Computational fluid dynamic analysis of hydrogen‐injected natural gas for mixing and transportation behaviors in pipeline structures

The transportation of hydrogen is a weak link in the large‐scale development of the hydrogen energy industry. Injecting hydrogen into the natural gas pipeline network for transportation is an efficient way to achieve the large‐scale, long‐distance, and low‐cost transportation of hydrogen. Hydrogen can lead to hydrogen embrittlement in natural gas pipelines and cause safety incidents if hydrogen and natural gas are not mixed uniformly. Therefore, it is necessary to study the blending process and blending uniformity of hydrogen and natural gas. In this study, a three‐dimensional model of the hydrogen‐injected natural gas pipeline was constructed. The effects of hydrogen injection inlet and turbulator configuration on the mixing process of hydrogen and natural gas were investigated using a computational fluid dynamics approach. The results show that increasing the number of hydrogen injection inlets shortens the distance L98% of uniform mixing of hydrogen and natural gas. Increasing the radial distance r from the initial hydrogen mixing positions to the center of the pipeline will shorten the distance for uniform gas mixing in the pipeline. The addition of turbulator configurations in the pipeline significantly reduces the distance to uniform gas mixing. Changing the distance Lturb from the turbulator to the initial mixing position further shortens the distance between hydrogen and natural gas mixing uniformly. The results of this study provide a reference for the structural design of the hydrogen–natural gas mixing pipeline and the gas distribution state during the mixing process.


