Indian Journal of Engineering & Materials Sciences

Vol. 16, August 2009, pp. 229-236

CFD approach for design optimization and validation for

axial flow hydraulic turbine

Vishnu Prasad, V K Gahlot* & P Krishnamachar

Department of Civil Engineering, Maulana Azad National Institute of Technology, Bhopal 462 051, India

Received 30 July 2008; accepted 3 June 2009

The conventional method to assess turbine performance is its model testing which becomes costly and time consuming

for several design alternatives in design optimization. Computational fluid dynamics (CFD) has become a cost effective tool

for predicting detailed flow information in turbine space to enable the selection of best design. In the present paper, 3D real

flow analysis in an experimentally tested axial flow turbine has been carried out and different flow parameters are computed

at three operating regimes to find the best operating regime. The computed efficiencies are critically compared with

experimental values and found to bear close comparison.

Keywords : Computational fluid dynamics, Efficiency, Lift, Blade circulation, Degree of reaction

In axial flow turbine, water passes through the series

of blade rows and changes its direction from radial to

axial. Runner is the most important component of the

turbine and its blade profile is designed at different

sections from hub to casing to get the best

performance. The rotation of runner and operation of

turbine either below or above the rated conditions1,2

cause variation of flow parameters from hub to tip.

Hence, actual flow pattern in turbine space deviates

from the simplifying assumptions made in design thus

affecting the turbine performance. The experimental

testing of turbine models at different operating

regimes on specially designed test rigs is the

conventional approach to assess the performance. But

this approach provides global performance at varying

operating conditions and does not give detailed

information about the flow behaviour and variation of

local design parameters like blade circulation, lift and

degree of reaction. The model fabrication and testing

for any change made in design make this method

costly and time consuming.

The combination of advanced numerical

techniques and computational power has lead to

computational fluid dynamics (CFD). It is an efficient

and inexpensive tool to make internal flow

predictions to good accuracy and, any sort of flow

problems can be detected and further improvements

can be made on the geometry of turbine components.

It has made possible to obtain a significant

enhancement in efficiency3-6

of the hydro turbine.

CFD can be used to check efficacy of alternate

designs7,8

of turbines for optimization before final

experimental testing of selected designs is resorted.

However, in order to prove reliability of these tools

for application to turbines, validation9-11

with known

experimental results is required. In present work, 3D

viscous flow simulation with SST κ-ω turbulence

model is carried out in an experimentally tested

model of an axial flow hydraulic turbine using

ANSYS CFX10 software. The variations of flow

parameters from hub to tip of runner are presented in

graphical form and average value of cascade

parameters are computed at different operating

regimes. The computed efficiencies have been

compared with experimental values at three regimes

for validation of simulation results.

Geometric Modeling and Boundary Conditions

The axial flow turbine consists of casing, stay ring,

distributor, runner and draft tube. The energy transfer

takes place in runner hence, present work is focused

on runner only and therefore, analysis is carried from

stay ring inlet to draft tube outlet where proper

boundary conditions can be applied. There are 12 stay

vanes, 28 guide vanes and 4 runner blades in the

model being analyzed. The blade rows of stay ring, ——————

*For correspondence (E-mail: gahlot_vk@rediffmail.com)

INDIAN J. ENG. MATER. SCI., AUGUST 2009

230

distributor and runner are axi-symmetric and

therefore, only single runner blade assembly is

modeled for simulation using periodicity to minimize

the total size of mesh. The draft tube is fully modeled

because of no symmetry about any axis. Each

component is modeled separately and then assembled

through proper interfaces. The guide vane is modeled

for three different openings. The flow parameters at

inlet and exit of runner blade with velocity triangles

are defined in Fig. 1. The meridional view with

dimensional parameters and assembled 3D view are

shown in Figs 2 and 3. The unstructured tetrahedral

mesh is generated in Ansys ICEMCFD for all the

domains. The y+

varies between 24 to 186, which is

the acceptable range for automatic wall function

treatment in boundary layer in SST κ-ω turbulence

model. The maximum values other mesh quality

parameters like face angle (163.56), edge length ratio

(28.758), connectivity number (48) are within the

acceptable limits of Ansys CFX10.

