International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 5, May 2013)
A New Approach for the Study of Silt Erosion of Hydro
Turbine
H. N. Patel1, S. K. Singal2, R. P. Saini2
Alternate Hydro Energy Centre, Indian Institute of Technology Roorkee, Uttaranchal 247667, India
Sundararajan and Shewmon [1] have suggested that
during erosion material loss from a metal surface occurs
when a critical facture strain is achieved at the surface.
There are some research work done on the silt erosion of
hydro turbines and developed correlation of erosion rate
of turbine with respect to operating condition and
effecting parameters of the silt. All the parameters
responsible for silt erosion of turbine were not considered
in these models. There are so many research work done
in this field and mathematical model were developed to
find out the erosion rate of turbine in terms of silt size,
concentration, flow velocity, turbine material etc. The
models are developed on the basis of experimental study.
This paper is organised as follows. In section II,
factors affecting silt erosion are described. In section III,
mathematical erosion model is presented, in section IV,
calculation for eroded material verified with
experimental results are presented, In section V, results
and discussions are presented and in section VI,
conclusions are presented.
Abstract— Turbine is the most important part of hydro
power plant which converts the potential energy of water
into mechanical energy. The presence of silt in water erodes
the turbine material. Erosion of turbine decreases the
performance of turbine, life of the turbine as well as loss of
power generation. This paper presents a new approach for
the study of silt erosion of hydro turbine. In this study,
weight of eroded material of turbine have been determined
by employing criterion of plastic strain which include
parameters (silt size, silt hardness, concentration of silt,
flow velocity, hardness of turbine material) affecting silt
erosion of turbine. Results have been verified with
experimental work for Pelton turbine having 16 buckets
made up of brass material. It is seen that the results of
analytical study matches with the experimental work.
Keywords- silt erosion, plastic strain, hydro turbine, Silt
effecting parameter and Mass loss.
I. INTRODUCTION
Hydropower as a regenerative energy source is of
increasing importance for future sustainable power
generation. The increasing worldwide demand for
electric power resulted in an intensified utilization of
available hydropower resources. Most of the water
resources contain silt. The presence of silt particles in the
water flow often causes abrasive degradation of
components of hydraulic machinery exposed to the flow.
In particular, stay and guide vanes, turbine blades and
labyrinth seals bear high risks of being damaged by
abrasive processes. Among all the parts, runner blades of
turbine are most affected. The degradation of these parts
results in considerable reduction of performance of the
power plant. It also leads to reduced lifetime which in
turn reduces time between overhauls [5]. The more
number of repair periods decreases the total energy
production, too.
Generally, erosion damage is considered as the gradual
removal of material caused by repeated deformation and
cutting actions [13]. Silt erosion is designated as abrasive
wear. This type of wear will break down the oxide layer
on the flow guiding surfaces and partly make the surfaces
uneven which may also be the origin for cavitation
erosion [6]. Sand erosion therefore may be both releasing
and contributing cause for damages that are observed in
power plants with a large transport of wearing
contaminants in the water flow. The actual mechanism of
erosive wear was not fully understood. Therefore, a
simple, reliable and generalized quantitative model for
erosion could not be developed.
II. P ARAMETERS EFFECTING S ILT EROSION IN
T URBINES
The sediment erosion damage is due to the dynamic
action of sediment against a solid surface. Characteristics
of the sediment, fluids (carrying sediments) and base
material are jointly responsible for sediment erosion. The
erosion intensity depends on followings.
A. The Sediment Type and Its Characteristics
The intensity of erosion is directly proportional to the
size of the particles. Particle sizes above 0.2 to 0.25 mm
are extremely harmful [7]. The fine sediment can also be
dangerous, if the turbine is operating under high head.
Generally, particle shapes are described qualitatively
such as round, angular and semi‐round based on visual
observation. Sharp and angular particles cause more
erosion in comparison to rounded ones. Round shape of
silt particle have been considered in the analysis.
The intensity of the erosion is also directly
proportional to the hardness of particles (irrespective of
sizes) [8-12].
