Investigation of radial force and hydraulic performance in a centrifugal pump with different guide vane outlet angle

3.1. Research model

The research model is a centrifugal pump with guide vanes. Main parameters of the research model are shown in Table 1.

The guide vane in the pump is straight. Therefore, the parameters on the meridional plane of the guide vane will not be changed, when the blade outlet angle of the guide vane is redesigned. In the present research, the inlet angle of the guide vane is 8° and the outlet angle of the guide vane was designed to be 28°, 20 °, 15°, 10°, 5°and 3° respectively. All the research schemes are shown in Fig. 3.

Fig. 3Research schemes

a)${\beta }_4=$3°

b)${\beta }_4=$5°

c)${\beta }_4=$10°

d)${\beta }_4=$15°

e)${\beta }_4=$20°

f)${\beta }_4=$28°

3.2. Calculation domains

In order to improve the simulation precision, the whole flow field is considered in the calculation domains, including the leakage domain in labyrinth seal and between the impeller and the guide vane, as is shown in Fig. 4(b). The entire flow domains in the CFD model consists of annular casing, guide vane, leakage flow domain, impeller and inlet domain. The three dimensional model of calculation domains was built by Pro/E 5.0. The inlet domain and the outlet of the annular casing were properly extended to reduce the effect of boundary conditions on the inner flow. The whole calculation domains are showed in Fig. 4(a).

Fig. 4Calculation domains

a) Drawing of assembly

b) Partial enlarged view of leakage flow near the labyrinth seal

3.3. Grid generation

Geometrical discretization of research model is made before the numerical simulation. As the domains for calculation are quite complex, unstructured mesh of tetrahedral cells is generated by commercial code ANSYS ICEM. In addition, the flow field has already split into 5 components, whose separation enables each mesh to be generated respectively and tailored to that particular part. Due to the significant size difference between the global domain and local details, mesh for some areas was locally refined. In the leakage flow domain, the mesh near the labyrinth seal was refined to match the actual flow domain more closely. Grids for different parts are shown in Fig. 5.

3.4. Boundary conditions

Boundary conditions should be specifically chosen to give more physical meaning for pump flow simulations. At the inlet of the pump, the total pressure is used. And mass flow is used for the outlet of the annular casing. For the outlet on the leakage flow domain, the boundary condition is set as “opening”. All surfaces except the interfaces connecting different parts are imposed with a smooth nonslip boundary condition and the standard wall function is used to process the flow near the wall. Roughness of all the surfaces except interfaces is set to be 0.025 mm.

Fig. 5Grid of different parts

a) Annular casing

b) Guide vane (${\beta }_4=$28°)

c) Impeller

d) Leakage flow domain

e) Refined mesh of leakage flow domain near the labyrinth seal

3.5. Numerical scheme

The fully three dimensional incompressible Navier-Stokes equations are performed using ANSYS CFX code. Discretization of the equations is carried out by using finite volume method based on finite element method. Three dimensional incompressible unsteady simulations are performed by adopting the steady simulation results as the initial conditions. As the impeller in the model keeps rotating while other parts remain stationary, multiple frames of references must be used. The impeller is set in rotary frame and the other parts are set in stationary frame. In addition, interfaces between impeller and other parts are set to be “Transient rotor-stator” while other interfaces remains to be “General connection”. Time-step for unsteady simulations is given 1.126×10^-4 s, which namely means the impeller rotates for 1 degree during 1 time-step. The maximum residuals for calculations are set to be 10^-5. Pressure at the inlet and outlet of the pump are monitored. Each unsteady simulation is calculated for 5 rotation cycles in order to get a stable result. This makes the total time setting for calculations to be 0.20207207 s. However, only data from the last rotation cycle is extracted for the result processing.

3.6. Validation of grid independence

Grid independence is necessary before simulations as grid number may exert an effect on the calculation precision. So guide vane with ${\beta }_4=$28°is selected to validate the grid independence. 5 sets of grids are generated and the results are shown in Table 2. As it can be seen from the table, with the grid number increasing, the head difference is less than 0.7 %. So the possibility of grid dependence can be excluded. Given the time cost for calculation considered, Grid C is selected for calculation in the end. The grid numbers for different flow domains are given in Table 3.

