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Failure analysis of runner blades in a Francis hydraulic turbine —Case study

Alberto Luna-Ramírez ⁎, Alfonso Campos-Amezcua, Oscar Dorantes-Gómez,Zdzislaw Mazur-Czerwiec, Rodolfo Muñoz-Quezada

Instituto de Investigaciones Eléctricas, Reforma 113, Col. Palmira, Cuernavaca, Mor., México

a r t i c l e i n f o a b s t r a c t

Article history:

Received 4 June 2015

Received in revised form 6 October 2015

Accepted 20 October 2015

Available online 23 October 2015

Failure analysis of the moving blades in the runner of a 200 MW Francis type hydraulic turbine

is presented. Analysis consisted of the determination of the pressure on the blade surface using

computational uid dynamics (CFD), the calculation of the stress distribution in the turbine

runner at different operating conditions using thenite element method, and a simplied fatigue

analysis. Natural vibration modes in water and Von Kármán's vortex frequencies serve as

reference. Results showed a large concentration of stresses in the T-joint between the blade and

crown where the cracks originated. Finally, possible causes of the damage are discussed.

© 2015 Elsevier Ltd. All rights reserved.

Keywords:

Turbine failure

Cavitation

Vibration

Fatigue crack

Runner blades

1. Introduction

The operating regime of a hydraulic turbinecanbe divided into steady stateoperationand transient state operation [1]. During steady

state, the forces acting on the turbine are: the static weight of the runner including water weight, residual stresses and dynamic forces.

Residual stresses can be generated not only during construction and assembly of the turbine, but also during the commercial

operation of the turbine due to weld repair and uneven heating. The effect of residual stress is accentuated on intricate shapes or in

certain turbine components. Dynamic forces are generated during rotation of the unit as a result of the combination of unbalance and

misalignment with other transient perturbations, namely intermittent water ow or foreign objects in the water.

During steady state,the unit operates at a constanthead, speed, load and constant opening of the guide vanes. The forcesacting during

this period are constant in magnitude, direction and frequency. However, due to defects such as excess pressure pulsations generated in

the intake pipe, cavitation or misalignment, random non-periodic forces have different directions, amplitudes and frequencies.

Transient state operation occurs when there is a change in the head or load or wicket gate opening, i.e. starting, synchronizing,changing load, stopping, load rejections, tripping, turbine failures and overspeed. During these periods, vibrations do not follow a

single pattern but change in magnitude, direction and frequency; their values increase or decrease depending on the amount of

water that enters. Other factors that can induce stresses or a non-steady state are the increase or decrease in load or frequent

starts or stops. For instance, Casanova [2] has reported that the fracture of the draft tube connecting bolts in Francis turbines is

especially frequent when the machine operates at partial loads.

During operation, several steady and unsteady forces act on turbine components. Unsteady state forces are superimposed on

steady state forces, resulting in vibrations. Since several components are fastened to each other, the vibration of a component is

Engineering Failure Analysis 59 (2016) 314–325

⁎ Corresponding author.

E-mail address: [email protected] (A. Luna-Ramírez).

http://dx.doi.org/10.1016/j.engfailanal.2015.10.0201350-6307/© 2015 Elsevier Ltd. All rights reserved.

Contents lists available at ScienceDirect

Engineering Failure Analysis

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transferred from one to another, so the rigidity of each component must be ensured. These vibrations result in deformation of the

different components, which in turn causes additional stress on the affected components [3].

Although the units are designed with a suf cient margin of safety to withstand normal stresses, high vibrations and dynamic

stresses result in a gradual development of cracks. For this reason, if no precautions are taken to reduce these vibrations, the

affected component failure may occur without notice. Excessive vibrations and resulting stresses in the affected components

can cause fatigue and thus component failure. This vibration can also cause wear and fatigue failure of the runner blades, guide

vane ring, bearings, shafts, runner labyrinth seals and shaft seals, and shear or loosening of various nuts and bolts in all affected

areas, as well as loosening of bolts and stator core blocks [4–6].

Fig. 1. Tailwater level difference.

Fig. 2. a) Crack located on the trailing edge prole at the junction between the runner blade and crown, b) cavitation pitting damage near the trailing edge of theblade, c) magnication of cavitation damage on the underside of the blade.

315 A. Luna-Ramírez et al. / Engineering Failure Analysis 59 (2016) 314– 325

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In Francis turbine runners, fatigue cracks tend to occur early or after decades of operation. The failure mechanism is considered

a combination of low-cycle fatigue caused by startups and high cycle fatigue caused or induced by rotor–stator interaction [7,8].

