Purdue University
Purdue e-Pubs
International Refrigeration and Air Conditioning
Conference
School of Mechanical Engineering
2010
Characterization of Friction Loss in Pelton Turbine
Yannick Beucher
ARMINES / Ecole des Mines de Paris
Elias Voulawz Ksayer
ARMINES / Ecole des Mines de Paris
Denis Clodic
ARMINES / Ecole des Mines de Paris
Follow this and additional works at: http://docs.lib.purdue.edu/iracc
Beucher, Yannick; Ksayer, Elias Voulawz; and Clodic, Denis, "Characterization of Friction Loss in Pelton Turbine" (2010).
International Refrigeration and Air Conditioning Conference. Paper 1077.
http://docs.lib.purdue.edu/iracc/1077
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2274, Page 1
CHARACTERIZATION OF FRICTION LOSS IN PELTON TURBINE
Y. BEUCHER1, E. BOULAWZ KSAYER1, D. CLODIC1
1
Center of Energy and Processes, Ecole des Mines de Paris,
Paris, FRANCE
E-mail : yannick.beucher@mines-paristech.fr, elias.boulawz_ksayer@mines-paristech.fr
ABSTRACT
The Pelton turbine can be used as a two-phase expander. The characterization of the Pelton turbine as two-phase
expander consists in analyzing the power loss sources to evaluate the machine performance. In this study, the
friction loss of a Pelton wheel is presented.
A Pelton wheel has been realized with aluminum buckets and has been mounted on a test bench. The
examination of experiments dealing with drag force in the Pelton turbine shows that the wheel friction losses are
an important part of turbine losses when it is shrouded and operate in high density atmosphere. Experimental
results show that losses by drag friction of a turbine enclosed in 0.5 MPa of R-134a atmosphere and rotating at
3000 rpm, can reach 3000 W, which is equal to the available power in the fluid jet.
A CFD model of Pelton wheel has been done to analyze and reduce the friction losses in order to develop an
efficient turbine. Modeling shows that with lowering the number and the size of the buckets, friction loss can be
decreased by 30%.
1. INTRODUCTION
In conventional vapor compression cycle, energy available in the high-pressure refrigerant is not recovered.
During the isenthalpic expansion, the kinetic energy in liquid flow is dissipated to the refrigerant as friction heat.
Due to the separation between refrigerant expansion step and kinetic energy recovery step, kinetic turbines are an
attractive process for refrigerant expansion energy recovery. Many studies have been performed on turbine as
two-phase expansion device but essentially for geothermic applications (Elliott, 1982, Comfort and Beadle,
1978, Austin et al., 1973). Some researches have been performed more specifically on two-phase mixture flow
(air and water) on the Pelton turbine, or with kinetic turbine for refrigerant expansion (with CO2 and R-22)
(Elliott, 1982, Akagawa and Asano, 1986, Tondell, 2006).
The Pelton turbine, which is an impulse turbine, composed of a wheel with buckets and a nozzle (Figure 1) can
be used as expansion device for refrigerant as R-134a. The nozzle converts the potential pressure energy of
refrigerant into kinetic energy. The jet hits buckets and forces the wheel to rotate, which generates mechanical
energy on the shaft. The Pelton wheel is enclosed and undergoes mainly vapor refrigerant density (which
corresponds to evaporator pressure). This atmosphere increases friction losses that are generally neglected when
the Pelton turbine is used in hydroelectric dam surrounded by air at atmospheric pressure.
Figure 1: Schematic view of a Pelton Turbine.
A Pelton wheel will be analyzed to evaluate and characterize drag loss due to the fluid friction on the Pelton
buckets during wheel rotation.
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2274, Page 2
2. DRAG THEORY
A solid body moving in a fluid is subjected to a force, called drag, which is opposed to body motion. The drag
force depends on the fluid (or body) velocity, the contact surface area, the fluid density and an empiric factor
called drag coefficient. The power loss by drag friction is estimated by Eq. 1:
ܲௗ௥௔௚ ൌ ‫ܥ‬஽
ߩܸ ଷ
‫ܣ‬
ʹ
(1)
The Pelton wheel is composed of three elements: the disk or runner, the buckets, and the shaft. All components
generate some losses by friction with the fluid. Tondell (2006) uses a general formula with an empiric coefficient
to evaluate the overall loss:
ܲ௥௢௧ ̱߱ଷ ܴସ ሺܴ ൅ ݇Ǥ ݄ሻ
(2)
With h the bucket height and k an empiric coefficient taking into account the influence of the three elements.