The sediment concentration is one of the dominating
factor influencing erosive wear rates. It can be
represented in terms of percentage of particles in a given
fluid mass (or volume). Especially for river
sedimentation, concentration is usually expressed in
grams per liter (g/l).
599
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 5, May 2013)
However, often parts per million (ppm) by weight is
used, which is equivalent to mg/l, with the approximation
of 1,000 ppm equal to 1 kg/ m3 of water being normal
usage (1,000 ppm is equivalent to 0. 1%). Erosive wear
rate is proportional to the concentration up to a certain
limiting value of the wear [5].
III. MATHEMATICAL EROSION M ODEL
A new theoretical model is proposed for the erosion of
metals by particles at normal incidence. The model
employs a criterion of critical plastic strain to determine
when the material will be removed. This critical plastic
strain is defined as the strain at which the deformation in
the target localize sand hence results in the lip formation
[1]. This model is used for mechanical application and
not used for hydro turbines. It can be used for hydro
turbines which are operating under silty water. This
model have been for the hydro turbine for calculation of
mass loss and obtained results have been verified with
mass loss obtained by the experiment carried out on the
Pelton turbine of brass material.
The erosion rate depends strongly on the magnitude of
the deforming volume. The plastic deformation spreads
on the target surface is related to the impact crater area,
i.e. proportional to crater radius (W), while the depth to
which the deformation spreads depends on the crater
depth (d). Thus the plastic volume V, should be
proportional to W2d, i.e. to the crater volume Vc, [1]
Thus
V = α Vc
B. Characteristics of Fluids
The main characteristics of fluids include velocity and
acceleration of water carrying sediment, impingement
angle, media of the flow, temperature, and turbulence.
The effect of each characterizes on erosive wear is
important.
(a) Velocity of Water Carrying Sediment
In actual practice, material damage due to plastic
deformation and cutting occur simultaneously and the
ratio of these damage mechanisms depends on the
velocity of particle and the impingement angle together
with other parameters [14]. Up to certain velocity, also
referred as critical velocity or threshold velocity, the
particle cannot skid on the surface due to friction and
cutting action does not take place. As the velocity
increases higher than critical velocity, both cutting and
plastic deformation component increases, which amplify
the erosion rate drastically.
=
(b) Impingement Angle
The impingement angle is defined as the angle
between the eroded surface and the trajectory of the
particle just before impacting a solid surface [15]. If the
particles are moving parallel to the surface, impingement
angle is almost 0 ° and minor erosion may take place.
When particles are moving normal to the surface, than
the impingement angle is 90 °.
(1)
Where, α is a constant of the order of unity. „N‟ is
number of particle strike on the surface of target material.
„r‟ is the radius of the particle which strike on the surface
in meter. „ρb‟ is the density of particle in Kg/m3. „ʋ‟ is
velocity of particle through which it strikes over the
surface. „C‟ is the temperature dependence of the shear
modulus.
The relation of the C with melting point
temperature(Tm) of the metal is given below.
(c) Effect of Temperature on Erosive Wear
The primary effect of temperature in wear is to soften
the eroded material and increase wear rates [5].
C=
C. Characteristics of the Base Material
The material used for the turbine components is
equally important factor in the sediment erosion damage.
Hardness of the material, its chemical composition,
microstructure and its work hardening property influence
the intensity of erosion. The choice of the material for a
particular component is to be made considering its ability
to meet the functional requirements like impact strength
and ability to withstand cyclic loading in addition to its
wear resistance. Experience has shown that it is sufficient
for components, which are not very susceptible to
abrasion, such as spiral casings, nozzle pipes and draft
tubes, to be made of plain structural steel or castings of
adequate strength, if their wetted surfaces are protected
by a tough, elastic coating. Experience also indicates that
the erosion resistance of stainless steel is very good
compared to other materials [16].