| INTRODUCTION
The increase in fossil energy consumption has led to a global ecological crisis. 1 It is imperative to improve the energy mix and replace fossil fuels with noncarbon fuels to achieve carbon neutrality. The Paris Agreement provides direction and plans for a carbon-free future and carbon neutrality. China, 2 the United States, 3 the European Union, 4 and the Intergovernmental Panel on Climate Change 5 are promoting the development of global renewable energy to reduce carbon emissions. Hydrogen energy is a potential energy carrier for the "power-to-gas" conversion of renewable energy sources and a bridge between fossil and renewable energy sources. 6 It is expected that hydrogen will account for more than 19% of final energy demand by 2050. 7 However, the higher transportation cost of hydrogen energy leading to lower utilization is currently an important factor limiting its development. According to the analysis, the transportation cost of hydrogen accounts for 30%-40% of the final hydrogen selling price. 8 The use of pipelines for the transport of pure hydrogen allows for low transport costs and high speed, allowing for the massive transport of hydrogen. However, each mile of a pure hydrogen pipeline cost is three times more expensive to build than a natural gas pipeline. 9 The current global mileage of natural gas pipelines in service has exceeded 1.35 × 10 6 km. The total mileage of trunk gas pipelines in China has reached 1.16 × 10 5 km, 10 accounting for 8.6% of the global total. It provides the basis for the large-scale and long-distance pipeline network transportation and distribution of hydrogen. Mixing hydrogen with natural gas in a certain volume fraction and using existing natural gas pipelines to transport hydrogen is the best method. 11 In 2017, the "HyDeploy" project in the United Kingdom was put into operation, enabling the small-scale provision of hydrogen-blended natural gas. 12 In 2019, Germany's Avacon increased the volume fraction of hydrogen in the natural gas pipeline network to 20%. The 2021 project "Key Technology Research and Application Demonstration of Natural Gas Hydrogen Mixing," in which the State Power Investment Group is involved, is expected to deliver 4.4 × 10 6 m 3 of hydrogen to Zhangjiakou city annually. These small-scale demonstration projects provide technical and practical experience for the largescale application of hydrogen-injected natural gas.
However, injecting hydrogen into natural gas changes the flow state and thermodynamic properties of the original gas in the pipeline and affects the gas delivery state. Nonuniform mixing of hydrogen and natural gas in the pipeline increases the probability of hydrogen embrittlement. The effect of hydrogen embrittlement on the whole equipment of the hydrogen mixing natural gas transmission system, such as compressors, 13 pipelines, 14 welds, 15 valves, 16 storage, 17 and so on. Eames et al. 18 investigated the effect of T-joint geometry (diameter ratio, direction of hydrogen injection) and hydrogen injection rate on the mixing process of natural gas and hydrogen. The results showed that high hydrogen concentration on the pipeline wall significantly increases the risk of hydrogen embrittlement and pipeline rupture. Hydrogen injection from the bottom side of the pipeline facilitates hydrogen and natural gas mixing. Baowei and colleagues 19 investigated the mixing distribution of hydrogen and natural gas in the chamber with low-, medium-, and highpressure injection modes. Villuendas et al. 20 used CFD methods to simulate the mixing and transport behavior of natural gas and hydrogen. The gases were well mixed at 20D-30D pipe lengths at the mixing station. The transport behavior of the gas in pipes of different diameters was also investigated. Zhou et al. 21 took 33 h for the ratio to regain stability in the pipeline network by changing the hydrogen mixing ratio (HMR) at the inlet of the pipeline in a natural gas pipeline system. The propagation rate of the hydrogen concentration is much lower than the pressure and flow rate. Kuczyński et al. 22 concluded that the content of hydrogen should not exceed 15%-20% for long-distance transport. Dz et al. 23 studied the relatively small energy loss to the natural gas pipeline system caused by the input of hydrogen mixed with natural gas at the outlet location of the natural gas pipeline network. Kong et al. 24 studied the effect of the structure of a Kenics static mixer (KSM) static mixer on the mixing process of hydrogen and natural gas. The distribution and number of mixer arrangements were optimized based on the results of the study. Dell'Isola et al. 25 injected hydrogen into natural gas and analyzed the effect of hydrogen injection on the flow rate, relative density, specific heat, and speed of sound of the gas. Li et al. 26 investigated the physical properties of hydrogen mixed with natural gas. To ensure the stability of the physical properties of the mixtures of hydrogen-natural gas, the HMR should be controlled within 30%. Guandalini et al. 27 studied the effect of hydrogen injection on the components, density, velocity of fluid, and pressure distribution of natural gas. Hydrogen injection enhances the gas perturbation in the pipeline network and the density of the gas decreases. The effect of hydrogen injection on the pressure drops in the pipeline network is negligible (the difference is less than 0.1%). Abd et al. 28 studied the effect of different HMRs on the transport properties of natural gas. Hydrogen mixing reduces the density of natural gas; a 10% HMR records an 11.78% reduction in the density of natural gas. Hydrogen mixing increases the pressure loss on the transport pipeline; a 10% HMR leads to a 5.39% increase in the pressure drop of the gas. Zhang et al. 29 investigated the effect of different HMRs on the natural gas transmission process. The results showed that hydrogen mixing can reduce the frictional resistance of the pipeline. The higher the HMR, the higher the volume flow rate at the outlet. The pressure drop of the pipeline increases with the increase of the HMR. Liu et al. 30 compared and analyzed the mixing effect of KSM-type static mixer, S-shaped static mixer, orifice plate static mixer, and venturi static mixer on different gas sources of natural gas. The best mixing effect had been found in the KSM-type static mixer. Kong et al. 31 showed that the addition of an SK-type static mixer in the manifold can significantly reduce the distance of uniform gas mixing. The addition of a mixer improved the mixing efficiency of natural gas. Most studies on hydrogen mixing with natural gas have focused on the effects of hydrogen mixing on gas properties and transport processes. There is a lack of studies on the mixing process and mixing uniformity of hydrogen and natural gas.
The physical properties of natural gas and hydrogen are different, and the mixing process is complicated. Further study of the mixing process and mixing uniformity of hydrogen and natural gas can provide data reference and guidance for natural gas-hydrogen mixing projects. The number of hydrogen inlets, the initial mixing positions of hydrogen, and the installation positions of turbulators in the pipeline were changed. The effect of the pipeline structure on the mixing process and mixing uniformity of hydrogen and natural gas was investigated. Shortening the distance for uniform mixing of hydrogen and natural gas can reduce hydrogen aggregation during hydrogenblended natural gas delivery.

