Numerical Investigation of Gas-Liquid Flow in a Multiphase Pump with Special Emphasis on the Effect of Tip Leakage Vortex on the Gas Flow Pattern

Abstract

In this paper, the gas-liquid flow is comprehensively analyzed under different inlet gas void fractions, and the effect of tip leakage vortex (TLV) on the gas flow pattern in multiphase pumps is revealed. The results show that the gas flow pattern in an impeller is closely related to the centrifugal force, low-pressure region, and vortex motion. Most gas is present near the hub and suction surface of the blade as well as in the TLV. The two- and three-dimensional spatiotemporal evolution of the gas is presented, and the gas motion during the inception, development, and dissipation of TLV is revealed. It is reflected that the gas volume fraction is the highest at the TLV core and gradually weakens along the radial direction with the vortex core at the center. Additionally, the TLV energy dissipation is closely related to the gas and pressure difference, and strong energy dissipation occurs in the jet-wake flow.

1. Introduction

Energy is the cornerstone of human survival and technological development, particularly oil and natural gas resources. Owing to exploitation and consumption, oil and gas resources on land are being increasingly exhausted. However, the exploitation of subsea oil and gas resources is still in its infancy, accounting for only 15% of the total global oil and gas production; thus, this exploitation has great development potential. As a floating offshore structure, the multiphase transportation system can simultaneously transport oil and gas, simplifying the transportation process and reducing the maintenance cost [1]. As the core equipment of the system, a multiphase pump can be divided into blade type [2] and screw type [3]. Blade-type multiphase pumps have become a research hotspot due to their simple structure, abrasion resistance, and wide operating conditions [4].

Various design methods have been established for multiphase pumps. The inverse design [5] and three-dimension design methods [6] were applied to the impeller of multiphase pumps, and tests showed that they have high pressurization performance with a high inlet gas void fraction (IGVF) condition. Kim et al. [7] optimized the multiphase pump model using the response surface method. The optimized model could significantly suppress inhomogeneous flow and reduce energy loss. By combining the genetic algorithm and boundary vortex flux diagnosis, Zhang et al. [8] proposed a new optimal design method for impellers in a multiphase pump. The results showed that the optimal design effectively suppressed the gas-liquid separation, clearly reduced the size of bubbles and vortices, and increased the pressure difference and efficiency. Suh et al. [9] used a multi-objective algorithm to optimize the performance of the second stage of a multiphase pump. The design parameters of the impeller were selected as constraint conditions to control the inlet and outlet angles, which promoted gas-liquid mixing, static pressure recovery, and smooth flow. Recently, Xiao and Tan [10] proposed a design method of controllable velocity moment to determine the range of dimensionless parameters, which effectively suppressed the area of strong gas-liquid interactions and significantly reduced the pressure fluctuation intensity. Additionally, the Oseen vortex theory [11] and orthogonal design method [12] were proposed to optimize the gas-liquid flow field and improve performance.

The performance of multiphase pumps differs from that of conventional pumps, which is affected by the IGVF, impeller speed, and tip clearance [13,14,15]. Experimental results have shown that the pressure pulsation can be significantly enhanced under gas-liquid conditions and can be excited in multiples of the impeller rotation frequency [16]. The head and efficiency gradually decrease for pumps with increasing IGVF [17]. When the pump speed is low, the surge phenomenon occurs due to gas aggregation which blocks the flow passage in the impeller [18]. When the speed is increased, the gas-liquid mixture becomes more uniform, which improves the pressurization and broadens the efficient operation range [19,20]. Zhang et al. [21] tested impellers with different tip clearance sizes (0.2, 0.5, and 0.8 mm); under the water condition, the head decreased by 10.72%, 24.96%, and 41.39%, respectively. When IGVF was 10%, the head decreased by 17.10%, 25.35%, and 38.11%, respectively. This denotes that the energy performance of pumps gradually decreases with increasing tip clearance. Moreover, Shi et al. [22] found that the gas aggregation area was significantly reduced in the flow passage of a split impeller compared to that of an ordinary impeller. A split impeller usually performs better than an ordinary impeller, especially under the condition of high IGVF.

