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ГИДРАВЛИКА. ГЕОТЕХНИКА. ГИДРОТЕХНИЧЕСКОЕ СТРОИТЕЛЬСТВО
RESEARCH PAPER / НАУЧНАЯ СТАТЬЯ UDC 532.542:004.9
DOI: 10.22227/1997-0935.2023.6.901-916
Numerical modelling of multiphase flow hydrodynamics by CFD analysis methods in a double-elbow pipeline
Alireza Taherifard, Victor V. Elistratov
Peter the Great St. Petersburg Polytechnic University (SPbPU); Saint Petersburg, Russian Federation
ABSTRACT
Introduction. Prediction of multiphase flow patterns in pipelines of gas and oil industry is a complicated hydrodynamic process. Hydraulics of gas-liquid flows and erosion processes in pipelines with many bends in which gas, water, oil and air move are insufficiently studied. There are known studies of movement in single-phase flow conditions with one elbow, which is insufficient for design of modern pipeline systems. Therefore, there is a need for in-depth analysis of interaction of media in multiphase flow and transported sand particles. In this paper the effects of elbows on multiphase flow hydraulics and erosion of pipe sections are investigated using computational fluid dynamics (CFD) modelling tools for 100 seconds' of process. Materials and methods. A liquid volume model (VOF) was used to simulate three-phase flow: air-water with solids in a pipe with two elbows. Turbulence effects have been accounted for with the RNG k-z model. The model verification methods from previous studies have been used. For the numerical solution, the Ansys Fluent version 20.1 software package has been used. The results of CFD modelling of the volumetric gas content have shown a good agreement with the available experimental data.
Results. The results showed that the change in the flow regime remains unchanged before the first elbow and after the se- <S" ¡5" cond elbow in the cork flow. However, for the initial churn flow regime, the flow regime varies at different segments of the flow n T area before and after each elbow. k U
Conclusions. The preliminary churn flow in the upper vertical section was transformed to wavy stratified flow in the hori- ^ zontal section between the two elbows and wavy annular flow in the vertical pipe after the second elbow. The flow pattern in ^S slug flow maintained same after the first elbow, but the Taylor bubbles are lengthier in the horizontal section between the first W C and second elbows. ^ y
KEYWORDS: multiphase flow, churn flow, void fraction, slug flow, two elbows pipe, Ansys, CFD, probability density function °
l z
FOR CITATION: Taherifard A., Elistratov V.V. Numerical modelling of multiphase flow hydrodynamics by CFD analysis 9
methods in a double-elbow pipeline. Vestnik MGSU [Monthly Journal on Construction and Architecture]. 2023; 18(6):901- o 7
916. DOI: 10.22227/1997-0935.2023.6.901-916 (rus.). n 0
S> 8
Corresponding author: Alireza Taherifard, taherifard.a@edu.spbstu.ru. o (
Численное моделирование гидродинамики многофазного потока методами CFD-анализа в трубопроводе с двойным коленом
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Алиреза Тахерифард, Виктор Васильевич Елистратов 6
Санкт-Петербургский политехнический университет Петра Великого (СПбПУ);
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Введение. Прогнозирование характера движения многофазных потоков в трубопроводах газовой и нефтяной про- О Н мышленности является сложным гидродинамическим процессом. Гидравлика газожидкостных потоков и эрозион- с | ные процессы в трубопроводах со многими коленами, в которых движутся газ, вода, нефть, воздух, недостаточно 3 1 изучены. Известны исследования движения в условиях однофазного потока с одним коленом, что недостаточно при 1 ® проектировании современных трубопроводных систем. Поэтому существует необходимость в углубленном анализе со П взаимодействия сред в многофазном потоке с транспортируемыми частицами песка. Исследовано влияние колен — Е на гидравлику многофазного потока и эрозию участков трубы с использованием инструментов моделирования вы- — у числительной гидродинамики (CFD) в течение 100 с процесса. ф к
Материалы и методы. Применили модель объема жидкости (VOF) для моделирования трехфазного потока: воздух- о» о
2 2
вода с твердыми частицами в трубе с двумя коленами. Эффекты турбулентности учтены с помощью модели RNG k-£. Использованы методы верификации модели по ранее выполненным исследованиям. Для численного решения О О применили программный комплекс Ansys Fluent версии 20.1. Полученные результаты CFD-моделирования объемно- 3 3 го содержания газа показали хорошее соответствие с имеющимися экспериментальными данными.
© А. Тахерифард, В. В. Елистратов, 2023 901
Распространяется на основании Creative Commons Attribution Non-Commercial (CC BY-NC)
Результаты. Изменение режима потока остается неизменным до первого колена и после второго колена в пробковом потоке. Однако при начальном режиме вспенивания потока режим потока изменяется на разных сегментах области потока до и после каждого колена.
Выводы. Предварительный вспенивающий поток в верхней вертикальной части трубы был трансформирован в волнообразный стратифицированный поток в горизонтальной части между двумя коленами и волнообразный кольцевой поток в вертикальной трубе после второго колена. Форма потока в пробковом течении остается неизменной после первого колена, но пузырьки Тейлора стали длиннее на горизонтальном участке между первым и вторым коленами.
КЛЮЧЕВЫЕ СЛОВА: многофазный поток, поток вспенивания, фракция пустоты, пробковое течение, труба с двумя коленами, Ansys, CFD, функция плотности вероятности
ДЛЯ ЦИТИРОВАНИЯ: Тахерифард А, Елистратов В.В. Numerical modelling of multiphase flow hydrodynamics by CFD analysis methods in a double-elbow pipeline // Вестник МГСУ. 2023. Т. 18. Вып. 6. С. 901-916. DOI: 10.22227/19970935.2023.6.901-916
Автор, ответственный за переписку: Алиреза Тахерифард, taherifard.a@edu.spbstu.ru.
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INTRODUCTION
Multiphase flows with the presence of sand particles are commonly encountered in many industries, including the oil and gas production process. This process involves extracting fluids from underground reservoirs, which can contain a mixture of oil, gas, water, and sand. The fluids are then transported through a series of pipes and processing facilities to separate the different phases and extract the valuable components. The multiphase flow in the oil and gas production process can occur across the entire production line, from the reservoir to the surface processing facilities. This includes the well completion, which involves connecting the reservoir to the surface through tubulars, as well as any surface facilities on land, seashore, or offshore structures. Pipelines are also used to transport the extracted fluids to additional processing facilities.
