Investigations of the Formation Mechanism and Pressure Pulsation Characteristics of Pipeline Gas-Liquid Slug Flows

Abstract

The pipeline system is widely used in marine engineering, and the formation mechanism and flow patterns of two-phase slug flows are of great significance for the optimal design of and vibration prevention in a complex pipeline system. Aiming at the above problems, this paper proposes a modeling and solving method for gas-liquid slug flows. First, a VOF-PLIC-based coupling gas-liquid slug flow transport model is conducted. Second, to reduce the fuzzy boundary between the gas-liquid coupling interfaces, an artificial compression term is added to the transport equations, and the formation and evolution mechanism of severe slugging flow in piping systems is investigated. The pressure pulsation and gas content characteristics of the gas-liquid coupling process are explored. Research results found that the slugging phenomenon occurs at the gas-liquid interface, where liquid slugging frequency reaches its peak. The pipeline system has prominent periodic characteristics of the slugging phenomenon, and the period decreases when the gas-phase converted speed rises; pressure fluctuation amplitude increases, and the gas-phase velocity change is the inducing factor for the drastic change of pressure fluctuation. The research results can offer theoretical references for optimal designs of and vibration prevention in marine pipeline systems.

1. Introduction

With the progress of science, technology, and economic development, people’s demand for energy is increasing, and exploration for and exploitation of oil and gas by the original ground mining technique has gradually moved to more far-reaching marine oil and gas field transfer systems. Many oil companies have joined in the development of deep water and ultra-deep-water oil and gas fields. With the exploitation of land oil fields entering the middle and late stage, sea oil and gas production will gradually become the main growth point. A schematic diagram of marine oil and gas extraction is shown in Figure 1, as are the two main methods of transferring the products from subsea wells to the coast or offshore platforms, which include oil and gas sub-transmission and oil and gas mixing [1,2]. The oil and gas mixing and transmission method only requires the construction of an oil and gas pipeline, which reduces the cost of extraction. Furthermore, the platform does not need a separation device, which saves platform space, so this extraction and transmission method has been favored by many oil companies. Submarine mixing pipelines are mainly horizontal and near-horizontal pipelines, which need a submarine pipeline network system to transfer oil continuously, and submarine oil-gas pipelines have just become the lifeline of offshore oil and gas production systems. Hence, it is important to explore the two-phase transport characteristics of offshore oil and gas pipelines and pipeline optimization design.

In offshore pipelines, gas-liquid two-phase media are prone to form liquid slugs in risers at low flow rates, resulting in segmental slug flow with an alternating gas-liquid outflow. Segmental slug flow, as a highly hazardous flow pattern, widely exists in submarine pipeline manifolds and crossover tubes connecting various submarine equipment [3,4,5]. Because of the randomness and intermittency of slug flows, research on their hydrodynamic properties and flow patterns isincomplete. A pressure fluctuation will lead to structural vibration of the pipeline and affect the performance of the mixing pumps, bearings, and sealing components, which has an essential impact on the development of deep-sea oil fields and production device design [6,7]. Therefore, investigation of the transient features of slug flows and an understanding of the dynamics inside the pipe during the process of segmented slug flows will help us to understand the vibration excitation source and impact process and provide an important reference and technical support for piping system designs and vibration prevention.

When segmented slug flow occurs in a marine pipeline system, the medium in the pipe appears complex and has a variable gas-liquid alternating flow state. Related scholars have gradually shifted from their early studies of the macroscopic laws of the average length of liquid slugs and long bubbles, the average holding rate, and other averaging parameters to the study of the generation course, merging, and disappearance of liquid slugs as well as the study of the transient gas-liquid interfacial structure of the liquid slugs and long bubbles [8,9,10]. Due to the complexity of the segmented slug flow, there is still much room for research on slug formation, merging, and disappearance due to experimental technique limitations. At present, the transient flow characteristics of liquid slugs and long bubbles, as well as the gas-liquid phase interface structure, are studied mainly using CFD simulation. Most of the segmented flows depend on one-dimensional and two-dimensional models, which do not characterize the flow features of actual situations very well [11,12,13,14,15]. Malekzadeh focused on the generation mechanism, flow process, prevention, and control of segmental slug flows [16]. Pineda-Pérez investigated segmental slug flows and found that the method agrees well with experimental results regarding the segmental slug frequency and velocity distribution [17]. Schmelter chose the VOF modeling approach to study gas-liquid segment slug flows numerically, and the work verified numerical simulation’s feasibility [18]. Ratkovich used the VOF model to establish two-dimensional vertical tube models to discuss the gas contents of segmental slug flows [19]. Abdulkadir simulated air-silicone oil section flows with the VOF and RANS turbulence models and compared them with experimental results. It was found that the simulation yielded flow patterns before and after the bend that were consistent [20].

