Technical Papers - latiniahr.comlatiniahr.com/docs/journal_6.pdf · Marra, João M.; Gramani,...

American Journal of Hydropower, Water and Environment Systems, july 2016 1

Volume 6 • Jan. 2018ISSN 2317-126X • US$: 15.00

AmericAn JournAl of Hydropower, wAter And

environment SyStemS

Technical Papers

06 PUMPED HYDROELECTRIC ENERGY STORAGE SYSTEMS (PHES): CHALLENGES AND PERSPECTIVES IN THE BRAZILIAN ENERGY SCENARIORaimundo, Danielle Rodrigues; Filho, Geraldo Lúcio Tiago

11 HYDRODYNAMIC BEHAVIOR ON KAPLAN TURBINES: EXPERIMENTAL METHODOLOGY FOR THE EVALUATION OF CAVITATION DEVELOPMENT BASED ON DYNAMIC MEASUREMENTSRivetti, ArturoL; ANGULO Mauricio A.; LUCINO Cecilia V.; BOTERO Francisco.; LISCIA, Sergio O.

16 TECHNICAL AND ECONOMIC EVALUATIONS FOR DECISION-MAKING ON THE REPOWERING OF SMALL HYDROPOWER PLANTS AND THE OPTIMUM EXPLOIT OF EXISTING PLANTS IN BRAZIL Oliveira, Marcos André

25 EVALUATION OF HYDROELECTRIC, WIND AND SOLAR POTENTIAL: A CASE STUDY OF EXISTING PLANTSFilho,Wilson Pereira Barbosa; Silva, Lívia Maria Leite da; Silva, Nathan Vinícius Martins da; Oliveira, Karina Aleixo Benetti de; Abreu, Anna Luisa de Oliveira; Swiatovy, Gabriel Hepp

33 PREDICTION OF PRESSURE PULSATION IN FRANCIS TURBINES USING RANS SOLUTION: AN APPLIED STUDY OF EFFECTS OF THE TURBULENCE MODELS, MESH, DOMAIN EXTENSION AND MULTIPHASE FLOWMarra, João M.; Gramani, Liliana M.; Zubeldia, Luiz F.; Kaviski, Eloy

Published with the support of Hydraulic Machinery and Systems

International Association

WORKING GROUPlatinamerican

Editorial Demand for electricity is increasing rapidly in Latin America. Expanding and enhancing the

current power generation infrastructure is thus a major concern for the region. In that context, renewable energy is bound to play a relevant role in the coming years and hydroelectric energy especially so in view of its relatively unexploited potential, which is estimated in around 690,000 MW in the region.

Our mission is to contribute to the regional integration by means of the production of knowledge in the field of hydroelectric power generation and hydromechanical systems, with focus on technological advance and the rise of quality standards, but with an eye on the priorities of a region where, well into the XXI century, millions of people find themselves deprived of electricity. That includes the topics such as the evaluation of the development of projects of low environmental impact, the role of hydroelectric powerplants in the face of the diversification of the energy matrix as well as mini- and small-hydro projects to meet the demand of areas with no access to the electrical network.

Three symposia have been held and six editions of this Journal have been published since the creation of this, the Latin Group, in 2012. Added to that are postgraduate courses and exchange programs that are being organized at present. Mexico, Brazil, Ecuador, Colombia, Uruguay and Argentina are the most active members of the Group and it is our goal to get more involved in the future.

We firmly believe in the ability of our universities to conduct the research in the field of hydraulic turbomachinery and that this knowledge will have a beneficial impact on the policy making of our countries, whether on matters related to existing infrastructure as well as the development of long-term projects and strategies.

We understand that keeping and strengthening the link between the nations currently participating is a major challenge in the framework of a constantly evolving reality, seen reflected in the availability of economic resources, the technological tools and the swings of institutional management. May this new edition of the Journal serve as evidence that, however difficult, such challenge is achievable.

Eng. Sergio O. LisciaPresidente Latin Group 2017-2021

IAHR DIVISION I: HYDRAULICSTECHNICAL COMMITTEE: HYDRAULIC

MACHINERY AND SYSTEMS

Editors in Chief Prof. Geraldo Lucio Tiago Fº - UNIFEIProf. Eduard Egusquiza - UPC

Executive Editors Prof. Carlos Martinez - UFMGEng. Humberto Gissoni - VOITH

Technical EditorsProf. Regina Mambeli Barros - UNIFEIProf. Cecilia Lucino - UNLP

Journalist in chargeAdriana Barbosa MTb - MG 05984JP

Graphic Projec/ DiagrammingLidiane Silva

Circulation1,000 copies

Federal University of Itajubá - UNIFEIAv. BPS, 1303 - Bairro Pinheirinho

Itajubá - MG - Brasil - CEP: 37500-903

ISSN 2317-126X


environment SyStemS

LAWG-IAHR Executive Secretariat Lucia Garrido Rios

[email protected]

Catalographic card prepared by Mauá Library – Librarian Margareth Ribeiro – CRB_6/1700

R454

American Journal of Hydropower, Water and Environment Systems, LAWG-IAHR, v.1, 2014 – Itajubá: LAWG- IAHR, 2015 - v.6, jan. 2018.

Trimestral, Editors Chief: Geraldo Lúcio Tiago Filho/Eduard Egusquiza Journalist in Charge: Adriana Barbosa – MTb_MG 05984 ISSN 2317-126X

1. Hydropower. 2. Water. 3. Enviroment Systems. II. Latin American Working Group

2 American Journal of Hydropower, Water and Environment Systems, jan 2018

American Journal of Hydropower, Water and Environment Systems

A publication of Latin American Working Group of the International Association for Hydro-Environment Engineering and Research-IAHR

All papers must be submitted in English. In case the author wants to translate the article through the journal all costs for the translation will be charged on the account of the author.

1. Formatting articles

1.1. Article structure

1.1.1 Subdivision - numbered sections

Divide your article into clearly defined and numbered sections. Subsections should be numbered 1.1 (then 1.1.1, 1.1.2, ...), 1.2, etc. (the abstract is not included in section numbering). Use this numbering also for internal cross-referencing: do not just refer to ‘the text’. Any subsection may be given a brief heading. Each heading should appear on its own separate line.

1.1.2 Format

All text of the manuscript must be located within a 170 mm by 252 mm rectangle of a white A4 page or within 170 mm by 240 mm for the letter format. The margins are given in Table 1. An example of the page format is given in Fig. 1

[Table 1]: Page margin for manuscripts.

Margin Position Top Bottom Left Right

Margin size (cm) 2.0 2.5 2.0 2.0

All text should be single spaced, black and in 12-point type. “Times News Roman” or a similar proportional font should be used. Total length 15 pages in Word.

The terminology given in the IEC Technical Report for the Nomenclature of Hydraulic Machinery is recommended.

Introduction State the objectives of the work and provide an adequate

background, avoiding a detailed literature survey or a summary of the results.

Material and methods Provide sufficient details to allow the work to be reproduced.

Methods already published should be indicated by a reference: only relevant modifications should be described.

Theory/calculation A Theory section should extend, not repeat, the background

to the article already dealt with in the Introduction and lay the foundation for further work. In contrast, a Calculation section represents a practical development from a theoretical basis.

Results Results should be clear and concise.

Discussion This should explore the significance of the results of the

work, not repeat them. A combined Results and Discussion section is often appropriate. Avoid extensive citations and discussion of published literature.

Conclusions The main conclusions of the study may be presented in a

short Conclusions section, which may stand alone or form a subsection of a Discussion or Results and Discussion section.

INSTRUCTIONS FOR AUTHORS

References

Within the text, references should be cited in numerical order according to their order of appearance. The numbered reference citation within text should be enclosed in brackets.

After the second edition all papers must have at least one reference of the American Journal of Hydropower, Water and Environment Systems.

Example: It was shown by Prusa [1] that the width of the plume decreases under these conditions.

In the case of two citations, the numbers should be separated by a comma [1,2]. In the case of more than two references, the numbers should be separated by a dash [5-7].

List of References. References to original sources for cited material should be listed together at the end of the paper; footnotes should not be used for this purpose. References should be arranged in numerical order according to the sequence of citations within the text. Each reference should include the last name of each author followed by his initials.

(1) Reference to journal articles and papers in serialpublications should include:

• last name of each author followed by their initials• year of publication• abbreviated title of publication in which it appears• full title of the cited article in quotes, title capitalization• volume number (if any) (Do not include the abbreviation,

“Vol.”)• issue number (if any) in parentheses (Do not include the

abbreviation, “No.”)• inclusive page numbers of the cited article (include “pp.”)

(2) Reference to textbooks and monographs shouldinclude:

• last name of each author followed by their initials• year of publication• titles in examples may be in italic• publisher• city of publication• inclusive page numbers of the work being cited (include “pp.”)• chapter number (if any) at the end of the citation following

the abbreviation, “Chap.”

(3) Reference to individual conference papers, papersin compiled conference proceedings, or any othercollection of works by numerous authors shouldinclude:

• last name of each author followed by their initials• year of publication• full title of the cited paper in quotes, title capitalization• individual paper number (if any)• full title of the publication• initials followed by last name of editors (if any), followed by

the abbreviation, “eds.”• publisher• city of publication• volume number (if any) in boldface if a single number,

include, “Vol.” if part of larger identifier (e.g., “PVP-Vol. 254”)• inclusive page numbers of the work being cited (include “pp.”)

(4) Reference to theses and technical reports shouldinclude:

• last name of each author followed by their initials• year of publication• full title in quotes, title capitalization• report number (if any)• publisher or institution name, city

American Journal of Hydropower, Water and Environment Systems, jan 2018 3


Sample References[1] Ning, X., and Lovell, M. R., 2002, “On the Sliding

Friction Characteristics of Unidirectional Continuous FRPComposites,” ASME J. Tribol., 124(1), pp. 5-13.

[2] Barnes, M., 2001, “Stresses in Solenoids,” J. Appl. Phys.,48(5), pp. 2000–2008.

[3] Jones, J., 2000, Contact Mechanics, Cambridge UniversityPress, Cambridge, UK, Chap. 6.

[4] Lee, Y., Korpela, S. A., and Horne, R. N., 1982, “Structure ofMulti-Cellular Natural Convection in a Tall Vertical Annulus,”Proc. 7th International Heat Transfer Conference, U. Grigulet al., eds., Hemisphere, Washington, DC, 2, pp. 221–226.

[5] Hashish, M., 2000, “600 MPa Waterjet Technology Development,”High Pressure Technology, PVP-Vol. 406, pp. 135-140.

[6] Watson, D. W., 1997, “Thermodynamic Analysis,” ASMEPaper No. 97-GT-288.

[7] Tung, C. Y., 1982, “Evaporative Heat Transfer in the ContactLine of a Mixture,” Ph.D. thesis, Rensselaer PolytechnicInstitute, Troy, NY.

[8] Kwon, O. K., and Pletcher, R. H., 1981, “Prediction of theIncompressible Flow Over A Rearward-Facing Step,” TechnicalReport No. HTL-26, CFD-4, Iowa State Univ., Ames, IA.

[9] Smith, R., 2002, “Conformal Lubricated Contact of Cylindrical Surfaces Involved in a Non-Steady Motion,” Ph.D. thesis,http://www.cas.phys.unm.edu/rsmith/homepage.html

1.1.2 Essential title page information• Title. Concise and informative. Titles are often used in

information-retrieval systems. Avoid abbreviations andformulae where possible.

• Author names and affiliations. Where the family name maybe ambiguous (e.g., a double name), please indicate this clearly. Indicate all affiliations with a number immediately after theauthor’s name and in front of the appropriate address. Providethe full postal address of each affiliation, including the countryname and, if available, the e-mail address of each author.

• Author résumé. The author must inform the graduationdegree, post graduation, affiliation and email address. Therésumé must not exceed 150 characters.

• Corresponding author. Clearly indicate who will handlecorrespondence at all stages of refereeing and publication,also post-publication. Ensure that e-mail address and thecomplete postal address are provided. Contact details mustbe kept up to date by the corresponding author.

• Present/permanent address. If an author has movedsince the work described in the article was done, or wasvisiting at the time, a ‘Present address’ (or ‘Permanentaddress’) may be indicated as a footnote to that author’sname. The address at which the author actually did thework must be retained as the main, affiliation address.Superscript Arabic numerals are used for such footnotes.