3.7. Selection of turbulence model

Turbulence model selection is a crucial part for numerical simulation as inappropriate turbulence model may lead to high calculation error. Therefore, the SST $k$-$\omega$, Standard $k$-$\epsilon$, $k$-$\epsilon$-$earsm$, $k$-$\omega$, RNG $k$-$\epsilon$ turbulence models have been used to simulate the inner flow of the pump (${\beta }_4=$28°). Compared with the data obtained from the experiment, the final calculation results of different turbulence models are listed in Table 4. It is found results calculated by Standard $k$-$\epsilon$ are closest to the experiment data. So the Standard $k$-$\epsilon$ turbulence model is adopted to perform the simulations in this paper.

Fig. 6Comparison of numerical and experimental results (β4= 28°)

5.1. Influence of guide vane outlet angle on the pump performance

Fig. 7 shows the head and efficiency variation of the pump with the decrease of ${\beta }_4$. It can be clearly seen that, with the ${\beta }_4$ decreasing, the head and efficiency of the pump increase at first and when ${\beta }_4=$10°, the values of head and efficiency are the highest. When ${\beta }_4<$10°, the head and efficiency decrease with β₄ diminishing. Conclusion can be thus drawn that there is an optimal outlet angle of guide vane to achieve the highest head and efficiency. The optimal value of ${\beta }_4$ for this model is 10°.

Fig. 7Performance comparison

5.2. Analysis of flow field in the pump

Variations of pump performance can be reflected from the changes of inner flow field. To understand the reasons for the changes of pump performances under different ${\beta }_4$, the velocity contours and streamlines at the middle span of the guide vane are presented in Fig. 8. It can be seen from Fig. 8 the distributions of streamlines and velocity under different ${\beta }_4$ are quite similar. The velocity gradually decreases from the guide vane to the annular casing for all the cases. Streamlines in the interior of guide vanes are constrained by the edges of the guide vane. But in the annular casing, the streamlines expand in a shape of helix. Meanwhile, there is a high-speed zone near the inlet of guide vane for all the cases. This should be attributed to the dash of the flow from the impeller outlet.

The distributions of the velocity under different ${\beta }_4$ also show some differences. With the ${\beta }_4$ decreasing, the overall uniformity of the flow gradually gets better. There are many vortexes in the guide vane when ${\beta }_4=$28° and 20°, but when ${\beta }_4$ is smaller than 15°, all vortexes disappear. This is because the length of the flow passage in the guide vane becomes bigger and its width gets smaller with the decrease of guide vane outlet angle ${\beta }_4$, which can control the flow pattern in the guide vane more strictly. In this case, the flow in the annular casing also becomes smoother and the vortex disappears.

It is also can be seen from Fig. 8 that with the ${\beta }_4$ decreasing, the overall absolute velocity in the pump increases. For the distribution of velocity in the guide vane, the high speed zone gets bigger with ${\beta }_4$ decreasing. When ${\beta }_4$ is smaller than 10°, high speed area has basically occupied the entire flow passage. The velocity in the annular casing also changes obviously. When ${\beta }_4$ is 28°, the magnitude of the velocity is mainly in the range of 2-6 m/s, but when the ${\beta }_4$ is equal to 3°, the magnitude of the velocity rises to the range of 7-13 m/s.

Therefore, the explanation for the change of pump performance with the variation of ${\beta }_4$ can be given. The decrease of the guide vane outlet angle ${\beta }_4$ makes the internal flow in the pump more uniform, which would lead to higher head and efficiency of the pump. But if the ${\beta }_4$ is too small, the flow passage of the guide vane will become too narrow. In this case, the flow velocity in the guide vane is very high and the guide vane cannot covert kinetic energy into pressure energy very well, which means more hydraulic loss in the pump. The above analysis can be verified by Fig. . In Fig. 7, the head and efficiency of the pump decrease dramatically when the ${\beta }_4$ is smaller than 10°.

