Introduction to cavitation in hydraulic machinery

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Scientific Bulletin of the
Politehnica University of Timisoara
Transactions on Mechanics Special issue
The 6th International Conference on
H
y
draulic Machiner
y
and H
y
drod
y
namics
Timisoara, Romania, October 21 - 22, 200
4
INTRODUCTION TO CAVITATION IN HYDRAULIC MACHINERY
François AVELLAN, Professor
Laboratory for Hydraulic Machines, School of Engineering
EPFL Swiss Federal Institute of Technology Lausanne
Avenue de Cour 33 Bis, CH-1007, Lausanne, Switzerland
Tel.: +41 21 693 2524, Fax: +41 21 693 3554, Email: francois.avellan@epfl.ch
ABSTRACT
Design, operation and refurbishment of hydraulic
turbines, pumps or pump-turbine are strongly
related to cavitation flow phenomena, which may
occur in either the rotating runner-impeller or the
stationary parts of the machine. The paper presents
the cavitation phenomena featured by fluid
machinery including type of cavity development
related to the specific speed of machines in both
pump and turbine mode, the influence of the
operating conditions, such as load, head and
submergence. Therefore, for each type of cavitation
illustrated by flow visualization made at the EPFL
testing facilities, the influence of cavitation
development on machine efficiency, operation and
integrity are discussed.
KEYWORDS
Cavitation, Hydraulic Machinery and Systems,
Model Testing
NOMENCLATURE
A [m2] Area of the Flow Cross Section
Q
C
A
= [ms-1] Mean Flow Velocity
Cm [ms-1] Meridian Velocity Component
Cu [ms-1] Circumferential Velocity Comp.
c
pp
Cp E
ρ
−
= [-] Static Pressure Factor
D [m] Runner Reference Diameter
1
EgHgH=−
2
[Jkg-1] Specific Hydraulic Energy
E
Fr
g
D
= [-] Froude Number
NPSE [Jkg-1] Net Positive Suction Energy
P [W] Mechanical Power of the Machine
h
P
QE
ρ
=
[W] Machine Hydraulic Power
Q [m3s-1] Discharge
2
D
R
=
[m] Runner Reference Radius
UR
ω
=
[ms-1] Circumferential Velocity
WCU
=
−
u
ururur
[ms-1] Relative Flow Velocity
Z [m] Elevation
a
Z
[m] Elevation of the Tail Water Level
ref
Z
[m] Machine Reference Elevation
rd
e [-] Factor of Specific Energy Losses
for the Machine Draft Tube
k [-] Geometric Factor
g
[ms-2] Acceleration Due to Gravity
2
2
p
C
gH gZ
ρ
=+ +
[Jkg-1] Mean Specific Energy
s
r
hZZ
a
=
− [m] Machine Setting Level
n [s-1] Speed of Revolution
p [Pa] Absolute Static Pressure
a
p [Pa] Atmospheric Pressure
v
p [Pa] Vapor Pressure
r
g
H [Jkg-1] Specific Energy Loss
v
Epp
E
χρ
−
= [-] Local Cavitation Factor

2
c
ψ
κ
ϕ
= [-] Cavitation Number
22
2E
R
ψω
= [-] Specific Hydraulic Energy Coeff.
22
2
cNPSE
R
ψω
= [-] Net Positive Suction Specific
Hydraulic Energy Coeff.
22
2r
r
g
H
R
ψω
= [-] Energy Loss Coefficient
η
[-] Efficiency
3
Q
R
ϕπω
= [-] Flow Coefficient
0
ϕ
[-] Whirl Free Flow Coefficient
ρ
[kgm-3] Water Density.
σ
[-] Thoma Number
i
σ
[-] Value of
σ
corresponding to the
onset of cavities
0
σ
[-] Lowest value of
σ
for which the
efficiency remains unchanged as
compared to cavitation free op.
