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Effect of Surface roughness for Hydro
Turbine Step-up Efficiency
Ermias Beraki
Sustainable Energy Engineering, master's level
2018
Luleå University of Technology
Department of Engineering Sciences and Mathematics
Preface
This report presents my Master Thesis in the program Sustainable Energy Engineering with specialization in
Wind and Hydro power at Luleå University of Technology (LTU). The project was performed at Skellefteå
Kraft AB with assistance from LTU. I sincerely thank my main supervisors; Prof. Michel Cervantes at LTU,
and Ms Jenny Jungstedt at Skellefteå Kraft. Distinctive thanks to Prof. Michel Cervantes for familiarizing me
to this project and to Ms. Jenny Jungstedt at Skellefteå Kraft for the valuable support she provided throughout
the development of the thesis and for concrete information about various parts. I would also like to thank Mr.
Mikael Sendelius at Sweco for his extended cooperation for providing invaluable theoretical information about
the step-up calculations.
Luleå, May 2018
Ermias Beraki
Abstract The energy produced by the flow of water is known as hydropower. It is an easily accessible and available source
of energy in large quantity in the form of, rivers, lakes, streams and runoffs around the world. Hydropower is
dependent upon hydrological cycle hence; this beneficial characteristic of hydropower makes it a renewable
source of energy. Hydropower is free from poisonous emission; therefore, it is considered as a safer and pollution
free source of energy. It is usually used to develop electricity from generators. These generators are connected to
the hydro turbines by means of shaft. The electricity produced from hydropower is stable and steady because of
its higher capacity, thus it can be a suitable source to work as base-load and used to balance the power fluctuations
caused by varying loads. The hydropower can also be accommodated with different sources such as solar and
wind system. This way of power sharing needs quick regulation as the deviation in the power grid changes rapidly.
To fulfil this power demand with higher stability prompted to the development of modern turbines with more
efficient, reliable and robust design.
To achieve the above target, it is of prime importance to improve efficiency of hydro turbine. Nevertheless, many
methods are in practice for improvement for efficiency of the turbine; though one of the prime elements which
influence the turbine efficiency is surface roughness. The effect of surface roughness differs for different turbine
components like stay vanes, guide vanes, runner, draft tube and spiral casing.
The main purpose of this thesis is to examine the effect of surface roughness for hydro turbine step-up efficiency.
It is based on reduced scale model to prototype conversion method. For this purpose, IEC_62097 has provided an
excel sheet as an attachment for calculation. There has been always a need to perform model test, since performing
test on the prototype itself is very accurate, and calculations too, do not yield reliable results. Therefore, the model
to prototype conversion method is considered a better solution.
A sensitivity analysis is conducted on a Kaplan turbine situated at the Granfors power station located along the
Skellefteå river about 30 km from the city of Skellefteå. The results obtained after applying the latest step-up
expressions are described and presented. These outcomes have shown significant positive impact on the hydro
turbine efficiency improvement, which are presented in graphs.
The most significant variations of step-up efficiency against surface roughness were observed in the runner part
of the turbine. This specific characteristic makes it evident that more focus and test should be conducted on this
part to improve efficiency.
Contents Preface ....................................................................................................................................................................
Abstract ...................................................................................................................................................................
1. Introduction ....................................................................................................................................................... 1
1.1 Problem description ........................................................................................................................................ 4
1.2 State of Art ...................................................................................................................................................... 4
1.3 Aim of thesis ................................................................................................................................................. 5
2. Theory ................................................................................................................................................................ 6
2.1 Principle of hydropower ............................................................................................................................... 6
2.2 Types of turbines .......................................................................................................................................... 7
2.2.1 Impulse Turbines ................................................................................................................................... 9
2.2.2 Reaction Turbines .................................................................................................................................. 9
2.2.3 Francis turbines ..................................................................................................................................... 9
2.2.4 Axial-flow Kaplan Turbine .................................................................................................................. 11
2.3 Surface roughness ....................................................................................................................................... 13
2.4 Efficiency .................................................................................................................................................... 14
2.4.1 Hydraulic efficiency ............................................................................................................................. 14
2.4.2 Step-up of hydraulic efficiency ............................................................................................................ 15
2.5 Loss distribution in a turbine ...................................................................................................................... 16
2.5.1 Penstock and spiral case ..................................................................................................................... 16
2.5.2 Stay vanes and guide vanes ................................................................................................................. 16
2.5.3 Runner .................................................................................................................................................. 16
2.5.4 Draft tube ............................................................................................................................................. 16
3. Method ............................................................................................................................................................. 17
3.1 Literature ..................................................................................................................................................... 17
3.2 Calculation data .......................................................................................................................................... 17
3.2.1 Efficiency step-up between reduced model and prototype................................................................... 17
3.3 Generated figures of surface roughness versus step-up efficiency ............................................................. 17
4. Results .............................................................................................................................................................. 18
4.1 Model efficiency step-up versus surface roughness ................................................................................... 18
4.1.1 Stay vanes ............................................................................................................................................ 18
4.1.2 Guide vanes ......................................................................................................................................... 19
4.1.3 Runner .................................................................................................................................................. 20
4.1.4 Stay vanes, guide vanes and runner .................................................................................................... 21
4.2 Prototype efficiency step-up versus surface roughness .............................................................................. 22
4.2.1 Stay vanes ............................................................................................................................................ 22
4.2.2 Guide vanes ......................................................................................................................................... 23
4.2.3 Runner .................................................................................................................................................. 24
4.2.4 Stay vanes, guide vanes and runner .................................................................................................... 25
5. Discussion ........................................................................................................................................................ 26
6. Conclusion ....................................................................................................................................................... 27
7. Recommendations ........................................................................................................................................... 27
Bibliography ........................................................................................................................................................ 28
Appendix .............................................................................................................................................................. 31
Appendix A Step-up formula for power efficiency (IEC 62097, 2009, p.23&p.27) ...................................... 31
Appendix B Efficiency step-up (IEC 62097, 2009, p.28) .............................................................................. 31
Appendix B.1 Component wise step-up & whole turbine step-up method (IEC 62097, 2009, pp. 63-69) ...... 31
Appendix C Input required data for model and prototype. ............................................................................ 34
Variable list
The used parameters are summarized below, see Table 1.
Table 1: Summary of used parameters (IEC 62097, 2009)
Variable Symbol unit
The turbine component CO −
The stay vane SV −
The guide vane GV −
The draft tube DT −
The spiral case SP −
The stationary part ST −
The runner RU −
Model M −
Prototype P −
The reference diameter 𝐷
[𝑚]
Roughness Arithmetic mean 𝑅𝑎 [µ𝑚]
The Rotational speed 𝑛 [1 𝑠⁄ ]
Specific hydraulic energy efficiency 𝜂𝐸 −
Volumetric efficiency 𝜂𝑄 −
Power efficiency
𝜂𝑇 −
Hydraulic efficiency 𝜂ℎ −
Reynolds number 𝑅𝑒 −
Efficiency step-up Δ𝜂 −
The loss of relative scalable hydraulic energy 𝛿𝐸 −
Factor of flow velocity for every component passage 𝜅𝑢𝐶𝑂 −
Loss index of scalable hydraulic energy for every
component passage 𝑑𝐸𝐶𝑂𝑟𝑒𝑓 −
Loss index of scalable disc friction 𝑑𝑇𝑟𝑒𝑓 −
The discharge 𝑄 [𝑚3 𝑠⁄ ]
Machine specific hydraulic energy 𝐸 [𝐽 𝑘𝑔⁄ ]
The specific speed 𝑁𝑄𝐸 −
1
1.Introduction Hydropower is one of the greatest sources of renewable energy. It is available, in an abundant
quantity around the world. This source of energy offers a solution for the energy requirements for
different activities. Hydropower has been utilized by humans for thousands of years for performing
various types of activities. The Greeks have been utilizing water wheels for crushing wheat into
flour, more than 2,000 years ago. The advancement of the present hydropower initiated in the middle
of the 1700s when a French military hydraulic engineer, Bernard Forest de Bélidor wrote
Architecture Hydraulique (Mulu , 2012).
