Energy and Power En gi neering, 2011, 3, 227-237
doi:10.4236/epe.2011.33029 Published Online July 2011 (http://www.SciRP.org/journal/epe)
Theoretical and Numerical Analysis of the Mechanical
Erosion in Steam Turbine Blades. Part I
Fernando Rueda Martínez, Miguel Toledo Velázquez, Florencio Sánchez Silva, Aldo Antonio Rueda
Martínez, Samuel Alcántara Montes, Oliver Marciel Huerta Chávez
Applied Thermal and Hydraulic Engineering Laboratory, Lindavista, Mexico
Received April 1, 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 the
flow 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 last
stage 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 in
Fortran 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 pressure
section 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 as
random events due to the thermal vibration of atoms
(collisions). In terms of classical nucleation theory, the
spontaneous fluctuations lead to the formation of small
embryonic droplet that can grow beyond some critical
radius, being possible to overcome this barrier and to
hold its spontaneous growth; that is, it can only survive
and grow up if there is a reduction in free energy [1].
However, if the energy barrier to spontaneous growth is
large and the droplet cannot achieve its critical size, it
remains 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 levels
being 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 might
nucleate with undesirable effects on the performance of
the machine, including the erosion of turbine blades due
to the repeated impact on them. In the case of condensed
phases, the principal idea is that exist a bottleneck in the
transformation, 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 in
all directions: vertical, horizontal, etc., that establishes a
functional interdependence for the development of its
processes. The bottleneck is narrowest when the clusters
reach a so-called critical size. The capillarity approxima-
tion is employed, whereby the critical cluster, however
small, is considered as a scaled-down macroscopic drop-
let of the condensed phase. Until recently, the moisture
nucleation in turbines has been assumed as a homogene-
ous process with the effects of steam impurities being
negligible, as in this case of study.
Generally, depending of the conditions of work of the
turbine, 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 expansion
continues into the final stage, significant supercooling is
again possible, leading to further secondary homogene-
ous nucleation along the final rotor stage. Finally,
smaller droplets generated along the third rotor inlet and
outlet stage can be collected on blades and re-entrained
as secondary droplets into the flow at the trailing edges
of rotating components [2]. Importantly, the droplets
generated along the inlet of third rotor blades through
rotor fifth stage remain quite small, can be adequately

F. R. MARTÍNEZ ET AL. 228
approximated with no-slip assumption relative to the
continuous vapor phase.
Droplets in the last stage are entrained with sizes that
are generally greater than 100 µm 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 blade
surface, 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 impacts
against 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 the
breakage and low performance of the stages. It has often
been argued that from the thermodynamic point of view,
a cluster of drops behaves, in fact, as one large drop of
the same dimension as the cluster. Classical nucleation
theory is built on the thermodynamics treatment of drop-
lets by the capillarity approximation, where the small
droplets have the same properties as bulk condensed
phases, with bulk surface properties [5] and considered
as a drop. There also would be occasional clusters con-
taining a larger number of molecules; however, a motion
picture of these larger clusters would show that most are
very short lived; they grow rapidly and then shrink rap-
idly. Nucleation occurs when a cluster of two, three, four,
grows (fluctuates in size) to a size large enough that it
then continues to grow rather than shrink [6]. Eventually,
agglomeration by coalescence of large clusters enters
until thermodynamic equilibrium [7] colliding with each
other, forming larger clusters [8], and these drops with
several sizes always have a spherical shape, which are
forced by the surface tension and keeping constant into
the turbine, impacting on the blades and causing dam-
ages.
2. Droplets Formation in Steam Turbines
Erosion is of significance when drops impact on a hard
surface. The continuous impact of drops forms a liquid
film on the surface, which would attenuate the forces
during the impact at subsequent times and, hence, the
long-term wear on the surface [9].
In the last stages of the turbines, very high expansion
rates are achieved, leading to supercooled flow condi-
tions and nonequilibrium droplet formation by several
mechanisms that mean an impact on turbine efficiency.
The two-phase flow behavior in a low pressure section of
a conventional steam turbine beginning with the first
transition, 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 in
Figure 1.
Generally, in the third rotor stage is found heteroge-
neous nucleation transition. In the fourth stator stage can
creates 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 further
secondary homogeneous nucleation along the final rotor
stage. Finally, smaller droplets generated along the inlet
third rotor stage and output third rotor stage can collect
on blades and be re-entrained, as secondary droplets, into
the flow at the trailing edges of rotating components, in
particular. Importantly, the droplets generated along the
inlet of third rotor blades through fifth rotor stage remain
quite small, can be adequately approximated with a
no-slip assumption relative to the continuous vapor
phase.
In the last stage of the low pressure steam turbine the
droplets localized have sizes that are generally greater
than 100 µm [10] and have a considerable slip relative to
the vapor. These droplets have a significant influence on
blade erosion, and the fact that the small nucleated drop-
lets provide the source for entrainment of large droplets
into last stage, describe a highly coupled two-phase flow
system.
The process of steam expansion on the rows is very
complicated. The drop velocities are different of the
steam velocity as much by their magnitude as by their
direction; in fact, it can’t give a general scheme of the
movement of wet steam. The path of the droplets in the
channel of the blade rows can be different, as is shown in
Figure 2. In this case, the drops in the steam flow can
lose 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 drops
of 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 S
and R, respectively.