Abstract A concise and factual abstract is required. The abstract

should state briefly the purpose of the research, the principal results and major conclusions. An abstract is often presented separately from the article, so it must be able to stand alone. For this reason, References should be avoided, but if essential, then cite the author(s) and year(s). Also, non-standard or uncommon abbreviations should be avoided, but if essential they must be defined at their first mention in the abstract itself.

Keywords

Immediately after the abstract, provide a maximum of 6 keywords, using American spelling and avoiding general and plural terms and multiple concepts (avoid, for example, ‘and’,

‘of’). Be sparing with abbreviations: only abbreviations firmly established in the field may be eligible. These keywords will be used for indexing purposes. Abbreviations

Define abbreviations that are not standard in this field in a footnote to be placed on the first page of the article. Such abbreviations that are unavoidable in the abstract must be defined at their first mention there, as well as in the footnote. Ensure consistency of abbreviations throughout the article. Acknowledgements

Collate acknowledgements in a separate section at the end of the article before the references and do not, therefore, include them on the title page, as a footnote to the title or otherwise. List here those individuals who provided help during the research (e.g., providing language help, writing assistance or proof reading the article, etc.). Nomenclature and units

Follow internationally accepted rules and conventions: use the international system of units (SI). If other quantities are mentioned, give their equivalent in SI. Math formulae

Present simple formulae in the line of normal text where possible and use the solidus (/) instead of a horizontal line for small fractional terms, e.g., X/Y. In principle, variables are to be presented in italics. Powers of e are often more conveniently denoted by exp. Number consecutively any equations that have to be displayed separately from the text (if referred to explicitly in the text).

Footnotes Footnotes should be used sparingly. Number them consecutively

throughout the article, using superscript Arabic numbers. Many wordprocessors build footnotes into the text, and this feature may be used. Should this not be the case, indicate the position of footnotes in the text and present the footnotes themselves separately at the end of the article. Do not include footnotes in the Reference list. Table footnotes

Indicate each footnote in a table with a superscript lowercase letter.

Artwork

Electronic artwork General points

• Make sure you use uniform lettering and sizing of youroriginal artwork.

• Save text in illustrations as ‘graphics’ or enclose the font.• Only use the following fonts in your illustrations: Arial,

Courier, Times, Symbol.• Number the illustrations according to their sequence in the text.• Use a logical naming convention for your artwork files.• Provide captions to illustrations separately.• Produce images near to the desired size of the printed

version.• Submit each figure as a separate file.• Pictures, graphics and images must be submitted in a JPG

or GIF format with 300 dpi.

2 Conducting the Review

2.1 OriginalityYou might wish to do a quick literature search using tools

such as Scopus to see if there are any reviews of the area. If the research has been covered previously, pass on references of those works to the editor.


2.2 StructureConsider each element in turn: Title; Abstract; Introduction (It should describe the experiment, the hypothesis(es) and the

general experimental design or method); Method; Results; Conclusion/Discussion; Language: you do not need to correct the English. You should bring this to the attention of the editor, however.

2.3 Previous Research

If the article builds upon previous research does it reference that work appropriately? Are there any important works that have been omitted? Are the references accurate?

2.4 Ethical Issues

Plagiarism: If you suspect that an article is a substantial copy of another work, please let the editor know, citing the previous work in as much detail as possible

Fraud: It is very difficult to detect the determined fraudster, but if you suspect the results in an article to be untrue, discuss it with the editor

AUTHORIZATION FOR PUBLICATION OF PAPERS

LICENSE FOR USE OF INTELLECTUAL WORK (Author)

For this private instrument the AUTHOR, below signed authorizes the IAHR Latin American Working Group, to publish its work authorship, without any obligation and in exclusiveness character for the period of six months starting from the publication in the AMERICAN JOURNAL OF HYDROPOWER, WATER AND ENVIRONMENT SYSTEMS, or in another official publication of IAHR.

In case of joint authorship, the first author signs as AUTHOR, assuming before IAHR the commitment of informing the other authors of the granted license.

AUTHOR (full name in form letter):

Title of the Paper:

JOINT AUTHORS [full name in form letter]:

ADDRESS:

.

Email:



Technical Papers

06 PUMPED HYDROELECTRIC ENERGY STORAGE SYSTEMS (PHES): CHALLENGES AND PERSPECTIVES IN THE BRAZILIAN ENERGY SCENARIORaimundo, Danielle Rodrigues; Filho, Geraldo Lúcio Tiago

11 HYDRODYNAMIC BEHAVIOR ON KAPLAN TURBINES: EXPERIMENTAL METHODOLOGY FOR THE EVALUATION OF CAVITATION DEVELOPMENT BASED ON DYNAMIC MEASUREMENTSRivetti, Arturo; Angulo Mauricio A.; Lucino Cecilia V.; Botero Francisco; Liscia, Sergio O.

16 TECHNICAL AND ECONOMIC EVALUATIONS FOR DECISION-MAKING ON THE REPOWERING OF SMALL HYDROPOWER PLANTS AND THE OPTIMUM EXPLOIT OF EXISTING PLANTS IN BRAZIL Oliveira, Marcos André

25 EVALUATION OF HYDROELECTRIC, WIND AND SOLAR POTENTIAL: A CASE STUDY OF EXISTING PLANTSFilho,Wilson Pereira Barbosa; Silva, Lívia Maria Leite da; Silva, Nathan Vinícius Martins da; Oliveira, Karina Aleixo Benetti de; Abreu, Anna Luisa de Oliveira; Swiatovy, Gabriel Hepp

33 PREDICTION OF PRESSURE PULSATION IN FRANCIS TURBINES USING RANS SOLUTION: AN APPLIED STUDY OF EFFECTS OF THE TURBULENCE MODELS, MESH, DOMAIN EXTENSION AND MULTIPHASE FLOWMarra, João M.; Gramani, Liliana M.; Zubeldia, Luiz F.; Kaviski, Eloy

IAHR DIVISION I: HYDRAULICSTECHNICAL COMMITTEE: HYDRAULIC

MACHINERY AND SYSTEMS

Scientific Committee

Alexandre Kepler

André Mesquita

Antonio Brasil Júnior

Arthur Leotta

Augusto Nelson Viana

Benedito Márcio de Oliveira

Carlos Barreira Martinez

Cecilia Lucino

Daniel Fernández

Daniel Rodriguez

Edmundo Koelle

Facundo González

Fernando Zárate

Gabriel Tarnowski

Geraldo Lucio Tiago Filho

Humberto de Camargo Gissoni

Jaime Espinoza

José Carlos Amorim

José Cataldo

José Geraldo P. de Andrade

Juan Carlos Cacciavillani

Lubienska Cristina Lucas Jaquie Ribeiro

Luciano dos Santos

Miguel Tornell

Orlando Anibal Audisio

Rafael Acedo Lopes

Regina Mambeli Barros

Ricardo Vasconcellos

Roque Zanata

Segen Farid Estefen

Sergio Galván

Sergio Liscia

Ticao Siguemoto

Victor Hidalgo

Zulcy de Souza

Number 6 Jan 2018


environment SyStemS


Pumped Hydroelectric Energy Storage Systems (PHES): challenges

and perspectives in the Brazilian energy scenario1 Raimundo, Danielle Rodrigues; 2Filho, Geraldo Lúcio Tiago

1Universidade Federal de Itajuba, Itajubá, MG BRAZIL2Universidade Federal de Itajubá, MG Brasil - [email protected]

ABSTRACT

The expansion of renewable energy sources, encouraged by the growing concern for the environment and for combating global warming effects, has raised the issue of energy storage to regulate the intermittent characteristic of alternative sources, such as solar and wind. In this way, pumped hydroelectric energy storage systems (PHES) emerge as the oldest storage technology on the planet, presenting high technological maturity, low environmental impacts and high efficiency. A PHES study is proposed in this article, showing its main characteristics and challenges in the world energy scenario, with a special focus on the Brazilian scenario. The presence of reversible plants already adds over 127 GW of installed power worldwide, with particular reference to countries such as Japan and USA. In Brazil, this type of enterprise still faces many barriers, such as lack of regulation, economic and environmental issues. However, the government has already made efforts to insert this technology in the energy market, establishing criteria, prospecting possible locations and proposing regulatory measures for tariff regulation. Pilot projects should be encouraged to observe in practice the effectiveness of government efforts and begin to expand this form of energy storage.

KEYWORDS: pumped hydro energy storage, energy storage, Brazilian energy market.

1. INTRODUCTION

The increase in renewable sources consumption, consideredas intermittent sources, allied to demand fluctuations, has raised the issue of energy storage and its effects on the grid [1]. This increase has been motivated by concern about global warming and climate change, and, in this scenario, the development of energy storage systems is crucial to allow the expansion of renewable energy production, both in small and large scale. The function of these systems is to regulate and level the daily fluctuations of renewable energies, ensuring greater stability and reliability to the electrical system [2]. In addition, besides being technical managerial solutions of the network, the storage systems also contribute to the use of clean energies and their autonomy [3].

There are a number of energy storage systems, such as compressed air, batteries, flywheels, capacitors, hydrogen and pumped hydroelectric energy storage systems (PHES). PHES are a versatile type of hydroelectric plant, which use two reservoirs at different heights. At peak times, water flows from the upper reservoir to the lower, driving an electric generator through a hydraulic turbine. During periods of low consumption, the water is pumped to the upper reservoir in order to be used again in the hours of high consumption [4].

The present article aims to present a PHES’ study, showing its main technical, environmental, operational and economical characteristics, beyond the challenges in the world energy scenario. In addition, special attention will be given to state of art of this technology in Brazil, the government's plans and the challenges of PHES in the Brazilian energy matrix.

2. LITERATURE REVIEW

2.1. PUMPED HYDROELECTRIC ENERGY STORAGE (PHES)

As already mentioned, pumped hydroelectric energy storage systems (PHES) are a versatile type of hydroelectric,

which have two reservoirs. During daytime, period of greatest energy consumption, PHES uses water from the upper reservoir to generate electricity and stores it in the lower reservoir. At night, when energy consumption is lower, PHES pump back the water stored in the lower reservoir to the upper reservoir, establishing a sort of closed loop, which continually reuses the water [5]. Figure (1) shows the operational scheme of a PHES.

[Figure 1: Operational scheme of a PHES (THE HEA, 2013) apud [4].]

As reported by Pasten and Santamarina [6], the bigger level difference between the two reservoirs and the bigger flow, the more energy will be produced. Reservoir planning is the most critical element of a reversible plant, and its construction can be by two forms, according to Schreiber (1978) apud [7]. The first form is the closed circuit plants, or also called "pure pumping plants". They are independent of the river, where water flow transits between the two reservoirs and, possibly, an additional flow is necessary to replace the losses by evaporation and infiltration. The second form is open or semi-open power plants, where the reservoirs are built on riverbed, being used as conventional hydroelectric plants during daytime, and at night, surplus renewable energies are used for pumping [7].

2.2. TECHNICAL ASPECTS

The technical characteristics of reversible hydroelectric plants are not only points of energy supply, but also electric

American Journal of Hydropower, Water and Environment SystemsPublisher: Acta Editora/LAWG-IAHRDOI:10.14268/ajhwes.2018.00051ISSN: 2317-126XSubject Collection: Engineering, Subject: engineering, measurement, environment Systems


grid execution tools [8]. A PHES can operate as much a charge source as a energy source. The PHES is used as a pump, consuming energy in hours of low demand, or as a generator, generating energy during peak hours, and this is not possessed by any other type of power plants [8].

Reversible pump drops range from 100 to 800 meters. The turbines output power varies between 10 and 500 MW, not requiring high levels of water quality, can be operated even at sea [9]. The PHES’ efficiency can reach from 70 to 85% [6]. Some PHES can pass from pumping stage to the maximum power generation in just 2 minutes, and the standby for maximum load in just 12 seconds. This advantage can bring numerous benefits to these plants when installed near the consumption centers, because it avoids investment in transmission lines and, consequently, reduces energy losses [10].