The previous century has witnessed several advancements in hydropower that have assisted it to
become a central part of the renewable energy around the globe.
In the 21st century, hydropower continued to increase. Currently, it shares about 16% of worldwide
electricity generated and could contribute even further in the upcoming century. In Sweden, there
are 2057 hydropower plants, of which 1615 have a capacity of 10 MW at most. The entire capability
is nearly 16197 MW out of which 1050 MW comes from minor hydro plants having less than10
MW (Statistics, 2018).
Figure 1. Shows the production of hydropower in Sweden from the year 1998 to year 2016
(equivalent to oil of Million metric tons)
The entire electricity generated is estimated to be around 66 TWh, out of which 4.6 TWh is produced
by small hydropower plant (SHP) during a normal year. As per the BlueAGE survey, given by ESHA
in 2001, Sweden has a fifth position in energy produce by small hydropower in Europe (2018, 2016).
Figure 1: Shows the intake of hydropower in Sweden from the year 1998 to year 2016
(equivalent to oil of Million metric tons) (Statistics, 2018)
Future hydropower plant development seems to be limited for upgrading and renovating purpose
only, due to ecological and political concerns. Most of the large hydropower plants were
constructed through the period of 1940-70s.
2
There is always a need to refurbish old hydropower plants, for improving efficiency. In the present
global situation, the growing energy cost along with the numbers of nuclear power plants being
steadily reduced provides a scope to develop additional small-scale hydropower plants.
Nevertheless, the activity within the large scale hydropower plant is typically restricted to
renovations and preservation work only (IEC 62097, 2009). There are nearly 30 main hydroelect
plants around the world with at least 2,000 MW capabilities; the largest is situated in China.
(Statistics, 2018)
Hydropower has played a vital role in helping many countries to increase their growth into a higher
GDP. As the world efforts to stall environmental changes by reducing toxic emissions and
necessity of fossil fuels, the energy from renewable sources has become popular. Figure 2 presents
data from 2016 for the hydropower generation.
Figure 2: Hydropower production worldwide in year 2016, by leading countries (in terawatt
hours) (Statistics, 2018).
Hydropower is a renewable source of energy that produces less emission in terms of toxic gases
compared to other power sources. The production of electricity from hydropower is nearly 16% of
the world’s total power generated. Furthermore, it has continued to be steady since the 1990s and
expected to increase in the future. The International Energy Agency suggested that the electricity
production from hydropower and other sources is predicted to rise at a normal yearly rate of 1.7%
from 2004 to 2030, for a whole growth of 60% by 2030 (UNESCO, 2017).
Skellefteå Kraft presently owns 18 large hydroelectric power units mainly along the Skellefteå
River, distributed into 11 stations. By improving the present units with recent ones with more
ecologically friendly turbines and generators, along with performing minor modification, the power
may be improved to 490 MW compared to the actual 455 MW (Skelleftea Kraft, 2016).
3
Figure 3: Different sources of energy in Sweden (IVA, 2018).
In seven of the total stations own by Skellefteå Kraft, there is a possibility to increase the power
with the installation of another unit in the future. Skellefteå Kraft estimates that the power could be
increased to 655 MW, a significant increase of 210 MW (Skelleftea Kraft, 2016).
A slight increase in the efficiency is estimated to provide an enormous amount of economic benefit.
Therefore, when determining the efficiency, it is required a precision of 0.2%. Usually, the
efficiency is evaluated with the help of a reduced model. (Skellefteå Kraft, 2018)
Figure 4: Production of electricity in Sweden in the year 1970-2014 TWh. Source: Energiläget i
siffror, Swedish Energy Agency (IVA, 2018)
Experiments on a geometrically similar model to the prototype are performed in the preliminary
step for computing the prototype efficiency, from a step-up formula. Prototype test is difficult to
perform, and calculations do not yield reliable results. Therefore, model tests are required (IEC
62097, 2009).
It is observed that the prototype efficiency is higher, compared to that of the model efficiency. This
difference between the models to prototype is caused by the difference in Reynolds number amid
the model and for the prototype and the surface roughness. This deviation from the elemental
similarity law is named ‟scale effect‟. For instance, the Reynolds number of the prototype is at least
10 times the Reynolds number of the model, the exact assessment of scale effect is thus significant
(IEC 62097, 2009).
4
Wall friction not only affects the main flow dissipation of specific hydraulic energy E, but also the
power loss due to disc friction at the rear surface of a Francis runner. Thus, the change in wall
friction among model and prototype results in a difference of specific energy efficiency and power
efficiency (IEC 62097, 2009).
The standard IEC 62097, titled ‟Hydraulic machines, radial and axial-performance conversion
method from model to prototype” (IEC 62097, 2009) was published in the year 2009. This includes
steps to analyse the component-wise step-up for model to prototype, to evaluate the performance of
turbine. It also presents the necessary formulas for the calculation of step-up hydraulic efficiency
along with the three most significant scale factors (Nakanishi, 2016).
The most significant point of the new edition IEC62097 standard is a component-wise conversion.
In the earlier publication, S008-1999, the scale effect was calculated for the entire machine. In the
new edition, IEC 62097, the conversion formula is improved such that the performance conversion
can be completed for every component.
In case of machines with radial flow, the scale effect calculation is suitable for components, those
are listed as: 1. draft tube, 2. guide vanes, 3. spiral case, 4 stay vanes and 5. runner. On the other
hand, for machines with an axial and diagonal flow, the passageway from the outlet of the guide
vanes to the inlet of the runner needs also to be considered.
1.1 Problem description Several hydroelectric power plants in Skellefteå Kraft needed to be refurbished because of reaching
their technical life time (Skelleftea Kraft, 2016).. Skellefteå Kraft wants to know which emphases
should be on the surface roughness of the different components of a turbine following the new
international standard IEC 62097.
1.2 Previous work The investigation of the impact of surface roughness of the different prototype and model
components on efficiency step-up on hydraulic turbine is crucial, in the process of turbine
modernization. Numerous articles have been published for the transformation of each component’s
performance from model to prototype turbine, with one-step calculation such as, stay vane, spiral
case, guide vane, runner and draft tube. Several theoretical and practical techniques have been
conducted for performance conversion method. Nakanishi et al. (2016) has studied the impact of
surface roughness on efficiency step-up for hydraulic turbines in accordance with IEC 62097
standard. In their research, Nakanishi et al. (2016) calculated the efficiency step-up for optimum
operating point for a Kaplan turbine and a Francis turbine for both the hydraulic smooth and practical
rough condition of the different turbine components. As a result of their work, they showed that the
efficiency step-up for a Kaplan turbine and a Francis turbine is larger for smooth surface than for
practical roughness (Nakanishi, 2016).
