FEA Blade Errosion

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Energy and Power Engineering, 2011, 3, 227-237doi:10.4236/epe.2011.33029 Published Online July 2011 (http://www.SciRP.org/journal/epe)

Copyright 2011 SciRes. EPE

Theoretical and Numerical Analysis of the MechanicalErosion in Steam Turbine Blades. Part I

Fernando Rueda Martnez, Miguel Toledo Velzquez, Florencio Snchez Silva, Aldo Antonio RuedaMartnez, Samuel Alcntara Montes, Oliver Marciel Huerta ChvezApplied Thermal and Hydraulic Engineering Laboratory, Lindavista, Mexico

E-mail: [email protected] April1, 2011; revised May 2, 2011; accepted May 13, 2011

Abstract

The methodology of calculation of the velocity distribution for the stream frictionless and the drops in theflow line, on the basis of the frictionless, two-dimensional, stationary, transonic and homogenous flow is es-

tablished. The knowledge of conditions that govern the low pressure section of steam turbines in the laststage to have an approximate movement of the droplets in the blade cascades and the accumulation of drop-lets on the stator blades, flowing through the steam, is presented. This study is used for developing a code inFortran about the velocity distribution in the output of stator blades that have flow conditions of wet steam,in order to understand the causes that originate the erosion on the blades of the last stages in the low pressuresection of steam turbines.

Keywords:Steam Turbine, Drop Distribution, Erosion Stator-Rotor Blade, Transonic Flow

1. Introduction

Nucleation is the energy necessary to form a stable

droplet, also named thermodynamic barrier of germina-tion. In a microscopic level, phase fluctuations occur asrandom events due to the thermal vibration of atoms(collisions). In terms of classical nucleation theory, thespontaneous fluctuations lead to the formation of smallembryonic droplet that can grow beyond some criticalradius, being possible to overcome this barrier and tohold its spontaneous growth; that is, it can only surviveand grow up if there is a reduction in free energy [1].However, if the energy barrier to spontaneous growth islarge and the droplet cannot achieve its critical size, itremains unstable and possibly will evaporate. As a result

of this energy barrier, the system can exist in a metasta-ble state with unfavorably high supersaturation levelsbeing maintained in the gas phase. The existence of wa-ter droplets formation presents practical difficulty con-cerning the behavior of steam in turbines. The tempera-ture and pressure gradients are such that droplets mightnucleate with undesirable effects on the performance ofthe machine, including the erosion of turbine blades dueto the repeated impact on them. In the case of condensedphases, the principal idea is that exist a bottleneck in thetransformation, which is passed through only by frag-

ments, or molecular clusters, of the new phase. The clus-ter is a group of individual units mutually interrelated inall directions: vertical, horizontal, etc., that establishes a

functional interdependence for the development of itsprocesses. The bottleneck is narrowest when the clustersreach a so-called critical size. The capillarity approxima-tion is employed, whereby the critical cluster, howeversmall, is considered as a scaled-down macroscopic drop-let of the condensed phase. Until recently, the moisturenucleation in turbines has been assumed as a homogene-ous process with the effects of steam impurities beingnegligible, as in this case of study.

Generally, depending of the conditions of work of theturbine, in the two or third rotor stage is found heteroge-neous nucleation transition (molecules nucleate onto

surfaces). In the fourth stator stage can creates the pri-mary nucleation toward the shroud. As flow expansioncontinues into the final stage, significant supercooling isagain possible, leading to further secondary homogene-ous nucleation along the final rotor stage. Finally,smaller droplets generated along the third rotor inlet andoutlet stage can be collected on blades and re-entrainedas secondary droplets into the flow at the trailing edgesof rotating components [2]. Importantly, the dropletsgenerated along the inlet of third rotor blades throughrotor fifth stage remain quite small, can be adequately


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F. R. MARTNEZ ET AL.228approximated with no-slip assumption relative to thecontinuous vapor phase.