Many scholars have studied the two-phase flow pattern in multiphase pumps. According to the diameter and number of bubbles, flow patterns can be divided into isolated bubbly flow, bubbly flow, gas pocket flow, and segregated gas flow [23,24]. As IGVF increases, the head sharply decreases in the gas pocket flow range and then smoothly decreases in the separated gas flow range. The motion and distribution characteristics of bubbles are complex in multiphase pumps. Zhang et al. [25,26] established a model considering the coalescence and fragmentation of bubbles. They found that bubbles move from the blade pressure surface (PS) toward the suction surface (SS) along a similar path in the impeller, where they aggregate. Then, the bubbles decrease in size when they impact the wall. Based on the above study, Li et al. [27] introduced the bubble number density equation into the flow model. They determined that the bubble size barely changes in the impeller, but the bubbles coalesce due to the interaction between the impeller and diffuser. Then, the bubble size reaches the maximum in the diffuser. Furthermore, the interphase force plays an essential role in the numerical simulation of gas-liquid flows. Wang and Yao [28] analyzed the prediction characteristics of interphase forces using different correlation quantities and verified the prediction ability of each model for bubbly flow patterns. The bubble state and flow patterns in different Reynolds number ranges should be considered while selecting the drag, lift, and wall lubrication forces. Based on the two-fluid model, Yu et al. [29,30] found that the drag force is a crucial interphase force, while the turbulent dissipation force can be ignored. Additionally, the drag force, lift force, and virtual mass force are affected by the diameter of the bubbles.

In summary, extensive research has been conducted on multiphase pumps, and remarkable achievements have been obtained. However, the effect of tip clearance on the gas-liquid flow in an impeller has not been well studied. Between the blade tip and the pump body wall of an impeller, a specific gap (tip clearance) is reserved, and the resulting tip leakage flow interacts with the main flow to form a complex tip leakage vortex (TLV). TLV disturbs the gas-liquid flow and reduces the impeller performance. Note that the influence of TLV on the gas flow pattern has not been revealed to the best of our knowledge. In this study, the gas-liquid flow is comprehensively analyzed based on the two-fluid model. First, the relevance between the TLV pattern and gas motion is discussed. Then, the two- and three-dimensional (2D and 3D, respectively) evolutions of the gas are shown, and the gas motion during the inception, development, and dissipation of TLV is revealed. Finally, the influence of IGVF on turbulent eddy dissipation (TED) and blade load is summarized.

2. Physical Model and Grid Generation

2.1. Research Object

The multiphase pump comprises an inlet section, an impeller, a diffuser, and an outlet section, as shown in Figure 1. The design parameters of the pump are as follows: the flow rate is 100 m³·h⁻¹, the impeller speed is 3000 rpm, and the tip clearance is 1 mm. Other parameters of the impeller and diffuser, such as diameter, hub diameter, axial length, and blade number, are listed in

Table 1. Design parameters of the impeller and diffuser.

Parameters	Impeller		Diffuser		Units
	Symbols	Values	Symbols	Values
Shroud diameter	DS	161	DS	161	mm
Hub diameter at inlet	Dh1	113	Dh3	126	mm
Hub diameter at outlet	Dh2	126	Dh4	113	mm
Blade inlet angle	αh/αs	9.05°/6°	αh/αs	0	-
Blade outlet angle	βh/βs	27.05°/24°	βh/βs	35°	-
Axial length	LI	60	LD	66	mm
Blade numbers	BI	3	BG	11	-

.

