Numerical analysis for the effect of tip clearance in a low specific speed mixed-flow pump

Abstract

To study the influence of tip clearance on performance (external characteristics, pressure fluctuation and tip loss) of a low specific speed mixed-flow pump, unsteady simulation was performed for the whole flow passage with five tip clearance sizes (δ₀ = 0 mm, δ₁ = 0.10 mm, δ₂ = 0.25 mm, δ₃ = 0.75 mm and δ₄ = 1 mm). The reliability of the numerical methodology was verified in external characteristics (efficiency, head and power) and fluctuation. The performance of the pump was obtained under different discharges and tip clearance sizes using ANSYS CFX. The results showed that the variation of tip clearance size has greater effect on the external characteristics under large discharges. Meanwhile, along the flow direction, the fluctuation coefficients near the impeller shroud increase gradually with the smaller tip clearance sizes (δ = 0.10 and 0.25 mm), while for the larger tip clearance sizes (δ = 0.75 and 1.00 mm), the significant increase of fluctuation near the shroud of impeller inlet is closely associated with the clear leakage vortex and the large region of low pressure. Besides, with the increase of tip clearance size, the effect of tip clearance will become more remarkable under different discharge conditions. According to this study, for the optimization design of such pumps, the size of the tip clearance is suggested to be about 0.9% times the blade height at middle of the impeller passage.

Keywords

Mixed-flow pump tip clearance low specific speed external characteristics pressure fluctuation tip loss

Introduction

Because the tip clearance (TC) of the mixed-flow pumps exists between impeller shroud and pump case, so the leakage of fluid is easily to happen. Also, the tip leakage vortex aroused by the TC may seriously affect the mainstream flow, resulting in the enhancement of pressure fluctuation and the degradation of overall performance of the pump.^1–6

In recent years, many studies have been carried out in the aspects of the effect of TC on external characteristics, pressure fluctuation and tip leakage for pumps. In the first aspect, by setting different TC sizes of a mixed-flow pump, Li et al.⁷ found the positive slope characteristic of the head curve could be effectively suppressed when TC was 0.5 mm. Meanwhile, Dong et al.⁸ and Tan et al.⁹ also found that the impeller TC effect could change the head curve of the mixed-flow pump. Also, Bing et al.¹⁰ experimentally determined the external characteristics of a mixed-flow pump with different TCs and found that they all decrease with the TC increases. However, few quantitative studies were performed on the sensitivity of the external characteristics of pump to the TC size, especially for the low specific speed mixed-flow pump (LSSMFP).

For the aspect of pressure fluctuation, by simulating an axial flow pump, Feng et al.¹¹ demonstrated that the existence of TC will increase the pressure fluctuation from hub to shroud of the impeller, while no obvious impact on the pressure fluctuation in the diffuser. Meanwhile, Zhang et al.¹² found that the tip leakage had larger impact on the pressure fluctuation in impeller than that in diffuser by investigating the TC effect of a mixed-flow pump. Besides, Zhang et al.¹² and Liu and colleagues^13,14 obtained a similar conclusion, that is, the pressure fluctuation will increase dramatically if the TC increases to 1 mm. Many studies have shown that the pressure fluctuation in the pumps will be enhanced with the increase of TC size. However, when the TC size is small enough, the pressure fluctuation will also be enhanced as a result of the enhancement of the rotor–stator interaction between impeller shroud and pump case, while few studies have been performed on this case.

For the aspect of tip leakage flow, Li et al.¹⁵ explored the phenomenon of rotating stall in a mixed-flow pump and found that some vortexes were generated due to the mixture between mainstream and leakage flow. Also, many studies so far have focused on the leakage vortex. By investigating the evolution of tip leakage vortex, Miorini et al.¹⁶ obtained that the leakage vortex could cause the flow separation. However, Yang et al.¹⁷ found that the leakage vortex in a synchronal rotary multiphase pump could be effectively suppressed by reducing the rotor radial clearance.