The above literature review shows that the current research on segmented slug flow in marine pipeline systems mainly focuses on the generation mechanism, flow process, velocity distribution, etc. Some of the existing research mainly focuses on experimental research. Still, due to the experimental research being limited by the experimental site and equipment limitations, the research results deviate from actual field data. In addition, there is a big gap between the local structure of the liquid slug, transient motion characteristics, velocity, and pressure field distribution and the macroscopic law of flow characteristic parameters. The actual situation and the numerical simulation aspects of segment slug flow need to be further studied. Therefore, it is necessary to carry out a numerical simulation study of segmented slug flow for marine pipeline systems. The related multiphase flow modeling and solution methods also need to be further explored.

Given this, this paper proposes a two-phase slug flow modeling and solution method for complex pipeline systems. Our method combines the RNG turbulence model, establishes a gas-liquid slug flow model, simulates the transient flow properties, calculates the volume fraction, gas rates, and pressure pulsation, and simulates slugging and the development of slugging in different working conditions. Simulations are carried out to analyze the motion characteristics, phase interface structure, transient structure of long bubbles, and slug pressure to explore the flow characteristics and flow pattern in complex multi-inlet pipelines. The results offer important guidance for analyzing segmented slug flow characteristics in offshore pipeline transportation systems and provide technical support for the optimal design of offshore transportation pipes and slug flow suppression.

2. Mathematical Models

2.1. Pipe Segment Slug Flow Model

At present, there are still debates on the formation conditions and formation mechanisms of severe segment slug flow, but for a riser system consisting of inclined pipes and risers, most of the literature has the same viewpoints: the inclined riser can form a liquid slug that prevents the gas phase, and the gas’s continuous inflow into the inclined pipe squeezes the liquid into entering into the riser system. At the same time, due to rising liquid pressures, the liquid blocks gas from entering into the pipeline [21,22,23]. At the same time, due to the rising pressure in the standpipe, the gas is blocked from entering the pipeline, and finally, the liquid slug grows to reach the standpipe height [24,25,26,27]. The formation principle can be summarized: When the downward pipeline lets in air and liquid layers flow in, the liquid will accumulate in the elbow under the action of gravity into a liquid slug. The liquid slug will compress the gas in the downward pipeline, making the downward pipeline gas pressure increase, increasing the slug height. The increase in the liquid slug’s height will further compress the gas, which will make the gas pressure in the downward pipeline increase further. When the slug height rises, a severe slug flow phenomenon exists. When the liquid slug height exceeds the riser’s height, a severe segment slug flow is formed.

Numerical methods can be implemented to study the phenomenon of segmental slug flow in pipes. The fluid volume VOF method, as a surface tracking method fixed under the Eulerian mesh, tracks the fluid volume in a mesh, so it is easy to implement and computationally small [28,29,30,31]. In the VOF model, volume rates are recorded in each computational cell of flow fields. Combined with the conditions of the VOF model and according to the flow state of the two-phase oil and gas flow, that is, when under different gas-liquid velocities, the oil and gas pipeline will produce laminar flow, segmented slugging flow, and other liquid flow patterns that contain large bubbles, all of which satisfy the conditions for selecting the VOF model.

For the VOF model, the interfaces between the phases are tracked via solving the volume fraction of single or multiple phases. For the qth phase, the equation can be expressed:

$$\frac{\partial \alpha }{\partial t}+\nabla \left(\alpha u\right)=0$$

(1)

$$\alpha \left(x,y,z,t\right)=\left\{\begin{array}{c}1\\ 0<\alpha <1\\ 0\end{array}\right.$$

(2)

where α is volume fraction, α = 1 indicates liquid phase, if 0<α<1, the cell denotes the interface, and α = 0 indicates gas phase. Volume fraction conservation is essential for the flow, and small volume fraction errors can lead to large changes in the interface position. To reduce the fuzzy boundary between gas-liquid interfaces, the transport equation is added to the artificial compression term, and the improved equation is as follows.

