numerical and experimental study of the leakage flow in guide vanes with different hydrofoils

Sailesh Chitrakare-mail: sailesh.chitrakar@ntnu.no Department of Energy and Process Engineering, Norwegian University of Science and Technology, Norway Biraj Singh Thapa e-mail: biraj.s.

Numerical and experimental study of the leakage flow in guide vanes with

Please cite this article as: S Chitrakar, B.S Thapa, O.G Dahlhaug, H.P Neopane, Numerical and experimentalstudy of the leakage flow in guide vanes with different hydrofoils, Journal of Computational Design and

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Sailesh Chitrakare-mail: sailesh.chitrakar@ntnu.no Department of Energy and Process Engineering, Norwegian University of Science and

Technology, Norway

Biraj Singh Thapa e-mail: biraj.s.thapa@ntnu.no Department of Energy and Process Engineering, Norwegian University of Science and

Technology, Norway

Ole Gunnar Dahlhaug e-mail: ole.g.dahlhaug@ntnu.no Department of Energy and Process Engineering, Norwegian University of Science and

Technology, Norway

Hari Prasad Neopane e-mail: hari@ku.edu.np Department of Mechanical Engineering, Kathmandu University, Nepal

ABSTRACT

Clearance gaps between guide vanes and cover plates of Francis turbines tend to increase in size due to simultaneous effect

of secondary flow and erosion in sediment affected hydropower plants The pressure difference between the two sides of the guide vane induces leakage flow through the gap This flow enters into the suction side with high acceleration, disturbing the primary flow and causing more erosion and losses in downstream turbine components A cascade rig containing a single guide vane passage has been built to study the effect of the clearance gap using pressure sensors and PIV (Particle Image Velocimetry) technique This study focuses on developing a numerical model of the test rig, validating the results with experiments and investigating the behavior of leakage flow numerically It was observed from both CFD and experiment that the leakage flow forms a passage vortex, which shifts away from the wall while travelling downstream The streamlines contributing to the formation of this vortex have been discussed Furthermore, the reference guide vane with symmetrical hydrofoil has been compared with four cambered profiles, in terms of the guide vane loading and the consequent effect on the leakage flow A dimensionless term called Leakage Flow Factor (Lff) has been introduced to compare the performances

of hydrofoils It is shown that the leakage flow and its effect on increasing losses and erosion can be minimized by changing the pressure distribution over the guide vane

Keywords: Leakage flow, guide vane, clearance gap, PIV, CFD, hydrofoil

INTRODUCTION

The relation between the guide vane wear, leakage flow through clearance gaps and efficiency

drop in high head Francis turbines was studied by Brekke [1] in 1980s It was seen that the erosion of

the facing plates underneath the edges of guide vanes increased the size of the clearance gaps, adding to

1

Corresponding author: Sailesh Chitrakar, Email: sailesh.chitrakar@ntnu.no , Tel No.: +47-46431989

exposed to hard sand particles in higher concentration [2-4] Figure 1 shows the guide vanes in

Nepalese power plants, which are eroded at the span ends These ends are connected to the facing plates

leaving a small clearance, which provides possibility to change the opening angle based on operating

conditions When the sand particles pass through these gaps with high acceleration, eroded grooves are

formed, which eventually increase the gap size The pressure difference between the pressure and the

suction side of the guide vane profile drives the flow into the clearance gap and mixes with the main

flow in the suction side This flow contains circulations, which travels downstream into the runner,

causing more damages and losses The simultaneous nature of the erosion and flow phenomena in

Francis turbines and the role of guide vane in this process have been explained by Thapa [5] and

Chitrakar [6] In Kaligandaki-A hydropower plant running with the net head and flow of 115m and 47

m/s3 respectively, Koirala et al [7] reported that the size of the clearance gap increased from the

designed value of 0.6 mm to 2.5 mm in the leading edge and 4.2 mm in the trailing edge in average after

16500 operational hours due to erosion

The practices of using numerical techniques (CFD) for predicting the flow fields and erosion in

turbines can be found in literatures [2] [8] These techniques are also used to optimize the design of the

turbine components and investigate the performances of several designs with minimum cost [9] [10]

However, fidelity of the numerical results depend on the validation with the results from experiments

In general, the prototype turbine is usually scaled down and/or simplified to minimize the cost and

effort involved in experiments In recent studies, the prediction of flow phenomena in Francis turbines

using Laser Doppler Anemometry (LDA) and Particle Image Velocimetry (PIV) are becoming popular

