Introduction

Liquid-ring pump is widely used for transporting gas. During the operation of the liquid-ring pump, the liquid is subjected to centrifugal force acting on the inner wall of the pump casing and the concentric liquid ring of the casing. As a result, gas cavities with periodic variations in volume are formed between the impeller hub, the inner surface of the liquid ring, and the blades. As the impeller rotates, the gas completes a periodic process of suction-compression-exhaust in the gas cavity. Thus achieving the purpose of transporting gas. The internal flow of the liquid-ring pump is complex gas-liquid two phase flow1,2. This results in lower hydraulic performance. The axial clearance exists between the impeller blade tip and pump casing, and the gas-liquid leakage flow exists in the clearance. Gas-liquid two phase leakage flow will significantly reduce the vacuum degree and efficiency of the liquid-ring pump3. Therefore, suppressing leakage flow can effectively improve the hydraulic performance of liquid-ring pump. Zhang et al.4,5 proposed several different axial blade tip designs to suppress axial clearance leakage flow and improve the hydraulic performance of liquid-ring pump. These studies provide a certain theoretical basis for the suppression of axial tip clearance leakage flow in liquid-ring pump.

There is relatively little research on leakage flow suppression in the field of liquid-ring pump, but the research on leakage flow suppression is widely used in the field of turbomachinery. In recent years, researchers have conducted extensive research on leakage flow suppression. The control methods are divided into active control and passive control methods based on whether additional energy needs to be introduced. Active control methods have better suppression effects, but usually have low reliability6,7,8. Passive control method generally achieved suppression effect by tip modification, mainly including winglet blade tip9,10,11 and squealer blade tip. The squealer blade tip method suppresses leakage flow by the squealer at the blade tip. Senel et al.12 found that the vortex inside the squealer can effectively suppress leakage flow. Wang et al.13 found that inclined squealer suction surface can enhance the aerodynamic sealing effect of the squealer. Yan et al.14 analyzed the influence of squealer structural parameters on the suppression effect of leakage flow. Zeng et al.15 studied the flow structure inside the squealer and captured the squealer vortex structure. Zou et al.16 analyzed the evolution of the flow structure inside the squealer and its impact on the leakage flow suppression effect. Zeng et al.17 found that inclined squealer pressure surface can better reduce the intensity of leakage flow. Liu et al.18 proposed a C-shaped squealer design and found that modified squealer has better suppression effect. Huang et al.19 found that the inflow angle has a significant impact on the suppression effect of the squealer blade tip. Yan20 analyzed the influence of the squealer vortex structure on the aerodynamic and thermal performance. Maesschalck et al.21 analyzed the effect of squealer blade tip on turbine heat transfer performance. Li et al.22 analyzed the combined pressure-side squealer tip structures and effect of pressure-side coolant injection on the cooling and aerothermal performance of the blade tip, and found that this combination structure achieved the maximum reduction of leakage flow. Zhou et al.23 analyzed the heat transfer, cooling efficiency, and aerodynamic performance of two different structures of squealer blade tips.

In this paper, in order to reduce the axial clearance leakage flow of the liquid-ring pump and improve its hydraulic performance, the squealer blade tip was introduced to liquid-ring pump. Through the numerical simulation method, the suppression mechanism of squealer blade tip would be analyzed.

Research model

Geometric model and mesh division

The research object of this paper is the 2BEA-203 liquid-ring pump. The main structure of the liquid-ring pump is divided into four parts, as shown in Fig. 1. The intake port and exhaust port are concentric with the impeller, and the impeller is eccentrically installed inside the pump casing. The axial length of the intake port and exhaust port is 70 mm. The Hub diameter is 182 mm. The axial length of impeller is 363.6 mm. The blade length is 103 mm. The thickness of the impeller blades increases uniformly from the hub to the rim. The thickness of the blades at the hub is 8.5 mm, and the thickness at the rim is 7.5 mm. The curvature radius of the pressure surface of the blade is 102 mm. The squealer is located at the axial tip of the blades(z-axis direction). The curvature radius of the suction surface of the blade is 104.5 mm. The main parameters are shown in Table 1.

Table 1 Main parameters of liquid-ring pump.
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Fig. 1
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Computational domain.

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In order to suppress the gas-liquid two phase leakage flow in the axial clearance of the liquid-ring pump, the squealer blade tip is located at the axial end of the blades, as shown in Fig. 2. The squealer extends from the hub(sc−1=0) to the rim(sc−1=1), where sc−1 is the dimensionless coordinates along the blade chord length. The distance between the squealer and both sides of the blade is 2 mm. The width of the squealer varies with the width of the blade. The depth of the squealer is 2 mm. In order to improve the suppression effect of the squealer, the pressure surface of the squealer is inclined outward. The squealer shape is designed according to the field of turbomachinery, and its structural parameter optimization will be carried out in subsequent research.

Fig. 2
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Structure diagram of squealer.

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The computational domain was discretized by hexahedral structured grids, as shown in Fig. 3. The grid layer of the squealer was set as 17 layers grid, as shown in Fig. 4.

