- Email: [email protected]
Three-dimensional Numerical Simulation of Vertical Vortex at Hydraulic Intake
Available online at www.sciencedirect.com
ProcediaProcedia Engineering 00 (2011) Engineering 28000–000 (2012) 55 – 60
Procedia Engineering www.elsevier.com/locate/procedia
2012 International Conference on Modern Hydraulic Engineering
Three-dimensional Numerical Simulation of Vertical Vortex at Hydraulic Intake Yunliang CHENa,b, Chao WUa, Bo WANGa, Min DUa,b, a* a
State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China b College of Hydraulic and Hydroelectric Engineering, Sichuan University, Chengdu 610065, China
Abstract To investigate an effective numerical model for simulating vertical vortex, turbulent models with VOF method are compared. The effects of the turbulent kinetic energy, the turbulent dissipation rate and the turbulent viscosity on formation and development of vertical vortex are analyzed. It shows that RNG k-ε model is more suitable than standard k-ε model to the rapidly strained and great curving streamline flows. The calculated spiral flow agrees with the laboratory tests. It may be helpful to the study on generating mechanism of vertical vertex. Keywords: Vertical vortex; Three-dimensional numerical simulation; RNG k-ε model; Standard k-ε model; VOF method
1. Introduction The vertical vortex occurs frequently at hydraulic intakes due to unfavorable approach flow conditions or low submergence. The boundary conditions of free water surface and hydraulic structure are various and the occurrence of vertical vortex is still unpredictable. Hydraulic scale models are main tools in the research for vertical vortex, but the law of similitude is argued at present. It showed that scale effects could distort prediction by model test as the influencing factors are too complex[1]. The model scale can be overcame and different types of boundary conditions can be simulated easily by numerical simulating prototype. The vertical vortex core often wanders, is little scale, and physical quantities are great gradient. Therefore, it is a big challenge for numerical simulation, including turbulent model and tracing free surface. Li et al. [2] and Lai et al. [3] simulated the vortex at the intake of pump and the water-surface was approximated by Solid-Lid method. Zhao et al. [4] simulated the vortex in a tub by using VOF method. Chen et al. [5] analyzed the flow pattern in the intake at a hydroelectric station * Corresponding author: Min DU. Tel.: +86-28-85407449 E-mail address: [email protected]; [email protected].
1877-7058 © 2012 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Society for Resources, Environment and Engineering doi:10.1016/j.proeng.2012.01.682
562
Yunliang CHEN et al. / Engineering Procedia Engineering (2012) 55 – 60 Author name / Procedia 00 (2011)28 000–000
based on the model test and the numerical simulation. The numerical calculation of vertical vortex is on the initial step in sum. Can the spiral flow and funnel-shaped free water surface of vertical vortex be simulated by applying an effective turbulent model? The simulated results by RNG k and standard k turbulent models are compared in this paper. The calculated spiral flow is compared with experimental tests. 2. CFD model 2.1. RNG k and standard k turbulent models RNG k model has a similar form to the standard k model with additional terms and functions in the transport equations for k and : ( k ) k ( ui k ) [ k eff ] G t x i x j x j
(1)
2 ( ) ( ui ) [ eff ] C1 G C2 k k t x i x j x j
(2)
The turbulent viscosity is constant for each component of Reynolds stress in standard k turbulent model. RNG k model provides an option to account for the effects of swirl or rotation by modifying the turbulent viscosity appropriately.
k
(3) t t 0 f s , , where t 0 is the value of turbulent viscosity calculated without the swirl modification, s is swirl constant, is characteristic swirl number. RNG k model has an additional term containing strain rate S in equation, so the accuracy for rapidly strained flows is improved significantly. The effect of swirl on turbulence is included by modifying the turbulent viscosity. Therefore, RNG k model is more responsive to the effects of rapid strain and streamline curvature than standard k model. Two models coefficients are shown in table 1, where ~ Sk , S 2Si , j Si , j 1 2 , ~0 4.38 , 0.015 , Si , j ui x j u j xi 2 . i, j
Table 1. Model coefficients
C
C1
C 2
k
standard k
0.09
1.44
1.92
1.0
1.3
RNG k
0.085
1.68
0.7179
0.7179
Turbulent model
C1 1.42
~1 ~ ~0 1 ~ 3
2.2. Mesh division and boundary conditions The calculated region is shown in Fig.1. The meshes near vortex zone and the vertical direction near water surface are fined to improve the accuracy of water-air interface. The inflow sections are given as velocity inlet boundary condition and the outlet of intake is given as outflow. The water surface is defined as the atmospheric pressure. The viscous sub-layer for the wall is simulated by the standard wall function.