An LDA measurement was conducted in a guide vane case rig to study the formation of wakes for

different guide vane profiles [11] The wake flow and Rotor-Stator-Interaction (RSI) phenomena were

Francis hydro-turbine model of diameter 0.15 m by using transparent vanes and covers and drilling a

hole on the casing at the measurement location for capturing the flow [13]

The leakage flow through clearance gaps and consequent vortices are studied in many

turbomachinery applications The effect of reduced tip clearance was studied using 3D Navier-Stokes

CFD code in a linear turbine cascade [14] The study focused on types of streamlines at different planes

and vortices formed from the gap region for each line A Stereo Particle Image Velocimetry (SPIV) was

used to study the tip leakage vortex (TLV) in a NACA0009 hydrofoil in a simplified case study [15]

This study also used high-speed flow visualization and showed a strong influence of the wall proximity

on the vortex path The authors explained that the shifting of TLV away from the hydrofoil as the result

of potential flow effect Eide [16] explained by building a 2-D numerical model of guide vanes

including clearance gap, that out of 5-6% of the total losses developed in a high head Francis runner,

around 1.5% is due to the leakage flow in guide vanes Some qualitative experimental approaches for

studying tip leakage vortex through hydrofoils and their effects on cavitation can also be found in

literature [17]

A single guide vane cascade rig was recently developed in the Waterpower Laboratory at the

Norwegian University of Science and Technology [18] [19], which contains a 1:1 scale guide vane of

Jhimruk Hydropower Plant, located in Nepal The power plant (3 x 4.2 MW) runs with a net head of

201.5 m, and 2.35 m3/s flow in each of the three units By using PIV, the velocity field around the guide

vane can be measured The rig also allows the measurement of the effect of the clearance gap on the

main flow by milling one end of the blade The pressure measurements can be carried out along the

mid-span surface and another end of the blade The objective of this study is to perform numerical study

of the flow inside the same test rig and validate with PIV results The numerical model is used to

compare the leakage flow between different hydrofoil shaped guide vanes Following sections contain

definition of the quantities, which are used to compare the results between CFD and PIV, and between

the hydrofoils studied numerically

Measured quantities

Figure 2 shows the boundary of the measurement, which contains two guide vane passages (one on each

side) The guide vane is oriented in the opening angle corresponding to the design condition The figure

also shows the circumferential locations corresponding to stay vane outlet (SVout), guide vane inlet

(GVin), guide vane outlet (GVout) and runner inlet (Rin) of the real turbine Although the rig does not

include the runner, Rin position is required to investigate how the flow enters the runner The space

between guide vane outlet and runner inlet represents vaneless region of the real turbine The secondary

flow in the form of wakes and leakages through clearance gaps undergo dissipation in this space before

reaching the runner inlet The dissipation of these flows can be visualized in between these two curves

The velocities in Cartesian co-ordinate system is converted into the cylindrical co-ordinate system with

The velocities measured by PIV and calculated by CFD are in Cartesian co-ordinates initially, but are

converted later to infer the flow condition of the real turbine Cu component is responsible for the work

done and power produced by the turbine, whereas Cm component is responsible for directing the flow

downstream

In the region inside the clearance gap, leakage flow factor has been defined in this study as the sum of

the velocity component normal to the guide vane chord from leading edge to trailing edge, compared to

a reference velocity

In Figure 4, the velocities u and v are converted into Vx’ and Vy’ based on the angles α and β α

represents the angle of the chord and β represents the direction of the velocity vector, with respect to horizontal The conversion of the co-ordinate system is based on following equations:

1 2 1tan

X X

Y Y

Y X i

y ff

V n

V L

) , (

2 2

1 1

(7)

Where Vo is the reference velocity, n is the number of the points taken and Lff is the leakage flow factor