Maruzewski1 et al. (2009) investigated the impact of surface roughness of the different prototype
radial turbine components on the efficiency step-up in Gordon Merritt Shrum, GMS, power station
in British Colombia. In their work, they analysed the impact of surface roughness from nearly 0
microns, representing an ideal smooth wall prototype to 150 microns, implying a severe rough wall.
The wall of prototype of GMS, power station was rough. After rehabilitation, the existing prototype
were sanded and pained, resulting in a sand grain roughness height equivalent to a Ra-value of 10
5
microns. As the result of this work, they showed that the efficiency step-up for an ideal smooth wall
prototype was +1.37%. The efficiency step-up for a rehabilitation case was nearly 0.81%.
Eventually, the efficiency step-up for a severe roughness case, negatively decreased to -0.15%. A
positive value of efficiency step-up implies, the effect of surface roughness remains week to keep
acceptable performances. A negative value of efficiency step-up indicates that the effect of surface
roughness is so large that the performance significantly decreases. Consequently, the authors
showed that the surface roughness makes significant impact on the efficiency step-up (Maruzewski1
et al., 2009).
Yun et al. (2005) analysed turbine efficiency reduction due to blade surface roughness. In their work,
they carried out a performance test on a single-stage axial turbine with roughened blades. The
authors used sheets of sandpaper with equivalent sand grain roughness of 106 and 400 m to
roughen the blades. As the result of this work, they showed that in the transitionally rough regime
(106 m), the efficiency reduced by nearly 4% with either roughened stator or roughened rotor and
by 8% with roughness on both the stator and rotor blades. In the fully rough regime (400 m), the
efficiency reduced by 2% with roughness on the pressure side and by 6% with roughness on the
suction side. Furthermore, the researchers determined that the efficiency was reduced by 11% with
roughness only on stator vanes, 8% with roughness only on rotor blades, and 19% with roughness
on both the stator and rotor blades. Consequently, the authors showed that blade surface roughness
severely reduced turbine efficiency (Yun et al., 2005).
1.3 Aim of thesis The main objective of this thesis is to perform a sensitivity analysis of the surface roughness (Ra
parameters) on each water passage component, such as spiral casing, stay vanes, guide vanes,
runner, draft tube etc., on the step-up efficiency performance based on the IEC 62097 edition
standards, “Hydraulic machines, radial and axial-Performance conversion method from model to
prototype” (IEC 62097, 2009). As the time for the project is limited and SKAB has many power
plants at the far end of the Skellefteå River, the work is limited to evaluate Granfors power station.
The Granfors power station is composed of vertical Kaplan units. Therefore, this thesis focuses on
Kaplan turbine, more specifically on Granfors power station and the effect of surface roughness on
this turbine on the efficiency step-up (Skelleftea Kraft, 2011) .
6
2. Theory This section covers the principle of hydropower plant, turbine kinds, surface roughness and
efficiency.
2.1 Principle of hydropower The potential energy from water depends on the natural water cycles or hydrological process which
occurs in oceans. As the sun energy creates temperature that heats up the ocean surface of water,
thus water gets vaporized and clouds are formed. Then, these clouds move towards lower
temperature areas and the water precipitates in the form of rain or snow. The melted snow and rain
water flow towards the lower levels. Eventually, the water is transported by streams and rivers and
returns to the ocean where it evaporates again. This is known as hydrological cycle. The working
principle of a hydropower plant is to convert some of the water kinetic and potential energy into
electrical energy. Hydropower is dependent of the hydrological cycle (©2018 Encyclopædia
Britannica, 2018).
The two essential factors in hydropower are a continuous inflow of water and a hydraulic head. The
needed hydraulic head can be developed in many ways. For example, building a dam across a stream
or river can collect water and discharge it by means of a channel. The different ways of doing this
is to direct a portion of a river by building a low-head diversion arrangement, more like a barrier. A
sequence of combined power plants lengthwise a river extract the water energy before it streams out
to the sea, as in the case of the Skellefteå River in Sweden (J Luis, et al., 2018).
A standard hydropower plant is composed of a dam, penstock, spiral casing, turbine, generator,
distributor, draft tube, etc., see Figure 5. The dam creates a reservoir accumulating the water and forms
the head, i.e., the difference of water level between the upstream and downstream of the power plant,
creating a source of potential energy. The water carried from the dam by means of the penstock moves
in the spiral casing then into the distributor, along the turbines where the energy of the water rotates
the runner and in turn is transformed into electrical energy with a generator. Lastly, the water moves
out across the draft tube and finally into the river. The connection between the turbine and the generator
is made with a shaft (©2018 Encyclopædia Britannica, 2018).
Figure 5: Hydropower station diagram (Blackboard, 2002-2018).
7
The function of the draft tube is to change most of the residual kinetic energy moving out of the runner
into pressure energy. The purpose of the spiral casing is to spread the water evenly to the guide vanes
and stay vanes to make an axis-symmetric flow around the runner. The stay vanes offer a physical
support to the system. The purpose of the guide vanes is to control the flow rate through the turbine.
The benefits of hydropower are very vast. It has least effect on the environment, much lower
operational and servicing overheads, and an extended service life; which can characteristically span
about 40 years prior to a major refurbishment. Hydropower has the capability to regulate load
quickly. This capability makes hydropower appropriate for pairing with additional renewable
sources of energy to stabilize grid frequency fluctuations. Although, hydropower is a highly
effective and consistent, renewable source of energy and it can extract up to 96% of the available
energy.
Nevertheless, the preliminary venture cost is very high, and the remuneration time is long.
Additionally, certain social and ecological concerns might arise during the feasibility studies, some
of them are the population displacement, landscape corrosion, water quality anomalies. Further it
could have a negative impact on flooding and fish. For the implementation of hydropower projects
in a justifiable manner, all ecological and societal influences must be worked out earlier to the
deployment process (David Anderson, et al., 2014).
Figure 6: Installation of turbine at hydroelectric plant (Krivchenko, 1993)
2.2 Types of turbines Water turbines are classified into two categories: impulse turbine and reaction turbine. Principally,
the impulse turbine converts pressure energy of the water into kinetic energy when it moves through
the nozzle and creates a high-speed jet. The water jet is used to drives the runner. The runner is
entirely exposed to the atmospheric pressure, i.e., the impulse turbine runner is always installed
above the tailrace. Impulse turbines are suitable for high- to very high-head and small discharge
units, see Figure 7.
The runner in reaction turbine is entirely immersed in the water, which makes the runner to use
both the kinetic energy and pressure energy of the water. The flow through a reaction turbine may
be axial, axial-radial, or mixed. The reaction turbines are suitable for low-head and high discharge
8
units and for medium -head and medium discharge (Mulu , 2012).The basic types of impulse and
reaction turbines are listed in Figure 8.