To evaluate disk friction (in the Pelton wheel, the disk is the runner on which buckets are attached) several
studies have been done. Gülich (2003) presents many correlations for different flow regimes and geometric
parameters. Some studies on computer hard disk have been done and can be useful for high rotating speed. To
evaluate the influence of buckets on friction, theory about gear friction loss is used. Actually geometries of
Pelton wheels are similar to gear where buckets should be substituted by teeth. Diab et al (2004) evaluate the
power loss due to friction on gear teeth by:
‫ݔ‬
ܲ ൌ ܼߩ‫ܾ߱ݔ‬ଷ ሺܴ െ ሻଷ
ʹ
(3)
Diab et al. add a variable, x, which represents the teeth active length. The active length is the teeth length that
enters in contact with the fluid. In fact, when the gear is rotating, each tooth is hidden by the following tooth in
the runner and so a certain part of each tooth is not in contact with the fluid (Figure :2).
The active length depends on the size and number of buckets. The higher the number of buckets, the more the
buckets hide themselves, but in the same time, the whole active length increases. Considering the angle between
buckets, the active surface could be estimated for the tested Pelton wheel (Figure 3).
100000
90000
80000
Surface(mm²)
70000
Activesurface
60000
Totalsurface
(without
protection)
50000
40000
30000
Figure 2: Schematic view of the gear active length.
10
12
14
16
18
20
22
24
26
Bucketnumber
Figure 3: Comparison between the active surface and the
total surface of the Pelton wheel tested as a function of the
bucket number.
3. EXPERIMENTATIONS AND PELTON LOSSES EVALUATION
A test bench is mounted to evaluate the turbine losses. The Pelton wheel has 24 aluminum buckets (Figure 4).
The wheel axis is connected to a motor via a torque meter and the enclosure tightness is ensured by lip seal
(Figure 5). Characteristics of Pelton wheel are given in Table 1.
International Refrigeration and Air Conditioning Conference at Purdue, July 12-15, 2010
2274, Page 3
Table 1 Pelton wheel characteristics.
Wheel radius (without bucket) (mm) 130
Wheel thickness (mm)
14
Axis radius (mm)
10
Bucket height (mm)
60
Bucket width (mm)
60
Bucket depth (mm)
17
Bucket thickness (mm)
3
To evaluate the friction losses, the Pelton wheel is driven by the motor from 0 to 3000 RPM. The enclosure is
filled with air or R-134a gas from 0.05 MPa to 0.5 MPa. The resistive torque is measured by a torque meter
during the wheel rotation. A test is done with a vacuum enclosure in order to measure mechanical losses only
(seal and bearing frictions) and to substract it from others results.
Besides, the Pelton wheel will be modeled on the commercial CFD software Fluent. First, simulations are made
with the experimental conditions. Then, several simulations are performed to know the impact of material
roughness, of the number of buckets and of the shape of buckets on the friction losses.
Figure 5: Schematic view of the test bench.
Figure 4: Picture of Pelton wheel tested.
4. EXPERIMENTALS RESULTS
Summary of some experimentation results of the test bench is shown in Figure 6. The experimentation made in
vacuum shows linear losses. The resistive torque applied by seal and bearing is constant and the power loss is
proportional to the rotating speed.
The power loss increases with the gas density and the rotating speed. Loss paths are coherent with the drag
theory: they rise linearly with density and proportionally to the power three of the rotating speed. For high
density, mechanicals friction losses are negligible compared to drag friction losses.
4000
4000
r134a5bar
3500
3000
r134a4bar
3000
2500
r134a2bar
2000
r134a1bar
1500
air5bar
1000
500
Powerloss(W)
Powerloss(W)
3500
2500
r134a5bar
experimental
2000
r134a1bar
gearformula
1500
air2bar
1000
vacuum
500
0
R134a5bar
gearformula
r134a1bar
experimental
air2bargear
formula
0
0
1000
2000
3000
Rotatingspeed(RPM)
Figure 6: Experimental results of the Pelton friction losses
0
1000
2000
3000
air2bar
experimental
Rotatingspeed(RPM)
Figure 7: Comparison between experimental results of the
Pelton friction power losses and calculated results with gear
formula.