F. R. MARTÍNEZ ET AL.229
Figure 2. Path of droplets in the channel of blade rows [12].
flow; in addition, while greater are the size drops, less
will 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 than 0.1
mm), which, under the action of the friction forces of the
steam flow, is slipped slowly towards the trailing edges.
The drop that leaves of the blades of the stator rows with
smaller velocity has a direction of the relative velocity
and impacts against the suction side of the rotor
blade.
w
By consequence, on the performance of the stage the
losses due to steam (where =
TS – T) differ-
ence between the local saturation temperature TS and
measurement 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 are
characteristic for the stage altogether. With the increment
of steam pressure, the influence of the weak moisture in
the characteristics of the rows reduces the droplet dimen-
sions. The erosion can affect a considerable percent of
profile (sometimes to 0.2 - 0.3 of chord) causing the loss
of portion of the blade. Insignificant erosion even makes
change the vibration characteristics and resistance of the
blades, been the cause of the breakage, as well as the
performance 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 larger
droplets appear in the (inviscid) core flow of the same
cross section. The reason for this effect is that in the
outer part of the boundary layer less droplets are formed
(lower nucleation rate) than in the core flow of the same
cross section. However, these droplets grow faster and
get therefore larger since the reduction of the supersatu-
ration, i.e. the driving force of the growth, decreases
slower. This is, because the faster growth of the lower
number of droplets produces less condensate than the
weaker growth of the larger number of droplets in the
core flow and thus causes a slower reduction of the su-
persaturation. It has been observed that in low pressure
section occurs a decrement of the quality, beginning with
values without greater risks (x = 98%), till reaching
lower qualities (x = 90%) in the last stage [15]. The
blades, while working with this wet steam, suffer the
constant action of the impact of the liquid microparticles,
having as a consequence, the erosion of their surface (see
the example in the Figure 3 of a drop impacting on the
rigid surface).
The considerable quantity of steam humidity added to
the blade velocities, especially in the last one, is an im-
portant factor that has influence on the appearance of
erosion on the geometrical parameters of the turbine, the
design of the blades (height, chord, axial distance, stage
number, pass, entrance angles and exit profile, angles of
the bladeness, etc.) and has a direct incidence on the ve-
locity, as is shown in the Figure 4, where is noted in the
blades the damage by the erosion phenomenon.
Figure 3. Drop impacting on the rigid surface [14].
Figure 4. Coordinates of stator blade.

F. R. MARTÍNEZ ET AL. 230
The steam velocity and their influence on the charac-
teristics of clusters in condensed water vapor affect the
performance of the steam turbine, and the blades are oc-
casionally damaged by erosion due to the interaction
with 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 = 7.52
μm, and a cluster compound of 26 molecules of water
[17] calculated for a steam turbine of 300 MW [18]; this
average cluster can be dangerous for the blade. It is
shown that the value obtained about the critical radius
from free energy is 0.0023 μm and is observed the direct
condensation from the vapor at a rate βi of 2.22 × 1021
molecules per unit interfacial area per unit time. They
can shrink by evaporation of molecules to the vapor and
by evaporation of molecules to the adsorbed layer. Also
it is observed that the critical radius is identical for the
homogeneous 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 radius
that is superior to the critical, although it has the same
value that in the homogeneous nucleation. The mean free
path of the gas molecules is , aver-
age distance covered by a particle between collisions
with other moving particles, necessary to follow the
growth of the droplets in a condensation environment,
applying an energy balance around a spherical droplet
model undergoing phase change.
2
ˆ3.06 10μml

