i> in swirling annular flows to that in non-swirling annular flows decreased to unity with decreasing <i>s<sub>i</sub></i>* which is the arithmetic mean value of <i>s<sub>i</sub></i> for 0 ≤ <i>z</i>* (= <i>z/D</i>) ≤ 3.8, where <i>z</i> is the axial coordinate in the test section, and is higher in <i>D </i>= 20 mm than in <i>D </i>= 30 mm. The ratio of <i>f<sub>w</sub></i> in swirling annular flows to that in non-swirling annular flows decreased to less than unity with decreasing <i>s<sub>i</sub></i>* and is higher in <i>D </i>= mm than in <i>D </i>=30 mm.

Gas-liquid Interfacial Friction Factor under Flooding Conditions in Vertical Pipes

Gas-liquid Interfacial Friction Factor under Flooding Conditions in Vertical Pipes

Prediction of interfacial shear stress and pressure drop in vertical two-phase annular flow

The interfacial shear stress and pressure drop of an upward vertical annular flow of nitrogen–water, HFC134a–water, and nitrogen–95 % ethanol solution were comprehensively investigated considering the effect of the liquid–gas density ratio and surface tension. A direct link between the disturbance wave height and equivalent sand-grain roughness was noted through the analogy with the famous Moody chart for single-phase turbulent flows. A predictive model of the interfacial friction factor was developed based on this finding. To predict the pressure drop of the annular flow, a new model with good predictive performance for annular flows of various working fluids including steam–water under boiling water reactor operating condition (286 °C and 7 MPa) was proposed.

Effects of liquid viscosity on interfacial and wall friction factors of swirling annular flows in a vertical pipe

Experiments of gas–liquid swirling annular flows in a vertical pipe of diameter D = 30 mm were carried out to obtain interfacial and wall friction factors, fi and fw, based on a three-fluid model. The liquid phase was two kinds of glycerol-water solutions with the kinematic viscosity νL of two or four times larger than that of water. Experimental data were obtained in two axial sections with short and long axial distances from the swirler, which corresponds to swirling and non-swirling annular flow regimes, respectively. Both the azimuthal and axial components of interfacial velocity decayed with increasing νL. The interfacial swirl number si, which is the ratio of the azimuthal component to the axial component of interfacial velocity, was not affected by νL for z*(=z/D) ≤ 3.8, where z is the axial coordinate in the test section. The mean interfacial swirl number si∗, which is the arithmetic mean of si in z* ≤ 3.8, was expressed in terms of dimensionless numbers based on the gas and liquid volumetric fluxes without νL. The interfacial friction factor decreased with increasing νL in swirling flows. The functional form of the Colebrook equation had a prospect of correlating fi in both swirling and non-swirling annular flows. The wall friction factor ratio of fw in the swirling annular flow regime to that in the non-swirling annular flow regime decreased as νL increased for si∗ > 0.33. The wall friction factor ratio was well correlated in terms of si∗ and νL.

An optimize empirical correlations for liquid film thickness and interfacial friction factor in vertical gas-liquid annular flow

BackgroundThe annular flow regime is one of the most prevalent two-phase flow regimes, occurring throughout a broad range of gas and liquid flow rates. This flow pattern is distinguished by a thin layer of liquid around the walls and a core of quickly flowing gas in the middle. MethodsUsing image recording and processing methods, the generation of an annular flow pattern in a counter-current two-phase flow in a vertical transparent pipe was explored in the current experimental study. In this regard, the range of air (bottom to top) and water (top to bottom) velocities for annular flow was 20.94–3.66 m/s and 0.3–1.06 m/s, respectively. Significant findingsIn this paper, the liquid film thickness is provided as a novel five-variable correlation function of gas phase superficial velocity, liquid phase velocity, pipe diameter, Weber number, and Froude number, with an R2 value of 0.98. In addition, the interfacial friction factor (liquid and gas phases) is provided as a five-variable correlation based on gas flow Reynolds number, liquid flow Reynolds number, pipe diameter, liquid film thickness, and Froude number with coefficient of determination of 0.97. The sensitivity analysis of the acquired experimental findings reveals that the liquid film thickness and the interfacial friction factor are most sensitive to changes in the superficial velocity of the gas phase and the Reynolds number of the liquid phase, respectively. Also, for the thickness of the liquid film and the interfacial friction coefficient, the experimental values and suggested correlations deviate by a maximum of 3.15 percent and 4.56 percent, respectively.