$$\frac{\partial \alpha }{\partial t}+\nabla \cdot \left(\alpha u\right)+\nabla \cdot \left[u_r\alpha \left(1-\alpha \right)\right]=0$$

(3)

where u is the mean velocity and u_r denotes the velocity field at the compression interface, which restricts the solution interval to be from 0 to 1, i.e., the artificial compression term acts only on the phase interface and has no effect on the interior [32,33,34,35]. Here, density and dynamic viscosity can be obtained:

$$\rho =\alpha {\rho }_1+\left(1-\alpha \right){\rho }_2$$

(4)

$$\mu =\alpha {\mu }_1+\left(1-\alpha \right){\mu }_2$$

(5)

For n-phase systems, the average density can be expressed:

$$\rho ={\displaystyle \sum {\alpha }_q{\rho }_q}$$

(6)

Fluid properties such as viscosity can be calculated. The momentum equation is:

$$\frac{\partial }{\partial t}\left(\rho \overrightarrow{v}\right)+\nabla \cdot \left(\rho \overrightarrow{v}\right)=-\nabla p+\nabla \cdot \left[\mu \left(\nabla \overrightarrow{v}+\nabla T\right)\right]+\rho \overrightarrow{g}+\overrightarrow{F}$$

(7)

The energy equations are:

$$\frac{\partial }{\partial t}\left(\rho E\right)+\nabla \cdot \left[\overrightarrow{v}\left(\rho E+p\right)\right]=\nabla \cdot \left[k_{eff}\left(\nabla T\right)\right]+S_h$$

(8)

The model deals with energy and temperature as mass-averaged variables:

$$E=\frac{{\displaystyle \sum _{q=1}^n{\alpha }_q{\rho }_q{E}_q}}{{\displaystyle \sum _{q=1}^n{\alpha }_q{\rho }_q}}$$

(9)

During segmented slug flow, the gas-phase is intermittent and the liquid-phase is continuous. The phase interface is also a key point to be observed and detected. Therefore, it is feasible to choose the VOF model for gas-liquid slug flows.

2.2. Turbulent Kinetic Energy Model of Pipeline Slug Flow

Whether the turbulence model can be accurately selected will impact the calculation results [36,37,38,39,40]. The numerical simulation mainly analyzes the phenomenon of gas-liquid slug flows. Due to the blockage of liquid slugs, there is a large difference in the pressure distribution ahead of a slug, and a liquid slug top will be pushed out, absorb the liquid film in front of it, and fall back under the action of gravity to form a certain eddy current. When the liquid slug does not move, the liquid film in front is equivalent to a jet into the liquid slug, and its flow state is more complex, so a more accurate RNG k-ε model is adopted:

$$\rho \frac{\partial k}{\partial t}=\frac{\partial }{\partial x_i}[({\alpha }_k{\mu }_e)\frac{\partial k}{\partial x_j}]+G_k+G_b-\rho \epsilon -Y_M$$

(10)

$$\rho \frac{\partial \epsilon }{\partial t}=\frac{\partial }{\partial x_i}[({\alpha }_{\epsilon }{\mu }_e)\frac{\partial \epsilon }{\partial x_i}]+C_{1\epsilon }\frac{\epsilon }{k}(G_k+C_{3\epsilon }{G}_b)-C_{2\epsilon }\rho \frac{{\epsilon }^2}{k}-R$$

(11)

where G_k denotes a turbulent energy term because of the change in mean speed gradients; Y_M is the total dissipation rate with respect to the pulsatile expansion, G_b is the turbulent energy term due to buoyancy, which is the same as those in the standard k-ε model, and α_k and α_ε are effective Planck’s number inverse with respect to turbulence and the turbulence dissipation rate, respectively.

2.3. Interface Refactoring Methodology

After a pipe segment slug flow forms, its evolution process has typical shear flow field characteristics. The PLIC method is effective to simulate free interfaces in a shear velocity field, and the constructed interfaces are highly refined [41,42,43]. Therefore, to accurately track VOF on the phenomenon of segmental slug flow in pipeline systems, the PLIC method can be used to track free interfaces.