Droplets in the last stage are entrained with sizes thatare generally greater than 100 m and have a consider-able slip relative to the vapor. The path of the droplets in

the channel of the blade cascades can be different [3].The part of the moisture that is deposited on the bladesurface, form a fine liquid film less than 0.1 mm, which,under the action of the friction forces of the steam flow,is slipped slowly towards the trailing edges and impactsagainst the suction side of the rotor blade [4]. The ero-sion can affect a considerable percent of chord profile(25%) causing the loss of portion of the blade. Insignifi-cant erosion even makes change the vibration character-istics and resistance of the blades, been the cause of thebreakage and low performance of the stages. It has oftenbeen argued that from the thermodynamic point of view,

a cluster of drops behaves, in fact, as one large drop ofthe same dimension as the cluster. Classical nucleationtheory is built on the thermodynamics treatment of drop-lets by the capillarity approximation, where the smalldroplets have the same properties as bulk condensedphases, with bulk surface properties [5] and consideredas a drop. There also would be occasional clusters con-taining a larger number of molecules; however, a motionpicture of these larger clusters would show that most arevery short lived; they grow rapidly and then shrink rap-idly. Nucleationoccurs when a cluster of two, three, four,grows (fluctuates in size) to a size large enough that itthen continues to grow rather than shrink [6]. Eventually,agglomeration by coalescence of large clusters entersuntil thermodynamic equilibrium [7] colliding with eachother, forming larger clusters [8], and these drops withseveral sizes always have a spherical shape, which areforced by the surface tension and keeping constant intothe turbine, impacting on the blades and causing dam-ages.

2. Droplets Formation in Steam Turbines

Erosion is of significance when drops impact on a hardsurface. The continuous impact of drops forms a liquid

film on the surface, which would attenuate the forcesduring the impact at subsequent times and, hence, thelong-term wear on the surface [9].

In the last stages of the turbines, very high expansionrates are achieved, leading to supercooled flow condi-tions and nonequilibrium droplet formation by severalmechanisms that mean an impact on turbine efficiency.The two-phase flow behavior in a low pressure section ofa conventional steam turbine beginning with the firsttransition, localized in the stator in the third stage denot-ing the saturation line, where, under equilibrium, as-

sumptions phase transition would appear, as is seen inFigure 1.

Generally, in the third rotor stage is found heteroge-neous nucleation transition. In the fourth stator stage cancreates the primary nucleation toward the shroud and

occurs in the following stage component (the third rotor).As flow expansion continues into the final stage, signifi-cant supercooling is again possible, leading to furthersecondary homogeneous nucleation along the final rotorstage. Finally, smaller droplets generated along the inletthird rotor stageand output third rotor stagecan collecton blades and be re-entrained, as secondary droplets, intothe flow at the trailing edges of rotating components, inparticular. Importantly, the droplets generated along theinlet of third rotor bladesthrough fifth rotor stageremainquite small, can be adequately approximated with ano-slip assumption relative to the continuous vaporphase.

In the last stage of the low pressure steam turbine thedroplets localized have sizes that are generally greaterthan 100 m [10] and have a considerable slip relative tothe vapor. These droplets have a significant influence onblade erosion, and the fact that the small nucleated drop-lets provide the source for entrainment of large dropletsinto last stage, describe a highly coupled two-phase flowsystem.

The process of steam expansion on the rows is verycomplicated. The drop velocities are different of thesteam velocity as much by their magnitude as by theirdirection; in fact, it cant give a general scheme of the

movement of wet steam. The path of the droplets in thechannel of the blade rows can be different, as is shown inFigure 2. In this case, the drops in the steam flow canlose their stability and be divided [11].

When the wet steam expands in the row stator blades,the additional condensation of the steam takes place,which it depends of the dimensions that have the dropsof the liquid phase. The drops accelerate by the steam

Figure 1. Phase transition in a low pressure section of a

steam turbine. Stator and rotor components labeled with SandR, respectively.



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F. R. MARTNEZ ET AL. 229

Figure 2. Path of droplets in the channel of blade rows [12].

flow; in addition, while greater are the size drops, lesswill be their velocity in comparison with the steam.