Although many studies on the effect of TC on the performance of pump have been investigated by far, the effect of TC has not been quantitatively evaluated and no unified standard for the selection of TC size in the optimization design of pumps. In this study, under different TC sizes, the unsteady flow in a LSSMFP was simulated with ANSYS CFX 14.0. The sensitivity of the efficiency variation to the TC variation was analysed, and the relationship between tip leakage and pressure fluctuation was discussed, which will help in the optimization design for the LSSMFP.

Configuration description of the mixed-flow pump

The configuration descriptions of the pump are listed in Table 1. According to equation (1),¹⁸ the specific speed of this pump is determined to be 149. Meanwhile, the three-dimensional calculation model and the experimental pump model are presented in Figures 1 and 2, respectively.

Table 1.

Configuration descriptions of the pump.

Mixed-flow pump	Items	Values	Units
Impeller	Blade numbers of impeller Z₁	6	–
	Shroud diameter of impeller inlet D_1S	106	mm
	Shroud diameter of impeller outlet D_2S	177	mm
	Hub diameter of impeller inlet D_1H	51	mm
	Hub diameter of impeller outlet D_2H	168	mm
Diffuser	Blade numbers of diffuser Z₂	8	–
	Shroud diameter of diffuser outlet D_3S	160	mm
	Hub diameter of diffuser outlet D_3H	30	mm
Design operating point	Discharge Q_d	1.39	m³/min
	Head H_d	14.6	m
	Rotational speed n	2000	r/min

Figure 1.

Calculation model.

Figure 2.

Experimental model.

Furthermore, the relevant content of experiment has been described in previous published literature¹²

n_{s} = \frac{3.65 n \sqrt{q_{v}}}{H_{d}^{3 / 4}}

(1)

Numerical methodology

Governing equations

To simulate the turbulence flow in the pump, unsteady Reynolds-averaged Navier–Stokes (URANS) equations were solved using the commercial code ANSYS CFX 14.0. The continuity and momentum equations in the Cartesian coordinates can be written as

\frac{\partial u_{i}}{\partial x_{i}} = 0

(2)

\begin{matrix} \frac{\partial ρ u_{i}}{\partial t} + \frac{\partial}{\partial x_{j}} (ρ u_{i} u_{j}) = - \frac{\partial p}{\partial x_{i}} \\ + \frac{\partial}{\partial x_{j}} [(μ + μ_{t}) (\frac{\partial u_{i}}{\partial x_{j}} + \frac{\partial u_{j}}{\partial x_{i}})] + F \end{matrix}

(3)

where F is the sum of body forces, $μ$ is the viscosity of the fluid, $μ_{t}$ is the turbulence viscosity and p is the pressure.

To verify the applicability of the turbulence model, the turbulence is modelled by the $k - ε$ , renormalization group (RNG) $k - ε$ , $k - ω$ and shear stress transport (SST) $k - ω$ models under design condition with the TC value of 0.25 mm (0.25 mm is the design TC size). The results for simulation and experiment are shown in Table 2; here, the relative error is defined as

Δ = | R_{sim} - R_{\exp} | / R_{\exp} \times 100 %

(4)

where R_sim and R_exp denote the performance value from simulation and experiment, respectively. From Table 2, the relative errors of the efficiency and the head calculated by SST $k - ω$ and RNG $k - ε$ turbulence models are smaller. On the other hand, the SST $k - ω$ model uses standard $k - ω$ model at near-wall region and $k - ε$ model away from the wall, so it has been designed to avoid the freestream sensitivity of the standard $k - ω$ model, which determines that the flow separation from smooth surface can be accurately solved by this model.^19,20 Therefore, the SST $k - ω$ turbulence model is selected in present study.

Table 2.

Comparison results between simulation and experiment.

