1. Introduction
As important liquid transporting equipment in hydraulic systems, centrifugal pumps have been widely used in national economic fields such as agricultural irrigation, water transfer projects, petroleum, and chemical engineering [
1,
2]. There is a high standard for safety and reliable operation of centrifugal pumps in these important areas [
3]. Meanwhile, the centrifugal pump operates an off-design, where the inner flow inside the pump becomes unstable and complex. At the same time, a variety of unstable factors such as cavitation, stator-rotor interaction, rotating stall, and backflow [
4,
5], lead to poor pumping, suction performances, wild vibration, and noise.
In particular, when the centrifugal pump runs at low flow rates, the unstable flow will trigger hydraulic excitation, induce vibration and noise in the pump system, and threaten the stable operation of the centrifugal pump, even damaging the centrifugal pump impeller, hydraulic seal, and other equipment. Therefore, it is necessary to study the fluid-structure interaction between the flowing fluid and the flowing components in the centrifugal pump.
With respect to the research into unsteady flow in the centrifugal pump, more and more researchers have given their attention to studying the influence of the impeller on the inner flow characteristics and the pressure pulsation analysis of the vibration [
6,
7,
8,
9]. For example, Cui proposed a cutting method for a straight blade trailing edge in order to improve unsteady flow and vibration in centrifugal pumps [
10]. Zhang et al. pointed out that rotor–stator interaction is the main cause of high amplitude pressure pulsation and flow-induced vibration in centrifugal pumps [
11]. To predict the vibration under certain flow rates, Birajdar et al. proposed a one-way fluid-structure interaction method, and this vibration was significantly correlated with experimental data [
12]. Wu et al. explored a numerical study of the unsteady flow field and structural properties of a centrifugal pump by using a two-way coupling fluid-structure interaction simulation method [
13]. Zhou et al. applied a two-way coupling method to define the structural response or rotor. The flow field and structural response were calculated by using a joint turbulent flow calculation method. Based on fluid-structure coupling and stress-strain analysis, Zhang et al. conducted pressure pulsation analysis on vertical axial flow pumps. It provided an important theoretical basis for the optimal design and safe operation of vertical axial flow pumps [
14,
15]. Huang et al. explored the cause of rotor stress-strain on the centrifugal pump [
16,
17,
18]. The deformation and stress distribution in the impeller was calculated by using FSI simulation. The blade deformation and stress were analyzed to determine the critical region of the structure. The results ensure the reliability of the pump device [
19]. The impellers were analyzed by static and modal analysis [
20]. By analyzing the flow mechanism of the split blade impeller centrifugal pump, Li Guowei revealed the distribution law of the speed and pressure in the centrifugal pump. The results show that the splitter blade is beneficial to improve the uniformity of velocity and pressure distribution in a centrifugal pump [
21].
Based on the review on the unsteady flow as reported by the open literature, the previous research focused on the backflow and cavitation of pumps. However, few works have been reported on fluid-structure interaction and vibration characteristics which are induced by backflow in a centrifugal pump. In the present study, the ANSYS Workbench simulation platform was applied to simulate the centrifugal impeller structure. The vibration characteristics of the structural system and the modal analysis of different impeller rotating systems were obtained through with one-way fluid-structure interaction method. In addition, the velocity and pressure distribution were analyzed for the inlet backflow of centrifugal pump, and the inlet flow states of different impellers were obtained. A closed hydraulic test rig was designed and built to test the hydraulic performance, and the performance curve was obtained and compared with the curve obtained by numerical simulation.
2. Numerical Method and Strategy
2.1. Parameters of Centrifugal Pump
A single-stage single-suction centrifugal pump was chosen in the present research. Three different impeller structures were designed and classified as Case A, Case B, and Case C.
Pump Case A: closed impeller.
Pump Case B: semi-open impeller.
Pump Case C: impeller with split blades.
The main parameters of the centrifugal pump are shown in
Table 1.