Part of the humidity is deposited on the blade surface,

forming a fine liquid film (of ordinary, no more than0.1mm), which, under the action of the friction forces of thesteam flow, is slipped slowly towards the trailing edges.The drop that leaves of the blades of the stator rows withsmaller velocity has a direction of the relative velocity

and impacts against the suction side of the rotorblade.w

By consequence, on the performance of the stage thelosses due to steam (where = TS T) differ-ence between the local saturation temperature TS andmeasurement temperature T) and the mechanical interac-tion of phases not only exert influence, but also the ac-

tion of the wet steam, the energy consumption to trans-port the liquid films by the blade surface, under the ac-tion of centrifugal forces and other factors, they arecharacteristic for the stage altogether. With the incrementof steam pressure, the influence of the weak moisture inthe characteristics of the rows reduces the droplet dimen-sions. The erosion can affect a considerable percent ofprofile (sometimes to 0.2 - 0.3 of chord) causing the lossof portion of the blade. Insignificant erosion even makeschange the vibration characteristics and resistance of theblades, been the cause of the breakage, as well as theperformance of the stages diminishes [13].

T T

The effect of the interaction of the boundary layer and

the condensation is localized in the outer part of the(turbulent) boundary layer where considerably largerdroplets appear in the (inviscid) core flow of the samecross section. The reason for this effect is that in theouter part of the boundary layer less droplets are formed(lower nucleation rate) than in the core flow of the samecross section. However, these droplets grow faster andget therefore larger since the reduction of the supersatu-ration, i.e. the driving force of the growth, decreasesslower. This is, because the faster growth of the lowernumber of droplets produces less condensate than the

weaker growth of the larger number of droplets in thecore flow and thus causes a slower reduction of the su-persaturation. It has been observed that in low pressuresection occurs a decrement of the quality, beginning withvalues without greater risks (x = 98%), till reaching

lower qualities (x = 90%) in the last stage [15]. Theblades, while working with this wet steam, suffer theconstant action of the impact of the liquid microparticles,having as a consequence, the erosion of their surface (seethe example in the Figure 3 of a drop impacting on therigid surface).

The considerable quantity of steam humidity added tothe blade velocities, especially in the last one, is an im-portant factor that has influence on the appearance oferosion on the geometrical parameters of the turbine, thedesign of the blades (height, chord, axial distance, stagenumber, pass, entrance angles and exit profile, angles ofthe bladeness, etc.) and has a direct incidence on the ve-locity, as is shown in the Figure 4, where is noted in theblades the damage by the erosion phenomenon.

Figure 3. Drop impacting on the rigid surface[14].

Figure 4. Coordinates of stator blade.



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F. R. MARTNEZ ET AL.230

The steam velocity and their influence on the charac-teristics of clusters in condensed water vapor affect theperformance of the steam turbine, and the blades are oc-casionally damaged by erosion due to the interactionwith this condensed water. However, the accurate me-

chanism of the erosion is still unknown [16].As an analysis is examined a size of droplet,R = 7.52m, and a cluster compound of 26 molecules of water[17] calculated for a steam turbine of 300 MW [18]; thisaverage cluster can be dangerous for the blade. It isshown that the value obtained about the critical radiusfrom free energy is 0.0023 m and is observed the directcondensation from the vapor at a rate iof 2.22 10

21

molecules per unit interfacial area per unit time. Theycan shrink by evaporation of molecules to the vapor andby evaporation of molecules to the adsorbed layer. Alsoit is observed that the critical radius is identical for thehomogeneous and heterogeneous nucleation.

Usually, the homogeneous nucleation has more prob-able that appears and is required a less atoms in the het-erogeneous nucleation to achieve a nucleus of a radiusthat is superior to the critical, although it has the samevalue that in the homogeneous nucleation. The mean freepath of the gas molecules is , aver-age distance covered by a particle between collisionswith other moving particles, necessary to follow thegrowth of the droplets in a condensation environment,applying an energy balance around a spherical dropletmodel undergoing phase change.

