- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Advances in Mechanical Engineering
Volume 2013 (2013), Article ID 109048, 11 pages
Investigation on Flow-Induced Noise due to Backflow in Low Specific Speed Centrifugal Pumps
Research Center of Fluid Machinery Engineering and Technology, Jiangsu University, Zhenjiang, China
Received 7 April 2013; Accepted 15 August 2013
Academic Editor: Moran Wang
Copyright © 2013 Qiaorui Si et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Flow-induced noise causes disturbances during the operation of centrifugal pumps and also affects their performance. The pumps often work at off-design conditions, mainly at part-load conditions, because of frequent changes in the pump device system. Consequently numerous unstable phenomena occur. In low specific speed centrifugal pumps the main disturbance is the inlet backflow, which is considered as one of the most important factors of flow-induced noise and vibration. In this study, a test rig of the flow-induced noise and vibration of the centrifugal pump was built to collect signals under various operating conditions. The three-dimensional unsteady flow of centrifugal pumps was calculated based on the Reynolds-averaged equations that resemble the shear stress transport (SST) k-ω turbulence model. The results show that the blade passing frequency and shaft frequency are dominant in the spectrum of flow-induced noise, whereas the shaft component, amplitude value at shaft frequency, and peak frequencies around the shaft increase with decreasing flow. Through flow field analysis, the inlet backflow of the impeller occurs under 0.7 times the design flow. The pressure pulsation spectrum with backflow conditions validates the flow-induced noise findings. The velocity characteristics of the backflow zone at the inlet pipe were analyzed, and the dynamic characteristics of the backflow eddy during one impeller rotating period were simultaneously obtained by employing the backflow conditions. A flow visualization experiment was performed to confirm the numerical calculations.
Determining flow-induced noise and its corresponding physical parameters is important for design engineers and system operators in the fields of aerospace, automotive, and civil engineering, marine structures, electricity generation, and chemical processing . As essential energy-conversion device and fluid-transporting equipment, low specific speed centrifugal pumps have been widely used in various fields, such as in the industry, agriculture, ship propulsion, and daily life . The use of noise and vibration of pumps as key performance indicators has received increasing attention in recent years because of stricter environmental noise level restrictions and increasing customer demands.
The pumps often work at off-design conditions, mainly at part-load conditions, because of frequent changes in the pump device system. In this case, numerous unstable phenomena may occur in low specific speed centrifugal pumps. One of these phenomena is the inlet backflow, which is one of the most important factors for flow-induced noise and vibration [3, 4]. The present research mainly focused on the following aspects: the influence of the shape of volute and impeller on the flow-induced noise of centrifugal pumps , the influence of the pipe system and the measuring instrument on test error [6, 7], and the detection and diagnosis of the cavitation and other failures of pumps by analyzing the noise and vibration signals [8, 9]. The generation principle of noise and vibration sources caused by an unsteady flow field in centrifugal impeller has been investigated by Choi et al. . Backflow at the inlet of impeller is caused by fluid breakdown that occurs at the blade import. The presence of backflow inevitably consumes energy and produces nonuniform flow, which further decreases the efficiency of pumps. Furthermore, flow-induced vibration and noise are produced because of the formation and rupture of whirlpool accompanied by corresponding changes in the pressure and velocity fields. Simultaneously, reflux can also exacerbate the cavitation inside the impeller, which releases high impact energy in the form of strong vibrations and noise when bubbles collapse. Therefore, researchers have to analyze thoroughly the relationship between backflow flow and flow-induced noise.
Many scholars have studied the unstable reverse flow of low specific speed centrifugal pumps. Toyokura and Kubota  measured the pressure distribution on the suction surface of the impeller and the flow direction outside the impeller. They argued that flow separation and reverse flow direction around the suction surface of the impeller may trigger reverse flow. Moreover, the effect of the laying angle of the impeller on reverse flow was determined. Gopalakrishnan et al.  pointed out that the process of reverse flow occurs as follows: flow separation → primary reverse flow → prerotation occurrence. Huang [13, 14] used dynamic probes to investigate and perform visual observation on the inlet flow field with different inlet angles, numbers of impellers, and open types of tip clearance and inlet flow field of the shrouded impeller. Moreover, the influence of different impeller parameters on the critical reverse flow at the inlet and inlet flow field has been studied. With the fast development of computational fluid dynamics (CFD), Kimura et al.  and Yamanishi et al.  used large eddy simulation and analyzed the areas of backflow zone when the form, structure, quantity, and flow of eddy in the front of the inducer are different.
