Numerical Calculation of the Influences of Uneven Blade Spacing on a PAT

doi:10.3969/j.issn.1004-132X.2026.10.025

Abstract

Abstract:

Two non-axisymmetric uneven blade designs were developed based on traditional axisymmetric equidistant blades. A comprehensive three-dimensional computational domain was constructed， incorporating front/rear chambers， sealing clearances， and balance holes， with structured meshing applied for discretization. Unsteady internal flow simulations were performed using computational fluid dynamics （CFD）， with the reliability of the numerical method confirmed by experimental validation. The results demonstrate that non-axisymmetric uneven blade distribution may moderately enhance the energy recovery efficiency of the PAT systems. Under low-to-medium flow conditions， uneven blade spacing increases axial thrust on the impeller， whereas at high flow rates， it exhibits a measurable mitigation effect on axial loading.

Key words: pump as turbine （PAT）, impeller, unevenly spaced blade, efficiency, axial thrust

摘要：

在传统轴对称等距叶片基础上设计了两种非轴对称不等距叶片，建立了包含前后腔、口环间隙、平衡孔等在内的全三维计算域，对其进行了结构化网格划分；基于计算流体动力学方法对其进行了内部非定常流动的数值计算；通过性能实验验证了数值计算方法的可靠性。研究发现，非轴对称不等距叶片分布能适当地提高泵作透平的能量回收效率。在中小流量工况下，不等距叶片分布会导致叶轮所受轴向力增大，而在大流量工况下，不等距叶片分布对削减叶轮所受轴向力有一定作用。

关键词: 泵作透平, 叶轮, 不等距叶片, 效率, 轴向力

CLC Number:

TH311

ZHANG Yuliang, YANG Zezhou, TONG Jiangbo, ZHAO Yanjuan, ZHU Zuchao. Numerical Calculation of the Influences of Uneven Blade Spacing on a PAT[J]. China Mechanical Engineering, 2026, 37(10): 2618-2630.

张玉良, 杨泽洲, 童江波, 赵燕娟, 朱祖超. 叶片不等距分布对泵作透平影响的数值计算[J]. 中国机械工程, 2026, 37(10): 2618-2630.

Figures/Tables 24

Tab. 1 Main structural parameters of centrifugal pump

参数	数值
进口直径D_S/mm	62
出口直径D_d/mm	50
叶片数Z	5
叶轮直径d₂/mm	160
进口安放角β₁/（°）	37.0
出口安放角β₂/（°）	34.5
叶片包角φ/（°）	124.7
叶轮出口宽度b₂/mm	9.5

Fig.1 Pump as turbine calculation model

Fig.2 Computational grid

Fig.3 Grid independence verification

Tab.2 Discretization error statistics table of numerical calculation［26］

网格数量	扬程H/m	网格收敛指数	数值/%
642 753	31.74
1 865 628	31.49	I_GCI，21	2.38
2 366 209	31.45	I_GCI，32	0.49

Tab.3 Grid details

过流部件	网格数量	长宽比	最低正交质量	y⁺
进口管	144 298	0.30～1.0	0.84	15.12
蜗壳	704 810	0.05～1.0	0.21	67.92
前后泵腔	750 360	0.10～1.0	0.63	31.58
叶轮	628 309	0.05～1.0	0.33	19.18
出口管	138 432	0.10～1.0	0.78	28.42

Fig.4 Comparison of experimental and numerical simulation performance characteristics

Fig.5 Schematic of blade arrangement

Tab. 4 Impeller blade spacing plan

	间距1	间距2	间距3	间距4	间距5
原型叶轮	72°	72°	72°	72°	72°
叶轮A	66°	69°	72°	75°	78°
叶轮B	60°	66°	72°	78°	84°

Fig.6 Impeller grid schematic

Fig.7 Hydraulic performance of various impellers

Tab. 5 External characteristics at BEP

	q_V /（m³·h $- 1$ ）	H/m	P/kW	η/%
原型叶轮	42.5	64.91	5.33	70.98
叶轮A	45.0	70.82	6.22	71.78
叶轮B	42.5	66.26	5.41	70.64

Tab. 5 External characteristics at BEP

	q_V /（m³·h $- 1$ ）	H/m	P/kW	η/%
原型叶轮	42.5	64.91	5.33	70.98
叶轮A	45.0	70.82	6.22	71.78
叶轮B	42.5	66.26	5.41	70.64

Fig.8 Hydraulic losses in flow passage components

Fig.9 Percentage distribution of hydraulic losses in flow passage components

Fig.10 Vortex structure distribution maps in impellers

Fig.11 Characteristic streamline patterns of impeller cross-section

Fig.12 Entropy generation distribution maps in impellers

Fig.13 Probe line distribution plot

Fig.14 Pressure distribution along probe line 1

Fig.15 Pressure distribution along probe line 2

Fig.16 Pressure distribution along probe line 3

Fig.17 Axial force time-domain plots across different impellers

Fig.18 Radial force radar charts across different impellers

Fig.19 Radial force vector plots across different impellers

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