In this study, the reference velocity is taken as the velocity at stay vane outlet (SVout) In the ideal

scenario, the flow is directed along the chord, such that Vy’ is zero The pressure difference between the pressure and the suction side of the guide vane results in the velocity component in the direction normal

to the chord The absolute value in the numerator takes into account the negative leakage flow and

avoids canceling with the positive values

Hydrofoils studied

This study compares the performance of five different NACA profiles NACA0012 is the reference

hydrofoil, which is symmetric along the chord and has the maximum thickness of 12% (of the chord

length) at 30% chord Jhimruk hydropower plant currently uses the reference hydrofoil shaped guide

vanes and the test rig present in the lab was designed according to this profile NACA1412, NACA2412

and NACA4412 are the cambered hydrofoils with similar configuration as the reference case, but has

camber of 1%, 2% and 4% respectively at 40% chord NACA63212 has the maximum thickness of 12%

at 35% chord and the maximum camber of 1.1% at 55% chord The test rig is designed for a particular

thickness and profile of the guide vane Hence, to avoid the change in flow condition due to change in

the passage area, all the studied profiles have the same maximum thickness The experiment was

conducted with a maximum Reynold’s number of 1.15E+07, which was at 80% of the Best Efficiency Point (BEP) The comparison of the GVs were done at BEP, with the Reynold’s number of 1.52E+07

All the GVs compared had an equal chord length of 0.14 m Apart from the hydrofoil, the geometry of

the test rig and operating conditions were kept constant As the neighboring walls were designed

according to NACA0012, it was assumed that the change in the hydrofoil have a negligible influence on

the overall flow behavior

GV CASCADE RIG AND EXPERIMENT SETUP

Figure 5 shows the complete layout of the experimental setup, including the measuring devices The

flow was circulated inside a closed loop that contains the section of one GV cascade rig The maximum

flow of 0.155 m3/s was developed in this study by a centrifugal pump The maximum pressure of 750

kPa was developed inside the pressure tank The outlet of the test rig contains a flowmeter and two

pressure taps were fixed at inlet of the rig and outlet of the GV, to measure the correct operating point

for measurement The flow was sent back to the pump, from where the loop continued The detail

design of the rig is explained in a previous study [18]

The actual PIV measurement was done inside the PIV room, indicated in Figure 5 and shown in Figure

6 using Dantec System A light plane was generated from two double cavity Nd-YAG lasers, which

provides 120 mJ by pulse This plane was visualized as paired images by a HiSense 2M CCD PIV

camera Fluorescent seeding particles with a density of 1.016 kg/m3 and mean diameter of 55µm were

used These particles were inserted into the rig from the low pressure seeding point, as indicated in the

figure The paired image was acquired at 70 µs, such that the particle movement was between 3-6

pixels depending upon the high and low velocity regions in the frame The PIV system was calibrated

using a 2D calibration target in the planes of measurement

The GV inside the rig contains a clearance gap of 2mm height at one end The captured field was two

dimensional, but by measuring the velocities at several spans of the GV, the velocity profiles in the

direction of the GV span could be inferred A single plane of measurement contained the boundary, as

shown in Figure 2 This study captured and measured the velocity field for two planes, one at the

mid-span and one at the clearance gap for validating the results of CFD

The pressure distribution around the GV was measured to characterize the effect of GV loading on

leakage flow 14 pressure taps were attached to the facing plate at the end opposite to the clearance gap

These taps were distributed symmetrically around the GV profile with 2mm offset, one each at leading

and trailing edge, and six each at pressure and suction side respectively Each pressure tap was

connected to a piezo-resistive pressure transducer, calibrated using deadweight calibrator

NUMERICAL MODEL

This study uses a 3D- Reynold’s Averaged Navier Stokes to solve the governing equations for an

incompressible and isothermal flow The commercial CFD solver ANSYS-CFX-15.0 was used for

numerical simulations in steady conditions The simulations used high-resolution discretization in

advection scheme and first order upwind scheme in turbulence equations The convergence criteria of

Root Mean Square (RMS) residuals less than 10-5 was used Some backgrounds of the governing

equations, turbulence models and other parameters of the numerical model are explained below

Governing equations and turbulence models

The governing equations (equation of continuity and momentum) for an incompressible and isothermal

fluid are written in the form of Navier-Stokes equations given as:

2 2

z y

This equation has four unknowns: velocity components in all directions, V

and pressure, p Although

there are four equations to solve four unknowns, they are highly non-linear Partial Derivative Equation

(PDE), which generally requires computational approaches to solve This study follows Reynolds

average method, where a variable, for example, uiis divided into an average component, ui and a fluctuating term,u i The substitution of these new terms in the original transport equation gives:

i j

x

u x

x

p x

u u t

ij uu

 These terms arise from the non-linear convective term in the un-averaged equations and represents the effect of the turbulence on the mean flow Consequently, the governing equation contains

6 unknowns, which are solved using different turbulence models

The RANS turbulence models can be divided into eddy-viscosity models and Reynolds stress models