As long as the loads are high enough, the start–stop cycles may propagate fatigue cracks from manufacturing defects or even

trigger fatigue cracks at areas of stress concentration. With rotational runner speed up to several hundred revolutions per minute,

the number of vibration cycles or high cycle fatigue due to wakes behind the stationary blades and guide vanes is increased to

several million per day. Therefore, once a crack has reached a critical size in relation to high cycle fatigue loading, the crack

may grow and can cause a catastrophic failure in a short period compared to the design life of the turbine runner [4,8].

The purpose of this article is to determine the cause or probable causes of failure (cracking) of the runner blades in a Francis

200 MW type Hydraulic Turbine. Failure analysis is based on the historical unit operation analysis, which determines pressure

distribution and stress analysis, and compares the natural frequencies in water with the excitation frequencies due to the Von

Kármán vortex and simplied fatigue analysis, which together serve to determine the cause or causes of blade failure.

1.1. Damage description

Given the excess water in the storage reservoir of the hydroelectric power plants, it became necessary to discharge a lot of

water. When the three units of the power plant operate under normal conditions, the water level in the landll is 418 m; during

discharge, the water level rose 10 m above the normal operating level, as it is shown in Fig. 1. The turbines did not stop operating

during the venting operation, so excess water was used to carry out work on the turbine.

The discharge lasted several hours and the peak level (427 m.a.s.l.) remained for three days. The temperature of bearings did

not increase during this special operation and, since their vibration sensors were not implemented on the turbine, it was not

possible to measure or detect possible episodes of vibration during the reservoir discharge period.

During the turbine maintenance period, NDT with magnetic particles were conducted on the 13 runner blades in the turbine.

Large cracks in four consecutive runner blades were detected during the test. Fig. 2a) shows the size and location of the cracks,

which began near the junction between the runner blade and the crown of the hydraulic turbine at the trailing edge, then raninto the body of the blade. Fig. 2b) shows cavitation pitting damage near the trailing edge of the blade. The cavitation damage

indicated in Fig. 1b) may be related to the interblade vortex cavitation or sometimes known as the Von Kármán vortex cavitation

phenomenon [3,9], which occurs mainly on the trailing edge of the blade, usually when the turbine is operated at partial loads.

Such cavitation produces structural vibrations at the blade trailing edge [10]. Fig. 2c) shows a magnication of cavitation damage

on the bottom surface of the blade.

1.2. Turbine operation history

Before commencing failure analysis of the unit, operating conditions of the three power units in the power plant are presented

in order to compare the modes of operation of each turbine. Table 1 summarizes the extraordinary conditions of operation for the

increased tailwater level. Table 2 outlines the operating hours and the number of times that units operated at low loads (30 MW)

in the 2001–2014 period.

2. Fluid ow analysis

2.1. Hydraulic turbine characteristics

The dimensional characteristics and nominal operation parameters of the analyzed hydraulic turbine are: number of runner

blades 13, number of guide vanes 24, number of stay vanes 12, and turbine ratings, which are presented in Table 3. The runner

Table 1

Behavior in the storage reservoir hydropower plant.

Date (Maximum elevation reached)

(haverage) (m)

Tailwater level

difference Δh (m)

Approximate running

time of this event (h)

Power output (average)

in (MW) during the event

16 Sep. 2013 427.6 427.62–418⁎ = 9.62 6 192.5

17 Sep. 2013 427.6 427.65–418 = 9.65 11 192.2

18 Sep. 2013 423.4 423.44–418 = 5.44 – 194.7

19 Sep. 2013 422.2 422.25–418 = 4.25 – 192.7

20 Sep. 2013 419.3 419.34–418 = 1.34 – 194.7

⁎ Reference elevation (see Fig. 1).

Table 2

Operating hours of the three units and number of times they operated at low load (30 MW) from 2001 to 2014.

Unit 1 Unit 2 Unit 3

Hours of operation at low load 75 66 25

Number of times units operated at low loads 72 78 66



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material is 13Cr/4Ni (ASTM A487 Grade CA-6NM) martensitic stainless steel. The properties of the runner material, used for all

the analyses reported in this paper, are described in Table 4.

Fluid analysis through the turbine runner is required to determine the hydraulic load on the surface of the runner blade. The

computational model domain comprises the guide vanes and turbine runner. Since both the blade distributor and runner blade

are periodic, a guiding vane and runner blade were modeled in addition to the curves dening the crown and band of the

impeller. A 3D model, using periodicity conditions, was created.