57 3
Yunliang CHEN / Procedia Engineering 28 (2012) 55 – 60 Author nameet/ al. Procedia Engineering 00 (2011) 000–000 X
Y Z
-0.1
z/m
0
0.1
0.2
0.3
0.2
-0.2 0.1 -0.1 0
y/m 0
m x/
-0.1
0.1 -0.2
0.2
Fig.1. mesh sketch of simulating region
3. Results and analysis 3.1. Free water surface The development of free water surface simulated by two models is shown in Fig.2. The surface depression occurs after 70 second and a superficial vortex at 84 second as shown in Fig.2 (a). Air core reaches the intake after 120 second and the funnel-shaped free water surface forms in Fig.2 (b). A stable vertical vortex is simulated by RNG k model, but no vertical vortex occurs at all time by standard k model as shown in Fig.2 (c). Volume fraction of water
Volume fraction of water
0.4
0.6
0.7
0.9
0.0
1.0
0.1
0.3
0.4
0.6
0.7
0.9
1.0
0.0
-0.2
-0.1
0
0.1
0.3
0.4
0.6
0.7
0.9
1.0
-0.1
-0.1
0
0
0
0.1
0.1
0.1
0.2
0.2
0.2
0.3
0.3
0.3
0.2
y/m
Fig. 2. (a) t=84s by RNG k model;
3.2. Difference analysis
0.1
-0.1
-0.2
-0.1
0
0.1
0.2
z/m
0.3
z/m
0.1
z/m
0.0
Volume fraction of water
-0.2
-0.1
0
0.1
0.2
y/m
y/m
(b) t=120s by RNG k model;
(c) t=300s by standard k model
584
Yunliang CHEN et al. / Engineering Procedia Engineering (2012) 55 – 60 Author name / Procedia 00 (2011)28 000–000
It demonstrates that RNG k model is more suitable than standard k model for simulating vertical vortex. The air-core vortex starts from surface depression, so the condition of water surface is key predisposing cause. The analysis of key physical quantities on free water surface as follows: (1) The turbulent kinetic energy is great only at vortex core because of air-core rotation, but it decreases rapidly outside vortex core as shown in Fig. 3 (a). As enhanced flow fluctuation in vortex zone can oppose the formation of vertical vortex, strong turbulent fluctuation will be helpful to anti-vortex. The calculated turbulent kinetic energy is great in whole vortex zone by standard k model. It may be the first cause of failure simulation by standard k model. Z
X
Z
Turbulent Kinetic Energy (k) 0.0040 0.0036 0.0032 0.0028 0.0024 0.0020 0.0016 0.0012 0.0008 0.0004 0.0000
0.003 0.002 0.001 0
0.2
0.2 0.1
Turbulent Kinetic Energy (k)
Y
Turbulent Kinetic Energy (k) 0.0040 0.0036 0.0032 0.0028 0.0024 0.0020 0.0016 0.0012 0.0008 0.0004 0.0000
0 -0.1
0.003 0.002 0.001 0
0.2
0.1
y/m 0
0.2 0.1
0.1
y/m 0
x/m
-0.1 -0.2
X
0 -0.1
-0.2
x/m
-0.1 -0.2
(a) by RNG k model;
Turbulent Kinetic Energy (k)
Y
-0.2
(b) by standard k model
Fig. 3. turbulent kinetic energy of free water surface
(2) The distribution of turbulent dissipation rate is similar to of the turbulent kinetic energy as shown in Fig.4. The turbulent dissipation rate is great only at vortex core by RNG k model, but great in whole vortex zone by standard k model. Enhanced turbulent dissipation rate can helpful to anti-vortex too. It may be the second cause of failure simulation by standard k model. Z
X
Y
0.06
0.04
0.02
0 -0.2
-0.2 -0.1
-0.1
y/m 0
0 0.1
x/m
0.1 0.2
0.2
(a) by RNG k model;
Turbulent Dissipation Rate (Epsilon)
X Turbulent Dissipation Rate (Epsilon) 0.010 0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0.000
Y
Turbulent Dissipation Rate (Epsilon) 0.010 0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0.000
0.009
0.006
0.003
0 -0.2
-0.2 -0.1
-0.1
y/m 0
0 0.1
Turbulent Dissipation Rate (Epsilon)
Z
x/m
0.1 0.2
0.2
(b) by standard k model
Fig. 4. turbulent dissipation rate of free water surface
(3) The calculated turbulent viscosity is greater much in vortex zone by standard k model than by RNG k model as shown in Fig.5, so greater resistance occurs on free water surface. The structures installed directly in vortex zone to destroy vortex is general anti-vortex measure. Its’ principle is that the energy supporting vortex motion is dissipated because of flow resistance increase. It may be the third
59 5
