A Review of Fluid-Induced Excitations in Centrifugal Pumps

Abstract

This paper describes the related research work in the field of fluid-induced vibration of centrifugal pumps conducted by many researchers. In recent years, all walks of life have put forward higher demands for the vibration performance of pumps which drives the investigation on the root cause of pump vibration and the development of guidelines for the design of low-vibration pumps. Fluid-induced excitation is the most important and significant source of pump vibration. Understanding its generation mechanism and dominant characteristics is important for developing low-vibration pump design methodology. This paper starts with the analysis of unsteady flow in the centrifugal pump and summarizes unsteady flow characteristics such as jet–wake structure, secondary flow, and rotational stall in the operating pump. Based on the understanding of the unsteady flow structure in the pump, the fluid-induced excitation mechanism and its characteristics based on the investigation of unsteady pressure pulsation and excitation forces in the pump are summarized. For the pump operating at nominal flow rate, the excitation at blade passing frequency (BPF) dominates and related suppression methods are classified and summarized to provide reference for the design of a low-vibration pump.

1. Introduction

Pumps are the most commonly used fluid machines which convert electrical energy into hydrokinetic and hydrostatic energy, and which consume about 20% of the world’s total energy [1]. About 70–80% of the total pumps are centrifugal pumps, which are widely used in national economic fields such as petroleum, electric power, the chemical industry, and agriculture, as well as high-tech fields such as aerospace, nuclear energy, and the medical field. In recent years, with the development of pump equipment in the direction of large-scale, high-speed, and high-energy density, the continuously improving requirements of hydraulic performance have put forward more severe tests on various performance indicators of pump system operation. Many scholars are dedicated to developing new technologies and solving critical technical problems to improve the performance of pump systems. In addition to focusing on external characteristics and energy efficiency, the stability and reliability of pumps are also the focuses of current research. According to statistics, vibration is the main constraint factor for unstable operation and the failure of centrifugal pump systems. The vibration generated during pump operation will, on the one hand, cause mechanical failures such as fatigue damage to hydraulic components, reduced life of bearing, seal failure, and the fracture of shaft; on the other hand, it will spread downstream, causing unstable operation or the failure of pipelines, other related equipment, and even the entire pumping system.

Since the vibration performance of the pump directly determines the reliability and stability of the pump operation, pump vibration is an important indicator in the pump design process. In order to ensure the reliable and safe long-term operation of the pump, while minimizing the harmful effects on the connected equipment, the International Organization for Standardization has issued relevant standards based on the statistics vibration data of a large number of rotating equipment operating in the industry. Meanwhile, the vibration measurement methods of rotating machines and the allowable value have been specified in detail. ISO 20816-3 [2] has detailed regulations on the vibration measurement methods and evaluation standard of industrial general machinery with a power greater than 15 kW and a rotating speed ranging from 120 rpm to 30,000 rpm, using shaft vibration, related structural vibration, and characteristic frequency components to evaluate the vibration level of machines. In terms of pump equipment, the standard ISO 10816-7 [3] specifically specifies the vibration assessment of industrial pumps in detail. It is mainly applicable to general pump equipment with a power greater than 1 kW and operating under the best efficiency points (0.7 Q_d–1.2 Q_d). According to different requirements for reliability and safety, the permissible vibration standards have been divided into two categories: high-standard pumps (Category I) and ordinary pumps (Category II). Meanwhile, for each category, the vibration level has been divided into four different levels (ABCD) based on the measured value of vibration velocity and the shaft vibration displacement of stationary parts (bearings and pump casings) of the pump.

Table 1. Vibration standards for stationary parts of pumps (more than three blades, >1 kW).

Zone	Description	Vibration Velocity Limit: r.m.s Value (mm/s)
		Category I		Category II
		$\le 200 \mathbf{kW}$	$>200 \mathbf{kW}$	$\le 200 \mathbf{kW}$	$>200 \mathbf{kW}$
A	Newly commissioned machines in preferred operating range	2.5	3.5	3.2	4.2
B	Unrestricted long-term operation in allowable operating range	4.0	5.0	5.1	6.1
C	Limited operation	6.6	7.6	8.5	9.5
D	Risk of damage	>6.6	>7.6	>8.5	>9.5

lists the vibration standards for the stationary parts of pumps with more than three blades and power greater than 1 kW. In terms of vibration measurement equipment, it is necessary to meet the requirements of ISO 2954 [4], and it should be able to measure the broadband r.m.s vibration velocity of 10–1000 Hz. In addition, the vibration measurement of the non-rotating parts of the pump and the shaft vibration measurement must be carried out according to ISO 20816-1 [5].

With the development of science and technology, all walks of life have put forward higher requirements for the vibration and noise performance of pumps during operation, not only to meet the basic requirements in the ISO standard for safe operation, but also to require the pump to have a good quality of sound and vibration, longer life, and more stable outflow. The demands for the pump with low sensitivity vibration drive the investigation of the root cause of pump vibration and the development of guidelines for the design of low-vibration pumps.