2 3.06 10 ml

When droplets reaches considerable collision veloci-

ties of drops on the blade, the impact pressure of the dropPcan surpass the creep limit of the metal and produceson the surface a residual deformation. Nevertheless, ithas been determined experimentally that at smaller colli-sion velocities (300 m/s), it even causes the wearing byerosion, due to the breakage by fatigue of the boundarysurfaces by the action of the multiple shocks of the drops,which serve as concentrators of tensions and lead later tothe destruction of isolated zones and the deterioration ofthe metal of the blades. For the case of this steam turbine,the great velocities in the last stages, in the order of 500m/s, displayed loss mass in approximately 4% of the

total mass of blade, appearing cavities of 6 mm andwearing areas by erosion of impact drops of 58 190mm2 to the length of blade. The numerous microscopicsurface irregularities in the material that conform theblade, may act as nucleating sites [19].

All this values are considered in the nucleation theoryfor the calculation of energies and rates for homogeneousand heterogeneous nucleation and can compare them andunderstand their original causes. For this low pressuresteam turbine in the last stage is observed that, whenincreasing the contact angle between surface cluster and

environment increments the critical free energy of thecluster, as in the homogeneous case as in the heteroge-neous case. At the same time, increases the free energyof formation of a cluster on a surface for both cases,while decreases the net number of clusters per unit time

which grow larger than the critical size.But, it is impor-tant to remember the differences between the problemsconditions and what kind of particles are taking into ac-count or, like in this case, its not considered waterchemistry issues.

In the steam turbines the situation is that, particularly,is not possible to predict the droplet size distribution in acorrectly form only with the turbine geometry and theinlet and exhaust steam conditions. As it were observedin the last section I, in the Figure 1, exists differentstages where the phases of nucleation take form and ap-pear the homogeneous and heterogeneous cases, indicat-ing clearly the differences between levels of energy forthe born of each one. For homogeneous nucleation, thephase occurs of spontaneous way from the vapor phaseand usually needs more Tthan the heterogeneous case.Homogeneous nucleation creates droplets with the criti-cal radius of the germs, while the heterogeneous nuclea-tion creates droplets with similar size of the initial chem-istry contaminant.The understanding of the equations ofthe nucleation theory, is an essential prerequisite to cal-culate the features of the born of droplets responsible ofdangerous wetness, related to the behavior of the steamturbines with erosion problems in their blades. A littleknowledge of the physical processes involved is the main

problem for better advances. The existence of waterdroplets formation presents practical difficulty concern-ing to the behavior of steam in turbines. The impact ofdroplets on the blade surfaces is essentially based in therange of particles with sizes affected by the forces ofinertia. These droplets cannot follow the stream of thesteam flow in the blade cascade. The water becomes toescape from the stator blades in form of large drops,generally toward the suction side of the following rotorblade, causing there erosion problems. The movement ofwater on the blade channel is the distribution of velocityand local density of steam. As condition for the calcula-

tion of the drop movement, first the velocity field of thesteam in the blade cascade with a procedure suitable fortransonic condition is needed. The calculation of the ve-locity distribution permits the treatment of generation ofa stator blade mesh in a programmable code develop-ment for this work.

3. Calculation of Transonic Velocity Fields

For a calculation of the transonic stream, the time stepprocedure is suitable. In future, the ideal gas with con-



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F. R. MARTNEZ ET AL. 231stant relationship of the specific thermal capacities k isaccepted for a medium of flow, and the isentropic statechange and the well-known gas dynamics basic relationsare described.

If this condition prevails in t = 0 and if is kept as con-

stant t > 0, then an iterated transition adjusts itself to astationary condition, which is the flowing state searched.The theory determines this temporal transition, whichoffers the advantage that the problem receives a para-bolic character everywhere in the field, since the solutionin the time t + tfrom t, is sufficiently closed in the finalstate. However, first the law of change of state is ac-cepted as polytropic, in accordance with

11

,

n

p p

(1)

the index 1 always refers about flow condition. The

polytropic exponent n is given by1

.1 1p

n

n

(2)

In each case, the base factors serve to the Mach num-ber and speed sound in the flow, which provide the index1, and the small quantities with the indexR.

11

1

,p

a

(3)

11

1

,c

Ma

(4)

121 1

11

2Rp p M

,

(5)

1

11

.RRp

p

(6)

A condition for the application of the Equation (6) isthat the function of the mesh and the leading edge cross-ing compression shocks are weak.

