design optimization of a high specific speed francis turbine

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Design optimization of a high specific speedFrancis turbine runnerTo cite this article: Y Enomoto et al 2012 IOP Conf. Ser.: Earth Environ. Sci. 15 032010

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https://doi.org/10.1088/1755-1315/15/3/032010

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https://doi.org/10.1007/s42241-021-0038-4

Design optimization of a high specific speed Francis turbine runner

Y Enomoto, S Kurosawa and H Kawajiri

Toshiba Corporation, 20-1 Kansei-cho, Tsurumi-ku, Yokohama, 230-0034, Japan

E-mail: [email protected]

Abstract. Francis turbine is used in many hydroelectric power stations. This paper presents the development of hydraulic performance in a high specific speed Francis turbine runner. In order to achieve the improvements of turbine efficiency throughout a wide operating range, a new runner design method which combines the latest Computational Fluid Dynamics (CFD) and a multi objective optimization method with an existing design system was applied in this study. The validity of the new design system was evaluated by model performance tests. As the results, it was confirmed that the optimized runner presented higher efficiency compared with an originally designed runner. Besides optimization of runner, instability vibration which occurred at high part load operating condition was investigated by model test and gas-liquid two-phase flow analysis. As the results, it was confirmed that the instability vibration was caused by oval cross section whirl which was caused by recirculation flow near runner cone wall.

1. Introduction Hydroelectric power generation is one of the environment-friendly power generation systems compared with other existent electric power generating equipment and extremely outstanding renewable energy. In particular, Francis turbines are the most widely used in various hydraulic machines. The demands for improvement of turbine performance in wider operating range have been increasing in recent years. Main characteristic of turbine performance are 1) efficiency, 2) cavitaion and 3) pressure fluctuation.

In order to improve the turbine performance such as efficiency and cavitation, runner shape optimization of various optimization methods, for example a genetic algorithm and design of experiments, were carried out for balancing the load distribution on the runner blade surfaces [1-4].

On the other hand, recently the pressure fluctuation which occurred at high partial load operating condition was reported[5-6]. This phenomenon occurs in a very small domain and is accompanied by very big instable vibration. Therefore, it is important to investigate the mechanism of the instability vibration phenomena and find out the countermeasures. This phenomenon is caused by runner outlet whirl which has oval cross section. However, the mechanism of outbreak of this oval cross section whirl was not solved.

In this study, we have two purposes. One is optimization of runner shape which has high efficiency, and another one is investigation of this instability vibration phenomenon. As for the optimization of the runner shape, a new runner design method which combined the latest CFD and a multi objective optimization method with an existing design system was introduced. In this study the optimization runner shape was conducted for high specific speed about 0.21. As for the investigation of instability

26th IAHR Symposium on Hydraulic Machinery and Systems IOP PublishingIOP Conf. Series: Earth and Environmental Science 15 (2012) 032010 doi:10.1088/1755-1315/15/3/032010

Published under licence by IOP Publishing Ltd 1

vibration phenomenon which occurred at high partial load operating condition, model test and CFD analysis was conducted. CFD analysis were conducted using compressible cavitation analysis based on LES turbulence model. By using this model, CFD analysis can successfully catch the oval cross section whirl and be able to help investigating the mechanism of outbreak of oval cross section whirl.

2. Optimization runner shape

2.1. Methodology Conventional hydro turbine runner design is tuned by using follow method. At first, the runner shape is optimized at design point (maximum efficiency point). Next, this runner performance at other operating points is confirmed and tuned runner shape based on the results. In this case, CFD is performed, but this method depends on the skill of designer too much. While in this study, turbine efficiency on whole operating range were chosen in order to evaluate turbine performance with changing various runner design parameters. This whole optimization method is shown in figure 1. In this method, turbine efficiency at 12 operating points from partial load to over load and from high head to low head were defined as multi objective functions and total weighted efficiency was evaluated. It is possible to explore optimized runner shape effectively and systematically by this method.

The concept of design system is shown in figure 2. At first, whole flow passage analysis from spiral case inlet to draft tube outlet was conducted for conventional turbine. Next some runner design parameters to define a runner shape were chosen by using Design of Experiments (DOE) and all matching of runner design parameters were executed on runner design and CFD. And then turbine performance prediction was carried out based on CFD results and the optimized runner shape was decided by sensitivity analysis of design parameters. In the search of optimized runner shape, optimized design parameters were sought in order that multi objective turbine efficiency values were maximized and restricted conditions were sufficient. The points of parameter design method, which mainly involves evaluated functions and restricted conditions, are as follows.