Figure 7: categories of turbines according to the action of the water on the moving blades (Mulu ,
2012)
The net head available and the discharge are the main parameters required for the selection of a
water turbine type. The selection of an appropriate turbine for any hydropower stations also depend
on the site characteristics as well as the market. The specific speed is one of the important parameters
used to find out the type of turbine. It is defined as the angular speed, in revolution per minute, of
geometrically homologous turbine that would develop 1 hp under a one-meter head. Turbines with
low specific speed operate under high-head conditions, while turbines with high specific speeds
works under low-head conditions. Table 2 presents the range of specific speeds and heads for
different turbines (Mulu , 2012).
Table 2: Types of turbines with specific speed and head (Mulu , 2012)
Turbine Type Specific speed in
[rpm] Head in [m]
Kaplan 450–1200 6–70
Deriaz 300–500 30–130
Francis 80–400 40–700
Cross-flow 20–200 5–200
Turgo 20–70 300–300
Pelton 10–50 400–1700
9
2.2.1 Impulse Turbines
The impulse turbines use pressure of the liquid (water) to rotate the runner and discharge it to
atmospheric pressure. These turbines are encompassing a jet nozzle or sequence of nozzles that
convey water to the blades of a runner. Several nozzles are generally used where a large wheel isn’t
suitable. The blade’s velocity varies when the water hits the blades (specially designed to decrease
drag), this causes force to act on a turbine blade which leads to change in momentum of turbine
blades. These turbines are dependent on the capability to consume all kinetic energy from the water
to have high efficiencies. In contrast to reaction turbines, impulse turbines do not need to be
submerged. An impulse turbine is commonly used for low flow applications and high head. Types
of impulse turbines include Pelton turbines, Turgo turbines, and Cross flow turbines.
Figure 8: Pelton Turbine (Mechanical, 2018).
2.2.2 Reaction Turbines
The reaction turbine is one of the two basic types of hydro turbines. The sub category of reaction
turbine encompasses, Kaplan and Francis turbines (Energy, 2018).This turbine fundamentally works
on the principle of newton’s third law (“For every action, there is an equal and opposite reaction”).
The reaction turbine produces mechanical power with unified activity of flowing water and thrust.
This type of turbine uses pressure and kinetic energy of the water to rotate the runner. The reaction
turbines must be submerged in water entirely to develop enough pressure. Furthermore, the reaction
turbine components must be capable of withstanding high pressure levels inside the turbine. The
reaction turbines are extensively incorporated in Sweden because of country’s geographical
orientation.
2.2.3 Francis turbines
In the Francis turbines, the water enters the runner in a radial direction and exits in an axial direction.
Francis turbines have fixed runner blades and adjustable guide vanes. The number of runner blades
usually ranges from 12 to 17 (M.J, 2009). Francis turbines are best suitable for medium head stations
(Mulu , 2012). They usually operate with a head varying from 40 to 60 to 500 to 700 m. The guide
vanes are used to regulate the flow rate and guide the flow to match the runner blade angle, and to
shut down the unit. The design of the spiral casing has a decreasing cross-sectional area to maintain
a constant velocity in the volute as part of the flow moves in the distributer toward the runner.
10
Figure 9: Francis turbine (Krivchenko, 1993) (Mechanical, 2018)
In figure 9, the runner blades (1) are rigidly fixed to the crown (2’) and the band (2’’) as a result the
runner acquires the necessary strength and rigidity. The shaft flange (3) connects to the runner. The
cone (12) of the runner provides a better condition for the water leaving the runner blades. The shaft
and runner are the rotating components of the turbine. The Francis turbine size is decided by the
diameter of the runner above the inlet edges of the blades, D1.
The meridional section of Figure 9 shows the water enters the runner in a radial direction and exits
the runner in an axial direction. This type of turbine is therefore called radial-axial turbine. Water is
supplied to the runner through spiral casing (4), stayring (5), and wicket gate (6). The external
vision of the runner of a radial-axial turbine is showed in Figure 10. The turbine spiral case is usually
made of steel and is a circular cross- section to improve the conditions under which the case walls
take up the water pressure load of the turbine. The stayring vanes are designed for transporting the
load from the higher stayring band (7) to the lower (8). Therefore, the main function of the stayring
is to provide strength. Hydraulic losses are reduced by using streamlined vanes.
The wicket gate is usually made up of 20 to 24 guide vanes (6), which are designed to of the flow
to the runner inlet with a minimum of losses (Figure 9, section B-B). They also regulate the amount
of water flow through turbine and its capacity by turning the vanes and changing the opening a0 (see.
Figure 11). Cover (11) is an essential component part of the Francis turbine, in which the turbine
guide bearing (11) is secured. The pivot pins (6) and their operating gear are also secured in the
Cover.
Figure 3
11
Figure 10: A radial-axial turbine external view of the runner (Meskauskas, 2007).
The water leaves the runner to enter the draft tube diffuser, ensuring smooth reduction of velocity
and a reduced kinetic energy of the flow at the turbine outlet.
Figure 11: Adjustment of a turbine flow rate by the wicket gate (Krivchenko, 1993).
2.2.4 Axial-flow Kaplan Turbine
A Kaplan turbine is mainly a type of propeller turbine with moveable blades inside a tube. It comes
under category of axial flow turbine as the flow enter and leave the rotor axially. Figure 12 shows a
cross sectional view of a Kaplan turbine.
12
Figure 12: Kaplan Turbine (Donfang, 2014)
The Kaplan turbine is also known as inward flow reaction turbine. When fluid passes through the
turbine its pressure changes, this pressure difference produces energy. The kinetic energy and the
hydrostatic head of the flowing water help in the development of power.
The inlet of a Kaplan turbine consists of a tube, usually a scroll type. This tube is wrapped around
the wicket gate of the turbine. Fluid is conveyed tangentially through the wicket gate and spirals
around the runner.
The specially designed draft tube is an outlet that assists in decelerating the water velocity to recover
kinetic energy.
The position of the runner at a higher location may decrease the risk for cavitation (IEC 62097, 2009).
Figure 13: Comparison of Kaplan Types (Water21, 2014)
13
The most commonly used turbines in Sweden are Francis and Kaplan, due to the environmental
nature of the country. This thesis focuses on Kaplan turbines. A typical drawing of a Kaplan turbine
is shown in Figure 13. In Kaplan turbines, the flow of water moves in and exits the runner in an
axial direction. The total number of blades in runner may differ from 4 to 8; the number of blade
decreases, as the speed increases (M.J.Cervates, 2009).
Kaplan turbines can be of type single- or double-regulated turbines, i.e. only the runner blades or
both the runner blades and guide vanes are adjustable. The doubly regulated turbines are well suited
for a wider range of discharge and head conditions, due to this ability their highest efficiency can be
attained over a wider range of flow conditions.
The guide vanes and spiral casing are comparable to those used in Francis turbines. Another
important part of the reaction turbines is the draft tube, which connects the runner exit to the tailrace.
The key role of the draft tube is to permit the installation of the turbine above the tailrace level
without head loss and to convert part of the remaining kinetic energy into pressure energy.
The lower is the head, the more important the draft tube. For low-head turbines, the overall
efficiency is significantly affected by the draft tube performance, because the kinetic energy
discharging from the runner represent a substantial amount of the total head.
