Jtam-A4.dvi


JOURNAL OF THEORETICAL

AND APPLIED MECHANICS

51, 3, pp. 649-660, Warsaw 2013

NUMERICAL INVESTIGATION OF THE INNER FLOW IN

A CENTRIFUGAL PUMP AT THE SHUT-OFF CONDITION

Houlin Liu, Xianfang Wu, Minggao Tan

Research Center of Fluid Machinery Engineering and Technology, Jiangsu University, Zhenjiang, Jiangsu, China

e-mail: tmgwxf@gmail.com

The unsteady flow fields in a centrifugal pump at the shut-off condition (SOC) are simu-
lated by the Unsteady Reynolds Averaged Navier-Stokes (URANS) approach. To improve
simulation accuracy and assign the boundary condition, special 3Dmodels aremade.Three-
-dimensionalURANS equations are solved onhigh-quality unstructured gridswith the shear
stress transport turbulence model by using the computational fluid dynamics (CFD) code
CFX-11.0. Furthermore, the numerical simulation results are validated by particle image
velocimetry (PIV) measurements. The main goal of the study is, on one hand, the valida-
tion of the numerical procedure proposed, and on the other hand, the detailed analysis of
the unsteady inner flow field distribution and pressure fluctuation in the centrifugal pump
at SOC. In addition, the head of the pump at SOC is predicted based on CFD results.
The flow analysis indicates that there exists two eddies in each impeller flow passage, and
the velocity at the volute diffusion part is very low. The amplitudes of pressure fluctuation
at fr (impeller rotation frequency) and 3fr dominate in the impeller, while the pressure
fluctuation at fb (blade passing frequency) is dominant in the volute.

Key words: centrifugal pump, numerical simulation, shut-off condition, PIV

Nomenclature

b2,b3 – width of blade outlet and volute inlet, respectively
D1,D2,D3 – diameter of impeller inlet, impeller outlet and volute inlet, respectively
Ft – area of volte throat
fr,fb – frequency of impeller rotation and blade passing, respectively
H,Hso – head at nominal condition and at SOC, respectively

n,ns – rotation speed and specific speed (3.65n
4
√

Q2/H3), respectively
Q,q – rate of flow and rate of leakage flow, respectively
Z – blade number
β2 – angle of blade outlet
η – efficiency at nominal condition

1. Introduction

Traditionally, hydraulic design for centrifugal pumps only considers the best efficiency point
(BEP) requirements. Up to now, the traditional method is not feasible for modern centrifugal
pumps such as pumps used in nuclear power plants and solar photovoltaic pumps. The former
design needs considering more than 3 operation conditions, including characteristics at SOC
(Yuan et al., 2010), and the latter design should decrease pump power at SOC as much as
possible to start the pumpas soon as possible during a day (Short andOldach, 2003). Therefore,
to control the characteristics at SOC, it is currently urgent to study the inner flow field in
centrifugal pumps at SOC.



650 H. Liu et al.

With the development of computer technology and numerical methods, CFD has become a
main tool to research the inner flow in fluid machinery. In the past, it was common practice
to start the pump simulation with a steady assumption. The information provided by this
approach is sufficient if only the mean flow is of interest. In general, a quite good agreement
with experiments can be obtained from classical RANS computations. However, these models
suffer frompredictingdetails like flow separation or vortex.Theflow inside a centrifugal pumpat
SOC is fully turbulent andhighly unsteady,which requires an unsteady simulation.URANSand
large eddy simulation (LES) are the two choices. Pure LES requires very fine and many grids,
especially in boundary layers, and the generation of boundary conditions ismore complex. Also,
LESneedsmore computer resources (Lucius andBrenner, 2010). For these reasons, a turbulence
resolving URANSmodel is used in the present investigation.