The eddy viscosity model assumes that the Reynolds stress is related to the mean velocity gradients and

eddy (turbulent) viscosity by the gradient diffusion (Boussinesq) hypothesis, such that:

ij k

k t i

j j

i t j i ij

x

u k x

u x

u u

= turbulent kinetic energy, ij= Kronecker delta, t= Turbulent or eddy viscosity

In two-equation eddy-viscosity turbulence models, the velocity and turbulent length scale are solved

using two separate transport equations, one for kinetic energy, k and one for turbulent dissipation rate, ε,

or the specific dissipation rate, ω In k-ε model, the turbulence viscosity,t, is related to the turbulence kinetic energy, k and the dissipation rate, ε by the relation:



Where, C = Constant [20] 

Although k-ε model was used widely for its robustness and faster computations compared to other

turbulence models, the model shows limitations in adverse pressure gradient, flow containing

separations, rotation and near wall regions In the near wall boundary region, k-ω gives more accurate

result, but this model is strongly sensitive outside the boundary layer A blending between the k-ω

model near the boundary and k-ε model in the free stream was developed by Menter [21] BSL

turbulence model was introduced as the first step by introducing a blending function F1 In addition to

this function, the SST model accounts for the transport of the principal turbulent shear stress in the

prediction of the eddy-viscosity The sensitivity study of turbulence models SST, BSL and Omega RS

with respect this test rig was performed earlier [22], which showed that SST turbulence model is suited

for the CFD of this test rig

Mesh and boundary conditions

The fluid domain is extended from the conduit outside the pressure tank flange to the first bend after the

guide vane outlet The diameter of the inlet pipe is 400mm and the chord length of the guide vane is

142.77mm The entire domain, shown in Figure 7 is composed of around 13 million hexahedral cells

generated with ICEM O-grid technique was used at inlet and outlet round channels The near-wall

regions of the domain was refined to resolve high gradients Similarly, the mesh density was higher in

the regions of wakes and separations With the same pressure and flow conditions as carried out in the

experiment, the y+ value around the guide vane was 9.3 in average For the clearance gap of 2mm, 50

elements were used with finer distribution near wall boundaries

The mass flow rate at the inlet of the test rig at the designed condition is 195.83 kg/s This value

corresponds to two guide vane passages For experimental validation of CFD, the flow rate

corresponding to the experiment, i.e 155.5 kg/s was chosen This case is referred as the reference case

in this paper In the reference case, the guide vane has NACA0012 profile in both CFD and experiment

The validated reference model is used to compare 4 hydrofoils at the designed condition A static

pressure of 900 kPa was specified at the outlet The blade and the pipes were defined as non-slip smooth

walls At the inlet, a turbulence intensity of 5% was used

The estimation of the discretization error and extrapolation values were done by using the GCI method

[23] This technique is found to be effective in predicting the numerical uncertainties for the case of

Francis turbines [24] Three different mesh sizes corresponding to the mesh count of 0.22M, 1.52M and

12.83M were used in the independence test The mesh refinement was done by increasing the

distribution in each direction, i.e the grid refinement factor (r) by 2X The tangential velocity (Cu) at the

mid-point of GVout and Rin, corresponding to Figure 2 were chosen as the monitored variables These

values obtained by the three mesh densities are noted as Cu1, Cu2 and Cu3, where Cu1 represents the

results of the fine mesh and Cu3 represents that of the coarse mesh The approximate and extrapolated

relative errors were calculated using the GCI method as:

1

2 1 21

u

u u a

C

C C

21 1 21 21

uext

u uext ext

C

C C

Similarly, the grid convergence index was estimated as:

1

25.1

21

21 21

Table 1 shows the uncertainties and extrapolated values at the two locations The numerical

uncertainties in the tangential velocity at the mid-point of the runner inlet was calculated to be 3.6% and