2.3 Surface roughness The surface roughness of any solid material can be defined as the deterioration of surface smoothness,
due to irregularities on the surface profile. It is usually caused by rough particles, feed of the machine,
painting and coating etc. This profile of surface that deviates from its actual smooth texture has a
significant impact on the performance of hydro turbine. Ra is effective and widely known surface
roughness measures usually implemented in overall engineering preparation.
The Ra units are quantified in micro-inches or micro-metres. The mean roughness is termed as
roughness average Ra which is in fact the arithmetic mean values of the roughness contour ordinates
(IEC 60193, 1999).Ra is defined as the mean absolute roughness irregularities from mean line over
one sample length as shown in Fig.14.
Figure 14: Definition of arithmetic mean surface roughness (Ra) (Gadelmawla, ES et al./Journal
of Materials Processing Technology 123(2002) 133-145)
Ra value is considered as an average value of any deviation of the surface from its ideal smoothness
devoid of the direction concerned of the deviance (top or bottom). This infers that it is usually used
to regulate the smoothness. Ra value is comparatively insensitive to single high or deep deviation
14
of the surface from its factual smoothness form. This property makes Ra value reliable from
measurement point of view. Therefore, the Ra value is applicable for indefinite surface conditions
and also applicable where certain deviation of the surface smoothness does not have any effect
(Ytstruktur-Terminologi, kravsättning och mätning” SIS handbok 539:2003 utgåva 2, ISBN 91-
7162-570-4).
There have been a lot of development in surface profile measuring devices with high accuracy, but
the most widely used device is a profile-meter, which offers a high degree of precision. Nevertheless,
a depth indicator device or a dial indicator could also be used to measure the average depth of
surfaces. There should be approximately a 30 degree angle difference between the tips of the plunger
of the indicator with respect to a vertical line, provided that the indicator plunger tip is sharp. The
projected corresponding Ra value is worked-out by division of the mean roughness depth by value
of 10 for measured values of each component. On the other hand, deep voids developed surfaces are
considered quite small because of the area of these surfaces developing deep voids related to the
total area of components under study is quite negligible (Next edition of IEC 62097, 2009).
2.4 Step-up formula This section provides information regarding the hydraulic efficiency and its step-up from model to
prototype.
2.4.1 Hydraulic efficiency
There are three components of efficiencies such as, specific hydraulic energy efficiency 𝜂𝐸 ,
volumetric efficiency (𝜂𝑄) and power efficiency (𝜂𝑇). These three efficiencies are the basis of the
hydraulic efficiency of a turbine. Apart from this, there exist some losses related with each of these
constituent efficiencies. These losses are categorised into two losses and are defined as scalable
losses and non-scalable losses. The scalable losses are relative to the Reynolds number Re. The
friction losses and leakage losses in the seals are regarded as scalable losses. The different share of
the losses which is not considered scalable with Re is termed as non-scalable loss or kinetic losses.
The non-scalable uniform losses are considered the same for both model and prototype. On the other
hand, the leakage losses Δ𝑄 in the seals have a lower importance. Furthermore, if there exists a
similarity in seals geometry among model and prototype, then it is considered as 0. In case of Kaplan
turbine, it is always 0 but it provides contribution for calculation prototype efficiency for Francis
turbine. However, this contribution is almost always negligible. In case of dissimilarity in seals
geometry between the model and prototype, then the leakage losses would vary (IEC 62097, Mikael
Sendelius Powerpoint presentation).
2.4.1.1 Specific energy efficiency
The specific energy efficiency 𝜂𝐸 is a portion of the hydraulic efficiency and is termed Δ𝐸. It has a
significant role in prototype efficiency calculation. This efficiency is affected by the Reynolds
number difference between the model and prototype, and by the difference of surface roughness Ra
of the model and prototype (IEC 62097, Mikael Sendelius Powerpoint presentation).
2.4.1.2 Power efficiency
The power efficiency, 𝜂𝑇 is also a portion of the hydraulic efficiency. The calculation part of the
power efficiency is termed Δ𝑇 . It is calculated by taking the difference of parameter of relative
roughness and Reynolds number among the model and prototype (see Appendix A). Δ𝑇 is always
0 for Kaplan turbine. In case of Francis turbine efficiency calculation for prototype, it has a little
15
influence. Nonetheless this influence is almost negligible (IEC 62097, Mikael Sendelius Powerpoint
presentation).
2.4.1.3 Volumetric efficiency
The volumetric efficiency, which is denoted by the symbol 𝜂𝑄 , is calculated by taking the difference
induced by the seals of the model and prototype. The calculation part of volumetric efficiency is
termed ΔQ. The parametric value of ΔQ for Kaplan turbine is zero and almost always zero for Francis
turbine (see section 2.4.1 Hydraulic efficiency approximately) (IEC 62097, Mikael Sendelius
Powerpoint presentation).
2.4.2 Step-up of hydraulic efficiency
The step-up hydraulic efficiency is mathematically expressed as the product of the model hydraulic
efficiency, 𝜂ℎ𝑀, times the sum of Δ𝐸 , Δ𝑇 and ΔQ (see Appendix B). In case of Kaplan turbine Δ𝑄
and Δ𝑇 are zero and for Francis turbine approximately zero (see section 24.1.2 power efficiency and
section 2.4.1.3 volumetric efficiency). Consequently, only the specific energy efficiency, Δ𝐸 , needs
to be calculated as it has an influence on the step-up efficiency of the turbine. In case of axial
machine, step-up efficiency is specified as the product of model efficiency at optimum point, i.e., at
maximum efficiency point in hill diagram for turbine and Δ𝐸 (see Equation B.3 in Appendix B).
There are two calculation methods to calculate the step-up of hydraulic efficiency Δ 𝜂ℎ according
to the IEC 62097 standard. They are namely the component wise step-up efficiency method and
whole turbine step-up efficiency method (IEC 62097, 2009). These will be explained more in
subsection below.
2.4.2.1 Component wise step-up and whole turbine step-up methods.
The Kaplan turbine step-up efficiency is specified as the product of model efficiency at optimum
point, i.e., at maximum efficiency point in hill diagram for turbine and Δ𝐸 (see section 2.4.2 Step-
up of hydraulic efficiency & Appendix B). Δ𝐸 is affected by the difference of Reynolds number and
the difference in surface roughness among the model and prototype. In the component wise step-up
method, scalable losses for each component passage, Δ𝐸𝐶𝑂 , are calculated for every single
component passage and ultimately added to obtain the whole turbine step up (see Appendix B.1). In
case of Kaplan turbine, the calculation of Δ𝐸𝐶𝑂 is carried out into two parts; stationary components
and runner part. However, for Francis turbine it is carried out on five different turbine components
such as: stay vanes, spiral case, guide vanes, runner and draft tube. The whole turbine hydraulic
step-up efficiency method, in contrast to the component wise step-up method, calculates Δ𝐸 directly
for a whole machine (see Appendix B.1). To represent the whole machine, the reference flow
velocity index 𝜅𝑢𝑂 and the representative roughness of the machine 𝑅𝑎𝑂 are defined (see Equation
B.11 & B.22 in Appendix B.1). In the calculation of Δ𝐸 to represent the whole machine (see
Equation B.10 in Appendix B.1), the representative roughness value of the machine 𝑅𝑎𝑂 and the
reference flow velocity index 𝜅𝑢𝑂 for the whole machine are much lower than when they are
compared to the flow velocity index (see Equation B.6 in Appendix B.1) and surface roughness for
each component passage (see Equation B.7 in Appendix B.1). This yields that the calculation of Δ𝐸
for a whole machine is lower in value than the calculated Δ𝐸𝐶𝑂 for each component passage based
on the component wise step-up method. Higher value of Δ𝐸𝐶𝑂 , yields higher value of step-up
efficiency. Hence, the calculation performed on the component wise step-up method of step-up
efficiency produces higher value of efficiency step-up, in comparison with whole turbine step-up
method (IEC 62097, 2009).
