Two-phase Pipe Flow Research Articles

Theoretical and experimental research on interfacial shear stress and interfacial friction factor of gas-liquid two-phase wavy stratified flow in horizontal pipe

The external flow field over wave interface is reached by the aid of conformal transformation thought, and velocity boundary layer of inner flow field is deduced also, which gives fundamental description of shear stress over wave interface. The viscous drag coefficient is induced with considering the characteristics of interface wave, such as wave height, wave length and ratio between wave lengths of both ascending and descending semi periods, which significantly impact the velocity gradient over the wave interface that accounts for the differences in distribution of local shear stress. The influence of fluid flow is studied also, which gives support that the earlier separating point of the fluid flow over wave interface the stronger depression to the turbulent perturbation is made, and a reduced drag force arrived. There are otherness and commonness between fluid flow over wave interface and interface appearing in air-water wave stratified flow, and a new model is proposed to intrinsically construct the interfacial friction factor encountered in wave stratified flow. The models for viscous drag coefficient and interfacial friction factor are tested, different models are studied, predicted values are compared with experimental data and that computed by solving there-dimension unsteady Navier-Stokes equations, which gives proof that the values predicted by newly proposed models well fit the real values.

Nonlinear Model Predictive Control for Disturbance Rejection in Isoenergetic-isochoric Flash Processes

Abstract We present a nonlinear model predictive control (NMPC) algorithm for semi-explicit index-1 stochastic differential-algebraic equations. It is natural to model isoenergetic-isochoric (constant energy-constant volume) flash processes with such equations. The algorithm uses the continuous-discrete extended Kalman filter (EKF) for state estimation, and it uses a single-shooting method to solve the involved optimal control problems. It computes the gradients with an adjoint method. The isoenergetic-isochoric flash is also called the UV flash, and it is important to rigorous models of phase equilibrium processes because it is a mathematical statement of the second law of thermodynamics. NMPC algorithms for UV flash processes are therefore relevant to both safe and economical operation of phase equilibrium processes such as flash separation, distillation, two-phase flow in pipes, and oil production. We design the NMPC algorithm for disturbance rejection, and we therefore augment the state vector with the unknown disturbance variables in the continuous-discrete EKF. We present a numerical example of economical NMPC of a UV flash separation process. It involves output constraints and the estimation of an unknown and unmeasured disturbance. The computation time of the NMPC algorithm does not exceed 3.14 s in any of the 5 min control intervals. This indicates that real-time NMPC of UV flash separation processes is computationally feasible.

Experimental investigation of upward vertical two-phase high-velocity flows in large-diameter pipes

An experimental investigation is carried out to analyze the effect of the diameter and high fluid velocities on two-phase flow in vertical large-diameter pipes. This study generated and gathered experimental data for diameters ranging from 97 to 297 mm. The working fluids for the experimental database are water and air, for superficial liquid velocities ranging from 0.2 to 4.7 m/s; and superficial gas velocities ranging from 0.1 to 30 m/s.From the experimental observations of flow regimes for diameters larger than 97 mm, cap-bubble flow is observed for conditions which slug flow would be expected in smaller diameter pipes. Based on experimental results obtained in this work and available in the literature, it is observed that pressure gradient only varies around 50% for changes of one order of magnitude on the pipe diameter (from 19 to 297 mm), for superficial gas velocities lower than the minimum point in the pressure gradient curve. The measurements of liquid holdup and pressure gradient are compared to a numerical model based on the drift-flux approach, which shows good agreement with the experimental observations.