Figure 1 shows the sources of pump vibration which come from motor vibration, mechanical excitations, and fluid-induced excitations. With the development of mechanical design and manufacturing, motor vibration and mechanical excitations caused by rotor imbalance, shaft misalignment, resonance, and so on have been effectively controlled. However, pump vibrations, especially low-frequency vibrations, are still significant. The local pressure pulsation generated by the internal unsteady flow acts on the rotor, shaft, and casing to form unsteady excitation forces, which are important sources of pump vibration. Compared with mechanical vibration, the fluid-induced excitations generated by the unsteady flow in the pump are more difficult to accurately predict and effectively control. In the process of low-vibration pump hydraulic design, the amplitude of internal pressure pulsation and unsteady radial forces are widely used indexes to measure the intensity of internal fluid-induced excitations. Benefiting from the accumulated experiences in pump design and the development of CFD technology, combined with common vibration reduction methods, engineers can basically realize the low-vibration hydraulic model design of the pump after continuous optimization attempts. However, the entire optimization process requires a lot of time, energy, and computational resources. Therefore, understanding the basic characteristics of fluid-induced excitations in the pump, revealing the mechanism of excitations, clarifying the dominant factors, and establishing a predictive model are very important for improving the design of low-vibration pumps and developing fluid-induced vibration control methods. This paper summarizes the research on the fluid-induced excitations and vibration control methods of centrifugal pumps in the past half century, aiming to provide a reference for the design of low-vibration hydraulic models.

2. Internal Unsteady Flow of Centrifugal Pump

In a rotating pump, the internal flow structure is extremely complex with inherent properties such as high three-dimensionality, and uneven distribution of time and space. The complex unsteady flow inside the centrifugal pump is the main reason for the fluid-induced excitations. Therefore, understanding the unsteady flow structure and its generation mechanism inside the centrifugal pump is important for the investigation of fluid-induced excitations. In a rotating impeller, the fluid particles are subjected to centrifugal force, Coriolis force, the force caused by the curvature of the blade profile, and the shear force caused by viscosity. The internal flow of the impeller presents a three-dimensional boundary layer, secondary flow, backflow, flow separation, jet–wake structure, vortexes, and other complex unsteady flow structures which directly determine the working capacity, loss characteristics, and vibration performance of the pump.

In the 1950s, the vigorous development of aerospace technology and aerodynamics drove the study of unsteady flow in centrifugal impellers. During 1948–1955, NASA [6,7,8] first found that the impeller outflow contains a considerable amount of wake flow and turbulent disturbances, and it will gradually attenuate as propagating to the downstream stationary components. Subsequently, Dean, 1960 [9], realized that the flow in a rotating pump has complex unsteady flow characteristics. Some scholars have tried to study the non-uniform flow at the impeller outlet through theoretical analysis based on the assumption of two-dimensional flow [10,11]. However, due to the complex geometric structure of the impeller, the internal flow presents complex three-dimensional space–time distribution characteristics which make it difficult to accurately predict the real flow inside the impeller based on the traditional potential flow theoretical calculation. So, many scholars explored the complex unsteady flow structure inside the impeller by combining experimental tests and theoretical analysis and then established flow models.

Fowler [12] carried out experimental tests on a simplified impeller flow channel; results show that the shape of the flow channel, flow rate, and rotational speed will affect the stability and uniformity of the outflow, and at the same time observed the flow separation on the suction side (SS) of the blade. Moore [13,14] investigated the flow structure in a rotating radial flow channel by using pressure and hot-wire measurements, and the results indicated that under large flow rates, there is a large wake area near the SS, while at low flow rates, a pressure side (PS) eddy was observed. Further theoretical analysis established a flow model to predict the whole channel flow considering the effects of potential flow and the boundary layer. Eckardt [15,16] conducted transient measurements of the flow at a centrifugal compressor impeller outlet. The results showed that the flow at the impeller outlet presents an obvious jet–wake structure and the wake accumulates on the corner of shroud and SS at the impeller outlet. As shown in Figure 2, the accumulation of wake comes from three main parts: the first is the cross-flow close to a dominating main vortex in the shroud region (Arrow 1) which removes low-energy fluid material from the channel surfaces and feeds it into the wake; the second is a relatively weaker secondary vortex in the region of the hub and SS (Arrow 2); the third is low-energy fluid transported from the tip clearance (Arrow 3). The development of secondary flow and the accumulation of wake at the impeller outlet is attributed to the streamline curvature and rotation of the runner. Since then, the jet–wake structure at the impeller outlet has been widely recognized. Adler [17] used laser Doppler technology to test the velocity of a swept-back centrifugal impeller at the design point and found that there was no obvious wake area at the outlet and that the outflow was almost uniform. Fraser [18] summarized the causes and effects of the backflow at the inlet and outlet of the centrifugal impeller. Compared with the design point, the backflow at the impeller outlet under off-design conditions was significant. Ubaldi [19] used thermal probes and miniature pressure sensors to measure the relative velocity, Reynolds stress, total pressure loss, and turbulence distribution at the outlet of a backward centrifugal impeller. Results observed an obvious jet–wake structure and secondary flow at the impeller outlet, as well as vortex shedding from the trailing edge (TE).

