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Abstract
ABSTRACT
Bend pipe is a commonly used part of long‐distance pipelines. It is very important to study the flow law of hydrate particles in the bend pipe to optimize pipeline design. In addition, the efficiency and safety of pipeline gas transmission will be improved. The flow of hydrate particles in the bend pipe is the research object of this paper, and the short twist tape is used as the spiral device, and numerical simulation methods are used to study the effects of the bend angle and the twist rate on the velocity distribution, turbulence intensity distribution, wall shear, particle movement and pressure drop distribution of the spiral flow carrying hydrate particles. The results show that as the twist rate of the twist tape is smaller, and the spiral flow is stronger, the fluid can generate a larger tangential velocity when flowing through the bend. The maximum speed at the section closest to the entrance is 28% higher than at the section furthest. Maximum tangential speed increased by 2 times. When the angle of the bend is larger, and velocity is more conducive to maintaining the spiral flow pattern of the particles, it is also more conducive to maintain. However, the twist rate is smaller, and the resistance is greater, then the pressure drop is greater, and the resistance coefficient of the bend pipe section is greater. With the increase of torsion, the pressure drop decreased by 52%. When the angle of the bend pipe section becomes smaller, it increases the collision frequency between the pipe wall and the natural gas. Unit pressure drop loss increased by 13%. When the angle is smaller, the change in the direction of the velocity of the particles will be more violent, and the pressure drop is larger, and the drag coefficient is larger. In the same section, the maximum turbulence intensity is about twice the minimum.
Full text
Introduction
Pipeline transportation is currently the main form of natural gas transportation. However, the low temperature and high pressure of the deep sea can easily lead to the formation of natural gas hydrates [1]. After Hammerschmidt published data in 1934 on the blockage of gas pipelines caused by hydrates, people began to pay attention to such problems. With the development of the natural gas industry, the application of natural gas is becoming more and more widespread. During natural gas transportation, hydrates form and pipelines clog. Due to the pipeline freezing caused by hydrates, blockage repair operations are complex and lengthy, which seriously affects the normal production of natural gas, and may cause serious safety hazards. Therefore, the study of the formation process of natural gas hydrates has become a key research direction in the process of marine oil and gas transmission [2, 3].
In recent years, the hydrate slurry pipe flow technology that allows a certain amount of natural gas hydrate particles to be generated in the pipeline and enables them to flow smoothly along the pipeline with the fluid has attracted attention. This technology can be applied to the prevention and control of hydrate clogging of pipelines. It provides a new development direction for ensuring the safety of natural gas transportation pipelines [4, 5]. Accordingly, Wang's group proposed the use of spiral flow transport to ensure the safe flow of hydrate slurry [6]. Pipeline spiral flow is a kind of flow form that changes the pipeline flow boundary by installing a spinning device in the pipeline to change its flow direction, so that the fluid in the pipeline has axial and tangential velocities [7]. Axial velocities provide the impetus to keep the fluid-carrying hydrate particles moving forward, while tangential velocities allow the particles to remain “in suspension.” Tangential velocities make it less likely that the hydrate will collect and deposit at the bottom of the pipe after it is generated, and extends the safe flow range of the hydrate [8, 9]. This ensures the safe delivery of natural gas. Wang summarized the change of flow pattern during gas-liquid two-phase flow by studying the spiral flow with twist tape or impeller as the spinning device. At last, they came up with the law of the transition boundary of the flow pattern [10–13], and invented a new pipeline spiral flow gas hydrate transport method. This method can effectively avoid pipeline clogging and improve the safety and economy of natural gas transportation [14].
In the actual pipeline transportation of hydrate slurry, the volume fraction of slurry hydrate should be avoided as far as possible to the area of rapid increase in pressure drop. However, in the curved pipe structure, when the particles first go through horizontal movement in the straight pipe section and then flow to the bend position, the two phases exhibit different movement forms at the bend due to the density difference between the liquid-solid phases, and the separation of the two phases causes the particle phase to deviate to the outside of the bend. The particle concentration on the outer wall is greatly increased. Near the exit of the bend, the particle concentration on the outer wall reaches the maximum and eventually causes the hydrate particles to accumulate at the bend, resulting in the increase of the volume fraction of hydrate particles at this position. Therefore, it is impossible to simply control the inlet volume fraction of hydrate particles to ensure that the volume fraction of hydrate in the curved pipe is far away from the area of rapid pressure drop growth. Therefore, it is necessary to investigate the influence of different factors on the maximum concentration of hydrate particles in the curved pipe.