In comparison to other large-scale storage systems, such as battery banks and compressed air, investment in PHES is lower, with longer lifetime and greater stability. Therefore, pumped storage hydropower plants are considered the best tools for large-scale energy storage, and currently the most mature and practical technology [8], as shown in figure (2).

[Figure 2: – Maturity of energy storage technologies (IRENA, 2014) apud [4].]

2.3. ADVANTAGES AND ENVIRONMENTAL IMPACTS

World energy systems are highly dependent on fossil fuels today, that causing greenhouse effect by emitting toxic substances. In this sense, PHES can be utilized to reduce the environmental emissions of CO2, SO2, and NO2, besides decreasing the dependency on thermal generating units [22].

Due to the similarity in reservoirs construction, environmental impacts of reversible plants are much closer to conventional hydroelectric plant, such as changes in the flow rate, widening of riverbed, impacts on flora and fauna, socioeconomic impacts, and others [7]. Reversible plants’ construction has few negative consequences, in relation to conventional plants, such as no air pollution and small losses of land resources [11]. Moreover, the impact of hydroelectric plants is observed only at the local level, and it is possible to take mitigating measures to reduce damages to environment, making them tolerable, considering the benefits of this energy type [12], which also applies to PHES.

The positive effects, observed by [11] with data collected on-site in some European reversible plants, are intensification of water circulation, improvement of water quality due aeration, sedimentation, intensification of oxidation and mineralization of some organic and biogenic substances, improvement of self-purifying capacity of the reservoirs, among others. The increase of biogenic substances into the photic zone promotes an increase of planktonic organisms’ reproduction. The greater

water aeration allows the elimination of oxygen stratification, which reduces the portion of blue-green algae.

Also in agreement with [11], some negative effects were also observed, such as fish death in pumping phase and turbidity increase. During operation of one of the plants observed, in a pump regime, up to 90% of zooplankton in the water being pumped dies. Death is most considerable in the spring, when rotifers dominate in the zooplankton. Despite high reproduction rates are characteristic for zooplankton, this factor is very significant. About fish death, in some of the observed PHES, the amount was not significant, and in other places, the diversity of organisms was higher in the reservoirs than in the river [11].

About socio-economic impacts, reservoirs used for hydropower purposes, both nature and artificial, has multiple uses and are important part of a nature. One of this multiple purposes is the recreational usage, where people can do fishing, swimming, kayaking, and many others. When introducing pumping, there will be changes which can affect the recreational and aesthetical values. This changes could lead to changes in water quality, visible changes in the shoreline zone and possibly significant areas of exposed littoral zone can cause undesirable odors [23].

About the advantages of reversible plants, a study by Companhia Energética de São Paulo [13], in partnership with Eletronorte, enumerated the benefits of this type of energy storage. Among them is the support for expansion of intermittent renewable sources, such as solar and wind power, as well as support to run-of-river power plants and increase reliability and quality of energy supply. There is still reactive power control, system stability, modulation of load variations, decrease of thermoelectric plants dispatch, better installed capacity utilization and cost reduction of acquiring energy at peak times, among other advantages.

3. METHODOLOGY

This study uses articles available in literature to build thestate of art of PHES technology in the global energy scenario. For Brazil, in addition to articles, government documents and symposium presentations were used in order to know the plans of Brazilian government for PHES resumption in the national matrix.

3.1. DATA COLLECTION

To compose the study, scientific articles and works available in the literature were selected, which had the theme of energy storage from the reversible hydroelectric plants, their main characteristics, challenges and perspectives. The analysis was carried out both for worldwide scenario and for Brazil, in order to establish a comparison between the development stages of this technology type and to propose suggestions for PHES advancement in the national energy market.

4. RESULTS AND DISCUSSION

4.1. PUMPED HYDROELECTRIC ENERGY STORAGE IN THE WORLD

The hydraulic potential utilization through the reversible plants appeared around 1890 in Europe and today it reaches over 127 GW of power worldwide [2, 5]. At a country level, Japan has the largest installed capacity of PHES, with 25 GW, followed by China and USA [14], as shown in table (1) and figure (3) below.


[Table 1]: Installed PHES capacity by country in 2014.

Country Installed

PHS capacity (GW)

Under construction

(GW)

PHES power capacity as a % of installed electrical

generating capacity

Japan 24.5 3.3 8.5

China 22.6 11.6 1.8

USA 20.5 - 1.9

Italy 7.1 - 5.7

Spain 6.8 - 6.6

Germany 6.3 - 3.5

France 5.8 - 4.4

India 5.0 1.7 2.2

Austria 4.8 0.2 21

Great Britain 2.7 - 3.0

Switzerland 2.5 2.1 12

Portugal 1.1 1.5 6.1

[Figure 3: Figure (3) – Global installed PHES capacity [15].]

At the beginning of its development, the reversible hydroelectric plants were built up only in geographically favorable locations. The most significant expansion occurred in the post-war period of World War II, when economies began to recover and there was an increase in the complexity of electric power systems. The 1990s saw an abrupt decline in the number of new PHES installed worldwide, but in the beginning of 21st century, there has been a renewed worldwide interest in the PHES technology, as an integrator for intermittent solar and wind power production [15].

4.2. PUMPED HYDROELECTRIC ENERGY STORAGE IN BRAZIL

In Brazil, there are only two plants that could be classified as reversible, but do not act as such PHES: the Pedreira Elevatory Plant and the Traição Plant, both in the state of São Paulo [10]. A study [16] of the EPE (Energy Research Company) carried out a survey of the potential of PHES in Brazil, presented at the X Symposium on Small and Medium Hydroelectric Plants and Reversible Plants, occurred in 2016. As stated in the study, the regions with the greatest potential for reversible plants installation are São Paulo, Rio de Janeiro, Minas Gerais, Ceará and Pernambuco [16].

4.3. CHALLENGES OF PUMPED HYDROELECTRIC ENERGY STORAGE

Pumped storage hydropower plants have many advantages, already described in the course of this paper, as reducing the instability due to intermittent renewable sources. However, this type of energy storage technology also has its challenges. In accordance with [17], reservoirs are under water flow variation, which makes them vulnerable to rain, melting,

evaporation, infiltration, etc. Climate change also affects the reversible system when exposed to years of drought and higher temperatures, as well as environmental issues that must be taken into account during the installation and operation phase. However, the author [17] argues that these challenges can be considered insignificant, since well-planned and executed projects can solve these problems.

In relation of the operation of PHES, Pérez-Díaz et.al. [18] discusses three main challenges: uncertainties of real-time use, revision of long-term guidelines and definition of optimal strategies for the operation of PHES, according to their characteristics. Uncertainties in energy delivery are an ongoing and current challenge, which if it is solved, could increase the participation of PHES and intermittent sources, consequently improving the economic viability of reversible plants [18]. As reported by the authors, there are several models of price forecasting, but none of them were applied in real time in the energy reserves. In addition, around the world, backup power services are remunerated by two different concepts: availability and delivery. The amount of energy, in real time, for system equilibrium purposes depends on the system imbalances themselves. In places with large amounts of non-dispatchable energy, the need for balancing services is higher, and the opposite is also true.

The concern about uncertainties in energy prices in short-term generation has been a much discussed topic during the last decade, as said in [19]. In this article, more sophisticated forecasting methods in the USA are mentioned, such as Conejo et.al (2002, apud [19]), where market compensation prices for the following day are modeled by a density function of probability. And the offers of energy sales are obtained by the MILP, deterministic mixed integer linear programming. This model aims to maximize the weekly profit of a PHES. The uncertainty of hourly prices of energy market and regulation are considered through the variation of the corresponding forecasts errors. The uncertainty of the energy delivery and its use in real time is modeled by means of a probability parameter, included in the equation of the upper reservoir water balance. Although it is an approximate approach, it is the first attempt to model the use of water for the purposes of load frequency control [19].

For the review of the long-term guidelines, the authors [18] consider a new operating strategy, executing the short-term scheduling models for longer periods of one or moreweeks. Thus, several historical scenarios characteristic ofeach enterprise would be run, beginning on different days,to obtain the periods of greater profit, within the conditionsof each model. For the strategies definition, the authors [18]commented that new operating models are mandatory, such asthose of variable speed equipment and plants that operate in ahydraulic short-circuit. The hydraulic short-circuit was definedby [19] when the operation allows to provide load frequencycontrol through simultaneous pumping with rated power andturbine power generation control.

In addition to uncertainties of PHES operational schemes, there are also the competitive challenges, which contribute to the uncertain outlook of PHES development in the United States, for example. In recent years, natural gas production in the USA has been expanding quickly, which causes a decrease of its price and render PHES uncompetitive. On the other hand, the carbon dioxide emissions and the advance of intermittent renewable power can increase the development of PHES [24]. Another impasse is the question of how hydroelectric are still seen by the population. Many people don’t consider it as a “green energy”. In this way, much research is still needed in the area, but these changes of vision take time [25].


In terms of costs, a study in [26] shows that in a few years, from the specialists’ point of view, the cost trend of a PHES system would be as profitable as diesel, overcoming the competitiveness of batteries, which today constitute the most common form of energy storage.

4.4. CHALLENGES OF PUMPED HYDROELECTRIC ENERGY STORAGE IN BRAZIL

As already seen in this article, the hydroelectric reversible plants have numerous challenges of operation and control, within an energy market. The potential of PHES on the planet is significant and several countries, such as Japan, China and USA, are already able to develop methods and technologies that can getting around the difficulties of this storage system and expand its facilities. Unfortunately, this type of enterprise has not been explored yet very well in Brazil, although many studies of the federal government point to great potential throughout the country [4, 5, 7, 10, 13, 16 e 20].

Brazil was the first country in the world to install a reversible turbine, but the vast amount of water resources provided greater conditions for the development of conventional hydroelectric plants [4]. Some authors argue that the main challenges for reversible plants in Brazil are economic viability and lack of regulation [16, 20].

Other challenges of the PHES in the Brazilian energy scenario are the geographic question, for implantation of the two reservoirs; difficulty in allocating reversible plants in an energy category, since it presents generation and consumption within the same enterprise; differentiated tariffs that allow their viability [4]. About environmental regulation, the study in [20] proposes that the PHES in Brazil are under the application of the norms of the National Policy of Environment and National Policy of Water Resources, including granting water use and all the resulting environmental licenses of each phase of the project, with due regard to the type of plant.

The study in [10] proposes that the PHES be dispatched by ONS - National System Operator, and that a regulatory model be created to makes economically this type of plant, in addition to considering the various possible arrangements, as isolated or allied reversible plants sources such as solar, wind or even thermal.

There is also the possibility of a generation link between wind power and reversible hydroelectric plants (figure 4), presented by [4, 10]. In this case, wind energy would serve as an energy supply for the pumping hours at the reversible plant, managing to reuse from 70% to 85% of electricity. The advantage of these systems is the cost savings, as well as the environmental benefits, since no fuel is needed, considerably reducing the emission of pollutants [21].

[Figure 4: Model of wind-hydro pump storage systems [21].]

5. CONCLUSION

Pumped hydroelectric energy storage is a mature energystorage technology with great potential for use throughout the world. Its expansion will benefit not only the grid systems, but also the evolution of renewable sources, ensuring greater reliability and energy stability. As the oldest form of storage on the planet, PHES are well established in developed countries, such as the USA and Japan, which allows new methods and innovations to be available and getting around the difficulties in the operation of these enterprises. In Brazil, there is already a concern for the insertion of PHES in the energy market, but the lack of regulation, feasibility and economic incentives and the difficulty of obtaining fast and consistent environmental assessments are still a barrier. However, there are already solutions and examples of methods used by other countries, in addition to attempts by the government to frame the PHES within the Brazilian scenario. In this sense, pilot projects should be encouraged in order to observe in practice the effectiveness of suggested models and begin to expand this form of energy storage. In this way, Brazil will also be able to use the reversible hydroelectric plants, ensuring the expansion of wind and solar energy in a stable way, contributing to an increasingly clean and sustainable electric matrix.

6. REFERENCES

[1] Guney, M.S. Tepe, Y. Classification and assessment ofenergy storage systems. Renewable and Sustainable EnergyReviews. V. 75, p. 1187 – 1197, 2017.

