Effect of the tip clearance on tip leakage vortex and pressure fluctuation characteristics in a helico-axial flow multiphase pump

In the past few years, with the depletion of land mineral resources inch by inch, the imperious demands to find new energy sources to alleviate the crisis are drawn in. Actually, the deep-sea resources are very rich, mainly including oil and gas, minerals, natural gas hydrate, etc., especially natural gas hydrate. In the deep-sea, the distribution area of natural gas hydrate reaches 40 × 10⁶ square kilometers, which accounts for 1/4 of Earth’s ocean area. In 2011, 116 natural gas hydrate distribution regions were discovered in the world. Compared with the conventional natural gas fields, the scale and scope of the natural gas hydrate are very large. Therefore, the world’s countries are focusing the energy exploration in the deep sea. With their constant efforts, the contributions are increasing yearly. In the process of deep-sea energy, the multiphase transportation is a core technology since it improves the production efficiency, saves the cost of infrastructure and equipment management, optimizes the layout transportation system, and reduces environmental requirements.^1–4 Furthermore, multiphase pumps play an essential role in deep-sea energy. Since multiphase pumps are successfully tested, they have been widely used in land and deep-sea energy exploration.^5–8 

After years of research, at present, the more refined pump types are mainly helico-axial flow multiphase pumps (rotodynamic pump) and twin-screw multiphase pumps (positive displacement pumps). Because of the compact construction, large discharge, and the insensitive characteristic to a small amount of particulate matters, rotodynamic pumps are considered an ideal piece of equipment for deep-sea energy transportation. However, the rotor–stator interaction (RSI), consequently, leads to pressure fluctuation, flow instability, and the external vibration and noise of the whole unit, which seriously threaten the safety and stability of the unit. Moreover, with respect to inevitable tip clearance (Fig. 1), the tip leakage vortex (TLV) is generated, and it complicates the flow pattern and degrades the pump performance.

So far, multiple extensive research studies have been carried out on pressure fluctuation. Zhang et al.⁹ used numerical simulation methods to investigate the pressure fluctuation traits under different tip clearances. The dominant frequency of pressure fluctuations gradually increases with increasing tip clearance. Zhang et al.¹⁰ took advantage of the two-fluid model to study the pressure fluctuation properties under air–water two-phase conditions. The trend of pressure fluctuation is similar to that of a single phase, and RSI is still the primary cause for it. By applying identical manners, Feng et al.¹¹ uncovered the effect of tip clearance in the axial flow pump and found that the tip clearance amplifies the pressure fluctuation in the pump impeller. However, the increased tip clearance did not have the same effect on the pump diffuser. Xu et al.¹² disclosed the identities of the flow and pressure fluctuation in a mixed-flow pump in the cavitation case. The increased tip clearance significantly degraded the pump performance, and the dominant frequency altered at different cavitation states. Ji et al.^13,14 utilized the numerical simulation method to uncover the energy traits in the mixed pump. The expansion of tip leakage flow (TLF) increased the energy losses in the pump impeller, while the hydraulic losses in the pump diffuser were decreased. In addition, the flow instability at the inlet augmented with the increase in the tip clearance. Pei et al.¹⁵ used computational fluid dynamics (CFD) technology to probe into the pressure fluctuation features in a radial single blade pump. According to the research, the larger pressure fluctuations occurred at the pressure side (PS), while the larger fluctuation gradient occurred at the trailing edge (TE). In short, the RSI in the rotodynamic pump is the primary cause for the pressure fluctuation. Similarly, the tip clearance had a greater effect on the pressure fluctuation.^16–18 The effect of tip clearance on pressure fluctuation is related to the TLV. Accordingly, many scholars have carried out related research on the TLV. The formation and evolution of the TLV in rotating machinery are very complicated. To conveniently reveal its rules, the research on a single hydrofoil is usually carried out at the beginning.^19–21 By taking numerical simulation approaches, Liu and Tan²² took a hydrofoil with a gap as the object and investigated the effect of C-shaped grooves on vortex suppression. The C-shaped grooves can suppress vortexes under different conditions. In addition, Guo et al.²³ also investigated the impact of rounding on the hydrofoil property. Through research, the sharp shape decreased the leakage loss and aggrandized the velocity gradient. Furthermore, many scholars have conducted research on turbomachinery. Zhang et al.²⁴ chose numerical and experimental methods to investigate the cavitation characteristics of the TLV. As results revealed, when the flow rate grows, the beginning point of the TLV moves toward the TE. Wu et al.^25,26 adopted particle image velocimetry (PIV) technology to reveal the three-dimensional (3D) structure of the TLV. At the beginning, the TLV entrained on the blade suction side (SS) and then propagated toward the adjacent PS. David et al.²⁷ utilized high-speed photography and PIV technology to study the flow features. When the flow rate decreases, the TLV entrained in the upstream of the compressor rotor, and the initial direction changed to the circumferential direction. Liu and Tan²⁸ applied the numerical simulation approach to investigate the vortex identities. The TLV structures were divided into four categories. Tan et al.²⁹ investigated the impact of a T-shaped structure on the pump performance, applying numerical simulation methods, and found that the T-shaped tip clearance reduced the maximum amplitude of the pressure fluctuation.