A great deal of research has also been done by domestic and foreign researchers in the area of bend pipe multiphase flow, especially regarding particle transport. Al-Obaidi [15] found that the effects of changes in flow structure, such as velocity magnitude and radial velocity, and velocity magnitude and radial velocity profiles in different configurations, are studied. An experimental design strategy using the Taguchi method (TM) is chosen according to the variance of the orthogonal L16 sequences. Optimization results show that higher differential pressure values are related to shaft diameter. Al-Obaidi [16] used computational fluid dynamics (CFD) to study the impact of different diameter Ball Tabulator Inserts (BTI) on the three-dimensional flow pattern and heat transfer characteristics within a circular tube. Al-Obaidi [17] analyzed the behavior of a flow field, characteristic of pressure drop, and hydraulic thermal performance, and the results revealed that the value of pressure drop between each cross section in the pipe decreases as pipe length increases. When the NTTIs increase that leads to a pressure difference also increasing as compared to the smooth pipe. Al-Obaidi [18] used the CFD technique to study the influence of four geometrical parameters, including the distance between dimples, number of dimples, dimple diameter, and dimple pitch on the enhancement of thermo-hydraulic heat transfer. The results revealed different patterns of flow field and heat performance due to the use of dimples on the inner pipe surface. Moreover, utilized dimples can raise heat performance due to the interactions between the dimpled wall surfaces and swirling flow; hence, that can raise the area of heat transfer. The above scholars have done pioneering research on internal flow. Sun [19] studied the hydrate slurry transportation process in the bend pipe system. It was found that the maximum volume fraction of hydrate increased faster when the hydrate particle size was larger; and the maximum volume fraction of hydrate was less affected with the increase of flow rate. Xiaonan et al. [20] took the transport of deposited naphthalene in gas pipelines as the research object, and simulated and analyzed the transport law of deposited naphthalene in horizontal bends and other pipe types. The effects of particle size, gas velocity, temperature, and pressure on the transport of deposited naphthalene were mainly investigated at different pipe diameters, bend ratios, and pipe diameter ratios. Tong et al. [21] investigated the transport characteristics of solid-liquid two-phase flow with large particles in a U-bend pipe using simulation analysis. The distribution and motion characteristics of the particles and the flow field in the U-bend were obtained, and it was found that the secondary flow in the bend would also have some influence on the motion and distribution of the particles. Hui et al. [22] applied particle image velocimeter (PIV) to measure the spiral tube flow field of gas-water-sand three-phase flow in a combined bend, and found that the region of uniform distribution of the main flow velocity was concentrated at the bottom of the tube section. In the process of flowing through the bend, the particles will be shifted to the outside of the bend due to centrifugal force; the flow in the ascending section is hindered by gravity, and compared with the flat section at the bottom, the main flow velocity is reduced, the centrifugal force is weakened, and the particles have a lower radial time-averaged velocity. Zhai Yinping [23] used CFDs software to simulate the spiral pipe flow in the 90 ° bend, and studied the change rule of spiral flow intensity. The results show that the tangential flow rate is highest when the tangential inlet angle is 60°, which is conducive to the removal of sedimentary impurities in the bend.
Karino, Kwong, and Goldsmith [24] studied the flow of particles in a curved tube and recorded the flow of particles. The particles were found to spiral in a large main vortex, some particles then pass above or below the main flow into a side pipe and through a side vortex, with a double spiral flow downstream of the side vortex. Yamagata, Ishizuka, and Fujisawa [25] performed numerical simulations of the thinning of the pipe wall at the mouth of a cyclonic elbow. The simulation results show that a cyclonic flow with a certain level of cyclonic intensity produces a spiral motion downstream of the elbow and maintains it for a longer distance than an elbow flow without cyclonic flow. This type of non-axisymmetric flow triggers a strong bias flow at the orifice. Takano et al. [26] investigated the phenomenon of non-axisymmetric mass transfer in an elbow cyclone flow. It was found that the effect of secondary flow combined with cyclonic flow in a long elbow produces non-axisymmetric mass transfer phenomena. Kalpakli and Örlü [27] studied turbulent flow downstream of a 90° bend using 3D particle image velocimetry and compared it with the effect of cyclonic versus non-cyclonic flow on the flow. The flow of carboxymethylcellulose in a curved pipe was studied numerically by Kadyirov [28]. He found that upon entering the bend, the cyclonic flow forms two complex vortices of different sizes, with the largest vortices appearing on the inside of the bend, which are eventually carried to the outside of the bent channel due to the inertial forces generated in the bend pipe. Chang and Lee [29] used particle image velocimetry to study the flow of particles in a 90-degree circular tube with rotational flow, and longitudinal cross-section at different Reynolds numbers. time-averaged velocity, and time-averaged turbulence intensity distribution. Wang et al. [30], Rao et al. [31], and Rao, Wang, and Li [32] conducted a systematic study on the hydrate flow law inside a straight pipe, and derived the hydrate deposition law under different working conditions. Al-Obaidi and Alhamid [33] used numerical analysis to evaluate the heat transfer characteristics and performance of a circular pipe with geometrical dimple patterns. Using CFD codes, we examine the effects of geometrical configurations on the flow and thermal behavior of circular pipes with concavity (dimple) diameters. Al-Obaidi [34] found that the best design of twisted tape in this study by using CFD numerical methodology, combined with TM, the enhancement in heat transfer and hence the overall performance evaluation factor is higher than 1.2. Al-Obaidi et al. [35] have studied based on the commercially available CFD codes on the turbulent flow in three-dimensional tubular pipes. Various concavity (dimple) diameters with corrugation and twisted tape configurations are investigated. The study has shown that perforated geometrical parameters lead to a high fluid mixing and flow perturbation between the pipe core region and the walls, hence better thermal efficiency.
