Investigation of the influence of the gap between impeller and diffuser in the pressure pulsation characteristics of a centrifugal pump

The volute centrifugal pump is the core equipment in large-scale water transfer project. The instability of the unit during operation is mainly due to the hydraulic vibration inside the mechanical parts, and pressure pulsation in the “bladeless area” of impeller and diffuser is the main reason for the hydraulic vibration. This paper investigated the change of pump efficiency and head on different values impeller-diffuser gap, and comparatively analyzed the pressure pulsation characteristics of centrifugal pump. The findings demonstrated that the large gap between the impeller and diffuser, the higher pump efficiency and the lower head. The high pressure regions at the impeller outlet and diffuser inlet were significantly narrowed at gap values of 10 mm and 12 mm. With the increase of the gap, the distribution of the flow field in the impeller and diffuser region became more uniform and the intensity of pressure pulsation was decreased. While the gap value was 12 mm, for the impeller monitoring point on the pressure coefficient ranged within ±0.05. This study illustrated the impact of impeller-diffuser gap value on the internal pressure pulsation of centrifugal pumps, it offered as a certain reference for improving the operational stability of the pumps.


Introduction
Volute pump is a kind of commonly used large capacity centrifugal pump that has the characteristics of high head and large flow rate, is extensively used in the fields of sewage treatment, irrigation and water conservancy engineering.In practical engineering applications, due to the large single pump flow and supporting motor power, and the complex three-dimensional unstable flow is easy to exist in the pump, especially affected by the pressure pulsation at the static and static interface, the unit operation efficiency and stability are faced with problems [1][2].
The rotor-stator interaction is a typical transient flow phenomenon which causes high pressure pulsation and makes the pump unable to run stably.At present, many researches have considered unsteady pressure pulsation in pumps, especially the interactive mechanism between stator and rotor, the influence rules of pressure pulsations and flow characteristics [3][4][5][6][7].The pressure pulsation in the bladeless area between the diffuser and the impeller is extremely crucial.It is the core to ensure the stability of the operation of the unit, and is a straight reflection of the interaction among the rotating and stationary machinery.In the absence of a diffuser, pressure pulsation will occur because of uneven flow distribution from the outlet of the blades.However, the pressure pulsation between impeller and diffuser is more complex than that with diffuser [8].Liu et al. [9] analyzed the particular pressure pulsation in the bladeless region of pumturbine, with an emphasis on pressure pulsations at double and twice the rotational frequency.The magnitude and frequency of pressure pulsation were analyzed from the angle of numerical calculation and model test.Zhang et al. [10] studied the influence on the unsteady hydraulic performance of a pump that had an equal number of blades on the impeller and diffuser.It was found that when the number of blades was the same, the fluid force on the impeller was small, and the local pressure pulsation in the diffuser passage was large.Song et al. [11] studied the static and dynamic interventions of a bifurcated pump turbine under computational fluid dynamic conditions.It was discovered that the pulsation amplitude of the runner and diffuser increases with the increase of diffuser opening.Feng et al. [12] analyzed the effects of different rotor and stator distances on the performance and interaction intensity of mixed-flow centrifugal pumps.It was found that the interaction strength of shock wave and wake decreased as stator-rotor distance increased.However, there are few researches on the influence characteristics of the bladeless area size of impeller-diffuser in centrifugal pump on pressure pulsation.Therefore, this paper specifically studied and analyzed the impact of different impeller-diffuser gap values on pump hydraulic performance and pressure pulsation.

Model parameters
The subject of this paper is a vertical single-stage single-suction volute centrifugal pump model WM-235.The principal design parameters are shown in Table 1, where the pump speed n = 1250r/min, flow rate Qd =920 m 3 /h, head H = 21m, specific speed ns = 235, specific speed calculation formula is:

Grid generation and numerical calculation method
NX UG software was used to conduct three-dimensional modeling of the centrifugal pump, as shown in Figure 1, where the number of impeller was 6 and diffuser was 8.The fluid domain of the pump was divided into five parts: inlet pipe, impeller, diffuser, volute and outlet pipe, and each drainage basin was meshed.The impeller and diffuser adopt structured meshing, and the volute adopts unstructured meshing, as shown in Figure 2. Through grid independence analysis, it was finally determined that the number of grids was approximately 6.93 million in total.The number of grids for each fluid domain is presented in Table 2.
In addition, the Shear Stress Transport (SST k-ω) model was implemented to perform the steady calculation.The inlet boundary condition was set as the total pressure inlet, and the outlet boundary condition as the mass flow outlet, and the wall condition as no slip.The maximum number of iteration steps was 800 and the convergence accuracy was 10 -5 .The time step set unsteady was 1.33×10 -4 s, and the total time was 0.384s.

Experimental verification
Figure 3 shows the comparison between the performance experiment and numerical calculation results of the centrifugal pump.Under the design condition, the error in numerical calculation and experimental head, was 4.5%, and the error obtained in the numerical calculation and the experimental efficiency was 0.18%.This indicated that the numerical method in this paper was effective in the prediction of centrifugal pump performance under design conditions.The error under off-design condition was also within the reasonable range of engineering application.The major reason for the error was that this paper did not consider the clearance flow loss and ignore the influence of roughness on the numerical simulation results.Generally speaking, the curves of experiment and simulation were in good agreement, so the numerical simulation results were feasible and could be used for further study.