The composition of the multiphase flow in the oil and gas production process can vary depending on the stage of production. For example, it may include a saturation stage, a gas/air phase, and a water phase. Different modes of three-phase flow can occur due to the interactions between the different phases. Some common industrial flow regimes include slug flow, churn flow, and annular flow. To better understand and optimize the multiphase flow in the oil and gas production process, a range of simulations and numerical methods can be used. This includes computational fluid dynamics (CFD) modelling, which allows researchers to simulate and analyze the complex behavior of multiphase flows in different conditions. By gaining a better understanding of the behavior of multiphase flows, researchers can improve the efficiency and safety of the oil and gas production process, as well as other industries that use similar flow systems [1, 2]. Researchers have tirelessly focused their attention on geometrical structures with a single bend or fixed vertical or horizontal pipes. However, sophisticated pipelines such as those with multiple bends and U-bends require more attention to study due to limited space availability and design economics. Nevertheless, a comprehensive understanding of the behavior of two-phase flow in bends is crucial for various industrial applications. Zhao
has demonstrated two particular comparisons of two fluids at several bends to highlight the complexity. He has developed a method for calculating oil-gas processing systems, where two-phase flows encounter several turns due to the installation of bends in the pipeline [3]. Zao concluded that there is a significant difference in the behavior of two-phase flow patterns in horizontal and vertical pipes. This finding suggests that annular flow is presented in both horizontal and vertical pipes, whereas vertical pipes also exhibit diffused bubble, slug, stratified, and churn flows [4].
Flow regimes can rapidly change at bends when the flow direction shifts from a vertical to horizontal or horizontal to vertical perspective. Kerpel [5] investigated the behavior of a sharp return stepped elbow both upstream and downstream using capacitance sensors. The elbow had an interior diameter of 0.008 m and a radius of curvature of 1 mm. He used the refrigerant R134a, with mass flux and void fraction ranging from 210-410 kg/m2s and zero to one, respectively. Depending on the experimental conditions, Kerpel equipped the elbow upstream and downstream with seven capacitance sensors to collect a series of void fraction results over time to assess how the elbow influenced the experiment's results. He found that, for a short period before the first elbow, the flow exhibited slug, wavy and annular flow regimes.
Abdulkadir [6] investigated the conductance of two-phase air-water flow in churn and annular flow regimes in a large diameter vertical 180-degree return elbow with a diameter of 0.135 m and a curvature ratio of three. The air velocity ranged from 3.8 to 15.8 m/s, while the water velocity ranged from 0.03 to 0.3 m/s. The mean film of probability density function (PDF) profiles were used to determine that the flow patterns were located within the slug-to-churn transition zone. Although churn flow was observed upstream of the elbow, the liquid was found to be draining towards the elbow's base due to gravity forces, and the gas was situated in the pipe's center, resulting in an annular flow pattern downstream. These findings suggest that the flow regimes in the elbow were influenced by gravity forces and could change based on the flow rates of the two phases. It is necessary to carry out further
studies to fully understand the behavior of two-phase flow in large diameter vertical return elbows.
The researchers conducted experiments to analyze the flow patterns before and after elbows in a 75.3 mm pipe. They discovered that the churn/annular flow patterns were nearly identical before and after the pipe elbows were installed. The void fraction distributions were measured before and after the elbow using a wire mesh sensor that was directed vertically upward and horizontally at gas velocities of 12 m/s and liquid velocities of 0.015 m/s. During the investigation, they observed a flow transition from annular churn flow at one point in the pipe's length to wavy stratified flow at the opposite point. These findings suggest that the flow patterns in the pipe are affected by several factors such as the pipe geometry, flow rates, and the positions of the wire mesh sensors. Further investigations are necessary to fully understand the behavior of the two-phase flow and its characteristics in pipes with elbows [1].
Vieira conducted a comprehensive investigation to study the impact of a 90-degree standard elbow on the flow characteristics of horizontal gas-liquid stratified and annular flows in a stratified-wavy horizontal pipeline. To accomplish this, the author employed dual wire-mesh sensors to measure void fraction distributions. The horizontal test section was constructed with a 17-meter-long pipe having an inner and outer diameter of 0.0851 m, which produced stratified-wavy and annular flows. Two sensors with a 16 x 16 wire-mesh design was placed 0.81 and 0.59 m upstream and downstream of the elbow, respectively. The tests were performed at various superficial liquid velocities ranging from 0.03 to 0.3 m/s and superficial gas velocities ranging from 10 to 33 m/s using wire-mesh sensors.
The author analyzed the cross-sectional averaged void fraction time series for stratified and annular flows in the upstream and downstream regions and found that they had a significant resemblance, indicating that they were produced by the same mechanism. The transition from stratified to slug flow was also investigated, and it was observed that wave instability was the most prominent characteristic. After passing through the 90-degree horizontal elbow, there was a slight increase in cross-sectional time-averaged void fraction values, and more liquid was present in the pipe's perimeter, with smaller waves than upstream conditions. The findings suggest that the presence of a standard elbow in a horizontal pipeline does not significantly affect the churn and annular flow patterns [7].
Suleimanov [8] and his colleagues proposed a comprehensive approach that involves analyzing the characteristics of the transported fluid and the pipeline. They discuss the different methods that can be used to determine the fluid composition, including laboratory testing and mathematical modelling. They also discuss the importance of accurately predicting the pipeline route profile, which can help to identify potential prob-
lem areas. Gromov [9] and colleagues presented a new measurement and computing system for diagnosing thermodynamic processes of multiphase flows in pipelines. The authors discussed the challenges associated with diagnosing the thermodynamic processes of multiphase flows in pipelines, including the lack of accurate measurement and computing systems. They introduced their new system, which combines advanced measurement techniques with modern computing technology to provide accurate and reliable data on the thermodynamic processes of multiphase flows.
Serov [10] conducted a numerical study to investigate the effect of the inclination angle of the pipeline on the pressure drop and flow regime in a multiphase flow system. His research highlights the importance of accurate modelling and simulation of multiphase flow systems to optimize pipeline design and operation. The authors concluded by recommending further research on the effect of pipeline position on multiphase flow regimes and the development of more accurate modelling techniques to improve the efficiency and safety of pipeline operations.
Buznikov [11] discussed the impact of the choice of a hydrate inhibitor on ensuring uninterrupted flow in long offshore multiphase fluid pipelines. The authors examined the performance of two commonly used hydrate inhibitors and their impact on pipeline flow stability. They provided an overview of the challenges associated with maintaining uninterrupted flow in long offshore multiphase fluid pipelines, including the formation of hydrates and their impact on pipeline integrity. The authors then described the experimental study they conducted to investigate the effectiveness of two hydrate inhibitors in preventing hydrate formation and ensuring uninterrupted flow in the pipeline.
Kopteva [12] presented a method for developing an intelligent information-measuring system for controlling complex parameters of multiphase flows in conditions of uncertainty. The focus was on creating an adaptive information-measuring system for the transport parameters of oil and the detection of organic deposits on the inner surface of pipelines to improve the efficiency of the state information system of the fuel and energy complex.
Taherifard utilized Computational Fluid Dynamics (CFD) to investigate the characteristics of both water and gas within the pipeline, and to make predictions about potential erosion. Specifically, he focused on a pipeline with a diameter of 76.2 mm, and conducted simulations of churn, slug, and annular flow in order to identify where erosion may occur and estimate its size. By analyzing the behavior of fluids under these different flow conditions, Taherifard was able to gain insight into how erosion is likely to develop in the pipeline over time. The results of his investigation may have significant implications for pipeline safety and maintenance [13, 14].