1
σ
[-] Lowest value of
σ
as compared to
cavitation free operation for
which an efficiency drop of 1%
is noticed
ω
[rads-1] Runner Angular Velocity
Subscripts and Superscripts
1 High Pressure Side of the Machine
2 Low Pressure Side of the Machine
c Low Pressure Side of the Runner
1. INTRODUCTION
Design, operation and refurbishment of hydraulic
turbines, pumps or pump-turbine are strongly
related to cavitation flow phenomena, which may
occur in either the rotating runner-impeller or the
stationary parts of the machine. The economic trend
to increase the specific power of the machine
combined with the modern operating conditions to
operate the machine over an extended range of
discharge and specific energy challenges the
scientific community to develop advanced
knowledge of cavitation physics for this type of
machines. The paper presents the cavitation
phenomena featured by fluid machinery including
type of cavity development related to the specific
speed of machines in both pump and turbine mode,
the influence of the operating conditions, such as
load, head and submergence. Therefore, for each
type of cavitation illustrated by flow visualization
made at the EPFL testing facilities, the influence of
cavitation development on machine efficiency,
operation stability and integrity are discussed.
After introducing the general definitions and
notations in use in the field of hydraulic machinery,
we describe how the level setting of a hydraulic
machine through so called cavitation tests of
reduced scale models. Then we present for each
type of machines, storage pumps or pump turbines,
Francis turbines and Kaplan or Bulb turbine the
different types of cavitation developments and the
resulting performance alteration and risk of
erosions.
2. MODEL TESTING
2.1. General definition and notation
We examine in this paper the case of reaction
hydraulic machines including hydro-turbine, storage
pump or pump-turbine. Irrespective of the flow
direction, the subscript 1 defines the high pressure
reference section of the machine and the subscript 2
the low pressure reference section, as defined Fig.
1. The low-pressure section of the runner is quoted
with the subscript .
c
2
1
Fig. 1 General sketch of a run-off power plant with
Kaplan Turbines.
By introducing , the absolute pressure,
p
Z
, the
elevation of a point and the mean velocity
defined by the ratio between the discharge and
the section area ,
CQ
A
g
H, the mean specific
hydraulic energy of a given flow passage cross
section, is defined as:
2
2
p
C
gH gZ
ρ
=+ + [Jkg-1]
where
ρ
is the water density and
g
the gravity
acceleration.
Therefore, the specific hydraulic energy of the
machine is defined as the difference of the mean
specific energy values between the high and the
low-pressure limiting sections of the machine.
E
12
EgHgH
=
−

The breakdown of the expression of the mean
specific hydraulic energy gives the following
expression for : E
22
112
2
122
pCp C
EgZ gZ
ρρ
⎡⎤⎡
=++ −++
⎢⎥⎢
⎣⎦⎣
2
⎤
⎥
⎦
[Jkg-1]
The product of the discharge by the machine
specific energy then defines the hydraulic power h
P
of the machine
h
P
QE
ρ
= [W]
The mechanical power of the machine including
the mechanical power dissipated in guide bearings,
thrust bearings and shaft seals of the hydraulic
machine, is related to the hydraulic power by the
overall efficiency,
P
η
, of the machine by the
following definitions:
h
P
P
η
=for a pump and
h
P
P
η
=for a turbine.
Geometrical and kinematical similarity principles
allow defining the dimensionless terms, which
determine the hydraulic characteristics of the
machine.
The angular velocity
ω
and the reference radius
of the machine runner/impeller define the reference
area
R
2
R
π
and the reference specific kinetic
energy 1
222
R
ω
, which in turns provide the definition
of
ϕ
and
ψ
, the dimensionless discharge and energy
coefficients.
3
Q
R
ϕπω
= 22
2E
R
ψω
=
All along this paper, we will use preferably these
coefficients since they are conveniently directly
proportional to the discharge and the specific
energy . Q
E
Therefore, for any machine at a given
α
setting, the
opening angle of the guide vanes the discharge-
energy relations will collapse to a single function
whatever the runner/impeller rotational speed. For
every opening angle
α
, we can plot the
ϕ
-
ψ
characteristic as per Fig. 2;
()
,
ψψϕ
α
=
Thus, the set of discharge and specific energy
coefficients,
ϕ
,
ψ
, and,
α
, the opening angle of the
guide vanes, defines the operating conditions, for
which we can express the efficiency :
(
)
,,
ηηϕψ
α
=
In a similar way, we can plot on the diagram,
ϕ
-
ψ
,
the contours of efficiency iso-values to define the
so-called efficiency hill chart of the machine, see
Fig. 2.
85 %
90,5 %
91,5 %
80%
20.0
25.0
85%
91 %
80 %
70 %
0,14 0,16 0,18 0,20 0,22 0,24 0,26 0,28 0,30 0,32 0,34
0.5
0.7
0.9
1.1
1.3
ϕ
(-)
ψ
(-)
90 %
Fig. 2 Typical hill chart of a Francis turbine,
0.500
ν
=
.