| GEOMETRIC MODEL
To study the influence of pipeline structure on the mixing process of hydrogen and natural gas, two types of mixing pipeline models are constructed. The structural configuration of the pipeline is shown in Figure 1. Type A adjusts the number of hydrogen injection inlets (NHIIs) and the initial mixing positions of hydrogen; Type B is to add turbulators on the basis of Type A and adjusts its installation position accordingly. Hydrogen is injected into the natural gas pipeline through a 90°bend pipeline. When the NHII = 1, the initial mixing position of hydrogen is set at the center of F I G U R E 1 Hydrogen injection pipeline structure configuration. NHII, number of hydrogen injection inlet. the natural gas pipeline; When NHII ≥ 2, the initial mixing positions of the hydrogen are uniformly distributed in a circle around the center of the pipeline. The initial mixing position of the hydrogen is adjusted by adjusting the radial distance r from the hydrogen pipeline to the center of the natural gas pipeline. Each hydrogen injection port corresponds to a circular cylinder, and the three turbulator models designed are shown in Type B in Figure 1. The installation position of the turbulators is adjusted by changing the distance L turb from the turbulator to the initial mixing position. The hydrogen injection into the pipeline is mainly concentrated in the area 0-150 mm from the initial mixing position. The turbulator was adjusted to vary between L turb = 50 and L turb = 150 mm from the initial mixing position. To mix the hydrogen and natural gas sufficiently, the length of the pipeline is set to 22D, where D is the diameter of the natural gas pipeline. The diameter of the single hydrogen injection inlet is d 1 = 80 mm, and the diameter of the turbulator is D 1 = 40 mm. The HMR in the pipeline is controlled by adjusting the diameter d of the hydrogen injection inlet. The diameter of the hydrogen injection inlet is d n = (1/n) 1/2 × d 1 , where n is the NHIIs. L mix indicates the mixing distance between hydrogen and natural gas in the pipeline; L 98% represents the distance to 98% uniformity of mixing of hydrogen and natural gas in the pipeline. The specific parameters of the pipeline structures are shown in Table 1. A total of 21 monitoring cross-sections were taken at 1D millimeter intervals in the pipeline from the initial mixing position. Thirty-three monitoring points are set up within each cross-section, which are uniformly distributed around the center of the pipe (the black dots in the section are the monitoring points).

| Mathematical equation
When hydrogen and natural gas are mixed, the volume of the mixed gas is the sum of the volumes of hydrogen and natural gas. The calculation formula of the density ρ of the mixed hydrogen and natural gas is where ρ is the density of mixed gas, kg/m 3 ; P op is the working pressure of the mixed hydrogen gas, Pa; P is the local relative pressure with respect to P op , Pa; R is the molar gas constant, J/(mol K); T is the gas temperature, K; Y i is the mass fraction of gas i, and M i is the relative molecular mass of gas i. The compression factor z of the gas mixture is calculated as where z is the compression factor of the gas mixture, Z c is the critical compression factor, P r is the comparison pressure, V r is the comparison volume, and T r is the comparison temperature. The viscosity of the gas mixture μ is calculated as where μ i is the kinetic viscosity of gas i, N s/m 2 ; and x i is the volume fraction of gas i. Component transport equation: where D i is the diffusion coefficient of component i, s/m 2 ; and  u is the vector velocity of the fluid, m/s. The distribution of hydrogen and natural gas in the pipeline is predicted by solving the component transport equation.

| 2915
The flow of mixed hydrogen and natural gas in the pipeline follows the continuity equation, momentum equation, and energy equation. The expression is as follows: The continuity equation is the equation of mass conservation. Any fluid problem must satisfy the law of conservation of mass. The sum of the masses flowing out per unit time is equal to the masses reduced within the control body due to density change at the same time interval. The velocity and density within the flow are solved by the continuity equation. Continuity equation: where x is the distance from the initial mixing position, m; v i , v j , and v k are the components of the velocity vector in the x, y, and z directions. The flow velocity and turbulence intensity in the fluid domain are predicted analytically by solving the conservation of momentum equation. Momentum conservation equation: where v v v ,¯, andī j k are the fluid velocity vectors, m/s; v i , v j , and v k are the components of velocity in the x, y, and z directions, m/s; S i , S j , and S k are the generalized source terms for momentum conservation, N/m 3 , where F x , F y , and F z are the components of the volume force in the x, y, and z directions, and λ is the second viscosity. The mixed transport of hydrogen and natural gas obeys the equation of conservation of energy where k is the heat transfer coefficient of the gas, w/(m 2 k); c p is the specific heat capacity of the gas mixture, J/(kg K); T is the temperature, K; S T is the internal heat source of the fluid, w/m 3 .
The velocity values and HMRs of the gases at different positions in the pipeline are counted through 33 monitoring points. The velocity COV 32 is the ratio of the standard deviation to the mean value, which reflects the flow distribution of the mixed gases in the pipeline, and the formula is where n is the number of monitoring points selected in the cross-section, v i is the velocity of the monitoring point, m/s; v is the average value of the velocity over the monitored section, m/s. The mixing uniformity is used to evaluate the mixing of hydrogen and natural gas in the pipeline. The greater the mixing uniformity, the more uniformly the hydrogen and natural gas are mixed. Celik et al. 33 were the first to propose the use of mixing uniformity (mixing index) to evaluate the degree of mixing of a mixture. Montante et al. 34 and Zhuang et al. 35 used a mixing uniformity greater than 95% to determine whether the gas in the vessel was well mixed. With reference to industry standards, it is considered that the gas is well mixed with a uniformity of mixing U ≥ 95%. Therefore, the mixing uniformity U ≥ 98% is used in this study to determine whether the hydrogen and natural gas are uniformly mixed in the pipeline. The gas mixing uniformity U is calculated by the following formula: where c i the HMR at the monitoring points, and c is the average value of the HMR at the monitoring crosssections.