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Zhao [3] and colleagues conducted an experimental investigation in the laboratory to study the transition between two-phase flow regimes in a double-bend pipeline. They investigated gas-liquid flows at two 90-degree bends in sequence with a constant separation distance and measured the phase distribution using capacitance measurements inside and outside the elbows. The results showed that the two-phase flows underwent transformative flow due to secondary flows and gravity forces at the bend. Slug and churn flows were observed upstream of the elbow, whereas stratified churn, wavy, and slug flows were recorded downstream of the bend at different gas and liquid surface velocities. The bend transformed upstream bubbly flow into stratified flow downstream of the elbow at certain liquid and gas superficial velocities whereas upstream slug flow transformed into churn flow downstream of the elbow at other liquid and gas superficial velocities. The liquid phase drained to the pipe's bottom during the passage of the two-phase flow around the bend and into the horizontal sections, due to gravity, and converted to stratified flow. They found that a minimum distance of 10 to 50 D from the 90-degree bend was required for the formation of the flow after the bend, depending on the flow rates. The study highlighted a knowledge gap in the previous literature regarding two-phase current switching on curves with different separation lengths. These pipe designs are widely used in offshore oil and gas drilling rigs, refineries, and food processing facilities to create novel curved connections.
According to the aforementioned literature study, there is a knowledge gap in the understanding of two-phase flow transition in pipeline with two elbows. Such pipe structure is predominantly reported on offshore oil and natural gas processing facilities. This work seeks to provide a knowledge of two-phase flow (gas/water) pattern, and its behavior in the pipe with two elbows including slug and churn flow. The instability of two-phase gas-liquid flow is still one of the most important issues in the study of multiphase flows, whether it is done experimentally or numerically. CFD analysis for the flow and moving phase interaction can provide important information about the interaction of the two-phase gas-liquid flow and moving phase. It is a commonly used as an approach for multiphase flow modelling that includes accurate interfaces, such as layered flow patterns or slugs, and is known as volume of fluid method (VOF) [4, 15-19]. The Euler model was employed in this work, together with the multifluid VOF model. The multifluid-VOF model is one of the hybrid approaches that have been produced by combining the Two-Fluid approach with the Volume of Fluid (VOF) method proposed by Cerne [20]. The volume interface model is employed to analyze evolution prior to and following the emergence of multiphase flows with a various separation length of elbows.
MATERIALS AND METHODS Simulations numerical
To simulate the slug and churn flow regimes and capture the interface between gas and liquid phases, this study used the Eulerian two-phase model along with the Multifluid-VOF model, an interface capture method in Ansys Fluent. The simplified modelling assumption of Interfacial Area Concentration (IAC) transport equation was used in this hybrid model to account for different bubble sizes, bubble breakage, and coalescence without delving into the details of bubble size distribution as in the population balance model.
Eulerian-Eulerian two-phase flow modelling
The phase continuity equations are:
dp, a ,
dt
-V(a,pv ) = 0; Éa, = 1,
(1)
(2)
where a, p. and are the volume fraction, density and velocity of the individual phases.
The momentum formulas for the stages are as follows:
d(a p v,)
dt K 'P' ' _ (3)
= -a, Vp + V • I,. + apg + F ,j,
where p and t. are the pres sure and stress-strain tensor of the individual phase, g is acceleration due to gravity and Fyj is the interfacial force between the phases.
The governing equation of the interfacial force Fyj from equation (3) is given as:
F, = K
(4)
where K.. is the interphase momentum exchange coefficient between the phases. The second phase in Eulerian-Eulerian two-phase flows is considered as bubbles, and the interphase exchange coefficient is given by:
(5)
where X is the interfacial area concentration; f is
p ' J
the drag co-efficient and t. is the particle relaxation time given by:
P, d,2
t, = -
18n,
(6)
To compute the drag coefficient f, the Schiller model is employed.
Eulerian-Eulerian two-phase flow modelling is needed to understand fluid behavior in pipes because it can track two different fluid phases simultaneously and predict flow pattern, pressure drop, velocity distribution, and phase holdup. This approach is necessary to optimize system design and operation in various industries.
s
Turbulence simulation
k-e turbulence models with Re-Normalization Group (RNG) equations were used to model the processes in the pipe [21]. The RNG k-e transfer formulas are as follows.
Kinetic Energy, k:
| (Pk )+A (p^ ) =
dx,
a kMf
dk dx
(7)
-Gk - pE.
J y
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d d d — (pE) +-(pEV. ) =-
dr ' dx, dx,
dE dx
J y
(8)
+ C'E k (Gk C2EpEr-
R
where ak and ae are given in which the inverse effective Prandtl numbers for k and e respectively; Gk is the production of turbulent kinetic energy as a result of mean velocity gradients; G1e and C2e are 1.42 and 1.68; is the effective viscosity. The effective viscosity is given by:
^ eff = ^ + ^ t and ^ t =
pc k2
(9)
where G is 0.085.
RNG k-e is more precise and dependable over a broader range of flows. They are also more sensitive to the effects of fast strain and streamline deformation, making them ideal for flow through elbows [22]:
C,pn3 (1 -n/no)e2.
R =
Sk
1 + ßn3
k
n = — ; no = 4.38, ß = 0.012,
(10)
(11)
nique was used to discretize the velocity and turbulence equations, and the velocity and pressure equations were linked through the SIMPLE phase-coupled algorithm. The under-relaxation factor for pressure, momentum, and interfacial area density equations was set to 0.3, while the volume fraction was set at 0.5, and the turbulence kinetic energy and power dissipation rate equations were set at 0.6. The solutions were obtained using a transient method with a time interval of 0.001 s, and convergence was achieved when the particles of all equations were less than 106. Each time step required between ten and twenty iterations to achieve convergence.
Flow
The two elbows pipeline with a standardized gap distance (Length/Diameter) of 15 between two elbows were created in Ansys. There are three-meter vertical pipes and 2-meter horizontal pipes upstream and downstream of a typical 90-degree elbow, respectively, and fluid flows from an upward vertical to a horizontal direction, similar to the 3-D discrete mathematics employed by Parsi [23]. The pipe's diameter and the radius of the elbow's curve are both 0.0762 m and 1.5 of diameters, respectively. The input parameters of boundary conditions are represented in Table 1, regarding the pipe size, and the sand particles data.
Table 1. Input parameters for the calculation
where S is strain rate of fluid flow.
The k-e turbulence model with RNG is necessary to use in computational fluid dynamics (CFD) to accurately model the turbulence in confined flows such as pipes. It takes into account the effects of turbulence on fluid properties such as velocity and pressure. The model uses two transport equations to model kinetic energy and the rate of dissipation of turbulence. The RNG approach is used to improve the accuracy of the model in certain flow situations. Overall, the k-e turbulence model with RNG is widely accepted and effective for predicting the behavior of fluid flows in pipes.
