Energy Procedia 14 (2012) 2060 2065

1876-6102 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the organizing committee of 2nd International Conference on Advances in Energy Engineering (ICAEE).doi:10.1016/j.egypro.2011.12.1208

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Numerical simulation for flow characteristics of axial flow hydraulic turbine runner

Dr. Vishnu Prasad Civil Engineering Department, M. A. National Institute of Technology, Bhopal-462 051, India

Abstract

The design of runner blade of turbine is done for certain flow velocities and angles but these parameters vary with operating conditions. The experimental testing of turbine model is costly, time consuming and gives performance characteristics of turbine as whole based on global parameters. The component wise performance of turbine based on local parameters is more useful for efficient design and it is very difficult to get these from model testing. The computational fluid mechanics (CFD) is an effective tool to provide detailed flow information inside turbine space and it can also give performance characteristics of turbine in terms of global as well as local parameters. The viscous 3D turbulent simulation has been carried out in an experimentally tested model of axial flow hydraulic turbine at different operating regimes and global and local parameters have been computed. The variation of computed parameters justifies with the characteristics of axial flow turbine. The computed efficiencies at some regimes of operation are critically compared with experimentally tested model results and found to bear close comparison.

2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [name organizer]

Keywords: Hydraulic turbine; computational fluid dynamics; flow angles; runner; efficiency.

1. Introduction

The hydraulic turbines have to operate under varying conditions of design parameters. The flow inside hydraulic reaction turbine is very complex and flow behavior in turbines varies from hub to tip due to inter-action of stationary and rotating blade rows. Further, the flow conditions also change due to variation in the opening of guide vanes and rotational speed of the runner. The turbines are designed based on the simplifying assumptions and therefore, it is customary to predict the performance of the turbines at different operating regimes. Generally, performance of the turbine is predicted through experimental testing of geometrically similar scaled down turbine models on specially designed test rigs. This testing gives performance of the turbine based on global parameters like head, discharge and speed but it is very difficult to get performance characteristics of the individual components in terms of local flow velocities and angles. The flow characteristics are expressed as variation of velocities in non-dimensional form [1]. The runner is the most important component of turbine as energy is transferred from flowing water to it due to twisting

Nomenclatures D diameter of turbine runner (m), g gravitational acceleration (m/s2)HR head utilized by runner (m) H total head (m) n rotational speed of runner (rpm) Q discharge through turbine (m3/s)p pressure on blade surface (Pa) W velocity on runner blade surface (m/s) mass density of water (Kg/m3)The subscript 1 and 2 indicates values of concerned parameter at inlet and outlet of runner.

2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the organizing committee of 2nd International Conference on Advances in Energy Engineering (ICAEE).

Vishnu Prasad / Energy Procedia 14 (2012) 2060 2065 2061

of runner blades [2]. The twisting of blade leads to angular momentum change and hence develops torque to rotate the runner. The growth of computational power and advance numerical techniques made it possible to carry out numerical simulation in the turbine space [3,4,5] to get detailed information on pressure and velocity distributions along and across the streamlines. CFX-TASC flow code had been used for optimization of axial flow turbine using genetic algorithm and compared velocity distribution with experimental results. The numerical analysis using CFX is carried in draft tube and results are validated. The CFX code has also been validated for predicting Francis turbine performance results based on global parameters. As one blade row affects the flow pattern at other blade rows, the numerical flow analysis of individual blade rows has problem of application of proper boundary condition because of unknown flow behavior at upstream and downstream of any particular blade row. In the present paper, viscous 3D turbulent flow simulation using shear stress transport (SST) - turbulence model is carried out at different operating regimes i.e. different guide vane opening and rotational speeds of an experimentally tested model of axial flow turbine using Ansys CFX software. The local and global flow parameters are computed and their variation with guide vane opening and rotational speed is presented graphically. A critical comparison of computed and experimental efficiencies has been done to validate the results of numerical simulation.

2. Geometric modeling

The specification of geometry of complete flow domain is an important input for the numerical simulation. The axial flow turbine consists of spiral casing, stay ring, distributor, runner and draft tube. The numerical simulation is done of an experimentally tested axial flow turbine model with 12 stay vanes, 28 guide vanes and 4 runner blades and a draft tube. The diameter of runner is 400mm. In hydraulic turbine, stay vane and draft tube are stationary components. The runner rotates about the turbine axis and guide vanes rotate about their own axis. Hence, geometric modeling of each component is done separately. A separate domain is created for each component of turbine and assembled through proper interfaces. The blade rows of stay ring, guide wheel and runner are axi-symmetric and therefore, only single blade from each blade row is modeled for simulation by using the periodic planes. This has minimized the total size of mesh nodes to one fourth. As the main objective is to derive the performance of runner, hence the casing is not considered in analysis. The draft tube affects performance of runner and its full geometry is modeled because of no symmetry about any axis. The complete assembled modeling is shown in fig.1

Fig.1. 3D geometry of axial flow hydraulic turbine

The position of guide vane changes with its opening and hence geometry for guide vane domain is generated for three different guide vane openings (a from tangential direction). The geometry of all other component such as stay vanes, runner and draft tube modeled remains the same but assembled with changed guide vanes to develop the complete model for different guide vane openings. The meshing of all flow domains is done in Ansys ICEM CFD taking tetrahedral elements. The tetra mesh has been used for all flow domains and mesh quality checks are applied.