Fig. 8Velocity contours and streamlines (m/s)

a)${\beta }_4=$3°

b)${\beta }_4=$5°

c)${\beta }_4=$10°

d)${\beta }_4=$15°

e)${\beta }_4=$20°

f)${\beta }_4=$28°

5.3. Analysis of radial force in the pump

5.3.1. Average value of radial force

The radial force on the impeller is a vector with magnitude and direction and it changes with the rotation of impeller. In order to compare the radial force under different ${\beta }_4$, the radial force vector’s modulus at every time-step in the last calculation cycle is extracted and the average values of all the radial force modulus are calculated based on these data. The average values of the radial force under different ${\beta }_4$ are displayed in Fig. 9.

Fig. 9Average radial force on the impeller

It can be seen from Fig. 9 that the radial force on the impeller reduces obviously as ${\beta }_4$ decreases. When the ${\beta }_4$ varies from 28° to 20°, the average value of the radial force on the pump impeller decreases from 299 N to 156 N, which results in a significant falling as much as 47.8 %. But when ${\beta }_4$ is smaller than 20°, the variation gradient is not obvious. The average value of the radial force decreases from 156 N to 116 N, only 25.6 %, when the ${\beta }_4$ varies from 20° to 3°.

The origin of the radial force on the impeller is from the nonuniform internal flow in the pump. So the more uniform the internal flow becomes, the smaller the radial force gets. Based on the analysis above, the decrease of the guide vane outlet angle ${\beta }_4$ can improve the uniformity of the internal flow. Therefore, the average value of the radial force shows a trend of dropping as the guide vane outlet angle decreases.

5.3.3. Analysis for frequency domain characteristics of radial force

Radial force pulsations result from the rotor-stator interaction, but only through the time domain analysis, it could not be fully understood. In order to determine the main source motivating the radial force pulsations and determine the frequency components of radial force, frequency analysis should be conducted. Fig. 11 shows the frequency spectra of radial force pulsation with different ${\beta }_4$. As it can be seen from the graph, the pulsation of radial force mainly appears at low frequencies. The pulsation amplitude at the blade passing frequency and its harmonic frequencies usually are very big. The largest pulsation amplitude of radial force under different ${\beta }_4$ is at the same frequency and the frequency is 247 Hz, which is 10 times of the rotational frequency and 2 times of the blade passing frequency. This illustrates that the change of ${\beta }_4$ does not alter the frequency of the largest amplitude.

Fig. 10Time domain curves of radial force pulsation

a)${\beta }_4=$3°

b)${\beta }_4=$5°

c)${\beta }_4=$10°

d)${\beta }_4=$15°

e)${\beta }_4=$20°

f)${\beta }_4=$28°

According to Eisenmann [23], for centrifugal pumps with guide vanes, the pulsation frequency for the largest amplitude in the pump may be $N$× impeller blade passing frequency, $N$× guide vane passing frequency or an interference frequency ($N$× rotation frequency) determined by interaction between impeller and guide vane ($N$ is a positive integer). In reference [22], he pointed out when the blade number of the impeller and guide vane are 5 and 9 respectively, the frequency for the largest amplitude is more likely to be 2× impeller blade passing frequency. For the research model in this paper, the pulsation frequency for the highest amplitude is just 2× impeller blade passing frequency, which indicates the main factor of the radial force fluctuations is the interaction between impeller and guide vane. This is mainly due to the small gap between rotary impeller and stationary guide vane, the gap is just 3 mm. Therefore, the interference frequency is the main pulsation frequency in the pump. Also, this result can validate the CFD method in this paper.

Fig. 11Frequency spectra of radial force pulsation

Fig. 12Distribution of radial force vectors

a)${\beta }_4=$3°

b)${\beta }_4=$5°

c)${\beta }_4=$10°

d)${\beta }_4=$15°

e)${\beta }_4=$20°

f)${\beta }_4=$28°