In the present study, a test rig for flow-induced noise and vibration was developed. The variation of sound pressure level with the flow rate and spectrum of each flow was determined. The three-dimensional unsteady flow of centrifugal pumps at the part-load conditions was calculated based on Reynolds-averaged equations that resemble the shear stress transport (SST) k-ω turbulence model. The results describing the velocity and pressure distribution of the backflow flow field and the development process and the dynamic characteristics of the reflux whirlpool in the rotation of the impeller were displayed. Combined with theoretical analysis, system analysis was performed to determine the relationship between reflux whirlpool and flow-induced noise generation. Finally, visualization tests were carried out to verify the reverse flow at the import pipe.
2. Flow-Induced Noise Measurement of Centrifugal Pump
2.1. Pump Model
A commercial single-stage, single-suction, horizontal-orientated low specific speed centrifugal pump with a six-blade impeller was selected as the model. The design parameters of the pump are shown in Table 1. The casing of the pump is typically combined with a spiral-volute unvaned annulus. The design specific speed of this pump is very low, namely, 65.56, calculated by (1). The increased flowrate design method was used to improve the efficiency at the design point:
2.2. Test Rig Setup
Experiments were conducted in a closed-loop system, which is composed of two parts, namely, the water circulation system and the data acquisition system. The water circulation system supplies the necessary environment for centrifugal pump operation, whereas the data acquisition system changes all kinds of physical quantities at different conditions to the corresponding electrical signals by using sensors. The final data are directly discernible after processing. The installation diagram of the test system is shown in Figure 1. The silencing tank was used to eliminate noise disturbance from the turbine flow meter and valve. The pump, together with the motor, was fixed on a solid base. A vibration isolator was placed between motor and base and was used to diminish the motor impact. The hydrodynamic and noise signals of the pump have always been closely associated with each other, as shown in previous theoretical analyses and experiments. Therefore, these signals are an effective means to measure those parameters simultaneously. The data acquisition system was designed by LabVIEW and was based on a virtual instrument development platform that we have previously developed . The components’ structure of the measurement system is shown in Figure 2.
The inlet gate valve was kept open during the measurement and the outlet gate valve was used to regulate the flow. A turbine flowmeter was used to measure the flow . The turbine flowmeter precision is , and the output standard electrical signal is in the range of 4 mA to 20 mA. Speed is measured by a tachometer (PROVA RM-1500, Taiwan). During the experiment, two dynamic pressure transmitters (CYG1401) were used to measure the inlet pressure () and the outlet pressure (). The precision of CYG1401 is , and it is capable of producing standard electrical signals. The measurement range at the inlet is −100 kPa to 100 kPa, and that at the outlet is 0 MPa to 1 MPa. The twisting moment () imposed on the pump shaft was measured using HBM T5 (Germany), whose measurement range is 20 N·m. Four hydrophones (B&K 8103, Denmark) were equipped to collect noise signal in pipes at the inlet and outlet at a range of 0.1 Hz to 180 kHz. The sensitivity of the hydrophone is −211 dB/1 VμPa. All signals were synchronously collected using NI-PXI-6251, a multifunctional acquisition card. The NI-PXI-6251 resolution is 16 bits and the maximum sampling rate is 250 kHz. Based on the Nyquist sampling theorem and the obtained test range of induced noise, the time interval is s, hits is 80000, and the corresponding sampling rate () at the moment is 10000 Hz.
2.3. Experimental Results
2.3.1. Pump Performance Results
External characteristic factors such as pump head and efficiency were calculated using the following : In the experiment, 13 flow points were tested and are used to form the performance curve. Hence, the maximum head is not at the shut-off condition, as shown in Figure 3. Humps appear in the flow field-head curve; that is, unstable areas exist at low flow. The obtained hump is around . The efficiency-flow curve indicates that the maximum efficiency is around , which may be derived from the increased flow rate design method.