Mathematic approaches to solving problems
The governing equations for mass, velocity, phase volume fraction, and turbulence were numerically solved using Ansys Fluent version 2020R1. The simulations were three-dimensional and transient, with the assumption that the fluid and gas phases were immiscible and did not exchange mass. The upwind tech-
Input parameters Value
Pipe Diameter, mm 76.2
Elbow Radius of curvature 1.5
Sand Diameter, ^m 300
Sand Density, kgm-3 2,650
Sand Flow Rate, kg/s 0.0265
Gas velocity, m/s, in validation study 18.1
Gas velocity in churn flow, m/s 15.3
Gas velocity in slug flow, m/s 0.8
Liquid velocity, m/s 0.3
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To define the boundary conditions for velocity-inlet and pressure-outlet, the researchers established conditions at both the inlet and outlet of the system. The wall was constructed using the conventional log-law method. The inlet was designed to have a 9 percent flow velocity. To facilitate faster flow development, the pipe intake surface was divided into two sections, as shown in Fig. 1, which is similar to the CFD simulation conducted by Parsi [23]. The diagram shows that the gas was introduced into the domain through the center of the inlet, while the liquid was added circumfe-rentially. The velocities from formulas (1) and (2) were used to incorporate both the fluid and gas phases into the domain. Initially, the liquid phase was introduced
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In this equation, Vsg as well as Vd are the subsurface gas and liquid kinematics, A is the perimeter of the pipe, and Ag as well as At are the gas and liquid intake areas, respectively.
0.1
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Fig. 1. Phase injection is accomplished through the intake, and the colors red and blue represent air and water, correspondingly
Creation of mesh
The mesh cells used in this study had an element size of 281,608 grids, according to the research made by Parsi which the mesh size of 236,250 was used for modelling in Ansys for particle tracking in multiphase flow [23]. Parsi used smaller mesh size due to lower computational expense, however, the bigger mesh size, the more accurate the result will be.
o.ooi
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Bubbl {
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0.01
0.1
1
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10
100
It was found that simulations are to implement for both single and double bend pipes under two different flow conditions, with superficial liquid and gas velocity values of 0.3 and 18.1 m/s, respectively. The gas and water phases of the experiment were air and water, cor-relatively. There are two types of fluid properties in vertical pipes for this study: slug and churn. Fig. 2, a shows the map of vertical fluid flow developed by Liu [24]. Fig. 2, b shows the flow conditions in horizontal pipes, which are closer to the elongated bubble/slug boundary and therefore include the slug and annular fluid flow. The points on the figures demonstrate the chosen velocity for case 1, and case 2.
RESULTS OF THE RESEARCH Validation of a single elbow
Previously, Parsi conducted a study on void fraction at a location 1m before the elbow and published
Case 1 15.3 m/s) Case 2 0.8 m/s)
Fig. 2. The formation of the flow's structure multiphase flow: a — vertical pipes; b — horizontal pipes
a paper. The aim of the study was to compare experimental and modelling data to identify any discrepancies and validate the experiments. The surface gas velocity was 18.1 m/s, and the liquid surface velocity was 0.3 m/s. In Fig. 3, the average steam quality in a cycle section with an internal gas velocity Vsg of 18.1 m/s and a liquid velocity Vd of 0.3 m/s was compared. Parsi presented experimental and numerical time series data on void fraction content [25], characterized by a high value of 0.9 representing the gas component with few drops and a low value of 0.2 representing the periodic transition of the liquid. The minimum void fraction decreases in the experimental and numerical data presented by Parsi was 0.69 and 0.73, respectively, while this study has a minimum volume fraction of 0.75. The maximum void fraction in the Parsi's experimental and CFD data was 0.97, while it was 0.98 in this study.
As can be seen in Fig. 3, when V is 18.1 and
O > sg
V d is 0.3, the results of the current investigation and the experimental work of Parsi are in agreement. Thus, the next step is to investigate pipe with two elbows.
Fig. 3. Time series of averaged cross-sectional void fraction from Parsi's experiment and the current study
of V = 18.1 m/s and V, = 0.3 m/s
sg sl
Geometries with two elbows and multiphase flows Flow visualization
This study investigated the velocity distribution of a multiphase slug/churn flow with a constant liquid velocity, considering two different gas velocities ranging from 0.8 to 15.3 m/s. The liquid velocity was fixed at 0.3 m/s. The study included four observation levels, and their positions are illustrated in Fig. 4.
Case 1 and Case 2 contour are plots after 100 seconds of simulation time (Vsgg = 15.3 m/s; Vd = 0.3 m/s) which are shown in Fig. 5, a, b, respectively. Conurbation flows are used to differentiate flow rates upstream of Elbow 1 when the standardized separation distance is zero, as indicated by the contour plots. When running a churn flow, there are no clearly defined boundaries be-
Fig. 4. Domains in the field of computation
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tween the liquid and gas phases. This is despite the existence of oscillations and periodic gas cores [26, 27]. Some authors believe that this sort of flow is essentially annular in character, with massive perturbation waves transported by the gas flow; similarly to the findings of this study, massive waves in churn stream have also been reported by Parsi and Riva Col [16, 28].
The aim of this analysis was to investigate the multiphase flow behavior in the horizontal section follo-wing bend 1, with the standardized separation distance set at 15. The contour plots presented in Fig. 6 depict the mean void percentage over a homogeneous surface of the flow at a gas velocity of 15.3 m/s and a liquid velocity of 0.3 m/s. In the first bend, the gas and liquid phases split, forming a wavy stratified flow in the churn regime. As the relatively stable displace-
ment vector increases, a subtle but noticeable difference in the flow advancement in the cross pipe (between the elbows) is observed due to the effect of secondary flow and gravitational forces inside the elbow. When the length to diameter ratio (L/D) is equal to 15, the liquid phase flows behave more like a thin layer pushed towards the outer perimeter of the second elbow. Table 2 shows the constant flow development across the four flow sectors, which is influenced by various factors in the flow sectors spanning L/D equivalent to 15. The analysis reveals that the flow behaves more like annular flow in the transverse surface prior to the first elbow, as evidenced by the presence of gas. Whereas, the phases detach into a stratified flow at the outlet of the upstream elbow (elbow 1) as the flow traverses into the horizontal section after passing through elbow 1.
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Table 2. Contour graphs the monitoring cross-sections, of void fractions for the multiphase flow with gas velocity of 15.3 m/s
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Table 3. Contour graphs the monitoring cross-sections, of void fractions for the multiphase flow with gas velocity of 0.8 m/s
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The analysis was conducted on a ten-second flow in the axis of symmetry, where the internal gas velocity was 0.8 m/s and the boundary fluid velocity was 0.3 m/s. The average void fraction content of the flow is presented in Table 3. The contour plot shows that the flow is divided horizontally, and the liquids in various portions of the pipe fill over 50 % of the fluid flow and part of the surface area including location 1, resulting in a sinusoidal shape of the gas phase. These parameters depict the slug's passage across the horizontal pipe, where the liquid slug at the pipe's bottom connects the gas phases in different locations including location 2 and 3, leading to the formation of air pockets referred to as Taylor bubbles. On location 4, we observe the huge bubble which demonstrates the churn flow.