Items	Simulation				Experiment
Items	SST k–ω	RNG k–ε	k–ε	k–ω	Experiment
Efficiencyη (%)	84.74	84.31	85.13	85.64	80.87
Head H (m)	14.46	14.38	14.65	14.76	14.55
Efficiency error Δ_η (%)	4.79	4.25	5.27	5.90	0.00
Head error Δ_H (%)	0.62	1.17	0.69	1.44	0.00

SST: shear stress transport; RNG: renormalization group.

Structured grid and numerical solutions

Structured grids are generated for all parts of this pump, for the inlet and outlet pipes, the grids are generated with ICEM CFD 14.0, while for the impeller and diffuser passages, the grids are created with TurboGrid 14.0. Furthermore, H/J/C/L topologies are applied to the impeller and diffuser passages,¹⁹ the values of Yplus at the blade wall are about 25, which is acceptable for the SST $k - ω$ turbulence model.¹² The grids for the impeller and diffuser passages are presented in Figure 3. Meanwhile, four grid densities are used to test the grid independence under steady simulation condition (Q = Q_d), as listed in Table 3. Simulation results indicate that these four grid densities have no remarkable influence on head and efficiency of the pump. Therefore, Grid₁ with 3,624,513 elements is chosen ultimately.

Figure 3.

Grids for (a) impeller and (b) diffuser passages.

Table 3.

Analysis of grid independence.

Item	Grid₁	Grid₂	Grid₃	Grid₄
Impeller	202,720 (×6)	237,728 (×6)	272,160 (×6)	302,400 (×6)
Diffuser	200,124 (×8)	236,656 (×8)	274,554 (×8)	305,060 (×8)
Inlet pipe	293,930	293,930	293,930	293,930
Outlet pipe	513,271	513,271	513,271	513,271
Computational domain	3,624,513	4,126,817	4,636,593	5,062,081
H/H₁	1	0.9994	0.9974	0.9961
η/η₁	1	1.0003	0.9994	0.9987

At the inlet and outlet of the computational domain, the discharge and average pressure are specified, respectively. Nonslip condition of viscous fluid is imposed on the near-wall region and a transient rotor–stator approach is adopted for data exchange in the rotor–stator interaction region (namely the impeller–inlet pipe interface region and impeller–diffuser interface region). The unsteady simulation is initiated with the results of steady simulation. At the unsteady simulation stage, the timescale plays a key role in determining the numerical results, so two time steps (Δt₁ = 0.00015 s, Δt₂ = 0.0002 s) were analysed, as shown in Figure 4. There is little difference in the pressure variation of monitoring points PS₂–PS₄ at these two time steps. Therefore, Δt₂ = 0.0002 s was selected finally to improve the computational efficiency. Meanwhile, the total time is 0.3 s, namely 15 cycles are calculated for the unsteady simulation;²¹ root mean square (RMS) residual < 1 × 10⁻⁴ is regarded as the convergence criteria. The schemes of high-resolution and second-order backward Euler are adopted for the advection and transient terms, respectively.

Figure 4.

Time domain characteristics of monitoring points PS₂–PS₄ at two time steps.

Setting of numerical and experimental points

The numerical monitoring points are set near the impeller shroud to acquire the effect of TC on the pressure fluctuation therein, as shown in Figure 5(a), where points PS₁–PS₄/SS₁–SS₄ are located near the pressure/suction surfaces, respectively. Due to the technical reasons, the pressure sensors are only deployed on the hub of diffuser in this test. The experimental points in the diffuser are displayed in Figure 5(b); also, the numerical monitoring points in the diffuser are set accordingly to compare with the experimental results.

Figure 5.

Setting of numerical and experimental points: (a) numerical points in the impeller and (b) points on the hub of the diffuser.