2.2. Grid Generation

A 3D model of the computational domain was established using UG software, including the inlet, impeller, diffuser, and outlet domains. A high-quality structural grid is critical for reliable and accurate numerical simulations. The grid covering the computational domain was arranged using a hexahedral structure, as shown in Figure 2. The boundary layer grid near the wall was refined to ensure good quality, and the O-topology was used to surround the blade. Particularly, 30 and 25 layers were arranged in the radial and circumferential directions of the tip clearance region, respectively. The Y+ value was kept below 60 in the impeller. A scalable wall function was used as the wall function, which improved the computing accuracy [1].

3. Numerical Method

3.1. Numerical Model

Numerical simulations of a multiphase pump were performed using ANSYS CFX. The Eulerian–Eulerian model was used to determine the gas-liquid two-phase flow. The gas and liquid in the two-phase model were air and water, respectively, which were maintained at 25 °C. The SST $k-\omega$ turbulence model was used for the liquid phase, as it can effectively predict the flow separation point, separation region, and TLV trajectory. The gas-phase diameter was set to 0.1 mm, and the zero-turbulence model for the dispersed phase was used as its turbulence model. The rotational speed of the impeller was set as 3000 rpm in the pump, and the impeller shroud was set as the counter-rotating mode in the relative coordinate system. Velocity inlet, pressure outlet, and no-slip wall conditions were imposed at the boundaries. The convergence precision was 10⁻⁵.

3.2. Analysis of Grid Discrete Error Verification of Time Step Independence

The grid discrete error is an important factor affecting the precision of numerical calculations. The grid discrete error was analyzed according to the grid convergence index (GCI) based on Richardson extrapolation [31,32,33]. According to the GCI criterion, three sets of grids, coarse, medium, and fine, were established, and the pump efficiency was selected as the extrapolated parameter. The estimation grid error is shown in

Table 2. Evaluation of grid error.

Parameters	Symbols	Error Estimates
Grid 1	N1	8,961,543
Grid 2	N2	3,956,482
Grid 3	N3	1,702,813
Grid ratio 21	r21	1.313
Grid ratio 32	r32	1.324
Efficiency 1	η1	45.59%
Efficiency 2	η2	45.42%
Efficiency 3	η3	44.95%
Estimated efficiency	ηext21	45.69%
Relative error	eext21	0.228%
GCI	GCIfine21	0.285%

. The analysis showed that the relative errors of the extrapolated parameter and the fine GCI were 0.228% and 0.285%, respectively. Additionally, the fine grid (N₁) had a low discrete error and met the GCI convergence criterion. Therefore, a fine grid (N₁) was suitable for subsequent numerical calculations.

Although smaller time steps more accurately capture the unsteady information, they consume more computing resources. Thus, time steps of 5.56 × 10⁻⁵, 1.11 × 10⁻⁴, and 1.67 × 10⁻⁴ s corresponding to 360, 180, and 120 steps per revolution, respectively, were used to conduct the simulations. Figure 3 showed that the fluctuations in pressure at the monitoring point on the leading edge of the diffuser were almost similar under the different time steps, indicating that the influence of the time step size on the results was negligible. Ultimately, a time step of 1.11 × 10⁻⁴ s was selected for the transient simulations.

3.3. Experimental Verification

Experimentation was conducted using a test system and multiphase equipment. As the system started operation, air and water entered the mixing tank through the respective pipelines, and the valve was controlled to homogeneously mix the gas and liquid in different proportions. Figure 4 displays the test system. The multiphase pump was tested, and optimal values for the head and efficiency were obtained. The results of the test and simulation with external characteristics under different flow rates are shown in Figure 5. The numerical simulation results well agree with the experimental results. Thus, the numerical simulation scheme established herein accurately predicts the energy performance of the multiphase pump.