The gas velocity for two different flow types, churn and slug flow, was measured and compared using monitoring points during a 100-second simulation, as shown in Fig. 6. The results of the analysis revealed that for churn flow, the gas velocity decreases as it moves towards the horizontal side of the pipeline, specifically at locations 2 and 3, while increasing in the vertical section. Conversely, the gas velocity for slug flow at locations 2 and 3, which represent the horizontal side of the pipe, is higher than in the vertical sections. Notably, for churn flow, the gas velocity at location 1 on the vertical pipe is higher than at location 4, whereas for slug flow, the velocity of gas at location 4 is higher than at location 1.
In summary, the findings suggest that the behavior of the gas flow varies depending on the flow type and the location within the pipeline. Churn flow exhibits a decrease in velocity as it moves towards the horizontal side, while slug flow displays higher gas velocity in these sections. Furthermore, the velocity of gas in churn flow is higher in the vertical pipe at location 1 compared to location 4, whereas for slug flow, the opposite is true. These insights can provide valuable information for designing and optimizing pipeline systems for improved performance.
Evaluation of different flow characteristics caused by double bend using quantitative methods
The development of two-phase flow induced by double bends was studied utilizing the area-average
void fraction throughout the length of the pipe, as well as the cumulative distribution function and probability density function. Statistical analysis of the behavior in void fraction is a method for elucidating flow patterns in a double bend pipe design. According to Costigan and Rezkallah [26], each two-phase flow pattern has a unique probability density function (PDF) of void percent. The PDF curve of churn flow has a solitary peak at high porous proportions and a wide tail at low void fractions. A single peak at high void percentage indicates that the flow is approaching annular flow, while the broad tail indicates the presence of unstable slugs. According to Lowe and Rezkallah, a typical churn flow PDF curve has an average void fraction ranging from 0.7 to 0.9. Conversely, slug flow displays two peaks in the PDF curve of the mean void fraction data set, with one peak at low aspect fraction and another at high void fraction. These peaks correspond to the passage of two distinct characteristics of slug flow; the Taylor bubble at high porosity and the fluid slug at low porosity. In this research, MATLAB's Ksdensity function was utilized to produce the Probability Density Function (PDF) features for average void fraction time series. Multiple researchers, such as Liu and Hanafizadeh, have used this method [29], Ye and Guo [30], Franca [31], and Bouyahiaoui [32] have also employed PDF to denote distinct flow regimes.
The study was conducted by positioning the reference point at four different locations, namely 1.1 m before the first elbow, 0.2 m after the first elbow, 0.7 m after the first elbow, and 0.2 m after the second elbow. The contour plots in Fig. 7 show that the periodic fluctuations observed in the flow instability and uncertainty can be attributed to the complex interconnections between the liquid and gas phases in these flow circumstances.
The results indicate that there is a drop in the monitored surface as the liquid structure passes through it, with more droplets being produced as more liquid flows through the control surface. On the other hand, the liquid phase expands in response to the rising apparent gas velocity, resulting in a massive disturbance wave. The amplitude of the time series grows in proportion to the flow inflation level.
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Вестник МГСУ • ISSN 1997-0935 (Print) ISSN 2304-6600 (Online) • Том 18. Выпуск 6, 2023 Vestnik MGSU • Monthly Journal on Construction and Architecture • Volume 18. Issue 6, 2023
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The graph in Fig. 8 clearly displays the time-dependent behavior of the average steam performance in low surface gas velocity conditions. The periodic variations in the performance can be attributed to the discontinuous flows of gas and liquid phases across the monitoring plane, as shown in the cross-sectional image. The high values of the performance metric indicate
that a large amount of air or gas has passed through, which occurs when the Taylor bubbles, mentioned earlier, pass through the monitoring surface. On the other hand, the low values of the performance metric indicate the passage of fluid slugs with low porosity.
It should be noted that these variations in steam performance are influenced by various factors such as
Fig. 8. Averaged void fraction time series across cross-sections (Vd = 0.3 m/s and Vg = 0.8 m/s)
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the velocity of the gas and liquid phases, the cross-sectional area of the pipe, and the presence of any obstructions or bends in the pipe. These factors can cause significant changes in the flow pattern, resulting in complex behavior and periodic fluctuations in the performance metric.
Understanding the behavior of these multiphase flows is critical for the design and optimization of various industrial processes, such as chemical reactors and oil pipelines. Therefore, further studies are needed to explore the intricate dynamics of multiphase flows and develop accurate models that can predict their behavior under different operating conditions.
When the peaks in the inclination angles are high, it is an indication of turbulent flow, and there is no clear distinction between phases. However, when the peaks are low and sustained for a short period of time, it is indicative of bubble deformation flow. The PDF curve, in this case, shows a large peak at porous structure and a wide body at low porosity, which is a characteristic feature of bubble deformation flow.
On the other hand, when the flow is on the verge of becoming annular, it is reflected in the PDF curve as having a single summit with a large proportion of empty space. In contrast, when unstable slugs pass through the flow, the PDF curve shows a broad tail.
In the case of slug flow, the probability density function (PDF) of the transitional air portion of the time series exhibits multiple peaks. One peak is at small pores, while the other is at highly porous, indicating the presence of slug-like flow. These peaks represent the periodic passing of the two features of slug flow, namely, Taylor bubbles for high porosity and liquid slugs for low porosity. Furthermore, the flow data in the investigated slug flow patterns are spread across two PDF peaks because the flow transitions from primary slug flow to Taylor bubble flow as it ex-
pands. As a result, the proportion of voids in the slug to voids in the Taylor bubble increases. Fig. 9 illustrates the PDF curve for the slug flow patterns studied in this research.
In summary, the PDF curves provide valuable insights into the nature of multiphase flow patterns, such as slug flow and bubble deformation flow. By examining the peaks and widths of the curves, it is possible to discern the characteristics of the flow and the transitions between different flow regimes.
CONCLUSION
The simulation results have revealed significant insights into the behavior of different flow patterns in the pipeline system. Specifically, the initial churn flow observed in the upper vertical portion of the pipeline was found to transform into a wavy stratified flow in the horizontal section between the two elbows. This transition can be attributed to the changes in the flow dynamics resulting from the geometry of the pipe and the interaction between gas and liquid phases. Subsequently, the flow pattern was observed to transition into a wavy annular flow in the vertical pipe after the second elbow.
In contrast, the slug flow pattern remained unchanged after the first elbow. However, it was observed that the Taylor bubbles were longer in the horizontal portion between the first and second elbows. Additionally, the initial slug flow in the upper vertical portion continued as slug flow throughout the horizontal and downward vertical sections following the bend. These findings have significant implications for the design of various industrial applications such as boiling/condensing heat exchangers, new integrated bend/T-junction separators, and oil and gas pipelines in offshore processing platforms. A better understanding of the flow behavior can help improve the efficiency and reliability of these systems, reduce operational costs, and minimize the risk of accidents.