Reduced-order description of phase fraction data measured using wire-mesh sensor in two-phase pipe flows

Proper Orthogonal Decomposition (POD) technique has been applied to the three dimensional (cross-sectional and time) void fraction data acquired by the application of wire-mesh sensor (WMS) measurement technique. The measurements are performed in a 76.2 mm ID horizontal pipe with air and water as fluids, and with 16 × 16 WMS located at a distance of 17 m from the inlet (L/D=223). In order to perform the detailed analysis using the POD technique, flow patterns covering stratified-wavy, slug, pseudo-slug, and annular low liquid loading are investigated in the paper. Thanks to the time-resolved data obtained using the WMS, classical POD method is applied in spectral space after converting time-dependence to frequency. The analysis showed that for all the cases considered, substantial part of the original data can be recovered using a couple POD modes and a few frequency modes. The most dominant two phase flow features are captured at near perfect accuracy. The global flow parameters like space- and time-averaged liquid holdup values are compared between the original and reconstructed fields and the agreement is found to be very good. The phase portraits obtained from the random coefficients associated with different POD mode diagrams correlate with the characteristics of the flow pattern, such that it is possible to observe two distinct orbits in slug and pseudo slug flow cases, and single orbit indicating more random behaviour for the stratified wavy and annular flow cases.

The Characteristic of Two-Phase Flow Pattern on Air-Water Countercurrent Flow in Vertical Pipe

Two-phase flow is widely encountered in several engineering and industrial facilities. The purpose of this study is to investigate the characteristic of slug countercurrent flow pattern in a vertical small diameter pipe. An experimental investigation in this study has been performed toward a transparent tube of 19 mm diameter (outside diameter 22 mm, length 200 mm), water and air as the liquid and gas fluid in the vertical pipe followed by taking a picture of flow pattern in the transparent pipe using the high-speed camera. Two differential pressure sensors were set in transparent tube in order to receive slug countercurrent flow rate associated with the acquisition data as media to record data and then displayed on the screen. The two-phase flow was always preceded by the instability of flow rate and bubbles appearance. It occurred after the steady flow data acquisition rate was turned on for recording the differential pressure. The result showed that the flow pattern characteristic of two-phase flow (air-water) in the vertical pipe caused by the superficial velocity of air.

A unified pipe-network-based numerical manifold method for simulating immiscible two-phase flow in geological media

A unified pipe-network-based numerical manifold method (NMM) is developed to simulate immiscible two-phase flow in a geological medium. Both heterogeneous and non-heterogeneous geological media can be discretized as numerical pipe networks, which have high efficiency and accuracy in simulating fluid and mass transfer in fractured rock masses. A manifold element method is developed to solve the governing equations of immiscible two-phase flow in pipes. The developed NMM can simulate moving and deforming of two-phase flow interface. A grid-based front-tracking method updates the marker points constructing the fluid interface explicitly in each time step. The effectiveness of the NMM is verified through analytical and finite element analysis. Parametric studies are conducted by simulating immiscible two-phase flows with various fluid properties in homogeneous and inhomogeneous geological conditions. The results show that the developed method can efficiently simulate the moving interface of two-phase flow in geological media, including effects such as “viscous fingering”, a noteworthy phenomenon in enhanced oil recovery. When the mobility of the driving fluid is larger than that of the driven fluid, the inhomogeneity of the medium can cause the fluid interface to roughen, which increases over time during the process of two-phase flow. For the inverse situation, although the fluid interface remains rough, the roughness variation throughout the process is not prominent.

Experimental study on the hydrodynamic behavior of gas-liquid air-water two-phase flow near the transition to slug flow in horizontal pipes

The knowledge of the slug flow is essential the design safety of hydrocarbon transportation in the pipeline system of petroleum industries. However, the suitable models to predict the transition condition to slug flow are limited due to insufficient availability of experimental data. In the present study, the hydrodynamic characteristics of the near the transition to slug flow of air-water two-phase flow in horizontal pipes were investigated experimentally for inner pipe diameters of 16 mm, 26 mm, and 50 mm. The superficial velocities of water and air ranged from JL = 0.03 to 0.30 m/s and JG = 0.7 to 10.0 m/s. The hydrodynamic behavior was obtained from the combination of the visualization detected by using a high-speed video camera, the pressure gradient, and instantaneous volumetric liquid fraction measurements.The experimental results indicate that the wave growth and the wave coalescence are involved in the mechanism of the slug flow formation. Both gas and liquid superficial velocities have a significant effect also of those mechanisms. The average volumetric liquid fraction near the transition to slug flow is not affected by superficial gas velocities. Next, under a constant superficial gas velocity, an increase in the inner pipe diameter requires a larger superficial liquid velocity to change the flow patterns from stratified smooth to slug flow, and from pseudo-slug to slug flow.