When droplets reaches considerable collision veloci-
ties of drops on the blade, the impact pressure of the drop
ΔP can surpass the creep limit of the metal and produces
on the surface a residual deformation. Nevertheless, it
has been determined experimentally that at smaller colli-
sion velocities (300 m/s), it even causes the wearing by
erosion, due to the breakage by fatigue of the boundary
surfaces by the action of the multiple shocks of the drops,
which serve as concentrators of tensions and lead later to
the destruction of isolated zones and the deterioration of
the metal of the blades. For the case of this steam turbine,
the great velocities in the last stages, in the order of 500
m/s, displayed loss mass in approximately 4% of the
total mass of blade, appearing cavities of 6 mm and
wearing areas by erosion of impact drops of 58 × 190
mm2 to the length of blade. The numerous microscopic
surface irregularities in the material that conform the
blade, may act as nucleating sites [19].
All this values are considered in the nucleation theory
for the calculation of energies and rates for homogeneous
and heterogeneous nucleation and can compare them and
understand their original causes. For this low pressure
steam turbine in the last stage is observed that, when
increasing the contact angle between surface cluster and
environment increments the critical free energy of the
cluster, as in the homogeneous case as in the heteroge-
neous case. At the same time, increases the free energy
of 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 problems
conditions and what kind of particles are taking into ac-
count or, like in this case, it’s not considered water
chemistry issues.
In the steam turbines the situation is that, particularly,
is not possible to predict the droplet size distribution in a
correctly form only with the turbine geometry and the
inlet and exhaust steam conditions. As it were observed
in the last section I, in the Figure 1, exists different
stages where the phases of nucleation take form and ap-
pear the homogeneous and heterogeneous cases, indicat-
ing clearly the differences between levels of energy for
the born of each one. For homogeneous nucleation, the
phase occurs of spontaneous way from the vapor phase
and usually needs more ΔT than 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 of
the nucleation theory, is an essential prerequisite to cal-
culate the features of the born of droplets responsible of
dangerous wetness, related to the behavior of the steam
turbines with erosion problems in their blades. A little
knowledge of the physical processes involved is the main
problem for better advances. The existence of water
droplets formation presents practical difficulty concern-
ing to the behavior of steam in turbines. The impact of
droplets on the blade surfaces is essentially based in the
range of particles with sizes affected by the forces of
inertia. These droplets cannot follow the stream of the
steam flow in the blade cascade. The water becomes to
escape from the stator blades in form of large drops,
generally toward the suction side of the following rotor
blade, causing there erosion problems. The movement of
water on the blade channel is the distribution of velocity
and local density of steam. As condition for the calcula-
tion of the drop movement, first the velocity field of the
steam in the blade cascade with a procedure suitable for
transonic condition is needed. The calculation of the ve-
locity distribution permits the treatment of generation of
a 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 step
procedure is suitable. In future, the ideal gas with con-

F. R. MARTÍNEZ ET AL.231
stant relationship of the specific thermal capacities k is
accepted for a medium of flow, and the isentropic state
change and the well-known gas dynamics basic relations
are described.
If this condition prevails in t = 0 and if is kept as con-
stant t > 0, then an iterated transition adjusts itself to a
stationary condition, which is the flowing state searched.
The theory determines this temporal transition, which
offers the advantage that the problem receives a para-
bolic character everywhere in the field, since the solution
in the time t + Δt from t, is sufficiently closed in the final
state. However, first the law of change of state is ac-
cepted as polytropic, in accordance with
1
1
,
n
pp







(1)
the index 1 always refers about flow condition. The
polytropic exponent n is given by
1.
11
p
n
n




(2)
In each case, the base factors serve to the Mach num-
ber and speed sound in the flow, which provide the index
1, and the small quantities with the index R.
1
1
1
,
p
a 

 (3)
1
1
1
,
c
Ma  (4)
1
2
11
1
1
2
R
pp M






 


,


(5)
1
1
1
.
R
R
p
p





(6)
A condition for the application of the Equation (6) is
that the function of the mesh and the leading edge cross-
ing compression shocks are weak.
It is accepted that in the flow, the angle

1 takes place.
In the zone of flow of the mesh profile the velocities of
the compressible stream with the given variables of state
become pressure and density of inlet and outlet plane
after is calculated
1
221
1
R
RR
pp
cp














,


(7)
In the outline of the profile the condition is fulfilled if
the 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:
1
11 11
21 21
2 min
222
11
sin1 ,
22
isis is
lMM
t











 



 


 