Bend pipe is a commonly used part of long-distance pipelines. It is very important to study the flow law of hydrate particles in the bend pipe, and pipeline design will be optimized. At present, the study of spiral particle flow in gas-phase-based gas transmission pipelines is mostly based on straight pipes. The bend angle is one of the important parameters in the bend of natural gas transmission pipeline, and the bend angle directly affects the flow law of the medium in the tank. Due to the significant difference between the spiral flow and the normal flow, it is necessary to study the flow characteristics of spiral flow in a bend pipe. Therefore, it is meaningful to carry out the research on the flow law of natural gas hydrate particles under the influence factors of bend angle to ensure the safe and stable operation of pipelines.
Numerical Simulation Methods
Physical Model
Geometric Models
The physical model of the pipeline was built using SolidWorks. The inner diameter of the model is set to 25 mm, and the front and tail sections of the pipe are long straight pipes, and the middle section is a bend. The model of the pipe containing a 90° bend is shown in Figure 1.
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At the entrance of the pipeline, a twist tape is installed as a spinning device, the length of which is 0.5 m. The model adopts three different twist rates Y (The ratio of length H of 360° to width D of twist tape per twist) of the tape, which are 6.2, 7.4, and 8.8. In addition, the twist tape takes into account the effect of the wall thickness according to the actual situation, which makes the results reflect the movement of the two phases of the gas and solid phases in the pipeline more realistically and accurately. The results can more realistically and accurately reflect the movement of gas and solid phases in the pipeline. The model diagram of the twist band and the schematic diagram of the twist rate are shown in Figures 2 and 3.
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Boundary Conditions
Velocity inlet conditions were used for the inlet boundary. The gas phase is natural gas and the solid phase is hydrate particles with a particle mass flow rate of 10−6kg/s. The particles are generated continuously at the inlet location. Reynolds number Re = 5000, 10,000, 20,000 is selected for inlet for comparative analysis. Pressure outlet was used for the outlet boundary. Pipe wall conditions are adopted as fixed wall without slip, considering the effect of gravity.
Physical Conditions
In this paper, we mainly simulate the flow as well as the settling of gas-solid two-phase flow under the spiral flow generated by twist tape. This paper mainly simulates the flow as well as the settling of gas-solid two-phase flow under the effect of spiral flow generated by twist tape. The gas phase uses methane (CH4) as the medium. The solid phase uses natural gas hydrate as the medium, and the natural gas hydrate particles are set to be homogeneous spheres with the same particle size. The basic setup is shown in Table 1, where ρg is the gas-phase density, kg·m−3; ρs is the solid-phase density, kg·m−3; and μg is the gas-phase kinetic viscosity, μPa·s. Other basic physical parameters are set according to the standard conditions.
Table 1 Basic parameters table.
| ρg/(kg·m-3) | Ρs/(kg·m-3) | μg/(μPa·s) | Average particle size (mm) |
| 0.717 | 650 | 11.067 | 0.06 |
Grid Division
In the meshing process, the model can be divided into two parts: one part is the region where the twist tape is located, and the other part is the space formed by the twist tape and the inner wall of the pipe (the basin). We adopt the structured mesh method for the twist tape, which has the advantages of high mesh quality, relatively small computational volume and high computational efficiency. For the watershed part, the existence of the twist tape leads to the complex shape and structure of this part of the space. Since the unstructured mesh has better adaptability to the complex model, the unstructured mesh division method is adopted. However, this method is relatively large in calculation. The grid of the twist tape, the quality of the grid and the grid at the bend are shown in Figures 4–6.
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Mathematical Models
Governing Equations
Continuity equation:
Momentum equation:
Turbulent Equations of Motion
The RNG k-Ɛ model is used for turbulence model. Compared with the standard k-Ɛ model, this model has a better performance in flow fields with rotations, bends or vortices. Moreover, it is able to better handle high strain rates and flows with a large degree of streamline curvature like spirals in the swirl-dominated flow mode with high accuracy. In addition, the RNG model provides an analytical formula for the Prandtl number of turbulence and takes into account the effect of low Reynolds number. RNG theory derived the differential equation for turbulent viscosity, allowing the model to better deal with low Reynolds numbers and near-wall flows. The RNG model also provides eddy current correction options to take into account the effects of rotation or eddy currents in the average flow.
In the k-Ɛ model, the equation is as follows,
Discrete Phase Model
The gas-solid two-phase spiral flow was simulated using a discrete phase model (DPM, Discrete phase model). This model is based on the Eulerian-Lagrangian method, where the fluid is treated as a continuous phase and the solid particles are treated as discrete phases, and finally the flow field distribution can be obtained by solving the Navier-Stokes equations. By calculating the coupling between the particles and the fluid, it is possible to track the trajectories of a certain number of particles and describe them in the Eulerian coordinate system. The concentration of solid particles in the discrete phase is typically below 10%.