For real flow, viscous and turbulence dissipation
influences the machine efficiency and leads to the
so-called scale effect between reduced scale model
and full-scale prototype.
2.2. General Model tests
According to IEC 60193 standard, [1], model tests
require that the geometric, the kinematics and the
dynamic similitude principles be fulfilled between
model and prototype. Model dimensions must be
sufficient to achieve an excellent geometrical
similarity with the prototype; the typical outlet
diameter of Francis and Kaplan runners is of the
order of 0.3 - 0.4 m. Test installations should fulfill
requirements of the IEC standards regarding their
capacity.
D
As an example, a view of the PF1 EPFL universal
test rig for all types of reaction machines, turbines,
pumps and pump-turbines is reported Fig. 3. This
test rig has a 900 kW maximum pumping power,
leading to test heads of up to 100 m (1'000 Jkg-1)
and a maximum flow rate of 1.4 m3/s. The
dynamometer is limited to a 320 kW maximum
generated power at 2'500 rpm.
In general, a test procedure consists in measuring:
• the overall hydraulic characteristic of the
machine and the corresponding efficiency
hill chart over a wide range of operating
conditions;
• guaranteed operating point efficiencies and
power output;
• cavitation characteristics;
• pressure fluctuations at the draft tube inlet,
at the spiral case inlet and on the head cover
of the machine;
• runaway speed ;
• index test and flow velocity distribution in
various locations.

In addition, mechanical measurements are often
carried out, such as torque and bending moment on
guide vanes, runner axial thrust etc....
A hill chart corresponding to the model test of a
typical Francis hydro-turbine is reported Fig. 2.
Fig. 3 Reduced Scale Model of a Francis Turbine
installed on the EPFL PF1 Test Rig
2.3. Standard cavitation tests
Standard cavitation tests consist in investigating the
influence of cavitation development on the
hydraulic characteristics and the type of cavity
susceptible to develop during the operation of the
prototype machine.
1
Z
ZI
Za
2
hs
Zref
ZcD
Fig. 4 Setting level definitions for a hydraulic
machine
These investigations are very important for the
evaluation of the setting level
s
h of the machine to
the tail-water level a
Z
, see Fig. 4, defined as:
s
r
hZZ=−
a
(m)
According to the IEC standard nomenclature, the
Net Positive Suction specific Energy, , of a
hydraulic machine is the difference of the specific
energy at Section 2, with the specific energy due to
the vapor pressure v, referred to the reference
level
NPSE
p
ref
Z
of the machine.
2
2
22
22
vref
vref
p
NPSE gH gZ
p
pC
g
Zg
ρ
ρρ
=−−
⎡⎤
=++−−
⎢⎥
⎣⎦
Z
(Jkg-1)
For a turbine, it can be assumed that all the specific
kinetic energy at the turbine outlet is dissipated in
the tail race water channel therefore can be
approximated as follows, NPSE
2
2
2
av s
pp C
NPSE gh
ρρ
≈−−+ (Jkg-1)
Meanwhile for a storage pump or a pump-turbine in
pumping mode, the intake of the machines should
have negligible specific energy losses and therefore
the can be approximated as follows
NPSE
av
s
pp
NPSE gh
ρρ
≈−− (Jkg-1)
Depending on the reference quantities chosen either
the Thoma’s cavitation factor
σ
, so called Thoma
number or the net positive suction specific energy
coefficient c
ψ
can be chosen to define a
dimensionless cavitation number.
NPSE
E
σ
=, 22
2
cNPSE
R
ψω
=
In both cases, we can observe that these terms are
simply related to the setting level
s
h, which is easily
determined. However, the problem arises in
estimating the static pressure at the low-pressure
section of the runner. The mean specific energy
conservation law between these sections leads to the
following expression for the absolute pressure pc,
c
()
2
2
cv c
ref c rd
pp C
NPSE g Z Z E
ρ
−=+−−+
(Jkg- 1)
where rd is the mean specific energy losses
between the sections c and 2 of the draft tube.
According to the flow direction, these losses are
positive for a turbine and negative for a pump.