With experimental results, it is possible to extract a coefficient (corresponding on CD*A in the drag equation (1))
specific to the tested Pelton turbine. Nevertheless, this coefficient is not constant if the Pelton wheel is used with
air or R-134a. It means that the drag coefficient takes into account a large number of phenomena that are
International Refrigeration and Air Conditioning Conference at Purdue, July 12-15, 2010
2274, Page 4
difficult to evaluate theoretically. However, Equation (3) for the gear friction loss can be used to estimate the
power loss by friction (Figure 7). This formula gives good results compared to experimental data and can be
used in first approximation to evaluate the Pelton turbine losses (calculated losses are majored by 20% in Figure
7).
With these turbine loss results, it is possible to evaluate the energy potential of the Pelton wheel in a refrigeration
system. Assuming that the expansion in the nozzle is isentropic, the maximum power of the jet and its speed can
be calculated. So, for a given refrigerant flow, the turbine maximum recoverable power can be estimated.
ܸ௝ ൌ ඥʹɄ୬ ሺ݄௦ െ ݄௘ ሻ
ܲ௝ ൌ ݉ᇱ ‫כ‬
ܸ௝ଶ
ʹ
(4)
(5)
ܲ௥௘௖ ൌ ʹ ‫ כ‬Ʉ୵ ‫݉ כ‬ᇱ ‫ܷ כ‬൫ܸ௝ െ ܷሻ൯
(6)
The evaluation is done for a 100 kW cooling capacity chiller (Table 2). The maximum available jet power is
3000 W, and the Pelton wheel must rotate to 3000 RPM to recover all the jet power. At this evaporating
pressure, and rotating speed, the friction losses (Figure 6) are almost equal to the available maximum jet power
(Figure 8).
Maximumpoweravailable
3500
3000
2500
Table 2: Characteristics points of a 100-kW chiller.
2000
1500
1000
500
0
0
500
1000
1500
2000
2500
3000
3500
RotatingSpeed(RPM)
100 kW chiller
T condenser (°C)
45
P condenser (bar)
11.6
Subcooling (°C)
3
T evaporator (°C)
2
P evaporator (bar)
3.14
R134a flow (kg/s)
0.677
Vj isentropic (m/s)
95
Figure 8: Theoretical maximum power recoverable by the Pelton
wheel used in 100-kW chiller
The energy available during the fluid expansion is compared to the energy lost by friction. In considering a
chiller (7-12 °C) having an evaporation temperature of 2°C, a condensing temperature of 45°C, a sub-cooling of
3 K and a superheat of 5 K, the available power from the Pelton turbine has been calculated (with an expansion
efficiency of 80% and a recovery yield of the wheel of 60%). For the evaporation temperature of 2°C, the
isentropic speed of exit from the nozzle is 95 m/s, so the optimal radial velocity of the Pelton wheel is 47.5 m/s,
which corresponds to 2800 RPM for the tested whee. Friction losses are estimated with the gear formula majored
by 20%. Several fluids are evaluated and calculations show that the Pelton turbine becomes interesting for a
chiller capacity of 100-kW (Figure 9). The turbine efficiency can reach 40% for a chiller of 200 kW operating
with R-152a (Figure 10).
International Refrigeration and Air Conditioning Conference at Purdue, July 12-15, 2010
5
45%
4,5
40%
4
35%
Turbineefficiency
RecoverablePower(kW)
2274, Page 5
3,5
3
r134a
2,5
propane
2
1,5
r152a
1
30%
25%
r134a
20%
propane
15%
r152a
10%
1234yf
1234yf
5%
0,5
0
0%
0
50
100
150
200
250
0
50
ChillerCapacity (kW)
100
150
200
250
ChillerCapacity (kW)
Figure 9: Recoverable power by the Pelton turbine tested for
several fluids.
Figure 10: Turbine efficiency depending on the chiller
capacity.
5. SIMULATIONS RESULTS
For friction power losses, one of the most influencing parameters is the surface area in contact with the fluid. To
characterize this influence, simulations using a commercial CFD software Fluent® are done.
Several simulations are made by varying the density inside the turbine enclosure. The frictional losses are
evaluated for densities of 1.225 kg/m3 (representing an air pressure of 100 kPa), and 2.5 kg/m3 (air at 200 kPa),
3.6 kg/m3 (air 300 lPa) and 21.4 kg/m3 (R-134a at 500 kPa) (R-134a has been overheated by friction losses
during testing on the bench, which has reduced the density from 25 to 21.4 kg/m3). Experimental results obtained
in the same initial conditions are compared with simulation results.
3000
Density
(kg/m3)
Powerloss(W)
2500
21.4mod
2000
21.4exp
3.6mod
1500
3.6exp
1000
2.5mod
2.5exp
500
1.2mod
1.2exp
0
0
500
1000
1500
2000
2500
Rotatingspeed(RPM)
Figure 11: Comparison between experimentations and simulations of friction losses.