It is accepted that in the flow, the angle 1takes place.In the zone of flow of the mesh profile the velocities ofthe compressible stream with the given variables of statebecome pressure and density of inlet and outlet planeafter is calculated

1

2 2 11

R

R R

p pc

p

,

(7)

In the outline of the profile the condition is fulfilled ifthe velocity is tangential. Thus is possible if the velocity,pressure and density of the fields regarding the size in

the inlet and outlet plane linear can be interpolated.In the closest section lmin the exit angle 2 in the fol-

lowing form can be written:11 1 1 1

2 1 2 12min2 2 2

1 1sin 1 ,

2 2is is is

lM M

t

(8)

min2sin for 1.0,is is

lM

t 2 (9)

with

1

21 .

1R

is

pM

p

(10)

Then, the theoretical exit angle 2isof the mesh turbine

results in the case of isentropic expansion on a givenpressure side. The velocities in x andy direction towardthe trailing edge are calculated

2

2

cos ,

2

sin .

2

x is

y is

c c

c c

(11)

The velocity, pressure and density fields are intro-duced as initial values for the iterative methods. Thepressure sizes p1 and p2are well-known from the givenstate of flow. Also is known c1 and c2 in each case with

p1 and p2 from the Equation (7). In Equation (2) thepolytropic efficiency p considers the friction in sum-mary way and allows to understand the friction strengthconstantly distributed in the area. It can suppose the fieldstrength per mass unit, in the direction of the increasingmeridian coordinate against the each point n'. Then is

dd d d

pF n T s h ,

(12)

d dph p , (13)

d

d 1pp

F n .

(14)

If these equations are divided by dn', then dp/dn' re-places in such a way the developing p/n', where pand n'are the total differences from inlet to outlet; then

1 pp

Fn

(15)

where is an average value of the density. Thus, thepolytropic exponent n and the friction force F can bedetermined for a given p. For the transition the continu-ity equation applied on the volume element Vkreads



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F. R. MARTNEZ ET AL.


232

1

sin cos dx yc ct V

b s (16)

The circulation is extended thereby over the wholeelement. Thus the impulse equation

( ) sin cos sind

xkx y xcV c c c

t

b s V F

p

where ij is the angle of inclination of the side thatconnects the points designated with i andj. For the rep-resentation of the calculation procedure, the dimen-sionless formulation may be introduced in addition of thefollowing definition:

1

:bBb

Stream width.

(17a) :ijija

sS

l

Length of the element.

Therefore

1sin cos sin

d

xk

x y x

cc c c p

t V

b s F

21

:a

VK

l b

Volume of the element.

(17b) 21 1 1:

pP

a M Pressure.

In the same way the impulse equation in tangential di-rection is deduced itself.

1

sin cos cos d

xk

x y y

ct

c c c p bV

1

:

Density.

s

(18) 21

:al F

c

Friction Force.

1 1

:xc

Uc

Axial Velocity.

The circulations can be represented as sums of theconnected distances sij, in each case are multiplied bythe average value integrating along the distance. TheEquation (16) is read

1 1

:yc

Vc

Peripheral Velocity.

Here, index 1 refers to the inlet level, with dependenceof time t = 0. The axial width of the mesh is la. Then theEquations (16), (17), (18) and (1) are represented in next(20), (21), (22) and (23).

1( sin cos )

2

( sin cos )

i xi ij yi ij i

j xj ij yj ij j ij

c c

c c b

b

s

(19)

1 sin cos sin cos2 i ij i ij i j ij j ij j ijM

U V B U V BK

S

1 11

sin cos sin cos sin2

j ji ii ij i ij j ij j ij i i j j ij ij

i j

U BU BUM U V U V B P B P S M

K

,

11

sin cos sin cos cos2

j ji ii ij i ij j ij j ij i i j j ij ij

i j

V BV BVM U V U V B P B P

K

S

1n

P P

and the magnitude ofUk, Vk, k in the time + andthe Equation (23) are associated toPk.