Experimental study of supply pressure on spraying materials in horizontal pipe

In this work, the pressure drop and flow characteristics of solid–gas two-phase flow in a horizontal pipe were investigated experimentally. The pressure drop was measured by pressure transmitters, and the particle flow behaviour was observed using a high-speed camera. The particle concentration and gas pressure drop were systematically compared under different supply standard air fluxes. It was found that the particle materials exhibited a dune flow at a lower airflow velocity, and the pressure drop decreased first and then increased with increasing supply airflow velocity, until the critical wind speed for spraying materials was achieved. The coefficient of variation and power spectral density (PSD) analysis of the pressure drop were introduced to study the flow stability in pneumatic conveying; the fluid flow stability increased with decreasing coefficient of variation, and the results of the PSD analysis were consistent with those of the flow characteristics and pressure drop. When the standard airflow velocity exceeded the critical wind speed, the solid–gas ratio had a slight impact on the flow stability, and the optimum supply pressure for pneumatic conveying of these spraying materials was 0.4 MPa.

Simulations of intermittent two-phase flows in pipes using smoothed particle hydrodynamics

Slug flows are a typical intermittent two-phase flow pattern that can occur in submarine pipelines connecting the wells to the production facility and that is known to cause undesired consequences. In this context, computational fluid dynamics appears to be the tool of choice to understand their formation. However, few direct numerical simulations of slug flows are available in the literature, especially using meshless methods which are known to be capable of handling complex problems involving interfaces.In this work, a 2D study of the instability processes leading to the formation of intermittent flows in pipes is conducted using an existing multiphase smoothed particle hydrodynamics formulation associated with inlet and outlet boundary conditions. This paper aims to demonstrate the applicability of smoothed particle hydrodynamics to a given set of close-to-industry cases.First, we check the ability of our implementation to reproduce flow regimes predicted by Taitel and Duckler’s flow map. Then, we focus on the transition processes from one flow pattern to the other. Finally, we present the results obtained for more realistic cases with high density and viscosity ratios.

Experimental Study of Horizontal Gas-liquid Two-phase Flow in Two Medium-diameter Pipes and Prediction of Pressure Drop through BP Neural Networks

Horizontal gas-liquid two-phase flow is of crucial importance in oil-gas storage and transportation. In view of previous researches with the lack of horizontal gas-liquid two-phase flow in medium-diameter pipes (60-75 ㎜), experiments were conducted in DN 60 and DN75 at medium-high liquid velocity (50-250 m3/d) and high gas-liquid ratio (20-500 m3/m3). Comparison between flow patterns maps in DN60 and DN75 and the Taitel-Dukler model showed that only flow patterns map in DN60 agreed well. On the basis of experimental data analysis, variation laws of liquid holdup and pressure drop were determined. Besides, this paper developed a method to predict liquid holdup and pressure drop through BP neural networks. Results proved the capability of BP neural networks. The further validation can be made in practical applications.