2.3.2. Noise Analysis
In this study, the sound pressure level () was used to indicate the degree of noise. The sound pressure was measured via the passive four-pole network method . Thus, the sound pressure data of incident and reflected waves can be calculated. The LabVIEW software was used to calculate the sound pressure level. The value of the sound pressure level was calculated using the following: where represents the reference sound pressure, whose value in water is 10−6 Pa , is 0.25 Hz, and represents the maximum frequency that can be calculated (10000 Hz). The sound pressure levels of the inlet and outlet noises change with the flow, as shown in Figure 4. After FFT spectrum transformation, the temporal information was transformed into frequency domain. The peak of the flow-induced noise is mainly concentrated at low frequencies, usually below 1 kHz. Thus, the peaks at high frequencies are almost covered by the broadband noise signals. Zoom-FFT was used for spectrum zooming treatment. This algorithm carries out FFT calculation on one subset in the whole frequency range. The Zoom-FFT aims to zoom locally a specific frequency range in the signal frequency spectrum. Furthermore, the advantage of the Zoom-FFT is a higher frequency resolution than that of common FFT in the same Fourier transform point . The frequency domain processing results are shown in Figure 5, where represents the reference impeller passing frequency, namely, 48.3 Hz.
As shown in Figure 4, the sound pressure level in the case of small flow is higher, which may be due to the rider peak in the hump. In such working conditions, the inlet exhibits severe instability and generates backflow, which further results in greater fluctuations in pressure and severe noise. After the sound pressure level initially decreases, reaches the minimum between and , and then subsequently increases with increasing flow. From the frequency domain graph (Figure 5), the blade passing frequency (290 Hz) and the frequency doubling are the main frequencies of the flow-induced noise. Peaks also occur at the shaft frequency (48.3 Hz) and frequency doubling (or superharmonics). Below , the amplitude of the low-frequency noise increases with decreasing flow.
3. Numerical Calculation
From the flow-induced noise test results, the instability phenomenon occurred in cases of small flows for the low specific speed centrifugal pump. Further studies on the internal flow field of the pump are necessary to determine the influence of the instability phenomenon on pump noise. Recently, CFD has been routinely used in the research and development process of hydraulic machinery designs.
ANSYS CFX is a commercial 3D Navier-Stokes CFD code that utilizes a finite-element based on the finite-volume method to discretize the transport equations. This method has the advantage of retaining the geometric flexibility of the finite-element methods while retaining the conservation properties of the finite-volume method; that is, the numerical error on nonsmooth grids is low. Moreover, ANSYS CFX has a coupled solver that simultaneously solves the momentum and continuity equations. It has a proven track record in turbomachinery applications, and its reliability has been confirmed by numerous published studies. For example, several papers [20–22] have used CFX to investigate the general flow patterns within pumps and to solve particular pumping-related problems in relation to the pump design process.
The pump was divided into its component parts, namely, the suction inlet, the pump impeller, and the volute, to build a numerical model for a complete pump, as shown in Figure 6. This process allows each mesh to be individually generated and tailored to the flow requirements in that particular component. The influence of boundary conditions was investigated to discard any impact on the numerical results especially in the discharge channel and to verify the capabilities of the model. Therefore, assuming that the flow closer to a fully developed condition at the inlet and outlet provides better pressure amplitude levels, whereas a pressure outlet imposed at the inlet and outlet has an important influence on the variations in pressure.
The grids for the computational domains were generated using the grid generation tool ICEM-CFD 12.1. The grid details in the rotating domain and the volute wall are partially shown in Figure 7. The independence of the solutions from the number of grid elements was proven by simulating the flow field with different numbers of grid elements. The resulting pump model consists of 3164708 elements for both rotating and stationary domains. Structured hexahedral cells were used to define the inlet, impeller, and volute domains, which had 548274, 1488384 and 1128050, elements, respectively. The total number of grid nodes is 3294345, and the maximum nondimensional wall distance was obtained in the complete flow field.