[2] Couto, J. R. C. de Sá. Energy Storage. Master's DissertationIntegrated in Electrical and Computer Engineering. Universityof Porto, 2012. (In Portuguese)

[3] Silva, B. F. G. Study of alternative energy storage solutionsfor different time horizons. Master's Dissertation Integratedin Electrical and Computer Engineering. University of Porto,2008. (In Portuguese)

[4] Filho, G. L. T. Reversible Hydroelectric Plants - CombiningWind with Hydroelectric Plants. PowerPoint file. Presentationin the Wind Energy New Technologies. São Paulo. 2016. (InPortuguese)

[5] Vasconcelos, Y. Versatile Plants. FAPESP Research 236, p.70-73, 2015. (In Portuguese)

[6] Pasten, C. Santamarina, J. C. Energy Geo-Storage –Analysis and Geomechanical Implications. Journal of CivilEngineering. Accepted in February, 2011. In Press. https://doi.org/ 10.1007/s12205-011-0006-6.

[7] Canales, et.al. Reversible hydroelectric plants in Brazil andin the world: application and perspectives. Journal of Centerfor Natural and Exact Sciences – UFSM. Federal University ofSanta Maria. V. 19, n. 2, p. 1230-1249, 2015 (In Portuguese).

[8] Kong, et. al. Pumped storage power stations in China: Thepast, the present, and the future. Renewable and SustainableEnergy Reviews. V. 71, p. 720 – 731, 2017.

[9] Venneman, et.al. Pumped Storage Plants in the FuturePower Supply System. Hydropower in Future Energy Supply.VGB Power Tech, 2010.

[10] CESP. The Resumption of the Concept of Efficiency ofPumped Storage Hydropower Plants (PSHP) in BrazilianElectricity Sector. Energy Company of São Paulo. R&D Project,2014. (In Portuguese)

[11] Dmitrieva, et.al. Ecological Aspects of Operating aPumped-Storage Station. Gidrotekhnicheskoe Stroiterstvo,No. 9, p. 14-15, 1992.


[12] Queiroz, et.al. Generation of electricity through hydropower and its environmental impacts. Journal of Center for Naturaland Exact Sciences – UFSM. Federal University of SantaMaria. V. 13, n. 13, p. 2774-2784, 2013. (In Portuguese)

[13] Zuculin, et.al. The Resumption of the Concept of Efficiencyof Pumped Storage Hydropower Plants (PSHP) in BrazilianElectricity Scenario. PowerPoint file. Presentation in theTechnical Seminar on Reversible Hydroelectric Power Plantsin the Brazilian Electricity Scenario. Eletrobras, Eletronorte.Brasília, 2014. (In Portuguese)

[14] Barbour, et.al. A review of pumped hydro energy storagedevelopment in significant international electricity markets.Renewable and Sustainable Energy Reviews. V.61, p. 421 –432, 2016.

[15] Guittet, et.al. Study of the drivers and asset managementof pumped-storage power

plants historical and geographical perspective. Energy. V.111, p. 560 – 579, 2011.

[16] EPE. Reversible Plants - Perspectives in the Brazilian Electric Sector. PowerPoint file. Presentation in the X Symposium onSmall and Medium Hydroelectric Plants and Reversible Plants.Energy Research Company. 2016. (In Portuguese)

[17] Schoppe, C. Wind and Pumped-Hydro Power Storage:Determining Optimal Commitment Policies with KnowledgeGradient Non-Parametric Estimation. Bachelor of Sciencein Engineering. Department of Operations Research andFinancial Engineering. Princeton University. 2010

[18] Pérez-Díaz, et.al. Trends and challenges in the operationof pumped-storage hydropower plants. Renewable andSustainable Energy Reviews. V.44, p. 767 – 784, 2015.

[19] Cavazzini, G. Pérez-Díaz, J. I. Technological developmentsfor pumped-hydro energy storage. Joint programme onenergy storage. Mechanical storage subprogramme. EERA –European Energy Research Alliance, 2014.

[20] Zuculin, et.al. The resumption of the concept of reversiblehydroelectric plants in the Brazilian electric sector. StateUniversity of Campinas, S/d. (In Portuguese)

[21] Dursun, B. Alboyaci, B. The contribution of wind-hydropumped storage systems in meeting Turkey’s electric energydemand. Renewable and Sustainable Energy Reviews. V.14,p. 1979 – 1988, 2010.

[22] Nazari, et.al. Pumped-storage unit commitment withconsiderations for energy demand, economics, andenvironmental constraints. Energy. V.35, p. 4902-4101, 2010.

[23] Patocka, F. Environmental Impacts of Pumped StorageHydro Power Plants. Norwegian University of Science andTechnology. Department of Hydraulic and EnvironmentalEngineering, 2014.

[24] Yang, C. Jackson, R. B. Opportunities and barriersto pumped-hydro energy storage in the United States.Renewable and Sustainable Energy Reviews. V.15, p. 839 –844, 2011.

[25] Gurung et.al. Rethinking Pumped Storage Hydropowerin the European Alps. BioOne Research Evolved. MountainResearch and Development. V.36, No 2, p. 222-232, 2016. InPress. https://doi.org/10.1659/MRD-JOURNAL-D-15-00069.1

[26] Kear, G. Chapman, R. ‘Reserving judgement’: Perceptionsof pumped hydro and utility-scale batteries for electricitystorage and reserve generation in New Zealand. RenewableEnergy. V. 57, p. 249-261, 2013.


Hydrodynamic behavior on kaplan turbines: experimental methodology for

the evaluation of cavitation development based on dynamic measurements

1Rivetti, Arturo; 1Angulo Mauricio A.; 1 Lucino Cecilia V.; 2Botero Francisco.; 1Liscia, Sergio O.

1Laboratorio de Hidromecánica, Facultad de Ingeniería, Universidad Nacional de La Plata, 47 Nº 200, La Plata, Argentina.2Mecánica Aplicada – Escuela de Ingeniería – Universidad EAFIT – Colombia

ABSTRACT

The gap between the discharge ring and the tip blade of Kaplan turbines favors the formation of tip vortices in which cavitation tends to develop even at Sigma plant values. The volume and location of such vortices vary with both the blade pitch angle and the gap size.

Under overload operating conditions, the intensity of tip vortex cavitation rises and its consequence is twofold: on the one hand, erosion at the discharge ring and runner blades; on the other hand, mechanical vibration and cracks on the stationary parts of the turbine. Furthermore, the resulting erosion pattern (consisting of as many eroded patches as guide vanes) suggests that tip vortex cavitation could be modulated by the number of guide vanes wakes.

In this work, a methodology is presented for the evaluation of the hydrodynamic behavior of Kaplan turbines based on dynamic signal processing. An experimental layout (including the instrumental consisting of accelerometers and a hydrophone) for physical models was proposed and tested.

The location of the sensors, sampling characteristics and signal processing, as detailed herein, are capable of describing the dynamic response of the turbine, characterized by the point that signals the onset of cavitation and its intensity. The dependence of cavitation on slight deviations of the geometry of the blades was also investigated.

KEYWORDS: cavitation, turbines, hydrodynamic.

1. INTRODUCTION

Kaplan turbines present a particular dynamic behavior, in which tip blade cavitation plays a very important role, especially at high loads. The most harmful effects that can occur are excessive vibration level and cavitation erosion on the blades and, in some cases, can also compromise the structural integrity of the discharge ring. These damages impact on maintenance costs and eventually also on the productivity of the plant because of power output limitations generated to preserve the units. Experimental studies on the dynamic behavior of Kaplan turbines are scarce when planning diagnostic tests [1, 2, 3], so the authors intend to share some methodological orientations, result of the experience accumulated in the matter and with the theoretical-conceptual support that validates them.

Pressure pulsations, vibration and acoustic emission can account for the degree of aggressiveness of the cavitation and its incipient Sigma condition with particular sensitivity in model tests, provided that the sampling frequency and signal processing techniques are appropriately chosen. An adequate processing of the dynamic signals allows detection of other phenomena of interest as well, like the modulation by typical frequencies, i.e. the passage of the blades and the corresponding rotor – stator interaction phenomena.

Although the question of scalability of dynamic behavior from model to prototype needs to be carefully studied, it is possible to get a good diagnosis of hydrodynamic phenomena in model for predictive purposes, since it has been possible to verify its validity by means of measurements on prototype turbines of high output, homologous to the models tested.

This paper deals with the question of what to measure, how to acquire the signals (suitable instruments and frequencies of

acquisition), where to install the transducers and how to process the information obtained in order to get a general description of the main aspects involved in hydrodynamic behavior of Kaplan turbines, mainly related to cavitation development at overload condition.

2. CONCEPTUAL FRAME

The potential energy contained in a cavitating flow isdefined by eq.1 [4], as a function of the cavity volume and the difference of the surrounding and vapor pressure. When the cavity collapses, this energy is liberated producing shock waves, micro jets formation and vibration. The potential of erosion is then proportional to the amount of energy available for the collapse.

(1)

Where Ep = potential energy of the cavitating flow, Vvap = vapor volume, p∞= Surrounding pressure, pv = vapor pressure.

As cavitation number σ decreases, cavitation develops mainly as tip leakage cavitation. The interaction of tip cavitation volume with guide vanes wakes produces cavitation collapse at fixed spots over the discharge ring (Fig 1). The location of this spots and the dynamics of each cavity depend of the rotational speed ω, and the number of guide vanes (Z0) and runner blades (Zb).

The influence of the non-uniform flow leaving the guide vanes can be identified by the analysis of the modulation process generated by the stationary flow field of the 24 guide vanes, and the rotating flow field due to the 5 runner blades, as proposed by Ruchonnet et al. [5]. Table 1 shows the RSI patterns for several orders of harmonics for the first



diametrical mode number k1. The highest amplitude expected is for the first order of harmonics of flow through the guide vanes (n = 1) and the fifth order of harmonics of flow through the runner (m = 5), since k1 is the minimum in absolute value (k1=1). The characteristic frequency of 25 fn (where fn is the runner rotation frecuency), given by the expression f/fn = mZb, has to be present if the interaction exists.

[Table 1]: First diametrical mode number k1 according to harmonic order m for the runner blades (Zb=5) and for the guide vanes (Z0=24).

[Figure 1: Conceptual model of the RSI interaction between the guide vanes and tip vortex development. The cavitation volume collapse is modulated by the guide vane wake and the discharge ring erosion is located at fixed spots.]

3. METHODS AND MATERIALS

3.1. Experiments

Experiments were performed at the Laboratory of Hydromechanics of the National University of La Plata, Argentina. The test rig is a closed circuit that allows for the testing of Kaplan and Francis turbines (Fig. 2). The model test was carried out in compliance with the IEC 60193 standard [6]. The error estimated for the hydraulic efficiency is less than 0.24 %.

The scale model was a five-blade Kaplan turbine with twenty-four stay and guide vanes. Its diameter was D = 340 mm and its specific speed was ns = 614. The rotational speed during the test was n = 1000 rpm, which yields a Reynolds number of Re = 6.05x106, based on the blade tip velocity. The model was placed in the test rig between the high- and low-pressure tanks. The head was adjusted by varying the rotational speed of the recirculation pump. The low-pressure tank is equipped with a vacuum pump and a pneumatic controlled valve allowing for the variation of the absolute pressure of the system, in order to set the desired σ, given by equation 2.

(2)

Where pb = pressure at low-pressure tank, pv = vapor pressure, γ =water specific weight, hs = suction head, H = net head, Ec2=Kinetic energy at the draft tube outlet. Given

that the test was carried out at constant head, flow rate and rotational speed, it becomes apparent from Eq. 2 that can be modified only by varying the pressure at the low pressure tank.

[Figure 2: Test rig facility at the Laboratory of Hydromechanics of La Plata, Argentina. (1) Ventury Flow-meter; (2) Recirculation pump; (3) Dissipation valve; (4) High-pressure tank; (5) Low-pressure tank; (6) Model scale; (7) Motor-generator.]

3.2. Monitoring system

Acceleration measurements: Three Endevco Isotron 7259B accelerometers, with a flat frequency response from 0.1 Hz to 30 kHz, were placed at the discharge ring (Fig. 3). The typical resonance frequency is 90 kHz. The AC1 is located above the centerline of the runner; the AC2, on the blade passage plane; and the AC3, at the draft tube inlet.