CFD modeling and validation for two-phase medium viscosity oil-air flow in horizontal pipes

This study presents the results of a Computational Fluid Dynamics (CFD) simulation of two-phase medium viscosity oil-air flow in a 50.8 mm internal diameter horizontal pipe. Void fraction and pressure gradient predictions were validated using experimental data for four different oil viscosities (0.039, 0.06, 0.108 and 0.166 Pa s) and different flow rates varying from 0.1 to 2.9 m/s for the gas phase and from 0.01 to 2.95 m/s for the liquid phase, where four flow patterns were predicted (stratified, dispersed bubble, bubble elongated and slug flow). The obtained results of void fraction and pressure gradient presented a mean relative error of 30.04 and 21.38%, respectively. Furthermore, the CFD results were compared against 66 empirical correlations and predictions from OLGA. It was found that between the three studied methods (CFD, OLGA and empirical correlations) the CFD model outperformed the other two methods regarding the predicted flow patterns, pressure gradients and void fractions on most cases.

A fully-implicit solution for the single-pressure two-fluid model with sharp discontinuities

Transient two-phase flow in pipes is a common phenomenon in nuclear and petroleum engineering. Due to complex interactions at phase interfaces and the large variation on fluid properties, multiphase flows are much more complex than single-phase flows. However, modeling pressure, temperature, phase velocities and volumetric fractions is essential for design, management, optimization and safety analysis. Two approaches are generally applied for modeling multiphase flow: (a) local instant formulation and (b) averaged formulation. In this paper, the averaged Single-Pressure Two-Fluid model (together with Bestion’s correlation for interfacial pressure) is studied and a fully-implicit numerical solution is proposed. The obtained numerical solutions were compared to reference solutions for benchmark problems (water faucet tests and phase segregation) available in the literature. Aiming to verify if the aforementioned averaged model and the proposed fully-implicit solutions can be applied to study problems with counter-current flow and sharp discontinuities in pressure, velocities and volumetric fractions, new reference solutions for a generalized transient frictionless segregation test are proposed. Comparison between the proposed reference and numerical solutions allowed for a detailed verification of the studied averaged model. Finally, sudden multiphase fluid injection with subsequent tube closure was studied and the numerical results were discussed. As expected, it was observed transient surge pressure and co-current/counter-current flow with phase appearance and disappearance.

Experimental investigation of airflow above waves in a horizontal pipe

We investigate the effect of waves on the airflow in horizontal two-phase pipe flow. Velocity fields in the gaseous phase were acquired by particle image velocimetry (PIV), while interfacial elevation was measured with conductance wave probes. The velocity fields were sampled on a wave-following coordinate system which allows for a decomposition of the velocity field into a mean, wave-coherent and fluctuating component by means of a three-component Reynolds decomposition. Additionally, coherent vortical structures were identified by the swirling strength criterion, and their distribution along the waves is investigated.Results suggest that the interaction between turbulent airflow and propagating waves in a pipe has a number of features reminiscent of wind-wave interaction in open systems. Above waves generated by sufficiently high gas flow rates, there is a distinct region of sheltered airflow, and a lifting of the critical layer on the leeward side of the crest. Streamlines of the phase-averaged flow field show a cat’s eye structure located close to the crest in this region. Above waves of moderate steepness, we observe a shear layer that remains adjacent to the wave surface. Above steeper waves and higher gas flow rate, this layer detaches from the surface just downstream of the crest. Shear layer separation above waves is traditionally linked to the onset of wave breaking, and it is interesting to note that the case where we observe a separated shear layer in the phase-averaged vorticity field is in a regime of amplitude saturation.The swirling strength criterion reveals that vortical structures are shed from the interface and populate the detached shear layer above the trough. Below the detached shear layer, there is a region populated by counter-rotating vortices. The critical height coincides with the border between these two regions.