The principle can be moving interfaces and cell fluid ratios to match the VOF function value. The vertical distance can be obtained by the iterative solution of the cut-line method [44,45,46,47]. By determining the free surface shapes through the fluid volume fraction, the free interface will transfer phase volumes. Taking the two-dimensional flow field as an example, as shown in Figure 2, assuming that fluid interfaces exist at a junction within a cell (i, j). The dashed line A₁C₁ indicates the free interface shape within the cell and AC describes reconstructed interface shapes. It is assumed that the normal vector n can be the mesh center. The normal vector n can be acquired thus:

$$n_{i,j}=\frac{1}{4}\left(n_{i+1/2,j-1/2}+n_{i-1/2,j-1/2}+n_{i+1/2,j+1/2}+n_{i-1/2,j-1/2}\right)$$

(12)

Assuming that the components are in the positive direction, as shown in Figure 1, a linear equation between phases can be developed:

$$n_{x}x+n_{y}y=b$$

(13)

where b denotes the distance from point B to interface AC. The liquid zone can be obtained thus:

$$E_{ij}=S_{ABC}$$

(14)

Based on the obtained b and E_ij, it is possible to find the line segments in the mesh where the interface is uniquely determined, thus determining the interphase interface.

3. Pipeline Slug Flow Dynamics Model

3.1. Geometrical and Numerical Modeling

The modeling of segmental slug flows in marine pipeline systems can include two sections: a geometric model and a finite element model. According to the established mathematical model, i.e., the partial differential equation system, it is difficult to solve a slug flow directly. This chapter relies on the Fluent 15.0 software platform to resolve partial differential equations and obtain approximate solutions that meet the needs of the analysis. The principle is to replace a continuous physical quantity field (such as pressure, temperature, velocity, etc.) in space and time coordinates with a finite set of values at discrete nodes, then use certain rules to establish the algebraic equations of the relationship between the values of the discrete point variables, thus obtaining an approximate solution as the solution of the continuous physical quantity field. For complex flow patterns, it is crucial to set reasonable calculation regions and carry out numerical discretization to obtain accurate numerical results.

Usually, the method used to create a numerical simulation of severe section slugging flow is to build a three-dimensional model directly to solve the calculation. To study the dynamics of the oceanic pipe section’s slug flow, a geometric and numerical model of the pipe section’s slug flow is built (Figure 3a,b). A geometrical model contains eight symmetrically distributed inlets. The center coordinates of each branch pipe are shown in the figure. The inlet diameter is 220 mm, and the outlet diameter is 508 mm. Air enters a horizontal pipe and exits from the outlet.

Based on the geometrical model of the 3D multi-inlet pipeline, a numerical model of the gas-liquid slug flows is conducted, as shown in Figure 3c,d. The parameters of the fluid medium are listed in

Table 1. Parameters of the fluid medium.

Fluid Medium	Density (kg/m3)	Dynamic Viscosity (mPa⋅s)	Apparent Velocity (m/s)
Water	998.203	1.01	0.28–1.42
Air	1.205	1.79 × 10−2	0.17–1.36

. Considering the apparent viscous effect and the large gradient of flow field change near the pipeline’s wall, it is necessary to encrypt the grid at the wall and inlet and outlet. Using ICEM CFD 15.0 meshing software for non-structural meshing of the model, mesh encryption is required at the gas-liquid inlet, and the mesh encryption is also required at the bends, with a mesh number of 347,820, and a mesh quality of 0.6. For the other fluid domains of the 3D numerical model, unstructured meshing is carried out using a mesh scale of 0.03 mm with a total number of grids of 458,760 and a mesh quality of 0.5 or more. The total number of meshes in the fluid domain is 806,580, which provides a mesh quality within the computationally permissible range to guarantee that the mesh quality meets the computational accuracy requirements.

3.2. Initial and Boundary Conditions

The gas phase denotes a compressible gas. The liquid phase is incompressible. In compressible fluids, when the pressure decreases, the density decreases and the volume increases. Still, its mass flow rate remains unchanged, and the pipeline mass inflow boundary applies to compressible fluids. The pipe outlet is a pressure outlet, and pressure outlets lead to good convergence, especially when reflux occurs during the iteration process. The vessel wall is a fixed wall boundary condition. The non-slip boundary condition is at the wall, and the heat flux is considered to be zero heat flux. The setup of the pipe wall has important effects on air mass flows, segmented slug flow, and annular flows. It has less of an effect on the bubble flows, stratified flows, and diffuse flows, because the gas in bubble flows and segmented slug flows generates a large air mass in direct contact with the pipe wall, which has an adhesion force. There is a contact angle between the bubbles and the pipe wall, which is assumed to be 60° in this paper, and between the air and the water. Air is assumed to be an ideal gas; the initial temperature is set to 300 K, and the piping system is filled with gas at the initial stage.

