Numerical investigation on cavitation performance for centrifugal pumps with different impeller inlet geometry

In the centrifugal pump, cavitation often leads to the noise and pressure pulsation, further affects the performance and operation of the pump. Therefore, it is essential to improve cavitation performance at the stage of pump design. In this paper, three centrifugal pump impellers are designed by using different inlet geometry, where one is the conventional type and has cross section diffusion of flow passage along flow direction, and other two impellers are proposed and have cross section contraction of flow passage from impeller inlet to exit. For comparison of cavitation performance, the three-dimensional cavitating turbulent flows are simulated using the RANS method for the pumps. The results show that the pumps with the proposed meridional section have much better cavitation performance at design point while their hydraulic efficiency is also improved at larger flow rate, compared with that with the conventional meridional section design. Extending the blade leading edge of the proposed impeller is very helpful to obtain better cavitation performance further due to the uniform flow and smaller pressure drop around impeller inlet.


Introduction
Centrifugal pump is widely used in various areas of the society.With technology development, the centrifugal pump of large scale, high speed, high power, high performance, et al. is increasingly required, and its efficiency, cavitation and stability are necessary to be improved according to its application [1] [2].Especially, cavitation, leading to the noise level and pressure pulsation as well as harmful to the operation life and stability [3], is an important factor to consider when designing the pump.Previous studies have shown that cavitation performance is related with the geometry of impeller inlet [4].Many researches indicate that the optimization of impeller inlet [5], such as extending the blade leading edge (LE) [6] [7], which can improve better cavitation performance.Previous research shows that the impeller with larger section area at the inlet is beneficial to improve cavitation performance [8] [9].In this study, a novel meridional section of impeller is proposed for centrifugal pump, whose section area at impeller inlet is significantly increased compared with the conventional impeller.The centrifugal impeller with extremely large section area at the inlet is designed for some special applications, where cavitation performance is crucial for pump operation.For comparison, three impellers are designed, in which two impellers have enlarged inlet, and one impeller is the conventional type.Based on numerical simulation, hydraulic performance and cavitation performance are predicted numerically, and the effects of inlet geometry on pump performance are further discussed with the analysis of the cavitating turbulent flow in centrifugal pumps.

Theoretical model
In this study, the RANS method coupled with Shear Stress Transport (SST) k-ω turbulence model is applied to simulate the cavitating turbulent flow in centrifugal pumps [10].In RANS, the equations of continuity and momentum are as follows: ∂(ρu i ) In order to close the equations, SST k-ω turbulence model is used.For cavitation prediction, the Zwart cavitation model, which based on the Rayleigh-Plesset equation, is chosen [11].In the cavitation model, the source terms for vaporization and condensation are as follows: where the subscripts v and l represent vapor-phase and liquid-phase respectively.Ce and Cc are two empirical coefficients, αnuc and αv are the nucleation site or vapor volume fraction [12].
For the convenience of pump performance comparison, dimensionless parameters are adopted for flow rate, pump head, and input power and defined as , ψ and τ as follows [13]: where Pin is the power input for pump shaft, i.e. the product of the torque of the fluid acting on the impeller and rotational angular velocity.NPSH and pressure coefficient Cp are given below [14]: where pinlet is the total pressure at pump inlet, p is the static pressure at specific position.

Calculation model
The pumps treated in this paper are centrifugal pumps with shrouded impeller, whose volute casings are the same.Three impellers based on the performance requirements are designed and presented in table 1. Impeller A1 is designed by the conventional method, having section area diffusion of flow passage from inlet to exit.For Impeller A1, five blades are chosen based on the consideration of both hydraulic performance and cavitation performance.The impellers B1 and B2 are designed by a novel concept, having section area contraction of flow passage.These two impellers have four blades in order to further achieve better cavitation performance.What's more, the blade leading edge (i.e.LE) of impeller B2 is extending toward impeller inlet and a larger wrap angle is applied compared with the impeller B1.The geometrical parameters of three impellers are shown in table 2. Figure 1 shows the meridional sections of three impellers.As an example, figure 2 shows the computation domain of the pump with the impeller A1 and the generated meshes.Structured hexahedron mesh is generated for the flow passage of impeller, inlet pipe and outlet pipe.The unstructured mesh mixed of tetrahedron and hexahedron is used for volute casing.The total number of nodes and elements for each pump case are shown in table 3.

Numerical simulation options
In this paper, static-state internal flow is simulated by using the commercial CFD code CFX 18.0.The boundary conditions are as follows: Total pressure at the plane of pump inlet is given, and the mass flow rate is designated at the pump outlet.All the solid surfaces of flow passage are set as no slip wall.The flow passage of the impeller is set as the rotational coordinate system, while that of other flow components like the inlet pipe, volute casing and the outlet pipe is set as the stationary coordinate system.For the interface between the rotational and stationary coordinate systems, the sliding technique is adopted.
For simulating cavitation in all pumps, the total pressure at pump inlet is decreased gradually.Thus, the correlation of hydraulic performance with NPSH can be obtained.
The fluid is the glycol aqueous solution.In the solution, ethylene glycol is of 60% volume fraction, whose density and viscosity at 20℃ are obtained from Ref. [15].The vapour pressure is set to 1633.4Pa, obtained by Linear interpolation.
The residual RMS is set as 1×10 -6 for numerical simulations in this study.