Yunliang CHEN / Procedia Engineering 28 (2012) 55 – 60 Author nameet/ al. Procedia Engineering 00 (2011) 000–000
cause of failure simulation by standard k model. Z
Z
Y
X
0.005 0.004
Turbulent Viscosity
0.003 0.002 0.001 0 -0.2
-0.2 -0.15 -0.1
-0.1
-0.05 0
y/m 0
0.05
x/m
0.1
0.1
Turbulent Viscosity 0.1500 0.1350 0.1200 0.1050 0.0900 0.0750 0.0600 0.0450 0.0300 0.0150 0.0000
0.15
0.1
0.05
0 -0.2
-0.2 -0.15 -0.1
-0.1
-0.05 0
y/m 0
0.05
0.2
0.15 0.2
(a) by RNG k model;
x/m
0.1
0.1
0.15 0.2
Y
X
Turbulent Viscosity
Turbulent Viscosity 0.0060 0.0054 0.0048 0.0042 0.0036 0.0030 0.0024 0.0018 0.0012 0.0006 0.0000
0.2
(b) by standard k model
Fig. 5. turbulent viscosity of free water surface
3.3. Spiral flow The simulated particle trajectory, water surface, and air-core are shown in Fig.6 (a) that is translucent for visual observation. The experimental result is shown in Fig.6 (b). It can be seen that the spiral flow of vertical vortex simulated agrees with the laboratory tests well. They represent clearly fluid particles flow spirally from the water surface to the underwater and rotate around the vortex-axis.
(a) simulated result;
(b) test photograph
Fig. 6. Particle track of vertical vortex
4. Conclusion Aim to the key hydraulic characteristics of the spiral flow and funnel-shaped free water surface of vertical vortex, the simulated results by RNG k and standard k turbulent models are compared. It shows that greater turbulent kinetic energy, turbulent dissipation rate, and turbulent viscosity in vortex
606
Yunliang CHEN et al. / Engineering Procedia Engineering (2012) 55 – 60 Author name / Procedia 00 (2011)28 000–000
zone may suppress the formation and development of vertical vortex, so failure simulation by standard k model. RNG k model is more suitable for simulating vertical vortex as the rapidly strained and the great curving streamline flows. It may be applicable to the prediction of vertical vertex. Acknowledgements Authors acknowledge financial supports of the National Natural Science Foundation of China (Grant No: 51109149). References [1] Daggett LK and Keulegan GH. Similitude conditions in free-surface vortex formation. ASCE Journal of the Hydraulics Division 1974;170(11): 1565–1581. [2] Li SH and Lai YG. Validation of a three-dimensional numerical model for water-pump intakes. Journal of Hydraulic Research 2004;42(3): 282–292. [3] Lai YG, Weber LJ, Patel VC. A non-hydrostatic three-dimensional numerical model for hydraulic flow simulation-Part I: Formulation and Verification. ASCE Journal of hydraulic Engineering 2003;129(3): 196–205. [4] Yongzhi ZHAO, Zhaolin GU, Yongzhang YU. Numerical simulation of the vortex in a tub. Journal of Hydraulic Engineering 2002;33(12): 1–6. (in Chinese) [5] Yunliang CHEN, Chao WU, Mao YE. Research for flow pattern in intake of hydroelectric station. Journal of Hydrodynamics Ser. A 2005;20(3): 340–345. (in Chinese)
ProcediaProcedia Engineering 00 (2011) Engineering 28000–000 (2012) 55 – 60
Procedia Engineering www.elsevier.com/locate/procedia
2012 International Conference on Modern Hydraulic Engineering
Three-dimensional Numerical Simulation of Vertical Vortex at Hydraulic Intake Yunliang CHENa,b, Chao WUa, Bo WANGa, Min DUa,b, a* a
State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China b College of Hydraulic and Hydroelectric Engineering, Sichuan University, Chengdu 610065, China
Abstract To investigate an effective numerical model for simulating vertical vortex, turbulent models with VOF method are compared. The effects of the turbulent kinetic energy, the turbulent dissipation rate and the turbulent viscosity on formation and development of vertical vortex are analyzed. It shows that RNG k-ε model is more suitable than standard k-ε model to the rapidly strained and great curving streamline flows. The calculated spiral flow agrees with the laboratory tests. It may be helpful to the study on generating mechanism of vertical vertex. Keywords: Vertical vortex; Three-dimensional numerical simulation; RNG k-ε model; Standard k-ε model; VOF method