Results and discussions

Validations of external characteristics and fluctuation characteristics

The results of unsteady simulations under 10 discharge conditions (δ₁ = 0.25 mm) are shown in Figure 6. The variation trend of the numerical efficiency, head and power curves is in agreement with the experimental ones. The pressure fluctuation characteristics of points H_5C–H_8C (Figure 5(b)) with the TC of 0.25 mm under design condition are displayed in Figure 7. On the whole, the fluctuation characteristics from simulation are consistent with the experiment; 6 fn and 12 fn are the dominant frequency and subdominant frequency in these two cases, respectively. Therefore, based on the above analysis, it can be concluded that the numerical method used in our study is reasonable.

Figure 6.

Comparison results for simulation and experiment (relative discharge m = Q/Q_d).

Figure 7.

Fluctuation characteristics of points H_5C–H_8C under conditions of m = 1, δ₁ = 0.25 mm.

Effect of TC on the external characteristics

In order to provide a theoretical basis for the TC’s selection in the optimization design of the LSSMFP, the effect of TC size on the external characteristics and internal flow is explored. Here, five discharge conditions (0.5Q_d, 0.75Q_d, 1Q_d, 1.25Q_d and 1.5Q_d) with each TC size (δ₀ = 0 mm, δ₁ = 0.10 mm, δ₂ = 0.25 mm, δ₃ = 0.75 mm and δ₄ = 1 mm) are studied; the results are presented in Figure 8. For the same relative discharge, the values of efficiency and head of this pump decrease gradually with the increase of TC size; this is mainly because the volumetric loss caused by the tip leakage increases with the TC increases. Besides, the differences of external characteristic values (efficiency, head and power) under large discharge conditions (1.25Q_d, 1.5Q_d) are greater than for small discharge conditions (0.5Q_d, 0.75Q_d). This is because the flow separation occurs near the pressure surface under large discharge condition; thus, the fluid therein will be subjected to a weaker driving effect by the mainstream. Then, under the action of pressure difference between the two sides of the blade, the tip leakage is easier to happen and results in greater hydraulic and volumetric losses. Meanwhile, it indicates that the effect of the TC variation on the internal flow is more prominent under large discharge conditions.

Figure 8.

Comparison of external characteristics from simulation with different TCs: (a) relative discharge–efficiency characteristics, (b) relative discharge–head characteristics and (c) relative discharge–power characteristics.

According to Figure 8(a), the relationship between the efficiency reduction Δη and the relative discharge m can be obtained under different TC variations (Δδ₁ = δ₄ − δ₃ = 0.25 mm, Δδ₂ = δ₃ − δ₂ = 0.5 mm, Δδ₃ = δ₄ − δ₂ = 0.75 mm), as shown in Figure 9. It can be seen that under different TC variations, the trend of efficiency reduction is similar to each other, while the slope of the relative discharge-efficiency reduction (m – Δη) curve increases gradually with the TC variation increases. Meanwhile, the variation range of efficiency reduction Δη is small under different TC variations at m < 1; while it expands significantly at m > 1. This is because more serious leakage loss happens under larger discharge conditions, and which is in accordance with the experiment results obtained by Bing et al.¹⁰

Figure 9.

Relative discharge m–efficiency reduction Δη characteristics.

In addition, the variation trend of the relative discharge–the ratio of efficiency reduction to the TC variation (m – Δη/Δδ) is displayed in Figure 10. The variation trend of m – Δη/Δδ curves is similar under different TC variations, which illustrates that the effect of different TC variations on the efficiency of pump is similar. Besides, the m – Δη/Δδ curves are approximately parabolic under different TC variations, so a mathematical expression (5) can be obtained by fitting. Here, the value of R² for the fitting effect is 0.987

\frac{Δ η}{Δ δ} = 16.5 m^{2} - 14.7 m + 9.2

(5)

Figure 10.

The relative discharge–the ratio of efficiency reduction to TC variation (m – Δη/Δδ).