In recent years, based on the above-mentioned analysis, research has been conducted on the pressure fluctuation traits in rotodynamic pumps. However, because of the pressure fluctuation and TLV, the flow pattern and action mechanism in multiphase pumps are very complicated. As far as the current literature is concerned, there are few correlation analyses between the pressure fluctuation and the TLV. The characteristics and mechanism of the pressure fluctuation and the TLV are still unclear, but their impact on performance is huge. Hence, the research is urgent and necessary. In view of this, on the strength of the combination approaches of numerical simulation and experiment, with different tip clearances (R_tc = 0.5, 1.0, and 1.5 mm) under off-design operating conditions, the TLV and pressure fluctuations characteristics are studied in the present work. Clearly, its aims are to reveal the flow law and pressure fluctuation mechanism and give a reference to the safe, stabilized, and high-efficient operation of the pump.

For numerical simulation, a single pressurization unit of a six-stage pump was selected. To reduce the effect of the inlet backflow and outlet backflow, and to fully develop the flow, the pump impeller inlet as well as the diffuser outlet was extended as shown in Fig. 2. The main design and performance parameters are provided in Table I. To analyze the flow and pressure fluctuation, three different tip clearances (R_tc = 0.5, 1.0, and 1.5 mm) are purposefully designed. The meridian plane parameters of the pump impeller and the diffuser are presented in Fig. 3.

The quality of the mesh is very crucial to the accuracy and convergence of the numerical results. Therefore, a high-quality hexahedral structure mesh is employed for all parts of the numerical computational domain. In addition, the balance of the mesh size on the interface of each computational domain is considered. In addition, to adjust the boundary layer and mesh quality, the mesh around the blade is arranged by the O-shape topology, and to capture the flow details, the mesh near the tip clearance is refined, as shown in Fig. 4.

Mesh density is of great importance to the simulation accuracy and results, and to make sure the mesh number for numerical simulation is optimum, the independence verification is performed, as provided in Table II. From Table II, it can be seen that the error of the pump head and efficiency between mesh 5 and mesh 4 do not exceed 0.2%; however, the number of mesh 5 is more than 1 × 10⁶ than that of mesh 4. The accuracy and cost are comprehensively weighed. Then mesh 4 is finally selected in the present work.

After the mesh independence verification is completed, for the sake of eliminating the effect of time step on the results, the final simulation mesh is adopted to verify the time step. The time steps are 5.56 × 10⁻⁵, 1.11 × 10⁻⁴, and 1.67 × 10⁻⁴ s, and they correspond to an impeller rotation time of 1°, 2°, and 3°, respectively. Figure 5 shows the time history of pressure fluctuation at the impeller outlet and the diffuser inlet under different time steps. As shown in Fig. 5, the pressure at the monitoring points is almost coincident, so the impact of the time step is ignored. In addition, the time and accuracy are taken into consideration, and the time step is chosen as 1.11 × 10⁻⁴ s.

The Reynolds averaged Navier–Stokes (RANS) equations were employed to simulate the steady and unsteady 3D flow patterns in the pump. In the process of simulation, the finite volume method (FVM) was used, and the governing equations are discretized. Meanwhile, the pressure and velocity are coupled by the semi-implicit method for pressure linked equations (SIMPLE) algorithm. The specific settings are shown in Table III. The steady-state results were the initial values for the unsteady simulation. The entire unsteady simulation was conducted for 16 revolutions of the impeller, and the last 6 revolutions for stable flow were taken for analysis.

Figure 6 shows the schematic of the multiphase pump test bench, which is mainly composed of a mixing tank, motor, multiphase pump, control system, lubrication system, water supply system, gas supply system, and cooling system and pipelines and valves. Besides, to capture the tip flow field more accurately, an impeller shroud is made of transparent Plexiglas.

To validate the accuracy of the simulation methods, the flow patterns in test is used to compare with the simulated results. Figure 7 provides the flow patterns between the experiment and simulation. As shown in Fig. 7, there is a TLV structure near the blade SS and the adjacent blade leading edge (LE), and the same phenomenon appeared in the numerical simulation as well. The numerical flow patterns correspond with that of the experiment.