When the particles are in suspension, the forces on them in the fluid balance each other and the equation of motion of the particles is:
And the combined forces that the particles are subjected to during the flow include the added mass force, inertia force, gravity force, pressure gradient force, trailing force, buoyancy force, and the Saffman lift force. The additional mass force is known from ideal (inviscid) fluid dynamics: the mass that generates this force is equal to half the mass of the fluid that the solid particles displace during the flow. So the additional mass force can be expressed as:
Inertial force refers to when the object has acceleration, the object has the inertia will make the object has the tendency to maintain the original state of motion. This action in the opposite direction of the force is called inertial force, and can be expressed as:
Solid particles are also subjected to their own gravitational force as they move. Since the hydrate particles are treated as uniform spheres in the simulation, this part of the force can be expressed as:
Solid particles in the pipe flow, along the flow direction, there is a pressure gradient, so that the particles are subject to its force. This force is called the pressure gradient force and can be expressed as:
The force exerted by a fluid on a solid in which there is a relative velocity is called the trailing force. The composition of the trailing force is more complex, involving more factors, and it is difficult to express a fixed formula, so the trailing force coefficient was introduced as a concept, which is expressed as:
Therefore, the trailing force can be expressed as the following equation:
Buoyancy refers to the difference (combined force) of the fluid pressure on each surface of an object in a fluid and can be expressed as:
The Saffman force is the lift from low to high velocities due to the velocity difference between the particle and the surrounding fluid when there is a velocity difference between the particle and the surrounding fluid and the velocity gradient of the fluid is perpendicular to the direction of motion of the particle. However, in turbulent flows, its magnitude can often be neglected. This force can be expressed as:
Calculation Method
In this study, a discrete-phase model is selected in the calculations. The pressure-based, implicit solver is used for the transient simulation of gas-solid two-phase three-dimensional spiral flow in gas hydrate pipelines. The turbulence model used in the simulations is the RNG k-Ɛ model. k-Ɛ model expresses the turbulent stress as a function of turbulent viscosity through the introduction of turbulent viscosity. Whereas, the RNG k-Ɛ model is based on the k-Ɛ model with additional terms added to the Ɛ equation. This move improves the adaptability to flow fields where rotation occurs, resulting in higher accuracy of the computational results. The particle motion model is based on the DPM model, and the physical parameters, velocity, and mass flow rate of the injected particles can be changed by parameter settings. The momentum component, turbulent kinetic energy component, and dissipation rate are all in second-order windward interpolation format with second-order accuracy. The pressure and velocity coupling is performed using the SIMPLEC algorithm. The calculation defines that the absolute value of the residuals is less than 1 × 10−6, the convergence condition is reached and the calculation is finished.
Grid-Independent Verification
In this paper, three kinds of grids with the numbers of 608,251, 811,362 and 1,023,746 are selected for the grid-independence verification. In addition to the different number of grids, other parameters are set the same, and the velocity distribution at the center of the cross-section at 8D from the inlet is selected for comparison, and the comparison graph is shown in Figure 7. The r is the radius of the pipe, which is the distance between the center of the pipe and the inner wall of the pipe in the figure. The r is 0 when it's in the center of the pipe, and the distance between the center of the pipeline and the upper wall is positive, and the distance between the center of the pipeline and the lower wall is negative. The 8D is the distance between the selected pipe section and the entrance is eight times the inner diameter of the pipe. From the velocity comparison graph, it can be seen that the three groups of grids have similar velocity trends, indicating that the simulation results can be verified with each other. However, when the number of grids is 608,251, the velocity change error is relatively large compared with the other two groups of grids. This indicates that the grid still has a large deficiency in precision division compared with the other two groups, and the data accuracy is low. The data comparison error derived from the other two sets of grids is relatively small, but considering that the time spent on the 1 million grid is larger than that of 811,362, it is more appropriate to use the grid number of 811,362 for the calculation.
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Model Feasibility Validation
To verify the reliability of the model, a pipe with a length of 1.2 m and an inner diameter of 25 mm was constructed for the experiment. Color sand particles with a particle size of 0.06 mm were used instead of hydrate particles to flow with the gas in the pipe. The experiment was carried out at room temperature and pressure. The experimental results were compared with the simulation results, and the comparison results are shown in the following figure, which is represented as the curve of pressure drop (ΔP) with the change of Reynolds number (Re). The Reynolds number Re is calculated as Re = vdρ/μ, where v is the average velocity of the flow, d is the diameter of the pipe, ρ is the density, and μ is the dynamic viscosity. As can be seen in Figure 8, the error of the results is small in the range of Reynolds number between the experimental and simulated conditions, so the model can be used for the simulation of natural gas transportation containing hydrate particles. In Figure 9, from the verification results of simulation and experiment, the simulation results of tangential velocity are basically consistent with the experimental results, and the asymmetric distribution of tangential velocity in numerical simulation in this paper is also consistent with the experimental results. The numerical value of the axial velocity simulation results is slightly larger than the experimental results, and its error is within an acceptable range.
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Results and Discussion
The spiral flow of a bend pipe with different bend angles is modeled by SolidWorks software, and the flow law of the spiral flow of a gas pipeline is investigated by numerical simulation with the spin-up device as the twist tape. In this chapter, the velocity distribution, turbulence intensity distribution, wall shear, particle motion, and pressure drop distribution are obtained by analyzing the flow under the conditions of twist tape twist rate of 6.2, 7.4, and 8.8 when the bend angle is 45°, 90°, and 135°, respectively.