Figure 1. Whole optimization for hydro turbine Figure 2. Optimization design system

2.2. Parameter design points Design parameters were defined based on considering following points.

1) As for whole runner blade shape optimization, pressure distribution on the blade surface was gradual from inlet and outlet in order to restrict increasing hydraulic loss.

Speed factor nED

Dis

char

ge f

acto

r Q

ED

Whole flow passage analysis

Runner + Draft tube

Runner design parameter setting by DOE

CFD analysis

Sensitivity analysis

Optimization of design parameters

Design and CFD of NEW runner

Evaluation of CFD results

Contour line of efficiency

Operating range

Discharge line


2

2) In the optimization of the blade inlet shape, the occurrence of flow separation and inlet cavitation was reduced and good turbine performance was achieved in wider operating range.

3) In the optimization of the blade outlet shape, outlet angle and outlet width distributions, secondary flow was decreased in wider operating range to achieve high turbine efficiency.

4) In the optimization of outlet width distributions and runner band shape, improvements of turbine efficiency and anti-cavitation characteristics had been consistent.

2.3. Evaluated function and restricted condition Evaluated functions were defined as hydraulic efficiency that was calculated based on hydraulic losses at 12 operating points. Restricted condition was defined as the pressure coefficient on the blade surface (minimum value).

2.4. CFD analysis method When the optimization of runner shape is carried out by using CFD, calculation time and precision of the solutions become important. In order to improve CFD accuracy, it is desirable to carry out analysis of the whole flow passage, but it involves great deal of time. Therefore when the runners shape optimization is carried out, the analysis domain is limited to the region from runner to draft tube. The boundary condition of the runner inlet was set applying the velocity distribution obtained from CFD results of a whole flow passage from the spiral casing to draft tube.

2.4.1. Whole passage flow calculation. As for the whole flow passage analysis, turbulence flow simulation based on Reynolds–Averaged Navier-Stokes (RANS) equation was adapted. As for RANS simulation, it is important to employ the anisotropy of the Reynolds stresses in the turbulence model since the secondary flow and rotational force effect are strong in runner and draft tube flow. Therefore Reynolds-Stress model (RSM) is adopted as the turbulence model in the numerical model test. RSM model approximates RANS equations by solving the transport equations for Reynolds stresses, together with an equation of the dissipatetion rate. As for the wall modeling, the non-equilibrium wall function is used. This wall function is more suitable in regions, where the mean flow and turbulence are subjected to severe pressure gradients and change rapidly, and it is effective for the off-design flow simulation, which is involving the separation and reattachment. The non-equilibrium wall function is based on two layers concept in computing the budget of turbulent kinetic energy at the wall adjacent cells, which is needed to solve the k equation at wall-neighboring cells. The computational models are shown in figure 3(a). The number of grid points is about 14 million. The computational boundary conditions were applied at the inlet surface and at the outlet surface of the computational domain. About the inlet boundary condition, it was assumed the uniform velocity distribution. As for the outlet boundary condition, the average pressure was set fixed. Furthermore, about the surface of the wall, the non-slip boundary condition was prescribed, i.e. the velocity components were set to zero.

2.4.2. Runner shape optimization. Figure 3(b) shows computational domain which is used in runner shape optimization. The three-dimensional Reynolds-averaged Navier-Stokes code was used to calculate the flow. The discretization of the governing equation was done by finite volume method, and the convective terms were approximated by Self Filtered Central Differencing scheme. RNG k-ε turbulence model, which had been confirmed accurate in prediction of many hydro turbine and pump-turbine, was applied to calculate the Reynolds stress (Ref 7). As mentioned above, the inlet boundary condition at runner inlet was set applying the velocity distributions obtained from whole flow passage analysis. Outlet boundary condition was defined as the fixed average pressure. The number of grid points is about 5,500,000.


3

(a) for whole passage flow calculation (b) for runner shape optimization

Figure 3. Overview of computational models

2.5. Runner shape optimization In order to carry out runner shape optimization by DOE, flow-passage shape must be defined by parameter values, so geometry definition programs were used to design the runner shape. As for the runner shape definition program, its 3D shape is defined by design parameters, and runner meridian passage and blade shape can be generated accordingly by changing the parameters. In this study, 8 design parameters were used to optimizing the variables such as blade inlet diameter, blade inlet angle, runner crown shape, runner band shape and so on.