Parametric analysis of interfacial friction factor for liquid film dynamics sheared by turbulent gas flow

Water droplet impingement on a low-pressure steam turbine blade causing erosion has been recognized as a crucial issue. It is essential to elucidate a comprehensive droplet detachment mechanism, not only from the trailing edge but also from the liquid film surface. In the present paper, we investigate the influence of interfacial friction factor against liquid film dynamics on a wall sheared by a turbulent gas flow, including the liquid film thickness, liquid film velocity and entrained droplet detached from liquid surface for both pipe flow and plate flow conditions. We conduct the analyses by using a liquid film dynamics model, recently established, considering the three-dimensional destabilized waves and droplet entrainment from the liquid surface. As a result, the film thickness and velocity greatly depends on the interfacial friction factor. Interestingly, the rate of entrained droplet to initial liquid film has a minimum value when the interfacial friction factor equals to the inverse of the liquid film Reynolds number, while the remaining liquid film flow rate becomes maximum.

Effects of swirl intensity on interfacial and wall friction factors of annular flows in a vertical pipe

Interfacial and wall friction factors, fi and fw, of air-water swirling annular flows in a vertical pipe of diameter D = 30 mm were measured in three sections of L* (=L/D) = 7.3, 13 and 31, where L is the distance from a swirler. The gas and liquid volumetric fluxes, JG and JL, were 12.5 ≤ JG ≤ 20.0 m/s and 0.071 ≤ JL ≤ 0.213 m/s, respectively. The interfacial swirl number, si, defined by Viθ/Viz, where Viθ and Viz are the azimuthal and axial components of interfacial velocity, was introduced as an indicator of swirl intensity. For z* (=z/D) ≤ 7, where z is the axial coordinate in the test section, the si increased with z* at low JG and JL, and slightly decreased with z* at high JG and JL. The si decreased for z* > 7 and reached zero at z* ≈ 30. The fw estimated using the three-fluid model was larger than that estimated using the two-fluid model since the droplet flow rate was not negligible even in swirling annular flows. The three-fluid model was therefore more appropriate for evaluation of fi and fw than the two-fluid model. The ratio fw∗ increased with s¯i for s¯i > 0.25, where fw∗ is the ratio of fw to that of non-swirling flows and s¯i is the averaged value of si in the section. The ratio fi∗ increased with s¯i for s¯i > 0.18, wherefi∗ is the ratio of fi to that of non-swirling flows. Correlations in terms of s¯i have prospect to evaluate the fi and fw in swirling annular flows.

Development of a dimensionless flooding correlation based on experimental study on air-water countercurrent flow limitation in a vertical tube

The flooding phenomenon has an important influence on the safety of equipment, especially the nuclear power plant. A new semi-empirical correlation for flooding was proposed based on the experimental investigation of the physical characteristics of the flooding in our previous work. The model was derived from the momentum equations in the annular flow model. The liquid volume fraction, the wall and interfacial friction have been taken into account. The interfacial friction factor is emphatically discussed in this study since the interfacial friction has a significant influence on flooding. A modified model of interfacial friction factor was presented containing the Bond number since the Bond number can remove the influence of the geometry. The predicting error was basically within 20% compared with the existing experimental data obtained in different geometries and sizes.

Studying the Effects of Negative Skin Friction on Single Piles in Basrah Governorate

The finite element method capable of simulating the behavior of deep foundations subjected to negative skin friction in Basrah soil is investigated. Single piles under drag forces are analyzed using the PLAXIS program with an axisymmetric model. Linear elastic, Soft Soil and Mohr-Coulomb constitutive relations are adopted, where higher order triangular element is chosen for pile and soil clusters. Both pile and soil are modeled using (15)-node triangular elements. Three sites in Basrah province (Umm Qasr Port, Khor Al-Zubair, and Shatt AlArab Hotel) were selected to perform this study. The soil profile and layer characteristics are obtained from the soil investigation reports. Where the negative skin friction is evaluated due to filling loads. It is Conclusion thatSmall relative displacements are necessary to activate the negative skin friction. The elastic shorting for pile effect negative skin friction, due to increase relative displacement. The elastic shorting of the driven pile is more than that of the bored pile due to the less cross-sectional area of the driven pile. The results revealed proportional relation between the developed drag forces and pile section dimensions, interface friction factor, and fill height, with a maximum effect on the section dimension and minimum effect on the interface factor. The locations of neutral points are not sensitive to the above-mentioned factors.