Analysis of Gas-Phase Flow Pattern of Spiral Flow in Pipeline
Velocity Distribution Pattern
Figure 10 shows the distribution of velocities at different cross-section locations of the pipe under the action of a twist band with a twist rate of 7.4 and a Reynolds number of Re = 20,000. From the figure, it can be seen that under the action of the twist band, the velocity at the cross section of the spinning section is split into two regions. The maximum value of the velocity in the region shows a centrosymmetric distribution and is concentrated on one side of the region. Due to the effect of the twist band, the fluid flows forward in this zone with high speed and spiral shape. From the change of the velocity vector in the figure, it can be found that with the increase of the flow distance, the effect of spiral flow is gradually weakened. Eventually, the region with the highest velocity gradually merges into one region at the center of the pipe. When the fluid enters the bend, due to the resulting centrifugal force, the region of maximum velocity is shifted to the outside of the pipe. As can be seen from the velocity distribution graph at the position where the angle α is 30° to the inlet cross-section of the bend (α30°), the region of maximum velocity concentration is located on the upper outer side of the bend, rather than on the positive outer side. This phenomenon indicates that the effect of spiral flow can reach here, which ensures that the fluid carrying hydrate particles can pass through the bend smoothly so that the particles do not deposit at the pipe wall. Once the fluid exits the bend, it continues to flow along the tail section of the straight pipe, thus weakening the spiral flow effect and the centrifugal effect of the bend, and finally the region of maximum velocity returns to the center of the pipe.
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Figure 11 shows the velocity distribution curves on the centerline of different sections, which can better help to understand the variation of velocity. In the figure, it can be found that in the spiral section, the velocity distribution on the centerline of the cross-section is in the shape of “m” bimodal structure. This is because the pressure gradient is larger in the region of viscous substrate near the wall and on both sides of the twist zone, and the region of maximum velocity due to spiral flow is distributed on both sides of the center. The maximum speed at the section closest to the entrance is 28% higher than at the section furthest. With the increase of the flow distance, the spiral flow is gradually weakened, and the velocity distribution curve becomes a structure with three inconspicuous peaks. In the bend pipe, the centrifugal force under the action of the flow will be extruded to the outside of the pipe, and the combined effect of the spiral flow will lead to the velocity shift. Subsequently, as the fluid continues to flow, the spiral flow effect gradually disappears, resulting in the curve no longer appear obvious peaks and a stable “n” structure.
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Effect of Bend Angle
Figure 12 compares the velocity distributions of bends with different bend angles at the same Reynolds number (Re = 20,000) and the same twist rate (Y = 6.2). From the figure, it can be seen that due to the influence of the bend angle, the velocity distribution produces a more obvious change. Before entering the bend section, due to the gradual attenuation of the spiral flow leads to the extreme value of the velocity being gradually concentrated in the center of the pipe, after entering the bend due to the influence of different bend angles, the change of velocity is also different. It can be clearly seen from the figure, after flowing through the 45° bend, due to the bend section of the greater degree of curvature, which leads to greater obstruction, while the collision is also more intense, so that the speed of the great value of the obvious decline. Finally, in the flow out of the bend section until after the exit, failed to form a high-speed region before entering the bend. Flow through the 90° bend, in the exit of the straight section about the center of the beginning of the formation of a discontinuous high-speed region. After flowing through the 135° bend, due to the bend section of the smaller degree of curvature, the obstruction of the flow is also smaller. Therefore, after flowing out of the bend, the region of maximum velocity is quickly restored.
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Effect of Twist Rate
Figures 13 and 14 compare the velocity distributions at the same Reynolds number (Re = 20,000) and at the same location (outlet of the spinning section) for different twist rates. From Figure 14, it can be seen that when the fluid flows through the twist tape, the spiral flow generated by the action of the twist tape continues to develop along the pipe and keeps the axial velocity in the form of a bimodal parabola. However, due to the different twist rate of the twist tape, resulting in a different range of velocity distribution. With the gradual decrease of the twist rate, the velocity distribution range is wider. From the tangential velocity distribution curve can be seen more clearly that due to the gradual decrease of the twist rate of the twist tape, the spiral flow in the center of the pipe on both sides of the tangential velocity gradually increased. Maximum tangential speed increased by 2 times. In the flow, the generation of tangential velocity can make the hydrate particles have a rotational effect, so that they are less likely to be deposited on the pipe wall. This facilitates the transportation of natural gas pipelines containing hydrate particles.
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Turbulence Intensity Distribution Pattern
Turbulence intensity is a measure of the strength of turbulence, with greater intensity indicating more homogeneous mixing between fluid phases. For uniform isotropic turbulence, the turbulence intensity I can be defined as:
Figure 15a shows the turbulence intensity distribution on the centerline of the cross-section at different locations in the front straight section of the pipe. The curve of the twist tape spinning section shows a “w”-shaped inverted bimodal structure, with higher turbulence intensity at the wall and the center of the twist tape, and lower on both sides of the center. For the section 200 mm away from the entrance, the turbulence intensity in the center of the pipeline is 0.35, and that in the section 8 mm away from the center of the pipeline is 0.18, and the former is about twice as strong as the latter. The pulsation velocity is zero at the wall, but increases rapidly and reaches the maximum value in the region close to the wall, and then decreases again. Therefore, in the cross-section of the spinning section of the twist zone, after the pipe wall—twist zone—pipe wall, the root mean square value of pulsation velocity firstly reaches the peak rapidly and then decreases—reaches the valley and then rises to reach a new peak and then decreases to the valley—rises and reaches the peak value. After the separation of the twist tape, due to the absence of the twist tape perturbation, the pulsation velocity only in the two sides of the wall to reach the peak and in the center of the pipe to reach the valley, resulting in the turbulence intensity distribution curve gradually become “v” shape. In the pipe shown in Figure 15b bend section, due to the fluid by the centrifugal force and the role of the spiral flow, resulting in a certain shift in the valley value, but does not affect the overall shape of the curve. Just into the bend section when the valley value is low, into the bend, the role of centrifugal force brought about by the secondary flow to a certain extent increases the intensity of turbulence. However, with the increase of the flow distance, the spiral flow gradually attenuates and the turbulence intensity gradually decreases. The distribution of turbulence intensity in the straight pipe section of the tail section is similar to the shape of the curve in the bend, and due to the gradual weakening of the centrifugal force effect of the bend, the closer to the exit, the lower the degree of offset of the curve, as shown in Figure 15c.