Fig. 3(a) shows the guide vane, runner blade and diffuser section, whereas Fig. 3(b) shows the runner full model using

periodicity conditions. Analyses were conducted at steady state operation for different loads, considering the working uid in

three dimensions as a continuous medium. The Navier–Stokes equations were used to model the ow, and the Spalart–Allmaras

turbulence model was used to complete the equation system. Flow analysis was performed using the Computational Fluid

Dynamics (CFD) technique using NUMECA [11] commercial software.

The computational mesh is an unstructured grid of almost 3 million of hexahedral cells, with a higher density of nodes in areas

where the uid ow was expected to considerably change, as at the leading edge and trailing edges of guide vanes and runner

blades, where a ner grid resolution was assumed to be benecial for achieving an accurate resolution, Fig. 4.

A preliminary mesh was worked out including a more rened boundary-layer, for which the ow solution no longer changed

with subsequent rening. A detail of blade to blade mesh can be seen in Fig. 5.

Boundary conditions to be imposed on the model for normal operating conditions of the turbine are shown in Table 5. The

angle at which the ow enters the model (inlet to the guide vanes) corresponds to the output angle of the stay vanes.

When the level increased in the lower reservoir of the Power Plant to 9.65 m, the outlet head raised to 436,695 Pa, that is,

there was an increase of 94,655 Pa compared to the nominal head. Computational runs at partial loads and overload were

performed to determine the pressure on the surface of the blades, and subsequently calculate stress. The boundary conditions

of these models are the same as in Table 6, except for mass ow. The values of the variables (load, angle and throat) that are

modied in the model for each analysis are shown in Table 6.

2.2. CFD results

Pressure distribution for the pressure and suction sides of the runner blades for different load conditions is shown in Fig. 6.

Pressure differences for the pressure and suction sides are higher at higher loads (Fig. 6a5) and b5)).The increasing pressure

on the blades at the leading edge for all load conditions on both sides is clearly visible.

Under all load conditions, pressure is observed to gradually decrease in the direction of the ow, starting at the suction side of

the blade. The low pressure zone (blue) may be viewed after half the length of blade, at the bottom of the blade trailing edge. For

example, at 100% load, maximum pressure is 980 kPa at the leading edge and at least 2 kPa at the trailing edge. This low pressure

area is susceptible to cavitation. The pressure reduction on the runner blade suction side near the trailing edge region may be

explained by the higher magnitudes of the velocity speed at the trailing edge [12]. In all cases or load conditions, the pressure

differences on both sides of the blade (suction and pressure) are high; these differences result in a torque on the shaft. Similar

results have been documented in other studies [13].

3. Stress analysis in turbine runner

The stress analysis of the runner subjected to different loading conditions is an important issue in the analysis of failure since it

provides information on the structural integrity of the turbine. In this study, analysis was performed using ANSYS, which has

proven to be an effective tool for modeling stresses in hydraulic turbine components [5,12,13,14].

Mechanisms that can damage the hydraulic turbine runner are a combination of loads acting on the runner, and are divided

into two categories: stationary loads (the uid pressure on the surface of the blades, the centrifugal force and the runner's own

Table 3

Nominal operating parameters of the hydraulic turbine.

Net head (m) Output (MW) Discharge (m3/s) Speed (rpm)

101.3 214.25 227.7 128

91.2 200.5 237.9

75.5 151.1 216.2

Table 4

Properties of material in a hydraulic turbine runner.

Material property ASTM A487 Grade CA-6NM

Tensile strength (Su) 755 MPa

Yield strength (Sy) 550 MPa

Density (ρ) 7695 kg/m3

Young's modulus (E) 199.95 GPa



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weight) and dynamic loads (pressure uctuations caused by the rotor–stator interaction, as well as phenomena such as cavitation

and water hammer). In the Francis turbine, stresses caused by centrifugal force during normal operation condition are much

smaller than those caused by water pressure [12].

The geometric model with the established boundary conditions is shown in Fig. 7. Letter A corresponds to the zero displace-

ment condition (UX = UY = UZ = 0), which is represented as a xed support in the area of connection to the shaft ange. Letter

B represents the rotational clockwise speed, and letter C represents gravity acceleration.

Fig. 8 shows the results of stresses calculations at different loading conditions (15, 30, 50, 75, 100, 110%) on the runner blades,

considering the pressure distribution exerted by the water ow on the surface of the runner blades and centrifugal forces. The

stress distribution shown in Fig. 8 is expressed in terms of equivalent stress (Von Mises stress).