Because the boundary condition cannot be determined properly, the inner flow simulation at
SOC for centrifugal pumps is still a problem. A literature review shows that related research is
very few exceptDyson et al. (2004), Dyson andTeixeira (2009) andMuggli et al. (2002).Muggli
et al. investigated the flow field in amixed flow pumpwithCFD and test, and pointed out that
the flow field in the pump at a small flow rate (Q< 0.25QBEP) cannot be predicted by CFD
because of the convergence problem.With some approximation and assumption, Dyson studied
the inner flow ina centrifugal pumpatSOCbyusingCFD,which consisted of an impeller having
3 curved blades with a double volute. Also, he predicted the pump head based on CFD results.
Although his job is valuable, there is still something to be discussed. First, the shroud and hub
cavity are not included in the computational zone, which has direct effects on the inner flow
distribution and performance of the pump (Dong et al., 2010). Second, some influence fators,
such as calculation period and roughness (José et al., 2006; José and Santolaria, 2006), are not
considered in the simulation. Third, he did not do an inner flow experiment to validate CFD
simulation, and the pressure fluctuation was not analyzed in detail. The last is that his research
model is not normal, so the results may not be representative.

According to the above analyses, it can be known that there are still a lot of work to do
to reveal the inner flow field distribution in centrifugal pumps at SOC. The objective of this
study is twofold. First, based on Dyson’s job, a better numerical modeling of the flow field in
a centrifugal pump at SOC is carried out and validated. Second, flow patterns in the impeller
and volute at SOC are obtained and analyzed carefully, so valuable conclusions about the flow
structure at SOC are reported along the paper.

2. Numerical method

TheURANSmethod is an efficient numericalmethod to capture transient phenomena in centri-
fugal pumps (José et al., 2006; José and Santolaria, 2006). So in the present study, the URANS
method is used to simulate the inner flow in a centrifugal pump at SOC, and the 3D URANS
equations are solved using the CFX code.

2.1. Model description and grid

The pump has six backward column blades with a spiral volute. The detailed pump dimen-
sions and performance data are shown inTable 1. The full flowfield is considered to improve the
simulation accuracy. The full three dimensional (3D) model is generated by Pro/E, and Fig. 1
shows the 3D model. A quarter of the 3D model is removed in Fig. 1 to display the interior
structure of the pump. Given PIV test requirements, a semi-spiral suction is designed for the
pump. From Fig. 1, it can be seen that the computational zone includes semi-spiral suction,
impeller, volute, wear ring clearance, shroud chamber, hub chamber, and the impeller-volute



Numerical investigation of the inner flow ... 651

gap. Additionally, in order to set boundary conditions, the pump inlet and pump outlet are
extended properly. The extension sections are too long to be presented in Fig. 1.

Table 1.Main parameters of the model pump

BEP SOC Geometry parameters

Q H n ns η Hso D1 z D2 b2 β2 D3 b3 Ft
[m3h−1] [m] [rmin−1] [–] [%] [m] [mm] [–] [mm] [mm] [◦] [mm] [mm] [mm2]

25.2 12.0 1450 68.6 58.4 12.79 75 6 198 9 39 220 33 1291

Fig. 1. Computational zone of the model

Because the pump structure is very complex, unstructured grid cells are generated to define
the computational zones. The ICEM, preprocessor of CFX, is used to develop meshes. In order
to check the influence of the grid on the results, meshes with different cell numbers are tested,
and the test results are shown inTable 2. It indicates that the second and the third scheme have
the same Hso prediction accuracy. But the third scheme needsmore computation resource and
time because of more cells.

Table 2.Hso prediction results for different grids

No.
Cell Hso simulation Hso experiment Prediction
number results [m] results [m] accuracy [m]

1 2638196 12.49 12.79 −0.50

2 3842435 12.77 12.79 −0.02

3 4976843 12.81 12.79 +0.02

Finally, themodel has 3842435 cells in total, and the quality is satisfied. The quality ofmore
than eighty percent of cells is larger than 0.8, and the quality of theworst cell is bigger than 0.3.
The wall y+ is controlled to stay at less than 20 in all the zones. The information between the
static and rotation parts of the pump is transferred by using a slidingmesh technique.