4. Results and Discussion

4.1. Gas Motion Trajectory Due to TLV

When the multiphase pump was operational, TLV formed in the tip clearance, which affected the gas-fluid flow pattern. Q_c criterion is defined as $Q=1/2{(\nabla \cdot u)}^2+tr({(\nabla u)}^2)$, where u denotes relative velocity. Therefore, the Q_c criterion (Q_c = 1.5 × 10⁶ s⁻²) was adopted to display the TLV patterns in the impeller, and comparative analysis was performed with the experimental photos, as shown in Figure 6. A previous study [34,35] divided the TLV structures into the leading-edge vortex (LV), primary TLV (PTLV), secondary TLV (STLV), tip separation vortex (TSV), and trailing-edge vortex (TV). Figure 6 shows that the vortex pattern of the experimental flow field is highly consistent with that of the numerical simulation under different conditions. Particularly, the TSV, STLV, and TV are clear. When the IGVF is 5%, the vortex scales are small in the impeller. When IGVF is increased, scattered strip STLV appears near the SS and the entrainment of the PTLV and STLV is enhanced, which disturbs the flow field. Small-scale vortexes are filled in the passage when the IGVF reaches 20%, which worsens the flow pattern near the shroud. Moreover, the vortex affects the gas motion to a certain extent and plays a decisive role in the gas flow pattern.

Figure 7 shows the gas pattern and streamline in the impeller for the IGVF of 10%. The gas isosurface is displayed with a gas volume fraction of 20% in Figure 7a. A line segment was particularly added in the flow passage between the tip and the pump body wall that extends from the leading edge of the blade to the trailing edge. As shown in Figure 7b, the 3D streamline is released through the line segment to capture the gas trajectory. The gas distribution in the impeller is inhomogeneous and is mainly aggregated near the hub and SS of the blade as well as in the TLV. Since the physical properties of the gas and liquid phases are different (particularly, the density of the gas is much lower than that of the liquid), a lower centrifugal force acts on the gas than on the liquid. Consequently, the gas is squeezed into the hub. Additionally, the gas is adsorbed to the SS, which is a low-pressure area due to its low density. The TLV caused by the tip clearance is also an important reason for gas accumulation. Combined with the flow pattern of the TLV in Figure 6, most gas is present in LV, TSV, PTLV, STLV, and TV. From the leading edge to the trailing edge of the blade, the scale of STLV first increases and then decreases, and the degree of gas aggregation completely conforms to this law. Particularly, the gas volume fraction gradually increases along the PTLV trajectory. This phenomenon indicates that TLV plays a leading role in gas distribution in the impeller of multiphase pumps, and the volume fraction increases with the vortex scale. As shown in Figure 7b, the gas presents a spiral motion downstream through the tip clearance. Along the leading edge to the trailing edge of blade A, the gas velocity gradually increases in the tip clearance region, reaches the maximum near the leading edge of blade B, and then gradually decreases. The gas velocity generally decreases along the streamline direction, while it first increases and then decreases along the PTLV trajectory. This may be because the pressure difference of blade A reaches the maximum near the leading edge of blade B. An interesting phenomenon occurs: the reverse leakage flow flows along PS, and some of it reaches the middle of blade A and enters the tip clearance due to the pressure difference.

A total of eight sections, S₁–S₈, were evenly arranged in the trajectory area of the PTLV, and the axial distance of the sections only spans between the two blades of the flow passage, as shown in Figure 8.

Figure 9 displays the vorticity and gas volume fraction along the PTLV trajectory. The gas volume fraction on the sections is closely related to the vorticity. The larger the vorticity is, the more the gas aggregates. The leakage flow gradually increases from S₁ to S₆, and the vorticity in the jet-wake flow also gradually increases, leading to a high gas volume fraction in the vortex. However, as the leakage flow weakens from S₇ to S₈, the jet-wake flow tends to be long and narrow, and the gas pattern is segmented. This is because the flow pattern of STLV splits from a continuous sheet structure to a scattered strip structure, forming multiple vortex cores, and the gas gathers in the central region of the strip structure. More importantly, most gas is present in the center region of PTLV along the PTLV trajectory. Furthermore, the gas volume fraction gradually decreases along the radial direction with the vortex core at the center. Clearly, the gas volume fraction near PTLV is lower than that in other regions, verifying that the gas is trapped by the vortex. Additionally, the scale of PTLV gradually increases from S₁ to S₅, while the gas volume fraction decreases. In contrast, the gas volume fraction of PTLV increases from S₆ to S₈. This is because STLV interacts with PTLV near the leading edge of blade B, and the vorticity and scale of the vortex are enhanced, which enhances the adsorption capacity of PTLV to the gas.