Figure 4 shows runner shape. Where the conventional runner was optimized based on conventional optimization method. In this method runner shape was optimized by using CFD. However, boundary condition of runner inlet was used obtained by single component flow analysis of stay vane and guide vane. The velocity distribution was different from the velocity distribution that a whole flow passage analysis result provided. Thus, the optimized runner shape is different from conventional runner in the shape of the blade inlet. Figure 4 shows runner shape and surface flow near the design point of conventional and optimized runner. Figure 4 also shows surface flow near design point of conventional and optimized runner. As for the conventional runner, a secondary flow occurs from runner crown side to runner band side near the leading edge. However a secondary flow is restrained in the optimized runners because the runner shape was optimized based on inlet boundary condition obtained from whole flow passage analysis.

(a) Conventional runner (b) Optimized runner

Figure 4. Runner shape and surface flow Figure 5 shows velocity contour in draft tube. There was not the large difference in both velocity

contours, and the loss in draft tube was almost same.


4

(a) Conventional runner (b) Optimized runner

Figure 5. Velocity contours in draft tube

2.6. Model test In order to confirm the optimized runner performance, model test was conducted. The model runner was made based on CFD analysis results and tested turbine efficiency characteristics. Figure 6 shows model turbine view of the model test. Turbine discharge characteristics on design speed factor are shown in Figure 7. In this figure, the broken line indicates model test result of conventional runner and the solid line indicates the optimized runner’s one and vertical axis and horizontal axis indicate non-dimensional value based on the maximum efficiency point of conventional runner. The efficiency of the optimized runner was higher than the conventional one in whole operating range. It was confirmed that this optimizing method was a useful engineering tool of a Francis turbine development.

Figure 6. View of model turbine Figure 7. Model turbine performance

3. Investigation of instability vibration of Francis turbine Recently the case which pressure fluctuation enlarges with the high partial load of the Francis turbine is reported. In this study, in order to investigate the instability vibrations which occur at high partial load operating condition in Francis turbine, a model test and a flow analysis were conducted. The runner which causes especially large instability vibration was selected. The speed factor of maximum efficiency point was 0.4.

3.1. Investigation of instability vibration by model test The model test was conducted to investigate the area and phenomenon of the instability vibrations. In this test measurement of pressure fluctuation with 8 locations ((1)casing inlet , (2)(3) between runner and guide vane, (4)(5)upper draft tube, (6)draft elbow, (7)(8) draft elbow exit) and the observation of whirl by the high-speed video camera were conducted. Figure 8 shows schematic view of model test equipment. The test was conducted with 3 guide vane openings (aM=100%, 88%, 78%), which are normalized by the guide vane opening corresponding to the optimum operating point. By changing speed factor ( nED ) and Thoma number (σM) , the area that instability vibrations occurred was pinpointed. Figure 9 shows the area that instability vibration occurred. As an example, figure 10 shows the pressure fluctuation under the condition of aM=88%, nED=0.44. From this figure, the pressure

0.90

0.92

0.94

0.96

0.98

1.00

1.02

0.60 0.70 0.80 0.90 1.00 1.10 1.20Discharge QED/QED0 (-)

Tur

bine

eff

icie

ncy η/η 0

(-)

Model Test Results (Optimized runner)

Model Test Results (Conventional runner)

CFD (Optimized runner)

CFD (Conventional runner)

High Low


5

0.5

1

1.5

0.3 0.4 0.5 0.6

Speed factor nED

Rel

ativ

e D

isch

arge

QE

D/Q

ED

0

aM=100%

aM=88%

aM=77%

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Time （s）

fluctuation at casing, and between runner and guide vane increases withinσM condition from 0.15 to 0.27.