3. Boundary conditions

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The results obtained from numerical simulation in a flow domain depend on the specified boundary conditions. The mass flow of 0.525m3/s, 0.620m3/s and 0.714m3/s at 50, 40 and 35 respectively with flow angle at stay vane inlet is specified as inlet boundary condition and static pressure is specified at the outlet of draft tube as outlet boundary condition. The stay vane, guide vane and draft tube domain are set stationary. The rotational speed from 800 to 1300rpm at interval of 100rpm is specified for runner domain except shroud for each operating condition. All the walls are taken smooth. The Shear Stress Transport (SST) - turbulence model is used because of passage curvatures and rotating flows.

4. Computation of parameters

The numerical simulation gives pressure and velocity distributions and then flow parameters in non-dimensional form are computed. The actual velocity components are divided by spouting velocity (2gH) to get specific (non-dimensional) values of corresponding velocity. The following formulae are used for computation of different parameters:

Pressure coefficient 221

2 2p

p pC

W= (1)

Velocity coefficient 2

v

WC

W= (2)

Specific energy coefficient 4

2

gHD

Q = (3)

Speed factor nD

SFgH

= (4)

Discharge factor 2

QDF

D gH= (5)

Hydraulic efficiency RHH

*100H

= (6)

5. Validation of numerical simulation

The accuracy of numerical simulation depends on many factors. The Ansys CFX software is a commercial CFD code and is used for solution of wide variety of fluid flow problems. It is already validated for turbines application by many investigators [6,7,8]. It is very difficult to obtain pressure and velocity distribution experimentally on rotating runner blades. The experimental test of turbine model is carried out on a specially designed big test rig as per IEC codes and the most of model test results are available in terms of efficiency only at different operating regimes. The comparison of computed values with experimental tested results of an axial flow turbine model at three operating regimes [9] is given in Table 2. The maximum efficiency regime is same from both computed and experimental results. The difference between the computed and experimental values of efficiency is minimum at the best efficiency regime but difference between these efficiencies increases at off-design flow regimes. This could be due to more secondary losses at off-design conditions which are not computed accurately in CFD analysis.

Table 2. Comparison of computed and experimental results

Guide vane angle ( ) 50 40 35

Speed factor 55.51 46.51 42.58

Discharge factor 0.43 0.36 0.33

Numerical computed efficiency (%) 90.19 92.24 89.97

Experimental efficiency (%) 90.86 92.06 91.59

Vishnu Prasad / Energy Procedia 14 (2012) 2060 2065 2063

6. Results and discussions

The numerical simulation has been carried out for three guide vane openings (a1=50, a2 = 40, a3 = 35) from tangential direction and at different rotational speeds to get variation of speed factor between 30 and 75. The pressure and velocity vary from hub to casing and hence, mass averaged values of pressure,

Speed Factor

Spe

cifi

cM

erid

iona

lVel

ocity

30 40 50 60 70 800.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60cm1 : a1cm2 : a1cm1 : a2cm2 : a2cm1 : a3cm2 : a3

Speed factor

Spec

ific

Whi

rlV

eloc

ity

30 40 50 60 70 80-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

cu1 : a1cu2 : a1cu1 : a2cu2 : a2cu1 : a3cu2 : a3

Fig.2. Variation of meridional velocity; Fig.3. Variation of whirl velocity

velocity and flow angle are computed at inlet and outlet of runner. The variation of different non-dimensional parameters is presented graphically in fig.2 to fig.11. The meridional velocity at inlet and outlet of runner increases with rotational speed and guide vane opening as seen in fig.2 confirming the basic characteristics of axial flow turbine. It is again seen from fig.3 that the whirl velocity also increases linearly with rotational speed but it decreases with increase in guide vane opening. It is also observed that at outlet, whirl velocity is opposite to peripheral velocity of runner at lower speeds. The whirl velocity at outlet is much less as compared to inlet thus indicating energy extraction by runner. In fig.4, the relative flow angles at inlet are more at low guide vane opening and decreases with rotational speed. The flow angles at outlet are almost independent of rotational speed and guide vane opening because flow leaves the runner tangentially at the trailing edge. The variation of discharge factor in fig.5 indicates that discharge through turbine increases with speed and guide vane opening and match the characteristics of axial flow turbine from model tests. It is due to the fact that axial turbines suck more discharge as rotational speed increases and more discharge passes through turbine because of increase of flow area at distributor with increase in guide vane opening. The hydraulic efficiency in fig.6 has parabolic variation and this pattern is attributed to change in shock and secondary losses. The maximum efficiency occurs at speed factor where loss is minimum at all guide vane opening. The point of maximum efficiency shifts towards higher speed factor values as guide vane angle increases. The specific energy decreases with increase in rotational speed and guide vane opening as observed in fig.7.