4.2. Spatiotemporal Evolution of the Gas

To investigate the gas motion in a 2D evolution process for the multiphase pump, an axial plane was established on the leading edge of blade A in the impeller, and this axial plane was set to be absolutely stationary, as shown in Figure 10. The impeller was rotated from T₀ to T₀ + 8/15T, which is the period of time required for blade A to enter the axial plane from the leading edge until the trailing edge passes through the axial plane.

The transient gas volume fraction and streamline were recorded in the D region on the axial plane, as shown in Figure 11. The gas motion was analyzed according to the three stages of 2D evolution from TLV. [T₀, T₀ + 2/15T] is defined as the inception stage. The leakage flow flows from the SS to PS at T₀, tip separation vortices form near the SS in the tip clearance, and an opposite vortex appears. Gas blockage occurs as gas gathers in the center of the vortex, which prevents the fluid from entering the tip clearance. When the pressure difference increases to T₀ + 1/15T, the leakage flow disperses the vortex near the SS, which causes the gas flow to be more uniform. PTLV is generated for the first time at T₀ + 2/15T. Its vortex scale is small and its adsorption capacity to the gas is clearly weaker than that of TSV. [T₀ + 3/15T, T₀ + 6/15T] is defined as the development stage. The gas in TSV and STLV gradually increases as the leakage flow strengthens at [T₀ + 3/15T, T₀ + 5/15T], and PTLV moves downstream with a high gas volume fraction. The flow pattern of the STLV splits from a continuous sheet structure to a scattered strip structure at T₀ + 6/15T, forming multiple vortex cores, and the gas gathers in the central region of the vortex. At this time, a vortex forms due to the interaction between PTLV, and a reverse leakage flow is generated in the tip clearance of blade B, causing a gas blockage. [T₀ + 7/15T, T₀ + 8/15T] is defined as the dissipation stage. The gas wrapped by PTV enters the tip clearance of blade B as PTLV is adsorbed. At T₀ + 8/15T, the shape of the gas in the PTLV changes from round to irregular due to the strong adsorption in the tip clearance of blade B. Furthermore, a high gas volume fraction is present in TV.

To investigate the gas motion in the 3D evolution process for a multiphase pump, the gas isosurface is displayed with a gas volume fraction of 20% in Figure 12. The figure shows that the gas flow pattern is closely related to TLV in one impeller rotation period, and the gas velocity near the shroud is significantly higher than that of the hub. The gas motion was analyzed according to three stages of a 3D evolution from TLV. [T₀, T₀ + 2/9T] is defined as the splitting stage. As the PTLV splits, so does the gas distribution. Simultaneously, the gas enhances the STLV intensity and intensifies the interaction between STLV and PTLV. [T₀ + 3/9T, T₀ + 5/9T] is defined as the shrinking stage. Here, the PTLV shrinks, and the vortex scale gradually decreases; consequently, the gas absorbed by PTLV also gradually decreases. [T₀ + 6/9T, T₀ + T] is defined as the merging stage. As PTLV gradually develops and merges, the gas aggregates in the central region of the vortex, and its gas volume fraction gradually increases. Moreover, in the impeller revolution T, the gas volume fraction and velocity in the jet-wake flow are high. The gas volume fraction increases with the pressure difference of the blades, which is closely related to the scale of TSV and STLV. Furthermore, it can be concluded that TSV and STLV are the main regions of gas aggregation. Therefore, gas-liquid inhomogeneity is an important reason for increasing the hydraulic loss in a multiphase pump.