The first finding is that the model overestimates losses. The average value of the error reaches 25%. This error
increases with speed but not with density. The model is also more stable to high pressures (gap constant for all
speeds unlike the lower pressures where the gap fluctuates). However, the shape of the curve is identical for the
model as well as for the experiments. The model is valid to assess the relative influence of different parameters
of the wheel on friction losses due to the drag force. Parameters that will be analyzed are the number of buckets
and then shape.
5.1 Number of buckets
The bucket number of the Pelton wheel used for experimentation could be oversized. The optimal theoretical
number of buckets is easily quantifiable. Buckets should be in a sufficient number for all of the jets to come in
contact with the wheel. When the wheel is rotating, buckets intercept the jet one after another. If the wheel turns
too fast compared to the jet speed, the bucket may leave the jet path before it strikes the bucket and the energy of
the jet is lost. On the other hand, the maximum force applied by the jet on the wheel is achieved when the
trajectory of the jet is perpendicular to the height of the bucket. So a good wheel has enough buckets to recover
all the jet energy, but a number adequate to recover the full jet force.
International Refrigeration and Air Conditioning Conference at Purdue, July 12-15, 2010
2274, Page 6
ߙ௠௜௡ ൌ …‘•ିଵ ൬
ܴ௜ ൅ ݁
൰
ܴ଴
(7)
With :
e : distance between the base of the bucket and the jet
(mm)
Ri : disk (without buckets) radius (mm)
R0 : wheel radius (mm)
Figure 12: Schematic view of the angle between buckets
necessary to recover full force of the jet.
Using equation (7) and Figure 12, the number of buckets necessary to recover the maximum force is calculated.
The manufacturer data of the Pelton wheel tested (originally designed to recover the potential energy of a small
water stream with a jet diameter of 20 mm) allow calculating that to benefit of the maximum jet force, the wheel
must have 12 buckets. So the design of the wheel tested, with 24 buckets, is done to guarantee full recovery of
the jet energy.
The size of the buckets also changes the drag formation because the surface in contact with the flow is changed.
According to Hutchinson (1923), to achieve the best performance, the area occupied by the jet into the Pelton
bucket should not exceed 10% of the projected area of the bucket and the jet diameter should not exceed 30% the
bucket height. The jet size of the R-134a flow is not known. Nevertheless, assuming isentropic expansion of R134a, in a 100 kW chiller cycle, the jet diameter should be half as large as the water jet (designed for the Pelton
wheel tested). However, the bucket surface is four times more important than necessary for this jet diameter.
Several simulations are done to characterize impact of the surface on power loss. Normal buckets are buckets of
the tested Pelton wheel. Smalls ones have a surface four times as less as normal buckets (Figure 13).
Power loss by drag is 20% lower when the number of buckets is divided by two (Figure 14). This result is not
coherent with the drag equation; the total surface of the 12 buckets is half of what it is with 24, so friction loss
should be divided by two. Nevertheless, this result seems in agreement with the active surface theory because
divide by two the number of buckets does decrease the active area of 15% only (Figure 3).
Again, difference between power loss with 24 small and 24 normal buckets cannot be explained by normal drag
equation (Figure 14). The surface is divided by 4 but not the loss. Contrariwise active surface is just divided by
two while losses decrease by 50% (Figure 3).
3000
Powerloss(W)
2500
2000
24normal
buckets
1500
12normal
buckets
1000
24small
buckets
500
0
0
1000
2000
3000
4000
Rotatingspeed(RPM)
Figure 13 Pelton wheel modeled. One with 24 normal
buckets, one with 12 normal buckets and one with 24
smalls buckets
Figure 14 Comparison between simulation of power lost by
Pelton wheel of 24/12 and normal/small buckets
5.2 Shape of buckets
In general, the friction losses depend on the contact surface between the object and the flow (equation 1). The
losses generated by a single bucket are analyzed to know the influence of shape of the bucket surface on friction.
Only the back of the bucket is changed because it is this side which is taken into account in the calculation of
International Refrigeration and Air Conditioning Conference at Purdue, July 12-15, 2010
2274, Page 7
drag. The back of the first bucket has a slightly convex shape (as the bucket of the Pelton wheel tested), the
second has a flat surface because this form is the most generator of drag in the aerodynamic theory (Figure 15).