(2)
K is the strength coefficient. In the literature, the
erosion rate is invariably correlated with the static
hardness Hs of the target material. By contrast, the
present model is derived in terms of the strength
coefficient K. Thus an expression relating K and Hs is
required. K represents the flow stress of metal or alloy at
high strains, especially. For face cubic centre (f.c.c)
metals, which exhibit a saturation of the flow stress, K
should correspond roughly to this limiting strength. The
limiting strengths for a wide range of metals and alloys
have been collected by Moore et al. [3]. It is seen that K
and Hs have a linear relation of the form
K=AHs
Where Hs is the static hardness of the metal or alloy.
The value of A depends on the nature of the alloy.
600
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 5, May 2013)
Table 2.
Required parameters
Typical values of A are as follows: pure metals, A= 1.2
- 2.0; substitution solid solution alloys, A = 0.9 - 2.0;
steel (quenched and tempered), A = 0.6 - 0.7;
precipitation hardened, A = 0.3 -0.5. For the brass
material A is taken as 1.
„Єc‟ is the magnitude of the critical strain at which
localization of deformation and hence lip formation
occurs, and its magnitude can be find out by the equation
given below.
Єc =
Parameters
Type of silt
Density
quartz
(3)
Where nc, is the instantaneous strain-hardening
coefficient at a strain of Єc .The value of the exponent p
as a function of S and ni (the initial strain- hardening
exponent). Where S is a constant in the range of 0 - 0.5.
And ni is the initial apparent strain-hardening exponent.
For b.c.c. metals, S should lie in the range 0 - 0.1.
ɑ=
(4)
The value of the exponent t determines the steepness
of the strain gradient associated with each impact. Under
steady state erosion conditions, the strain increments
caused by successive impacts super-impose on each
other. Nevertheless, since the accumulated strain is the
sum of all the individual strain increments, as a first
approximation, it can be assumed that it will vary with
depth in the same fashion as the individual strain
increments, thus the variation in strain with depth for
eroded samples can be used to determine the value of t.
Such strain-depth data are not readily available in the
literature. The data of Ives and Ruff [2] for a copper
target indicate that t should lie in the range 4 - 6.
IV. ANALYTICAL RESULTS
of
2540 Kg/m3
Average Silt size
Concentration
Material
of
turbine buckets
302μm
10000ppm
Brass
Density of brass
8490 Kg/m3
Specific heat of
brass(Cp)
Melting
point
temperature (Tm)
strength
coefficient
of
brass (K)
Temperature
dependence
shear modulus
(C)
Strain-hardening
exponent (n)
Critical Strainhardening
exponent (nc)
310 J/Kg.K
Remark
In experiment 90.37% silt
is quartz.
If density is increase than
hardness of material is
increase so it is related to
hardness of silt.
For
the
experiment
material for brass is taken
so verified erosion weight
with it property of brass is
taken into account.
If density is increase than
hardness of material is
increase so it is related to
hardness of material.
1163K
310MPa
3.92 × 10-4
Shear modulus is depends
on
melting
point
temperature of material.
0.49
0.3
The results obtained by using the equations (1)-(4) and
experimental result comply each other. Parameters taken
for the calculation of eroded material are same as the
parameters has been used in experimental study.
Experiment is carried out for the Pelton turbine of brass
material. The turbine has 16 number of bucket. Erosion
of the turbine has been determined by striking the water
with silt of average size 302μm and 10000ppm silt
concentration. Operating head of the turbine is 45m and
discharge 0.00378cumec. Erosion results are taken at
every 2 hour. Mass losses of the buckets are given below
in Table 3.
The equations (1), (2), (3) and (4) have been used for
calculation of eroded material of turbine. The operating
parameters used for the calculation of weight loss of
turbine due to silt erosion are shown in table 1. The
parameters required for calculation of weight of silt
eroded material of Pelton turbine are given in Table 2.
Table1
Operating parameters
Parameters
Head (H)
Discharge (Q)
Flow Velocity (v)
Pitch circle diameter
Nozzle diameter
Number of buckets
Values
Quartz
45.2m
2.09 × 10-3 cumec
26.62 m/s
245mm
10mm
16
601
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 5, May 2013)
Table 3:
experimental mass loss from the turbine buckets [4]
The model employs a criterion of critical plastic strain
to determine when the material will be removed. This
critical plastic strain is defined as the strain at which the
deformation in the target localize sand hence results in
the lip formation.