In the numerical solution process, the discrete-time format is in first-order implicit Eulerian format, and the PISO algorithm can be utilized to couple pressure and speed to guarantee numerical convergence efficiency [48,49,50,51,52,53]. To capture the interphase flow characteristics, the Courant number can be guaranteed to be less than 2. The PRESTO method processes discrete interpolation of the pressure to prevent pressure oscillations [54,55,56,57]. The momentum discretization format, turbulent energy, and dissipation rate discretization formats can all be in second-order windward format, which guarantees calculation accuracy and stability [58,59,60].

3.3. Grid Independence and Model Validation

In the actual simulation, due to the limitations of the computer’s computational ability, it is necessary to select a reasonable number of grids for the calculation. The relative error values in

Table 2. Verification of grid independence.

Maximum Unit Size/mm	Total Number of Units	Maximum Static Pressure/Pa	Relative Error/%
0.005	578,469	4842	/
0.003	806,580	4861	0.39
0.002	1,138,548	4876	0.31

indicate the maximum static pressure measured by the maximum cell size grid model, the max cell sizes of 0.005 mm measured by the max static pressure, the relative error between the max sizes of 0.003 mm and max sizes of 0.005 mm in the simulation of the max static pressure, and the calculation of the relative error of the smaller sizes, for a result of 0.39%. The relative error in the maximum static pressure calculated by the mesh model with max sizes of 0.002 mm and 0.005 mm is even more minor at 0.31%. The error between the three grids is minimal, and to improve calculation efficiency, a max cell size of 0.003 mm is selected, along with a smaller number of grids.

The trend of the dynamic evolution of liquid-slug frequency is shown in Figure 4. Here, the experiment result is obtained using a water model experiment platform. The boundary conditions and container size in the experiment are consistent with the numerical simulation. The values and experimental results are tested three times, and the average values are taken. The liquid-slug frequency can be the same. Slug phenomena occur, and their frequency arrives at its peak value and then declines. The decreasing tendency gradually slows down and finally reaches stability at the outlet. This shows that the slug frequency reaches its maximum when slugging, and the frequency remains stable until a stable slug is generated. Simulation results closer to the inlet are greater than experimental results. This is due to a pressure change being the vital reason for the slugging, which does not have much influence on developed slugs. This leads to the slugging frequency at the inlet being larger than experimental values. The model in this paper quantitatively yields results consistent with the experiments, proving the effectiveness of the model for the simulation of segmental slugging flow.

4. Results and Discussion of Segmental Slug Flow

4.1. Slugging Characteristics of Horizontal Pipe Section Slug Flow

In the theory of multiphase flow numerical simulation, V_g and V_l are usually represented as gas and liquid velocities, respectively. Here, the gas-liquid inlet velocities of the gas-liquid segmented slug flows and pseudo-segmented slug flows in the horizontal pipe are given, and the inlet speeds of segmented slug flows in this numerical simulation are set to be V_g = 8 m/s, V_l = 3.5 m/s. Figure 5 represents the liquid-phase volume fraction cloud of the slugging process at the pipe entrance, where the capital letter t represents the flow time. The wave flow with a higher fluctuation and frequency appears at the inlet, and since there is a high flow rate at this time, the liquid layer will transiently jump up to touch the top of the pipe to block the pipeline, forming a shorter unstable liquid slug. The liquid slug body is driven by high gas velocity to move steadily downstream. Still, because there is not enough liquid downstream to maintain a stable liquid slug in the movement process, the liquid in its tail will soon fall off, which is why the bubbles before and after the rapid coalescence of this phenomenon are regarded as the inlet effect of the liquid slug.

The above phenomenon shows that many interfacial waves with tiny amplitudes are formed at the air drive. The momentum transfer between gas and liquid triggers the interface instability. The interfacial waves merge so that the frequency of interfacial waves becomes smaller and the wavelength and amplitude increase. When the gas upper flow space is minor, air improves the highest points of interfacial waves, and the pressure declines because of the Bernoulli effects of interfacial waves above gas spaces. As pressure differences overcome interface tensions and gravities, waves are raised, which generate slug phenomena. Driven by the air velocity, the interfacial wave top can form liquid slug heads and interfaces at the location of the slug after the slugging falls, forming a water jump surface.