It reveals from expression (5) that the Δη/Δδ value increases markedly if the relative discharge m increases, that is, for a given Δδ, the efficiency reduction Δη increases rapidly with the relative discharge m increases. Moreover, another form can be derived by deforming

Δ η = (16.5 m^{2} - 14.7 m + 9.2) Δ δ

(6)

Therefore, expression (6) shows that, for a given relative discharge m, there is a liner relationship between the efficiency reduction Δη and the TC variation Δδ, and its slope increases with the relative discharge m increases.

Effect of TC on the pressure fluctuation characteristics

The pressure fluctuation is a phenomenon that the pressure at any point in turbulence varies randomly around its time-averaged signal. Meanwhile, the pressure fluctuation coefficient C_p is usually used to indicate the degree of pressure fluctuation in the pump and it is defined as¹⁴

C_{p} = \frac{σ}{ρ g H_{d}} \times 100 %

(7)

where H_d is the design head; $σ$ is the standard deviation of pressure, namely

σ = \sqrt{\frac{1}{N} \sum_{i = 1}^{N} {[p_{i} (t) - \bar{p_{i}}]}^{2}}

(8)

here, p_i(t) is the instantaneous pressure while $\bar{P_{i}}$ is the average pressure.

The pressure fluctuation coefficients $C_{p}$ of points PS₁–PS₄, SS₁–SS₄ are listed in Table 4. From Table 4, along the flow direction, the C_p of monitoring points near the impeller shroud increases gradually when the TC is smaller (δ = 0.10 and 0.25 mm), which results from the rotor–stator interaction between the impeller and the diffuser. Meanwhile, the fluctuation intensity of the corresponding points at δ₁ = 0.10 mm is larger than that at δ₂ = 0.25 mm, which indicates that although the leakage is smaller at δ₁ = 0.10 mm, the rotor–stator interaction between impeller shroud and pump case is enhanced. For the larger TC size (δ = 0.75 and 1.00 mm), the fluctuation coefficients of monitoring points (PS₁, SS₁) increase dramatically. This is because the leakage increases with the increase of TC size, thus the tip leakage vortex may seriously affect the mainstream flow,¹² resulting in the enhancement of the pressure fluctuation.

Table 4.

C_p of points near the impeller shroud under design condition with different TCs (%).

TCs	Points at pressure surface				Points at suction surface
	PS₁	PS₂	PS₃	PS₄	SS₁	SS₂	SS₃	SS₄
0.10 mm	0.30	0.45	0.63	0.91	0.24	0.35	0.48	0.69
0.25 mm	0.22	0.30	0.38	0.61	0.20	0.24	0.30	0.43
0.75 mm	2.48	0.45	0.29	0.49	0.78	0.74	0.25	0.35
1.00 mm	3.45	2.64	1.35	1.01	2.21	2.16	1.51	0.89

TC: tip clearance.

It can also be obtained from Table 4, the fluctuation intensity of the corresponding points at pressure surface is larger than that at suction surface; thus, the time domain analysis of points PS₁, PS₄ (Figure 5(a)) with four TCs in one cycle is drawn in Figure 11. From Figure 11(a), compared with the smaller TCs (δ = 0.10 and 0.25 mm), the average pressure of point PS₁ under larger TCs (δ = 0.75 and 1.00 mm) is smaller while the fluctuation is larger, which manifests that the large TC size will increase the pressure fluctuation. Form Figure 11(b), the average pressure of point PS₄ decreases with the TC increases. Also, eight peaks and valleys occur during one cycle, which is consistent with the number of diffuser blades.

Figure 11.

Time domain analysis of (a) point PS₁ and (b) point PS₄ with different TCs (Q = Q_d).