4.3. Flow Pattern of the Gas in Impeller

To explore the gas aggregation in an impeller, Figure 13 displays the flow pattern of the gas under different gas volume fraction conditions. The distance between the hub and shroud in the impeller is dimensionless, and the hub and shroud are defined as 0 and 1, respectively. Overall, the gas-fluid flow is uneven near the hub, while the gas volume fraction gradually increases from the hub to the shroud. Combined with Figure 7, reverse leakage flow occurs in the tip clearance near the leading edge, which flows toward the hub along the PS and interacts with the main flow to form vortexes. Hence, the gas gathers near the middle of the PS when the span is 0.5. A low gas volume fraction is present at the span of 0.9 because the gas is adsorbed by the vortex in the middle of the passage. Moreover, a high gas volume fraction is present in TLV at the span of 0.9, which is sufficient to prove that the vortex has a strong adsorption capacity for the gas. Obviously, a high gas volume fraction is present in the PTLV trajectory, extending from the SS of blade A to the PS of blade B. With increasing IGVF, the scale and vorticity of TV increase, whose adsorption capacity significantly increases.

Most gas was present on the blade surface. Figure 14 presents a diagram of the gas volume fraction and streamline on the blade surface. When the impeller is operational, a certain degree of gas-liquid separation occurs due to the different density and viscosity between the gas and liquid, which causes the gas volume fraction on the SS to be considerably higher than that on the PS. As shown in Figure 14a, unstable flow occurs at the leading edge, where a small amount of gas gathers. Moreover, a strip region with high gas volume fraction extends from the leading edge to the middle of the blade, which is highly consistent with the trajectory of the reverse leakage flow. The reverse leakage vortex rolls up the gas to flow toward the hub along PS, which is an important reason for the uneven distribution of streamlines on PS. Figure 14b shows that the gas volume fraction on the SS gradually increases from the leading edge to the trailing edge under different IGVF conditions. The streamlines on SS are more uniform than those on the PS, indicating that the flow state is more stable on the SS. As IGVF increases, the range of streamline deflection caused by LV and TV increases, and the vortex center moves toward the hub.

To study the flow pattern of the gas in the clearance, the gas volume fraction and velocity vector were recorded in the C region of S₄ in Figure 8, as shown in Figure 15. TSV is generated when the fluid flows into the tip clearance due to the right-angle tip edge. The vortex region is close to the blade tip and extends from the PS to SS. Almost all the gases near the tip clearance are gathered in TSV. With increasing IGVF the radial width of the gas pattern remains almost unchanged, but the axial length of the gas pattern gradually extends to the SS. When IGVF is 20%, the gas covers the entire tip of the blade. Simultaneously, the gas trajectory is clearly captured by the velocity vector, and the gas accumulation yields a significant low-speed region. Overall, the gas velocity in the tip clearance increases from the PS to SS.

4.4. Variations of TED and Blade Load with IGVF

Gas disturbs the flow pattern in the tip clearance and causes non-negligible energy dissipation. To quantitatively research the distribution of TED in the blade tip clearance, the C region of S₄ was taken as the research object and its schematic is shown in Figure 16. In the figure, L denotes the thickness of the tip clearance, which is normalized (i.e., the PS and SS are 0 and 1, respectively); h represents the height of the tip clearance; and λ is the distance between a point in the tip clearance and the tip. The height of the tip clearance was normalized by λ/h, that is, the tip is 0 and the shroud is 1.

Figure 17 shows the TED curves in the tip clearance under different IGVF conditions. TSV causes local turbulence, which significantly increased the TED in the curves (λ/h = 0, 0.1, and 0.2). Particularly, the curve (λ/h = 0.1) presents the strongest TED with the widest range. This was determined as the TSV range, and the vortex core is [L = 0.5, λ/h = 0.1]. Furthermore, the curve (λ/h = 1) near the shroud exhibits a high TED, which is related to the generation of vortex groups on the pump body wall. When IGVF is 5%, a small region with high TED is present in the tip clearance. With increasing IGVF, the local turbulence intensifies. When IGVF reaches 20%, the region with high TED expands to the entire tip clearance, which is highly consistent with the conclusion from Figure 15.