The analyses were run at flow conditions ranging from to . Three-dimensional URANS equations were solved using the SST turbulence model, with boundary conditions of mass flow at the inlet and average static pressure at the outlet. All specific values were obtained from laboratory tests. The discretization in space is of second-order accuracy, and the second-order backward Euler scheme was chosen for time discretization. Smooth wall condition was used for the near-wall function. The interface between the impeller and the casing is set to “transient rotor-stator” to capture the transient rotor-stator interaction in the flow, because the relative position between the impeller and the casing was changed for each time step with this kind of interface. Two different coordinate systems were utilized for the rotation and stationary domains. The chosen time step () for the transient simulation is s for nominal rotating speed, which corresponds to a changed angle of 0.5°. Therefore, 720 transient results were included for one impeller revolution calculation. Within each time step, 20 iterations were chosen and the iteration stops when the maximum residual is less than 10−4. The convergence criterion for the transient problem is when the result has reached its stable periodicity. Moreover, nine impeller revolutions were conducted for each operational condition, and the results of the last four revolutions were kept for analysis. A nearly exact initial value distribution of the flow parameters was used to obtain the stable numerical simulation. Hence, a steady calculation with a frozen rotor strategy was completed in advance to provide this starting solution.
3.1. Results of Steady Calculation
3.1.1. Pump Performance
Experimental data were collected from laboratory analysis to verify the accuracy of the calculation for the model pump. The comparison of the delivery head curves obtained from numerical calculations and from the experiments for all operational conditions of nominal speed is shown in Figure 8. For the CFD results, the delivery head was obtained from the steady calculation. For the measuring procedure, the signals were obtained using two static pressure sensors at the inlet and outlet, and the head value was evaluated using (2). Under most conditions, the numerical prediction is somewhat lower than that of the corresponding experimental value, which may be due to the neglected roughness. The agreement at the part-load conditions operating points is better than that at the over-load operating points.
3.1.2. Flow Field Analysis
When the flow is less than the design flow, the change in the relative velocity in the impeller passage and the pressure gradient in the passage produces inlet backflow. The backflow intensity changes and the backflow eddy shows different shapes when the flow is changed. In this study, flow field simulation results at eight operating conditions (0.1 to 0.8) were selected to analyze of the eddy intensity and position in the impeller passage. Figure 9 shows the following occurrences: backflow eddies occur around the front shroud; the eddy intensity gradually increases with decreasing flow; the eddy center moves towards the upstream of the water inlet; and an increase in the volume of eddies results in passage blocking. The critical operating condition of the model pump’s backflow is 0.7. When , only large eddies occur at the impeller passage, which does not form backflow out of the blade inlet side. When the flow was decreased to , eddies extend out of the impeller passage and the centers can be located in front of the blade inlet side, which generates backflow. The eddy intensity gradually increases when the flow was continuously decreased. The eddy center moves towards the upstream of the water inlet, and most part of the passage is blocked with increasing volume of eddies.
When the centrifugal pump has the inlet backflow, some of the fluid flows back to the pipe inlet, which generates a fluid motion opposite to the mainstream inlet direction in the axial direction. Severely, backflow causes obstruction in the mainstream and blocks the flow passage, which results in nonuniform inflow. The produced backflow transfers the energy from the impeller rotation to the water inlet fluid because of impeller rotation, thereby causing fluid at the water inlet to rotate. Furthermore, the circumferential speed and backflow eddy are generated. A series of monitoring points are uniformly arranged along the water inlet wall. The distance between the monitoring points and the impeller inlet is . The mainstream direction is labeled as the positive axial direction and the rotation direction of the impeller is labeled as the positive circumferential direction for velocity analysis.
As shown in Figure 10, 0.7 is the critical point of backflow. When the flow is more than 0.7, the axial direction of the water inlet fluid is consistent with the mainstream direction and the circumferential speed at each point is generally equal to 0 with no backflow. When the flow is below 0.7, on the contrary, an axial velocity opposite to the mainstream direction occurs in the water inlet, and the backflow flows into the water inlet and generates prerotation. The axial velocity decreases to 0 at a distance of away from the impeller import. The axial velocity increases with decreasing flow. Moreover, the area of the opposite axial velocity in the water inlet increases and the length of prerotation in the water inlet increases. In the area with prerotation, a smaller flow results in a larger circumferential velocity.