| Boundary conditions
Methane accounts for more than 90% of all components of natural gas. 36 As far as the work in this manuscript is concerned, it is possible to use methane instead of natural gas for the analytical study. Methane is injected at the natural gas inlet. The inlet of hydrogen and natural gas was set to the velocity inlet, and the outlet was set to the outlet flow boundary. The natural gas pipeline inlet velocity is set to 8 m/s (flow rate: 1891.0 m 3 /h). The HMR was adjusted by controlling the velocity of the hydrogen inlet. The specific values are shown in Table 2. The initial turbulence parameters at the inlet of the natural gas pipeline and the hydrogen injection pipeline are the same. The inlet turbulence intensity is set to 5% and the turbulence viscosity ratio is set to 10. The turbulence intensity of the return flow at the outlet is 5% and the turbulence viscosity ratio of the return flow is 10.
The turbulator surface and natural gas pipeline walls were set to be smooth, adiabatic, and with nonslip standard walls. The initial temperature of the wall is set to 300 K. The heat flux of the wall and the heat exchange coefficient of the wall are both 0. The temperature of both hydrogen and natural gas is set to 300 K. During the mixing of hydrogen and natural gas, the flow field of the gas in the pipeline changes in a complex way. Simulation of the mixing process is computationally complex and large. The geometry of the model and the computed fluid domain have mirror symmetry. Setting the boundary of the natural gas pipeline as a symmetric wall boundary can reduce the computational effort. Using the component transport model, the calculation was solved using the Simplec algorithm. The pipeline was set up and filled with methane before hydrogen injection. Hybrid initialization was used to assign initial values to the computed fields before starting the calculation. A sufficient number of iterations was set to bring the calculation to a steady state.
The effects of four turbulence models (standard k−ε model, renormalization group k-epsilon model, standard k−ω model, and shear stress transfer k-omega model) on the simulation results are investigated with other boundary conditions unchanged. Taking the model with HMR = 10% and NHII = 2 as an example, Table 3 presents simulation results obtained using different turbulence models. From Table 3, it can be seen that the errors of the simulated values of the HMR at the outlet position are less than 5% using different turbulence models. When utilizing the standard k-ε model, the HMR at the pipeline outlet is 9.87%, exhibiting a deviation of merely 1.3% from theoretical values and thus possessing minimal error. The turbulence model is a standard k-ε turbulence model suitable for gas mixing calculations, which reduces the computational effort while maintaining the accuracy of the calculation. Consequently, the standard k-ε model is chosen as the final turbulence model.

| Mesh irrelevance testing
The quantity and quality of mesh partitioning are crucial to the simulation calculation process. The mesh division not only determines the accuracy and convergence of the calculation results but also places a demand on the hardware performance of the computer. There will be errors in the simulation, resulting in a slightly lower HMR at the exit position compared to the theoretical calculation value. The accuracy of the calculation, the turbulence model, and the solution algorithm will cause errors. But the quality of mesh division is the main cause of error. The tetrahedral and hexahedral meshing methods were chosen for meshing the calculation area. The walls of the model and the area around the turbulent flow device were locally meshed to provide a relatively accurate calculation of the flow processes at the boundaries. The mesh division of the pipeline is shown in Figure 2.
It is generally believed that the smaller the mesh size and the more meshes there are, the more accurate the T A B L E 2 Boundary condition parameters.

Name
Numerical value results of simulation calculations. However, an excessive number of meshes leads to little improvement in computational accuracy and also reduces the efficiency of the computer. It is important to balance the computational accuracy with the number of meshes. A pipeline model with a 10% HMR was chosen as a representative. The mesh irrelevance was verified for three meshing methods: sparse, medium, and dense. The results are shown in Table 4. Increasing the number of meshes has little effect on the outlet HMR. The error between the simulated and theoretical values of the HMR is within 1.5%, which is in accordance with the standard. The evaluation coefficients are in the range of 0-1. The closer the skew factor is to 0, the better the quality of the mesh. The closer the quality factor is to 1, the higher the quality of the mesh. The skewness and mesh quality were evaluated for the meshes. All three specifications met the requirements, and the mesh irrelevance was verified. In this study, meshes of medium size were selected. For the model of Type A, the mesh size was set to 20 mm. For the model of Type B, the mesh size was set to 10 mm, and local mesh encryption was carried out on the turbulent part.