The meshing for stay vane, guide vane, runner and

draft tube are given in Figs 4-7. The summary of

mesh data of each component is given in Table 1. The

magnitude of mass flow and its direction are specified

at stay vane inlet as inlet boundary condition and

reference pressure is specified at outlet of draft tube

as outlet boundary condition. The rotational speed of

runner is specified and other two blade rows are set

stationary. All boundary walls are assumed smooth

with no slip.

Experimental Model Testing

The experimental testing of axial flow turbine

model at reduced scale had been carried out on

specially designed test rig as per IEC codes. The

geometric specifications of tested axial flow turbine

model are given below:

Axis of turbine vertical

Type of draft tube elbow type

Draft tube exit area 0.5525 m2

Radius of turbine runner (R) 0.200 m

No. of runner blades 4

Radius of spherical hub (Rh) 0.080 m

Pitch diameter of guide vanes 0.552 m

No. of guide vanes 28

Radius at inlet of stay vane (R1) 0.338 m

No. of stay vanes 12

Height of stay vane & guide vanes (b) 0.174 m

Fig. 1 – Velocity triangles at inlet and outlet of runner blade

Fig. 2 – 2D meridional view of annulus space of turbine

Table 1— Summery of mesh data

Component No. of

nodes

No. of

elements

Type of

element

Stay vane 24811 126527 Tetrahedral

Guide vane 16212 78051 Tetrahedral

Runner 35267 180868 Tetrahedral

Draft tube 279151 1540907 Tetrahedral

Fig. 3 – Assembled 3D turbine model

PRASAD et al.: CFD APPROACH FOR DESIGN OF AXIAL FLOW TURBINE

231

In the model testing, variations of global

parameters like discharge, speed and power have been

observed. However, it is very difficult, rather

impossible to measure the local parameters like

velocities and flow angles at runner because of its

rotation. The efficiencies of axial flow turbine model

at three regimes, i.e., guide vane openings of 50°, 40°

and 35° from experimental results are 90.86%,

92.06% and 91.59% respectively.

Computation of Flow Parameters

The numerical analysis gives pressure and velocity

distributions and the non-dimensional parameters are

computed for presentation of results. The 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 2

212 2

P PCp

W

−=

ρ … (1)

Velocity coefficient v

2

WC

W= … (2)

Flow deflection 1 2ε = β −β … (3)

Degree of reaction

2 2

2 1

2

W W

gH

−ϕ = … (4)

Circulation

coefficient

( )1 2

2

U Ut C C

D gH

−τ = … (5)

Lift coefficient 2 12 sin (cot cot )

L m

tC

l= β β − β

… (6)

Runner energy

coefficient

4

2

RgH D

Qφ = … (7)

Total energy

coefficient

4

2

gHD

Qψ = … (8)

Fig. 4 – Meshing of stay vane domain

Fig. 5 – Meshing of guide vane domain

Fig. 6 – Meshing of runner domain

Fig.7 – Meshing of draft tube

INDIAN J. ENG. MATER. SCI., AUGUST 2009

232

Total head SVI DTE

TP TPH

−=

γ … (9)

Head utilized by

runner 1 2

( )R FR

TP TPH H

−= −

γ … (10)

Hydraulic efficiency *100R

H

H

Hη = … (11)

Draft tube efficiency 2

2

2*100DTR

DT

gH

Cη = … (12)

Results and Discussion

The numerical simulation of axial flow hydraulic

turbine using Ansys CFX10.0 is validated with

experimental results at three guide vane openings

near the points of maximum efficiency. The

comparison of computed and experimental values of

efficiency is given in Table 2. The values of SF and

QF are kept same in both experimental and numerical

simulation at individual operating regime. It is seen

from

Table 2 that peak efficiency regime obtained in both

numerical simulation and experiment is same. The

computed efficiencies at different regimes are in

close agreement with the experimental values. The

differences in efficiencies at off-peak regimes

obtained between simulation and experimental values

may be ascribed to (i) errors in discretization of

governing equations and flow domain, (ii) the losses

not accounted for fully and precisely and (iii) not

considering complete assembly of casing, stay vanes,

guide vanes and runner in CFD analysis. There can be

instrumentation and human errors in the experimental

investigation.