This model used for mechanical application. Now it
has been used for hydro turbines. It has been found that it
can be used for hydro turbines operating under silty
water. In this study, mass loss due to erosion has been
determined analytically by using the model as well as
experimentally.
It has been seen that the theoretical model can be
satisfactorily use for erosion assessment of turbine. It has
also been found that the silt erosion is directly
proportional to concentration level.
REFERENCES
[1 ] G. Sundararajan and P. G. Shewmon, “A new model for the
erosion of metals at normal incidence”, Wear, 84 (1983) 237 –
258.
[2 ] L. K. Ives and A. W. Ruff, ASTM Spec. Tech. PubJ. 664, 1979,
p. 5.
[3 ] M. A. Moore, R. C. D. Richardson and D. G. Attwood, Metall,
Trans., 3 (1972) 2435.
[4 ] M.K. Padhy and R.P. Saini, “Study of silt erosion on performance
of a Pelton turbine”, PhD thesis. AHEC, IIT Roorkee (2011).
[5 ] Hari Prasad Neopane, “Sediment erosion in Hydro Turbines”,
PhD thesis, Waterpower Laboratory,Department of Energy and
Process Engineering, Norwegian University of Science and
Technology (NTNU), Norway, February 2007 to March 2010.
[6 ] H. Brekke, Hydraulic design of turbines, in: C.G. Duan, V.Y.
Karelin (Eds.), “Abrasive Erosion and Corrosion of Hydraulic
Machinery”, ICP, London, 2003.
[7 ] J. Sato, K. Usami, T. Okamura, S. Tanaba, “Basic studies of
coupled damage caused by silt abrasion and cavitation erosion”,
ASME FED 136 (1992).
[8 ] Zu, J. B., Hutchings, I. M., and Burstcin, G. T., “Design of slurry
erosion test rig”, Wear, 1990, 140, 331–344.
[9 ] Feng, Z. and Ball A., “The erosion of four materials using seven
erodents – towards an understanding”, Wear, 1999, 233–235,
674–684.
[10 ] Tsai W., Humphrey J. A. C., and Cornet I. “Experimental
measurement of accelerated erosion in a slurry pot tester”, Wear,
1981, 68, 289–303.
[11 ] Levy A. V. and Cliik P. “The effects of erodent composition and
shape on the erosion of steel”, Wear, 1983, 89, 151–162.
[12 ] Liebhard M. and Levy A. “The effect of erodent particle
characteristics on the erosion of metals”, Wear, 1991, 151, 381–
390.
[13 ] Hutchings I. M. Tribology-friction and wear of engineering
materials, 1992 (Arnold, Pans).
[14 ] Mack, R., Drtina, P., and Lang, E. “Numerical prediction of
erosion on guide vanes and in labyrinth seals in hydraulic
turbines”, wear, 1999, 233–235, 685–691.
[15 ] G.P. Tilly, Treatise on Material Science and Technology, vol. 13,
Academic Press Inc., 1977, pp. 287–319.
[16 ] Akhilesh K. Chauhan, D.B. Goel, S. Prakash. “Solid particle
erosion behaviour of 13Cr–4Ni and 21Cr–4Ni–N steels”, Journal
of Alloys and Compounds 467 (2009) 459–464.
The amount of analytically determined eroded material
weight is 0.138gm and the weight loss found from the
experiment is 0.1369gm.
The mass loss has been calculated by using equations
(1)-(4) at varying concentration 1000 ppm to 10000 ppm
by keeping other parameters constant. The variation of
mass loss with different concentration level is shown in
Figure 1.
Figure 1.Mass loss (gm) vs concentration (ppm)
Figure 1 indicates that if concentration of silt
increases, mass loss from the turbine also increases.
From the model it is seen that mass loss from the turbine
surface is directly proportional to the silt size, density of
silt (hardness of silt), velocity of flow, silt concentration
and inversely proportional to the density of turbine
material (hardness of turbine material).
V. CONCLUSIONS
A new theoretical model was used for the assessment
of erosion of metals by silt particles at normal incidence.
602