The maximum amplitude of pressure fluctuation of points PS₁, PS₄ under different discharge conditions with different TCs is displayed in Figure 12. From Figure 12(a), the maximum amplitude of point PS₁ with different TCs changes little when the discharge is smaller (Q = 0.50Q_d, 0.75Q_d). For the larger discharge conditions (Q = 1.00Q_d, 1.25Q_d), the maximum amplitude of point PS₁ is small under conditions of δ = 0.10 and 0.25 mm, while it increases significantly under conditions of δ = 0.75 and 1.00 mm. that is, for Q = 1.25Q_d, the maximum amplitude of point PS₁ under conditions of δ = 0.75 and 1.00 mm is 22.09 and 8.4 times the condition of δ = 0.25 mm, and 13.86 and 5.27 times the condition of δ = 0.10 mm. This indicates that the maximum amplitude of fluctuation near the impeller inlet is closely associated with the leakage; it will increase markedly if the leakage is large (both the TC size and the discharge are large). Figure 12(b) shows that the maximum amplitude of point PS₄ with different TCs at 0.50Q_d condition is the largest, followed by the 1.25Q_d and 0.75Q_d conditions, then it is the smallest at 1.00Q_d condition.

Figure 12.

Maximum amplitude of (a) point PS₁ and (b) point PS₄ under different discharges with different TCs.

Effect of TC on the tip loss

The existence of TC is a major factor for the volumetric loss. Also, the hydraulic loss can be made by the disturbance of the tip leakage flow on the mainstream.^22,23 Therefore, the tip loss here represents the gross effect aroused from the tip leakage flow. Figures 13 and 14 show the velocity vector and the pressure distribution near the pressure surface, respectively. From Figure 13(a) and (b), the flow separation occurs near the shroud when the TCs are smaller (δ = 0.10 and 0.25 mm). This ascribes to the disturbance of the tip leakage flow and an imbalance between the fluid inertia force within the boundary layer and the inverse pressure gradient.¹² The corresponding pressure distributions of the meridional surface are presented in Figure 14(a) and (b). Meanwhile, some higher speed fluid appears near the shroud at δ₁ = 0.10 mm than that at δ₂ = 0.25 mm, which is closely associated with the larger pressure fluctuation near the shroud at δ₁ = 0.10 mm.

Figure 13.

Distribution of velocity vector near the pressure surface with different TCs (Q = Q_d): (a) δ₁ = 0.10 mm, (b) δ₂ = 0.25 mm, (c) δ₃ = 0.75 mm and (d) δ₄ = 1.00 mm.

Figure 14.

Distribution of pressure near the pressure surface with different TCs (Q = Q_d): (a) δ₁ = 0.10 mm, (b) δ₂ = 0.25 mm,(c) δ₃ = 0.75 mm and (d) δ₄ = 1.00 mm.

When the TC sizes are larger (δ = 0.75 and 1.00 mm), the flow separation area gets larger and the leakage vortex at the impeller inlet becomes more obvious (Figure 13(c) and (d)). It can be seen that a larger region of low pressure appears in the corresponding region, as shown in Figure 14(c) and (d). Then, combined with the results in Table 4, the significant increase in pressure fluctuation of point PS₁ under larger TC sizes is closely connected with the obvious leakage vortexes and the larger region of low pressure.

Based on the results presented in Table 4, Figures 13 and 14, for these four TC sizes, the C_p at corresponding points near the impeller shroud is smallest at δ₂ = 0.25 mm, which reveals that the smaller TC size is not necessarily the better. If the TC size is too small, the rotor–stator interaction between the impeller shroud and the pump case will enhance, while if the TC size is too large, the leakage and the flow separation will aggravate, resulting in the appearance of large leakage vortexes at the impeller inlet. According to this study, 0.25 mm is the most suitable for the TC size. Meanwhile, the blade height at the middle of impeller passage is 28 mm; thus, a suggestion can be made for the optimization design of the LSSMFP, that is, the TC size should be about 0.9% times the blade height at the middle of impeller passage.