16
2.5 Loss distribution in a turbine This section illustrates the losses in each component of a turbine.
2.5.1 Penstock and spiral case
In the penstock and spiral case, the losses are typically considered as friction losses. It is due to the
fact that the velocity in these turbine components is significantly lower in value. Thus, it has a
minimal portion of total losses. Nevertheless, extended tunnel can develop major losses
(Lindeström, Kap 11 Effektivare vattenturbiner, Grundkurs I turbinteknik: Kvaerner Turbin AB).
2.5.2 Stay vanes and guide vanes In stay vanes and guide vanes the losses are usually considered as vortex losses and friction losses.
These losses increase with the net head because of high speed in addition to large friction area at
higher net head. The losses increase as the guide vanes height decreases. This needs large demand
on surface quality. On the other hand, the guide vanes can develop leakage losses and vortex
shedding, which might cause secondary losses in the runner consequently (Lindeström, p.3).
2.5.3 Runner The runner losses are primarily considered as friction losses, since the blades can be adjusted after
the direction of the incoming flow. For Francis turbine, large vortex losses at partial load occurs,
added to the friction losses. For this reason, special attention should be considered for surface finish,
predominantly at the periphery (Lindeström, p.3).
2.5.4 Draft tube The losses in the draft tube are mostly friction losses. The fluid flow is comparatively axial at
optimum efficiency of a turbine. Furthermore, energy losses also arise when water leaves the draft
tube. Draft tubes relative loss portion increase at low net head (Lindeström, p.3).
The Granfors power unit in Skellefteå Kraft has a maximum net head of 20 m. The unit contains a
Kaplan turbine. The approximate losses shared by each component of Kaplan turbine at the
maximum net head is described below (Lindeström, p.3).
• Spiral case: nearly 10%.
• Stay vanes and guide vanes: about 20 %.
• Runner: almost 35%.
• Draft tube: about 35%
17
3. Method Below is a description how the author collected the information material and data for the calculation
of the step-up efficiency as well as how the resulting figures.
3.1 Literature The literature which is an essential part of the theory has been taken from various textbooks in the
subject. Furthermore, model test report from Litostroj Power and also doctoral thesis along with
various articles has been studied. A few numbers of webpages have also been the basis for most of
the details included. However, a few email contacts have provided some useful information in the
subject. The calculations have been worked out according to IEC 62097 standard. Excel sheet based
on these standards is given as an accessory to enable the step-up. Finally, a study visits at Granfors
power station had been conducted to get information about the unit and see the different turbine
components like stay vanes, guide vanes, runner, draft tube, spiral casing etc.
3.2 Calculation data
3.2.1 Efficiency step-up between reduced model and prototype
The efficiency step-up is calculated with the support of excel sheets that were provided as an
attachment to the IEC 62097 standard. The required input data of the model test and prototype to
run the calculation is generated from the model test report that Skellefteå Kraft received from
Litostroj Power in 2015 (Skelleftea Kraft, 2011) (see Fig.C.1 and Fig.C.2 in Appendix C).
3.3 Generated figures of surface roughness versus step-up efficiency
An excel sheet that is provided by the IEC 62097 standard has been used to calculated and analyse
as well as to plot several figures showing the effect of surface roughness versus the efficiency step-
up for axial turbine.
18
4. Results The results are illustrated below, for the effect of surface roughness on efficiency step-up of a Kaplan
turbine, the details have been provided in the form of figures accompanied with comments
4.1 Model efficiency step-up versus surface roughness
4.1.1 Stay vanes
Figure 15: Efficiency step-up versus model stay vanes surface roughness
In figure15, the y-axis represents the hydraulic efficiency step-up while the x-axis shows the
arithmetical mean roughness (Ra) of model stay vanes. As covered in the theory section of the report,
there are two hydraulic efficiency step-up methods to calculate the efficiency step-up. They are
specifically the component wise step-up method and whole turbine efficiency step-up method. The
blue full line in the figure illustrates the calculated efficiency step-up based on the component wise
efficiency step-up method and the blue dash line signifies the calculated efficiency step-up based on
the whole turbine efficiency step-up method. The vertical red full line shows data for the surface
roughness of the model stay vanes of Granfors power unit and its impact on the efficiency step-up.
The slopes of blue line and dash blue line demonstrates a slightly upward trend, i.e., the calculated
efficiency step-up increase to a certain level as the Ra-value of the stay vanes for the model increase.
The blue full line is above the blue dash line, i.e., the blue line shows higher value of efficiency
step-up compared to the blue dash line. The deviation in calculating efficiency step-up between the
blue full line and the blue dash line is converging as the Ra-value of stay vanes goes beyond Ra-
value of stay vanes for Granfors (see red vertical line).
19
4.1.2 Guide vanes
Figure 16: Efficiency step-up versus model guide vanes surface roughness
Figure 16 shows the step-up efficiency (y-axis) and Ra-value of the guide vanes (x-axis). The orange
line shows the calculated efficiency step-up established on the component wise step-up method and
the dash orange line indicates the whole turbine step-up method. The full orange line and dash
orange line show a relative similar upward trend as for the stay vanes of model (see figure 15), i.e.,
the step-up efficiency increase with increasing Ra-value of the guide vanes. The orange line is above
the dash orange line, i.e., the full orange line indicates higher value in calculated efficiency step-up.
The deviation in efficiency step-up between the full orange line and dash orange line is similar to
the stay vanes, i.e., the deviation converges as the Ra-value increase beyond the Ra value of guide
vanes for Granfors power unit model (see blue vertical line).
20
4.1.3 Runner
Figure 17: Efficiency step-up versus model runner surface roughness.
In figure 17, the efficiency step-up (y-axis) and Ra-value of the model runner (x-axis) is shown. The
red line represents the calculated efficiency step-up based on the component wise step-up method
and the dash red line shows the whole turbine step-up method. The vertical orange line indicates the
Ra-value of the Granfors power unit runner. The red line and dash red line shows an upward trend.
The red line is situated above the dash red line, i.e., red line illustrates higher value of calculated
efficiency step-up. Furthermore, the deviation in efficiency step-up between the red line and dash
red line diverge as the Ra-value of the runner model goes beyond the Ra-value of for the Granfors
power unit runner (see orange vertical line). The character of the deviation between the slope of red
lines for runner is much more different than for stay vanes (see figure 15) and guide vanes (see
figure 16) as their deviation between the slopes of their lines getting minimal for higher value of Ra.