Figure 6 gives a cloud view of the distribution of volume fractions and velocities of the two phases at different cross-sections of the long bubble perpendicular to the flow direction, where the long bubble along the flow direction determines the cross-sectional positions. The figure shows that gas-liquid flows in from both sides of the pipe, showing a non-uniform gas-liquid coupling distribution (Figure 6a–d). With the gas-liquid mixing, liquid-phase material is deposited, and gas-phase material floats on the upper side wall. A liquid-film-gas-liquid interfaces at different locations are not smooth, and the liquid surface height is different, indicating that the flow state inside the pipeline is not fully balanced. From Figure 6e,f, the liquid-phase velocity has a maximum value of 3.5 m/s at the pipeline inlet. The speed may be distributed in a band, and the velocity is smaller near the pipeline’s wall. The liquid-phase velocities at different locations do not differ much, which may be due to the interaction between the two phases.

From the above analysis, it can be inferred that when the gas phase is continuously filled into the liquid phase, a large disturbance will appear on the free liquid surface, resulting in fluctuations in the liquid surface height at different positions of the horizontal pipeline. The liquid at the end of the pipe jumps upward and touches the top of the pipe, with only a small amount of liquid film reaching the wall. The upward contact of the liquid layer in the tube to the top of the tube is caused by the intermittent slug. The liquid on top of the high-speed gas accumulates continuously by forming many tiny droplets covering the tube wall’s upper half. Under the airflow, the liquid layer rises rapidly, and the formation of a liquid plug blocks the pipeline section, as shown in Figure 6b. Therefore, slug flow can be identified by the distribution of gas and liquid in the cross-section of a slug flow.

4.2. Formation and Evolutionary Characteristics of Riser Section Slug Flow

Figure 7 represents the liquid-phase volume fraction cloud of slug flows. At the horizontal pipe and vertical pipe, the gas-liquid interface fluctuates, forming random bubbles with cross-scale and diversity characteristics, as shown in Figure 7a,b. When the bubbles at the bottom gradually rise along the flow direction, the rise in airspeed increases long bubble lengths, and the liquid level at the head gradually increases, forming a wedge-shaped long bubble head. Due to the increase in the length of the long bubbles, the liquid film is fully developed by the liquid film velocity driven by the long bubbles, as shown in Figure 7c–e. At the same time, the velocity of the long bubbles decreases rapidly, and the gas-liquid velocity reaches equilibrium in long bubbles. In the above process, pressure gradually decreases due to the fluid in the flow process generating energy losses along the flow direction of long bubbles. When a high gas velocity long bubble head forms into a wedge, the liquid film head pressure increases, and the air to the slug promotes a liquid film area under pressure, indicating that the gas velocity of the structure of the long bubble has an important effect.

4.3. Pressure Pulsation Characteristics of Pipe Section Slug Flow

Three pipeline pressure monitoring points are set up in the pipeline system to monitor the pressure change over time at the location points to reveal the pressure pulsation properties of the pipeline system (Figure 8). The monitoring points are P1, P2, and P3, where P1 monitors the pressure change over time in the mixing area of air and water phases, P2 is set at the riser bottom to monitor pressure changes over time, and P3 monitors the pressure change in the riser middle. As can be seen from the figure, when the air and water phases are mixed, both of them are always shown in laminar flows. Meanwhile, when the liquid phase is gradually moving toward the riser, it is easy for a liquid slug to gradually form at the bottom of the riser, preventing the gas in the tilted pipe from continuing to enter into the riser. As the gas pressure gets bigger and bigger, the liquid slug gradually accumulates at the height of the riser, which eventually leads to the liquid slug rushing out of the riser to form an eruption. At this time, the gas-liquid in a riser outlet forms a segment slug flow eruption phenomenon, the fluid falls back to the riser bottom, where following slug eruptions will originate.