Figure 8. Schematic view of model test equipment Figure 9. Instability vibration area

Figure 10. Pressure fluctuation at aM=88% and nED=0.44

Figure 11. Pressure fluctuation wave form

Figure 11 and figure 12 show the pressure fluctuation wave form and the FFT analysis results at the condition of aM=88%, nED=0.44,σM=0.24. And observation results of runner outlet are also shown in Figure 13. From FFT analysis results, it can be seen that, there are about 5 Hz dominant frequency at upper draft tube and 39.6 Hz dominant frequency at casing inlet and between runner and guide vane. The rotational speed of runner (nM) is 17.6 s-1. The 5 Hz dominant frequency at upper draft tube is about one third of rotational speed of runner, therefore the frequency was caused by whirl rotation. However the 39.6Hz dominant frequency at casing inlet has no relation to these runner rotational

0.0

2.0

4.0

6.0

8.0

10.0

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Thoma number σM

Pre

ssur

e F

luct

uati

on ⊿

H／

H (

%) Casing inlet

Between runner and guide vane 1


Upper draft tube １

Upper draft tube 2

Elbow

Elbow exit 1

Elbow exit 2

(1)

(2),(3)

(4) (5)

(6) (7),(8)

▲,●:Pressure transducer for pressure

High speed video camera

Instability vibration area

Maximum efficiency point

Casing inlet Between runner and guide vane 1 Between runner and guide vane 2 Upper draft tube 1 Upper draft tube 2 Elbow Elbow exit 1 Elbow exit 2


6

speed and whirl rotational speed. From figure 13 it can be found that the cross-section of the whirl is an oval and the oval cross section whirl rotates 1 round in the whirl core circumference in about 0.05 seconds (about 20 Hz). So the oval cross section whirl knocks the wall surface at 1 round twice and the frequency is about 40 Hz. This frequency is near the dominant frequency at casing inlet and between runner and guide vane. It is thought that the instability vibration is caused by this oval cross section whirl.

Figure 12. FFT analysis results

T=0.0s T=0.016s T=0.032s T=0.051s

Figure 13. Observation results at runner outlet

3.2. CFD analysis In order to investigate the mechanism of outbreak of oval cross section whirl, CFD was conducted.

3.2.1. Governing equation. Governing equation was used compressible Navier-Stokes Equations whose term was transformed by Gausian Filter.

0x

u

i

i =∂∂

(1)

∂∂

+∂∂ν

∂∂+

∂∂

ρ−=τ+

∂∂+

∂∂

i

j

j

i

jiijii

j

i

x

u

x

u

xx

p1)uu(

xt

u (2)

where ui is averaged velocity, p is averaged pressure, ρ is fluid density, ν is kinematic viscosity and τij is subgrid-scale is stress tensor.

0.E+00

5.E-02

0 10 20 30 40 50 60 70 80（

Am

plitu

de（

V）

Casing inlet



0.E+00

5.E-02

0 10 20 30 40 50 60 70 80

Am

plitu

de （ V

）

Upper draft tube 1

Upper draft tube 2

0.E+00

5.E-02

0 10 20 30 40 50 60 70 80

Frequency f （Hz)

Am

plit

ude （

V）

Elbow

Elbow exit 1

Elbow exit 2

nM=17.6Hz


7

sx

Yu

t

Y

jj =

∂∂+

∂∂

(7)

(8)

jijiij uuuu −=τ (3)

3.2.2. Turbulence model. Subgrid-scale Reynolds stress was formulated by Smagorinsky model.

ijSGSkkijij S23

1 ν−=τδ−τ (4)

where

ijij2

sSGS SS22)C( Δ=ν

∂∂

+∂∂

=i

j

j

iij x

u

x

uS

2

1

Cs is Smagorinsky constant and Δ is a bandwidth filter.

3.2.3. Cavitation modelling. It is known that when cavitation occurs, volume of the gas phase increases, and speed of sound suddenly decrease. Therefore it is important to consider the compressible condition and the speed of sound change Cavitation model was used locally homogeneous compressible medium model which use follow equations(8). Figure 14 shows the relation between void of fraction and speed of sound.

1) Transport equation of vapor mass fraction Y

(6)

s = < ∗ = (1 − ) ∗ −2

= (1 − ) ∗ −2

where Pv* is saturated vapor pressure, Ts is condensing temperature and A is interfacial area concentration. Subscript l means liquid and v means gas.

2) State equation (solution of speed of sound) = ( + )(1 − ) ( + ) + ( + )

where, = 1944.61 , = ( + + )/ − , K = 2aT + b, a = 3.353 × 10 p , b = −1.723 × 10 p , c = 1.222 × 10 p , andR = 461.6J/kg/K.

(5)


8

By using these parameter and state equation of liquid (9) and state equation of vapor (10), the common pressure of liquid and gas was defined (11).