With the development of measurement techniques, a non-contact digital particle imaging velocimetry (PIV) technique based on Lagrangian particle motion has gradually replaced laser Doppler velocimetry (LDV) as the most powerful measurement technique to study the internal flow of turbomachinery [20]. Paone [21] compared the velocity test results of PIV and LDV measurements in the diffuser of a centrifugal pump and introduced the advantages and disadvantages of PIV measurement in detail, which is also the first application of PIV technology in the flow field test of rotating machinery.

The research based on experimental tests and theoretical analysis has fully demonstrated that there are complex secondary flow, boundary layer effects, and flow separation in the rotating impeller and that the impeller outflow is non-uniform and presenting a jet–wake structure, as shown in Figure 3. A circumferential non-uniform transient outflow would interact with downstream static components and contribute to a more complex internal flow structure, which is also a focus of research. Inoue [22] compared the impeller outflow of a centrifugal pump with or without diffuser vanes by measuring local pressure and velocity at multiple points. Results show that the backflow at the impeller outlet increases significantly when decreasing the gap between the vanes’ leading edge (LE) and the impeller TE, while the number of guide vanes will affect the pressure and velocity distribution at the impeller outlet as well as wake intensity. Dong [23,24] used the PIV technique to study the turbulent flow structure in the volute of a centrifugal pump and observed pulsating flow at the impeller outlet which is also affected by the location of the blade relative to the tongue. Akin [25] investigated the wake interaction and transient flow in the gap between the impeller outlet and the LE of the diffuser blade via PIV experiments. Results show that the wake vortex shedding from the TEs would cause unsteady flow separation at the vanes’ LEs. The transient flow separation and the process of wake vortexes’ reattachment during the rotor–stator interaction (RSI) can be effectively characterized by using an instantaneous streamline and vorticity contour. Sinha [26] extended the PIV test to the overall flow in the region of guide vanes and the internal flow structure distribution is presented in Figure 4, in which the internal flow field is dominated by the wake and flow separation generated by the interaction between the impeller TEs and guide vanes. Choi [27] measured the internal flow of two different semi-open impellers via PIV technology and found that the external characteristics of the pump are closely related to the internal flow field, and there are obvious secondary flow and backflow in the flow channel of the low specific speed impeller. Keller [28] investigated the interaction between the shedding wake vortex and the volute tongue by using PIV technology to continuously capture the wake vortex at the blade TEs. The internal flow structure in the tongue region is presented in Figure 5, in which the impeller outflow has a strong interaction with the tongue. Li [29] conducted a PIV test on the flow field of a mixed-flow pump and results show that the RSI is the main reason for the unsteady flow in the pump. Li [30] carried out PIV experiments in a low-specific-speed centrifugal pump to investigate the correlation between internal flow structure and external characteristics. The effects of flow rate are revealed from the perspective of energy conversion.

PIV technology can effectively measure and characterize the flow in the two-dimensional plane of the dynamic and static parts in the pump. However, it cannot capture the complete three-dimensional flow structure inside the pump. In the last two decades, with the development of computational fluid dynamics (CFDs) and the popularization of commercial numerical simulation software such as Fluent, CFX, STAR-CD, etc., the combination of experiments and CFDs has become the main method of pump internal flow investigation [31].

Eisele and Muggli [32,33] use PIV and LDV to measure velocity distribution in the region of guide vanes of a centrifugal pump. Results observed the 3D unsteady periodic flow at the impeller outlet which decayed rapidly during propagation. At the same time, CFD investigation was carried out and results show that a quasi-steady-state numerical method can predict basic flow characteristics in guide vanes, but the accuracy still needs to be improved, especially for large flow rates. Pedersen and Byskov [34,35] for the first time captured an alternate rotating stall in two adjacent runner channels at off-design conditions via PIV. The transient large eddy simulation (LES) can effectively capture the details of the unsteady flow in the pump. Westra [36] focused on the development of secondary flow in the impeller. Results obtained from PIV and CFDs show that the secondary flow in the pump is an important cause of wake flow, and the intensity of wake flow decreases as the flow rate increases. Feng [37] used LDV and CFDs to investigate the unsteady flow in the region of guide vanes in a centrifugal pump; the periodical development of unsteady flow in the gap was analyzed based on the circumferential distribution characteristics of the impeller outflow. Posa [38,39] conducted a comprehensive study on the internal flow characteristics of a radial pump with guide vanes under small flow conditions via LES. The author discussed the effects of guide vanes with variable geometry on the performance of model pumps and revealed the correlation between internal flow characteristics and external characteristics of the centrifugal pump. Kye [40] compared the unsteady flow characteristics in the region of RSI of a centrifugal pump under design and off-design conditions using the LES method. Figure 6 presents the instantaneous vorticity magnitude which shows the strong interaction between blades and tongue, and for the off-design condition, the shedding vortex from the blade TEs caused large-scale flow separation near the tongue. Zhang [41,42] used the PIV test and delayed detached eddy simulation (DDES) to study the unsteady flow structure and its evolution in a low-specific-speed centrifugal pump. The results showed that the DDES model can effectively capture the jet–wake structure at the impeller outlet and that the cutting and deformation of the blade TEs’ shedding vortex caused by RSI are important sources of internal unsteady flow. The development of CFDs not only makes it easier for scholars to study the details of mainstream flow in the pump but also expands the research to the entire flow field of the pump, including the ring clearance, tip clearance, and front and back gaps [43,44].