Noise emission: One Brüel & Kjær type 8104 was located downstream the center-line at a distance of 1.0 D immersed in water.

Keyphasor: An inductive sensor Balluff BES00JY together with a cog in the shaft was implemented to obtain the runner passage key.

Data acquisition: Dynamic signals were simultaneously sampled with a 16-bit resolution at a 35 kHz sampling rate during 40 seconds for every measured point. Data sampling and post-processing were performed with software developed by LABVIEW.

[Figure 3: Instrumentation location on the Kaplan model scale.]

3.3. Operational condition and test proceeding

An operational point of high load for the nominal head corresponding to the prototype machine was chosen for the experiment. This point corresponds to an ON CAM combination.


For this condition, the speed factor [6] was nED = 0.769 and the discharge factor [6] QED = 0.589, where

Only the cavitation number was modified by adjusting the absolute pressure in the low-pressure tank covering a range going from σ = 2.40 (no cavitation) to σ = 0.919 (full developed cavitation).

A series of tests were performed wherein the cavitation number was swept over the range 0.919-2.40 in a stepwise manner. The upper limit corresponds to a cavitation-free operating condition. The cavitation number is decreased by gradually diminishing the pressure of the test rig circuit. A total of seven steps were considered until cavitation was fully developed. For every step the acceleration signal and the test rig state variables were acquired during 40 seconds.

3.4. Data processing

The suitable selection of sensors and its location as described above play a major role in the diagnostic assessment of tip vortex cavitation. Said phenomenon leaves a trace that can be unveiled both in the time and frequency domains. On the one hand, the proper parameters of the turbine design influencing the formation of vortices, such as number of blades, blade clearance and discharge ring, and permissible tolerances for manufacture, become sources of spectral components of the rotor frequency. On the other hand, the formation and subsequent implosion of vapour cavities become a source of wide-band noise. In addition, interactions among them and the interaction between fluid and structure (FSI) provide a plentiful mine to be exploited [7].

3.4.1 Time domain

The time-domain analysis for rotating turbomachinery can provide meaningful geometric and synchronous information if it is assumed that samples came from normal distributions; i.e., normal variables. In that sense, two types of strategies areproposed: inter-condition and condition-dependent analysis.Traditional estimators such as the variance (Eq. 3) and the rootmean square value (rms, Eq. 4), provide an overall measureof the variable x that can serve as an indicator for comparingdifferent operating conditions. In fact, they indicate if thevariable increases or decreases, globally, when the machinegoes from ones condition to the next (inter-condition). Here,x is understood as a series of N samples, successive, equallyspaced and indexed in time order; each sample denoted by xi. In the particular case of time series of zero mean (x

_=0), the

rms value is equivalent to the standard deviation, which in turn is the square root of the variance.

(3)

(4)

An estimation of the mean behavior of a random variable, during one shaft’s revolution, can be obtained averaging several (more than thirty) phased time-series samples of one revolution [8]. A review of Time Synchronous Average (TSA) algorithms was published by Bechhoefer and Kingsley [9].

Concisely, in our work it consists of: key phasor marks are used to index the time-ordered samples corresponding to one revolution length. An estimation of the variance is recovered by calculating the sample variance of the same set of time series (several revolutions of the rotor). Then a representation of the average revolution bounded by its confidence intervals can be plotted as a function of time, angular position or any other scale. Balanced fluctuations with constant variance are expected from a machine in good condition; if strong bumps or fluctuations in variance are observed, it is a sign of a defect located on the rotor oriented according to the horizontal scale used for the plot and the key phasor mark (condition-dependent analyses). Protuberances with low or constant variances can be explained by hydraulic, mechanical or electrical synchronized imbalances. High variance can be associated to stochastic phenomena like cavitation formation and implosion.

3.4.2. Frequency domain

Once cavitation incepts, the generated wide-band noise propagates from the collapsing bubbles, through the fluid, to the structure. This noise can be perceived as a global increase of the rms value of the collected signal, as stated above, but also as an energy pattern less rise-up along several thousand Hertz since it is wide-banded. For this reason, conventional representations in the frequency domain as the amplitude spectrum or the power spectrum are not the best tools for the detection of cavitation. In general, such analyzes are not suitable for the technical diagnosis of stochastic phenomena.

Therefore, assuming that the dynamic transducer is installed in the stationary frame of a Kaplan turbine, then the recorded noise intensity coming from a cavitating vortex attached to the tip of the rotating runner blades varies periodically depending on the distance measured form the tip of the blade to the monitoring point. Such effect produces the modulation of the noise at a multiple of the impeller blade passing frequency. That is to say, the noise emitted by the implosion of the bubbles becomes more and less intense in a harmonic way, as the rotating blade with the anomaly approaches or moves away from the sensor.

This sort of modulation has two desirable characteristics that can be profit from the technical point of view: the first is that instead of only one carrier frequency, there is a wide band of carrier frequencies; the second is that carrier frequencies may extend up to the highest sampled frequency. In other words, the information is carried by several frequency channels, and many of these channels are free of interference produced by other sources since their frequencies are high enough (several thousand hertz). Consequently, there are bands in the frequency domain where symptoms of tip vortex cavitation are preserved.

The demodulation technique described by Escaler et al. [10] is adopted to process the fluid and structure-borne. Thistechnique has proven to be successful in diagnosing othermanifestations of cavitation [7], [11]. A simplified scheme ofrequired processing is shown in Figure 4.

[Figure 4: Demodulation processing.]


In brief: (a) band-pass filter is applied to the signal. Fourth to ninth order Butterworth Infinite Impulse Response digital filter is a suitable choice. Low cutoff frequency is set above the maximum expected harmonic of the rotating speed; for most cases it is around 180fn. High cutoff frequency can be set just below the antialiasing bandwidth limit. A pre-centering is highly recommended, especially if the data acquisition system especially if the equipment lacks a capacitive coupling circuit (AC). Arithmetic mean of the signal is subtracted from every sample, Eq. (5). (b) The analytic signal is assembled with the filtered signals as real part and its Hilbert transform as the imaginary part; as it is complex valued, therefore it can be expressed in exponential notation. The Hilbert transform actually leads to the harmonic conjugate of the signal. (c) The modulated signal is the envelope of the analytic signal, i.e. the instantaneous amplitude and can be extracted as its modulus. (d) Centering the resulting signal by subtracting its arithmeticmean; see equation (3). Finally, the centered envelope istransformed from the time domain to the frequency domain inorder to extract its respective harmonic components and rmsamplitudes. This transformation can be achieved by applyingthe Fast Fourier Transform (FFT), which is a very efficientalgorithm to decompose discrete time series

(5)

It is expected that in the presence of tip vortex cavitation the most prominent frequency component corresponds to the passage of blades or one of its harmonics. On the contrary, a flat or decadent spectrum is anticipated.

4. RESULTS

4.1. Time domain

[Figure 5: TSA processing of the signal capture by the accelerometer (left) and signal capture by the hydrophone (rigth) at E05 (σ=1.229). The graphs at the top show a one second fragment of the raw measured signal. The bottom graphs show the average signal plus and minus its variance for a revolution. The domain identifies the passage of each of the blades of the impeller.]

The result of applying the introduced TSA procedure is presented in Figure 5. For this case, the operating point E05 (σ=1.229) was selected because it allows to show several advantages of the method. The graphs at the top show a fragment of a second of each of the raw signals, i.e. accelerometer (left) and hydrophone (right). The graphs at the bottom show the result. In the case of the accelerometer signal, the contribution that is made by superimposing the variance is evident; for each blade passage at least the twenty-fifth synchronous component is identified, not to mention the other attributes such as a fluctuation of the amplitude and the large magnitude of the variance compared to the average value of the acceleration. For the hydrophone, it can be observed something different. The variance is relatively low with respect to the variation of the acoustic pressure and therefore it is possible to identify the twenty-fifth harmonic, even from the averaged signal. Additionally, it is interesting to note, as each blade passes, on average, manifests a particular behavior, which could be associated with geometric tolerances of the machine.

4.2. Frequency domain

[Figure 6: Amplitude spectrum of the envelopes for accelerometer (a) and hydrophone (b). Frequencies are presented as multiples ofthe rotating frequency of the shaft. Every spectral vector corresponds to a specific sigma value. Tip vortex cavitation was firstly observedat E03 (σ= 1.488); this is consistent with the arisen of the spectralcomponent 25fn. Nevertheless, the hydrophone allowed to observemore details and even, to detect the said phenomenon in conditionsof extreme cavitation like E06 (σ=1.036) and E07 (σ=0.919).]

The signals that were collected with the accelerometer and the hydrophone were demodulated following the procedure


previously described and presented in a specific way. Each envelope was spectrally decomposed and the domain normalized with the frequency of shaft of the machine to be presented as orders of that frequency. Then, the spectra of all the operating points were ordered on a 3D chart based on the operating point, that is, as a function of the sigma value. The results are shown in Figure 6. According to the high speed images taken at each operating condition, it was determined that the tip vortex cavitation first appeared at E03 (σ=1.488) and thus, ascending to E07 (σ=0.919), where in addition other types of more violent cavitation were observed. This correlates quite well with the manifestation of the spectral component 25fn in signals, accelerometer and hydrophone. However, it should be mentioned that once the hydrodynamic inside the machine is sufficiently intemperate, as in E06 (σ=1.036) and E07 (σ=0.919), the accelerometer stops perceiving the said frequency.

5. CONCLUSIONS

The tip vortex cavitation that develops at lower cavitationnumbers was singled out as one of the main causes of the increase of vibration levels.

The analysis of the signal of the hydrophone reveals the presence of RSI-related phenomena which becomes apparent when tip vortex cavitation develops.

Both, the accelerometer and the hydrophone, allow detecting with sufficient sensitivity the manifestation of tip vortex cavitation. However, the hydrophone is able to detect it even under the interference of other phenomena, including other types of cavitation.

The 25fn spectral component of the envelopes was identified as a powerful indicator of tip vortex cavitation. This same component stood out differently in the results of the TSA. For the case of the accelerometer, it became more noticeable thanks to the superposition of the variances, whereas for the hydrophone, it became evident even from the average signal of the acoustic pressure.

The TSA results revealed a variation in the amplitude of the fluctuations corresponding to the passage of each impeller blade. This is attributed to the geometric tolerances of the model. In addition, it allowed to observe the component 25fn that later was associated with the cavitation.

The methodology presented in this paper could be easily applied on prototype since the use of accelerometers is a non-intrusive procedure.

6. AKNOWLEDGEMENTS

The authors would like to thanks to Leonardo Díaz andTomás Recofsky for their collaboration in the execution of the model tests.

7. REFERENCES

[1] Rus T, Dular M, Sirok B, Hocevar M and Kern I, 2007: Aninvestigation of the relationship between acoustic emission,vibration, noise and cavitation structures on a Kaplan turbine.ASME Transactions Vol 129.

[2] P. Kumar, R. P. Saini, "Study of cavitation in hydro turbines-Areview" Renewable and Sustainable Energy Reviews"14(2010) 374-383.

[3] M. Grekula, G. Bark," Experimental Study of Cavitation in aKaplan Model" Turbine" CAV2001:sessionB9.004.

[4] Brennen C. E., 1995 Cavitation and bubble dynamics. OxfordUniversity Press.

[5] Ruchonnet N, Nicolet C, Avellan F 2006: “HydroacousticModeling of Rotor Stator Interaction in Francis Pump-Turbine”.IAHR Int. Meeting of WG on Cavitation and Dynamic Problemsin Hydraulic Machinery and Systems. Barcelona, Spain

[6] IEC standars. Hydraulic turbines, starages pumps andpumps-turbines-model acceptance tests; IEC60193-1999.

[7] A. Castro and F. Botero, “Non-invasive detection of vortexstreet cavitation,” Ing. y Univ., vol. 21, no. 2, 2017.

[8] F. Botero, S. Guzmán, V. Hasmatuchi, S. Roth, and M.Farhat, “Flow visualization approach for periodically reversedflows,” J. Flow Vis. Image Process., 2012.

[9] E. Bechhoefer and M. Kingsley, “A Review of TimeSynchronous Average Algorithms,” 2009.