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Wall Shear Law
Wall shear is the force tangent to the cross section at the wall. The shear force is an important factor in ensuring that hydrate particles are not deposited by gravity, but move in a spiral with the fluid. When the gas carrying hydrate particles is transported through the twist tape, the hydrate particles will be driven by the spiral flow of the gas to do spiral flow. When just passing through the twist tape section, due to the strong spiral flow generated by the disturbance of the twist tape, the gas carries hydrate particles at a higher speed, which ultimately produces a large shear force on the pipe wall and the surface of the twist tape. As the fluid flows through the twist tape, the spiral flow gradually attenuates, and the shear force will gradually become smaller. When the gas flows through the elbow, the centrifugal effect of particles will be concentrated to the outside of the pipe, resulting in an increase in the range of shear force in this part of the wall. When the fluid gradually flows through the elbow, the particle distribution will gradually become uniform, and the distribution of the shear force on the wall is also gradually uniform, as shown in Figure 16.
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Figure 17 shows the wall shear distribution of pipes with different bend angles at the exit position of the bend. From the figure, it can be seen that when the spiral flow through the bend, taking into account the attenuation of the spiral flow and the centrifugal effect produced by the bend, the wall shear distribution is more uniform. Therefore, appropriate extension of the twist tape and other methods can be used to maintain the strength of the spiral flow, so that the gas can completely carry particles flow through the pipe.
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Analysis of Solid-Phase Motion in Pipe Spiral Flow
Due to the difference in twist rate and bend angle of the twist tape, the flow pattern of the gas phase will change, resulting in a change in its movement carrying solid phase particles.
Effect of Twist Rate
Figure 18 below shows the particle trajectory of a bend pipe with the same bend angle under the same flow parameters and different twist rates. Due to the effect of the twist band, the particles spiral rapidly with the gas in the spinning section. After the particles flow through the twist band, they can still maintain the spiral flow and continue to flow. When the twist rate of the twist band in the spinning section is small, most of the particles do not gather at the outer wall of the pipe under gravity and centrifugal force when passing through the elbow, but flow in a fluctuating manner. This phenomenon indicates that the strength of the spiral flow can be maintained up to this region, which is favorable to the pipeline transportation of natural gas containing hydrate particles. Moreover, it can be clearly seen from the figure that with the increase of twist rate, the strength of spiral flow gradually decreases; in the flow through the bend, the particles are weaker by the spiral flow; in the flow of the particles of the trajectory line is curved, and the spiral flow pattern basically disappeared. Therefore, to increase the strength of the spiral flow, to ensure that the particles are transported smoothly in the form of spiral flow, it should be appropriate to use a smaller twist rate of the twist tape as a spinning device.
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Effect of Bend Angle
The different bend angles will also have an effect on the movement of particles. Figure 19 below shows the distribution of particles under the same flow conditions, after the same twisting rate of the twist tape, at the same time under the action of different bend angle bends. As the bend angle of the bend section gradually becomes smaller, the particles due to the collision with the pipe wall intensifies, its velocity loss is larger, resulting in particles in the flow through the bend due to the smaller the angle of the bend and the centrifugal effect produced by the obvious. The smaller the angle of the bend, the more obvious the centrifugal effect is, which ultimately makes the particles more likely to concentrate in the outer wall of the pipe to produce the aggregation effect. And from the figure can also be seen, with the reduction of the bend angle, the speed of the particles also have obvious changes. When the particles flow through the pipe, the particles speed is obviously lower along the outside of the pipe wall, and when the bend angle is larger, the particles in the flow through the speed is reduced less, the speed recovery is also faster. The faster flow speed is the key factor to ensure that the particles are transported in a spiral flow pattern smoothly. The angle of the bend is larger, the safe transportation of particles is more conducive.
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Pipeline Spiral Flow Pressure Drop Distribution Law
Pressure drop is an important parameter reflecting the flow condition in pipeline. In the actual production operation, the monitoring, calculation and prediction of pipeline pressure have been highly valued, and only by obtaining correct and realistic data can we provide a guarantee for pipeline design. However, after reviewing the literature, it is found that most of the current research is focused on long straight pipes, and less attention has been paid to the pressure drop of spiral flow containing bends with twist bands. Therefore, the research in this area can provide theoretical guidance for the future of the actual production operation.