During themesh generation, special treatments are executed for the volute tongue andwear
ring clearance because of their special structures. The volute tongue is distorted highly, and the
radial dimension of the wear ring clearance is much smaller than its axial dimension. Therefore,
the virtual blockmesh and local refinement are used. The detailed grid and structure of the two
parts are shown in Fig. 2.



652 H. Liu et al.

Fig. 2. Grid refinement of local parts; (a) wear ring clearance, (b) volute tongue

2.2. Boundary condition

As mentioned above, the inlet and outlet boundary conditions are very hard to determine
according to the physical situation. At SOC, a lot of backflows occur in the pump inlet, and
the pump outlet runs at the zero flowrate. In order to assign the inlet boundary condition, a
feasiblemethod is to build a proper 3Dmodel. The inlet is extended twenty times the inlet pipe
diameter to accept the backflow, and the outlet is extended four times the outlet pipe diameter
to reflect the unsteady flow.
To set the outlet boundary condition, an assumption must bemade.When a pump runs at

SOC, the pump can be said to operate with a finite flow equal to the leakage flow through the
wear ring. According to the analysis, the velocity outlet can be applied to the outlet boundary
condition approximately, and the magnitude of leakage flow can be calculated from a formula
by Guan (2011). In other words, an extremely small flow rate is used to approximate the zero
flow rate

q=
Q

1+0.68 1
3
√
n2
s

At solid walls, the no-slip condition with a logarithmic law for boundary layers is employed,
and the roughness height is also considered according to the real condition.

2.3. Mathematical model

Considering incompressibility, viscosity and unsteadiness, the 3D URANS equations, which
include the source term for the centrifugal force in the impeller, are solved by using the com-
mercial code CFX. The effects of turbulence are modeled by using turbulence models. The
calculation results obtained by different turbulence models are compared. The SST k-ω model
is used to take the turbulence effects into account, because its simulation results are closest to
the experimental results. The time-dependent term is a first-order implicit scheme. The second-
-order upwind scheme with numerical under-relaxation is applied for the discretization of the
convection term, whereas the central difference scheme is applied for the discretization of the
diffusion terms.

2.4. Numerical solution control

The simulations are parallelized in a high performance cluster with 16 nodes. The numerical
calculations start with a steady simulation. The unsteady calculations are initialized from the
steady simulation results. In order to reveal the transient flow in the pump at SOC, the deter-
mination of the time step and iteration cycles play a pivotal role, andmany schemes are carried
out. The two parameters can only be determined by comparison. The time step for the unsteady
calculations is set to be 1.149 ·10−4 s, whichmeans that the impeller rotates 1 degree in a time



Numerical investigation of the inner flow ... 653

step. Finally, thirteen impeller revolutions are needed to achieve convergence for the periodic
solutions. The number of iterations is adjusted to reduce the residual for a given variable in all
cells below 10−4. As the simulation is transient, it is necessary to store the data for every time
step, which results in an output file of about 122 Gbytes.

3. CFD results and discussions

All the CFD results discussed in this part are from the thirteenth impeller revolutions. The
pump head, inner flow field and pressure fluctuation at SOCwill be discussed respectively and
carefully.

3.1. Head at SOC

Figure 3 shows the pumphead fluctuation at SOC in the impeller rotation period. It can be
seen that there are six wave peaks and troughs, and the value of each peak and trough varies.
The explanation for the former appearance is that the number of blades is six. The possible
reason for the latter phenomena is that there is lots of unsteady flows in the pump at SOC.
Therefore, the inner flow is very complex and transient. The average head of the curve is 12.77m
and the test head, as shown in Table 1, is 12.79m. The deviation of the prediction head is very
small, so the above CFDmethod is feasible.