The whole computational domain included: inlet pipe, pump casing, impeller, volute, outlet pipe. The 3D software Unigraphics NX (UG) was used to model all the flow parts. The inlet and outlet boundaries are extended during modeling to eliminate the interference of the physical model on the numerical calculation. The inlet pipe was extended by 800 m about eight times the inlet diameter, and the outlet pipe is extended by 320 mm, about four times of the inlet diameter. The whole model is shown in
Figure 1.
2.2. Division of Computational Grid
The grids used in this study were generated in ICEM CFD. In order to ensure the accuracy of the numerical simulation, six sets of grids with different numbers were applied for the grid-independence check, with the results shown in
Table 2. To select the appropriate number of grid cells, the deviation between prediction and experiment heads in six sets of different grid cell numbers was compared. It can be seen that the head deviation corresponding to the fourth set of grids is 2.17%, which is close to the experimental value, and the deviation value is stable as the number of grids continues to increase. Considering the limited computational resources and lower time consumption, the fourth set of grids was selected for subsequent calculations. The head of six computational grids under design conditions is shown in
Figure 2.
Numerical calculations were performed by ANSYS-CFX17.0 software. Considering the flow in the centrifugal pump, the renormalization-group (RNG)
k-ε turbulence model is chosen as it is concise, reliable, easy to build, has excellent performance, and is widely applicable [
22].
In the
model, the turbulence viscosity coefficient
is expressed as follows.
where
is the empirical coefficient.
Turbulent kinetic energy
and dissipation rate
are expressed as
The dissipation equation of turbulent kinetic energy is:
where:
,
,
.
2.3. Computational Boundary Conditions
The total pressure and mass flow rate were applied for the inlet and outlet boundary conditions during all the numerical simulations in the present study. The reference pressure was set to 1 atm, and different flow rates were calculated by adjusting the outlet flow rate. The computational impeller domain was set to rotating domain with 2950 rpm. The other computational domains were set to static domains. The
model was selected as the turbulence model, and a standard wall surface function was used with the convergence accuracy set to 10
−5.
Table 3 shows the setting of relevant conditions for numerical simulation.
2.4. Fluid-Structure Interaction Calculation of Rotor System
The rotor system mainly includes the impeller, pump shaft and other rotating parts. The rotor system of pump case A mainly includes vanes, the shroud and hub as well as rotating shaft; the case B and case C rotor system includes corresponding vanes, hub, and rotating shaft. The structures of the model pump impeller rotor system are shown in
Figure 3.
The rotor system is the key component of centrifugal pump’s internal energy conversion efficiency. In this research, the one-way fluid-structure interaction method was used to calculate the dynamic and static characteristics of rotor systems. The strategy of a one-way fluid-structure interaction solution is shown in
Figure 4.
In statics analysis, the impeller-rotor system was constrained and loaded. The load of the rotor system includes the gravity of the rotor, the centrifugal force generated by the rotor rotation and the internal and external pressure load of the fluid on the rotor. The gravity load is realized by setting standard earth gravity, with a value of 9806.6 mm/s2, the direction is vertical and the axis is downward. Centrifugal force load sets the speed of the rotating subsystem, the speed value is 2950 rpm, the direction is consistent with the impeller rotation direction. The flow field pressure load is obtained by loading the flow field calculation results, and transferring to the rotor system structure through the fluid-solid coupling interface. The cylindrical support of two rolling bearings was simplified for the impeller shaft. Cylindrical support was added to the shaft bearings for the axial and radial constraints.
The material of the rotor system is HT250, with a density of 7350 kg/m
3, Young’s modulus of 130 GPa, Poisson’s ratio of 0.25, yield strength of 250 MPa. Basic material properties are added to Static Structural by selecting Engineering Data. Constraints and load related settings of the impeller rotor structure are shown in
Figure 5.