10] X. Escaler, E. Egusquiza, M. Farhat, F. Avellan, and M.Coussirat, “Detection of cavitation in hydraulic turbines,” Mech.Syst. Signal Process., vol. 20, no. 4, pp. 983–1007, 2006.

[11] A. Rivetti, M. Angulo, C. Lucino, and S. Liscia, “Mitigationof tip vortex cavitation by means of air injection on a Kaplanturbine scale model,” IOP Conf. Ser. Earth Environ. Sci., vol.22, no. 5, p. 52024, Mar. 2014.


Technical and Economic Evaluations for Decision-Making on the Repowering

of Small Hydropower Plants and the optimum exploit of existing plants in Brazil

1Oliveira, Marcos André

1Water Engineer, PhD Student in Mechanical Engineering and Master in Energy Engineering by UNIFEI. Civil Engineering Teacher, Federal University of Tocantins - UFT (TO), Brazil. Quadra 109 Norte Avenida NS 15, Plano Diretor Norte, CEP 77001090, Palmas, TO. Tel (63) 32323219, email [email protected]: Generation Information Bank of the Brazilian Electric Energy Agency - ANEEL on July 14, 2017.3Referring to data from the last 12 months ending June 20064Source: Generation Information Bank of the Brazilian Electric Energy Agency - ANEEL on December 18, 2017.

ABSTRACT

In Brazil, the Law no. 9,074 presents, in its Article 5, the concept of "optimum exploit ", which is all potential defined in its overall design by the best dam axis, general physical arrangement, levels water, reservoir and power, which is part of the chosen alternative for the division of head in a watershed.

The careful estimation of the repowering potential for the increase of installed power in Brazil depends on an individualized analysis of the existing projects, identifying the technical restrictions and the best modality of intervention with their respective extension. However in Brazil, repowering is in a process of structuring in its technical, economic and regulatory aspects.

Therefore this paper presents a proposal for the systematization of the Technical and Economic Evaluations for decision making regarding the feasibility of the repowering of Small Hydroelectric Power Plants - SHPs. This paper also presents a case study about the repowering of Lajeado SHP, built in 1971 in Brazil (installed capacity of 1.8 MW).

The results indicated that the average cost of investment for repowering is well below the average cost of investment for the construction of new SHP in Brazil.

KEYWORDS: Repowering, small hydropower plant, optimal exploit.

1. INTRODUCTION

The production of electricity in Brazil is basically fromhydroelectric plants and currently these plants correspond to approximately 61.38%2 of installed capacity in the country, or approximately 98,736 MW with a total of 1,264 plants.

The Southeast, South and Northeastern regions make up more than 73% of the installed hydroelectric power in Brazil and according to the EPE [1] consumed approximately 88%3 of the electricity generated in the country in 2006, practically sustaining the National Interconnected System.

Much of the Brazilian hydroelectric potential to be exploited is concentrated in the North and Central-West regions. The biggest challenge is in the fact that 70% of this potential is located in biomes of great environmental value, those of the Amazon and Cerrado, which together cover 2/3 of the national territory.

Although the hydroelectric potential to be exploited in the country is significant, the restrictions for the expansion of large hydroelectric plants are several:• In the North and Central-West regions the relief is not

favorable (plains) and there is a need to flood large areasto the reservoir, with a combination of low head and largeflows. Furthermore, the geographical limitations imposed bythe indigenous reserves and the environmental preservationand conservation areas are added;

• The potential reduction in the availability of water resourcesfor the generation of energy in front of the other modalitiesof demand due to the guarantee of the multiple use of water.

• The need to make possible the transition of the nationalenergy matrix based on hydroelectricity to a matrix basedon integration with other sources of renewable energy.

• The need for expansion of the electric power transmissionsystem for the North and Central-West regions.

In the short and medium term repowering is an alternative to ensure the best use of the hydraulic potential in existing plants with energy, economic and socioenvironmental gains. In the long term repowering will be the starting point for facing the aging of the Brazilian hydroelectric park [2].In other words, repowering is one of the indispensable tools for the sustainable use of water resources for electricity generation in Brazil.

In Brazil, approximately 56%4 of installed capacity at the end of 2017 was already in operation before 1997. According to Bermann et al. [3] are considered old plants that have more than 20 years of operation and whose generators exceed 120 thousand hours of operation, requiring major maintenance.

In addition to the optimal exploit of the hydraulic potential in existing plants, which guarantees the rational and efficient use of water resources, among the main advantages of the repowering of SHPs can be highlighted:• Environmental costs are minimal or nonexistent;• There is the possibility of compensation in carbon credits;• Lower cost compared to new plant construction;• Possibility of implantation in the short term;• Potential availability of additional energy close to major

consumer centers (reduction of energy transmission losses).

Enabling the repowering of existing hydroelectric plants isto increase the generation of electric energy in places where socioenvironmental impacts have already been consolidated in substitution for the construction of new hydroelectric plants that also have higher costs and deadlines for implementation. Repowering contributes to the preservation and conservation of the environment in Brazil, mainly to maintain the quali-quantitative availability of water resources [4].

The careful estimation of the repowering potential for the increase of installed power in Brazil depends on an



individualized analysis of the existing projects identifying the technical restrictions and the best modality of intervention.

In Brazil repowering is in a process of structuring in its technical, economic and regulatory aspects. Since there is still no specific regulation capable of fully recognizing the gains made possible by repowering, that is, with the purpose of adequately reimbursing generation companies.

The objectives of this article are: (i) Present a proposal for systematization of the technical and economic evaluations made for decision making regarding the feasibility of the repowering of Small Hydroelectric Power Plants; (ii) To present the case study of the repowering of Lajeado SHP, built in 1971, located in the northern region of Brazil, in the state of Tocantins.

2. MATERIALS AND METHODS

2.1. Power generated in a hydroelectric plant

In a hydroelectric plant the process of energy conversion happens in stages with its corresponding amounts of energy lost during the process.

Defined the basic parameters for design, design flow and gross head, one can define the installed power and the energy generated by a hydroelectric plant.

The gross power of a hydroelectric plant is governed by the gross hydraulic potential of the point chosen for its installation and is given by the equation

PB=γQHB (1)

where: P_B is the gross power (W); H_B is the gross head (m), Q is the flow (m³/s) and γ is the specific weight of water (N/m³).

The electric power generated is given by the equation

Pel = ηglobal.PB (2)

where: Pel is the electric power generated (W) and ηglobal is overall efficiency.

Considering the main losses in the process the overall efficiency can be determined by

ηglobal = ηsa.ηt.ηg (3)

where: ηsa is the efficiency of the hydraulic system of water adduction (SA), ηt is the efficiency of the hydraulic turbine (TH) and ηg is the efficiency of the electric generator (GE).

[Figure 1: Energy coversion model in a hydroelectric plant.]

Figure 1 shows a schematic model of the process of converting hydraulic energy into electric energy, where P is the useful power, Pe is the power of the shaft, Psa is the power used for the auxiliary services of the plant and Pliq is net power (maximum active electric power available from the generating plant, defined in net terms at its point of connection).

2.2. Repowering of small hydroelectric plants

Repowering can be defined as an intervention or set of interventions in the structures, hydraulic systems and electromechanical equipment involved in the process of

energy conversion of a hydroelectric project already built, with simultaneous gain of power and efficiency, reconciled with economic and socioenvironmental benefits.

Among the indicators of the state of a SHP that allow to identify the applicability of a repowering intervention can be highlighted the age of the project, operating and maintenance costs, power generation capacity, flexibility in operation and the level of exploitation of the hydraulic potential available. Also considering current technology opportunities, government incentives and the energy market.

With regard to the generation capacity of a SHP the association of some indicators such as the reduction of the average generation of the power plant, the availability factor and the efficiencies of generating sets can show the possibility of a repowering process.

In a hydroelectric plant the repowering process can be structured in the following intervention modalities: rehabilitation (restoration of energy conversion equipment to its original behavior), revitalization (applicable in plants where there are margins of projects in their dimensioning) or expansion (structured in new constructions conserving part of the existing resulting in a rearrangement of the plant). These modalities can be integrated together, according to the original hydroelectric plant project, the extension of the desired improvement and the technical and economic viability of the interventions [2].

The minimization of the costs of the repowering interventions depends on a good Planning that must integrate the Project, the Engineering, the Supply, the Commissioning and the Tests.

2.3. Technical evaluations for repowering of small hydropower plants

Already in the first moment of the diagnosis for the studies of repowering it is of extreme importance to confront the basic technical documentation of the plant (projects, manuals, data, and history of the maintenance). This will allow the confirmation of the possible need for technical refinements with surveys, measurements, tests, and complementary studies to define the technical parameters that will guide decision making regarding the extent of interventions.

In Brazil there are cases of lack of historical technical documentation remaining from old plants.

With the results of the surveys, tests and complementary studies carried out and having a careful knowledge of the current state and the residual useful life of the components of the hydroelectric power plant it is possible to define the modality of intervention for repowering.

The following are briefly described the main surveys, tests and studies that may be required.

2.3.1. Hydrological studies

The updating of the hydrological studies is necessary due to the increase of data in the historical series of tributary flows obtained in the period of operation of the plant.

A complete hydrological study for repowering includes the survey of the hydrological and meteorological information base, the determination of physiographic and climatic characteristics, the calculation of the precipitations and flows typical of the watershed where the hydroelectric plant is located.

An important result of the hydrological studies is the definition of the flow duration curves (FDC), that shows for a particular point on a river the proportion of time during which the flow there equals or exceeds certain values. Souza et al. [5] points out that in the hydropower studies the monthly flowduration curve is used.


On the other hand flood flows allow the revaluation of the stability of the dam, the capacity of the discharge devices and other aspects related to the safety of civil structures. Which give subsidy for the technical evaluation of the possibility of gain of head by the increase of the height of the dam.

2.3.2. Topographical surveys

Topographic reassessments from surveys already in place or to be performed are important for redefining or confirming the gross head available on site and allocating new civil structures.

2.3.3. Dimensional survey in the hydraulic system of water adduction

In the water conduction system of hydroelectric plants there are several types of losses of energy by friction that are estimated by specific equations. The main results of these surveys are the definition of the equation of head loss in the system of water conduction and the dimensional revaluation of the maximum capacity of the components of this system (intake, channel, tunnel, forebay tank and penstock).

2.3.4. Surveys and tests on generator sets.

Parallel to the surveys in the system of water conduction, the tests are performed on the main electromechanical equipment of the plant (hydraulic turbine and electric generator).

The tests in the generator sets concentrate on the simultaneous measurement of the turbine flow, pressure at the turbine inlet and the electrical power generated for several turbine distributor openings, registering the respective upstream and downstream water levels. This allows determining the efficiency of each generator set.

2.3.5. Geological and geotechnical surveys

Except in very particular situations surveys and geological and geotechnical studies are applicable when repowering is in the expansion modality.

These surveys allow the characterization of foundation conditions in areas where new civil and hydraulic structures will be built and existing structures strengthened or expanded.

2.4. Economic evaluations for repowering of small hydroelectric plants

The economic analysis for repowering of a SHP is made using the same methods for the economic analysis of a new power plant.

Estimating all the costs involved for each alternative considered, the cash flow of the project is elaborated with the respective revenues and expenses to analyze the economic feasibility in the project horizon. Classically the most used methods are: Net present value – NPV, Internal rate of return- IRR, Payback; and the benefit-cost ratio.

The decision on the best alternative in economic terms for repowering is taken with the joint evaluation of these methods.

In the assessment of economic feasibility the costs of interventions, equipment and other issues that are not closely related to the repowering process should be excluded, as well as only the revenue obtained with the incremental energy coming from repowering.

In addition to the revenue from the sale of incremental energy to be generated, we can add the contribution of resources with the commercialization of carbon credits, since repowering allows the addition of clean and renewable energy to the Brazilian electric system in substitution of the generation of thermoelectric energy (burning of fossil fuels that emit greenhouse gases into the atmosphere).

[Figure 2: Schematic representation of the cash flow of a repowering project.]

Figure 2 shows in schematic form the generic cash flow of a repowering project. It is important to note that, in this case, the pre-repowering and post-repowering periods refer to the period before and after the energy increment respectively.