On the basis of U, V, P and into all points in themesh in a stream value the temporal derivatives Equa-tions (20)-(22) can be calculated

4. Particular Data of Stator Blade in the LastStage of Low Pressure ,

UU U

(24)

,V

V V

The presented equations previously are discretized toreach the development of the programming code of cal-culation procedure when coming out of this set of bladeswhen the flow has certain humidity degree. The main

(25)

, (26)


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F. R. MARTNEZ ET AL. 233detail is to know the behavior and the influence in thegeometry that can have this type of damages that are hadin the blades in normal operation. The set of blades mustbe analyzed of several forms: one of them is consideringthe amount of drops by cloudiness that exists in the same

steam when it begins to become water and cause dam-ages in the trailing edge of the blades stators as a set,appearing erosion problems, that they essentially causedamages in the edge of entrance of the crown rotorblades. Then is had the analysis of the influence of waterin the flow, seeing this like loss of damage of the wetsteam.

In this part of work the results are presented in ac-cording to droplet contact angleand its influence overthe characteristics of clusters conformed by certainnumber of molecules approximately. The mean valuesobtained from each case in where is taken the contactangle is shown in the Table 1.

The condensation on the last stage of this steam tur-bine shows the phase change may be governed by ho-mogeneous nucleation and the nonequilibrium process ofcondensation. It is known that condensed water vaporaffects the performance of the steam turbine, and theblades of the steam turbine are occasionally damaged byerosion due to the interaction with this condensed water.The nuclei are assumed to be spherical, chemically inert,equal in size, with a smooth surface and the interface haszero thickness.

The contact angles employment for calculating differ-ent equations presented were selected grated than zero

and less or equal to 90, due to the content of partially

wetting. The nucleation model used for introducing val-ues of calculation of the program shows that the valueobtained about the critical radius from free energy is0.0023 m and it is observed a condensate cluster with anumber of possible orientations of 26 molecules. They

Table 1. Resulted according to the contact angle.

VARIABLE = 30 = 45 = 60

R (droplet radius) 7.52 m

r * (critical radius) 0.0023 m

J(nucleation rate) 8.95 1024 8.15 1024 7.58 1024

Cr (cluster radius) 800 m

G*(critical Gibbsenergy)

1.51 1021 6.82 1020 18.37 1020

Ghom (homogeneus,Gibbs energy)

1.338 103 6.04 103 16.26 103

G(Gibbs energy) 1.33 103

T (TS T) 13.87 K

i (molec/L2*t) 2.22 1021

can shrink by evaporation of molecules to the vapor andby evaporation of molecules to the adsorbed layer.

Here is presented the particular characteristics data ofbidimensional flow in the used stator blade (Figure 4)into the program code.

Considerations of bidimensional steam flow: Subsonic-transonic, Inviscid, Compressible, Stationary, Free of friction before and later of the blade channel, Cluster as a drop is spherical, Constant diameter size of drop is 100 m, Boundary layer in surface of profile.

Flow properties of wet steam on stator blade: Inlet temperature = 64.5C, Inlet pressure = 0.245 bar,

Inlet steam quality = 0.89, Inlet flow angle = 5 degree, Inlet blade angle = 5 degree, Inlet axial velocity = 64.49 m/s, Inlet tangential velocity = 5.63 m/s, Inlet stator Mach number = 0.142, Exit temperature = 55.7C, Exit pressure = 0.163 bar, Exit steam quality = 0.892, Exit flow angle = 72.3 degree, Exit blade angle = 73.9 degree, Exit axial velocity = 83.2 m/s, Exit tangential velocity = 278 m/s, Exit Mach number = 0.655.

Considerations of code: Number of coordinates of the profile (x,y), Number of nodesx, Number of nodesy , Interval between nodes = 0.00080808, Long of the profile = 0.0495 m, Beta in rad, 0.08726.

The approximate results of calculation to the station-ary solution was effectuated several times and examined.For the demonstration of the possibility of the inflowangle changes and the influence of the stagnation point

situation, the calculation for the lattice with the poly-tropic efficiency is presented.