| Effect of hydrogen injection inlet configuration on mixing uniformity
The hydrogen and natural gas in the pipeline were subjected to turbulence and concentration differences for diffusion and eventual uniform mixing. In the mixing process of hydrogen and natural gas, the pipeline structure is the main factor that affects the mixing process. Changing the number of hydrogen inlets and the initial mixing positions of hydrogen, the HMRs were 5% (A), 10% (B), 20% (C), and 30% (D). The variation of the distance L 98% for uniform mixing of hydrogen and natural gas in the pipeline is shown in Figure 3. When the initial mixing positions of hydrogen are close to the center of the pipeline (r = 40 and 70 mm), the distance L 98% of gas mixing uniformly in the pipeline decreases and then increases with the increase of the number of hydrogen inlets. As the NHII increases, the effect of mixing with multiple inlets is similar to that of blending with a single inlet. Therefore, by continuing to increase the NHIIs, the distance L 98% for uniform mixing of hydrogen and natural gas increases instead. When the initial mixing positions of hydrogen are far from the center of the pipeline (r = 90 and 110 mm), the distance of gas mixing uniformity first decreases and then gradually smooths out with the increase of the number of hydrogen inlets. Increasing the proportion of blended hydrogen, the distance L 98% required for uniform blending of hydrogen and natural gas increases. In general, the distance L 98% for uniform gas mixing is effectively reduced by appropriately increasing the number of hydrogen inlets compared to single-inlet hydrogen injection. The initial mixing position of hydrogen is an important factor affecting the mixing process of hydrogen and natural gas in the pipeline. The variation of the distance of gas mixing uniformly in the pipeline at different inlets of hydrogen injection for r = 40, 70, 90, and 110 mm is investigated. At r = 40 mm, the distance for uniform gas mixing in the pipeline increases when the number of hydrogen inlets exceeds five or six.
Increasing the radial distance r can shorten the distance of uniform mixing of hydrogen and natural gas in the pipeline. The radial distance r increases and the distance between the hydrogen pipe to the wall of the natural gas pipeline becomes smaller. The injection of hydrogen into the natural gas pipeline increases the probability of contact between the hydrogen and the wall of the pipeline. The collision of hydrogen with the wall of the natural gas pipeline increases the disturbance of gas in the pipeline. The increased perturbation facilitates faster and more uniform mixing of hydrogen and natural gas. Therefore, with the increase of radial distance r, the distance between hydrogen and natural gas mixing uniformly in the pipeline gradually decreases. The shortest distance to achieve uniform mixing of hydrogen and natural gas in the pipeline is achieved when the radial distance r = 110 mm. At four HMRs, the distance to achieve uniform mixing of hydrogen and natural gas in the pipeline is relatively short for NHII = 8 and the radial distance r = 110 mm. With the increase of HMR, the radial distance r becomes the main factor affecting the distance L 98% of gas mixing uniformity. Selecting a suitable NHII and increasing the distance r from the hydrogen pipeline to the center of the natural gas pipeline can be very effective in shortening the distance between hydrogen and natural gas mixing uniformly in the pipeline.