The existence of the TC will lead to the decrease of pump efficiency. In order to measure the effect of TC on tip loss and pump efficiency, the following relation is defined

η_{1} \cdot (1 - ξ) = η_{2}

(9)

here, η₁ is the pump efficiency at δ = 0 mm, while η₂ denotes the efficiency considering the effect of TC; ξ is the impact factor of TC, and a larger value of ξ means the TC effect is more remarkable. The impact factor ξ with four TCs under different discharge conditions is displayed in Figure 15. It can be seen that with the increase of TC size, the impact factor ξ under these four discharge conditions increases. Compared with the smaller TCs (δ = 0.10 and 0.25 mm), the impact factor ξ increases dramatically under the larger TCs (δ = 0.75 and 1.00 mm), that is, for 1.0Q_d condition, the impact factors ξ at conditions of δ = 0.10 and 0.25 mm are 2.18% and 2.81%, respectively, while under conditions of δ = 0.75 and 1.00 mm, they increase to 8.94% and 12.25%, respectively. This is closely related with the complex flow near the impeller inlet under the large TCs (Figures 13 and 14). Meanwhile, the impact factor ξ varies slightly among these four discharges under the smaller TC sizes, while there is a great difference in the large TC sizes. It can also be seen that for 1.25Q_d condition, the impact factor ξ is the lowest under the smaller TC sizes, while it is the highest under the large TC sizes, which demonstrates that under the large discharge condition, the variation of TC has a significant influence on the flow in the pump, corresponding with the analysis of Figure 8.

Figure 15.

Analysis of impact factor ξ with four TCs under different discharge conditions.

Conclusion

Although the TC size is important for the optimization design of the pumps, there is no unified standard for its selection. In present paper, the effects of TC on the external characteristics, pressure fluctuation and tip loss of a LSSMFP were analysed. The main purpose of this study is to have a further understanding of the TC effect and propose a quantitative criterion for the selection of TC size of the LSSMFP.

For the same relative discharge condition, the efficiency and head of the pump decrease gradually with the TC increases, and the variation of TC size has a greater effect on the external characteristics under the large discharge conditions than for the small discharge conditions. Meanwhile, a quantitative relationship between TC variation, efficiency reduction and relative discharge is obtained.

Along the flow direction, the pressure fluctuation coefficients near the impeller shroud increase gradually under the smaller TC sizes (δ = 0.10 and 0.25 mm), while for the larger TC sizes (δ = 0.75 and 1.00 mm), the fluctuation intensity near the shroud of impeller inlet section increases significantly, which has a close correlation with the clear leakage vortex and the large region of low pressure therein.

Compared with the conditions of δ = 0.10, 0.75 and 1.00 mm, the pressure fluctuation of corresponding points near the impeller shroud is the smallest at δ₂ = 0.25 mm, which reveals that the smaller TC size is not necessarily the better. According to this study, for the optimization design of LSSMFP, the TC size is suggested to be about 0.9% times the blade height at the middle of impeller passage.

Due to the tip leakage, the flow separation occurs near the impeller shroud and the leakage vortex comes into being gradually. Also, with the increase of the TC size, the separation area gets larger and the effect of TC becomes more significant. In particular, in the case of large TC sizes (δ = 0.75 and 1.00 mm), this effect gets a great promotion relative to the case of small TC sizes (δ = 0.10 and 0.25 mm).

Footnotes

Appendix 1

Handling Editor: Jose Ramon Serrano

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship and/or publication of this article: The project was supported by National Natural Science Foundation of China (grant nos 51579006 and 51679122).

ORCID iDs

Wenwu Zhang

Baoshan Zhu

References

Guo

Zhu

Liu

Study on flow characteristics and flow ripple reduction schemes of spool valves distributed radial piston pump. Proc IMechE, Part C: J Mechanical Engineering Science 2016; 231: 2291–2301.

Yan

Kovacevic

Tang

et al . Numerical modelling of twin-screw pumps based on computational fluid dynamics. Proc IMechE, Part C: J Mechanical Engineering Science 2016; 231: 4617–4634.