Characteristic curves
Hydraulic performance of the pumps with three impellers is predicted based on numerical simulation.
Figure 3 shows the relationship between ψ, η, τ and .It is noted that both impellers B1 and B2 have lower efficiency at the flow coefficient less than d=0.071,compared with the conventional impeller, i.e. impeller A1.However, from the design point to larger flow rate, both impellers B1 and B2 have better performance gradually compared with impeller A1.Especially, impeller B2 has much better hydraulic performance with impeller A1.The improvement of hydraulic efficiency is related with the less power loss due to the lower flow incidence, which is resulted from the smaller velocity approaching the impeller inlet with larger section area.

Cavitation performance
Figure 4 displays cavitation performance for the pumps, where the ratio of head coefficient ψ*, hydraulic efficiency η* and power coefficient τ* to their corresponding maximum values (using simulation values without cavitation, refer figure 3) are applied under design flow conditions.The result shows that with NPSH decreasing, pump performance hardly changes before cavitation inception.With NPSH decreasing and the development of cavitation in the pump, the head coefficient drops firstly, and hydraulic efficiency and power coefficient drop subsequently.The results indicate that the occurrence of performance drop for the pump with the conventional impeller i.e. impeller A1 is earlier than that for the pumps with impeller B1 or B2.Generally, 3% head drop is set as the criterion for determining the critical condition with cavitation [13], which is denoted by NPSHc.It is clear that the pumps with different impeller have much different value of NPSHc: 0.128m for impeller A1, 0.109m for impeller B1, and 0.063m for impeller B2 roughly.That means cavitation performance for the pumps with impeller B1 or B2 is much better than that for the pump with impeller A1.

Cavity distributions
As shown in figure 1, a cross-section i.e. section A is defined along the middle section of the volute casing to observe the cavity distribution in whole computational domain at different NPSH.In figure 6, the vapour volume fraction on section A is shown, and the cavity in each pump is plotted using isosurface with vapour volume fraction of 0.1 except A1 at NPSH=0.053m with 0.2 [16].The following results are simulated at design flow rate.
As NPSH=0.316m,cavity can be obviously observed in impeller A1, while cavity cab can't be found for the cases of impellers B1 and B2 obviously.In impeller A1, cavity occurs near the leading edge and along suction surface of the blade.As NPSH decreases to 0.175m, cavity in impeller A1 grows rapidly and extends in the blade-to-blade passage, and seems to cause the blockage in the impeller.On the contrast, cavity in impellers B1 and B2 has very limited size, and hardly affects the flow inside the impeller.For the case of NPSH=0.053m,there is severe blockage of flow passage for impellers A1 and B1, but the blockage for impeller B1 is slighter compared with impeller A1.
Between impellers B1 and B2, the cavity in impeller B2 is much smaller than that in impeller B1.Thus, the impeller with contraction cross section is helpful to improve cavitation performance.Extending blade leading edge can make it better further.Because cavitation inception usually occurs around the impeller inlet, the static pressure from pump inlet to the leading edge of blades is crucial.The presence of cavitation at impeller inlet also affects the overall output of the impeller.The pressure coefficient on section B at noncavitation operations is shown in figure 7. Though the total pressure at pump inlet is the same for three impellers, the pressure coefficient distribution is much different.For the pumps with impellers B1 and B2, the absolute pressure is much higher and the pressure distribution on the section is much uniform compared with that with impeller A1.This confirms that the smaller pressure drop is resulted from the larger section area of impeller inlet for the cases of impellers B1 and B2.

A1
B1 B2 Extending LE allows the impeller to increase static pressure earlier and achieve better cavitation performance.Figure 8 shows the pressure coefficient distribution on section A with different NPSH.For each operation condition, the at smallest radius of the passage on this section is the highest for impeller B2, and the lowest for impeller A1.It makes B2 less easy to cavitate on the rear of passage.
Therefore, the higher static pressure at same position and more uniform pressure distribution for impeller B2 attribute to better cavitation performance compared with impeller A1.

Conclusions
In this paper, the RANS simulations with SST turbulence model and Zwart cavitation model have been conducted for three centrifugal pumps with different impeller inlet geometry.Through the present study, the following concluding remarks can be drawn: The proposed impeller with section area contraction of flow passage from inlet to exit is helpful to improve the pump performance, especially cavitation performance compared with the conventional impeller, whose flow passage has section area diffusion along flow direction.Further extending the blade leading edge toward impeller inlet is also important to obtain better pump efficiency for the operation at larger flow rate and improve cavitation performance further better.
It is depicted that the improvement of hydraulic and cavitation performance is related with the uniform incoming flow and smaller pressure drop around impeller inlet for the proposed impellers, compared with the conventional impeller.

Figure 3 .
Figure 3. Characteristic curves for the pumps.

Figure 4 .
Figure 4. Cavitation performance for the pumps.

Figure 5
Figure 5 shows the relationship between cumulated vapour volume fraction in impeller passage and NPSH.The vertical axis uses logarithmic coordinates to observe the changes in numerical values clearly.When NPSH=0.410m which is away from the critical point i.e.NPSHc, the vapour volume fraction in the pumps of three impellers is very small.With the decrease of NPSH, the values of vapour volume fraction in impeller A1 develops rapidly compared with the cases of impellers B1 and B2.With the cavitation development, the vapour in the impeller increases, and large vapour occurs near the impeller inlet and is apt to make the blockage of flow passage in the pump.The blockage of flow passage may result in flow separation and power loss, and consequently causes the drop of pump head.

Figure 7 .
Figure 7. Pressure coefficient distribution on section B without cavitation.

Table 1 .
The design requirements of centrifugal pump.

Table 2 .
Parameters of pump impellers.

Table 3 .
Total number of nodes and elements.