E
The corresponding dimensionless expression allows
introducing a local cavitation factor
E
χ
related to
σ
as follows
2
2
12
ref c
cv c
E
rd
ZZ
pp Ce
ED
Fr
χσ
ρ
−
⎛⎞
−
E
=
=+ − +
⎜⎟
⎝⎠
where the Froude number is defined as
E
Fr
g
D
=
The necessary condition of cavity onset v
pp
=
in
the runner is then, expressed by the condition:
E
Cp
χ
=
−

with the pressure factor defined as:
c
ppp
CE
ρ
−
=
Thus, it is apparent that the static pressure will
strongly depend on the operating point of the
machine, even though the Thoma cavitation number
is kept constant. This can be shown by introducing
the discharge coefficient
ϕ
of the machine.
For a turbine we have:
2
2
0
2
1
1ref c
E
rd
ZZ e
DFr
ϕ
ϕϕ
χσ ψ
⎛⎞
+−
⎜⎟
−⎝⎠
=+ − +
where 0
ϕ
corresponds to the discharge operation
with minimum whirl.
Therefore, from the expression of the cavitation
factor
E
χ
we see that as much the discharge is
increased, the pressure decreases up to reach the
pressure vapor. For this extreme condition we have:
0
E
χ
=
For the case of reference taken at the runner outlet,
by neglecting the draft tube loss factor and
assuming a whirl free condition we have:
2
0
E
ϕ
χσ
ψ
=≈− leading to 21
c
ψ
ϕ
≈.
Therefore, the above ratio allows us to introduce
κ
the dimensionless cavitation number, which
expresses the margin to vapor pressure that we have
for a turbine.
Fig. 5
κ
cavitation number as a function of specific
speed for the turbines taken from [18]
We have reported Fig. 5 the values
corresponding to the specific speed of turbines
taken from [18]. We see that in practice, the setting
of a turbine requires that
κ
κ
r fulfill the condition:
21.8
ϕ
κψ
=≥
For a pump with a pure axial inlet flow, we have in
the same way
2
2
11
ref c
E
rd
ZZ e
Dk
Fr
ϕ
χσ ψ
−
=
+−+,
where is a pure geometric factor to take into
account that the reference section can be arbitrarily
selected. In the case of a reference section taken at
the impeller eye, this factor reduces to unity.
k
1
c
kk
=
=
So, in both types of machines the local value of the
cavitation coefficient is strongly affected by the
discharge coefficient
ϕ
. We can observe that for a
given operating point, cavitation tests are in
similitude with the prototype flow provided the
Thoma numbers and the Froude numbers are the
same in both cases, model scale and prototype scale.
Owing to the scale length factor between the
prototype and the model of large units, it is often
impossible to fulfill the Froude similarity
requirement. For example, if we consider a runner
diameter of 5 m operating at 500 Jkg- 1 and the
runner diameter of the corresponding model being
0.4 m, the Froude similitude leads to a test specific
energy of 40 Jkg-1, which is far too low for testing.
Thus, very often the test head is higher than the
corresponding Froude head and in turns the cavity
vertical extension on the blades is squeezed by the
scale effects. A way to overcome as much as
possible the influence of the Froude number is to
define a reference level of the machine as close as
possible to the elevation where cavity development
takes place. Therefore, for vertical axis machines it
is strongly recommended to define the low pressure
elevation level c
Z
as a reference.
Nevertheless, standard cavitation tests are
performed for different operating points by keeping
constant the specific energy coefficient
ψ
and
following the influence of the Thoma number
σ
on
the efficiency
η
and the discharge coefficient
ϕ
.
Typical
η
σ
−
curves for a Francis turbine are
reported Fig. 6.

Fig. 6 Cavitation curve for a Francis turbine, by
keeping constant the machine specific energy
coefficient and for a given guide vane
opening angle.
While
σ
is decreased, observations of the
cavitation onset and the cavity development are
reported. Characteristic values of
σ
are defined
such as:
• i
σ
: onset of visible cavities;
• 0
σ
: lowest value of sigma for which the
efficiency remains unchanged;
• 1
σ
: 1% drop of efficiency.
2.4. Type of Cavitation and Setting Level
The objective of cavitation tests being to determine
the setting level of the machine in order to
overcome any efficiency alteration and to minimize
the erosion risk, each type of cavitation is
considered with respect to its dependence on the
value of the setting level and to the erosion risk.