The impact of the runner surface roughness is much larger than for the guide vanes and stay vanes.
21
4.1.4 Stay vanes, guide vanes and runner
Figure 18: Efficiency step-up versus surface roughness of stay vanes, guide vanes and runner.
Figure 18 shows the effect of model surface roughness of stay vanes, guide vanes and runner on the
efficiency step-up. The y-axis shows the calculated efficiency step-up and x-axis shows Ra-value
of the different model turbine components. The whole turbine calculation step-up method is
excluded in the coming of the IEC standard. Consequently, in this figure only the calculated
efficiency step-up based on the component wise step-up method is discussed. The calculated
efficiency step-up based on the component wise step-up method for stay vanes, guide vanes and
runner are represented by blue, orange and red lines, respectively. The corresponding blue, orange
and red vertical lines indicate the data for Ra-value of stay vanes, guide vanes and runner of Kaplan
turbine in Granfors power unit. The slopes of blue and orange full lines of stay vanes and guide
vanes respectively are shown nearly no variation in step-up efficiency. They are overlapping.
However, the slope of red line of the runner deviates a lot from the blue and orange lines. It shows
strongly upward trend and showing noticeable variation in efficiency step-up. The roughness of the
runner model is an important parameter in the step-u formula.
22
4.2 Prototype efficiency step-up versus surface roughness
4.2.1 Stay vanes
Figure 19: Efficiency step-up versus prototype stay vanes surface roughness
In figure 19, the efficiency step-up (y-axis) and Ra-value of the prototype stay vanes (x-axis) are
shown. The blue line shows the calculated efficiency step-up based on the component wise step-up
method. The dash blue line represents the whole turbine step-up method. The vertical red line
indicates the Ra-value of the Granfors power unit stay vanes. The blue line is situated above the
dash blue line, except they converge at the initial phase of the figure. Thus, the blue line illustrates
higher value of calculated efficiency step-up. Furthermore, the deviation in efficiency step-up
between the blue line and dash blue line diverge as the Ra-value of the stay vanes prototype extend
towards Ra-value of for the Granfors power unit prototype (see red vertical line).
23
4.2.2 Guide vanes
Figure 20: Efficiency step-up versus prototype guide vanes surface roughness.
Figure 20 shows the step-up efficiency (y-axis) and Ra-value of the prototype guide vanes (x-axis).
The orange line represents the calculated efficiency step-up based on the component wise step-up
method. The dash orange line indicates the whole turbine step-up method. The vertical blue line
shows the Ra-value of the Granfors power unit guide vanes. The orange line and dash orange line
show a downward trend. The orange line is situated above the dash line, i.e., orange line illustrates
higher value of calculated efficiency step-up. Moreover, the deviation in efficiency step-up between
the orange line and dash orange line diverge a lot as the Ra-value of the guide vanes prototype
increase beyond Ra-value of for the Granfors power unit prototype (see blue vertical line).
24
4.2.3 Runner
Figure 21: Efficiency step-up versus prototype runner surface roughness.
In figure 21, the efficiency step-up (y-axis) and Ra-value of the prototype runner (x-axis) is shown.
The red line shows the calculated efficiency step-up based on the component wise step-up method.
The dash red line represents the whole turbine step-up method. The vertical orange line indicates
the Ra-value of the Granfors power unit runner. The red line and dash red line show a downward
trend. The red line is situated above the dash red line, i.e., red line illustrates higher value of
calculated efficiency step-up. Furthermore, the deviation in efficiency step-up between the slopes
of red and dash lines getting minimal for higher value of Ra. The impact of the runner surface
roughness is much larger than for the guide vanes and stay vanes.
25
4.2.4 Stay vanes, guide vanes and runner
Figure 22: Efficiency step-up versus prototype surface roughness of stay vanes, guide vanes
and runner.
Figure 22 shows the effect of prototype surface roughness of stay vanes, guide vanes and runner on
the efficiency step-up. The y-axis shows the calculated efficiency step-up and x-axis shows Ra-
value of the different prototype turbine components. The whole turbine calculation step-up method
is excluded in the coming of the IEC standard. Consequently, in this figure only the calculated
efficiency step-up based on the component wise step-up method is discussed. The calculated
efficiency step-up based on the component wise step-up method for stay vanes, guide vanes and
runner are represented by blue, orange and red lines, respectively. The corresponding blue, orange
and red vertical lines show the data for Ra-value of stay vanes, guide vanes and runner of Kaplan
turbine in Granfors power unit. The blue, red and orange lines show a downward trend. The slopes
of blue and orange full lines of stay vanes and guide vanes, respectively are shown slightly variation
in step-up efficiency. They are lying over each other. However, the slope of red line of the runner
deviates a lot from the blue and orange lines. It shows strongly downward trend and showing
noticeable variation in efficiency step-up. The roughness of the runner model is an important
parameter in the step-up formula.
26
5. Discussion The result presented in the figures show the effect of model and prototype surface roughness of stay
vanes, guide vanes and runner on efficiency step-up. The results shown in figure 19-22 for prototype
agree well with theoretical fact in the IEC 62097 standard. Thus, a larger value of efficiency step-
up can be achieved by polishing the prototype finer. However, the impact of surface roughness of
stay vanes and guide vanes needed to be discussed. In the case of Kaplan aggregate, the standard
IEC-62097 weights the surface roughness of the stay vanes and guide vanes equally. There is an
equation for stationary parts about how much surface roughness affects the efficiency and it includes
a surface roughness that applies to both guide vanes and stay vanes. This surface roughness is
calculated by an average of the surface roughness of the stay vanes and guide vanes. That is, an
improvement on the surface finish of the guide vanes has the same impact as on the stay vanes. This
is quite strange since you usually have twice as many guide vanes as stay vanes. In addition, the
water velocity is higher between the guide vanes compared with the stay vanes. The guide vanes
surface roughness should have a greater impact on the aggregate efficiency compared to the stay
vanes.
Ra-value is expected to be higher over time. This is due to damage from particles in the water, paint
damages, cavitation, sand erosion and surface erosion etc. Higher prototype Ra-value means lower
efficiency step-up.
27
6. Conclusion In this thesis, the impact of surface roughness of stay vanes, guide vanes and runner on efficiency
step-up of Kaplan turbine in the Granfors power unit was investigated, in accordance with IEC
62097 standard. The figures shown in the result section provide an answer to this investigation.
The resulting figures underline that the impact of surface roughness of stay vanes and guide vanes
on efficiency step-up is very low, i.e., it is basically negligible. However, the impact of runner
surface roughness is much larger than stay vanes and guide vanes. Therefore, it can be concluded
that it is more important to measure roughness of the runner model and prototype.
7. Recommendations Regarding the impact of surface roughness of stay vanes and guide vanes, the number of guide vanes
and stay vanes should be taken into consideration in the official excel file attached to the IEC 62097
code. This is due to the surprising fact that in the case of Kaplan aggregate, the standard IEC-62097
weights the surface roughness of the stay vanes and guide vanes equally.
The thesis aims to investigate the impact of surface roughness of stay vane, guide vanes and runner
of Kaplan turbine in Granfors power unit. However, there are other power stations in Skellefteå
Kraft, for instance the power station, Rebnis, that consists of a Francis turbine. An investigation on
that kind of turbine is recommended for future work.