(8)
min
2
sinfor 1.0,
is is
lM
t
 
2
(9)
with
1
21.
1
R
is
p
Mp



















(10)
Then, the theoretical exit angle 
2is of the mesh turbine
results in the case of isentropic expansion on a given
pressure side. The velocities in x and y direction toward
the trailing edge are calculated
2
2
π
cos ,
2
π
sin.
2
xis
yis
cc
cc



 



 



(11)
The velocity, pressure and density fields are intro-
duced as initial values for the iterative methods. The
pressure sizes p1 and p2 are well-known from the given
state of flow. Also is known c1 and c2 in each case with
p1 and p2 from the Equation (7). In Equation (2) the
polytropic efficiency

p considers the friction in sum-
mary way and allows to understand the friction strength
constantly distributed in the area. It can suppose the field
strength per mass unit, in the direction of the increasing
meridian coordinate against the each point n'. Then is
d
ddd
p
Fn Tsh  ,

 (12)


dd
p
hp,

  (13)

d
d1
p
p
Fn  .

 (14)
If these equations are divided by dn', then dp/dn' re-
places in such a way the developing Δp/Δn', where Δp
and Δn' are the total differences from inlet to outlet; then

1p
p
Fn 


 
 (15)
where

is an average value of the density. Thus, the
polytropic exponent n and the friction force
F

can be
determined for a given ηp. For the transition the continu-
ity equation applied on the volume element ΔVk reads

F. R. MARTÍNEZ ET AL. 232

1sincos d
xy
cc
tV


  
 

bs (16)
The circulation is extended thereby over the whole
element. Thus the impulse equation

() sin cossin
d
xk
xyx
c
Vccc
t
bs VF




p




where ij

is the angle of inclination of the side that
connects the points designated with i and j. For the rep-
resentation of the calculation procedure, the dimen-
sionless formulation may be introduced in addition of the
following definition:
  





1
:
b
Bb


Stream width.
(17a) :
ij
ij
a
s
Sl

 Length of the element.
Therefore


1sin cossin
d
xk
xyx
ccccp
tV
bs F








 






2
1
:
a
V
Klb




 Volume of the element.
(17b) 2
11 1
:
p
PaM

 Pressure.
In the same way the impulse equation in tangential di-
rection is deduced itself.


1sin coscosd
xk
xy y
c
t
cc cpb
V



 






1
:



 Density.
s

(18) 2
1
:
a
lF
c

 Friction Force.
11
:
x
c
Uc


 Axial Velocity.
The circulations can be represented as sums of the
connected distances Δsij, in each case are multiplied by
the average value integrating along the distance. The
Equation (16) is read 11
:
y
c
Vc


 Peripheral Velocity.
Here, index 1 refers to the inlet level, with dependence
of time t = 0. The axial width of the mesh is la. Then the
Equations (16), (17), (18) and (1) are represented in next
(20), (21), (22) and (23).
1(sin cos)
2
(sin cos)
ixiij yiij i
j
xjij yjijjij
cc
cc b
 
 





b
s 
(19)

1sin cossincos
2iijiijijijjijj ij
MUVBU VB
K


 






S

1 1
1sincossincossin
2
jj
ii
iijiijjijjiji ijjijij
ij
UB
UB UMUVUVBPBPS M
K


 

 

 


 

 

 

,

1
1sin cossincoscos
2
jj
ii
iijiijjijjiji ijjijij
ij
VB
VB
V
M
UVU VBPBP
K


 

 

 


 

 

 
S
1
n
PP




and the magnitude of Uk, Vk, 
k in the time
 +   and
the Equation (23) are associated to Pk.
On the basis of U, V, P and  into all points in the
mesh in a stream value  the temporal derivatives Equa-
tions (20)-(22) can be calculated
4. Particular Data of Stator Blade in the Last
Stage of Low Pressure

,
U
UU






 

 (24)

,
V
VV






 

The presented equations previously are discretized to
reach the development of the programming code of cal-
culation procedure when coming out of this set of blades
when the flow has certain humidity degree. The main
 (25)







 

 , (26)