On the one hand, the onset of a leading edge cavity
is more influenced by the blade geometry and the
flow incidence angle than the value of σ. This
means that increasing to a very high value of σ in
order to prevent a leading edge cavity development
will cause unacceptable costs. Thus, this type of
cavity, which cannot be avoided for off-design
operation, has to be considered with respect to the
erosion risk. In this case, the Thoma number is
determined according to an acceptable cavity
development.
On the other hand, cavity development
corresponding to the design operating point such as
bubble cavitation and hub cavity are very sensitive
to the Thoma number value. However, for each case
of hydraulic machine, different types of cavitation
arise depending either on the blade design and the
operating point or on the Thoma number value.
Thus, it is important to examine, for each case of
hydraulic machine, the type of cavitation, which
occurs in the operating range.
3. CENTRIFUGAL PUMPS
3.1. Type of Cavitation
W
Cm
0
U
Cm<Cm
0
UU
Cm>Cm
0
W
W
Q
0
Q<Q
0
Q<Q
0
Fig. 7 Influence of the discharge value on the flow
velocity triangle at the impeller inlet
–
0,2
0,0
0,2
0,4
0,6
0,8
– 0,1 0,1 0,3 0,5 0,7 0,9 1,1 1,3 1,5
Q < Q
0
Q
0
Suction Side
L/L
ref
Pressure Side
Cp
E
Fig. 8 Computation of pressure distribution along
the mid span streamline of a storage pump
impeller for and , taken from [9].
0
Q0
QQ<
Cavity development in a centrifugal pump is fully
controlled by the discharge coefficient according to
the relative flow velocity incidence angle at the
impeller inlet, Fig. 7, which strongly affects the
pressure distribution on the blades at the inlet, [9],
Fig. 8.
Fig. 9 Traveling bubble development in a storage
pump impeller,
0
QQ
=
, during model testing.
At the rated discharge, traveling bubble cavitation
can be observed on the suction side of the blades,
Fig. 9. This type of cavity corresponds to a low
incidence angle of the flow and depending on the
design of the impeller, the minimum of pressure
being at the impeller throat.

Fig. 10 Leading edge cavity development in a
storage pump impeller,
, during model testing.
0
QQ<
For a lower discharge value, the flow incidence is
increased and then, a leading edge cavity appears,
as shown Fig. 10.
NPSE
Q
NPSE
P
Q
min
Q
0
Q
max
NPSE
i
NPSE
0
L/L
ref
= 5 %
NPSE
Q<Q
0
Q>Q
0
Fig. 11 Influence of the discharge value on a storage
pump NPSE.
For low values of σ, cavitation vortices can be
observed at the inlet of the runner coming from the
leakage flow through the shroud seal, Fig. 9.
3.2. Efficiency Alteration
Alteration of efficiency is due to the cavity
extension up to the throat of the flow passage in the
impeller. However, before this efficiency alteration,
cavitation erosion can occur at the closure region of
the cavity and can be dramatically increased when
transient cavities are advected downstream of the
impeller throat. For high discharge coefficient
value, leading edge cavities are developing at the
pressure side of the impeller blades leading to a
rapid drop of the efficiency.
The influence of the cavitation development on the
pump efficiency can be seen from the cavitation
curves drawn for different discharge values, Fig. 12.
80%
82%
84%
86%
88%
90%
0 0.2 0.4 0.6
σ
ηϕ/ϕ
^
= 100%
95%
85%
105%
115%
80% 120%
70%
60%
Fig. 12 Cavitation curves for a centrifugal pump for
different discharge coefficient values
3.3. Cavitation Erosion
In a centrifugal pump, leading edge cavity is the
main type of cavitation development over a wide
operating range of discharge. Then the setting level
of the machine is selected by evaluating the erosion
risk in the full operating range since for any
reasonable value of σ, a leading edge cavity still
exists for a sufficiently low value of the discharge
value.
In general cavitation erosion are observed on pump
impellers on the blade suction sides, 0 shaded area
A. Depending on how well the incoming flow is
controlled, erosion can be observed either on the
hub wall, 0 shaded area C, or on the wall of the
impeller shroud, if any, 0 shaded area B.
Fig. 13 Typical eroded areas of a pump impeller.
A very good correlation is obtained between the
cavity development observations made during
model tests and the field observations of the eroded
area on the corresponding prototype impeller, Fig.
14.

Fig. 14
Fig. 15
Cavitation erosion of a storage pump
impeller compared to the leading edge
cavitation development as observed during
testing of the homologous reduced scale
model.