Speed Factor

Rel

ativ

eFl

owA

ngle

s

30 40 50 60 70 8010

15

20

25

30

35

40

45

501

1122

2 : a1: a1: a2: a2

: a3: a3

Speed Factor

Dis

char

geFa

ctor

30 40 50 60 70 800.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60a1a2a3

Fig. 4. Variation of relative flow angles; Fig. 5. Variation of discharge factor

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Speed Factor

Hyd

raul

icE

ffic

ienc

y(%

)

30 40 50 60 70 8060

65

70

75

80

85

90a1a2a3

Speed Factor

Spec

ific

Ene

rgy

Coe

ffic

ient

30 40 50 60 70 802

3

4

5

6

7

8

9

10

11

12a1a2a3

Fig.6. Variation of hydraulic efficiency; Fig.7. Variation of input energy

The pressure and velocity distributions from leading edge (LE) to trailing edge (TE) at mid span of runner blade are shown in fig.8 and fig.9 respectively for constant speed of 1100 rpm. The pressure at any point increases with increase in guide vane (GV) opening and there is smooth variation except at hub region due to hub curvature. Similar distribution is seen for velocity and the increase in velocity with increase with GV opening is because of discharge increase with GV openings

Leading edge - Trailing edge ( 0 - 1 )

Pres

sure

Coe

ffic

ient

0.00 0.25 0.50 0.75 1.00-0.6

-0.3

0.0

0.3

0.6

0.9

1.2a1a2a3

Leading edge - Trailing edge ( 0 - 1 )

Vel

ocity

Coe

ffic

ient

0.00 0.25 0.50 0.75 1.000.4

0.6

0.8

1.0

1.2

1.4

1.6

a2a3

a1

Fig.8. Variation of pressure on runner blade surfaces; Fig.9. Variation of velocity on runner blade surfaces

Leading edge - Trailing edge ( 0 - 1 )

Pre

ssur

eC

oeff

icie

nt

0.00 0.25 0.50 0.75 1.00-0.6

-0.3

0.0

0.3

0.6

0.9

1.2n1n2n3

Leadding edge - Trailing edge ( 0 - 1 )

Vel

ocity

Coe

ffic

ient

0.00 0.25 0.50 0.75 1.000.4

0.8

1.2

1.6

2.0

2.4n1n2n3

Fig.10.Variation of pressure on runner blade surfaces; Fig.11.Variation of velocity on runner blade surfaces

Vishnu Prasad / Energy Procedia 14 (2012) 2060 2065 2065

The pressure distributions for three speeds (i.e. n1=950, n2=1100, n3=1300 rpm) at mid section of runner blade are shown in fig.10 for constant GV opening of 40 and it is seen that blade loading is more uniform for speed n=1100 rpm indicating the best operating regime while at other speeds, pressure plot is diverging at LE and indicates more shock loss. The pressure value on pressure side of blade profile from LE to TE decreases with increase in speed while on suction side it is independent of speed except in LE region. The velocity distributions in fig.11 show that velocity along blade profile on suction side decreases with increase in speed while on pressure side, velocity increases with speed towards LE and decreases with speed in TE region. It is seen that in both pressure and velocity distributions, difference between pressure and suction surface at any point decreases with speed indication more loading at low speeds.

7. Conclusions

It is found from simulation results that the most of local flow parameters like velocities and flow angles at inlet and outlet are affected by the operating regimes of turbine. The variation patterns of discharge factor, efficiency and specific energy obtained from numerical simulation are well agreed with experimental results for any axial turbine. The losses are minimum at the points of maximum efficiency. The computed values of different parameters may differ from experimental one because CFD gives approximate solution of flow governing equations and accuracy depends on many factors. It can be concluded that CFD is a cost effective computational tool for flow simulation and investigation for hydraulic turbines and can provide detailed flow information. This information will be useful in efficient design of turbine. Despite the rapid growth in the ease of use, speed and robustness of CFD tool, considerable expertise is still required to ensure accurate simulations and validation of numerical results.

References

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