The research on the unsteady internal flow characteristics of centrifugal pumps has made great progress in the last half century. The research methods range from LDV to PIV to fine CFD simulation of full flow fields; the research model has developed from a single flow channel to a rotating impeller without guide vanes and then to the full geometry of the pump; and the research objects range from low-speed radial impellers to 3D twisted impellers to special pumps such as pumps with high speed and low specific speed. R&D activities show that PIV and high-precision CFD simulation have been able to capture the typical flow structures in the centrifugal pump. Under the combining influence of Coriolis force and secondary flow, the rotating impeller outflow is non-uniform, presenting a typical jet–wake structure which contains a jet flow with a relatively higher velocity near blade PSs and a wake flow with lower velocity close to the blade SSs. At the blade TEs, the mixing of jet and wake would cause a large total pressure loss accompanied by periodically shedding vortices from the TEs. The circumferential non-uniform outflow would interact with downstream stationary components and aggravate the complex unsteady flow in the pump. The unsteady flow in the pump not only affects the external characteristics of the pump but, more importantly, the unsteady fluid-induced excitations are the fundamental source of pump vibration.

3. Fluid-Induced Excitations of Centrifugal Pump

The complex unsteady flow in the pump induces the local pressure and velocity fluctuation, and local pressure pulsation acting on the wall of the rotating and static parts would generate the unsteady excitation forces on the rotor and casing wall, thus causing the vibration of each hydraulic component and the whole pump body. Therefore, studying the excitation characteristics generated by the unsteady flow in the pump and revealing the internal mechanism is also an important part of developing the design technology of a low-vibration pump. At the end of 1980, Acosta [45,46] investigated the RSI in a diffuser pump by the experimental measurement of pressure pulsation in the impeller outlet and diffuser channel. It was found that the internal static pressure fluctuated periodically with the blade passing frequency (BPF) and the largest fluctuations occurred at the impeller blade TEs. Parameter analysis showed that its amplitude is greatly affected by the radial gap of the rotor and stator, which opens the curtain on the study of the unsteady fluid-induced excitation mechanism by measuring pressure pulsation in the pump.

In the beginning, some scholars try to conduct theoretical analysis of RSI pressure fluctuations based on the observed unsteady flow in the pump [47]. Qin [48,49] developed a singularity method to predict the interaction between impeller and guide vanes. They calculated the pressure fluctuations in the impeller, vanes, and volute, and investigated the effects of flow rate, volute casing, and gaps. However, the assumption of two-dimensional, non-viscous flow limits the accuracy of theoretical predictions; most related research is based on experiments and numerical simulations. González [50] investigated pressure pulsation circumferential distribution characteristics at the impeller outlet via experimental and numerical simulation methods, and results show that numerical simulation can effectively predict internal pressure pulsation, and its amplitude at BPF reaches its highest near the volute tongue. Parrondo-Gayo [51] measured pressure pulsations in the volute of a low-specific-speed centrifugal pump under all flow rates and the monitored pressure pulsations are presented in Figure 7 in both frequency and time domains. It can be observed that the pressure pulsation excitations were dominated by the BPF and its amplitude increased in off-design conditions.

The unsteady force caused by the unsteady pressure acting on the impeller and volute can also be measured and extracted to help investigate the mechanism of fluid-induced excitations in the pump. Guo [52] measured pressure pulsations, impeller radial fluid forces, and shaft vibration in a centrifugal pump for various diffuser vanes, flow rates, and rotating speeds. Results show that harmonics with a higher amplitude depend mainly on the number of stationary and moving blades. After that, Rodriguez [53] concluded the dominant frequency induced by RSI and proposed a theoretical method to predict the relative magnitude of each harmonic which gives guidelines to achieve lower amplitude at specific harmonics or to avoid them. The dominant frequency induced by RSI can be calculated by Equation (1).

$$\mathrm{n}·Z_r\pm \mathrm{k}=\mathrm{m}·Z_g$$

(1)

$Z_r$ and $Z_g$ are the number of blades of the impeller and vanes, respectively. n and m are positive integers. When k equals 0, the amplitude of the pressure pulsation at BPF will be amplified. This equation is still used now to guide the selection of the number of blades in pump designs. However, since this method does not consider the complex flow phenomenon in the pump, there are still limitations in the fine design of fluid-induced excitation suppression.