At 100% load, maximum stress (Fig. 8e)) was around 224.86 MPa, and at 110% load, maximum stress was 254.30 MPa

(Fig. 8g)); both values represent slightly less than half the material yield stress (σ y = 555 MPa). For all loading conditions,

maximum stress started at the trailing edge at the junction between blade and crown. Maximum stress obtained for a load of

100% but considering output pressure of 436.7 Pa (corresponding to 9.65 m increased level in the lower reservoir vent of the

Power Plant) was 241.55 MPa. This value is approximately 7% larger than the obtained at a nominal load of 100% and 5% less

than the 110% load (Fig. 8f)).

It is important to note that the location of the higher stresses in all cases coincides with the location of the cracks observed in

the runner blades. This suggests that although the stresses alone do not cause blade failure, they are the source of crack induction

and growth.

The literature [4,5,12,13,15,16] mentions that in a Francis turbine runner, the region near the trailing edge at the blade crown

intersection is identied as the region subjected to high stresses, and is therefore a critical area for cracks to occur due to fatigue.

From a numerical analysis standpoint, it can be concluded that the maximum calculated stresses are located at the transition

between blade and crown on the trailing edge, which correspond to the location of the cracks observed during maintenance of

the unit.

Fig. 3. Geometric model used in the simulation.

Fig. 4. Computational grid used in the model.


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3.1. Determination of natural frequencies of the runner in water and air

Since the runners work while submerged in water, dynamic behavior could be strongly affected by the presence of this heavy

uid [17]; therefore, the study on turbine runner structures considering water effect is of highly practical interest. A numerical

model was therefore developed, including a nite volume representing an added mass of water. Fig. 9 shows the numerical

model and natural frequencies of therunner that were calculated. This analysis considers only the added watermass; thus, theeffects

of vibration in the water surrounding the runner are not taken into account. Table 7 shows the mode and natural frequency of

vibration of the runner in water and air at 128.57 rpm.

When the obtained result in the runner's simulations in air and water are compared, it was observed that a decrease in the

natural frequencies does exist, because of the water that surrounds the structure. The ratio of frequencies reduction varies from

0.147 to 0.377 depending on the frequencies. The results presented in Table 7 were used to correlate Von Kármán vortex frequencies

and certain vibration modes by considering the water mass.

3.2. Von Kármán vortex frequencies

The computation of the possible Von Kármán excitation frequency ( f ) must be done for every load condition. These frequencies

are compared with the runner natural frequencies in water in order to evaluate the chance to have a natural mode shape excited

by any Von Kármán frequency. The Von Kármán frequency ( f ) is dened by the following Eq. (1) [18]:

f ¼ S t C =t þ δvð Þ………:: ð1Þ

It has been found that the value of S t varies between 0.16 and 0.24 [19]. For the following calculations a value of 0.2 is assumed

where:

S t Strouhal number

C velocity of water [m/s]

T thickness of the blade trailing edge [m]

δv 0.0293 (x/Rex)1/5 = virtual boundary layer thickness [m]

where

x blade length or chord length = 1.744 m

Rex Reynolds number = 9.5E7

Fig. 5. Fragment of the guide blade to blade mesh.

Table 5

Boundary conditions at rated load (214.25 MW).

Boundary condition Units Value

Mass ow kg/s 227,928

Temperature °C 20

Turbulent viscosity m2/s 0.0001

Static pressure at model outlet Pa 342,041

Rotational speed rpm 128.57


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Table 6

Variations in the model at different loads.

No. Load [%] Throat [mm] Angle [°] Mass ow [kg/s]

1 15 (30 MW) 63 82.8 34,189

2 30 126 77.1 68,378

3 50 210 69.4 113,964

4 75 315 59.9 170,946

5 100 (200 MW) 420 50.4 227,928

6 110 462 46.5 250,721

Fig. 6. Solutions for pressure on the blade; a) pressure on the pressure side of the blade, b) pressure on the suction side of the blade, under different loadconditions.




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Table 8 shows the results of frequency calculation by Von Kármán vortex for different condition loads.

Analysis of the results in Table 8 shows that at 30% load, the Von Kármán frequency (115.51 Hz) is very close to the natural

frequency (116.7 Hz) of the fourth vibration mode of the runner in water. Furthermore, by varying the turbine load from 15 to

30% (30 to 60 MW), the Von Kármán vortex frequencies range from 57.7 to 115.5 Hz, and they can result in the excitation of

the runner natural frequencies in water in second (71.1 Hz) and third mode (88.7 Hz) vibration; see Table 7.

This excitation can generate high levels of vibration, which in turn can produce high cycle fatigue failure on mechanical

components, especially on turbine runner blades [13]. Cases have been reported of cracking of runner blades attributed to the

occurrence of vibrations on account of resonance between the Von Kármán vortex shedding frequency and the natural frequency

of the blades [16,20–23].