Fig. 3. Head fluctuation

3.2. Relative velocity distribution in the impeller

Figure 4 presents the relative velocity distribution in the impeller at different times. It
illustrates that there are two eddies in each flow passage at any time, and one is very big, the
other is small. The big one is at the blade suction side, and it almost blocks the whole flow
passage. The small one is at the blade pressure suction side and near the impeller outlet. The
velocity in the big eddy is all very low, while the velocity in the small eddy is all high. It can be
called the rotation stall. Also, the jet-wake phenomenon is very evident in each flow passage at
any time.

When the blade passes the volute tongue, the blade orientation effects caused by the impeller
rotation are the most obvious. So, in the blade passing rotation (2π/z rad), the inner flow in
flow passage 1 is cared in detail. Figure 4a gives flow passage 1 orientation to the volute tongue,
which is indicated by θ. When θ increases, the zone of the big eddy declines, while the zone
of the small eddy becomes larger. With the increase of θ, the jet-wake phenomenon gets more
obvious, and themaximum of relative velocity gets low.



654 H. Liu et al.

Fig. 4. Relative velocity distribution in the impeller at differene times [m/s]

3.3. Absolute velocity distribution in the pump

The absolute velocity distribution in the pump at different times are shown in Fig. 5. The
impeller position in Fig. 5 is the same as that in Fig. 4. From Fig. 5, it can be seen that the
absolute velocity distribution at SOC is different from that at the nominal condition obviously,
especially for the velocity in the diffusion section of the volute. The velocity in the diffusion
of the volute is very low, which means that the water here nearly does not flow and the flow
circulation mainly occurs in the impeller and the spiral section of the volute. This is because
that the rotation stall eddies block the impeller flow passages. Also, there is a big eddy in
this diffusion zone, and it can result in eddy loss. From the stream line distribution, it can be
concluded that a flow shock occurs at the volute tongue. As θ increases, the flow shock gets
more obvious, which leads tomore hydraulic loss. Except for flowpassage 1 (as shown inFig. 4),
the absolute velocity distribution in the impeller and spiral section of the volute change little as
the impeller rotates. With the increase of θ, the high velocity zone in flow passage 1 becomes
larger.

Fig. 5. Absolute velocity distribution in the pump [m/s]



Numerical investigation of the inner flow ... 655

3.4. Pressure fluctuation in the pump

In order to discover the pressure fluctuation rule in the pump, many monitoring points are
set in the impeller and volute, as shown in Fig. 6. In total, there are 3 points in the impeller and
6 points in the volute. The position of these 9 points is uniform and representative. According
to pressure at these 9 points, the pressure fluctuation from the impeller inlet to the volute outlet
can be obtained and analyzed.

Fig. 6. Monitoring points in the pump

The pressure fluctuation in the impeller is indicated in Fig. 7. In time domain curves, there
are 360 data on each curve. In order to distinguish each curve and present it clearly, only a part
of thedata in formof point symbols are shownon each curve.The frequency spectrumcurves are
obtained from time domain curves by fast Fourier transform (FFT). FromFig. 7a, it can be seen
that the pressure fluctuation amplitudes at PI1 and PI2 are low, and themaximum fluctuation
amplitudes atPI1 andPI2 are 3619Pa and8739Pa, respectively. Thepressurefluctuation atPI3
is very obvious, and the maximum fluctuation amplitude is 16085Pa. The pressure fluctuation
curves at PI1 and PI2 are flat, and there are apparent peaks on the pressure fluctuation curve
at PI3. The above analyses indicate that the interactions between the impeller and volute have
more andmore effects as the impeller radius increases.