Gonzalez [54] studied internal pressure pulsation and radial force in a vaneless centrifugal pump via both experimental and numerical methods, focusing on the effects of impeller and tongue radial gaps on the steady and unsteady impeller radial force under different flow conditions. Spence [55,56] carried out a parametric study to investigate the effects of geometrical variations on the pressure pulsations of a centrifugal pump by CFDs; cutwater gap and vane arrangement were found to exert the greatest influence across the various monitored locations and the flow rates. Barrio [57] investigated the effects of impeller cutback on the fluid-dynamic pulsations and load at BPF in a centrifugal pump; numerical results show that working at part-load conditions and reducing the radial gap would cause a significant increase in radial force. After that, the author [58] quantitively evaluated the radial force on the impeller by means of CFDs under different flow conditions; it was found that the maximum amplitude of force pulsation could reach 40~70% of the average value at part-load conditions. Gao [59] validated the accuracy of numerical simulation for predicting the performance of a large centrifugal pump with guide vanes; the results showed that unsteady numerical simulation is more accurate for predicting the external characteristics of the model pump, especially for off-design flow rates, and it can also capture the dominant frequency of internal pressure pulsation with limited error in amplitude. Gao [60] comprehensively measured and analyzed the pressure pulsation in a low-specific-speed centrifugal pump and discussed the dynamic characteristics in different working conditions and measuring locations. Wang [61] also conducted experimental studies on the influence of flow and speed on pressure pulsation in the double-suction centrifugal pump. In addition, some scholars [62] have studied the time-frequency characteristics of pressure pulsation in the pump, and the results show that the time-frequency characteristics of pressure pulsation vary significantly between different measurement points and operation conditions. Zhou [63,64] investigated the effects of eccentricity ratio, flow rate, and whirl ratio on the fluid-induced force of a centrifugal pump impeller. Based on the data obtained from CFDs, a novel compound whirl model is proposed to predict the fluid-induced forces, which has been proven with good accuracy.

With a deepening understanding of the pressure pulsation characteristics in the pump, as well as the influence of flow rates, rotating speed, and geometry on it, scholars began to explore the mechanism of pressure pulsation by means of internal flow visualization. Barrio [65] extracted and compared the instantaneous pressure pulsation, local radial velocity, and tangential velocity at the near-tongue region under different flow rates; the analyzed results show that for medium and high flow rates, the jet–wake pattern and secondary flow developed in the blade channels are the dominant causes of pressure pulsation, while for the lowest flow rate, there is a large counter-rotating vortex in the flow channel and the mechanism of pressure pulsation is more complex. Liu [44] investigated the influence of gap leakage on the transient characteristics of mainstream flow in a mixed-flow pump by means of vorticity and the vortex identification method, and revealed the correlation between the development of transient vortexes and pressure pulsation intensity. Ni [66] investigated the transient characteristics of a nuclear reactor coolant pump via experimental and LES methods which can effectively predict the excitations at BPF and at low-frequency broadband. Figure 8 shows the flow structures at middle span and the pressure spectra of monitor point S16. In addition to the excitations at BPF generated by RSI, excitations at low-frequency broadband also have been noticed in the spectra. Post-processing results show that the complex unsteady tailing vortex is the main cause of the low-frequency excitations of the pressure pulsation spectrum. The LDV measurement followed by [67] gives more details of the fluid-induced excitation mechanism of the nuclear reactor cooling pump under various flow conditions.

With the development of measurement technology and numerical simulation, in addition to focusing on the excitation at BPF, other excitations generated by abnormal flow have also been studied. Lucius [68] investigated the rotating stall phenomenon in a centrifugal pump based on PIV and CFD methods, and a detailed analysis of velocity fluctuations in a relative frame revealed the eigenfrequency of the rotating stall. The velocity spectrum and vector are presented in Figure 9, 10 and 20 Hz correspond to the rotational speed and its first harmonic while 7.3 Hz is measured as stall frequency, and the peaks at 14 and 21 Hz are higher harmonics of the stall. According to the velocity vector in midspan, the deeply rotating stall can be observed in Channels 1, 2, and 4. Li [69] investigated pressure pulsation characteristics in a mixed-flow pump under rotating stall by numerical simulation; the pressure pulsation amplitude caused by the rotating stall is much higher than that of RSI, and transient internal flow analysis revealed the mechanism and propagation of the rotating stall. Zhang [70] also captured low-frequency excitations caused by the rotating stall at off-design conditions of a centrifugal pump. LDV measurements [71] detected that large-scale flow separation occurs in the diffusion section where velocity and pressure pulsation energy increased rapidly in the rotating stall region. Cavitation is also one of the most important fluid excitations in the centrifugal pump and cavitation-induced vibration and noise would affect the operating stability of the pump and even cause failure [72]. Christopher [73] carried out an experimental investigation concerning cavitation in a pump by measuring the noise and vibration; results revealed that the cavitation inception caused the increase in noise and vibration before the head drop. Zhang [74] measured the internal pressure pulsation of a centrifugal pump during the cavitation state and found that the pressure pulsation energy at a low-frequency band would raise rapidly with the development of cavitation. However, since the mechanism of cavitation bubble generation and development is extremely complex, the investigation of cavitation-induced excitations is mainly based on simple structures such as airfoils; there are few studies on cavitation excitation characteristics in centrifugal pumps.