Fig. 3
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Computational domain grid.

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Fig. 4
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Axial clearance grid and squealer grid.

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Figure 5 shows the verification of grid independence. In order to accurately capture the leakage flow structure, the number of grid layers at the clearance was set as 4, 8, 10, 14, 20, 24 respectively, and the total number of grids in the computational domain gradually increased from 1.42 million to 6.12 million. The final total number of grids is determined to be 4.781 million, and the clearance was set as 14 layers grid.

Fig. 5
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Grid independence verification.

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Experimental system and numerical computational model

The experimental system of the liquid-ring pump is shown in Fig. 6. During the operation of the Liquid-ring pump, some Liquid will flow out through the exhaust port, so it is necessary to replenish the water by the feeding pump 8. The vacuum degree was measured by vacuum gauge 5. The flow rate was measured by flow meter 4. The shaft power is monitored by control cabinet 9. The flow rate of the Liquid-ring pump was changed by adjusting control valve 6.

Fig. 6
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(a) Schematic of experiment setup; (b) Test system.

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Experimental system: 1 Water tank; 2 Motor; 3 Liquid-ring vacuum pump; 4 Orifice flow meter; 5 Vacuum gauge; 6 Control valve; 7 Gas-liquid separation tank; 8 Feeding pump; 9 Control cabinet; 10 Liquid level meter; 11 Pressure gauge; 12 Gate valve.

This study used Fluent software for numerical simulation. The numerical simulation of the liquid-ring pump is the transient simulation, and the RNG k - ε model was selected as the turbulence model. The VOF model was selected as the multiphase flow model. The sliding grid method was used to couple rotating and stationary parts. According to experimental data, the mass flow inlet was set as 0.02 kg/s, 0.04 kg/s, and 0.07 kg/s respectively. The outlet was set as atmospheric pressure outlet. The primary phase is gas, and the second phase is Liquid. The gas-liquid two phase temperature was set as 20℃. The gas was set as ideal gas. The computational domain outside the radius of 133 mm was initialized as liquid phase, and the other zones were initialized as gas phase. The time step was set as △t = 0.00001s.

Hydraulic performance and internal flow field analysis

Hydraulic performance analysis

Fig. 7
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Gas-liquid two phase distribution of liquid-ring pump (a) Numerical simulation result; (b) Experimental result.

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Figure 7 shows the gas-liquid two phase distribution of the liquid-ring pump under the design condition of Qm=0.07 kg/s. Figure 7.a shows the numerical simulation result, and Fig. 7.b shows the high-speed camera experiment result. It can be seen that the numerical simulation result of the phase distribution is basically consistent with the experimental result.

Fig. 8
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Performance curve of liquid-ring pump.

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Figure 8 shows the performance curves of the prototype impeller liquid-ring pump and the squealer blade tip impeller liquid-ring pump. In this figure, the numerical simulation result is larger than experimental result. The reason is that the numerical simulation results do not consider the bearing wear and the motor power loss, and the heat transfer between gas and liquid cannot be accurately set in unsteady calculations. There is a certain deviation between the gas temperature and the actual temperature. The numerical simulation results are consistent with the trend of experimental results. Based on the phase distribution in Fig. 7, the numerical simulation results have a certain degree of accuracy. Compared with the prototype impeller pump, the efficiency and vacuum values of the squealer blade tip impeller pump at three working conditions are significantly improved, where the vacuum values are improved by 2.4%, 2.9%, and 4.1% respectively.

Liquid-ring pump is divided into suction zone, compression zone, exhaust zone, and transition zone according to its working characteristics. In order to analyze the suppression effect of the squealer, the impeller blades were numbered as shown in Fig. 9.

Fig. 9
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Schematic diagram of section position.

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Suppression effect of leakage flow analysis

This paper analyzes the internal flow field under the design condition of Qm=0.07 kg/s, when the unsteady calculation tends to converge and t = 0.2125s.

Fig. 10
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Vorticity distribution with streamline.

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Figure 10 shows the vorticity distribution with streamline of section a (sc-1 = 0.6413). Q>0 indicates that the zone is dominated by rotational deformation and and there is vorticity. Q<0 indicates that the zone is dominated by shear deformation. The leakage flow is rolled up by the leakage flow corner vortex (CV) when it flows into the clearance from the pressure surface (PS). When the leakage flow flows into squealer, it interacts with the low-speed fluid in the squealer to form the pressure side corner vortex (PSCV) and the squealer vortex (SV). The rotation direction of the pressure side corner vortex is opposite to that of the squealer vortex. There is a strong shear effect between the pressure side corner vortex and the squealer vortex, which blocks the axial clearance flow channel and suppresses the leakage flow. When the leakage flow flows out of the clearance from the suction surface (SS), it interacts with the main flow to form the tip leakage vortex (TLV).

Figure 11 shows the relative velocity distribution of section a. The leakage velocity of the squealer blade tip is significantly reduced. Although the relative velocity of the leakage flow at the squealer has increased to a certain extent, its velocity is still smaller than the prototype impeller. The squealer blade tip can effectively suppress liquid leakage flow.