4.0% for the medium and fine grid densities respectively At the mid-point of the guide vane outlet, the

uncertainties were 14.21% and 7.7% respectively This is the position where the flow is distorted due to

boundary wake from the guide vane

Figure 8 and 9 shows the tangential velocity at 30 circumferential locations corresponding to the GVout

and Rin curve shown in Figure 2 respectively for three mesh densities along with the extrapolated

results These figures also show the discretization error bars computed using Equation 17 for the fine

mesh For the fine mesh at GVout, the uncertainty ranges from 0.03% to 7.7%, which is equal to ±0.01

m/s and ±1.55 m/s respectively The maximum uncertainty is near the trailing edge, where the effect of

the wake is prominent For the fine mesh at Rin, the uncertainty ranges from 0.0021% to 12.2%, which

is equal to ±0.0006 m/s and ±2.60 m/s respectively In this case, the maximum uncertainty is found to

be near wall boundaries, where the velocity gradient is highest

RESULTS

Validation of the reference case

The first half of this section contains the validation of the numerical model for the reference case To

make the comparison easier, the static pressure at the outlet in CFD was adjusted such that the pressure

at the stagnation point was same between CFD and the measurement The pressure comparison was

done based on the normalized pressure (Cp), which is the ratio of the pressure at a point to the pressure

at inlet The value of Cp takes into account the distribution of the pressure along the stream Figure 10

shows Cp distribution around GV from leading edge (LE) to trailing edge (TE) In the x-axis, another

dimensionless term x/c is used, which represents the position (x) from LE with respect to the chord

length (c) The figure also shows the location of the pressure taps with reference to GV in both CFD and

PIV The maximum pressure was found at LE, where stagnation occurs The distribution of pressure

around GV measured in the experiment is comparable with the CFD result In the pressure side (PS), the

average deviation between experiment and CFD was calculated to be 0.6% In the suction side (SS), this

deviation was 3.3% It can be explained from this difference in the two deviations that the pressure in

the SS is not as stable as the PS due to fluctuations in this region during the measurement The

fluctuations could have emerged due to unaccounted clearances from wall roughness and manufacturing

tolerances

The flow field obtained by PIV was post-processed using 32-pixel resolution cross-correlation

technique with 50% overlap Velocity vectors were obtained inside the un-masked area of the

rectangular field, which were time-averaged for 100 images at 4 Hz There were around 1100 approved

vector points for each plane inside the PIV boundary shown in Figure 2 The velocity field on the whole

plane was interpolated based on these approved vectors, to create the velocity contours The velocity

field obtained from these points are represented in Figure 11 in the form of contour for GV mid-span

The figure also shows the velocity contour obtained in CFD in the same region The velocity field

predicted by the two method is found to be comparable, as both the pictures represent same color-map

The stagnation point at LE, ‘C’ profile of the velocity around TE, velocity field around GV and

downstream velocities were accurately predicted by the two methods However, the PIV contour were

affected by some factors An abrupt change in velocity can be seen near the upper corner due to

shadows from the bent of LE It can be observed that the wake from TE travels downstream inside the

runner in CFD, but dissipates before the runner in PIV This could be because the vectors were

calculated in the interrogation space of 32x32-pixel size in PIV, corresponding to a physical size of 4.7

x 4.7 mm, which was not enough for capturing wakes In CFD, the boundary mesh refinements make it

possible to capture the velocity gradients within smaller width In addition, statistics involved in

averaging the images in PIV tend to cancel out instantaneous odd vectors Whereas averaging provides

better estimation of the flow in steady regions, the unsteady secondary flow regions could have

undergone the average-out procedure

Figure 12 shows the velocity contour inside the clearance gap for both CFD and PIV The leakage flow

is related to the GV loading discussed in Figure 8 Towards LE, the flow inside the GV follows the

mainstream flow because the pressure difference in this region is less than the region around TE, where

the flow is diverted into the suction side The shaft area in PIV is masked out, but the effect is seen

downstream, where the velocity is reduced due to circulations The accelerated flow near the TE can be

observed in both the cases However, the pattern in PIV is more irregular due to the effect from the wall

The fluctuations could have also happened due to induced cavitation inside the low-pressure clearance

zone

The formation of this cavitating flow was also seen from visual inspection during the experiment The

leakage flow shown in Figure 12 mixes with the SS flow and forms a vortex filament, which has the

tendency to shift towards the mid-span, while travelling downstream Figure 13 illustrates shifting of the

vortex in CFD compared to the picture of the rig taken while PIV was being conducted The intensity of

this vortex was found to be gradually dissipating Although the experiment was conducted by

controlling the cavitation in the highest velocity region by monitoring the pressure in this region, the

cavitating vortex was not possible to avoid, due to high acceleration of the flow inside the clearance

gap By incorporating cavitation models in CFD, the flow behavior can be predicted more accurately

However, prediction of the vortex filament due to the leakage flow can be done without cavitation

models The characteristic of this flow in CFD was found to match with the experiment