In this century, the research on fluid-induced excitations of centrifugal pumps is mainly based on the combination of experimental and numerical methods, focusing on the characteristics of pressure pulsation, radial force on the impeller, and complex unsteady internal flow structures. The investigation involved different types of pumps (pump turbine, pump with or without vanes, nuclear pump, and low-specific-speed pump), and considered the effects of geometries, tip clearances, operating conditions, and rotating speed, as well as special operating conditions such as rotating stall and cavitation. R&D activities show that there are two main categories of fluid-induced excitations in centrifugal pumps: the first is excitation at BPF induced by the interaction between the non-uniform impeller outflow and the stator downstream; the second is excitation at low-frequency broadband caused by the turbulence, local flow separation, rotating stall, cavitation, and other abnormal flow structures. However, the excitation at BPF plays a dominant role in centrifugal pumps operating under rated conditions. It is generally believed that the amplitude of local pressure pulsation can be used as an important indicator to predict the fluid-induced vibration and noise of the pump. However, the pump internal flow has strong time-space distribution characteristics, especially for the RSI region, and the mechanism of internal fluid-induced excitations is still not very clear; so, a lot of research is still based on qualitative analysis.

4. Fluid-Induced Excitation Control Methods

The fundamental purpose of investigations on characteristics and the mechanism of fluid-induced excitations in centrifugal pumps is to provide a reference for the hydraulic design of low-vibration-noise pumps. As mentioned before, the dominant fluid-induced excitations in the pump contain the BPF excitations induced by the non-uniform impeller outflow and the low-frequency broadband excitations caused by local flow separation and abnormal flow. Therefore, the development of fluid-induced excitation control methods in the pump are mainly based on two aspects: the first is to reduce the amplitude at BPF in the spectrum and the second is to suppress the excitations in low-frequency broadband which means to control the distribution characteristics of the flow field structure inside the pump to achieve the goal of reducing the amplitude of the local pressure pulsation spectrum, thereby reducing fluid-induced vibration and noise.

Most centrifugal pumps mainly operate under rated conditions in which the excitation at BPF is the most significant excitation in the spectrum. Therefore, the suppression of fluid-induced excitation is focused on reducing the amplitude of the pressure pulsation and unsteady radial force at BPF. Many scholars have proposed various geometry redesign methods and have investigated the effects of various geometrics on amplitude at BPF from the perspective of suppressing internal fluid-induced excitations.

Yang [75] studied the effects of the radial gap between impeller tips and the volute tongue on the performance and pressure pulsation of a pump as a turbine. By comparing the pressure fluctuation amplitude at BPF, it is believed that increasing the distance of the radial gap can significantly reduce the pressure fluctuation energy of hydraulic machinery. Gulich [76], based on a large number of statistics, concluded that when the gap ratio between the impeller tips and volute tongue of the centrifugal pump exceeds 10%, the pressure pulsation energy decline curve is relatively gentle, and continuing to increase the gap ratio has no obvious effect on reducing the pressure pulsation energy. Dong [77] studied the effects of volute tongue geometry on the internal flow structure and noise in the centrifugal pump. When the gap between the impeller and tongue is about 20% of the impeller radius, it can effectively reduce the impact of non-uniform impeller outflow (mainly jet/wake phenomenon) on the turbulence in the tongue region and fluid-induced excitations, yet further increasing the gap has a limited effect on reducing noise but will seriously deteriorate efficiency. Yan [78] redesigned the volute geometry of a large-flow centrifugal pump and found that compared with the original double volute, the redesigned single volute can effectively reduce the amplitude of the unsteady radial force of the pump. Zhang [79,80] investigated the effects of volute tongue shape and volute geometry on pressure pulsations in a low-specific-speed centrifugal pump. Results found that volute geometric parameters have significant effects on the pressure fluctuation intensity inside the pump. Figure 10 presents the effects of volute geometry on pressure pulsation in a pump and the design of slope volute can efficiently inhabit the pressure pulsation amplitude at BPF.

Feng [81] studied the effects of blade tip clearance on pressure fluctuation in an axial flow pump and found that the existence of tip clearance amplifies the pressure fluctuation in the impeller region, but has no obvious effect on the pressure fluctuation in the diffuser region. Ye [82] investigated the influence of the abnormal stagger angle of rotating blades on fluid-induced excitations in an axial flow fan via transient CFD simulation. The frequency spectrum and time-frequency analysis results of pressure fluctuation at multiple monitor points can effectively characterize the deviation degree of the abnormal blade. Meanwhile, the author introduced the sample entropy to characterize the influence of the abnormal blade deviation degree on the static pressure at the impeller outlet and guide vanes. Liu [83] studied the influence of inlet guide vanes on pressure pulsation characteristics in a centrifugal pump. CFD simulation results show that the dominant frequency of pressure pulsation occurs at BPF and installing suitable inlet guide vanes can effectively reduce the amplitude of pressure pulsation at BPF. Wang [84] focuses on the effects of relative circumferential location between guide vanes and volute tongue on the external performance and pressure pulsation characteristics of a centrifugal pump. Results based on spectrum and time-frequency analysis of pressure pulsation show that fluid-induced excitations in the volute are simultaneously affected by the impeller–vane interaction and vane–volute interaction, while the guide vanes’ position relative to the volute has a significant influence on the amplitude of pressure pulsation on dominant frequency and side frequency. Posa [85] used LES to study the influence of flow rate and the orientation of guide vanes on pressure pulsations in a centrifugal pump. It was found that the intensity of the pressure pulsation increased under small flow conditions and was significantly affected by the inlet angle of guide vanes, which also had different trends of effects on the pressure pulsation under different flow conditions.