Model scheme setting
Five groups were set in this model scheme, as shown in Figure 4, and the gap values between impeller and diffuser were set as △ d=4mm, △ d=6mm, △ d=8mm, △ d=10mm, and △ d=12mm.The corresponding efficiency and head of the five models were calculated by numerical calculation.Since the bladeless area of the impeller and diffuser was the region with the strongest static and static disturbances, the pulsating signal was strongest in this region which fully encompassed the characteristics of the pressure pulsations within the pump.Therefore, a monitoring point was set on the impeller-diffuser flow path to monitor the impact of each scheme on the pressure pulsation characteristics.

Analysis of the effect of gap value on efficiency head
Under design conditions, the corresponding head and efficiency values of different impeller-diffuser gap values are shown in Figure 5.It can be concluded that, when the gap value gradually increases, the efficiency of the pump was continuously enhanced, while the head was gradually reduced.On the basis of meeting the design parameters, the maximum efficiency could reach 88.18%, and the head was 21.68m.The results showed that different impeller-diffuser gap values had crucial effects on the hydraulic performance of the pump.

Pressure analysis
The corresponding pressure distribution of the impeller different gap values are shown in Figure 6.With the continuous increase of the gap value between the impeller and diffuser, the pressure distribution in the impeller runner basically remained unchanged, but the overall pressure tends to decrease, especially the low pressure region in the outlet of the impeller runner increased.When the gap value was 4mm, the high pressure region appeared on the impeller outlet side close to the suction surface, and when the gap value was 12mm, the high pressure region was significantly reduced.The corresponding pressure distribution of diffuser different gap values are shown in Figure 7.As the gap between impeller and diffuser increased, the area of low pressure region increased, and the overall pressure shows a downward trend.Especially, when the gap values were 10mm and 12mm, the high pressure region in the diffuser inlet region was greatly reduced, and the change was more obvious.

Pressure pulsation analysis
The pressure pulsation reflects the change law of the pressure in the flow passage with time.Through the analysis of the pressure pulsation of the centrifugal pump, the unsteady flow law of the fluid in the centrifugal pump with time can be obtained indirectly.Pressure pulsation monitoring points were set respectively at the outlet of the centrifugal pump impeller and the inlet of the diffuser under different gap values, which are represented by the pressure coefficient Cp.The calculation formula is as follows: where p is the transient pressure, Pa; p as the impeller's average pressure during the rotation period, Pa; 2 u is the impeller outlet circumferential velocity, m/s;  is density of the liquid medium.
Pressure pulsation time-domain diagrams of two monitoring points in impeller outlet and diffuser inlet under different gap values were obtained, as shown in Figure 8 and 9. Affected by the number of impeller and diffuser, the pressure pulsation at the various monitoring points changed periodically.The region between the impeller outlet and the diffuser was the most heavily disturbed region of the stator and rotor, and the amplitude of the pressure coefficients fluctuated considerably.As indicated in Figure 8, the pressure coefficient difference with different gap was large.When the gap value was 4mm, the periodicity of pressure pulsation was weakened and a secondary trough structure appears in each period.Along with the widening of the gap, the pressure pulsation amplitude at the impeller outlet also decreased gradually.When the gap value was 12mm, the pressure coefficient changed within the range of ±0.05.Similarly, it was observed from Figure 9 that the pressure pulsation in the diffuser inlet decreased with the increase of the gap value.When the gap value was small, the amplitude of the pressure coefficient was high.When the gap value was 12mm, the pressure coefficient Cp changed within the range of ±0.1.In conclusion, the influence of the gap value of the stator-rotor disturbance region of the impeller and diffuser was obvious.A reasonable increase of the gap value could effectively improve the pressure pulsation phenomenon in the impeller and diffuser region.

Conclusions
In this paper, the impact of impeller-diffuser gap value on the hydraulic performance and pressure pulsation of the centrifugal pump were studied and analyzed.The numerical calculation of the model under different gap value was carried out, and the efficiency and head under different gap value were compared.The internal flow in impeller-diffuser and the pressure pulsation in each monitoring point were analyzed.The results show that when the gap increased, pump efficiency gradually increased, but the head decreased.Through the pressure analysis on the impeller and diffuser, it could be concluded as the gap value increased, the overall pressure inside the impeller decreased obviously.In particular, the low-pressure region was significantly enlarged in the bladeless region of the impeller and diffuser.By analyzing the pressure pulsation in the monitoring points in the bladeless region, it was found that the size of the gap value had a significant influence on the placement of each monitoring point of the centrifugal pump.Along with the widening of the gap, the amplitude of the pressure coefficient decreased gradually.When the gap value was 12mm, the impeller pressure coefficient Cp changed within the range of ±0.05, and the diffuser pressure coefficient Cp changed within the range of ±0.1.

Figure 3 .
Figure 3.Comparison of experimental and numerical results.

Figure 5 .
Figure 5. Different gap values correspond to efficiency and head.

Figure 8 .
Figure 8. Pressure pulsation intensity of impeller outlet monitoring point.

Figure 9 .
Figure 9. Pressure pulsation intensity of diffuser inlet monitoring point.

Table 1 .
Principal design parameters of centrifugal pump.

Table 2 .
Grid number of each fluid domain.