The CFD prediction of the dynamic behavior of a pump-turbine

Aleš Skoták CKD Blansko Engineering, a.s. (CBE Blansko) Czech Republic

Abstract
The paper describes the design of the new runner for the uprating of the water pump storage Dalesice. The original
seven blades runner will be replaced with the new nine blades runner with higher turbine ouput. The purposes for the
uprating are efficiency improvement, wider operational range and smoother operation in pump and turbine regimes. The
commercial CFD code Fluent is used for flow simulation. The self made preprocessor for fast blade to blade channel
grid generation was used for fast and efficient meshing of the computational domain. The efficiency and performance
curves of the new runner are predicted by the one channel flow analysis. For the analysis of the phenomena at non
optimal regimes the simulation of entire turbine is analyzed including all vanes. The three blade cascades including the
elbow draft tube are considered. The sliding mesh method is used, where the runner domain is physically rotating. The
high frequency pressure pulsations are generated by the rotor-stator interaction. The resulting flow character is similar
in comparison to the one segment computation. The domain extension to the draft tube could suppress the back flow
problems at the partia l load operation at turbine mode. However, also the simpler method of the one segment simulation
can be used for the reliable efficiency prediction.

1. Introduction
The water pump storage Dalesice (Czech Republic) is fitted with four pump turbines, originally 105 MW each. The last
unit was put in operation in 1975. The original runner diameter is 6000 mm. The first uprating was made by CBE
Blansko by guide vanes and stay vanes slight geometry modification. The next unit uprating was carried out by VA
Tech in 2002 by runner replacement. The next unit uprating by runner replacement is planed to be realized in 2004 by
CBE Blansko. The development of the second new runner was carried out by the CBE Blansko designers. The
intention was to increase the turbine output to 125 MW, extension of the pump operation to the higher delivery head
and improvement of the dynamic and cavitation behavior of the pump turbine. The requirement for smooth operation in
both regimes for wide operation range was laid. For the satisfaction of all above mentioned requirements it is necessary
to use the modern CFD methods for the design and analysis of the new runner. However, beyond the stationary
computations used for the design procedure it was necessary also to perform the unsteady computations for the
prediction of the dynamic behavior of pump -turbine operation.

2. Design procedure of the new runner

The runner will be installed into the original turbine parts, therefore many important dimensions must be kept. Hence,
the designers possibilities are very restricted. The reliable CFD tool is nowadays necessary for the successful design and
analysis of high efficient machines. The CBE Blansko company is well experienced with the commercial CFD code
Fluent in the procedure of the turbomachinery design. The pump turbine runner in model scale was analyzed in the
model using rotating frames of reference. The isolated one blade channel steady state turbulent flow simulation is used
[Fig. 2]. There is the assumption of the periodical behavior in each blade channel. Also the influence by the upstream
and downstream components as guide vanes and draft tube is neglected in the design procedure. The special in house
software was developed for the blade channel computational domain creation and for automatic grid generation. The
software called “Turbomesh” is written in C++ and it is based on the usage of grid templates. Total time for the grid
generation can be then reduced to about 10 minutes. The generated grid is of high quality with the boundary layer mesh
around the blade surfaces.
a) turbine b) pump

Fig. 1 – Stream function at meridional channel Fig. 2 – One blade channel domain for design analysis

The number of runner blades was determined according to the theory of the dynamic behavior of the rotor-stator
interaction induced forces. The better runner blades/guide vanes combination 9/20 was used instead of original 7/20.
The blade geometry was designed on the stream surfaces determined from the simple meridional axisymmetric channel
flow in turbine regime [Fig. 1].

3. Design procedure - pump operation

The first attempts with conventional runner blades geometry design were not very successful. The high flow
redistribution was found at the runner outlet at the pump operation near expected optimal operation. The redistribution
of the stream lines was found even at the simple axisymetric flow at the meridional channel at pump operation [Fig. 1].
Using the non-conventional blade design with extremely long blades allows to shift the mentioned phenomenon to the
margin of the pump operation range (highest head). The results of the one isolated blade to blade channel computation
at minimum flow rate (maximu m required head ) are described in details . With the increasing of the delivery head the
maximum radial velocities ( ie. flow ) at the runner outlet are shifted near the runner hub. On the other hand the flow
near the shroud at the runner outlet is decelerated [Fig. 4]. The velocities here are negative and the back flow appeared
at the outlet boundary condition. The negative velocities in the form of separation can be found at the runner blade
suction side near the runner shroud [Fig. 3]. No separation and no back flow was indicated at the runner outlet at
optimal operational point.