2.5. Stages of hierarchy of technical and economic evaluations of repowering

The applicability of the hierarchical stages of technical and economic evaluations depends on the particularities of each enterprise, the economic reality of the company and the availability of reliable technical information.

2.5.1 First Stage - Simulation of theoretical maximum gain

It consists of a first approximation (estimation) of the energy gain, considering as a simplifying hypothesis the possibility of reaching the maximum theoretical efficiency for the generator sets. This can be combined with the hypothesis of optimal utilization of the tributary flows and heads available.

The maximum theoretical efficiency corresponds to the technological level of the new equipment available in the market. Currently the value of 0.92 can be considered for the maximum theoretical efficiency of a generator set.

The available technical information is readily used for preliminary simulation as input data. This will allow the definition of the characteristics of the repowering generator set and the projection of the energetic gains. Repowering costs are also estimated at this stage.

Already in this preliminary stage are raised the technical restrictions. Mainly environmental restrictions.

If this first approximation indicates potential technical, economic and environmental feasibility for the plant's repowering, then the surveys, tests and additional specialized studies that will be necessary to subsidize the subsequent stage should be defined.

2.5.2. Second Stage - Technical, economic and environmental feasibility study

Based on the results of the surveys, tests and complementary studies carried out and having a thorough knowledge of the current state of the equipments and the residual useful life of the equipments, it is possible to define the repowering mode (rehabilitation, revitalization or expansion).

The economic variables and the merit indices obtained in the technical and economic analyzes are used to choose the best repowering alternative, of which it can be highlighted: power gain (kW), energy gain (MWh), total cost to generate additional energy (US$/MWh), total cost to increase power (US$/kW), cost of unavailability (US$), net present value - NPV, Internal rate of return - IRR, time of return of investment and revenue-cost ratio.

If there are several plants that are candidates for repowering the same variables and indexes serve to choose or rank the best opportunities.


In Brazil, the variable that most influences the decision making as to the feasibility or not of a repowering project is the economic one. The environmental aspects do not constitute as restrictions that can make a repowering project unfeasible. Except in cases where there is an increase in the operational level of the reservoir (flooded area increase) or exceptional cases.

The environmental licensing of repowering follows the same guidelines of current regulations for new hydroelectric plants in Brazil.

3. RESULTS AND DISCUSSION

3.1. Location and general description of Lajeado SHP

Lajeado SHP was built in 1971 by Goiás Electric Power Plants - CELG and is currently managed by the Alvorada Energia concessionaire which was acquired by Enel Brasil in 2006.

The project is located in Lajeado city, state of Tocantins, Brazil, at coordinates 9°50'08.72"S and 48°17'37.82"W, distant approximately 57.45 km from the capital Palmas.

The Lajeado SHP is a plant of high head and starts with the derivation of the main river. It is 1.8 MW of original power, whose general arrangement is constituted by a dam with integrated spillway in the central part, intake, channel and tunnel, forebay tank, penstock, power house with a generator set. The average annual historical generation is 13,747 MWh.

The dam is of the gravity type in concrete with 9.3 m of maximum height and 90.0 m of length. The spillway is of the free overflow type (Creager profile) with 40.70 m in length and approximately 7.40 m in height.

[Figure 3: Schematic corss-section of the dam and spillway.]

According to Figure 3 there is the possibility of adding up to two wooden floodgates above the spillway to increase the head and optimize the generation of energy in the dry season.

The Lajeado SHP reservoir is formed by the derivation of the Lajeado river and has an area of 0.055 km2 at the normal water level. The useful volume of the reservoir is negligible (it is not intended to regulate flow). The operating water levels are: normal maximum at 337.64 m and minimum normal at 337.44 m.

The power house is of the sheltered type and has approximately 112 m² of built area. It is in very good condition.

The electrical substation is the homeless type and occupies an area of 685 m². Composed basically of a 2,500 kVA electrical transformer with voltages of 2,400/34,500 V. It is located near the power house.

The existing electric transmission system consists of a three phase line operating at 34.5 kV, with the capacity to carry 1.9 MW with inductive power factor 0.8 at a current

of 39.7 A per phase. Being that the energy produced by the existing arrangement is transported by this line to the Barra do Lajeado electrical substation, belonging to the local concessionaire.

According to standard ABNT 5422, considering an ampacity of 0.7 A/mm², for the cross section of the existing cable of 57 mm², cable 1/0, the transmission system is already at its maximum limit. Therefore it is necessary to build a new interconnection line in the expansion of the existing SHP [6].

3.2. Technical evaluations for repowering of Lajeado SHP

3.2.1. Hydrological studies

The watershed of the PCH Lajeado has a drainage area of 514 km². Since its physiographic characteristics indicate that it is a watershed that is less subject to floods and that has a relatively irregular and elongated form.

A historical series of flow with 33 years of data was obtained through the transposition of flows of fluviometric stations available in the region.

Through the hydrological analysis of the fluviometric stations shown in Table 1 it concluded that the hydrological behavior of the watershed of the Porto Alegre station and of the watershed under study is approximately similar, with a correlation coefficient of 0.78. The flow series for Lajeado SHP was obtained through a transposition relation considering the respective drainage areas.

Hydrological studies were completed in early 2008.From this point was obtained the duration curve of the

average monthly flows (Figure 4).

[Figure 4: Duration curve of the average monthly flows in the Lajeado SHP.]

It should be noted that the number of hydrometric stations in the northern region of Brazil is still insufficient. Therefore flow regionalization methods are used.

The ecological flow in the state of Tocantins corresponds to 25% of the flow with 90% of duration in the flow duration curve.

For the definition of flood flows the series of maximum flows were adjusted to the theoretical distribution of probabilities, Type I Extremes (Gumbel) and Log-Pearson III, with extrapolation for different recurrence times. The best fit was the Log-Pearson III distribution.

The review of the hydrological studies showed an under - sizing of the plant in comparison to the natural flows of the river. Table 2 summarizes the results of hydrological studies.


[Table 1]: Fluviometric stations analyzed.

Station name

Brazilian code

AreaDrainage

(km2)

CoordinatesData time

rangeLongitude (degrees)

Latitude (degrees)

Muricilândia 28150000 1.600 -48.6197 -7.15441974 – 2006

Arapoema 27550000 1.386 -49.0453 -7.61361988 – 2006

Fazenda Craveiro

27370000 295 -48.9708 -9.60362000 – 2007

Ponte Rio Dueré

26790000 1.442 -49.2667 -11.31672000 - 2007

Porto Alegre 22190000 1.930 -47.0453 -11.61081975 - 2006

Dois Irmãos 22850000 9.543 -47.8133 -9.31141973 - 2007

Itacajá 23150000 2.776 -47.7653 -8.39171973 - 2007

Jatobá 22680000 13.855 -47.4725 -9.99531973 - 2007

Bernardo Syão

27530000 1.541 -48.8789 -7.87892000 - 2007

Jacaré 23230000 5.069 -47.2611 -7.96331984 - 2007

3.2.2. Topographical surveys

A topographic survey was carried out in the area of interest by a specialized company. The gross head for the current arrangement was then confirmed to be 92 m.

It is important to note that there was no change in the water level of the reservoir (337.64 m) in the repowering studies. However the downstream water level was reallocated to a point with no significant slopes in order to enable head gains. The downstream water level reached the elevation 230.55 m. This resulted in a gross head of 107.09 m.

[Table 2]: Summary of the characteristic flows for Lajeado SHP.

Average long term flow 9.97 m³/s

Flow duration of 50% (median) 5.07 m³/s

Flow duration of 90% 1.70 m³/s

Flow duration of 95% (Steady flow) 1.60 m³/s

Ecological flow 0.425 m³/s

Flood discharge (recurrence time 100 years) 209.1 m³/s

Flow discharge (recurrence time 1,000 years) 281.1 m³/s

3.2.3. Surveys in the hydraulic system of adduction

The hydraulic system of adduction of the plant is composed of: intake (right side reservoir), channel (concrete), tunnel (concrete), forebay tank and penstock.

The evaluation of the hydraulic system of adduction was carried out through geometric measurements and corresponding dimensional analysis of all its components, as well as surveys the hydraulic losses from measured values of turbinated flow under load conditions of 25%, 50%, 75% and 100%.

Among the main results are: the adduction channel of rectangular section extends for 125 m and the calculations indicated that it supports a maximum flow of 4.59 m³/s; the forebay tank has a useful volume of 114.84 m3; the penstock is 320 m long and has a maximum adduct capacity of 6.78 m3/s.

3.2.4. Surveys and tests on generator sets

The Lajeado SHP generator set consists of a simple horizontal Francis turbine and synchronous electric generator. The tests carried out at the end of 2007 had as main objective to reveal the performance of the main equipment of the plant.

In parallel to the measurement of turbine flow under load conditions of 25%, 50%, 75% and 100%, electrical quantities and hydraulic quantities (flow, heads, pressure and losses in the adduct) were measured. The overall efficiency of the generator set was then obtained (Figure 5).

[Figure 5:Overall efficiency of generator set.]

The maximum power generated by the plant is 1,990 kW with the fully open hydraulic turbine distributor. However due to the high levels of audible noise resulting from excessive cavitation it was concluded that the operation of the plant should be limited to a maximum power of 1,770 kW.

In order to determine the efficiency of the electric generator, its electrical losses were determined by the calorimetric method, according to IEEE-115 and ABNT NBR-5452 standards. Defining the losses in the electric generator for the load conditions of 25%, 50%, 75% and 100% was obtained the efficiency of the same. Figure 6 shows the efficiency of the electric generator.

[Figure 6: Performance curve of the synchronous electric generator.]

In addition the the capability diagram of the electric generator was obtained with the parameters obtained in these surveys.

Although the current generators present a much higher efficiency, it is concluded that the generator of the Lajeado SHP, is in a range of satisfactory performance. Its efficiency reached a maximum value of 96.2%.

The results obtained for the performance of the hydraulic turbine are shown in Figure 7 for the same load conditions. The efficiency of the turbine is low and the maximum value was 83.9%. Currently the hydraulic turbines can achieve an efficiency of approximately 93%.


[Figure 7: Performance curve of the hydraulic turbine.]

3.3. Economic evaluations and Hierarchical stages of the technical and economic evaluations of repowering of Lajeado SHP

3.3.1 First Stage - Simulation of theoretical maximum gain

Due to the transitions of owners since the construction of the plant much of the historical technical documentation has been lost, leaving only basic technical information and scarce remnants of the projects. Thus, it was not possible to simulate the theoretical maximum gain.

However, knowing the underutilization of the available flows and the existence of a high gross head (atypical head for the North region of Brazil) the complementary studies to be realized to know the technical characteristics of the plant were defined.

The underutilization of the local hydraulic potential was verified by the observation of significant discharge of water by the spillway in some months of the year combined with the possibility of head gain.

3.3.2. Second Stage - Technical, economic and environmental feasibility study

Considering the technical information raised four possibilities of repowering in the expansion modality for the Lajeado SHP were established.

[Figure 8: Alternatives for repowering.]

The alternatives considered (Figure 8) are briefly described below:• Alternative I: It is based on the use of part of the existing

water intake system through a bypass in the penstock nearthe present power house to bring water to a new powerhouse located downstream (near the existing bridge)resulting in a gross head of 97.45 m;

• Alternative II: It is based on the use of existing dam, butdiscarding the entire current adduction system. A newadduction system (parallel to existing one) was then built fora new power house located downstream of the current one(below the existing bridge) totaling a gross head of 107.09 m;

• Alternative III: It is based on the use of the existing damand construction of a new adduction system, however withan alternative route to the first two (Alternatives I and II)totaling a gross head of 107.36 m;

• Alternative IV: It is similar to Alternative II but considersa power house built between the current power house andthe bridge located downstream providing a downstreamwater level of 234.47 m and a gross head of 101.98 m. Thiscorresponds to a reduction of 5.11 m in relation to the grosshead contemplated in Alternative II.Then an incremental simulation was performed to expand

the plant for each of the alternatives contemplated through pre-sizing and respective quantification of the costs involved. Following the energy benefits were converted into economic terms and thus could be generated the economic reference indicators: time of return of capital, net present value and internal rate of return.