REFERENCES
1. Asgharpour A., Zahedi P., Vieira R., Parsi M., Shirazi S.A., McLaury B.S. Investigation of churn/annular and pseudo-slug flow characteristics before and after pipe elbows. 11th North American Conference on Multiphase Production Technology. 2018.
2. Doroshenko Y., Doroshenko J., Zapukhliak V., Poberezhny L., Maruschak P. Modeling computational fluid dynamics of multiphase flows in elbow and T-junction of the main gas pipeline. Transport. 2019; 34(1):19-29. DOI: 10.3846/transport.2019.7441
3. Zhao D., Omar R., Abdulkadir M., Abdulka-reem L.A., Azzi A., Saidj F. et al. The control and maintenance of desired flow patterns in bends of different orientations. Flow Measurement and Instrumentation. 2017; 53:230-242. DOI: 10.1016/j.flowmea-sinst.2016.09.003
4. Parsi M. Sand particle erosion in vertical slug/ churn flow. The University of Tulsa, 2015; 175.
5. De Kerpel K., De Keulenaer T., De Scham-pheleire S., De Paepe M. Capacitance sensor measurements of upward and downward two-phase flow in vertical return bends. International Journal of Multiphase Flow. 2014; 64:1-10. DOI: 10.1016/j.ijmultiphase-flow.2014.04.003
6. Abdulkadir M., Zhao D., Azzi A., Lowndes I.S., Azzopardi B.J. Two-phase air-water flow through a large diameter vertical 180o return bend. Chemical Engineering Science. 2012; 79:138-152. DOI: 10.1016/j. ces.2012.05.029
7. Vieira R.E., Kesana N.R., McLaury B.S., Shirazi S.A., Torres C.F., Schleicher E. et al. Experimental investigation of the effect of 90 standard elbow on horizontal gas-liquid stratified and annular flow characteristics using dual wire-mesh sensors. Experimental Thermal and Fluid Science. 2014; 59:72-87. DOI: 10.1016/j. expthermflusci.2014.08.001
8. Suleymanov V.A., Buznikov N.A. Multiphase flow assurance in an extentional subsea pipeline: effects of the transported fluid composition and the pipeline route profile. SOCAR Proceedings. Transportation, Storage of Oil and Gas. 2021; 3:92-99. DOI: 10.5510/ OGP20210300534 (rus.).
9. Gromov V.A., Semenov T.V., Yashnik I.L., Petrov A.M. New generation measuring and computing complex for diagnosing thermodynamic processes of multiphase flows in pipelines. Scientific Bulletin of the Arctic. 2022; 13:101-105. DOI: 10.52978/25421220_2022_13_101-105 (rus.).
10. Serov N.V., Kurushina V.A. Modelling the effect of pipeline inclination on the multiphase flow regime. Architecture, Construction, Transport. 2022; 1(99):88-95. DOI: 10.31660/2782-232X-2022-1-88-95 (rus.).
11. Buznikov N.A., Suleymanov V.A., Trofi-mov I.A. Influence of hydrate inhibitor choice on flow
assurance in long subsea multiphase pipelines. Pipeline Transport: Theory and Practice. 2018; 1(65): 34-38. (rus.).
12. Kopteva A.V., Koptev V.Yu., Poddubnyi D.A. Information support for the process of multiphaseflows transportation based on the introduction of a radioisotope non-separation hydrocarbon measuring system. Dynamics of Systems, Mechanisms and Machines (Dynamics). 2019; 7(2):220-226. DOI: 10.25206/2310-97937-2-220-226 (rus.).
13. Taherifard A., Elistratov V.V. Numerical modeling of erosion in a pipe with a multiphase flow of oil and gas. Izvestiya VNIIG named after B.E. Vedeneeva. 2023; 307:16-28. (rus.).
14. Taherifard A., Elistratov V.V. 3D Modelling of double elbow pipeline erosion in methane - water -sand multiphase medium. Vestnik MGSU [Monthly Journal on Construction and Architecture]. 2023; 18(5):717-725. DOI: 10.22227/1997-0935.2023.5. 717-725 (rus.).
15. Karami H., Torres C.F., Parsi M., Pereyra E., Sarica C. CFD simulations of low liquid loading mul- < n tiphase flow in horizontal pipelines. Fluids Engine- $ o ering Division Summer Meeting. 2014; V002T06A011. El DOI: 10.1115/fedsm2014-21856 g £
16. Bortolin S., Da Riva E., Del Col D. Conden- G r
(A C
sation in a square minichannel: application of the VOF c y
method. Heat Transfer Engineering. 2014; 35(2):193- D I
203. DOI: 10.1080/01457632.2013.812493 § %
17. Hernandez-Perez V., Abdulkadir M., Az- y ^ zopardi B.J. Grid generation issues in the CFD mo- O 9 delling of two-phase flow in a pipe. The Journal of § o
a CD
Computational Multiphase Flows. 2011; 3(1):13-26. ° 5 DOI: 10.1260/1757-482x.3.1.13 C i
18. Ratkovich N.R., Majumder S.K., Bentzen T.R. § t
t I
Empirical correlations and CFD simulations of vertical a % two-phase gas-liquid (Newtonian and non-Newtonian) O DC slug flow compared against experimental data of void z 0 fraction. Chemical Engineering Research and Design. D — 2013; 91(6):988-998. DOI: 10.1016/j.cherd.2012.11.002 C 0
19. Saad S.B., Gentric C., Fourmigue J.-F., Cle- t (
CD O
ment P., Leclerc J.-P. CFD and experimental investiga- a i tion of the gas-liquid flow in the distributor of
a com- cd e
pact heat exchanger. Chemical Engineering Research ^ •
and Design. 2014; 92(11):2361-2370. DOI: 10.1016/j. | o
cherd.2014.02.002 3 1
20. Cerne G., Petelin S., Tiselj I. Coupling of ®C the interface tracking and the two-fluid models for I f the simulation of incompressible two-phase flow. Jour- $ y nal of Computational Physics. 2001; 171(2):776-804. 3 £ DOI: 10.1006/jcph.2001.6810 cc
21. Yakhot V., Orszag S.A., Thangam S., Gat- Q Q ski T.B., Speziale C. Development of turbulence mod- 3 3 els for shear flows by a double expansion technique.