5. Results

It is observed that the critical radius is identical for thehomogeneous and heterogeneous nucleation. It is usuallythat the homogeneous nucleation will be more probablythat creates and it is required a less atoms in the hetero-geneous nucleation for achieving a nucleus of a radiusthat be superior to the critical, although it has the same



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F. R. MARTNEZ ET AL.234value that in the homogeneous nucleation. The size ofdrop is R = 7.52 m and the radio of the cluster thatcause damages by erosion in the rotor blades is rc = 800m with a homogeneous nucleation volume of 1.73 1010 m3and with a heterogeneous nucleation volume of

2.94 1011

m3

. For calculating the equations presentedhere it was taken a cluster with 26 molecules of water.This is an average cluster that can be dangerous for theblade, due to its size. Optical measurements in turbinesshow that the mean droplet diameter is considerably lar-ger, typically in the range 0.3 - 0.7mm, and the distribu-tion is much broader, typically from to 1.0 mm. Thedroplet temperature TP obtained as a function of dropletradius is TP = 359.12 K considering the temperature atconditions of pressure in the last stage.

In Figures 5 to 12 are showed a clear difference be-tween suction and pressure velocity and proves the ef-fects of the rear stagnation point in the flow.

In the graphic of total enthalpy (Figure 10) shows thatfor certain number of time steps, presents convergence inthe calculation. The total enthalpy is constant only in astationary system. The simplification of the equationsystem was possible introducing the constant specifictotal enthalpy for the entire computing area.

In Figure 11 the border drop course for the blade pres-sure side is showed, i.e. the course of the drop affectsdirectly before the outlet of the stator surface. The dis-tance of the border drop course from the blade increasesdirectly with the drop radius, showing the drops ejectedto the pressure side directly.

Figure 5. Velocity and pressure pattern.

Figure 6. Direction of flow in calculated zone.




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F. R. MARTNEZ ET AL. 235

Figure 8. Isobars of flow zone.


Figure 10. Total enthalpy.

Figure 11. Streamlines in blade cascades.

6. Conclusions

In this first part of the work, the erosion phenomenon isseen as a technological problem that is tried to analyze in



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F. R. MARTNEZ ET AL.236

Figure 12. Mass flow and stream mass density.

the greater possible degree. It is only possible to be di-minished, is not possible to be eliminated; therefore, thestudy of the erosion is necessary from its origin, the

analysis of the phenomena that interact in their processof formation, the harmful effect that it causes on the sur-face of the blades, the revision of different recommenda-tions from protection against the erosion and, finally, togive a proposal of its prevention. The analyze carried outin this first part of study can not be used as a base for thecalculation of the turbine stages, because the humidityinfluence over the performance and reaction degree, de-pend also on other geometric and pattern parameters:blades configuration, clearance, relation between surfaceof the blade crowns, stage to treat, etc. Therefore it isnecessary to have efficient technological procedures toavoid the damages not only in the blades but also in the

whole turbine, avoiding with this bigger numbers ofbreak downs along the year and increases in cost ofmaintenance and economical losses caused because ofthis.

For another hand, depending of flow condition andtype of design, the shape of the droplets and the slidingcoefficient that are going to determine the parametersthat have an influence over the mechanical erosion, giv-ing entrance for the investigation of prevention of theblade erosion in the body of low pressure or, at least, tocontrol it, because for the investigation and experimental

field it is necessary to have a greater knowledge of therole that the variables have on a micro and macroscopiclevel, that causes the origin of humidity.

In next second part Theoretical and NumericalAnalysis of the Mechanical Erosion in Steam Turbine

Blades. Part II, the problem display the field of veloci-ties with influence of wet in the stator blade mesh in thelow pressure section of the turbine.

7. References

[1] M. F. Rueda, V. M. Toledo, S. F. Snchez, H. J. A. Or-tega and M. A. A. Rueda, Humidity Distribution in aTwo Dimensional Stator Blade Cascade of Steam Tur-bine, 7thInternational Conference on Heat Transfer,Fluid Mechanics and Thermodynamics, Antalya, 2010.

[2] D. Braukmann, Institut fr Thermodynamic der Luft undRaumfahrt, uni-sttutgart.de.