| Effect of turbulator configuration on the distance of mixing uniformity
During the mixing of hydrogen and natural gas, the hydrogen is mainly concentrated in the area between 0 and 150 mm from the initial mixing position. To further reduce the mixing distance between hydrogen and natural gas, turbulators were added in the pipeline at L turb = 50, 100, and 150 mm. The turbulator enhances the turbulence intensity of the gas in the pipeline and enhances the mixing efficiency of hydrogen and natural gas. The radial distance r = 110 mm from the initial mixing position of hydrogen to the center of the natural gas pipeline is the relatively shortest distance for uniform mixing of gas. At r = 110 mm, the NHIIs in the pipeline and the installation position of the turbulators are adjusted. The variation of the distance L 98% required for uniform mixing of hydrogen and natural gas for HMRs of 5% (A), 10% (B), 20% (C), and 30% (D) is shown in Figure 4. With the addition of the turbulator, the disturbance of the gas in the pipeline is enhanced compared to the absence of the turbulator. The distance between hydrogen and natural gas uniformly mixed in the pipeline is significantly reduced with the installation of turbulators. By changing the installation position of the turbulator in the pipeline, the distance between hydrogen and natural gas can be further reduced.
As seen in Figure 4, with the addition of a turbulator, the distance between hydrogen and natural gas mixing is significantly reduced. However, when the NHII is 1, if the turbulator is installed in an inappropriate position, it will increase the distance for uniform mixing of hydrogen and natural gas. With an HMR of 5% and turbulators set to L turb = 50 and 50 mm, the hydrogen and natural gas mix uniformly over a longer distance than without turbulators. The distances of gas mixing uniformly are 19.4D and 20D, respectively. The distance of gas mixing uniformly without the turbulator is 16.9D. However, with the addition of turbulators at a distance of 100 mm from the initial mixing position, the distance of uniform gas mixing was 58.8% of the distance without the addition of turbulators. At NHII = 1, HMR is 10%, turbulators are added at 50 mm from the initial mixing position, and the distance of uniform gas mixing is 19D. The distance of uniform gas mixing without the turbulator is 16.4D. The distance of uniform hydrogen and natural gas mixing is slightly farther than that without the turbulator. The turbulator was added under the above three conditions, the distance between the hydrogen and the natural gas is mixed uniformly is slightly further than without the turbulator, and the turbulator caused very little disturbance to the flow of hydrogen in the pipeline. The gas flows through the turbulator and there is no significant turbulence of the gas in the pipeline. Due to the pressure and inertia forces, the hydrogen gas flows through the turbulator and continues to flow forward at a greater velocity. The hydrogen in the pipeline slowly spreads from the center of the pipe to the surrounding area. Due to the low turbulence intensity of the gas in the pipeline, the mixing of hydrogen and natural gas in the pipeline is slow. Therefore, the distance between hydrogen and natural gas mixing uniformly is slightly farther than when the turbulator is not added. With mixing ratios of 20% and 30%, the addition of turbulators reduces the distance for uniform mixing of hydrogen and natural gas. At NHII = 1, the addition of turbulator shortens the distance of gas mixing uniformity. When the turbulators are set at L turb = 150 mm and L turb = 50 mm, respectively, the gas mixing uniformity distance is the shortest. At NHII = 2, the turbulator was set at L turb = 150 and 50 mm, the shortest distance for uniform gas mixing.
In single-pipe hydrogen injection mixing, changing the position of the turbulator has the greatest effect on the mixing of hydrogen and natural gas. As the NHIIs increase, the distance between the uniform mixing of hydrogen and natural gas decreases. The influence of the turbulator installation position on the mixing process of hydrogen and natural gas is reduced. By choosing the suitable number of hydrogen inlets and the installation positions of the turbulator, the distance between the hydrogen and natural gas mixing uniformly in the pipeline can be effectively shortened.

| Visualization
To visualize the mixing process of hydrogen and natural gas in the pipeline, the mixing process with an HMR of 10%, four-inlet hydrogen injection and eight-inlet hydrogen injection is taken as an example. The distribution of hydrogen gas inside the pipeline with different structures is shown in Figure 5. As can be seen in Figure 5A,C, the distance of uniform mixing of hydrogen and natural gas in the pipeline is shortening as the radial distance r increases from 40 to 110 mm. At the radial distance r = 110 mm, the distance L 98% of the hydrogen and natural gas mixing uniformly is the shortest. For fourinlet hydrogen injection, the shortest distance for uniform gas mixing is 9.83D. For eight-inlet hydrogen injection, the shortest distance for uniform gas mixing is 7.02D. Figure 5B,D indicates that the distance for uniform gas blending is significantly reduced by the addition of the turbulator. Adjusting the distance L turb from the turbulator to the initial mixing position, the distance L 98% for uniform mixing of hydrogen and natural gas is changing. With four-inlet hydrogen injection, the turbulator has the shortest distance for uniform gas mixing at L turb = 50 mm, which is 2.95D. With eight-inlet hydrogen injection, the turbulator is set to L turb = 125 mm and the shortest distance for uniform gas mixing is 1.99D. The distance over which the uniform mixing of hydrogen and natural gas mix uniformly is longer with eight hydrogen injection inlets compared to four. The addition of the turbulator creates a more intense disturbance of the gas in the pipeline with eightinlet hydrogen injection. As a result, the distance required for uniform gas mixing during eight-inlet hydrogen injection is shorter.

| Distribution of blending uniformity
At NHII = 8, the effect of radial distance r and turbulator position variation on the distance L 98% of gas uniform mixing is shown in Figure 6. As can be seen in Figure 6A, the distance r from the turbulator to the initial mixing position increases and the distance between hydrogen and natural gas mixing uniformly decreases. The distance L 98% between the hydrogen and natural gas mixed uniformly in the pipeline increases with the increase of the HMR. From Figure 6B, it can be seen that at HMR = 5%, 10%, and 20%, the distance L 98% of uniform gas mixing first decreases, then increases, and then decreases with the increase of L turb . When HMR = 30%, the distance L 98% for uniform mixing of hydrogen and natural gas decreases and then increases with the increase of L turb . Increasing the HMR in the pipeline, the distance between even hydrogen and natural gas mixing increases.