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Physics of Fluids A: Fluid Dynamics. 1992; 4(7):1510-1520. DOI: 10.1063/1.858424
22. Ferziger J.H. Large eddy simulation. Simulation and Modeling of Turbulent Flows. 1996. DOI: 10.1093/oso/9780195106435.003.0007
23. Parsi M., Agrawal M., Srinivasan V., Vieira R.E., Torres C.F., McLaury B.S. et al. CFD simulation of sand particle erosion in gas-dominant multiphase flow. Journal of Natural Gas Science and Engineering. 2015; 27:706-718. DOI: 10.1016/j.jngse.2015.09.003
24. Liu Y., Miwa S., Hibiki T., Ishii M., Mori-ta H., Kondoh Y. et al. Experimental study of internal two-phase flow induced fluctuating force on a 90° elbow. Chemical Engineering Science. 2012; 76:173-187. DOI: 10.1016/j.ces.2012.04.021
25. Parsi M., Agrawal M., Srinivasan V., Vieira R.E., Torres C.F., McLaury B.S. et al. Assessment of a hybrid CFD model for simulation of complex vertical upward gas-liquid churn flow. Chemical Engineering Research and Design. 2016; 105:71-84. DOI: 10.1016/j. cherd.2015.10.044
26. Costigan G., Whalley P.B. Slug flow regime identification from dynamic void fraction measurements in vertical air-water flows. International Journal of Multiphase Flow. 1997; 23(2):263-282. DOI: 10.1016/ s0301-9322(96)00050-x
27. Lowe D.C., Rezkallah K.S. Flow regime identification in microgravity two-phase flows using void
Received November 27, 2022.
Adopted in revised form on March 24, 2023.
Approved for publication on May 18, 2023.
Bionotes: Alireza Taherifard — postgraduate student; Peter the Great St. Petersburg Polytechnic University (SPbPU); 29 Politekhnicheskaya st., St. Petersburg, 195251, Russian Federation; Scopus: 57191530010, ORCID: 0000-0001-5973-7419; taherifard.a@edu.spbstu.ru;
Viktor V. Elistratov — Doctor of Technical Sciences, Professor, Professor of the Higher School of Hydrotechni-cal and Power Engineering; Peter the Great St. Petersburg Polytechnic University (SPbPU); 29 Politekhnicheskaya st., St. Petersburg, 195251, Russian Federation; elistratov@spbstu.ru.
Contribution of the authors: all authors have made an equivalent contribution to the publication. The authors declare no conflicts of interest.
fraction signals. International Journal of Multiphase Flow. 1999; 25(3):433 457. DOI: 10.1016/s0301-9322(98)00058-5
28. Parsi M., Vieira R.E., Torres C.F., Ke-sana N.R., McLaury B.S., Shirazi S.A. et al. Characterizing slug/churn flow using wire mesh sensor. Fluids Engineering Division Summer Meeting. 2014. DOI: 10.1115/FEDSM2014-21678
29. Hanafizadeh P., Eshraghi J., Taklifi A., Ghan-barzadeh S. Experimental identification of flow regimes in gas-liquid two phase flow in a vertical pipe. Mec-canica. 2016; 51(8):1771-1782. DOI: 10.1007/s11012-015-0344-4
30. Ye J., Guo L. Multiphase flow pattern recognition in pipeline-riser system by statistical feature clustering of pressure fluctuations. Chemical Engineering Science. 2013; 102:486-501. DOI: 10.1016/j. ces.2013.08.048
31. Franca F., Acikgoz M., Lahey R.T., Clausse A. The use of fractal techniques for flow regime identification. International Journal of Multiphase Flow. 1991; 17(4):545-552. DOI: 10.1016/0301-9322(91)90049-9
32. Bouyahiaoui H., Azzi A., Zeghloul A., Hasan A.H., Al-Sarkhi A., Parsi M. Vertical upward and downward churn flow: similarities and differences. Journal of Natural Gas Science and Engineering. 2020; 73:103080. DOI: 10.1016/j.jngse.2019.103080
СПИСОК ИСТОЧНИКОВ
1. Asgharpour A., Zahedi P., Vieira R., Parsi M., Shirazi S.A., McLaury B.S. Investigation of churn/annular and pseudo-slug flow characteristics before and after pipe elbows // 11th North American Conference on Multiphase Production Technology. 2018.
2. Doroshenko Y., Doroshenko J., Zapukhliak V., Poberezhny L., Maruschak P. Modeling computational fluid dynamics of multiphase flows in elbow and T-junction of the main gas pipeline // Transport. 2019. Vol. 34. Issue 1. Pp. 19-29. DOI: 10.3846/transport.2019.7441
3. Zhao D., Omar R., Abdulkadir M., Abdulka-reem L.A., Azzi A., Saidj F. et al. The control and maintenance of desired flow patterns in bends of different orientations // Flow Measurement and Instrumentation. 2017. Vol. 53. Pp. 230-242. DOI: 10.1016/j.flowmea-sinst.2016.09.003
4. Parsi M. Sand particle erosion in vertical slug/ churn flow. The University of Tulsa, 2015. 175 p.
5. De Kerpel K., De Keulenaer T., De Schamphe-leire S., De Paepe M. Capacitance sensor measurements of upward and downward two-phase flow in vertical re-
turn bends // International Journal of Multiphase Flow. 2014. Vol. 64. Pp. 1-10. DOI: 10.1016/j.ijmultiphase-flow.2014.04.003
6. Abdulkadir M., Zhao D., Azzi A., Lowndes I.S., Azzopardi B.J. Two-phase air-water flow through a large diameter vertical 180o return bend // Chemical Engineering Science. 2012. Vol. 79. Pp. 138-152. DOI: 10.1016/j.ces.2012.05.029
7. Vieira R.E., Kesana N.R., McLaury B.S., Shi-razi S.A., Torres C.F., Schleicher E. et al. Experimental investigation of the effect of 90 standard elbow on horizontal gas-liquid stratified and annular flow characteristics using dual wire-mesh sensors // Experimental Thermal and Fluid Science. 2014. Vol. 59. Pp. 72-87. DOI: 10.1016/j.expthermflusci.2014.08.001
8. Сулейманов В.А., Бузников Н.А. Обеспечение бесперебойности многофазного потока в протяженном морском трубопроводе: влияние состава транспортируемого флюида и профиля трассы трубопровода // SOCAR Proceedings. Transportation, Storage of Oil and Gas. 2021. № 3. С. 92-99. DOI: 10.5510/ OGP20210300534
9. Громов В.А., Семенов Т.В., Яшник И.Л., Петров А.М. Измерительно-вычислительный комплекс нового поколения для диагностики термодинамических процессов многофазных потоков в трубопроводах // Научный вестник Арктики. 2022. N° 13. С. 101105. DOI: 10.52978/25421220_2022_13_101-105
10. Серов Н.В., Курушина В.А. Моделирование влияния положения трубопровода на режим многофазного потока // Архитектура, строительство, транспорт. 2022. N 1 (99). С. 88-95. DOI: 10.31660/2782-232X-2022-1-88-95
11. Бузников Н.А., Сулейманов В.А., Трофимов И.А. Влияние выбора ингибитора гидратообра-зования на обеспечение бесперебойности потока в протяженных морских трубопроводах многофазного флюида // Трубопроводный транспорт: теория и практика. 2018. N 1 (65). С. 34-38.