Effects of Liquid Velocity on Pressure Gradient, Slip and Interfacial Friction Factor in Annular Flow in Horizontal Pipe

Experimental investigations on annular flow behaviour in two-phase (air/water) flow in horizontal pipe were conducted using 2-inch (0.0504m) with a total length of 28.68m closed loop system. The emphasis from the experiments were on pressure gradient, slip and interfacial friction factor in annular flow. For interfacial friction factor, the entrainment, gas quality, the droplets and slip mixture density values were obtained through the experimental results which were substituted to determine it. In all, effects of liquid velocity were felt, as increase in superficial liquid velocity, increases the interfacial friction factor and pressure gradient in annular flow in horizontal pipes. More so, increase in superficial gas velocity, reduces the interfacial friction factor. Thus, interfacial friction factor decreases with increases in superficial gas velocity, while the pressure gradient increases with increase in superficial liquid velocity. The lower the superficial liquid velocity, the higher the slip but the lower the pressure gradient. Likewise, the lower the superficial liquid velocity, the more ripple waves obtained while the higher the superficial liquid velocity, the more disturbance waves in annular flow in horizontal pipe from the experiments.

Effects of Liquid Velocity on Pressure Gradient, Slip and Interfacial Friction Factor in Annular Flow in Horizontal Pipe

Experimental investigations on annular flow behaviour in two-phase (air/water) flow in horizontal pipe were conducted using 2-inch (0.0504m) with a total length of 28.68m closed loop system. The emphasis from the experiments were on pressure gradient, slip and interfacial friction factor in annular flow. For interfacial friction factor, the entrainment, gas quality, the droplets and slip mixture density values were obtained through the experimental results which were substituted to determine it. In all, effects of liquid velocity were felt, as increase in superficial liquid velocity, increases the interfacial friction factor and pressure gradient in annular flow in horizontal pipes. More so, increase in superficial gas velocity, reduces the interfacial friction factor. Thus, interfacial friction factor decreases with increases in superficial gas velocity, while the pressure gradient increases with increase in superficial liquid velocity. The lower the superficial liquid velocity, the higher the slip but the lower the pressure gradient. Likewise, the lower the superficial liquid velocity, the more ripple waves obtained while the higher the superficial liquid velocity, the more disturbance waves in annular flow in horizontal pipe from the experiments.

Drift flux modeling of transient high-viscosity-liquid and gas two-phase flow in horizontal pipes

The drift flux model was develop by using two mass conservation equation, a single mixture momentum equation, an algebraic slip relationship, and the new closure relationship for the drift velocity for the case of air and high-viscosity-oil in horizontal and near horizontal pipe. The Finite Volume Method (FVM) with staggered grid system was employed. The flux-splitting scheme was used for discretizing the flux term. The explicit Euler method with the consideration of Courant number. The model was solved using a hybrid shock capturing scheme often used for gas dynamics. Totally 31 transient cases were simulated and compared with the transient experimental result of air and high-viscosity oil data. It is the first time in this study to show that the drift flux model is capable of predicting the transient hydrodynamics of the air and high-viscosity oil cases. This model performed reasonably well with average relative error of 13.55% (Standard Deviation of 11.62%) with respect to experimental results.

Computational Fluid Dynamics Simulations of the Air–Water Two-Phase Vertically Upward Bubbly Flow in Pipes

In this study, computational fluid dynamics (CFD) simulation of air–water two-phase flow in vertical pipe has been carried out. Wide ranges of superficial liquid and gas velocities, 0.376–3.53 and 0.0036–1.275 m/s, and dispersed phase holdup range from 0.3 to 38.74% is used in the simulation. In this study, for drag, lift, wall lubrication, and turbulent dispersion force the models of Grace, Tomiyama, Hosokawa, and Burns are used, respectively. The Eulerian–Eulerian multiphase approach with the k–ω shear stress transport (SST) turbulence model was used. Bubble diameter is an essential parameter to perform the Eulerian simulation. In the present study, we developed new correlation for bubble diameter and with this predicted bubble diameter simulations were performed. The developed CFD model is well capable of predicting gas void fraction, interfacial area concentration, pressure drop, gas/liquid velocity, and turbulent kinetic energy.