Figure 8 shows the pump head and efficiency under different tip clearances. From Fig. 8(a), it can be seen that the tip clearance makes a great difference on the head. The head gradually decreases as the tip clearance increases, whereas the trend and degree of the head are different as well. The head drop caused by the tip clearance from 0.5 to 1.0 mm is larger than that from the 1.0 to 1.5 mm. Concurrently, the table presents the magnification of the flow rate, where the head variation with R_tc = 0.5 mm shows a linear trend. However, the head with R_tc = 1.0 and 1.5 mm fluctuates with the variation in the flow rate. The larger the blade tip clearance size is, the more obvious the fluctuation becomes. In addition, from Fig. 8(b), it can be seen that the best efficiency point (BEP) with different tip clearance sizes is near the design discharge. Even when the tip clearance is small, it has a great impact on the efficiency. For example, the tip clearance from 0.5 to 1.5 mm is changed only by 1.0 mm, while the efficiency has dropped by 17.5% at the design discharge. After the design flow rate point, the larger the tip clearance is, the faster the decrease in the efficiency is.

To clearly illustrate the pressure fluctuation characteristics in the multiphase pump, the pressure fluctuation intensity as well as pressure coefficient is specially defined,

where N represents the sample points in the statistical period, p_i represents the pressure at every time step, and $p̄$ represents the arithmetic average. $p′̄$ denotes the pressure defined by the root mean square (rms) method. To easily compare and analyze, the value is nondimensionalized,

where U_tip represents the circumferential velocity near the tip at R_tc = 1.0 mm, and the value is 24.96 m/s. ρ represents the density of water.

Figure 9 shows the TLV patterns in the impeller passage and the pressure fluctuation intensity on the blade surface. Figure 9(a) shows that there is no obvious TLV in the blade flow passage with R_tc = 0.5 mm, except for a small-scale TLV near the adjacent blade inlet LE. The entrainment between the TLF and the mainstream in the tip region with R_tc = 1.0 mm is larger than that with R_tc = 0.5 mm. Simultaneously, there is a small scale of entrainment near the tip. The TLV near the adjacent blade LE is also more evident. When the tip clearance increases to 1.5 mm, the TLV structure becomes more obvious. With the extension of the tip clearance size, the TLF is increased, and the entrainment and mixing between the main flow and the TLF are more distinct, so the TLV structure is also more remarkable. Besides, from Fig. 9(b), it can be seen that there is a large pressure fluctuation intensity on the impeller blade surface. To sum it all up, with the growth of the tip clearance size, the pressure fluctuation intensity on the blade surface is also strengthened. The greater the pressure fluctuation intensity coincides with the TLV location, the greater the pressure fluctuation intensity near the LE and TE will be. The incoming flow direction is inconsistent with the blade angle, which causes the impact phenomenon at LE. Then pressure fluctuation intensity near the LE is greater. The flow from the blades PS and SS is converged at TE, and the pressure fluctuation intensity near the TE is also greater. The details of the flow behavior are shown in the enlarged red box in Fig. 10.

To thoroughly uncover the correlation properties of the TLV and pressure fluctuation, the pressure fluctuation intensity and TLV structure on the three sections (sections 1–3) are shown in Fig. 11. As shown in Fig. 11, when the tip clearance size increases, the TLV from section 1 to section 3 is gradually strengthened, and the TLV always corresponds to the larger pressure fluctuation intensity. Therefore, the TLV gradually amplifies the pressure fluctuation intensity.

To investigate the inherent correlation properties of the TLV and pressure fluctuation, the case at R_tc = 1.5 mm is taken as an example, and five sections are set in the tip clearance from the TLV formation location to the blade TE. The sections are named section TC1 to section TC5. The velocity vector and pressure fluctuation intensity are given on the sections, as shown in Fig. 12. From Fig. 12, it can be seen that when the TLF flows into the tip clearance, because of the right angle, the tip separation vortex (TSV) is generated at section TC1 and the pressure fluctuation intensity adjacent the TSV is stronger. Along the streamwise direction, the TSV is further enlarged at section TC2, and the maximum pressure fluctuation intensity also expands, whose proportion reaches the maximum in all the sections. From section TC3 to section TC5, the range of the TSV increases inch by inch, and the TSV penetrates the entire tip clearance at section TC5. Nevertheless, the pressure fluctuation intensity and the proportion gradually decreased. In addition, from section TC3, the low pressure fluctuation intensity appears, which is the TLF into the tip clearance, and its proportion gradually grows along the streamwise direction.