In the case of unshrouded impellers, tip clearance
cavities appear and can erode either the pump
casing or the blades themselves.
Statistical acceptable values of Thoma
cavitation number as a function of pump
specific speeds.
Statistical values of power statistical relation
between the acceptable value of the Thoma
cavitation number and the pump specific speed are
provided Fig. 15.
4. FRANCIS TURBINES
4.1. Type of Cavitation
In the case of a Francis turbine and for the design
operating range, the type of cavity developing in the
runner is closely driven by the specific energy
coefficient
ψ
, the flow coefficient
ϕ
influencing
only the cavity whirl.
Fig. 16 Inlet edge cavitation, Francis turbine.
High and low values of
ψ
correspond to a cavity
onset at the leading edge suction side and pressure
side of the blades respectively, see Fig. 16. This
type of cavitation is not very sensitive to the value
of the Thoma number and it can lead to a severe
erosion of the blades.
Fig. 17 Traveling bubble cavitation in a Francis
turbine runner.
Traveling bubble cavitation takes place for the
design value of ψ, at the throat of the runner flow
passage, close to the outlet and corresponds to low
flow angles of attack. This type of cavitation, see
Fig. 17, is very sensitive to the content of cavitation
nuclei and to the value of the Thoma number. For
this reason, the plant NPSE is determined with
respect to this type of cavitation. The drop of the η-
σ curve is noticed when cavities extend up to the
runner outlet in both types of cavitation.
Depending on the value of the flow coefficient ϕ, a
whirl cavity develops from the hub of the runner to
the center axis of the draft tube in the bulk flow, as
shown Fig. 18. The size of the cavity is dependent
of σ, but the vortex motion depends only on the

flow coefficient values. According to the outlet flow
velocity triangle of Fig. 18, inverse runner rotation
of the vortex corresponds to high flow regime and
leads to a large axi-symmetric fluctuating cavity. In
turn, low flow regimes are responsible for a helical
shape of the whirl, rotating at a speed, between 0.25
and 0.4 times the runner rotational frequency. The
whirl development is mainly concerned with the
stability of machine operation, since it is the main
source of pressure fluctuations in the hydraulic
installation [20][21].
C
u
U
W
Cm
C
C
u
U
Cm
W
C
Fig. 18 Cavitation whirl at low and high discharge
operation, in a Francis turbine discharge ring.
At low flow regime, one can observe complex flow
recirculation at the inlet of the runner leading to
vortex cavitation attached to the hub and extending
up to the blade to blade passage, see Fig. 19. This
type of turbine operation corresponds usually to off-
design operation. However this operation cannot be
avoided during for instance the reservoir filling up
period of a new hydro-power generation scheme.
Fig. 19
Fig. 20
Inter blades cavitation vortices in a Francis
turbine runner.
The different limits corresponding to the
development of each type of cavitation are reported
in the hill chart of Fig. 20.
Limits of cavitation development within the
operating range of a Francis turbine:
1-Suction side leading edge cavitation limit;
2-Pressure side leading edge cavitation limit;
3-Interblade cavitation vortices limit;
4-Discharge ring swirl cavitation limits.
4.2. Efficiency Alteration
The setting of a Francis turbine is determined
according to the risk of efficiency alteration, which
is higher for high discharge, or high load, operating
conditions as it can be seen from the expression of
the cavitation factor
E
χ
. Therefore, the runner is
usually designed in such a way that this corresponds
to the development of traveling bubble outlet
cavitation, Fig. 17. This type of cavitation is very
sensitive to the content of cavitation nuclei and to
the value of the Thoma number, [17]. For this
reason, the plant NPSE is determined with respect
to this type of cavitation.
Fig. 21 Influence of free stream nuclei content on
efficiency cavitation curves.
However, many tests carried out at EPFL, [4][16],
for Francis turbine of different specific speeds
confirm a strong influence of cavitation nuclei
content combined with the test head on the
efficiency alteration phenomenon by cavitation, Fig.
21 and Fig. 23. Nuclei content does not only
influence cavitation inception, [19], but also the
development of bubble traveling cavities [3].
Moreover, test head influence is found to be more
related to an effect of the active nuclei content than
of the Froude effect. According to the Rayleigh

Plesset stability analysis the lower radius limit of an
active nucleus depends directly on the test head
value leading to more or less active nuclei for a
given nuclei distribution.