separation
low
velocities

Fig. 3 – Velocity vectors near the runner shroud (pump) Fig. 4 – Radial velocities at the runner outlet (pump)

The results of the design computation procedure were analyzed and the Q-H curve and efficiency curve for the pump
operation were predicted and compared to the experimental values [Fig. 5]. The significant drop of the Q-H curve can
be found at the lower flow rate ( left from optimum ). Just this flow rate of the Q-H curve drop corresponds to the origin
of the back flow at the runner outlet. The typical illustrative shape of the Q-H curve of the pump inclusive the region of
instability is mentioned in Fig. 6. The two discontinous parts of the performance curve are evident. The right part of the
performance curve corresponds to the stable pump operation, the discontinuity represent the transmition and the left
represents new flow character. The similar shape can be found also on the predicted and measured Q-H curve of the
designed pump -turbine.
 101 120

Eta
99 110

97 100
eta rel [%]

Hp [m]
95 90
H
93 80
CFD

91 EXP 70

89 60
0.6 0.8 1 1.2 1.4
Q rel [-]

Fig. 5 – Q-H and efficiency curves ( pump ) Fig. 6 – Illustrative Q-H curve of a pump

The results of the computation of individual runner segment mentioned above can be affected by the back flow at the
domain outlet. That should be the reason of the results inaccuracy at the off optimal operational points. This task can be
solved by the extension of computation domain for guide vanes channel.

4. Design procedure - turbine operation

When the predicted operation parameters of the designed runner satisfy the pump operation requirements, the next
design phase consisted from turbine operation prediction, next modification and repeatedly pump operation check. This
iteration process was repeated many times in order to satisfy required parameters. The predicted turbine performance
and efficiency curves are compared to the experimentally determined values [Fig. 7]. The inaccuracy in the off design
points should be caused by the back flow indicated at the runner outlet [Fig. 8]. This back flow is produced by the
higher angular momentum at the turbine runner outlet at partial load turbine operation. The fluid is pressed by the
angular momentum to the shroud walls while the flow near the axis is decelerated and the back flow is appeared as its
consequence.

101 140
Eta
99 120

97 100
eta rel [%]

P
Pp [MW]

95 80

93 60
CFD
91 EXP 40

89 20
back
0.6 0.8 1 1.2 1.4
flow
Q rel [-]

Fig. 7 – Performance and efficiency curves ( turbine ) Fig. 8 – The back flow at runner domain outlet

The above mentioned back flow is symmetrical due to only one runner channel comp utation with presumption of the
symmetrical flow. The better results can be obtained by the simulation of the entire runner domain including the draft
tube. Only such way can help to simulate the real helical vortex downstream of the turbine runner known from the
partial load operation [Lit. 1].
5. Computation of the unsteady flow at entire pump-turbine
The results of the isolated one blade channel flow simulation showed the inaccuracy of the results. The back flows at
the domain outlets at both regimes indicate the ill-posed outlet boundary conditions. For the more accurate results it is
necessary to simulate the flow at the domain modeling the flow at the entire pump -turbine. The computational domain
consists of the stay vanes, guide vanes, runner draft tube and part of the spiral case. The spiral case shape is simplified
to the circumferentialy symmetrical half of the torus [Fig. 9]. The computational domain consists of the following blade
cascades: stay vanes zS =10 , guide vanes zG = 20 , runner blades zR = 9. The computational grid on all cascades is
displayed in Fig. 10. The computational domain for the entire pump -turbine consists from 1,2 mil cells. The unsteady
computational model uses the sliding mesh method, which is modeled real runner rotation. The turbulent flow model is
used. The time step size corresponds to the 1/300 of the one turn of the runner.

Fig. 9 – Computational domain of pump -turbine Fig. 10 – The surface grid on the cascades

It is known from the literature, that the periodical solution can be obtained after some revolutions of the runner.
Therefore , the results are analyzed after two runner revolutions. The computation was started from the initial data
directly as the unsteady one.