Fig. 7. Pressure fluctuation in the impeller, (a) time domain curves, (b) frequency spectrum curves

FromFig. 7b, it can be seen that the amplitudes of pressure fluctuation with frequencies for
PI1, PI2, and PI3 are obviously different. For PI1, the maximum amplitude of pressure fluctu-
ation is at 24.17Hz, which is equal to fr (rotation frequency). For PI2 and PI3, the maximum
amplitudes of pressure fluctuation are all at 72.5Hz (3fr). The second largest amplitude of pres-
sure fluctuation for PI1, PI2 andPI3 is at 72.5Hz, 24.17Hz and 24.17Hz, respectively. So, in the
impeller, the amplitudes of pressure fluctuation at fr and 3fr dominate under SOC. There are



656 H. Liu et al.

two possible reasons for such results. The first is that the rotation stall in the impeller is serious
and the flow is unsteady. The second is that the gap between D2 and D3 is big, so pressure
fluctuation at the blade passing frequency (fb = zfr) does not dominate.

The pressure fluctuation in the volute is shown in Fig. 8. From Fig. 8a, it can be seen that
the pressure increases gradually from PV1 to PV6. The pressure fluctuation amplitude at PV1
ismaximum, and the pressure fluctuation amplitude at PV4 isminimum,whichmeans that the
flow near the volute tongue is very unsteady. Beside the fluctuation amplitude curve at PV4,
there are six peaks on each pressure fluctuation curve, which indicates that the rotator-stator
interactions have more effects on the inner flow field in the volute. The pressure fluctuation at
PV6 is very similar to that at PV5, because the velocity of flow in the volute diffusion part is
very low, as analyzed in Fig. 5.

Fig. 8. Pressure fluctuation in the volute, (a) time domain curves, (b) frequency spectrum curves

FromFig. 8b, it can be seen that the amplitudes of pressure fluctuation with frequencies are
obviously different from those in the impeller. Themaximum amplitude of pressure fluctuation
forall points in thevolute is at145Hz,which indicates that theamplitudesofpressurefluctuation
at fb dominate in the volute. The second largest amplitudes of pressure fluctuation for all points
are all low, andbelow2000Pa.Theamplitudeof pressurefluctuation forPV3 is the lowest among
thesepoints, because it is far away fromthevolute tongue. In conclusion, at SOC, the amplitudes
of pressure fluctuation with frequencies in the volute are lower than those in the impeller.

4. PIV experiments

PIV has been successfully applied by several authors to obtain velocity fields in pumps (Westra
et al., 2010; Benra et al., 2006). In order to validate the simulation results, the inner flow field
in the pump at SOC has been tested at Jiangsu university by PIV.

4.1. Experiment description

To test the inner flow field by PIV, the test impeller and volute are made of transparent
perspex. Corresponding to the unsteady simulation, four blade orientations are considered in
the test, as shown in Fig. 4. The blades arrive at the next position after the impeller rotates by
15 degrees. So the impeller rotates 45 degrees in 4 different positions, which can reflect the inner
flow field distribution in a rotation period as the impeller has six blades. All the measurements
are conducted at themidspan.The encoder installed on the pumpshaft is utilized to synchronize
the measurement with the impeller position.

A PIV system from TSI has been utilized for the measurements. It consists of a YAG200-
-NWL pulse laser, whose single pulse energy is 200mJ and frequency is 30Hz. A digital camera



Numerical investigation of the inner flow ... 657

with a resolution of 2k×2k pixels is used for image acquisition. Al2O3 particles are employed
as seeding particles, whose diameter is approximately 8µm. The pump structure and optical
solutions are presented in Fig. 9. A sketch of the test rig is shown in Fig. 10. In the experiment,
the whole flow field can be obtained by PIV. But in fact, only the flow field in flow passage 4,
5 and 6 can be used to validate the simulation results, because the laser light in these 3 flow
passages are the best. Overall, the error fromPIVmeasurements is estimated to be 2%-3% (Liu
et al., 2012).