12. Коптева А.В., Коптев В.Ю., Поддуб-ный Д.А. Информационное обеспечение процесса транспортирования многофазных потоков на основе внедрения радиоизотопной бессепарационной системы учета углеводородов // Динамика систем, механизмов и машин. 2019. Т. 7. N 2. С. 220-226. DOI: 10.25206/2310-9793-7-2-220-226
13. Тахерифард А., Елистратов В.В. Численное моделирование эрозии в трубе при многофазном потоке нефти и газа // Известия ВНИИГ им. Б.Е. Веденеева. 2023. Т. 307. С. 16-28.
14. Тахерифард А., Елистратов В.В. Трехмерное моделирование эрозии трубопровода с двойным коленом в многофазной среде метан - вода - песок // Вестник МГСУ. 2023. Т. 18. N 5. С. 717-725. DOI: 10.22227/1997-0935.2023.5.717-725
15. Karami H., Torres C.F., Parsi M., Pereyra E., Sarica C. CFD simulations of low liquid loading multi-
phase flow in horizontal pipelines // Fluids Engineering Division Summer Meeting. 2014. P. V002T06A011. DOI: 10.1115/fedsm2014-21856
16. Bortolin S., Da Riva E., Del Col D. Condensation in a square minichannel: application of the VOF method // Heat Transfer Engineering. 2014. Vol. 35. Issue 2. Pp. 193-203. DOI: 10.1080/01457632.2013.812493
17. Hernandez-Perez V., Abdulkadir M., Azzopardi B.J. Grid generation issues in the CFD modelling of two-phase flow in a pipe // The Journal of Computational Multiphase Flows. 2011. Vol. 3. Issue 1. Pp. 13-26. DOI: 10.1260/1757-482x.3.1.13
18. Ratkovich N.R., Majumder S.K., Bentzen T.R. Empirical correlations and CFD simulations of vertical two-phase gas-liquid (Newtonian and non-Newtonian) slug flow compared against experimental data of void fraction // Chemical Engineering Research and Design. 2013. Vol. 91. Issue 6. Pp. 988-998. DOI: 10.1016/j. cherd.2012.11.002
19. Saad S.B., Gentric C., Fourmigue J.-F., Clement P., Leclerc J.-P. CFD and experimental investigation of the gas-liquid flow in the distributor of a compact heat exchanger // Chemical Engineering Research and Design. 2014. Vol. 92. Issue 11. Pp. 2361-2370. DOI: 10.1016/j.cherd.2014.02.002
20. Cerne G., Petelin S., Tiselj I. Coupling of the interface tracking and the two-fluid models for the simulation of incompressible two-phase flow // Journal of Computational Physics. 2001. Vol. 171. Issue 2. Pp. 776-804. DOI: 10.1006/jcph.2001.6810
21. Yakhot V., Orszag S.A., Thangam S., Gat-ski T.B., Speziale C. Development of turbulence models for shear flows by a double expansion technique // Physics of Fluids A: Fluid Dynamics. 1992. Vol. 4. Issue 7. Pp. 1510-1520. DOI: 10.1063/1.858424
22. Ferziger J.H. Large eddy simulation // Simulation and Modeling of Turbulent Flows. 1996. DOI: 10.1093/oso/9780195106435.003.0007
23. Parsi M., Agrawal M., Srinivasan V., Vieira R.E., Torres C.F., McLaury B.S. et al. CFD simulation of sand particle erosion in gas-dominant multiphase flow // Journal of Natural Gas Science and Engineering. 2015. Vol. 27. Pp. 706-718. DOI: 10.1016/j. jngse.2015.09.003
24. Liu Y., Miwa S., Hibiki T., Ishii M., Morita H., Kondoh Y. et al. Experimental study of internal two-phase flow induced fluctuating force on a 90° elbow // Chemical Engineering Science. 2012. Vol. 76. Pp. 173187. DOI: 10.1016/j.ces.2012.04.021
25. Parsi M., Agrawal M., Srinivasan V., Vieira R.E., Torres C.F., McLaury B.S. et al. Assessment of a hybrid CFD model for simulation of complex vertical upward gas-liquid churn flow // Chemical Engineering Research and Design. 2016. Vol. 105. Pp. 71-84. DOI: 10.1016/j.cherd.2015.10.044
26. Costigan G., Whalley P.B. Slug flow regime identification from dynamic void fraction measurements
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in vertical air-water flows // International Journal of Multiphase Flow. 1997. Vol. 23. Issue 2. Pp. 263-282. DOI: 10.1016/s0301-9322(96)00050-x
27. Lowe D.C., RezkallahK.S. Flow regime identification in microgravity two-phase flows using void fraction signals // International Journal of Multiphase Flow. 1999. Vol. 25. Issue 3. Pp. 433-457. DOI: 10.1016/ s0301-9322(98)00058-5
28. Parsi M., Vieira R.E., Torres C.F., Kesa-na N.R., McLaury B.S., Shirazi S.A. et al. Characterizing slug/churn flow using wire mesh sensor // Fluids Engineering Division Summer Meeting. 2014. DOI: 10.1115/ FEDSM2014-21678
29. Hanafizadeh P., Eshraghi J., Taklifi A., Ghan-barzadeh S. Experimental identification of flow regimes in gas-liquid two phase flow in a vertical pipe //
Meccanica. 2016. Vol. 51. Issue 8. Pp. 1771-1782. DOI: 10.1007/s11012-015-0344-4
30. Ye J., Guo L. Multiphase flow pattern recognition in pipeline-riser system by statistical feature clustering of pressure fluctuations // Chemical Engineering Science. 2013. Vol. 102. Pp. 486-501. DOI: 10.1016/j. ces.2013.08.048
31. FrancaF., AcikgozM., LaheyR.T., Clausse A. The use of fractal techniques for flow regime identification // International Journal of Multiphase Flow. 1991. Vol. 17. Issue 4. Pp. 545-552. DOI: 10.1016/0301-9322(91)90049-9
32. Bouyahiaoui H., Azzi A., Zeghloul A., Hasan A.H., Al-Sarkhi A., Parsi M. Vertical upward and downward churn flow: similarities and differences // Journal of Natural Gas Science and Engineering. 2020. Vol. 73. P. 103080. DOI: 10.1016/j.jngse.2019.103080
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Поступила в редакцию 27 ноября 2022 г. Принята в доработанном виде 24 марта 2023 г. Одобрена для публикации 18 мая 2023 г.
Об авторах: Алиреза Тахерифард — аспирант; Санкт-Петербургский политехнический университет Петра Великого (СПбПУ); 195251, г Санкт-Петербург, ул. Политехническая, д. 29; Scopus: 57191530010, ORCID: 0000-0001-5973-7419; taherifard.a@edu.spbstu.ru;
Виктор Васильевич Елистратов — доктор технических наук, профессор, профессор Высшей школы гидротехнического и энергетического строительства; Санкт-Петербургский политехнический университет Петра Великого (СПбПУ); 195251, г Санкт-Петербург, ул. Политехническая, д. 29; elistratov@spbstu.ru.
Вклад авторов: все авторы сделали эквивалентный вклад в подготовку публикации. Авторы заявляют об отсутствии конфликта интересов.
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