1. Introduction The vertical vortex occurs frequently at hydraulic intakes due to unfavorable approach flow conditions or low submergence. The boundary conditions of free water surface and hydraulic structure are various and the occurrence of vertical vortex is still unpredictable. Hydraulic scale models are main tools in the research for vertical vortex, but the law of similitude is argued at present. It showed that scale effects could distort prediction by model test as the influencing factors are too complex[1]. The model scale can be overcame and different types of boundary conditions can be simulated easily by numerical simulating prototype. The vertical vortex core often wanders, is little scale, and physical quantities are great gradient. Therefore, it is a big challenge for numerical simulation, including turbulent model and tracing free surface. Li et al. [2] and Lai et al. [3] simulated the vortex at the intake of pump and the water-surface was approximated by Solid-Lid method. Zhao et al. [4] simulated the vortex in a tub by using VOF method. Chen et al. [5] analyzed the flow pattern in the intake at a hydroelectric station * Corresponding author: Min DU. Tel.: +86-28-85407449 E-mail address: [email protected]; [email protected].
1877-7058 © 2012 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Society for Resources, Environment and Engineering doi:10.1016/j.proeng.2012.01.682
562
Yunliang CHEN et al. / Engineering Procedia Engineering (2012) 55 – 60 Author name / Procedia 00 (2011)28 000–000
based on the model test and the numerical simulation. The numerical calculation of vertical vortex is on the initial step in sum. Can the spiral flow and funnel-shaped free water surface of vertical vortex be simulated by applying an effective turbulent model? The simulated results by RNG k and standard k turbulent models are compared in this paper. The calculated spiral flow is compared with experimental tests. 2. CFD model 2.1. RNG k and standard k turbulent models RNG k model has a similar form to the standard k model with additional terms and functions in the transport equations for k and : ( k ) k ( ui k ) [ k eff ] G t x i x j x j
(1)
2 ( ) ( ui ) [ eff ] C1 G C2 k k t x i x j x j
(2)
The turbulent viscosity is constant for each component of Reynolds stress in standard k turbulent model. RNG k model provides an option to account for the effects of swirl or rotation by modifying the turbulent viscosity appropriately.
k
(3) t t 0 f s , , where t 0 is the value of turbulent viscosity calculated without the swirl modification, s is swirl constant, is characteristic swirl number. RNG k model has an additional term containing strain rate S in equation, so the accuracy for rapidly strained flows is improved significantly. The effect of swirl on turbulence is included by modifying the turbulent viscosity. Therefore, RNG k model is more responsive to the effects of rapid strain and streamline curvature than standard k model. Two models coefficients are shown in table 1, where ~ Sk , S 2Si , j Si , j 1 2 , ~0 4.38 , 0.015 , Si , j ui x j u j xi 2 . i, j
Table 1. Model coefficients
C
C1
C 2
k
standard k
0.09
1.44
1.92
1.0
1.3
RNG k
0.085
1.68
0.7179
0.7179
Turbulent model
C1 1.42
~1 ~ ~0 1 ~ 3
2.2. Mesh division and boundary conditions The calculated region is shown in Fig.1. The meshes near vortex zone and the vertical direction near water surface are fined to improve the accuracy of water-air interface. The inflow sections are given as velocity inlet boundary condition and the outlet of intake is given as outflow. The water surface is defined as the atmospheric pressure. The viscous sub-layer for the wall is simulated by the standard wall function.