Base on the analysis mentioned above, it can be said that the entrainment effect between the TLF and main flow is strong and then a more apparent TLV is formed. Thus, to further probe into the transient features of the TLV, the isosurface of swirling strength is used to show the spatial–temporal evolution within a revolution period T of the impeller, as presented in Fig. 13. In Fig. 13, it can be seen that the spatial–temporal evolution is mainly classified into the following three stages: split stage, contraction stage, and recurrence stage. (1) split stage [T0–T0 + 2/6T]: the TLV begins to split at the adjacent blade LE, and the split TLV gradually dissipates. (2) contraction stage [T0 + 2/6T–T0 + 4/6T]: the TLV on the blade SS gradually shrinks until it disappears completely. (3) recurrence stage [T0 + 5/6T–T0 + T]: the TLV gradually begins to appear, and that at T0 + T is already consistent with that at T0.

The TLV causes a complicated flow phenomenon, which aggravates trembling and extremely affects the operation. To disclose pressure fluctuation traits, three monitoring points are arranged—at the inlet, middle, and outlet—on the impeller blade, named IPS1–IPS3. In the meanwhile, three monitoring points are evenly arranged—at the inlet, middle, and outlet—near the tip, named TC1–TC3. The monitoring points in detail are shown in Fig. 14.

The multiphase pump in the present work is composed of an impeller with 3 blades and a diffuser with seven blades. In addition, the rotation speed is 3000 rpm, so the rotational frequency f_n = 50 Hz. Figure 15 shows the pressure fluctuation at those survey points. From Fig. 15, it can be seen that the pressure fluctuation presents a good periodic trend and there are seven similar waveforms in one period, which is consistent with the blade number of the diffuser. This is chiefly affected by the RSI. Meanwhile, the pressure fluctuation waveform at monitoring point ISS3 is different from that at IPS3, and the number of similar waveforms is also different at the different tip clearances because it is affected by both RSI and TLV at the blade SS outlet. As the tip clearance size varies, the effect of the TLV is altered too, which leads to different pressure fluctuation characteristics. As the monitoring point gradually moves away from the rotor–stator interface, the RSI is gradually weakened. Therefore, the number of similar waveforms of the pressure fluctuation at IPS1 and IPS2 also differs with the diffuser blade number. Moreover, apart from the RSI being weakened, it is also affected by the TLV. Then, a similar situation at ISS1 and ISS2 occurs.

To study the frequency properties of pressure fluctuation, the fast Fourier transform (FFT) is performed for each survey point. Figure 16 shows the spectral diagram of pressure fluctuation at the blade tip of the impeller. In the case with R_tc = 0.5 mm, the dominant frequency at each survey point is the low; meanwhile, the amplitude of the dominant frequency is relatively large. The effect of the strong wall jet strengthens the flow fluctuation near the tip, and the low-frequency high-amplitude pressure fluctuation is associated with the strong jet flow effect. With the enlargement of the tip clearance size, the jet effect weakens; synchronously, the closer it is to the rotor–stator interface, the stronger the RSI is. The pressure fluctuation is chiefly affected by the RSI when the tip clearance size is larger and the survey point is closer to the impeller outlet. Furthermore, the amplitude of the dominant frequency on the blade PS has no apparent correlation with the increase in the tip clearance size. However, the dominant frequency amplitude at the blade SS gradually increases as the tip clearance expands.

Under the pressure difference, the TLF passes through the tip clearance in the form of a jet flow. At the same time, the TSV, flow separation, backflow, and other phenomena also accompany, so the flow patterns are more complicated. Figure 17 shows the pressure fluctuation, and from Fig. 17, it can be seen that as the survey point gradually approaches the rotor–stator interface, the pressure fluctuation is affected by the RSI and is similar to the points at the impeller blade tip. In the meantime, the pressure fluctuation at different survey points at R_tc = 0.5 mm is similar. In addition, at different points, the pressure fluctuation at R_tc = 1.0 and 1.5 mm is quite different.

Figure 18 shows the spectral diagram of pressure fluctuation; as the survey point is close to the rotor–stator interface, the dominant frequency is easily affected by the RSI, which is the most evident feature of the spectral diagram. Simultaneously, the dominant frequency is the low-frequency for R_tc = 0.5 mm. This is consistent with the frequency traits on the impeller blade PS and SS. Furthermore, the amplitude of the low-frequency at point 2 is larger than that at the other two points at different tip clearances.