3.2. Results of Unsteady Calculation
The backflow of the model pump at an operating condition of 0.7, is unstable, and the stability of the backflow phenomenon occurs at an operating condition of 0.6. The monitored pressure pulsation data show the pressure pulsation characteristics of the flow field. Therefore, the data are selected from both time domain analysis and frequency domain analysis of the pressure pulsation in this section at an operating condition of 0.6 as shown in Figure 10. Moreover, three monitoring points are arranged along the center line of the water inlet, that is, the impeller inlet (point 1), three times the impeller inlet diameter (point 2), and five times the impeller inlet diameter (point 3) away from the impeller inlet. The pressure fluctuations are presented in a normalized form to allow the scaling of pressure pulsation data with respect to size and speed. Therefore, a nondimensional pressure coefficient, , is defined in (5) to determine the magnitude of the pressure fluctuations for an entire revolution period. is calculated using the standard deviation of the unsteady pressure normalized by the dynamic pressure based on the impeller tip speed, : In Figure 11(b), the peak values of the pressure pulsation gradually decrease with increasing distance of the impeller inlet from monitoring points. The pressure pulsations at monitoring points 1 and 2 show specific phase differences, whereas that at monitoring point 3 represents a distinct periodicity, which indicates that the influence of the circulation eddy on the flow field gradually decreases with increasing distance from the propeller import. In Figure 11(c), each monitoring point has a peak at the blade passing frequency (290 Hz). The pressure pulsation distribution around and beyond the blade frequency is similar. Monitoring points 1 and 2 also have peaks at the shaft frequency and frequency doubling, and point 1 (closer to the impeller inlet) has a larger value. This result indicates that the backflow generates the pressure peak at the shaft frequency and frequency doubling and strengthens the broadband pulsation below the shaft frequency. Thus, a larger low-frequency flow noise is generated in the inlet pipe near the impeller import.
This study investigated the occurrence and development process of backflow eddy in one impeller rotation period at an operating condition of 0.3 to further explain the reasons for the shaft frequency and low frequency pulsation of the backflow. Figure 12 shows that as the impeller rotates, the backflow eddy occurs at the impeller inlet when passage 1 passes the outlet section of the volute. The eddy rotates with the impeller and steadily occurs at the inlet passage (Figure 12(a)). As passage 1 completely leaves the outlet section of the volute, the intensity of the backflow eddy decreases while the intensity of the eddy in front of the inlet of phase passage 2 gradually increases (Figure 12(b)). The impeller continuously rotates and the eddy intensity at the inlet of passage 2 increases as the distribution broadens (Figure 12(c)). When the intensity increases to a specific value, an obvious backflow eddy is observed at the inlet of passage 2. At this time, passage 3 leaves the outlet section, and a backflow eddy is also observed at the inlet of passage 3 (Figure 12(d)). The impeller continuously rotates and the eddy intensities at the inlets of passages 1 and 2 gradually decrease while the eddy intensity at the inlet of passage 3 gradually increases (Figure 12(e)). When the impeller rotates at exactly one period, the eddy at the inlets of these three passages decrease and the eddy occurs at the inlet of the passage and leaves the outlet section of the volute (Figure 12(f)). The next round of period then continues.
4. Discussions on Numerical Results and Visual Verification
Backflow occurs in the impeller passage because of the change in the relative velocity in the impeller passage and the pressure gradient in the passage. When the flow decreases, the eddy intensity gradually increases, and the eddy center moves towards the upstream of inlet pipe, which results in a fluid motion opposite to the mainstream inlet direction in the axial direction. The development and fracture of backflow eddy accompany the corresponding changes in the pressure and velocity fields. Peaks occur at the shaft frequency and double shaft frequency. Furthermore, the broadband pulsation below the shaft frequency (48.3 Hz) increases, which further produces loud low-frequency flow noise.