Effect of Bend Angle
To study the effect of bend angle on the flow pressure drop, the pressure drop at the bend pipe segments with the same length and different bend angles were counted. The statistics are shown in Table 2 below. The bend angles were chosen as 45°, 90°, and 135°, the flow parameters were kept the same, and the pipe types were the same except for the bend angles. The final results show that the pressure drop of the 45° bend is the largest, followed by the 90° bend and the 135° bend is the smallest. When the angle of the bend section becomes small, the collision frequency between the inner wall of the pipe and the natural gas flow carrying hydrate particles will increase; and the angle of the bend section is smaller, the change of the velocity direction of the particles in the flow will be more intense; the more likely to occur particle aggregation and clogging, the velocity of the particles will be rapidly decreased and then gradually recovered, which leads to a more serious loss of velocity. According to Darcy's formula, the pressure drop is positively related to the square of the velocity, so the smaller the angle of the bend, the greater the pressure drop. Unit pressure drop loss increased by 13%.
Table 2 Statistical table of pressure drop of elbow at different bend angles.
| Bend angle | Pipe inner diameter (mm) | Starting torque | Gas phase velocity (m/s) | Pressure drop (Pa) | Unit pressure drop (Pa/m) |
| 45° | 25 | 6.2 | 13 | 38.13 | 76.26 |
| 90° | 25 | 6.2 | 13 | 37.56 | 75.12 |
| 135° | 25 | 6.2 | 13 | 33.70 | 67.40 |
Effect of Twist Rate
As shown in Figure 20 is a graph of pressure variation in the twist zone section at different twist rates. From the figure, it can be seen that the pressure drops continuously when the natural gas carrying hydrate particles flows through the twist zone. And the degree of pressure drop decreases gradually slows down as the twist rate becomes larger. With the increase of torsion, the pressure drop decreased by 52%. The reason for this phenomenon is that when the fluid flows into the existence of the twist zone, increasing the shape resistance pressure drop in the flow; and the twist is smaller, the twist zone under the same total length will be more dense, the resistance is also larger, also increase the friction pressure drop, resulting in a greater magnitude of the pressure drop. In addition, because the twist is smaller, resulting in a stronger spiral flow effect, the tangential is greater, the relative loss of axial velocity is greater, and the pressure drop is also greater. The relationship between twist rate and pressure drop is shown in Figure 21.
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Figure 22 below shows the relationship between the pressure drop in the bend section and the angle of the bend and the twist rate. As can be seen from the previous section, the angle of the bend is larger, the pressure drop is smaller. As can be seen from the figure, when the fluid flows through the twist tape into the bend, the effect of the twist tape twist rate on the pressure drop in the bend section continues; where the twist rate is larger, the pressure drop is smaller in the bend section. This is because the role of the fluid in the twist tape for spiral flow into the elbow, it also maintains a certain spiral flow intensity; due to the tangential force of the role of the fluid and the pipeline boundary layer between the friction, ultimately resulting in a pressure loss. The twist rate is smaller, and the intensity of the resulting spiral is greater, the strength of the spiral is stronger, the tangential is greater, the loss of axial velocity is relatively greater, resulting in a greater pressure drop.
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Variation of Resistance Coefficients of Bends
It is generally believed that the pressure loss of fluid flow through the bend is mainly caused by friction, separation of flow in the bend and secondary flow. However, given the flow process due to the role of particles and the influence of the spiral flow, the factors affecting the resistance coefficient of the elbow will increase, the elbow part of the resistance coefficient of the formula is shown below:
Figure 23 below shows the relationship between the resistance coefficient of the bend and the bend angle and twist rate. As can be seen from the figure, with the increase in the angle of the bend, the resistance coefficient of the bend part of the resistance coefficient gradually decreases; with the twist rate increases, the resistance coefficient gradually decreases. The reason for this phenomenon is due to the existence of the twist band, the flow process of local resistance is larger; and the twist rate is smaller, the resistance is larger, resulting in an increase in the pressure drop when the fluid flows through. As the twist rate decreases, the tangential velocity in the flow through the elbow gradually increases, which increases the friction between the fluid and the wall and increases the pressure drop. From the above, it can be seen that when the angle of the bend increases, the velocity decay slows down and the velocity recovers faster as the flow passes through the bend. From the formula for the drag coefficient, it can be seen that the pressure drop is smaller and the velocity is greater, the drag coefficient of the bend portion of the pipe is smaller. So the larger the twist rate, the larger the angle of the bend pipe, and the drag coefficient is smaller. However, from the simulation results found that the resistance coefficient brought about by the reduction of the twist tape twist rate changes in the range of 0.001 ~ 0.015 interval, the change is relatively small; and the change of the twist rate of the spiral flow of tangential velocity changes have a greater impact. Therefore, in the selection of the twist tape twist rate, should also be combined with the specific circumstances of the accounting, to ensure that the flow process of the fluid with a lower coefficient of resistance and higher spiral flow intensity of safe and smooth transportation.