F. R. MARTÍNEZ ET AL.233
detail is to know the behavior and the influence in the
geometry that can have this type of damages that are had
in the blades in normal operation. The set of blades must
be analyzed of several forms: one of them is considering
the 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 cause
damages in the edge of entrance of the crown rotor
blades. Then is had the analysis of the influence of water
in the flow, seeing this like loss of damage of the wet
steam.
In this part of work the results are presented in ac-
cording to droplet contact angle θ and its influence over
the characteristics of clusters conformed by certain
number of molecules approximately. The mean values
obtained from each case in where is taken the contact
angle 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 of
condensation. It is known that condensed water vapor
affects the performance of the steam turbine, and the
blades of the steam turbine are occasionally damaged by
erosion 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 has
zero 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 value
obtained about the critical radius from free energy is
0.0023 µm and it is observed a condensate cluster with a
number of possible orientations of 26 molecules. They
Table 1. Resulted according to the contact angle.
VARIABLE θ = 30˚ θ = 45˚ θ = 60˚
R (droplet radius) 7.52 μm
r * (critical radius) 0.0023 μm
J (nucleation rate) 8.95 × 1024 8.15 × 1024 7.58 × 1024
C
r (cluster radius) 800 μm
G* (critical Gibbs
energy) 1.51 × 10–21 6.82 × 10–20 18.37 × 10–20
Ghom (homogeneus,
Gibbs energy) 1.338 × 10–3 6.04 × 10–3 16.26 × 10–3
G (Gibbs energy) 1.33 × 10–3
T (TS – T) 13.87 K

i (molec/L2*t) 2.22 × 1021
can shrink by evaporation of molecules to the vapor and
by evaporation of molecules to the adsorbed layer.
Here is presented the particular characteristics data of
bidimensional 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 μm,
 Boundary layer in surface of profile.
Flow properties of wet steam on stator blade:
 Inlet temperature = 64.5˚C,
 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 = 55.7˚C,
 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 nodes x,
 Number of nodes y ,
 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 inflow
angle 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 the
homogeneous and heterogeneous nucleation. It is usually
that the homogeneous nucleation will be more probably
that creates and it is required a less atoms in the hetero-
geneous nucleation for achieving a nucleus of a radius
that be superior to the critical, although it has the same

F. R. MARTÍNEZ ET AL. 234
value that in the homogeneous nucleation. The size of
drop is R = 7.52 µm and the radio of the cluster that
cause damages by erosion in the rotor blades is rc = 800
µm with a homogeneous nucleation volume of 1.73 ×
10−10 m3 and with a heterogeneous nucleation volume of
2.94 × 10−11 m3. For calculating the equations presented
here it was taken a cluster with 26 molecules of water.
This is an average cluster that can be dangerous for the
blade, due to its size. Optical measurements in turbines
show that the mean droplet diameter is considerably lar-
ger, typically in the range 0.3 - 0.7 mm, and the distribu-
tion is much broader, typically from to 1.0 mm. The
droplet temperature TP obtained as a function of droplet
radius is TP = 359.12 K considering the temperature at
conditions 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 that
for certain number of time steps, presents convergence in
the calculation. The total enthalpy is constant only in a
stationary system. The simplification of the equation
system was possible introducing the constant specific
total 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 affects
directly before the outlet of the stator surface. The dis-
tance of the border drop course from the blade increases
directly with the drop radius, showing the drops ejected
to the pressure side directly.
Figure 5. Velocity and pressure pattern.
Figure 6. Direction of flow in calculated zone.
Figure 7. Velocity and pressure pattern.

F. R. MARTÍNEZ ET AL.235
Figure 8. Isobars of flow zone.
Figure 9. Velocity and pressure pattern.
Figure 10. Total enthalpy.
Figure 11. Streamlines in blade cascades.
6. Conclusions
In this first part of the work, the erosion phenomenon is
seen as a technological problem that is tried to analyze in

F. R. MARTÍNEZ 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, the
study of the erosion is necessary from its origin, the
analysis of the phenomena that interact in their process
of 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, to
give a proposal of its prevention. The analyze carried out
in this first part of study can not be used as a base for the
calculation of the turbine stages, because the humidity
influence over the performance and reaction degree, de-
pend also on other geometric and pattern parameters:
blades configuration, clearance, relation between surface
of the blade crowns, stage to treat, etc. Therefore it is
necessary to have efficient technological procedures to
avoid the damages not only in the blades but also in the
whole turbine, avoiding with this bigger numbers of
break downs along the year and increases in cost of
maintenance and economical losses caused because of
this.
For another hand, depending of flow condition and
type of design, the shape of the droplets and the sliding
coefficient that are going to determine the parameters
that have an influence over the mechanical erosion, giv-
ing entrance for the investigation of prevention of the
blade erosion in the body of low pressure or, at least, to
control it, because for the investigation and experimental
field it is necessary to have a greater knowledge of the
role that the variables have on a micro and macroscopic
level, that causes the origin of humidity.
In next second part “Theoretical and Numerical
Analysis 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 the
low pressure section of the turbine.
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