In addition to increasing the radial gap between rotor and stator, optimizing the structure of static parts, adjusting the blade layout, and optimizing the impeller structure are often used in the hydraulic design of low-vibration and low-noise pumps. Al-Qutub [86] found that the V-shaped cutting treatment of the impeller outlet can effectively reduce the pressure fluctuation and vibration of the double-volute centrifugal pump. In the process of low-vibration-noise pump hydraulic model design, increasing the number of blades is often used to reduce the load of a single blade and suppress the pressure pulsation at BPF [87,88], but too many blades will block the inlet of the impeller and worsen the anti-cavitation performance of the pump. So, splitter blades have been widely studied for low-vibration pump design. Kergourlay [89] investigated the influence of splitter blades on the performance of a centrifugal pump, and results showed that the installation of splitter blades can effectively reduce the intensity of pressure pulsation in the pump but with the costs of increasing radial force. Li [90] adopted the splitter blades in the design process of a low-vibration centrifugal pump, and the results showed that the improvement of the internal flow structure is the main reason for the suppression of internal flow excitations. Zeng [91] carried out a multi-objective optimization design for centrifugal pump splitter blades; the vibration amplitude at the BPF of the model pump can be efficiently inhabited by appropriately adding splitter blades. In addition, Zhang [92] investigated the effects of the cutting blade outlet on the pump performance via an experimental test. It is recommended that the 15° cut angle can be used to reduce pulsation considering its little influence on the head of the pump. For centrifugal pumps with back vanes, the staggered impeller design can effectively reduce the intensity of pressure pulsations [93]. The research results of different types of stacked blades also show positive effects on reducing the amplitude of pressure fluctuations by weakening the jet–wake structure at the impeller outlet [94]. Figure 11 illustrates various designs of impeller to reduce the pressure pulsation in centrifugal pumps.

In a rotating impeller, the work transfer from blades to the fluids and the pressure difference will be generated between blade surfaces. The static pressure on the SSs is relatively lower than that of PSs and the velocity distribution at the outlet of the blade channel presents a jet–wake distribution. Meanwhile, the mixing of wake and jet at the blade TEs would intensify the non-uniform velocity distribution at the impeller outlet. Therefore, the differential design of blade surfaces is also a research focus of current low-vibration-noise pump hydraulic design.

Eagleson [95] studied the effects of different TE geometries on the vortex-induced vibration of turbines and found that the shape of the blade TE would affect the frequency, intensity, and separation point of wake vortex shedding. Zobeiri [96] investigated the influence of airfoil TE shapes on vortex-induced vibration under high Reynolds number conditions. PIV and LDV measurement results show that the oblique cutting of airfoil TE will change the shedding characteristics of vortices on both sides, and the redistribution of vorticity caused by the collision of shedding vortices contributes to the reduction in vortex-induced vibration. Based on the research and experiences in aerodynamics design, some scholars applied the TE modification technology to the process of pump design. Wu [97] studied the influence of blade TE shapes on the performance of a mixed-flow pump; results show that by cutting the blade TEs, the performance of the pump and the uniformity of the impeller outflow can be effectively improved. Gao [98] studied the effects of TE shapes on the pressure pulsation characteristics of a low-specific-speed centrifugal pump and found that the ellipse on PS and the ellipse on both sides have positive effects on pump efficiency improvement and pressure pulsation reduction. Further research has been carried out to reveal the mechanism of pressure fluctuation reduction [99]. Internal flow analysis shows that the performance improvement is attributed to the reduction in shedding vortex intensity which is caused by the redistribution of the velocity and vorticity of the impeller outflow after blade TE modification. Cui [100] studied the effects of different blade TE cuts on the pressure pulsation and vibration performance of a centrifugal pump. Numerical simulation and fluid–solid coupling results showed that appropriate TE cuts could effectively suppress the shedding vortex intensity of the TE and reduce the vibration displacement and pressure fluctuations in the pump. Blade TE modification has been widely used in the design of low-vibration-noise pumps. Gangipamula [101] proposed a novel sawtooth-shaped blade TE and studied the influence of different geometric parameters on pressure pulsations and induced noise in detail via numerical simulation. The results show that the novel blade TE can effectively improve the dynamic characteristics of the pump which are attributed to the suppression of the wake jet intensity and reduction in interaction between shedding wake vortex and tongue.

In addition to modifying the blade TEs, some scholars extend the modification to the whole blade profile of each side. Wu [102,103] modified the blade PS of a centrifugal pump and found that by actively reducing the load on the blade PSs near the TE, the intensity of pressure fluctuations in the centrifugal pump under all concerned flow conditions can be effectively inhibited. The internal flow analysis shows that the decrease in pressure fluctuations at BPF is attributed to the increase in the energy uniformity of the impeller outflow and the decrease in the shedding vortex intensity from the blade TEs. Qian [104] optimized the blade thickness distribution of a low-specific-speed centrifugal pump and found that the energy distribution of the impeller outflow is more uniform after optimization, which leads to the decrease in pressure fluctuation and vibration acceleration amplitude at BPF. Wu [105] proposed a blade thickness redesign method based on the force balance in the impeller; experimental and numerical results show this has positive effects on energy efficiency and the suppression of pressure pulsation at BPF. Figure 12 presents diffident blade modifications used to suppress pressure pulsation.