Zhang

Zhu

et al . Numerical study of pressure fluctuation in the whole flow passage of a low specific speed mixed-flow pump. Adv Mech Eng. Epub ahead of print 12 May 2017. DOI: 10.1177/16878 14017707651

Murugesan

Rudramoorthy

Experiment and numerical study of efficiency improvement by surface coating on the impellers and diffusers of mixed flow submersible bore well pumps. J Sci Ind Res 2016; 75: 300–305.

Zhang

Shi

Pan

et al . Numerical and experimental investigation of tip leakage vortex cavitation patterns and mechanisms in an axial flow pump. J Fluid Eng: T ASME 2015; 137: 815–816.

Miyabe

Furukawa

Maeda

et al . A behavior of the diffuser rotating stall in a low specific speed mixed-flow pump. Int J Fluid Mach Syst 2009; 2: 31–39.

Numerical analysis of pressure pulsation characteristics of diagonal flow pump in adjacent area of tip clearance. J Hydraul Eng 2015; 46: 496–503.

Dong

Min

Jin

et al . A study of tip clearance effect for a mixed-flow pump on performance. In: ASME 2013 fluids engineering division Summer meeting, Incline Village, NV, 7–11 July 2013. New York: ASME.

Tan

Xie

Liu

et al . Influence of T-shape tip clearance on performance of a mixed-flow pump. Proc IMechE, Part A: J Power and Energy 2018; 232: 386–396.

10.

Bing

Cao

et al . Experimental study of the effect of blade tip clearance and blade angle error on the performance of mixed-flow pump. Sci China Technol Sc 2012; 56: 293–298.

11.

Feng

Luo

Guo

et al . Influence of tip clearance on pressure fluctuations in an axial flow pump. J Mech Sci Technol 2016; 30: 1603–1610.

12.

Zhang

Zhu

BS.

Influence of tip clearance on pressure fluctuation in low specific speed mixed-flow pump passage. Energies 2017; 10: 1–16.

13.

Liu

Tan

Hao

et al . Energy performance and flow patterns of a mixed-flow pump with different tip clearance sizes. Energies 2017; 10: 1–15.

14.

Liu

Tan

Tip clearance on pressure fluctuation intensity and vortex characteristic of a mixed flow pump as turbine at pump mode. Renew Energ 2018; 129: 606–615.

15.

Yuan

Pan

et al . Dynamic characteristics of rotating stall in mixed flow pump. J Appl Math 2013; 10: 1–12.

16.

Miorini

Katz

The internal structure of the tip leakage vortex within the rotor of an axial waterjet pump. J Turbomach 2012; 134: 031018.

17.

Yang

Qin

ZC.

Leakage loss study of a synchronal rotary multiphase pump with a full range of inlet gas volume fractions. J Fluid Eng: T ASME 2017; 138: 071301.

18.

Zhang

KW.

Theory of fluid machinery, Vol. 1. Beijing, China: China Machine Press, 2000, pp.76–80.

19.

ANSYS

Inc.

ANSYS TurboGrid users guide: release 15.0. Pittsburgh, PA: SAS IP, Inc., 2013.

20.

Chen

Ghoniem

AF.

Simulation of oxy-coal combustion in a 100 kW_th test facility using RANS and LES: a validation study. Energ Fuel 2012; 26: 4783–4798.

21.

Tan

et al . Role of blade rotational angle on energy performance and pressure fluctuation of a mixed-flow pump. Proc IMechE, Part A: J Power and Energy 2017; 231: 227–238.

22.

Kim

Choi

et al . Effects of inducer tip clearance on the performance and flow characteristics of a pump in a turbopump. Proc IMechE, Part A: J Power and Energy 2017; 231: 398–414.

23.

Shi

Zhang

Jin

et al . A study on tip leakage vortex dynamics and cavitation in axial-flow pump. Fluid Dyn Res 2017; 49: 035504.