A final recommendation to Skellefteå Kraft, as the conclusion clearly shows, is to measure Ra-value
of the model and prototype runner.
28
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Appendix
Appendix A Step-up formula for power efficiency (IEC 62097, 2009, p.23&p.27
Δ𝑇= 𝑑𝑇𝑟𝑒𝑓 [(7.5 ∗ 104𝜅𝑇
𝑅𝑎𝑇𝑀
𝐷𝑀+
7 ∗ 106
𝑅𝑒𝑀)
0.2
− (7.5 ∗ 104𝜅𝑇
𝑅𝑎𝑇𝑃
𝐷𝑃+
7 ∗ 106
𝑅𝑒𝑃)
0.2
]
Where
𝑑𝑇𝑟𝑒𝑓 =0 . 44 + 0.004 𝑁𝑄𝐸
2⁄
1 + 0.154𝜅𝑇0.4
𝜅𝑇 = −5.7𝑁𝑄𝐸 + 2 or 1.0 which ever larger for 0.06 ≤ 𝑁𝑄𝐸 ≤ 0.30
A.1
Appendix B Efficiency step-up (IEC 62097, 2009, p.28) The efficiency step-up of a turbine is given by the following formula:
Δ𝜂ℎ = 𝜂ℎ𝑀 (𝜂ℎ𝑃 − 1
𝜂ℎ𝑀) ≅ 𝜂ℎ𝑀(Δ𝐸 + Δ𝑇 + Δ𝑄)
B.1
For axial machine, Δ𝑇 &Δ𝑄= 0
𝜂ℎ𝑃
𝜂ℎ𝑀=
𝜂𝐸𝑃
𝜂𝐸𝑀= (1 + Δ𝐸) B.2
Or
Δ𝜂ℎ = 𝜂ℎ𝑀 ∗ Δ𝐸 B.3
Where 𝜂ℎ and 𝜂𝐸 are the hydraulic efficiency and the specific energy efficiency, respectively. The
subscripts M and P stands for model and prototype, respectively.
The component wise step-up method and whole turbine step-up method are explained in the section
below.
Appendix B.1 Component wise step-up & whole turbine step-up method (IEC
62097, 2009, pp. 63-69)
The component wise step-up method calculates Δ𝐸 for each component passage and is eventually
summed up to find the overall step-up efficiency for the entire machine. The whole turbine step-up
method calculates Δ𝐸 directly for the whole machine.
32
Calculation of Δ𝑬 based on the component wise step-up method for axial turbine (IEC
62097, 2009, p.63-65)
For axial machine, the component wise step-up method calculates Δ𝐸𝐶𝑂 for stationary parts and
runner and then summed up to find the overall step-up efficiency.
For runner:
Δ𝐸𝑅𝑈 = 𝑑𝐸𝑅𝑈𝑟𝑒𝑓 [(4 ∗ 105𝜅𝑢𝑅𝑈∗
𝑅𝑎𝑅𝑈𝑀
𝐷𝑀+
7 ∗ 106
𝑅𝑒𝑀)
0.2
− (4 ∗ 105𝜅𝑢𝑅𝑈∗
𝑅𝑎𝑅𝑈𝑃
𝐷𝑃+
7 ∗ 106
𝑅𝑒𝑃)
0.2
] B.4
Where
𝜅𝑢𝑅𝑈∗ is modified flow velocity factor for runner blades:
𝜅𝑢𝑅𝑈∗ = 1.25 ∗ 𝜅𝑢𝑅𝑈 = 1.29
For stationary part:
Δ𝐸𝑆𝑇 = 𝑑𝐸𝑆𝑇𝑟𝑒𝑓 [(4 ∗ 105𝜅𝑢𝑆𝑇
𝑅𝑎𝑆𝑇𝑀
𝐷𝑀+
7 ∗ 106
𝑅𝑒𝑀)
0.2
− (4 ∗ 105𝜅𝑢𝑆𝑇
𝑅𝑎𝑆𝑇𝑃
𝐷𝑃+
7 ∗ 106
𝑅𝑒𝑃)
0.2
] B.5
Where
𝜅𝑢𝑆𝑇 is the flow velocity factor for stationary parts
𝜅𝑢𝑆𝑇 = 0.8 ∗ 𝜅𝑢𝐺𝑉 ≈ 0.19
B.6
GV and SV represent guide vanes and stay vanes, respectively.
𝑅𝑎𝑆𝑇 is mean average roughness of guide vanes and stay vanes.
𝑅𝑎𝑆𝑇 =𝑅𝑎𝑆𝑉 + 𝑅𝑎𝐺𝑉
2
B.7
𝑑𝐸𝑅𝑈𝑟𝑒𝑓 = 0.0245 & 𝑑𝐸𝑆𝑇𝑟𝑒𝑓 = 0.01253
B.8
Finally, the efficiency step-up based on the component wise step-up method for an axial machine
can be calculated by the following formula:
Δ𝜂ℎ = 𝜂ℎ𝑀 ∗ Δ𝐸=𝜂ℎ𝑀 ∗ (Δ𝐸𝑆𝑇 + Δ𝐸𝑅𝑈) B.9
Calculation of Δ𝑬 based on the whole turbine step-up method for axial turbine (IEC
62097, 2009, p.69)
The whole turbine step-up method calculates Δ𝐸 directly to obtain the efficiency step-up.
33
Δ𝐸 = 𝑑𝐸𝑟𝑒𝑓 [(4 ∗ 105𝜅𝑢0
𝑅𝑎0𝑀
𝐷𝑀+
7 ∗ 106
𝑅𝑒𝑀)
0.2
− (4 ∗ 105𝜅𝑢0
𝑅𝑎0𝑃
𝐷𝑃+
7 ∗ 106
𝑅𝑒𝑃)
0.2
] B.10
The scalable loss in the stationary part of an axial machine is half as large as the runner (see Figure
B.1). Then, to represent the entire machine the reference flow velocity index, 𝜅𝑢0 and representative
roughness of the machine are given as follows:
𝜅𝑢0 =2 ∗ 𝜅𝑢𝑅𝑈 + 𝜅𝑢𝑆𝑇
3=
2 ∗ 1.29 + 0.19
3≈ 0.92
B.11
𝑅𝑎0 =2 ∗ 𝑅𝑎𝑅𝑈 + 𝑅𝑎𝑆𝑇
3
B.12
𝑑𝐸𝑟𝑒𝑓 = 𝑑𝐸𝑅𝑈𝑟𝑒𝑓 + 𝑑𝐸𝑆𝑇𝑟𝑒𝑓
B.13
Finally, the efficiency step-up based on the whole turbine step-up method for an axial machine can
be calculated by the following formula:
Δ𝜂ℎ = 𝜂ℎ𝑀 ∗ Δ𝐸 B.14
Figure B.1: 𝜹𝑬𝒓𝒆𝒇 axial turbine (IEC 62097, p.66)
34
Appendix C Input required data for model and prototype. The required input data of the model test and prototype to run the calculation is generated from the
model test report that Skellefteå Kraft received from Litostroj Power in 2015.
Figure C.1: Screenshot of model data from excel sheet
Figure C.2: Screenshot of prototype data from excel sheet