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Conclusions
(1) The bend angle has a more pronounced effect on the velocity distribution. As the angle of the bend section decreases and the collision between the gas and the inner wall of the tube intensifies, it causes the velocity to decay rapidly. Ultimately, the region of extreme velocity cannot be recovered. The reduction of the twist rate of the twist tape can make the axial velocity to maintain the bimodal parabolic form. This broadens the velocity distribution range, increases the tangential velocity, improves the strength of the spiral flow, and facilitates the transportation of natural gas pipelines containing hydrate particles. In the spiral flow due to the viscous substrate near the wall, the regional pressure gradient is larger, resulting in the velocity maximum region distributed in the center of the two sides, and the velocity distribution on the centerline of the cross-section is “m” shaped bimodal structure. The maximum speed at the section closest to the entrance is 28% higher than at the section farthest. Maximum tangential speed increased by 2 times. With the increase of the flow distance, the spiral flow is gradually weakened. And under the action of centrifugal force of the bend tube, the spiral flow disappears, and the velocity distribution curve no longer appears obvious peaks, showing a stable “n” shape structure.
(2) In the twist tape section of the pipe, the pulsation velocity increases rapidly and reaches a maximum value in the region close to the wall, and then decreases. Therefore, the turbulence intensity curve at this time is a “w”-shaped inverted bimodal structure. For the section 200 mm away from the entrance, the turbulence intensity in the center of the pipeline is 0.35, and that in the section 8 mm away from the center of the pipeline is 0.18, and the former is about twice as strong as the latter. After flowing through the twist tape, the pulsation velocity only reaches the peak value on both sides of the wall, and reaches the valley value at the center of the pipe. At this time, the turbulence intensity distribution curve gradually becomes “v” shape. After entering the bend, the fluid is subjected to centrifugal force and the role of spiral flow, resulting in a certain shift in the valley value. The centrifugal force brings the secondary flow to increase the turbulence intensity to a certain extent. However, with the gradual attenuation of the spiral flow, the turbulence intensity gradually decreases; and the closer to the outlet, the lower the degree of offset of the curve. When the twist rate of the twist tape is smaller, the strength of the spiral flow is greater, the particle dispersion effect is better, then it is less likely to occur aggregation. When the angle of the bend is larger, it is relatively flat, and the speed is recovered faster. This is more conducive to the maintenance of particle velocity to ensure safe transportation.
(3) When the twist rate of the twist tape in the pipe is smaller, the resistance is greater; and the smaller twist rate of the twist tape produces a stronger spiral flow effect, the tangential velocity is greater, and the relative loss of axial velocity is greater. That is why the pressure drop increases as the twist rate decreases. When the angle of the bend section becomes smaller, the collision between the pipe wall and the natural gas is more frequent; and the angle is smaller, the change in the direction of the velocity of the particles will be more drastic. The velocity of the particles will decrease rapidly and then recover gradually, resulting in serious velocity loss and affecting the change of pressure drop. Therefore, the angle of the bend is smaller, the pressure drop is larger. Unit pressure drop loss increased by 13%. The angle of the bend is larger, the twist rate is larger, and the resistance coefficient of the bend part is smaller. However, the resistance coefficient increase brought about by the reduction of twist rate is within the range of 0.001 ~ 0.015, which will significantly reduce the spiral flow strength. With the increase of torsion, the pressure drop decreased by 52%. Therefore, it should be combined with the specific circumstances of the calculation to select the appropriate twist rate of the twist tape. The centrifugal force of the bend and the effect of the spiral flow are superimposed so that the region of maximum velocity in the bend is located on the outside of the bend. This ensures that the fluid carrying hydrate particles pass smoothly through the bend and that the particles are not deposited on the pipe wall.
In this paper, the laws of spiral flow in curved tubes with different bending angles are studied by numerical simulation, and the characteristics of velocity distribution, turbulent intensity distribution, wall shear distribution, particle movement and pressure drop distribution are analyzed and studied. Small torsion belt and large bending angle can improve the permeability of hydrate particles inside the bending pipe, and provide a guarantee for the safe operation of gas transmission pipeline.
Nomenclature
- CD
- trailing force coefficient
- D
- twist tape width[m]
- Fa
- buoyancy[kg·m/s²]
- Fi
- inertial force[kg·m/s²]
- Fp
- pressure gradient force[kg·m/s²]
- Fr
- trailing force[kg·m/s²]
- Fs
- Saffman force[kg·m/s²]
- Fvm
- additional mass force[kg·m/s²]
- G
- gravitational force[kg·m/s²]
- Gb
- turbulent energy production term[kg·m/s²]
- Gk
- buoyancy generating term[kg·m/s²]
- H
- twist tape length[m]
- mi
- mass of particles[kg]
- r
- pipe radius[m]
- custom parameters
- t
- time[s]
- Y
- twist tape
- YM
- fluctuations due to diffusion in a compressible flow
- P
- static pressure[Pa]
- Re
- relative Reynolds number
- particle velocity[m/s]
- u, v, w
- speed[m/s]
- ρ
- gas density[kg/m3]
- gas-phase density [kg/m3]
- Viscous stress tensor
- ,
- turbulent Platt number of k and ε
- gas-phase kinetic viscosity[μPa·s]
- particle velocity[μPa·s]
- effective viscosity[μPa·s]
Acknowledgments
This work was supported by the Project of Emission Peak and Carbon Neutrality of Jiangsu Province (No. BE2022001-5), the General Project of Natural Science Research in Jiangsu Universities (No.22KJB440002), Quanzhou Science and Technology Planning Project (No.2022N045), Jiangsu Provincial Graduate Research and Innovation Program Project (No. KYCX24_3245), and Jiangsu Provincial Graduate Practice and Innovation Program Project (No. SJCX24_1682).
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