6. Pressure pulsations at pump mode operation

The dynamics behavior at the pump operation was investigated at the operation point corresponding to the maximal
delivery head of the prototype. The flow separation near the shroud inclusive the back flow at the runner outlet was
analyzed at the individual runner computation. The entire pump turbine computation is showing similar flow character,
however the intensity of the separation is lower [Fig. 11]. No unsteady behavior of that separation was found. The back
flow was shifted to the domain outlet to the vicinity of the stay vanes [Fig. 12]. Maybe, the presence of the full spiral
case could help to suppress the back flow at the domain outlet.

recirculation
separation

Fig. 11 – Instantaneous relative velocity vectors at runner Fig. 12 - Instantaneous velocity vectors at distributor
The dynamic behavior caused by the rotor–stator interaction is evaluated by the static pressure pulsation at the three
check points. The points are located in the vicinity of blade cascades between runner blades and guide vanes. The time
dependent CFD prediction of the static pressure pulsations at the check points are displayed in Fig. 13. The
instantaneous static pressure distribution is in Fig. 14.

-22000

-24000

-26000

-28000

-30000
ps [Pa]

-32000

-34000

-36000

hub
-38000 middle
shroud
-40000
0.100 0.105 0.110 0.115 0.120 0.125 0.130
time [s]

Fig. 13 – CFD predicted static pressure pulsations Fig. 14 – Instantaneous static pressure at runner

7. Pressure pulsations at turbine mode operation

The turbine mode unsteady behavior was in details studied for the partial load operation. The guide vane opening is set
lower, then in case of pump mode simulation. The similar computation carried out on the standard Francis turbine was
yet presented [Lit.3]. The flow rate corresponds to about 50% of the maximum turbine output. The presence of the draft
tube elbow at the runner outlet enables to exclude the back flow at the domain outlet. The symmetrical back flow zone
known from the individual runner computation was compensated by the helical vortex with precessing motion [Fig. 15].
The static pressure pulsation induced by the vortex precessing motion can not by analyzed due to small number of
computed time steps. The instantaneous snapshots of the hydrodynamics quantities at section downstream of the runner
are displayed in Fig. 16. The detailed description of this phenomenon was presented in [Lit. 1].

axial velocity static pressure velocity vectors

Fig. 15 – Isobar surface of the vortex core Fig. 16 – The hydrodynamics quantities downstream of the runner

The dynamic behavior caused by the rotor–stator interaction is evaluated at the same check points, as in the case of the
pump mode operation. The time dependent CFD results of the static pressure at the check points are displayed in Fig.
17. The instantaneous static pressure distribution is in Fig. 18.
 240000

230000

220000

210000

200000
ps [Pa]

190000

180000

170000
hub
160000 middle
shroud
150000
0.100 0.105 0.110 0.115 0.120 0.125 0.130
time [s]

Fig. 17 – CFD predicted static pressure pulsations Fig. 18 – Instantaneous static pressure at middle section

8. Concluding remarks
The simple one segment individual runner computation flow analysis can be reliable used in the design procedure of the
new pump -turbine runner. However, the ill-posed boundary conditions can be suppressed only by the simulation of
entire turbine domain. Hence, the computation of the unsteady behavior of entire pump -turbine was carried out. The
sliding mesh model allowed prediction of the rotor-stator interaction. The high frequency pressure pulsations induced
by moving runner blade cascade were successfully analyzed at pump and turbine operation regimes. The low frequency
pressure pulsations induced by the helical vortex motion in the draft tube at partial load turbine operation were also
predicted however for the periodic solution it is probable necessary to extend the computation time.
The research works were carried out thanks to the financing support of the Ministry of Industry of Czech Republic by
grant No. FD-K/109 - Innovation of pump -turbines, reduction of pressure pulsations, noise reduction and vibrations.

Literature

[1] Skotak, A., Lhotakova, L., Mikulasek, J.: Effect of the inflow conditions on the unsteady draft tube flow, XXI
IAHR Symposium on Hydraulic Machinery and Systems, Lausanne 9-12 September 2002, Switzerland

[2] Rudolf, P., Skotak A.: Unsteady flow in the draft tube with elbow, 10th IAHR WG1 meeting, Trondheim 2001,
Norway

[3] Ruprecht A., Helmrich T., Aschenbrenner: T., Scherer T.: Simulation of pressure surge in a hydr power plant
caused by an elbow draft tube, 10th IAHR WG1 meeting, Trondheim 2001, Norway

[4] Kolarcik W., Zapletal R., Pospisil Z., Franc Z.,Sedlacek P., Straskraba I., Vojtek J.: Identification of the
behavior of hydrodynamical pumps, 8th IAHR WG1 meeting, Chatou 1997, France