Figure 15 One bucket Pelton wheel modeled. One with convex shape, the other with flat surface
600
7000
500
6000
400
300
Flat
200
Convex
Powerloss(W)
Powerloss(W)
According to the literature, the drag coefficient of a convex body in a high speed flow (Re> 104) is between 2
and 3 times smaller than a flat body of the same size. The wheels were modeled with air at a pressure of 100 kPa
(or a density of 1,225 kg/m3) (Figure 16) and 1 MPa (or a density from 12.25 kg/m3) (Figure 17). The shape of
plate bucket generates 2 times more loss at 3000 RPM than the normal convex bucket.
100
5000
4000
3000
Flat
2000
Convex
1000
0
0
0
500
1000
1500
2000
2500
3000
0
500
Rotatingspeed(RPM)
1000
1500
2000
2500
3000
rotatingspeed(RPM)
Figure 16 Comparison between power lost by wheel with
one flat/convex bucket at 100 kPa
Figure 17 Comparison between power lost by wheel with
one flat/convex bucket at 1 MPa
300
3000
250
2500
200
150
Flat
100
Convex
50
Powerloss(W)
Powerloss(W)
The common form of buckets, with a slightly convex surface on the back, seems to be most relevant to limit the
formation of drag. This result is consistent with the theory of aerodynamics. However, this result is valid when
the flow does not encounter a single bucket and therefore the entire surface of the trough is a barrier to fluid. In
the case of the superposition of the buckets, the screening effect canceled common bucket advantage (Figure 18
and Figure 19).
2000
1500
Flat
1000
Convex
500
0
0
0
500
1000
1500
2000
2500
3000
0
Rotatingspeed(RPM)
500
1000
1500
2000
2500
3000
Rotatingspeed(RPM)
Figure 18 Comparison between power lost by wheel with 24
flat/convex buckets at 100 kPa
Figure 19 Comparison between power lost by wheel with 24
flat/convex buckets at 1 MPa
6. CONCLUSION
According to the simulation results, friction loss on Pelton wheel can be reduced by at least 30% if the turbine is
sized with jet specification and well designed. With this improvement, using Pelton wheel on refrigeration
system is competitive for chiller with a minimal cooling capacity of 100 kW.
The power lost by fluid friction can be estimated with gear formula. Pelton buckets protect each others from the
flow and the active surface theory is coherent with results.
To improve turbine efficiency research should be done on mechanicals losses (mainly in seals frictions).
Nevertheless, Pelton turbine is not really appropriate to recover energy from a two-phase fluid.
International Refrigeration and Air Conditioning Conference at Purdue, July 12-15, 2010
2274, Page 8
NOMENCLATURE
R
V
U
h
m’
P
CD
A
Z
b
wheel radius
speed
rotating speed
enthalpy
mass flow
power
drag coefficient
surface
number of teeth
tooth width
Greeks
ȡ
density
Ȧ
rotating speed
Ș
efficiency
m
m/s
m/s
kJ/kg
kg/s
W
adim
m²
adim.
m
Subscripts and superscripts
e
s
j
rec
n
w
inlet
outlet
jet
recovery
nozzle
wheel
kg/m3
rad/s
%
REFERENCES
Akagawa, K., Asano, Y., 1986, Performance of Pelton-type Turbine driven by gas-liquid two phase flow,
Bulletin of JSME, vol. 29, No. 247, p. 106-112.
Austin, A. L., Higgins, G. H., Howard, J. H., 1973, The total flow concept for recovery of energy from
geothermal hot brine deposits, Lawrence Livermore Laboratory, 45 p.
Comfort, W. J., Beadle, C. W., 1978, Design considerations for a two phase turbine, Polyphase Flow in
Turbomachinery, Lawrence Livermore Laboratory, 18 p.
Diab,Y., Ville, F., Velex,P., 2004, Windage loss in High speed gears – preliminary experimental and theorical
results, Journal of mechanical design, vol. 126, no 5, p. 903-908.
Elliott, D.G., 1982, Theory and Tests of Two-Phase Turbines, Jet Propulsion Laboratory, JPL Pub B1-105,
150 p.
Gülich, J. F.,2003, Disk friction losses of closed turbomachine impellers, Forschung im Ingenieurwesen, vol. 68,
p.87-95.
Hutchinson, E., 1923, The tangential impulse water wheel, Chapter 1, Impulse turbines, The electric journal,
p. 1-12
Tondell, E., 2006, CO2-expansion work recovery by impulse turbine, PhD at NTNU (norway) , 136p.
International Refrigeration and Air Conditioning Conference at Purdue, July 12-15, 2010