[3] A. E. Zaryankin, V. A. Zaryankin and B. P. Simonov,Several Ways of Improving the Efficiency of the FlowPaths of the Steam Turbines, Thermal Engineering, Vol.50, No. 6, 2003, pp. 442-448.

[4] M. F. Rueda, V. M. Toledo, S. F. Snchez and M. A. A.Rueda, Calculation of Drops Distribution in Steam Tur-bine Blades, 5th European Conference of Economicsand Management of Energy in Industry, Algarve, 2009.

[5] I. J. Ford, Thermodynamic Properties of Critical Clus-ters from Measurements of Vapour-Liquid HomogeneousNucleation Rates, TheJournal of Chemical Physics, Vol.105, No. 18, 1996, pp. 8324-8332. doi:10.1063/1.472687

[6] J. L. Katz, J. A. Fisk and M. M. Rudek, Nucleation ofSingle Component Supersaturated Vapors,Nucleationand Atmospheric Aerosols 1996:Proceedings of the 14thInternational Conference on Nucleation and AtmosphericAerosols, Helsinki, 26-30 August 1996, pp. 1-10.

[7] P. P. Wegner and J.-Y. Parlange, Condensation by Ho-mogeneous Nucleation in the Vapor Phase, Naturwis-senschaften, Vol. 57, No. 11, 1970, pp. 525-533.doi:10.1007/BF00625319

[8] A. Hanna, Kinetic Effect of Cluster-Cluster Processes onHomogeneous Nucleation Rates in One- and Two-Com-ponent Systems, TheJournal of Chemical Physics, Vol.107, No. 8, 1997, pp. 3196-3203.doi:10.1063/1.474669

[9] E. E. Michaelides, Particles, Bubbles and Drops, TheirMotion, Heat and Mass Transfer, World Scientific Pub-lishing, Singapore, 2006.

[10] J. W. P. Schmelzer, Nucleation Theory and Applica-tion, Wiley, Hoboken, 2005, pp. 40.doi:10.1002/3527604790

[11] D. W. Oxtoby, Nucleation of First-Order Phase Transi-tions, Accounts of Chemical Research, Vol. 31, No. 2,1998, pp. 91-97.doi:10.1021/ar9702278

[12] V. M. Toledo and W. Riess, Vorlessung Dampf-turbi-nen, Institut fuer Stroemungsmaschinen, UniversitaetHannover, Germany, 2008.



11/11

F. R. MARTNEZ ET AL.


237

[13] J. L. Katz, Homogeneous Nucleation Theory and Ex-periment: A Survey, Pure and Applied Chemistry, Vol.64, No. 11, 1992, pp. 1661-1666.doi:10.1351/pac199264111661

[14] K. K. Haller, High-Velocity Impact of a Liquid Dropleton a Rigid Surface: The Effect of Liquid Compressibil-

ity, Thesis, Swiss Federal Institute of Technology Zurich,Zurich, 2002.

[15] P. B. Heinz, Gua Prctica para la Tecnologa de lasTurbinas de Vapor, McGraw Hill, New York, 1996.

[16] S. Yamamoto, Computation of Practical Flow Problemswith Release of Latent Heat, Elsevier, Amsterdam, 2004.

[17] M. F. Rueda, V. M. Toledo, L. G. Jarqun, S. F. Snchez andG. Polupan, Erosion Study of a Rotor Blade from a SteamTurbine, 6thInternational Conference on Heat Transfer,Fluid Mechanics and Thermodynamics, Pretoria, 2008.

[18] M. F. Rueda, V. M. Toledo, M. I. Carvajal, F. J.Abugaber and E. G. Tolentino, Estudio Terico de la

Erosin Mecnica en un labe Rotor del ltimo Paso dela Seccin de Baja Presin de una Turbina de Vapor de300 MW, Cientfica Journal, Vol. 11, No. 3, 2007.

[19] J. C. Bellows, Chemistry in the Moisture TransitionRegion of the Steam Turbine, Journal of SolutionChemistry, Vol. 32, No. 10, 2003.

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