Fig. 11
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Relative velocity distribution: (a) Prototype impeller pump; (b) Squealer blade tip impeller pump.

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As shown in Fig. 12, establish the clearance sections on the suction side of each blades. The clearance sections extend from sc−1 = 0.7343 to the rim. Integrate the leakage velocity of the clearance sections to obtain the leakage flow rate.

Fig. 12
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Schematic diagram of clearance sections.

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Fig. 13
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Comparison of total liquid leakage flow rate.

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Figure 13 shows the total Liquid leakage flow of prototype pump and squealer blade tip pump with different gas flow rates. It can be seen that compared with the prototype pump, the total leakage flow of the squealer blade tip pump is lower than that of the prototype pump at three working conditions, and is reduced by 10.7%, 12.4%, and 13.8% respectively.

Figure 14 shows the vorticity distribution with velocity vectors of section b (sc−1= 0.0978). The gas leakage flow is similar to the liquid leakage flow. The pressure side corner vortex and the squealer vortex are generated inside the squealer, blocking the clearance flow channel and suppressing leakage flow. However, the intensity of gas leakage flow is relatively high, and the intensity of the pressure side corner vortex is greater than that in the liquid region. The pressure side corner vortex and the squealer vortex are both closer to suction side of the squealer. There is a significant axial velocity of gas in the compression zone. The leakage flow interacts with the mainstream to form the tip leakage vortex and flows downward. Compared with the prototype impeller, the tip leakage vortex intensity formed by the squealer blade tip is significantly reduced, indicating that the squealer has a certain suppression effect on gas leakage flow. It can also be seen that the region with high Q value near the suction tip of the squealer blade tip moves upward, approaching the clearance. This phenomenon indicates that the squealer has adjusted the vortex formation area and contributed to reducing leakage current.

Fig. 14
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Vorticity distribution: (a) Prototype impeller pump; (b) Squealer blade tip impeller pump.

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Suppression effect of leakage flow along the circumferential direction analysis

Figure 15 shows a comparison of the relative velocity distribution of blade 5 in the suction zone, blade 15 in the exhaust zone, and blade 1 in the transition zone. The cross-section of each blade is arranged equidistantly. It can be seen that the leakage flow velocity of blade 5 in the suction zone (Fig. 15. a) is highest near the hub. The leakage flow velocity of the squealer blade tip impeller is significantly lower than that of the prototype impeller. The leakage flow velocity of blade 15 in the exhaust zone (Fig. 15. b) is lower near the hub, while the leakage flow velocity is highest near the rim. The leakage flow velocity of the squealer blade tip impeller is reduced to a certain extent. Transition zone blade 1 (Fig. 15. c) has the highest leakage flow velocity near the rim. The leakage flow velocity of the squealer blade tip impeller is significantly lower than that of the prototype impeller. The squealer blade tip has a good suppression effect on the leakage flow in the axial clearance of the liquid-ring pump.

Fig. 15
figure 15

Velocity distribution in different zones: (a) Velocity distribution of blade 5 in the suction zone; (b) Velocity distribution of blade 15 in the exhaust zone; (c) Velocity distribution of blade 1 in the transition zone.

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Table 2 shows abbreviations and mathematical symbols used in this paper.

Table 2 Abbreviations and mathematical symbols.
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Conclusions

This paper aims to analyze the suppression mechanism of squealer blade tip. The suppression effect of the squealer blade tip in different zones of liquid-ring pump was analyzed. Three conclusions are summarized as follows:

  1. (1)

    The total leakage flow of the squealer blade tip pump is lower than that of the prototype pump at three working conditions, and is reduced by 10.7%, 12.4%, and 13.8% respectively. The vacuum degree has increased by 2.4%, 2.9%, and 4.1% respectively. The hydraulic performance of the liquid-ring pump has been improved to some extent.

  2. (2)

    The squealer blade tip can effectively suppress the axial clearance leakage flow of the liquid-ring pump. When the leakage flow flows into squealer, it interacts with the low-speed fluid in the squealer to form the pressure side corner vortex and the squealer vortex. The rotation direction of the pressure side corner vortex is opposite to that of the squealer vortex. There is a strong shear effect between the pressure side corner vortex and the squealer vortex, which blocks the axial clearance flow channel and suppresses the leakage flow.

  3. (3)

    The squealer blade tip has a certain suppression effect on liquid leakage flow in different zones, and the dynamic pressure of the squealer blade tip impeller can be significantly increased in the compression zone. The liquid dynamic pressure of the squealer blade tip impeller increases significantly, thus the compressibility of the liquid is also improved to a certain extent. Therefore, the inlet vacuum degree of the squealer blade tip impeller has increased to a certain extent.

In future work, investigating how to reduce the error band between numerical simulation results and experimental results might prove important. The reason for the certain error in performance may be that the heat transfer between gas and liquid cannot be accurately set in unsteady calculations. Further research is needed to confirm this novel finding.