The velocities measured by PIV and CFD at the circumferential locations of GV outlet (GVout) and

Runner Inlet (Rin), shown in Figure 2, were compared Figure 14 shows the average velocities at GVout

and Rin for mid-span The curve starts from PS (upper) wall and ends at the SS (lower) wall In each

curve, there are 29 points located at equidistant positions At mid-span, PIV and CFD follows the same

velocity profile trend As discussed above, PIV shows the dissipation of the wake before passing into

the runner At GVout, the mean of the average velocity was found to be 29.94 m/s in PIV, whereas this

value was 30.45 m/s in CFD The deviation was 1.67% The deviation calculated at each of the 29

points was 4.7% in average, with maximum at the region of the wake At Rin, the mean of the average

velocity was found to be 32.97 m/s in PIV, whereas this value was 33.14 m/s in CFD The deviation of

the mean of the average velocity at Rin between CFD and PIV was 0.5%, whereas the deviation of

individual point was 1.57% in average The lower values of the velocity in PIV was due to the losses

from the wall roughness, which were not accounted for the CFD analysis

Figure 15 shows the velocity profile at GVout and Rin inside the clearance plane, i.e 1mm away from

the wall At GVout, it can be seen that the velocity below the TE increased sharply due to the

accelerated leakage flow from PS to SS This gradient is stabilized at Rin as shown in the figure The

PIV results are fluctuating around the curve of CFD, which was also seen in the contour At Rin, the

deviation in the mean of the average velocity between CFD and PIV was 3.75%, whereas the mean of

the deviation at each point was 5.6% At GVout, the deviation in the mean of the average velocity was

3.57%, whereas the mean of the deviation at each point was 5.52%

Comparison between different hydrofoils

The validated numerical model was used to compare 5 different profiles at design condition Figure 16

shows the pressure difference, represented as ΔCp on the GV mid-span positions between PS and SS It

can be observed that the GV loading in the reference case (0012) is maximum Although the pressure

difference towards the LE is similar, the difference is significant towards the TE Compared to the

reference value of 1, the area of the polygon represented by ΔCp around hydrofoils of 1412, 2412, 4412 and 63212 were 0.85, 0.56, 0.17 and 0.64 respectively This means that the GV loading induced due to

the pressure difference between the two sides in 4412 profile is around 5.6 times less compared to the

symmetric 0012 profile

The pressure difference around the GV shown in Figure 16 has a direct effect on the leakage flow

though the clearance gap Figure 17 shows the velocity component normal to the chord length (Vy), as

defined in Figure 4 from LE to TE of all hydrofoils In the case of 0012, the Vy component gradually

grows from LE and after mid-stream position of the chord, the growth rate increases At 75% of the

chord, the Vy component is maximum After 75%, Vy decreases with the same rate and becomes

minimum at TE again This trend of Vy was found in all the hydrofoils In the case of 4412, negative

values of Vy was observed until mid-stream position After mid-stream, the values were positive, but

less than other profiles The negative value shows that the flow is directed from SS to PS, which is the

result from the negative pressure difference between PS and SS, as shown in Figure 16 The Leakage

flow factor (Lff) calculated according to Equation 7 for all the hydrofoils are shown in Table 1 The

reference velocity, Vo in the equation was taken as the average velocity at the outlet of the stay vane,

SVout shown in Figure 2 The table shows that Lff is maximum in 0012 Compared to the minimum Lff,

which was measured in 4412, the Lff in 0012 is 4.45 times greater

DISCUSSIONS

Comparison between the results of CFD and experiment shows a good agreement in overall The

velocity distribution at mid-span is more accurate than the regions near the clearance gap The clearance

gap region in PIV gives fluctuating results, due to the near wall effect and induced cavitation Some

specific areas of the PIV boundary were also affected by the rig geometry However, the mean of the

average velocities at GVout and Rin between CFD and PIV is comparable The passage vortex due to

leakage flow observed in the experiment is also accurately predicted by CFD By using CFD, the

characteristics of this flow can be studied

It was seen that Lff affected the SS flow travelling downstream For easy comparison, the leakage flow

shown in Figure 13 was categorized into four sections This category is shown in Figure 18 The first

category (i) is the flow in between the guide vanes close to the SS inside the clearance plane This type

of flow is not contributing to the leakage flow directly, but mixes with them to form the passage vortex