A transparent inlet pipe made of organic glass was adopted for the visual verification of the flow field. When the centrifugal pump works at different operating conditions, air injected into the pipe through air holes causes air bubbles to move with the fluid. The bubbles are considered as trace particles that can be used to observe the fluid movement at the inlet. At the same time, a high-speed camera was used to record the flow field. The result of this study was compared with the analysis results of the velocity field obtained through steady simulation. Flange is used to connect the pump body to the inlet pipe, which may result in a long distance between the inlet pipe and the impeller import. This study improved the inlet structure of the pump casing as shown in Figure 13, which enables the inlet pipe to be as close as possible to the impeller import, so that the flow field at the impeller import can be observed better. The adopted high-speed camera is IDT Y-series 4L with a maximum resolution of 1024 × 1024 and a maximum frame rate of 4000 frames/second at full resolution.
The centrifugal pump was operated starting from the outer closing valve. After a stable operation for one minute, the columnar eddy strip in the water inlet was observed, which continuously stretched and swung at the center of the water inlet. The valve was then opened. When the flow was adjusted to 0.1, the eddy strip in the water inlet disappeared. No fluid movement in the water inlet could be observed with the naked eyes. At this time, air was injected into the water inlet through air holes and the movements of bubbles were observed. At first, these bubbles moved linearly along the water inlet and suddenly prerotated at a distance of five times greater than the inlet diameter from the impeller import. These bubbles were distributed in a spiral pattern. When the flow was increased, the distance of the bubbles’ prerotation from the impeller inlet gradually decreases. When the flow was increased to 0.4, the bubbles’ prerotation occurred at the impeller import. The inlet is under negative pressure when the model pump was being operated. The injected bubbles increased the pressure at the pump inlet, where backflow occurred. Therefore, the operation condition of the water inlet’s prerotation in the visual verification test can be as low as 0.4. However, this test still verified the backflow phenomenon of the model bump at small flow.
(1)Within the normal operating range (0.7 to 1.3) of the pump, the flow-induced noise of the pump initially decreased with the flow, until reaching a minimum at the peak efficiency point, and subsequently increases. The flow-induced noise is louder in the small flow region because of pump hump. The low-frequency peak value around the shaft frequency also increases, which is caused by unstable flow, specifically the backflow in the pump.(2)The three-dimensional numerical simulation method was adopted to forecast the critical flow point of the model pump in case of backflow. When the flow is less than 0.7, backflow is generated at the impeller import. The backflow eddy mainly occurs near the front shroud. The backflow intensity increases with decreasing flow. The volume of backflow eddy increases, and the eddy center moves towards the upstream, which leads to fluid prerotation in the inlet pipe.(3)The unsteady calculation results show that the pressure pulsations at the monitoring points all have peaks at the blade passing frequency and shaft frequency but the peak values at shaft frequency gradually increases with the decreasing distance. At the operating conditions with small flow, the influence of backflow eddy on the fluid field becomes more obvious. The pulsation range of the broadband frequency below shaft frequency (48.3 Hz) intensifies, so that a smaller flow results in a larger broadband pulsation.(4)The flow field visualization experiment validates the reliability of the simulation results. The backflow causes prerotation in the water inlet of the centrifugal pump, and hence strong eddy and eddy strip are formed. Moreover, pressure pulsation with a low frequency is generated in the water inlet as well as in the pipeline system at low frequencies. When the flow is increased, the prerotation position moves towards the impeller import.
This work was financially supported by the State Key Program of the National Natural Science foundation of China (Grant no. 51239005) and National Science & Technology Pillar Program (Grant no. 2011BAF14B04) of China and was sponsored by Research and Innovation Project for College Graduates of Jiangsu Province (CXZZ12_0679).
- W. K. Blake, Mechanics of Flow-Induced Sound and Vibration: General Concepts and Elementary Sources, Academic Press, 1986.
- F. G. Johann, Centrifugal Pumps, Springer, New York, NY, USA, 2008.
- Y.-D. Choi, J. Kurokawa, and J. Malsui, “Performance and internal flow characteristics of a very low specific speed centrifugal pump,” Journal of Fluids Engineering, vol. 128, no. 2, pp. 341–349, 2006.
- H. Benigni, H. Jaberg, H. Yeung, T. Salisbury, O. Berry, and T. Collins, “Numerical simulation of low specific speed American petroleum institute pumps in part-load operation and comparison with test rig results,” Journal of Fluids Engineering, vol. 134, no. 2, pp. 1–9, 2012.