Numerical study of statistically developed gas-liquid intermittent flows by the lens of three-dimensional simulations

Two-phase intermittent flows are characterized by an alternation between a region almost fully occupied by liquid (a liquid plug) and another one composed by a gas bubble. This type of flow is frequently found in industry, particularly in the transportation of oil and gas through pipelines. Their dynamics is commonly modeled with a one-dimensional approach, since long pipelines are employed, making 2D or 3D simulations unfeasible. The models always require an assessment of wall and interfacial friction factors, which are usually obtained by empirical correlations. In this work, from full 3D velocity fields across statistically developed slug unit cells, flow parameters needed for 1D models were determined. For that, several three-dimensional numerical simulations were performed using the open source platform OpenFOAM®. The two-phase flow was determined within a computational domain corresponding to a single slug unit cell, with periodic boundary conditions under imposed pressure gradient and overall void fraction, employing the Volume of Fluid (VOF) method. Both laminar and turbulent flows were studied. Turbulence was modeled with the k-ω Shear Stress Transport (SST) model. The axial velocity profile along the cross section, as well as slug parameters, were compared with available experimental data, showing a quite good agreement. From the results validated by experimental data, friction factors and momentum flux parameters were determined, allowing the development of corrections to improve the available 1D models.

Hydrodynamics of vertical upward and downward flow boiling in a millimetric tube

Upward and downward vapor-liquid vertical flows inside a vertical 6 mm sapphire tube was investigated using HFE-7000 as working fluid. The goal was to investigate the effect of flow direction and wall heating on two-phase parameters such as flow pattern, wall shear stress (τw), interfacial shear stress (τi) and interfacial wave structures. The mass flux, heat flux and vapor quality ranges were 50≤G≤400kg/m2.s,0≤q≤3W/cm2 and 0≤x≤0.7 respectively. Bubbly, slug, churn, annular flow patterns were observed in upward and downward flows. A falling film regime occurred in downward flow at low mass fluxes. Void fractions were higher in downward flow than in upward flow due to gravity effect, and were in good agreement with drift flux models of the literature. The wall shear stress increased with the wall heat flux due to the bubble nucleation at the wall. Following a similar approach to Kim and Mudawar (2013b), a correlation for the wall shear stress taking into account the forced convection and the bubble nucleation was derived and provided a good estimation of the experimental data within ±20%. From image processing of the high-speed visualizations, velocities (Uw) and frequencies (Fw) of the disturbance waves in annular flow were measured. The interfacial shear stress was found to directly depend of the product Uw×Fwand a prediction of the interfacial friction factor was proposed in flow boiling for both upward and downward flows.

Hybrid ANN approach for prediction of lubricant retention in compressor suction lines based on analytical model and parametric study

A modeling study for prediction of oil retention in compressor suction lines is presented in this article. A new flow-pattern-based analytical model called the double-circle model (DCM) was developed to evaluate the oil retention amount in suction lines. A new consolidated oil retention database was established to develop interfacial friction factor correlation. Parametric study was conducted by means of force balance analysis to determine the influence factors of oil transport. The DCM and parametric study were validated by the database, and the results showed that they display reliable accuracy. Finally, a hybrid artificial neural network (ANN) approach was proposed, which used the DCM and parametric study to produce extrapolation data and determine the input parameters, respectively. The hybrid ANN was optimized for the 6-13-1 configuration with logarithmic sigmoid (logsig) transfer function and the Lavenberg–Marquardt (L-M) algorithm. The hybrid ANN model prediction yields a mean relative error (MRE) and R 2 of 6.25% and 96.86%, respectively.

Slug Flow Hydrodynamics Modeling for Gas–Liquid Two-Phase Flow in a Pipe

Gas–liquid flow in a pipeline is a very common. Slug two-phase flow is dominated in the case of slightly upward flow (+0.25°) and considered to be the comprehensive flow configuration, and can be in close contact with all the other flow patterns. The models of different flow patterns can be unified. Precise prediction of the slug flow is crucial for proper design and operation. In this paper, we develop hydrodynamics unified modeling for gas–liquid two-phase slug flow, and the bubble and droplet entrainment is optimized. For the important parameters (wall and interfacial friction factors, slug translational velocity and average slug length), the correlations of these parameters are optimized. Furthermore, the related parameters for liquid droplet and gas bubble entrainment are given. Accounting for the gas–liquid interface shape, hydrodynamics models, i.e., the flat interface model (FIM) and the double interface model (DIM), of liquid film in the slug body are applied and compared with the experimental data. The calculated results show that the predictions for the liquid holdup and pressure gradient of the DIM agree with experimental data better than those of the FIM. A comparison between the available experimental results and Zhang’s model calculations shows that the DIM model correctly describes the slug dynamics in gas–liquid pipe flow.