The cavitation curves reported Fig. 21, are obtained
according to the usual cavitation tests. In addition,
air micro-bubbles are seeded in the upstream vessel
in order to vary the free stream cavitation nuclei
content. It can be observed that, for a given
threshold value of the nuclei content, the efficiency
is no longer affected by increasing the nuclei
content, the cavitation coefficient being kept
constant.
Fig. 22 Influence of head and cavitation nuclei
content on Francis turbine cavitation curves
Fig. 23
Fig. 24
Flow visualization of traveling bubble
cavitation developments corresponding to the
A, B & C points of Fig. 23.
Moreover, the efficiency alteration is strongly
related to the cavitation extent on the blade as it is
confirmed by flow visualizations. Photographs
reported Fig. 23, correspond to the cavitation curves
of a test head of 20 m in order to overcome any
Froude effect on the cavity extent. Photographs A,
B are taken for the same low σ value of 0.052 and
correspond to a low nuclei content and to a
saturated state, respectively. One can observe that
the performance alteration is mainly due to the
vaporization of a part of the blade to blade channel
region which is under the vapor pressure. Thus, the
saturation phenomenon occurs when the active
nuclei amount is large enough to occupy all this
region.
Evidence of the strong dependency between the
volume of vapor and efficiency drop can be found
in comparing the photographs B and C, taken for
closely the same efficiency drop of 0.2 %. Even
though, the sigma value of point C, σ = 0.039, is
rather lower than the σ value of case B, the nuclei
content in the case C is small enough to lead to a
same volume of vapor and then to the same
performance drop.
The drop of the η-σ curve is noticed when cavities
extend up to the runner outlet in both types of
cavitation.
Statistical values of power statistical relation
between the acceptable value of the Thoma
cavitation number and the specific speed are
provided Fig. 24 for a Francis turbine.
Statistical acceptable values of Thoma
cavitation number as a function of Francis
turbine specific speeds.
4.3. Cavitation Erosion
Typical runner areas where cavitation erosion can
be observed are reported Fig. 25.
In general severe cavitation erosion damages are
observed in Francis runners on the blade suction
sides, shaded area A of Fig. 25 or downstream in the
blade to blade channel, shaded area B of Fig. 25.
The cause of those types of erosion, Fig. 26 and Fig.
27, is due to unexpected leading edge cavitation
development Fig. 16 and can only be corrected by
reshaping the inlet edge. However, wall erosion can
be mitigated by welding a layer of cavitation
resistant alloy.

Fig. 25 Typical eroded areas of a Francis runner.
Fig. 26
Fig. 27
Typical erosion at the wall of the blade
suction side due to inlet edge cavitation,
shaded area A of Fig. 25.
Typical erosion at the wall of the blade
suction side due to inlet edge cavitation,
shaded area B of Fig. 25.
Fig. 28 "Frosted" area at the wall of the runner blade
trailing edge due to outlet traveling bubble
cavitation, shaded area C of Fig. 25.
In case of development of traveling cavitation
bubble at the runner outlet region, Fig. 17, a
"frosted" area can be observed, shaded area C of
Fig. 25., which usually leads to barely visible
erosion, Fig. 28, and is easily controlled by the
Thoma cavitation number.
Finally, low load inter-blade cavitation vortices,
Fig. 19, can lead to erosion of the runner hub wall,
shaded area D of Fig. 25 and Fig. 29.
Fig. 29 Typical erosion at the wall of the runner hub
5. KAPLAN AND BULB TURBINES
5.1. Type of Cavitation
turbines are axial with
due to inter-blades cavitation vortices, shaded
area D of Fig. 25.
Runners of Kaplan and bulb
adjustable blade pitch angle and the control of both
the guide vane opening and the blade pitch angle
allows optimized operation of the machine, so
called "on cam" operation.
Fig. 30 Hub cavitation development for a Kaplan
Fig. 31 an
For the design operating range a cavity
cavitation [14]. However, the air entertainment can
runner
Tip clearance and hub cavitation for a Kapl
runner
development takes place at the hub of the runner,
Fig. 30. This type of cavitation is very sensitive to
the Thoma number. Any effect of the water
cavitation nuclei content is observed for this type of

have a great influence on the extent of this cavity,
[22].