Further, numerical analysis has been carried out

for three different regimes of operation as given in

Table 3. The three regimes are selected such that one

regime is near the best operating point (α = 40°) to

enable the comparison of results at design and off-

design conditions. The mass averaged values of

specific velocities and flow angles given in Table 4

indicate that all velocity triangle components are

affected by guide vane setting except the flow angles

at runner outlet.

The specific meridional velocities (cm) at runner

inlet and outlet are nearly same for each guide vane

and it is indicative of axial flow. The specific whirl

(cu) and absolute (c) velocities decrease from inlet to

outlet due to energy extraction by the runner. The

specific relative velocity (w) increases from inlet to

outlet of runner because of reduction in pressure in

the form of reaction contributing to energy extraction

by runner. The values of cascade parameters in

Table 5 indicate that flow deflection, degree of

reaction, lift and drag and energy losses are minimum

at α=40° while blade circulation decreases with

decrease in guide vane (GV) opening. The efficiency

is more at α = 40° and decreases on either side of this

GV opening and thus indicative of best efficiency

operating regime. The computed losses mentioned in

Table 6 show that total loss is minimum at α = 40°

and hence maximum efficiency but loss in not

Table 2— Comparison of computed and experimental results

Guide vane angle (α) 50° 40° 35°

Rotational speed (rpm) 1140 1155 1260

Speed factor 55.51 46.51 42.58

Discharge factor 0.43 0.34 0.33

Numerically computed efficiency (%) 90.19 92.24 89.97

Experimental efficiency (%) 90.86 92.06 91.59

Table 3 – Input data for analysis at three regimes

α = 50° α = 40° α = 35°

n (rpm) 1150 1150 1150

Q (m3/s) 0.714 0.570 0.530

Table 5— Average values of cascade parameters at different GV opening

ε ϕ τ CL CD φ ψ SF DF η

50° 11.61 0.733 0.244 1.068 0.028 6.036 8.141 36.127 0.350 83.63

40° 10.00 0.619 0.207 0.974 0.013 5.893 7.419 47.609 0.367 91.27

35° 12.469 0.622 0.195 1.155 0.021 6.454 8.193 48.97 0.349 90.17

Table 4— Average values of velocity triangles parameters at

different GV opening

α = 50° α = 40° α = 35°

inlet outlet Inlet outlet inlet outlet

cm 0.363 0.364 0.395 0.387 0.356 0.361

cu 0.265 -0.179 0.419 0.070 0.497 0.197

w 0.832 1.194 0.935 1.238 0.934 1.222

c 0.451 0.425 0.584 0.422 0.614 0.393

β 28.89 17.28 27.65 18.27 30.049 17.579

PRASAD et al.: CFD APPROACH FOR DESIGN OF AXIAL FLOW TURBINE

233

minimum in all components. It is observed that main

components affecting efficiency of turbine are runner

and draft tube.

The pressure and velocity from leading edge (LE)

to trailing edge (TE) at mid span of runner blade are

shown in Figs 8 and 9 respectively. The blade loading

at any point increases with increase in guide vane GV

opening and there is smooth variation except at hub

region due to hub curvature.

The increase in velocity with increase with GV

opening is because of discharge increases with GV

openings. The blade circulation in Fig. 10 depicts that

it has maximum value near to quarter of span and

decreases towards hub and tip indicating decrease in

difference of whirl velocities at tip side and

circulation is less at hub due to small pitch. It

decreases with decrease in GV opening at any span.

The flow deflection decreases from hub to tip as seen

in Fig. 11. This indicates the decrease in inlet flow

angle towards tip as outflow angles are constant for

all guide vanes.

The degree of reaction decreases with decrease in

GV at faster rate near hub region as compared to tip

region as shown in Fig. 12. This indicates more

change in pressure in hub region at larger GV

opening. The lift variation in Fig. 13 depicts that it

Table 6 — Computed losses in different components

Component α = 50° α = 40° α = 35°

Stay ring loss (%) 0.638 0.740 0.642

Distributor loss (%) 0.766 1.302 2.037

Runner loss (%) 7.112 4.151 3.782

Draft tube loss (%) 7.845 2.532 3.362

Total loss (%) 16.361 8.725 10.496

Draft tube efficiency (%) 52.626 78.246 73.87

Fig. 8 – Pressure distribution at mid span of blade

Fig. 9 – Velocity distribution at mid span of blade

Fig. 10 – Variation of blade circulation

Fig. 11 – Variation of flow deflection

INDIAN J. ENG. MATER. SCI., AUGUST 2009

234

decreases from hub to tip and its variation becomes

steeper with decrease in GV opening. This variation

is attributed to the variation of flow deflection and

pitch-chord ratio.