- O. P. Srivastav, K. R. Pandu, and K. Gupta, “Effect of radial gap between impeller and diffuser on vibration and noise in a centrifugal pump,” Emerging Trends in Mechatronics for Automation, vol. 84, no. 1, pp. 36–39, 2003.
- J. Wang, T. Feng, and K. Liu, “Experimental research on the relationship between the flow-induced noise and the hydraulic parameters in centrifugal pump,” Fluid Machinery, vol. 35, no. 5, pp. 8–11, 2007.
- S. Yuan, J. Yang, J. Yuan, Y. Luo, and J. Pei, “Experimental investigation on the flow-induced noise under variable conditions for centrifugal pumps,” Chinese Journal of Mechanical Engineering, vol. 25, no. 3, pp. 456–462, 2012.
- Y. Ni and S. Yuan, “Diagnosing the running condition of pump by its vibration character,” Drainage and Irrigation Machinery, vol. 25, no. 2, pp. 49–52, 2007.
- M. Čudina and J. Prezelj, “Use of audible sound for safe operation of kinetic pumps,” International Journal of Mechanical Sciences, vol. 50, no. 9, pp. 1335–1343, 2008.
- J.-S. Choi, D. K. McLaughlin, and D. E. Thompson, “Experiments on the unsteady flow field and noise generation in a centrifugal pump impeller,” Journal of Sound and Vibration, vol. 263, no. 3, pp. 493–514, 2003.
- T. Toyokura and A. Kubota, “Studies on back-flow to the suction side of mixed-flow impeller blades,” Bulletin of the JSME, vol. 12, no. 50, pp. 215–221, 1969.
- S. Gopalakrishnan, P. Cooper, C. Grennan, and J. Switzer, “Performance prediction of centrifugal pump and compressors,” in Proceedings of the 25th Annual International Gas Turbine Conference and Exhibit and the 22nd Annual Fluids Engineering Conference, New Orleans, La, USA, March 1980.
- J. Huang, “Studies on inlet reverse flow for open-type and closed type centrifugal pump,” Journal of Engineering Thermophysics, vol. 18, no. 1, pp. 43–47, 1997.
- J. Huang, “The effect of the impeller geometrical parameters of centrifugal pump on the inlet reverse flow,” Journal of Engineering Thermophysics, vol. 19, no. 4, pp. 449–453, 1998.
- T. Kimura, Y. Yoshida, and M. Shimagaki, “Relation between geometries of inducer inlet and backflow and vortex structures,” in Proceedings of the 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Fort Lauderdale, Fla, USA, July 2004.
- N. Yamanishi, S. Fukao, X. Qiao, C. Kato, and Y. Tsujimoto, “LES simulation of backflow vortex structure at the inlet of an inducer,” Journal of Fluids Engineering, vol. 129, no. 5, pp. 587–594, 2006.
- Y. Luo, S. Yuan, and Y. Tang, “Test system for pressure pulsation and hydrodynamic noise in centrifugal pump based on virtual instrument technology,” in Proceedings of the ASME-JSME-KSME Joint Fluids Engineering Conference, Hamamatsu, Japan, July 2011.
- K. Heinrich, Acoustics: An Introduction, Taylor & Francis Press, 2007.
- J. R. M. Hosking and J. R. Wallis, Regional Frequency Analysis, Cambridge Press, Cambridge, Mass, USA, 2005.
- P. Cooper, E. Graf, and T. Luce, “Computational fluid dynamical analysis of complex internal flows in centrifugal pumps,” in Proceedings of the 11th International Pump Users Symposium, pp. 883–1094, Houston, Tex, USA, March 1994.
- J. González, C. Santolaria, F. Castro, and M. T. Parra, “Numerical model for the unsteady flow behaviour inside a double suction pump,” in Proceedings of the 4th ASME/JSME Joint Fluids Engineering Conference, pp. 1149–1155, Honolulu, Hawaii, USA, July 2003.
- K. M. Guleren and A. Pinarbasi, “Numerical simulation of the stalled flow within a vaned centrifugal pump,” Journal of Mechanical Engineering Science, vol. 218, no. 4, pp. 425–436, 2004.