Fig. 6 (continued).




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4. Simplied fatigue analysis

The fatigue analysis serves to characterize the ability of a material subjected to cyclic loading, such as the hydraulic turbine

runner. Startups, shutdowns and load changes produce low cycle fatigue, whereas cyclic loads induced by vibration, ow

uctuations, recirculation and resonance produce high cycle fatigue. The fatigue strength of steel is dened by the following

Eq. (2):

N f ¼ t r f r ð Þ::::::::::::::::: ð2Þ

where [24]:

Nf resistance fatigue [cycles]

tr time in resonance [s]

f r resonance frequency

For steel, N f = 107 cycles are considered.

Solving t r in Eq. (2), time (t r ) to failure (cracking) is calculated when the component operates in resonance; see Eq. (3):

t r ¼ N f = f r ::::::::::::: ð3Þ

When Eq. (2) includes the fatigue resistance of the steel N f = 107 cycles and the natural frequencies calculated at the runner,

f r1 = 30.92 Hz (rst mode) and f r2 = 116.67 (mode) are obtained:

t r1 ¼ 107 = 30:92 ¼ 89:8 h½ ; t r2 ¼ 10

7 =116:67 ¼ 23:8 h½

The results indicate that if the runner operates in resonance with the rst or fourth mode of vibration, cracks in the runner

would appear within 24 to 90 h of operation. In case of resonance at higher modes of the runner, cracking would occur in less

time.

On the other hand, it is known that the runner has been operated for 26 years without cracking. This means that runner failure

could not be induced during normal operating conditions (constant nominal load). It is thus suspected that some other temporary

transients occurred, causing the excitation in one of the natural frequencies of the runner, resulting in high cycle fatigue failure.

It is known that normal fatigue life is around 90% the total life for crack initiation and 10% for the propagation phase [25]. This

implies that no signs of fatigue are noticed on the runner blade surface for a signicant period of time even if fatigue conditions occur

during operation (excitation, resonance). Fatigue damage is cumulative and becomes visible following a considerable number of fatigue cycles.

Fig. 7. Boundary conditions used in the nite element analysis.




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5. Conclusions

Taking into account the results of the calculated stresses at maximum operating loads, the stresses are below the yieldstrength (σ y = 550 MPa). Therefore, these stresses alone could not have caused blade failure.

Fig. 8. Stress distribution on the surface of the runner blades under different load conditions.




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The maximum stresses obtained for 100% load with additional 94,655 Pa outlet pressure were approximately 7% higher than

those obtained at 100% nominal load. On the other hand, these stresses were 5% lower than at 110% load, which also indicates

that this level of stress alone (without any other phenomena) could not be the direct cause of the “sudden” failure of the blades.

Namely, the rise in water level at the turbine outlet caused the stresses to increase, which in combination with another phenom-

enon could have accelerated blade failure.

All maximum stresses calculated on the runner were located near or at the transition radius between band and crown on the

trailing edge of the blades. Their locations coincide with blade failure, which indicates that this stress concentration was where

the crack started and spread. Static pressure values on model surfaces at 100% load, obtained by ow analysis, indicate that

cavitation prone areas were found, which coincided with cavitation damage recorded during inspection of the units 1 and 3.

Turbine operation at low loads may excite the natural frequency of the blades in three of the rst four modes of vibration,

resulting in high cycle fatigue of the runner blades. The most likely cause of failure in the turbine runner blades was turbine

operation at low loads, accelerated by detected cavitation, and high water levels in the upper reservoir and tailwater.

Fig. 9. Numerical model runner submerged in water mass.

Table 7

Vibration frequency for different vibration modes in water and air.

Vibration mode Vibration frequency (simulation) (Hz)

In water In air

ND1 30.92 43.01

ND2 71.12 83.39

ND3 88.76 142.51ND4 116.67 158.06

ND5 135.37 194.71

Table 8

Results of frequency calculation by Von Kármán vortex.

Load δv Velocity of water Thickness of blade trailing edge Von Kármán vortex

% [m] C (m/s) t (m) f (Hz)

15

0.00129

6.7

0.0219

57.7

30 13.4 115.51

50 22.3 192.2

75 33.4 287.8

100 44.6 384.4




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The Von Kármán vortex shedding phenomenon may explain the appearance of cracks in the runner blades, since some

excitation frequencies are similar or close to the natural frequencies of the runner in water, contributing to damage by high

cycle fatigue. However, more studies are needed to corroborate this conclusion.

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