Table IV lists the dominant frequency and amplitude of the tip clearance. From Table IV, it can be seen that the variation trend along the streamwise direction varies under different tip clearance sizes. (1) R_tc = 0.5 mm: The dominant frequency at points is 0.167 f_n, and the amplitude of the dominant frequency gradually declines. (2) R_tc = 1.0 mm: The dominant frequency on points TC1 and TC2 is the same; however, it is reduced to 0.667 f_n at the rotor–stator interface. The amplitude reaches the maximum at monitoring point TC2. (3) R_tc = 1.5 mm: The dominant frequency at the survey point gradually augments, and the value near the rotor–stator interface is 7 f_n. Based on the analysis mentioned above, under different tip clearance sizes, the amplitude at monitoring point TC2 reaches the maximum. Because the pressure difference is the largest, the TLF is most evident. Accordingly, the amplitude of the dominant frequency becomes larger.

Figure 19 shows the peak-to-peak amplitude of the pressure fluctuation near the blade tip. On the blade PS, the pressure fluctuation amplitude at survey point IPS2 is the smallest at different tip clearances, and the amplitude for R_tc = 0.5 mm is the largest. Simultaneously, on the blade SS, the pressure fluctuation amplitude at point ISS2 for R_tc = 0.5 and 1.0 mm is also the smallest. For R_tc = 1.5 mm, along the streamwise direction, the pressure fluctuation amplitude gradually increases. In total, when R_tc = 0.5 mm, the maximum pressure fluctuation amplitude appears at the impeller blade SS inlet and outlet. For R_tc = 1.5 mm, the minimum pressure fluctuation amplitude appears at the impeller blade SS inlet.

Based on the simulation and experiment, the TLV and pressure fluctuation characteristics are investigated, and the conclusions are drawn as follows:

1. Tip clearance has a great influence on the head and efficiency. As the tip clearance sizes aggrandize, the head and efficiency are gradually decreased. Concurrently, after the design flow point, the larger the tip clearance size is, the more obvious the head fluctuation develops. Moreover, the efficiency drops faster.

2. With the extension of the tip clearance size, the TLV is gradually obvious. All at once, the pressure fluctuation intensity close to the TLV is larger. The TLF flows into the tip clearance, the TSV is formed, and the range of the TSV from the TLV formation location to the blade TE increasingly enlarges. The maximum pressure fluctuation intensity appears near the TSV, and the proportion of the maximum pressure fluctuation intensity first increases along the streamwise, gradually decreasing after reaching the maximum. Furthermore, the greater pressure fluctuation intensity at the LE and TE is caused by the mixing effect. The spatial–temporal evolution is mainly divided into the following three stages: split stage, contraction stage, and recurrence stage.

3. Under different tip clearances, the RSI is still the main cause for the pressure fluctuation, especially near the rotor–stator. The dominating frequency is concentrated at seven times the rotational frequency. In addition, the low-frequency amplitude at monitoring points in the impeller blade tip at R_tc = 0.5 mm is larger, which is associated with the jet flow effect in the minor-scale clearance.

This work was supported by the Central Leading Place Scientific and Technological Development Funds for Surface Project (No. 2021ZYD0038), the Open Research Fund Program of the State Key Laboratory of Hydroscience and Engineering (Grant No. sklhse-2021-E-03), the National Key Research and Development Program (No. 2018YFB0905200), and the Key Scientific Research Fund of Xihua University of China (Grant No. Z1510417).

The authors have no conflicts to disclose.

Haigang Wen: Conceptualization (lead); Writing – original draft (equal). Wenjuan Lv: Formal analysis (equal). Guangtai Shi: Supervision (equal). Zongku Liu: Software (equal).

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

BEP

best efficiency point

CFD

computational fluid dynamics

f

frequency (Hz)

FFT

fast Fourier transform

f_n

rotational frequency (Hz)

FVM

finite volume method

H

head (m)

LE

leading edge

N

number of sample points in the statistical period

n

design speed (rpm)

p_i

pressure for each time step (Pa)

$p̄$

arithmetic average value in the statistical period (Pa)

$p′̄$

pressure defined by the rms method (Pa)

PIV

particle image velocimetry

PS

pressure side

Q

design flow rate (m³/h)

RNG

re-normalization group

RSI

rotor–stator interaction

rms

root mean square

R_tc

tip clearance (mm)

SIMPLE

semi-implicit method for pressure linked equations

SST

shear stress transport

SS

suction side

TE

trailing edge

TLV

tip leakage vortex

TLF

tip leakage flow

TSV

tip separation vortex

U_tip

tip circumferential velocity (m/s)

Z₁

impeller blades

Z₂

diffuser blades

ρ

water density (kg/m³)

Subscripts

1

impeller

2

diffuser

tip

blade tip