In Figure 8, the transient flow properties of severe segmental slug flows at pipeline system have prominent periodic characteristics. During the stage of segmental slug flow formation, the pressures at the three monitoring points P1, P2, and P3 gradually climbed with time, showing an approximately linear increasing trend. This is because the mass flow rate in the inclined pipeline section is kept in constant supply during the liquid slug formation stage, causing linear pressure rises at the three monitoring points. When the liquid slug height rises to equal the riser height, the liquid slug starts to flow out, and since the height of the liquid slug equals the constant height of the riser, the pressure at the riser bottom fluctuates around 37 kPa, and the amplitude of the fluctuation gradually decreases. This is due to the liquid slug outflow making the liquid-slug rising speed increase. The bottom pressure of the riser tube increases, but the liquid slug outflow to a certain stage will also cause the liquid slug to reduce, and the bottom pressure decreases. In the stage of liquid and gas eruption, the bottom pressure decreases rapidly, and the magnitude of the decrease is 21.5 kPa. This is due to the reduction of liquid in the riser. The air at the horizontal tubes enters into risers so that the pressure in the riser drops, which in turn intensifies air flow entering the risers, resulting in bottom pressures of risers decreasing rapidly. In the liquid slug reflux stage, residual fluids re-accumulate at the bottom under the effects of gravity to form a new liquid slug, so pressure oscillation rises during the liquid slug reflux stage. In addition, monitoring point P1 is in the horizontal pipe. Therefore, there is a phase difference between it and the other two monitoring points, and its pressure change value is slightly delayed.

As the liquid slug gradually flows out of the riser pipes, the pressure change of monitoring points at this time is small, and there is also a tiny fluctuation in its pressure, so the curve shows an up-and-down phenomenon. When liquid slugs climb up and reach the riser pipe’s outlet, the liquid slugs are lost continuously, which leads to the pressure in the riser pipe dropping rapidly to nearly 20 kPa, after which the falling liquid slug accumulates again, preparing for the next stage of the severe section of the slug flow eruption.

4.4. Gas Content Characteristics of Segmented Slug Flow

Figure 9 represents the motion process of the liquid slug inside the 3D pipe over time, which characterizes the gas-phase changes. When liquid-phase velocities are inevitable, with an increase of apparent air velocity, the liquid-slug holding rate, liquid level height, and liquid-slug length decline and the liquid-slug head throw is more prominent, which leads to the difference in the development processes of liquid slugs with different speed changes. As the velocity differences are slight, the liquid-slug head throws out a phenomenon that may not be apparent. A liquid-slug can be driven by the air phase to move forward with a balanced speed, absorbing a liquid film, and the liquid film level fluctuates little. As the gas-liquid velocity differences are great, a liquid slug has an apparent throwing phenomenon; the liquid slug, through the throwing periodic movement, falls forward to absorb the liquid film. As velocity differences are slight, the liquid level can be higher and the slug bodies longer, and the liquid slug bodies move forward uniformly under the impetus of gas.

5. Conclusions

Investigating the transient dynamics of gas-liquid slug flows in marine piping systems can provide a theoretical basis and technical support for designing piping systems and vibration prevention. This paper proposes a novel VOF-PLIC-based two-phase slug flow modeling and solution method to explore the gas-liquid evolution characteristics and flow pattern evolution of complex multi-inlet pipelines.

(1)

A two-phase severe slug flow dynamics model based on an improved VOF-PLIC coupling method is built up to investigate the formation mechanisms of gas-liquid slug flows. An artificial compression term is added to the transport equations to reduce the fuzzy boundary between the gas-liquid coupling interfaces. The slugging phenomenon occurs at the gas-liquid interface, and the slug frequency reaches its peak. The slug length changes irregularly during the development of the slug, reflecting the randomness of the slug merging and disappearing phenomena.

(2)

Gas velocity has an essential effect on the structure of long bubbles. Due to the loss of energy generated by the fluid, the head of the long bubble becomes wedge-shaped at high air speeds, the pressure at liquid film head rises, and the gas pushes of liquid film areas are pressurized.

(3)

Gas-liquid two-phase forms alternately at the riser outlet out of the slug flow eruption phenomenon, and the piping system of a severe segment slug flow with transient flow characteristics has prominent cycle characteristics.

(4)

When the pipe flow rate is low, liquid forms a liquid slug at the lowest location of the horizontal pipe. When the air flow rate is gradually increased, the riser will not appear as a gas cut-off phenomenon; the liquid intermittently goes out of the mouth of the pipe and begins the formation of a severe section of the slug flow.