In conclusion, there are three main categories of methods to reduce the fluid excitations at the BPF of centrifugal pumps: the first is optimizing the structure of static parts such as casing, volute tongue, and guide vanes; the second is increasing the radial gap between the rotor and stator to reduce the intensity of RSI; and the third is modifying the geometry of the impeller and blades to optimize the uniformity of the impeller outflow. Since the jet–wake structure at the impeller outlet is the main source of BPF excitations and there is often a certain limit on the clearance of moving and static parts, the suppression of BPF excitations in centrifugal pumps should focus on the optimization of impeller outflow. R&D activities have shown that cutting the blade TEs, adding splitter blades, and the redesigning of the blade profile of each side can reduce the pressure fluctuation amplitude at BPF by improving the uniformity of the impeller outlet velocity and reducing the intensity of wake vortices’ shedding from the TEs. In the process of low-vibration-noise centrifugal pump hydraulic design, the pressure pulsation amplitude at BPF is the most used index to measure the intensity of fluid-induced vibration and the noise of the model pump. Based on the existing design experiences and understanding of the fluid-induced excitation mechanism in the pump, engineers can obtain a relatively good hydraulic pump model which meets the vibration and noise requirements for most applications.

Compared with the BPF excitation, the low-frequency broadband excitations in centrifugal pumps are more complex which is mainly caused by inflow disturbance, local backflow and flow separation, complex internal flow structure under off-design conditions, rotating stall, cavitation, etc. Since the low-frequency broadband excitations are affected by multiple factors such as the geometry of the pump and inlet flow conditions, as well as operating conditions, the suppression of low-frequency broadband excitations in the pump is mainly focused on analyzing and solving specific problems encountered in a specific pump. So far, there is no universal suppression method that has been developed; therefore, the author will not conduct an in-depth review of low-frequency broadband excitations here.

5. Conclusions

In this paper, the research on the fluid-induced excitation mechanism and control methods in centrifugal pumps have been reviewed. Based on the analysis of the unsteady flow structure in centrifugal pumps, the causes of the fluid-induced excitation mechanism are described, and the relevant fluid-induced excitation control methods are summarized. The conclusions are as follows:

(1) The investigation of the internal flow structure of centrifugal pumps is mainly based on the PIV test and CFD numerical simulation methods. In a rotating centrifugal impeller, the fluids are under the combined effects of multiple forces and boundary layers. Internal flow distributions are highly three-dimensional with unsteady flow, and contain complex flow structures such as backflow, secondary flow, and wake. The velocity distribution at the impeller outlet presents a typical jet–wake distribution and at blades’ TEs, the mixing of wake and jet will generate periodically shedding vortexes. Meanwhile, the interaction between the impeller non-uniform outflow and the downstream static parts will lead to further flow separation and aggerate the complexity of the internal flow structure.

(2) The investigation of fluid-induced excitations in the centrifugal pumps is based on the monitored internal pressure pulsation and excitation forces via experimental and numerical methods. The correlation between unsteady flow structure and local pressure pulsation is built to reveal the mechanism of different types of fluid-induced excitations. R&D activities show that there are two main categories of fluid-induced excitations in centrifugal pumps: the first is excitation at the BPF, induced by the interaction between the non-uniform impeller outflow and the stator downstream; the second is excitation at low-frequency broadband caused by the turbulence, local flow separation, rotating stall, cavitation, and other abnormal flow structures. However, the excitation at the BPF plays a dominant role in the centrifugal pump operating under rated conditions.

(3) Fluid-induced excitations acting on the wall of the casing and rotor would cause the unsteady excitation force and lead to the vibration of the pump. There are three main categories of methods to reduce the excitation at the BPF of centrifugal pumps: the first is optimizing the structure of static parts such as casing, volute tongue, and guide vanes; the second is increasing the radial gap between the rotor and stator to reduce the intensity of the RSI; and the third is modifying the geometry of the impeller and blades to optimize the uniformity of the impeller outflow. Since the non-uniform impeller outflow is the root source of BPF excitation, the blade surface differential design method based on improving the uniformity of the impeller outflow has great potential in the reduction in BPF excitation intensity.

Based on the existing design experience and the study of the excitation mechanism, an excellent low-vibration hydraulic model of the pump can be obtained. The hydraulic model design of low-vibration pumps mainly takes the amplitude of pressure pulsation and excitation forces as the optimization indicators. However, centrifugal pumps involve many geometric parameters and there is no prediction model for pressure pulsation characteristics. The design of pumps with low sensitivity to vibrations still requires a lot of optimization attempts and consumes a lot of time and computational resources. Therefore, it is very important to study the mechanism of fluid-induced excitations and establish a prediction model for the development of low-vibration pump design.