Since the blades are adjustable, the runner is not
shrouded and, then as shown Fig. 31, tip clearance
erved at the inlet of the runner
development are reported
cavitation takes place in the gap between the blades
and the machine casing, leading to an erosion risk
even though the head could be low. This type of
cavitation is driven by the flow shear layer in this
gap and it is not very dependent of the Thoma
cavitation number.
Even for the case of on cam operation, leading edge
cavities can be obs
Cavitation development for
P
lant
σ
but can be avoided by improving the shape of the
blade leading edge [12].
The different zones in the hill chart corresponding
to each type of cavitation
Fig. 32.
0,2
0,6
1,0
1,4
1,8
2,2
2,6 a =cste
η
A=cste
0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0
/
η
∧
1
2
ϕ/ϕ
∧
ψ/ψ
∧
3
= 0,90
0,96
0,94
1
0,99
0,98
Fig. 32 Limits of cavitation development within the
operating range of a Kaplan turbine;
limit,
5.2. Eff
a Kaplan and bulbs
development of hub
1-Leading edge suction side cavitation limit,
2-Leading edge pressure side cavitation
3-Hub cavitation limit.
iciency Alteration
The efficiency alteration for
turbines is mainly due to the
cavitation, Fig. 30.
Fig. 33 Efficiency cavitation curve for a Kaplan
Turbine.
As this hub cavity edge,
we can notice an efficiency drop, Fig. 33. This type
Fig. 34
Depending on the head of the machine limited
develop avit ion can be
reaches the blade trailing
of cavitation has already mentioned is very sensitive
to the Thoma number and determines the plant
NPSE of the machine.
ment of tip clearance c at
admissible for plant NPSE, Fig. 34
Fig. 35 Influence of Thoma cavitation number on
Kaplan runaway speed.
Especia es, it
can be noticed a strong influence of the Thoma
a
lly for the case of Kaplan or bulb turbin
cavitation number on the runaway speed, Fig. 36.
Statistical values of power statistical relation
between the acceptable value of the Thom
cavitation number and the specific speed are
provided Fig. 36 for Kaplan turbines.
Fig. 36 Statistical acceptable values of Thoma
cavitation number as a function of Kaplan
turbine specific speeds.

5.3. Cavitation Erosion
Typical Kaplan runner areas where cavitation
erosion can be observed are reported Fig. 37
Fig. 37
Fig. 38
Typical eroded areas of a Kaplan runner.
Typical erosion at the tip of the runner blade
and at the discharge ring due to inter-blades
cavitation vortices, shaded area D of Fig. 25.
The most critical area where cavitation erosion is
observed are the blade tips and the machine casing,
shaded area A and B of Fig. 37. This erosion, Fig.
38, is due to the development of tip clearance
cavitation, which can take place even at plant
NPSE, Fig. 34.
Fig. 39 , Typical erosion at the suction side of the
blade due to leading edge cavitation, shaded
area E of Fig. 25.
Either for lasting operations at high head or at low
head erosion takes place at the suction side or the
pressure side of the runner inlet, dashed area D or E
of Fig. 37 respectively. This type of erosion is
caused by inlet edge cavitation, Fig. 39. Erosion
corresponding to dashed area F or G of Fig. 37 can
occurs during lasting low head operation. Finally,h
for high load operation conditions erosion can be
observed at the outlet of the runner at the suction
side, shaded area C of Fig. 37
CONCLUSION
A survey of the different types of caviation featured
by hydraulic machinery has been carried out. This
survey finally emphasizes the importance of model
testing for defining the proper setting level of the
machines. The determination of the plant NPSE of a
machine is a subtle process, which should include:
• the type of cavitation developments the
runner or the impeller is experiencing over
the operating range of interests;
• the risk of cavitation erosion associated to
this type of cavitation;
• the risk of performance alteration.
However, the assessment of those cavitation
developments can take benefits in a large extent by
developing monitoring instrumentation for the free
stream cavitation nuclei, which can influence the
cavitation development, [8]. Moreover, with respect
to the cavitation erosion, relevant indirect method,
such as measurement of vibratory levels, can be
very useful for quantifying the risk during model
tests, [5]-[7], [9] and [11].
ACKNOWLEDGMENTS
I would like to acknowledge all my colleagues of
the EPFL Laboratory for Hydraulic Machines. I am
very grateful to all the doctorate students I had the
pleasure to supervise in the field of cavitation and
hydraulic machinery.
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