Experimental study of the characteristics of an upward two-phase slug flow in a vertical pipe

Characteristics of the slug flow, mean void fraction, liquid slug and Taylor bubble lengths; and structure frequency were all extracted from the void fraction time series. Average void fractions at nine axial positions have been measured on a 6 m long (and 34 mm diameter) pipe test section by using conductance probes.For the flow conditions used, bubbly (with spherical cap bubble), slug/plug and churn/semi-annular flow patterns were observed. These observations were also confirmed by using statistical numbers.Time series analysis of the mean void fraction and its corresponding PDFs show that the effect of the mixer on the flow becomes, practically, negligible from a distance of 95 pipe diameter.It was found that, generally, the structure velocity can be well predicted from other available correlations in the literature.The theoretical model of Brauner and Ullmann was used to estimate the liquid in slug void fraction. It was inferred that this model is able to predict well the liquid slug void fraction; thus, it can be considered as one of the useful methods for predicting such parameter and to ascertain slug flow regime.The total pressure gradient was found to decrease with increasing gas superficial velocity.

Correlation of heat transfer coefficient for two-component two-phase slug flow in a vertical pipe

The prediction of heat transfer coefficient for gas–liquid two-phase flows in vertical pipes is important for designing many industrial and engineering apparatuses such as nuclear power plants, solar collectors and petroleum pipelines. The mechanism of two-component two-phase heat transfer is more complicated than that of single-phase heat transfer. This study aims at developing a robust correlation of heat transfer coefficient for two-component two-phase slug flows in vertical pipes. The theoretical framework for the correlation development is inspired by considering classic Reynolds and Chilton–Colburn analogies. The framework demonstrates that the functional dependence of the two-component two-phase heat transfer coefficient on a void fraction or a two-phase multiplier is expressed by the Reynolds and Chilton–Colburn analogies. The correlation for the heat transfer coefficient of two-component two-phase slug flows in vertical pipes has been developed and validated by more than 200 existing data. The newly developed correlation predicts 95.1% of the collected two-phase heat transfer data within ± 30% error and the mean absolute relative deviation of the correlation is estimated to be 14.2%. The extended applicability of the newly developed correlation to other flow regimes such as bubbly, churn and annular flow regimes has been verified by the existing experimental data. The possible application of the newly developed correlation to large pipes is also discussed. In summary, it is expected that the newly developed correlation can predict the heat transfer coefficient of two-component two-phase flows under various conditions such as vertical upward and downward flows, developing and fully developed flows, laminar and turbulent flows and all two-phase flow regimes. The application of the correlation to vertical large pipes is also considered to be reasonable.

Assessment of the CUPID Code for Bubbly Flows in Horizontal Pipes

Two-phase flow in a horizontal pipe has a pronounced feature; that is, two-phase-flow parameters are highly nonsymmetric because gravity is perpendicular to the mean flow direction. Thus, three-dimensional analysis is necessary for the accurate prediction of two-phase flow in a horizontal pipe, such as the hot leg and cold leg of a pressurized water reactor and the pressure tubes in a CANDU reactor. In this study, we simulated bubbly flows in horizontal pipes using the CUPID code, which adopts a two-fluid, three-field model for two-phase flow. In the preliminary calculations, it was found that the particle-averaged two-fluid momentum equation, rather than the standard two-fluid momentum equation, predicts a physically reasonable slip ratio and nondrag forces, except turbulent dispersion forces have negligible effects on the radial void distribution when the particle-averaged two-fluid momentum equation is used. Based on the results, we selected the physical models and computational mesh for subsequent code assessment using various bubbly flow experiments in horizontal pipes. The turbulent dispersion force model was improved to take into account the large void fraction change at the top. The results of the code assessment show good predictions for the axial pressure drop, liquid velocity, and turbulent kinetic energy profile and predict reasonably well the effects of jl and jg on two-phase-flow parameters. However, additional studies are needed for more accurate prediction of the nonsymmetric distribution of gas velocity and turbulent kinetic energy.