The leakage flow with high velocity traveling from PS strikes the SS flow and induces a pressure

difference between the two flows This difference in pressure results in the formation of a passage

vortex, which travels downstream in the form of a vortex filament In the case of 4412, the SS flow is

not disturbed by the PS flow The second category (ii) represents the flow entering the clearance gap

from the position just upstream of GV In the case of 0012, this type of flow enters the LE and after

around 30% of the chord length, moves away from the clearance gap and leaks through the SS In 4412,

the flow moves into SS, but since the velocity gradient is not prominent, this behavior can be regarded

as the effect of hydrofoil geometry The third category (iii) is the flow in the PS end that flows into the

gap due to the pressure difference between the two sides of the GV in the clearance gap plane In 0012,

the velocity gradient is higher than 4412 and it can be inferred from Figure 12 that this category of the

flow has the highest influence on the leakage flow The fourth category (iv) is the region in PS below

the clearance gap plane This flow is entrained by the high-pressure gradient along the span, which

makes it move into the clearance gap plane Higher the leakage flow due to ii) and iii), higher is the

pressure gradient along the span and higher is the effect of iv) Hence, in 4412, the effect is nullified due

to reduced impact of other categories of flow

All categories of the flow in 0012 mix together outside the TE, forming a passage vortex filament The

filament is further pushed towards the mid-span, due to pressure difference in the cross section of the

conduit In turbines, where runner is positioned near the TE of GV, the inlet of the runner blades, near

hub and shrouds are affected due to constant impact of these vortex filaments Furthermore, when the

flow contains fine eroding sand particles, the circulations present in the vortex wear the material,

causing more damages The consequences of these vortices at the inlet of Francis turbines in

sediment-affected power plants are reported in literatures [2] [25] The eroded turbine runners are shown in

Figure 19 The runner blades are designed based on an angle of stagnation corresponding to the best

efficiency However, the leakage flow through the clearance gap of guide vanes changes the stagnation

angle near the connecting ends Hence, in 4412, it can be inferred that since the intensity of the vortex is

reduced as shown in Figure 18, the consequent effect of erosion is also minimized However, it is to be

noted that the current research is based on one GV cascade rig The neighboring walls present in this rig

could have affected the results causing discrepancies compared to the real turbine

Whereas the GV loading is minimized, it is also necessary to check if the consequent effect on the

efficiency of the turbine is reduced due to the change in the geometry Figure 3 showed the average

velocity distributed into tangential (Cu) and meridional (Cm) components according to the geometry of

the turbine Out of these two components, Cu component is responsible for the work done by the turbine

and related to the efficiency of the runner At the inlet of the runner (Rin in Figure 2), if Cu is reduced,

the overall efficiency of the turbine reduces Figure 19 shows the Cu distribution at the inlet of the

runner for all the GV profiles The distribution of Cu component for all the GVs are similar Although

the GV loading is minimized significantly, there is negligible influence on the swirl component This

because the major parameters that control the Cu are chord line and GV opening angle, which changes

the swirl in the flow In this case, GV opening angle was kept constant, whereas the change in the chord

line was insignificant The position of the wake is shifted according to the position of TE for different

profiles Comparing the reference case of 0012, the mean value of Cu is reduced by 1.31% in 4412

Considering the reduction in Lff by 4.45 times, this deviation in Cu can be regarded as acceptable

In a straight passage containing a symmetrical profile like NACA0012, there should not ideally be any

lift force, when the angle of incidence is 0o This would mean that that at BEP, if the passage area was

straight, NACA0012 would have minimum the minimum blade loading However, the pressure

difference is created due to circumferential orientation of the guide vanes, as shown in Figure 21 To

find a correct GV profile, which would produce the same blade loading in BEP as NACA0012 in the

straight channel at 0o incidence is a rigorous process However, this study compares few NACA profiles

with the same thickness, which have shown positive indications related to the change of the profile

Total pressure contours at different planes normal to the chord length and downstream of the GV TE are

shown in Figure 22 The contours represent CTP, which is total pressure with respect to the average total

pressure at inlet The lowest total pressure represents the vortex filament, which forms circular contours

affecting the flow around it The vertical low CTP region around middle shows the wake from the GV

The figure also shows the position of GV with respect to the planes, so that PS and SS can be located

The maximum value of CTP is 1, which represents no loss The lower values represent the development

of losses and circulations into the turbine The contours are observed for five planes at a distance of 30

mm, starting from TE In 0012, the circular contours are seen towards the suction region, in the top right

corner of the plane The center of these contours represent the center of vortex traveling downstream