57 3
Yunliang CHEN / Procedia Engineering 28 (2012) 55 – 60 Author nameet/ al. Procedia Engineering 00 (2011) 000–000 X
Y Z
-0.1
z/m
0
0.1
0.2
0.3
0.2
-0.2 0.1 -0.1 0
y/m 0
m x/
-0.1
0.1 -0.2
0.2
Fig.1. mesh sketch of simulating region
3. Results and analysis 3.1. Free water surface The development of free water surface simulated by two models is shown in Fig.2. The surface depression occurs after 70 second and a superficial vortex at 84 second as shown in Fig.2 (a). Air core reaches the intake after 120 second and the funnel-shaped free water surface forms in Fig.2 (b). A stable vertical vortex is simulated by RNG k model, but no vertical vortex occurs at all time by standard k model as shown in Fig.2 (c). Volume fraction of water
Volume fraction of water
0.4
0.6
0.7
0.9
0.0
1.0
0.1
0.3
0.4
0.6
0.7
0.9
1.0
0.0
-0.2
-0.1
0
0.1
0.3
0.4
0.6
0.7
0.9
1.0
-0.1
-0.1
0
0
0
0.1
0.1
0.1
0.2
0.2
0.2
0.3
0.3
0.3
0.2
y/m
Fig. 2. (a) t=84s by RNG k model;
3.2. Difference analysis
0.1
-0.1
-0.2
-0.1
0
0.1
0.2
z/m
0.3
z/m
0.1
z/m
0.0
Volume fraction of water
-0.2
-0.1
0
0.1
0.2
y/m
y/m
(b) t=120s by RNG k model;
(c) t=300s by standard k model
584
Yunliang CHEN et al. / Engineering Procedia Engineering (2012) 55 – 60 Author name / Procedia 00 (2011)28 000–000
It demonstrates that RNG k model is more suitable than standard k model for simulating vertical vortex. The air-core vortex starts from surface depression, so the condition of water surface is key predisposing cause. The analysis of key physical quantities on free water surface as follows: (1) The turbulent kinetic energy is great only at vortex core because of air-core rotation, but it decreases rapidly outside vortex core as shown in Fig. 3 (a). As enhanced flow fluctuation in vortex zone can oppose the formation of vertical vortex, strong turbulent fluctuation will be helpful to anti-vortex. The calculated turbulent kinetic energy is great in whole vortex zone by standard k model. It may be the first cause of failure simulation by standard k model. Z
X
Z
Turbulent Kinetic Energy (k) 0.0040 0.0036 0.0032 0.0028 0.0024 0.0020 0.0016 0.0012 0.0008 0.0004 0.0000
0.003 0.002 0.001 0
0.2
0.2 0.1
Turbulent Kinetic Energy (k)
Y
Turbulent Kinetic Energy (k) 0.0040 0.0036 0.0032 0.0028 0.0024 0.0020 0.0016 0.0012 0.0008 0.0004 0.0000
0 -0.1
0.003 0.002 0.001 0
0.2
0.1
y/m 0
0.2 0.1
0.1
y/m 0
x/m
-0.1 -0.2
X
0 -0.1
-0.2
x/m
-0.1 -0.2
(a) by RNG k model;
Turbulent Kinetic Energy (k)
Y
-0.2
(b) by standard k model
Fig. 3. turbulent kinetic energy of free water surface
(2) The distribution of turbulent dissipation rate is similar to of the turbulent kinetic energy as shown in Fig.4. The turbulent dissipation rate is great only at vortex core by RNG k model, but great in whole vortex zone by standard k model. Enhanced turbulent dissipation rate can helpful to anti-vortex too. It may be the second cause of failure simulation by standard k model. Z
X
Y
0.06
0.04
0.02
0 -0.2
-0.2 -0.1
-0.1
y/m 0
0 0.1
x/m
0.1 0.2
0.2
(a) by RNG k model;
Turbulent Dissipation Rate (Epsilon)
X Turbulent Dissipation Rate (Epsilon) 0.010 0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0.000
Y
Turbulent Dissipation Rate (Epsilon) 0.010 0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0.000
0.009
0.006
0.003
0 -0.2
-0.2 -0.1
-0.1
y/m 0
0 0.1
Turbulent Dissipation Rate (Epsilon)
Z
x/m
0.1 0.2
0.2
(b) by standard k model