Fig. 9. Sketch of the test rig and light configuration

Fig. 10. Sketch of the test rig, 1 – pump, 2 – pressure transducer, 3 – electromagnetic flowmeter,
4 – outlet valve, 5 – inlet valve, 6 – water tank

4.2. Experiment results

As isknowntous, fromPIVtestdata, only theabsolutevelocity distributioncanbeobtained.
So, in order to obtain the relative velocity, a velocity decomposition programhas beendeveloped
according to the velocity triangle in centrifugal pumps. Figure 11 indicates the relative velocity
distribution in the impeller obtained from a PIV test. It can be found that, as we analyzed
above, the test data of the flow field in flow passage 1, 2 and 3 at each time are not good due
to the weak laser light. So the test data of the rest flow field are compared with Fig. 4. By
comparison, it can be found that the simulation results are not exactly the same as the test
results. The small eddy near the impeller outlet is captured, the location, size and magnitude
of the small eddy in simulation are greatly similar to those in the test. But the large eddy at
the blade suction side does not occur in the test. The reasonable explanation for the comparison
results is that the velocity of the large eddy is very low and lower than the dropping velocity of
an Al2O3 particle. Therefore, the large eddy is not captured in the test.
In order to compare the experimental data and simulation results in detail, the absolute

velocity data at point PI2 (as seen in Fig. 6) at different times are extracted from PIV test
results and simulation results respectively. The absolute velocity data are presented in Fig. 12.



658 H. Liu et al.

Fig. 11. Relative velocity distribution obtained from PIV

FromFig. 12, it can be concluded that the simulation results agreewell with thePIVdata. Also,
the difference in the absolute velocity at point PI2 between the test and simulation data is very
small. The biggest error of simulation is 2.44 percent (θ=15◦), the smallest error of simulation
is 0.76 percent (θ=45◦). And the average error of simulation is 1.425 percent.

Fig. 12. Comparison of absolute velocity between PIV data and CFX data at point PI2

So, analyzing the results depicted in Figs. 11 and 12 one may conclude that the inner flow
simulation for the centrifugal pump at SOC presented in this paper is successful.

5. Conclusions

In this paper, the inner flow field in a centrifugal pump at SOC is simulated and tested. The
URANS is used for simulations and the PIV is used to carry out the test. Through the analyses
on simulation and test results, the following conclusions can be obtained.

(1) To simulate the inner flow at SOC in a centrifugal pumpwith the URANSmethod, some
special treatments should be given. The pump inlet and outlet must be extended properly



Numerical investigation of the inner flow ... 659

in the 3D model. During grid generation, local refinement and virtual block technologies
are applied to deal with the volute tongue and wear ring clearance. A number of factors
can only be determined by careful comparison in the numerical simulation, such as the
turbulence model, time step, iteration cycles, and so on.

(2) The pump head curve at SOC in a cycle exhibits periodic fluctuation, but the fluctuation
amplitudes of each peak are not the same, which is caused by the unsteady inner flow.

(3) There are two eddies in each impeller flow passage, one is small and the other is big. The
velocity in the small eddy is high, and the velocity in the big eddy is very low. The big
eddy nearly blocks thewhole flow passage, which leads to poor flow rate circulation in the
volute. So, the velocity in the volute diffusion part is very small. There is obvious a flow
shock at the volute tongue as the impeller rotates.

(4) According to time domain pressure fluctuation curves, the rotator-stator interactions have
more effects on the inner flow in the volute than that in the impeller. The amplitudes of
pressure fluctuation at fr and 3fr dominate in the impeller, while the pressure fluctuation
at fb is dominant in the volute.

(5) In order to capture the inner flowwith low velocity in the pumpbyPIV, a kind of seeding
particles with better tracking performance is needed.

Acknowledgments

The authors gratefully acknowledge the financial support of National Natural Science Foundation of

China under Project No. 51109095, 51079062, National Natural Science Foundation of Jiangsu Province

under Project No. BK2010346, graduate student scientific innovation foundation of Jiangsu Province

No. CXLX11 0576, and a Project funded by the Priority Academic Program Development of Jiangsu

Higher Education Institutions.

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Manuscript received June 20, 2012; accepted for print November 19, 2012