| Distribution of hydrogen
Setting the NHIIs as 8, r = 110 mm, and HMRs as 5% (A), 10% (B), 20% (C), and 30% (D). Changing the distance L turb from the turbulator to the starting mixing position, the relationship between the hydrogen distribution in the pipeline and the cross-sectional position is shown in Figure 7. Because of the presence of the turbulator, the flow velocity and direction of the gas in the pipeline are disturbed when the gas hits the turbulator. The HMR in the pipeline changes drastically near the turbulator. As the blending distance L mix increases, the HMR in the pipeline gradually stabilizes around the initially set mixing ratio. During the gas mixing process, the HMR in the pipeline has been stabilized, but the gas has not been mixed uniformly at this location. The HMR in the pipeline in Figure 7A reaches 5% at L mix = 2D. The mixing uniformity of the gas at L mix = 2D is 96.8% (L turb = 50 mm), 95.7% (L turb = 100 mm), and 98% (L turb = 150 mm), respectively. The mixing uniformity of hydrogen and natural gas reaches 98% at 2.75D (L turb = 50 mm), 2.76D (L turb = 100 mm), and 1.98D (L turb = 150 mm). In the simulation process, the HMR in the simulated pipeline is slightly smaller than the theoretically calculated value of the HMR because of the error. The errors between the HMR and the theoretical values calculated from the simulations in this study are less than 2%. The simulation results are within the error tolerance. Increasing the HMR, the inlet velocity of hydrogen increases, and the disturbance of the gas when it hits the turbulator is more violent. As the HMR increases, the HMR in the pipeline needs longer distances to stabilize.

| Changes in turbulent dissipation rate
The turbulence intensity of the gas mixture in the pipeline can be expressed in terms of the turbulent dissipation rate. Setting the NHIIs as 8, r = 110 mm, changing the HMR in the pipeline to 5% (A), 10% (B), 20%(D), and 30% (D), respectively. The relationship between the turbulent dissipation rate and the location of the monitored crosssection is shown in Figure 8. the turbulator, a low flow velocity zone is formed behind the turbulator. Therefore, the turbulent dissipation rate of the gas in the vicinity of the turbulator increases rapidly and then decreases rapidly. There is a small fluctuation between 1D and 2D from the mixing center that finally stabilizes around 1000 m 2 /s 3 . The closer the turbulator is to the initial mixing position, the greater the turbulent dissipation rate of the gas near the turbulator. In this study, the HMR in the pipeline was adjusted by increasing the inlet velocity of the hydrogen. Therefore, by increasing the HMR, the flow rate of the gas in the pipeline increases, and the fluctuation of the turbulent dissipation rate caused by the turbulent flow device increases. The inclusion of turbulators in the pipeline disturbs the flow rate and direction of flow of the gas in the pipeline. The addition of turbulators enhances the turbulence intensity of the gas in the pipeline and improves the mixing efficiency of hydrogen and natural gas. The distance between hydrogen and natural gas mixing uniformly is significantly reduced.

| Velocity COV distribution
Velocity COV reflects the state of change of the gas velocity in the pipeline; the larger the value of velocity COV, the more chaotic the distribution of velocity in the pipeline. Setting the NHIIs as 8, r = 110 mm, changing the HMR in the pipeline to 5% (A), 10% (B), 20% (C), and 30% (D), respectively. The relationship between the velocity COV and the position of the cross-section is shown in Figure 9. As the gas in the pipeline flows through the turbulator, the flow field of the gas in the pipeline is disturbed. The velocity change of the gas in the pipeline is complicated, the turbulence intensity of the gas is increased, which improves the diffusion mixing efficiency of hydrogen and natural gas. The gas flows through the turbulator, a low flow velocity region is formed in the area of 1D-2D behind the turbulator. The disturbed gases converge behind the turbulator and continue to flow forward at a higher velocity. The velocity COV first decreases between 1D-3D and then increases rapidly. The velocity COV does not decrease as the mixing distance increases because the velocity of the gas in the pipe is disturbed by the turbulator. The final velocity COV fluctuates at a higher level.

