While larger and larger turbines are being developed, hydraulic stability has become one of the key issues for their performance assessments. An accurate prediction of their pressure fluctuations is vital to the success of new model development. In this paper, we briefly introduced the method, i.e., the three-dimensional unsteady turbulent flow simulation of the complete flow passage, which we used for predicting the pressure fluctuations of a model Kaplan turbine. In order to verify the prediction, the model turbine was tested on the test rig at the Harbin Electric Machinery Co., Ltd. (HEC), China, which meets all the international standards. Our main findings from this numerical prediction of pressure fluctuations for a model Kaplan turbine are as follows. (1) The approach by using 3D unsteady turbulent flow including rotor-stator interaction for the whole flow passage is a feasible way for predicting model turbine hydraulic instability. The predicted values at different points along its flow passage all agree well with the test data in terms of their frequencies and amplitudes. (2) The low-frequency pressure fluctuation originating from the draft tube is maximal and influences the stability of the turbine operation mostly. The whole flow passage analysis shows that the swirling vortex rope in the draft tube is the major source generating the pressure fluctuations in this model turbine. (3) The second harmonic of the rotational frequency $2fn$ is more dominant than the blade passing frequency $Zfn$ in the draft tube. This prediction, including the turbulence model, computational methods, and the boundary conditions, is valid either for performance prediction at design stage and/or for operation optimization after commissioning.

1.
Zhang
,
R.-K.
,
Mao
,
F.
,
Wu
,
J.-Z.
,
Chen
,
S.-Y.
,
Wu
,
Y.-L.
, and
Liu
,
S.-H.
, 2009, “
Characteristics and Control of the Draft-Tube Flow in Part-Load Francis Turbine
,”
ASME J. Fluids Eng.
0098-2202,
131
(
2
), p.
021101
.
2.
Rheingans
,
W. J.
, 1940, “
Power Swing in Hydroelectric Power Plants
,”
Trans. ASME
0097-6822,
62
, pp.
171
184
.
3.
Ruprecht
,
A.
,
Heitele
,
M.
, and
Helmrich
,
M.
, 2000, “
Numerical Simulation of a Complete Francis Turbine Including Unsteady Rotor/Stator Interactions
,”
Proceedings of the 20th IAHR Symposium on Hydraulic Machinery and Systems
, Charlotte, NC, Paper No. CFD-S03.
4.
Ruprecht
,
A.
,
Helmrich
,
T.
, and
Scherer
,
T.
, 2002, “
Simulation of Vortex Rope in a Turbine Draft Tube
,”
Proceedings of the 22nd IAHR Symposium on Hydraulic Machinery and Systems
, Lausanne, Swiss, Paper No. A86-HEYGMGJF.
5.
Skotak
,
A.
, 2000, “
Of the Helical Vortex in the Turbine Draft Tube Modeling
,”
Proceedings of the 20th IAHR Symposium on Hydraulic Machinery and Systems
, Charlotte, NC, Paper No. CFD-S07.
6.
Sick
,
M.
,
Dörfler
,
P.
,
Sallaberger
,
M.
,
Lohmberg
,
A.
, and
Casey
,
M.
, 2002, “
CFD Simulation of the Draft Tube Vortex
,”
Proceedings of the 22nd IAHR Symposium on Hydraulic Machinery and Systems
, Lausanne, Swiss, Paper No. A31-KZYRFXJV.
7.
Paik
,
J.
, and
Sotiropoulos
,
F.
, 2004, “
Numerical Simulation of Flow in a Hydroturbine Draft Tube Using Unsteady Statistical Turbulence Models
,”
Proceedings of the 22nd IAHR Symposium on Hydraulic Machinery and Systems
, Stockholm, Sweden, Paper No. A10(1).
8.
Muntean
,
S.
,
Balint
,
D.
, and
Susan-Resiga
,
R.
, 2004, “
3D Flow Analysis in the Spiral Case and Distributor of a Kaplan Turbine
,”
Proceedings of the 22nd IAHR Symposium on Hydraulic Machinery and Systems
, Stockholm, Sweden, Paper No. A10(2).
9.
Liu
,
S. H.
,
Shao
,
Q.
, and
Yang
,
J. M.
, 2004, “Unsteady Turbulent Simulation of Three Gorges Hydraulic Turbine and Analysis of Pressure in the Whole Passage,” Journal of Hydroelectric Engineering, 23(5), pp. 97–101.
10.
Hassan
,
O.
,
Probert
,
E. J.
,
Morgan
,
K.
, and
Weatherill
,
N. P.
, 2000, “
Unsteady Flow Simulation Using Unstructured Meshes
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
189
(
4
), pp.
1247
1275
.
11.
Yakhot
,
V.
, and
Orszag
,
S. A.
, 1986, “
Renormalization Group Analysis of Turbulence. I: Basic Theory
,”
J. Sci. Comput.
0885-7474,
1
(
1
), pp.
3
51
.
12.
Zhang
,
L.
,
Wu
,
W. Z.
, and
Wu
,
Y. L.
., 2002, “
Prediction of Pressure Fluctuation Through Francis Turbine
,”
Journal of Large Electric Machine and Hydraulic Turbine
,
5
, pp.
34
38
.
13.
Li
,
S. C.
, 1992, “
Pressure Fluctuations in Cavitating Draft-Tube Flows
,”
The Writer Annual Meeting of the American Society of Mechanical Engineers
, Anaheim, CA, Vol. FED
136
, pp.
1
6
.
14.
Li
,
S. C.
,
Zuo
,
Z. G.
,
Liu
,
S. H.
,
Wu
,
Y. L.
, and
Li
,
S.
, 2008, “
Cavitation Resonance
,”
ASME J. Fluids Eng.
0098-2202,
130
, p.
031302
.