The streamline plots on runner blade at mid span

for three regimes are shown in Fig. 14. It is seen that

flow is not smooth at α = 50° and with very little

shock in α = 40° and very smooth in case of α = 35°

Fig. 14 – Streamline pattern on runner blade at mid span for different operating regimes

Fig. 15 – Pressure contours on runner blade at mid span for different operating regimes

Fig.12 – Variation of degree of reaction

Fig.13 – Variation of lift coefficient

PRASAD et al.: CFD APPROACH FOR DESIGN OF AXIAL FLOW TURBINE

235

and hence accordingly loss in runner is maximum at

α = 50° and minimum at α = 40° as shown in Table 6.

The effect of boundary layer at the blade surface

can be clearly seen at α = 40°. Similarly the pressure

contour variation on suction and pressure side is more

smooth in case of α = 40° as compared to other

operating regimes as shown in Fig. 15.

The 3D plots for streamline and pressure contours

at α = 40° are shown in Figs 16-18. The streamline

and pressure contours for 3D flow in stay vane and

guide vane domains shown in Fig.16 depicts that

velocity increases and pressure decreases as flow

moves from stay vane to guide vane domain. The

velocity is more and pressure is less on suction side

(lower surface) and velocity is less and pressure is

more on pressure side (upper surface) of runner blade

as seen in Fig. 17. The streamline and pressure

contour pattern within draft tube shown in Fig. 18

indicate that low velocity zone is formed at concave

side of bend. The velocity decreases and pressure

Fig. 16 – 3D stream line and pressure contours in stay ring and distributor

Fig. 17 − 3D stream line and pressure contours in runner

Fig. 18 – 3D stream line and pressure contours in draft tube

INDIAN J. ENG. MATER. SCI., AUGUST 2009

236

increases from inlet to exit of draft tube due to

increase in flow area.

Conclusions

The validation of numerical simulation with

experimental results shows similar pattern for

efficiency variation. The maximum efficiency regime

indicated by both the approaches is nearly same. The

slight difference in computed and experimental

values of efficiency can be because of some errors in

numerical simulation which are mainly due to

discretization of domain and differential equations

and also instrumentation and human error during

experimental investigations. The total computed loss

is minimum at the point of maximum efficiency. The

streamline and pressure contour plots in different

components confirms with the actual flow behaviour

in axial flow turbine. The best operating regime can

be easily identified from computed flow parameters,

losses and flow pattern from numerical simulation.

Hence, it is concluded that CFD approach can be used

to study the flow pattern inside the turbine space and

to optimize the design by different combinations of

the design parameters and geometry at low cost in

lesser time. Finally, the performance of optimized

design need to be verified through model testing. This

procedure will minimize time and the amount spent in

development and optimization of hydraulic turbines.

Nomenclature C = absolute flow velocity (m/s)

CU = whirl velocity (m/s)

D = diameter of turbine runner (m)

G = gravitational acceleration (m/s2)

H = net head (m)

HDTR = head recovery in draft tube (m)

HFR = head loss in runner (m)

L = blade chord (m)

P = static pressure at any point on blade surface profile (Pa)

Q = discharge through turbine (m3/s)

TP = total pressure at runner (N/m2)

TPSVI = total pressure at stay vane inlet (N/m2)

TPDTE = total pressure at draft tube outlet (N/m2)

T = pitch of runner blades (m)

W = relative velocity at any point of blade surface (m/s)

α = guide vane angle from tangential direction (°)

β = relative flow angle (°)

βm = mean relative flow angle(°)

γ = specific weight of water (N/m3)

ρ = mass density of water (kg/m3)

subscripts 1 and 2 denote values of parameters at inlet and outlet

of runner respectively

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