| Pressure drop analysis
The flow of gas in the pipeline is influenced by the structure of the pipeline, the roughness of the pipeline wall, temperature changes, flow rate changes, and so on. The pressure of the gas in the pipeline decreases as the mixing distance increases. With a hydrogen injection inlet number of eight and r = 110 mm, the difference between the average pressure in the monitored section and the inlet pressure in the pipeline is calculated. Changing the HMR in the pipeline to 5% (A), 10% (B), 20% (C), and 30% (D), respectively. The pressure drop in the pipeline versus the blending distance is shown in Figure 10. Because of the disturbance of the turbulators, a zone of relatively low pressure is formed behind the turbulators, and the pressure drop in the pipeline at the turbulators increases. The gases converge behind the turbulator, the pressure of the gas in the pipeline increases, and the pressure drop in the pipeline decreases. As the mixing distance increases, the pressure of the gases in the pipeline decreases, and the pressure drop increases. The pressure drop of the gas in the pipeline is smallest when the HMR is 5% and the distance L turb = 50 mm from the turbulator to the initial mixing position is set. The pressure drop of the gas in the pipeline is highest when the turbulator is 150 mm from the initial mixing position. At an HMR of 10%, the turbulator is set to L turb = 150 mm, and the pressure drop in the pipe is minimal. The maximum pressure drop in the pipe is achieved when the turbulator is set to L turb = 100 mm. The pressure drops in the pipeline with an HMR of 20% are the opposite of that with an HMR of 10%; with the turbulator at L turb = 100 mm, the pressure drop in the pipeline is minimal. At L turb = 150 mm, the pressure drops in the pipeline are at maximum. At an HMR of 30%, the pressure drop in the pipeline is similar for turbulators at L turb = 50 and 100 mm. At L turb = 150 mm, the pressure drop in the pipeline is the highest.
When the gas flows through the turbulator, the flow rate and flow direction of the gas in the pipeline changes. Under the influence of the turbulator, the gas in the pipeline forms a low flow velocity and low-pressure region behind the turbulator. Because of the restriction of the pipe wall, the gas in the pipeline continues to flow forward after converging on the other side of the turbulator. The turbulent dissipation rate of the gas in the pipeline increases rapidly in the vicinity of the turbulator. The velocity of the gas decreases in the region between 1D and 2D from the initial mixing position. The gas flow continues at a higher velocity after convergence behind the turbulator. As a consequence, the velocity COV increases rapidly around the distance 3D from the initial mixing position. The pressure drop of the gas at the turbulator position increases and the pressure drop of the gas in the pipeline after the gas convergence decreases. The pressure loss in the pipeline gradually increases as the mixing distance increases.

| CONCLUSIONS
The effect of different pipeline structures on the mixing process of hydrogen and natural gas is investigated. Changing the NHIIs, the initial mixing position of hydrogen, and the installation position of turbulator, pipeline models of different structures were constructed for simulation. The mixing process of hydrogen and natural gas in the pipeline, the distribution, and the change of mixing uniformity were obtained. The details are as follows: 1. Increasing the NHIIs shortens the distance L 98% of hydrogen and natural gas mixing uniformly in the pipeline. After increasing the NHIIs to a certain number, further increases do not significantly shorten the distance of hydrogen and natural gas blending evenly. The distance of uniform mixing of gas in the pipeline grows with the increase of HMR. 2. The radial distance r from the initial hydrogen mixing positions to the center of the natural gas pipeline is an important factor affecting the uniformity of the mixing of hydrogen and natural gas. The distance L 98% required for uniform mixing of hydrogen and natural gas in the pipeline is shortened by increasing the radial distance r. When the radial distance r = 110 mm, the distance L 98% needed for uniform mixing of hydrogen and natural gas in the pipeline is the shortest. 3. The addition of a turbulator in the pipeline disturbs the flow rate and direction of the gas in the pipeline. The addition of the turbulator significantly reduces the distance for uniform mixing of hydrogen and natural gas in the pipeline. The distance for uniform mixing of hydrogen and natural gas is reduced by about half. Adjusting the distance L turb from the turbulator to the initial mixing position can further reduce the distance L 98% for uniform gas mixing. When the NHIIs are greater than 4, the effect of turbulator position change on the mixing effect of hydrogen and natural gas is reduced. 4. After the gas flows through the turbulator, the gas flow in the pipeline is disturbed, creating a low flow rate and low-pressure region behind the turbulator. Affected by the turbulator, the HMR fluctuates violently near the turbulator. The turbulent dissipation rate of the gas increases rapidly at the turbulator. The pressure drop in the pipeline increases in the vicinity of the turbulator.