Direct Pore-Scale Simulations of Fully Periodic Unit Cells of Different Regular Lattices

Abstract Open-cell metal foams are known for their superior heat dissipation capabilities. The morphological, pressure drop, and heat transfer characteristics of stochastic metal foams manufactured through traditional “foaming” processes are well established in the literature. However, employment of stochastic metal foams in next-generation heat exchangers is challenged by the irregularity in the pore- and fiber-geometries, limited control on the pore-volume, and an inherent necessity of a bonding agent between foam and the heat source. On the other hand, additive manufacturing (AM) is capable of printing complex user-defined unit cell topologies with customized fiber shapes directly on the substrates subjected to heat load. Moreover, the user-defined regular lattices are capable of exhibiting better thermal and mechanical properties than stochastic metal foams. In this paper, we present a numerical investigation on fully periodic unit-cells of three different topologies, that is, tetrakaidecahedron (TKD), rhombic-dodecahedron (DDC), and Octet with air as the working fluid. Pressure gradient, interfacial heat transfer coefficient, friction factor, and Nusselt number are reported for each topology. Rhombic-dodecahedron yielded the highest averaged interfacial heat transfer coefficient whereas Octet incurred the highest flow losses. Pore diameter, defined as the maximum diameter of a sphere passing through the polygonal openings of the structures, when used as the characteristic length scale for the presentation of Nusselt number and Reynolds number, resulted in a single trendline for all the three topologies.

Interfacial Friction Prediction in a Vertical Annular Two-Phase Flow Based on Support Vector Regression Machine

Accurate prediction of interfacial friction factor is critical for calculation of pressure drop and investigation of flow mechanism of vertical annular two-phase flows. Theoretical models of interfacial friction factor based on physical insight have been developed; however, these are inconvenient in engineering practice as too many parameters need to be measured. Although many researchers have proposed various empirical correlations to improve computation efficiency, there is no generally accepted simple formula. In this study, an efficient prediction model based on support vector regression machine (SVR) is proposed. Through sensitivity analysis, five factors are determined as the input parameters to train the SVR model, relative liquid film thickness, liquid Reynolds number, gas Reynolds number, liquid Froude number and gas Froude number. The interfacial friction factor is chosen as the output parameter to check the overall performance of the model. With the help of particle swarm algorithm, the optimization process is accelerated considerably, and the optimal model is obtained through iterations. Compared with other correlations, the optimal model shows the lowest average absolute error (AAE of 0.0004), lowest maximum absolute error (MAE of 0.006), lowest root mean square error (RMSE of 0.00076) and highest correlation factor (r of 0.995). The analysis using various data in the literature demonstrates its accuracy and stability in interfacial friction prediction. In summary, the proposed machine learning model is effective and can be applied to a wider range of conditions for vertical annular two-phase flows.

Modeling of lubricant retention in suction lines with R32/PVE oil mixture

Modeling study for predictions of oil retention and critical refrigerant mass flux in compressor suction line was presented in the current work. Three approaches were developed for prediction of oil retention amount in suction line, namely, annular flow model, flow-pattern based method and empirical void fraction model. The annular flow model assumed that annular flow exists as the flow pattern, while the flow-pattern based method described the flow behavior of refrigerant/oil mixture by the flow pattern classifications and double circle model. Based on the proposed models, new correlations of interfacial friction factor and void fraction were established. The experimental data for R32 with coexistence oil PVE68 inside horizontal, vertical and inclined suction lines were used as the foundation and validation of the models. The results showed that all the models display satisfying prediction for oil retention. The flow-pattern based method exhibited the best results, which yielded the mean absolute deviation of 9.35% and captured 87.83% of the data within ±20% error bands. Moreover, two models for prediction of minimum refrigerant mass flux were recommended in order to ensure successful oil return. These models could serve as tools for operation optimization incorporating the lubricant oil effect.

Void Fraction and Interfacial Friction in Vertical Circular Pipes with the Square Top End under Flooding Conditions

The objective of this study was to reduce the uncertainties of correlations for flow characteristics in vertical pipes under flooding at the top end. The void fraction α, pressure gradient dP/dz, and countercurrent flow limitation (CCFL) were previously measured with diameter D = 40 mm and working fluid of air and water. The wall friction and interfacial friction factors (fw and fi) were obtained based on the annular flow model, and CCFL and fw were evaluated in detail. Hence, attention was turned to detailed evaluations of α and fi. Liquid film thickness δ and interfacial friction factor fi for smooth film (SF) due to flooding at the top end were obtained using the previously derived fw correlation and existing dP/dz data with D = 20 to 50.8 mm and pressure P = 0.1 to 4.1 MPa, and empirical correlations for δ and fi were derived. The δ term was well expressed by a function of the liquid Reynolds number ReL, and the uncertainty of the δ correlation was ±0.0062 for α = 0.87 to 0.98. fi was expressed by a function of δ/L (where L is the Laplace length) or the Kutateladze parameter KG*, the dimensionless diameter D* (=D/L), and the density ratio of the gas and liquid phases ρG/ρL. The applicability of the derived correlations to conditions of D = 300 mm and P = 7 MPa was evaluated, and the fi correlation was modified based on fi values computed with the δ correlation. The drift-flux parameters for SF were also considered.