Fig. 4. turbulent dissipation rate of free water surface
(3) The calculated turbulent viscosity is greater much in vortex zone by standard k model than by RNG k model as shown in Fig.5, so greater resistance occurs on free water surface. The structures installed directly in vortex zone to destroy vortex is general anti-vortex measure. Its’ principle is that the energy supporting vortex motion is dissipated because of flow resistance increase. It may be the third
59 5
Yunliang CHEN / Procedia Engineering 28 (2012) 55 – 60 Author nameet/ al. Procedia Engineering 00 (2011) 000–000
cause of failure simulation by standard k model. Z
Z
Y
X
0.005 0.004
Turbulent Viscosity
0.003 0.002 0.001 0 -0.2
-0.2 -0.15 -0.1
-0.1
-0.05 0
y/m 0
0.05
x/m
0.1
0.1
Turbulent Viscosity 0.1500 0.1350 0.1200 0.1050 0.0900 0.0750 0.0600 0.0450 0.0300 0.0150 0.0000
0.15
0.1
0.05
0 -0.2
-0.2 -0.15 -0.1
-0.1
-0.05 0
y/m 0
0.05
0.2
0.15 0.2
(a) by RNG k model;
x/m
0.1
0.1
0.15 0.2
Y
X
Turbulent Viscosity
Turbulent Viscosity 0.0060 0.0054 0.0048 0.0042 0.0036 0.0030 0.0024 0.0018 0.0012 0.0006 0.0000
0.2
(b) by standard k model
Fig. 5. turbulent viscosity of free water surface
3.3. Spiral flow The simulated particle trajectory, water surface, and air-core are shown in Fig.6 (a) that is translucent for visual observation. The experimental result is shown in Fig.6 (b). It can be seen that the spiral flow of vertical vortex simulated agrees with the laboratory tests well. They represent clearly fluid particles flow spirally from the water surface to the underwater and rotate around the vortex-axis.
(a) simulated result;
(b) test photograph
Fig. 6. Particle track of vertical vortex
4. Conclusion Aim to the key hydraulic characteristics of the spiral flow and funnel-shaped free water surface of vertical vortex, the simulated results by RNG k and standard k turbulent models are compared. It shows that greater turbulent kinetic energy, turbulent dissipation rate, and turbulent viscosity in vortex
606
Yunliang CHEN et al. / Engineering Procedia Engineering (2012) 55 – 60 Author name / Procedia 00 (2011)28 000–000
zone may suppress the formation and development of vertical vortex, so failure simulation by standard k model. RNG k model is more suitable for simulating vertical vortex as the rapidly strained and the great curving streamline flows. It may be applicable to the prediction of vertical vertex. Acknowledgements Authors acknowledge financial supports of the National Natural Science Foundation of China (Grant No: 51109149). References [1] Daggett LK and Keulegan GH. Similitude conditions in free-surface vortex formation. ASCE Journal of the Hydraulics Division 1974;170(11): 1565–1581. [2] Li SH and Lai YG. Validation of a three-dimensional numerical model for water-pump intakes. Journal of Hydraulic Research 2004;42(3): 282–292. [3] Lai YG, Weber LJ, Patel VC. A non-hydrostatic three-dimensional numerical model for hydraulic flow simulation-Part I: Formulation and Verification. ASCE Journal of hydraulic Engineering 2003;129(3): 196–205. [4] Yongzhi ZHAO, Zhaolin GU, Yongzhang YU. Numerical simulation of the vortex in a tub. Journal of Hydraulic Engineering 2002;33(12): 1–6. (in Chinese) [5] Yunliang CHEN, Chao WU, Mao YE. Research for flow pattern in intake of hydroelectric station. Journal of Hydrodynamics Ser. A 2005;20(3): 340–345. (in Chinese)