From 0mm to 120mm, it can be seen that the size of the vortex is growing It also shows that the vortex

is gradually dissipating while traveling further The center of the vortex is shifting away from the upper

wall, while travelling downstream The size of the vortex in 0012 is bigger than in 4412 The

differences shown in this figure is directly related with Figure 18 In 4412, the vortex is close to GV and

is smaller compared to 0012 In addition, the size and position of the vortex remain almost constant in

all the planes The shifting of the vortex away from the wall can also be explained from Magnus effect,

which in this case, is the force induced on the rotating fluid in a direction at an angle to the axis of spin

[26]

CONCLUSION

The leakage flow through clearance gap of a guide vane (GV) in a cascade was studied in this paper In

the first section, a reference model, containing NACA0012 hydrofoil shaped GV with 2mm clearance

was used to validate the numerical result with experiments The normalized pressure (Cp) distribution

around the GV showed the average deviation of 0.6% on the pressure side and 3.3% on the suction side

between CFD and experiment At mid-span, the velocity contour of CFD and PIV showed a good

agreement in the leading edge, pressure and suction side and the ‘C’ profile around the trailing edge The mean of the average velocity at GVout in mid-span was found to be 29.94 m/s in PIV and 30.45

m/s in CFD The mean of the average velocity at Rin in mid-span was found to be 32.97 m/s in PIV and

33.14 m/s in CFD Some discrepancies were seen in the clearance gap plane because of the wall effect

The acceleration of the flow from PS to SS in the clearance gap region was observed in both CFD and

PIV, which contributed to the formation of a vortex filament

In the second section, the validated numerical model was used to do the in-depth study of the leakage

flow and compare the performances between five GV hydrofoils The streamlines contributing to the

leakage flow was divided into four categories depending upon their positions at the inlet of GV These

streamlines form a vortex filament, which has the tendency to move away from the wall, while

travelling downstream A dimensionless term, ‘Leakage Flow Factor’ (Lff) was used to compare the

potential leakage flow through the clearance gap of five hydrofoils, including the reference case

Compared to the Lff of 0.815 in the reference case, NACA4412 showed the reduction by 4.45 times

The value of Lff is directly related to the pressure difference between the two sides of GV On the other

hand, the mean value of the tangential velocity, (Cu) at the runner inlet was reduced only by 1.31% in

NACA4412, compared to the reference case It was seen that the size of the vortex in NACA4412 was

found to be reduced compared to the reference GV The reduction of size and intensity of leakage flow

and passage vortex signifies minimization of the simultaneous effect of secondary flow and sediment

erosion

ACKNOWLEDGMENT

This study was performed as a part of a joint PhD between Kathmandu University and Norwegian

University of Science and Technology The program is funded by Norwegian Research Council and

STATKRAFT

NOMENCLATURE

PIV Particle Image Velocimetry

SVout Stay Vane Outlet

GVout Guide Vane Outlet

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Figure Captions List

Fig 1 Erosion of the Guide vane ends in Jhimruk [2] and KG-A [7]

Fig 2 Boundary of the rig and measurement locations

Fig 3 Tangential and meridional velocity components

Fig 4 Velocity components in the axis of the chord

Fig 8 Tangential velocity at GVout with extrapolated values and discretization error bars

Fig 9 Tangential velocity at Rin with extrapolated values and discretization error bars

Fig 10 Cp distribution around GV

Fig 11 Velocity contour at mid-span from CFD (left) and PIV (right)

Fig 12 Velocity contour in the clearance gap from CFD (left) and PIV (right)

Fig 13 Vortex filament in CFD and experiment

Fig 14 Velocity profile at GV outlet and runner inlet in mid-span

Fig 15 Velocity profile at GV outlet and runner inlet inside clearance plane

Fig 16 Pressure difference around GV surface for 5 hydro profiles

Fig 17 Velocity Vy along the chord length

Fig 18 Streamlines through the clearance gap

Fig 19 Erosion of runner inlet at connecting ends due to the vortex filament carrying sediment

[2] [25]

Fig 20 Cu distribution at runner inlet for all GV

Fig 21 Velocity and pressure distribution around GV

Fig 22 Total Pressure contours for 2 GV profiles away from GV TE on planes normal to the

chord length

Table Caption List

Table 1 Discretization errors in the numerical solution

Table 2 Leakage flow factor (Lff) for all GV profiles