+ = ( + ) (9)

= (10)

= + (1 − ) ( + ) (11)

3) Calculation of speed of sound

(12)

(13)

(14)

(15)

Figure 14. The relation between void of fraction and speed of sound (8)

The discretization of the basic equations was done by finite volume method. Convective terms were approximated by the two order central differences, time was approximated by second order implicit method. As for numerical algorithm to solve the algebraic finite volume equations, the SIMPLE method was used. The analysis domain was modeled from the stay vane to draft tube exit. Figure 15 shows computational domain. The total number of grid is about 700 million and boundary between stationary part and rotating part was connected using sliding mesh boundary condition.


9

Figure 15. Computational domain

Figure 16 shows Iso-surface of void fraction and figure 17 shows velocity vectors on meridian plane. It can be seen from these figures that the oval cross section whirl occurred near the runner cone wall surface. And the oval cross section whirl is formed by the centrifugal force by the leaning of the runner corn shape and the dynamic pressure of the mainstream direction. Probably the reason why the instability vibration occurs at high partial load condition is that, if the discharge decreases less than this operating condition, the runner outlet flow tends to outer side and the boundary layer of the runner corn wall surface developed, so it cannot maintain the recirculation of oval cross section near the runner cone where the starting point of the whirl. Therefore, it is thought that the control a recirculation flow near a runner corn wall surface is effective to prevent the form of oval cross section whirl which causes instability vibration.

Distribution of void fraction Iso-surface of void fraction（void fraction =0.80）

Figure 16. Iso-surface of void fraction

Figure 17. Velocity vectors on meridian plane

4. Conclusions In order to develop high performance turbine for high specific speed Francis turbine, the optimization of runner shape and the investigation of mechanism of instability vibration phenomena was conducted. The results are obtained as follows:

1) This optimization system was a useful engineering tool of a Francis turbine development and the optimized runner had high turbine efficiency in whole operating range.

2) When the instability vibration at high partial load condition is caused, an oval cross section whirl occurred. This whirl may be caused by the recirculation flow near the runner cone wall.

As for the instability vibration, we will conduct forward examination more and am going to report measures.

Nomenclature DM HM nM

Model runner diameter [m]Model test head [m] Rotational speed of runner [m/s]

HΔ /H HΔ

aM

Root-mean-square of Pressure fluctuation [m]

Pressure fluctuation (= 2 2 /H HΔ ) [%] Guide vane opening [%]


10

g nED

σM

Gravity acceleration [m/s2] Speed factor ( =nM×DM/(H×g)0.5 ) Thoma number ( =NPSH／H )

T QM

QED

Time [sec] Discharge [m3/s] Discharge factor ( =QM/(DM

2×(H×g)0.5) )

References [1] Mazzouji F et al. 2004 Multicriteria optimization: viscous fluid analysis mechanical analysis

22nd IAHR Symp. on Hydraulic Machinery and Systems (Stockholm, Sweden, 2004) [2] Enomoto Y et al. 2006 Design Optimization of a High Specific Speed Francis Turbine Runner

using Multi-Objective Genetic Algorithm 23rd IAHR Symp. (Yokohama, Japan, 2006) [3] Manfred S 2000 The Design of Francis Turbine Runners by 3D Euler Simulations Coupled to a

Breeder Genetic Algorithm 20th IAHR Symp.( Charlotte,North Carolina, August 2000) [4] Laurent T et al. 2002 Automated Design of a Francis Turbine Runner Using Global

Optimization Algorithms 21st IAHR Symp. (Lausanne，Sweden, September 2002) [5] Shi Q H Expermental Investigation of Upper part Load pressure Pulsations for Three Gorges

Model Turbine Proc.24th IAHR Symp. (Parana ,Brazi, 27 October 2008) [6] Koutnik J, Faigle P, Moser W, “Pressure Fluctuations in Francis Turbines Theoretical

Prediction and Impact on Turbine Proc.24th IAHR Symp. (Parana ,Brazi, 27 October 2008) [7] Sugishita K et al. 2001 Rehabilitation of 57.4MW Francis Turbine by Using CFD Analysis J.

Waterpower & Dams September 2001 [8] Saito Y, Takami R, Nakamori I, Ikohagi T, ”Numerical analysis of unsteady behavior of cloud

cavitation around a NACA0015 foil”, Computational Mechanics 2007


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design optimization of a high specific speed francis turbine

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