In the dynamic research, because the fluid medium has a great influence on the vibration characteristics of the rotor, the wet modal analysis of the rotating subsystem was carried out based on the acoustic-structure coupling method. An acoustic (ACT) plug-in was added in ANSYS Workbench software, the surface where the impeller and fluid are in contact with each other was set as a fluid-solid interface, and the pressure load generated by the fluid is applied to the structure. The fluid is an acoustic fluid with a sound speed of 1430 m/s and a fluid density of 1000 kg/m
3. The flow chart of the fluid-structure coupling calculation is shown in
Figure 6.
2.5. Experimental Verification
To verify the accuracy of the numerical simulation results, a closed hydraulic test rig was set up.
Figure 7 shows the test bench site plan. The test system consists of two parts: a water circulation system and the data acquisition system. The closed test rig water circulation system includes a vacuum pump, reservoir, frequency converter, stainless steel pipeline, corrugated pipe, motor, test stand, test pump, inlet valve, and outlet valve. The data acquisition system consists of the data acquisition program, data acquisition card, data transmission line, and data acquisition equipment. The data acquisition card model used in this test is NI USB 6343X, which has 32 built-in analog signal input channels to meet the measurement requirements.
In the experiment, to assess whether it can operate in a good condition, firstly the test pump and the water circulation system were commissioned and operated. Then the inverter was started and the voltage gradually increased until the motor speed reached the rated speed of 2950 rpm. The inlet pressure was controlled by the vacuum pump, and the operating condition point was changed by adjusting the flow control valve. When the operation was stable, data were collected by the LabVIEW data acquisition program on the computer side. Finally, all the experimental procedures for the other pump cases were repeated with different impeller structures.
4. Conclusions
In this paper, the hydraulic characteristics of centrifugal pumps with different impeller cases were carried out, and the simulation results were compared with the test values. In addition, the one-way fluid-structure interaction calculation method was adopted in the structural statics and dynamics analysis of the rotor components of the pump based on the ANSYS Workbench platform. The main conclusions are as follows.
- (1)
The impeller runs at different flow rates, and the backflow strength is stronger at a small flow rate. Under the same flow rate, the inlet backflow strength of the closed impeller is the minimum, and the backflow strength of the split blade impeller is the maximum. Therefore, the operating stability of split blade impeller is the lowest, and the stability of the closed impeller is the highest.
- (2)
By comparing the simulated head coefficient and efficiency with the experimental results, the head error is less than 5%, which verifies the accuracy of the numerical simulation. Comparing the heads and efficiencies of different impeller cases under the optimal flow rates, it can be obtained that the hydraulic performance of the closed impeller is better, and the hydraulic performance of the split blade impeller is worse.
- (3)
The maximum equivalent force of the impeller rotor system increases as the flow rate decreases. The maximum equivalent force value of the closed impeller is the largest at the same flow rate, and the maximum equivalent force value of the split blade impeller is the smallest. The maximum total deformation of the impeller rotor system tends to decrease and then increase with the increase of the flow rate. By comparing the maximum deformation of different impellers at the same flow rate, the maximum deformation of the closed impeller is 0.085 mm, followed by that of the semi-open impeller at 0.055 mm, while the maximum deformation of split blade impeller is the smallest at 0.047 mm. This shows that at the same flow rate, the closed impeller is vulnerable to damage, the semi-start impeller is safer, and the split blade impeller is the safest.
- (4)
The vibration deformation forms of the first eight orders of the three impeller cases are mainly oscillation deformation around the axis, torsional deformation around the axis, and torsional deformation. The first-order natural frequency of each case is significantly different from the cascade frequency of the centrifugal pump. In three cases, the flow excitation generated during operation will not cause the resonance of the model pump, indicating that it meets the safety requirements.
Due to the limitation of research conditions, this article only uses one-way coupling for simulation. In the subsequent research, it is necessary to adopt the method of two-way fluid-structure coupling to carry out the influence of structural deformation on the flow field, at the same time considering the experimental analysis of vibration characteristics of the centrifugal pump.