To study the load distribution characteristics of the blades under different IGVF conditions, the pressure loads on the PS and SS of the blade, from the leading edge to the trailing edge tip, are shown in Figure 18. From the leading edge to the trailing edge, the loading laws are basically consistent under different IGVFs. Due to the impact of the impeller inlet flow, the load on the PS of the blade suddenly increases at the 0–0.1 chord and a larger tip clearance produces a greater load on the blade. Along the 0.1–0.5 chord, the impeller blades continuously work on the fluid, transforming mechanical energy into the pressure energy of the fluid, and the load on the PS gradually increases accordingly. Generally, the pressure difference from the leading edge to the trailing edge first increases and then decreases and finally reaches a maximum value at about the 0.5 chord. The energy dissipation is the greatest at the point of maximum leakage flow intensity. Moreover, a decrease in the IGVF causes the pressure difference to gradually increase, and then the jet intensity increases. Careful observations show that, with increasing IGVF, the load intersection between the PS and SS near the 0.1 chord gradually moves to the trailing edge, and the initial point of PTLV is closely related to the pressure difference. In addition, compared with the water condition, the gas disturbs the flow field in the gas-liquid condition, resulting in an uneven distribution of blade load, which is manifested as a tortuous blade load line.

5. Conclusions

In this study, the gas-liquid flow mechanism was studied in a multiphase pump under different IGVFs and the relevance of TLV to the flow pattern of the gas was revealed. Furthermore, the accuracy and reliability of the numerical results were verified through experimental results. The tip leakage flow is generated in the tip clearance, which interacts with the main flow to form TLV. According to the vortex pattern, TLV can be divided into LV, PTLV, STLV, TSV, and TV. TLV disturbs the gas-liquid flow pattern in pumps, affects the gas motion to a certain extent, and plays a decisive role in the gas flow pattern.

The gas flow pattern in the impeller is closely related to the centrifugal force, low-pressure region, and vortex motion. Most gas is present near the hub and SS of the blade as well as in TLV. Additionally, the gas presents a spiral motion downstream through the tip clearance, and the gas accumulation capacity increases with the vorticity of the vortex. The gas at the leading edge of the blade flows in the reverse direction along PS. More importantly, most gas is present in the center region of the vortex, and the gas volume fraction gradually decreases along the radial direction with the vortex core at the center. Furthermore, the 2D and 3D spatiotemporal evolution of the gas pattern was realized, and the gas motion in the vortex inception, development, and dissipation processes was revealed. As TLV develops, the gas wraps and gathers into a vortex. Moreover, STLV splits from the continuous sheet structure to a scattered strip structure, forming multiple vortex cores where the gas gathers. The flow pattern of the gas changes with the evolution of TLV in the 3D spatiotemporal evolution. Clearly, a high gas volume fraction is present in STLV and TSV.

The flow pattern of the gas in the impeller was comprehensively analyzed under different IGVFs. The turbulence intensifies from the hub to the shroud, resulting in flow separation for the gas and liquid. Clearly, a high gas volume fraction is present in TLV, which is sufficient to prove that the vortex has a strong adsorption capacity for the gas. Compared to PS, the streamlines are more uniform, and the gas volume fraction is higher on the SS. Additionally, the gas gathers in the low-speed region formed by TSV in the tip clearance. The energy dissipation of TLV is closely related to the gas and pressure difference, and strong energy dissipation occurs in the jet-wake flow. With increasing IGVF, the local turbulence intensifies and TED increases in the clearance. Furthermore, the pressure difference from the leading edge to the trailing edge first increases and then decreases, finally reaching a maximum value at about the 0.5 chord. The energy dissipation is the greatest at the maximum leakage flow intensity point.