3.3.2.1. Alternative I

Knowing that the restriction point in the water adduction system (complementary studies) is the channel whose maximum adduction capacity is 4.59 m³/s the plant's expansion costs were reached up to this limit. For this costs were calculated considering a unit increment of flow according to Table 3.

[Table 3]: Costs of Alternative I.

Flow (m³/s) 2.00 3.00 4.00 5.00

Power (kW) 1,746.95 2,620.42 3,493.89 4,367.36

Low pressure system (US$)

- - - -

High pressure system (US$)

303,800.41 362,215.00 552,223.61 605,529.30

Power house (US$)

1,475,000.00 2,145,280.00 2,784,000.00 3,360,000.00

Other costs (US$)

599,072.01 809,341.27 1,123,508.56 1,314,412.60

Total cost (106 US$)

2.378 3.317 4.460 5.280

Cost/power (US$/kW)

1,361.16 1,265.77 1,276.44 1,208.95

The incremental economic simulation revealed the best option as the installation of a power house downstream from the current power house, using all the available adduction system (4.59 m³/s), totaling 4 MW of installed capacity.

3.3.2.2. Alternative II

The turbine’s flow was sought to maximize the economic benefits since there were no operational restrictions. The plant expansion costs were estimated for a turbine flow rate of up to 20 m³/s. For this a flow increment of 5 m³/s was considered according to Table 4.

The incremental economic simulation, combined with the achievement of a typical capacity factor (0.6), for the considered head, revealed the best option as a new plant with a project flow of 9.4 m³/s representing an additional power of 7.9 MW.

During 4 months of the year there will be available flow to activate also the turbine of the existing power house. The power of 9.65 MW will be available for 3.5 months per year.


[Table 4]: Costs of Alternative II.

Flow (m³/s) 5.00 10.00 15.00 20.00

Power (kW) 4,367.40 8,734.79 13,102.19 17,469.59


66,165.50 97,042.50 142,731.88 168,356.00


1,568,859.86 2,870,765.28 3,886,570.41 5,422,106.48

Power house (US$)

3,360,000.00 5,835,000.00 8,228,000.00 10,575,000.00

Other costs (US$)

1,577,424.34 2,670,747.80 3,794,340.32 4,853,045.06


6.572 11.474 16.052 21.019

Cost/power (US$/kW)

1,504.89 1,313.55 1,225.11 1,203.15

3.3.2.3. Alternative III

In this alternative it was also considered a flow increase of 5 m³/s up to the limit of 20 m³/s for plant expansion (Table 5).

The incremental economic simulation combined with the achievement of a typical capacity factor (0.6) for the considered head revealed the best option as a new plant with a project flow of 9.4 m³/s representing an additional power of 7.9 MW.

[Table 5]: Costs of Alternative III.

Flow (m³/s) 5.00 10.00 15.00 20.00

Power (kW) 4,367.40 8,734.79 13,102.19 17,469.59


172,855.50 239,315.00 342,171.88 395,744.00


1,152,216.80 2,345,002.89 2,808,360.00 3,926,432.27

House of machines (US$)

3,360,000.00 5,835,000.00 8,228,000.00 10,575,000.00

Other costs (US$)

1,498,238.71 2,572,775.26 3,569,835.41 4,529,028.13


6.183 10.992 14.948 19.426

Cost/power (US$/kW)

1,415.79 1,258.43 1,140.91 1,112.00

3.3.2.4. Alternative IV

In this alternative it was also considered a flow increase of 5 m³/s up to the limit of 20 m³/s for plant expansion (Table 6).

Consistent with previous analyzes, the incremental economic simulation, coupled with the achievement of a typical capacity factor (0.6) for the considered head revealed the best option to be that of a new plant with project flow equal to 9.4 m³/s representing an additional power of 7.5 MW. However maintaining the existing power house.

During 4 months of the year there will be available flow to activate also the turbine of the existent power house. The power of 9.3 MW will be available for 3.5 months of the year.

[Table 6]: Costs of Alternative IV.

Flow (m³/s) 5.00 10.00 15.00 20.00

Power (kW) 4,148.54 8,297.07 12,445.62 16,594.16


66,165.50 97,042.50 142,731.88 168,356.00


1,176,644.90 2,153,073.96 2,914,927.81 4,066,579.86

Flow (m³/s) 5.00 10.00 15.00 20.00

House of machines (US$)

3,360,000.00 5,835,000.00 8,228,000.00 10,575,000.00

Other costs (US$)

1,577,424.34 2,670,747.80 3,794,340.32 4,853,045.06


6.180 10.756 15.080 19.663

Cost/power (US$/kW)

1,489.74 1,296.34 1,211.67 1,184.93

3.3.2.5. Definition of the best alternative for repowering

Table 7 presents the synthesis of the results that allowed the decision making regarding the best alternative of arrangement for repowering. The values practiced in the Brazilian market in January 2010 were considered for the composition of the parameters adopted for economic evaluations.

[Table 7]: Summary of economic analysis results of alternatives.

AlternativeFlow

(m³/s)Power (MW)

Investment (106 US$)

Payback (anos)

NPV (106 US$)

IRR (%)

I 4.6 4.0 4.8 4.7 13.2 55.0

II 9.4 7.9 10.6 5.5 20.9 42.4

III 9.4 7.9 10.1 5.3 21.3 44.7

IV 9.4 7.5 10.0 5.3 21.3 45.4

After integrated technical and economic analysis it can be defined that the most viable alternative is alternative IV.

At this stage the results indicated a cost of 1,328 US$/kW for a better alternative, excluding the cost of the associated transmission system and interest.

Through a study carried out by EPE [1] a parameterized investment cost for hydroelectric plants in Brazil was reached between 800 and 1,500 US$/kW. The research carried out by Tiago & Caetano [7] based on the cost sheet of 63 SHP projects in Brazil resulted in an average implementation cost of 1,033 US$/kW.

Canales & Beluco [8] carried out a study to elaborate parametric cost curves for SHP in Nicaragua, based on 18 pre-feasibility studies with costs and previous experiences in this country and other countries of the Central American region, reaching the average cost of approximately 5,000 US$/kW. The authors concluded that this value, considered high, is possibly justified by the inclusion of the cost of transmission lines and the geographic difficulties inherent in rural electrification.

3.3.2.6. Optimization of installed power and determine the new generator sets of the expanded part

Selecting the best alternative for plant repowering, power plant refinement was achieved through an optimization process that sought to maximize the utilization of available hydraulic potential (maximization of energy and economic benefits).

Starting from the updated monthly flow duration curve, the corresponding energy curve for the use was obtained (Figure 9).

As already presented in this paper the new gross head resulting from the technical evaluations is 107.09 m in contrast the original gross decrease of 92 m.

The conception of repowering (modality expansion) of the Lajeado SHP considers the use of the existing hydraulic system and power house, including generator set installed whose nominal turbine flow is 2.6 m³/s. Therefore the new installation will only start operating with availability of flows of more than 2.6 m³/s.


[Figure 9: Longitudinal section of the additional power house.]

This decision is justified because for the best alternative for repowering (alternative IV) a project flow of 9.4 m³/s was obtained for expansion. Because choosing to keep the additional turbines operating with equal or lower flows at 2.6 m³/s (approximately 28% of the load) would be to operate below the lower limit of the Francis turbine optimum operating range. That is, the new generator sets, even with relative efficiencies higher than the existing generator set, would operate with very low efficiency in part of the time, resulting in significant losses of power generation.

For the process of optimization of the installed power of the new power house reference values were adopted for certain quantities. The main reference values are summarized in Table 8.

The sale price of the energy generated (80.544 US$/MWh) was adopted as the average of the tariffs practiced in the free contracting marketin in Brazil at the beginning of 2010. From this amoun the estimated costs of operation and maintenance (4.354 US$/MWh) were subtracted.

[Table 8]: Assumptions adopted.

Item Valor

Adduction system losses 2.38 %

Nominal turbine efficiency 92 %

Minimum turbine efficiency 82 %

Efficiency of the electric generator generator 96.5 %

Scheduled unavailability 360 hours

Forced Unavailability 100 hours

Investment amortization period 30 years

Interest rate 10 % per year

Sale price of energy 80.544 US$/MWh

The result of the optimization process of the best repowering alternative of the Lajeado SHP indicated an optimum design flow of 8.8 m³/s and an installed power of 8.0 MW. What can be obtained in the curve that relates the net benefit to the installed power whose optimal point points to the maximum net present value.

The summary of the results of the technical and economic analyzes for the expand part are presented in Table 9.

[Table 9]: Results.

Item Valor

Upstream water level 337.64 m

Downstream water level 230.55 m

Gross head 107.09 m

Net head 104.50 m

Project flow 8.8 m³/s

Item Valor

Installed power 8 MW

Capacity Factor 0.55

Annual energy generated 36.3 GWh

Total cost of plant 15.97 x 106 US$

Annual gross revenue 2.07 x 106 US$

Annual net revenue 0.38 x 106 US$

Internal rate of return 12.98 %

The study to determine the new generator sets resulted in 2 additional units (Figure 10) with a rotation of 720 rpm and a maximum suction height of 1.56 m. Each turbine has a power of 4.124 MW and flow of 4.4 m³/s for a gross head of 107.09 m and respective net head of 104.5 m. The correlated generators have a unit power of 4.440 MVA.

All of this at a final cost of 1,966 US$/kW including a new electric transmission system for plant interconnection (and interest rate).

The total estimated period for completion of the works and the start-up of the first generator set of the expand part is 24 months.

The existing generator set will remain in operation for a large part of the time during interventions, minimizing the plant downtime. This is one of the advantages of repowering in the expansion modality.

Regarding the interconnection of the power plant with the regional transmission system, the results indicated the need to implement a transmission line from the plant to the nearest power grid. This line will have a voltage of 34.5 kV and approximately 3.5 km in length.

4. CONCLUSION

The repowering of SHPs is an important tool for the rational and efficient use of water resources in Brazil.

Old SHPs usually depend on the diagnosis of their technical characteristics through surveys, tests and complementary studies to make the decision on the best alternative of repowering intervention.

Usually the repowering modality that has the highest cost is thee expantion modality. However even in this modality the average cost of investment in repowering remains lower than the cost of investing in the construction of new hydroelectric plants in Brazil.

Through the case study of Lajeado SHP it was possible to confirm the applicability of the hierarchical stages of the technical and economic evaluations to define the viability of repowering.

In the economic evaluation stage of the alternatives for repowering the cost of 1,328 US$/kW was obtained for a better alternative (excluding the cost of the associated transmission system and interest rate) and an installed power of 7.5 MW. Already after the stage of optimization of the installed power to cost of 1,996 US$/kW (including associated transmission system and interest rate) was obtained and an installed power of 8 MW.

The case study also confirmed the need for prior technical analysis on the characteristics of the interconnection transmission system of the hydroelectric plant. If this system supports carrying the additional energy provided by the repowering can be characterized as a restriction that can make it unfeasible. For Lajeado SHP this cost reached 25% of the total cost.


5. REFERENCES

[1] EPE, 2007, "National Energy Plan 2030", Ministry of Mines and Energy & Energy Research Company, Report, Brasília, DF.

[2] Oliveira, M. A., 2012, "Gains made possible by the repowering of Small Hydroelectric Power Plants: Concepts and Definitions", VIII Congress of Energy Planning, Curitiba, PR.

[3] Bermann, C., Veiga, J. R. C., Rocha, G. S., 2004, “The Repowering of Hydroelectric Power Plants as an Alternative for the Increase of Energy Supply in Brazil with Environmental Protection”, Energy Policy Studies Group of WWW - Brazil.

[4] Oliveira, M. A., 2017, “Model for the Analysis of the Technical, Economic and Environmental Viability of Repowering of Small Hydropower Plants”, Hidro & Hydro – News SHP, UNIFEI/CERPCH, Itajubá, MG, v. 74, pp. 5-10.

[5] Souza, Z., Bortoni, E. C., Santos, A. H. M., 1999, "Studies

for the Implementation of Hydropower Plants", Eletrobras, Rio de Janeiro, RJ, Chap 3.

[6] Domínio Engenharia, 2010, “Basic Repowering Project – Lajeado SHP”, Technical Report, Itajubá, MG.

[7] Tiago, G. L., Caetano, G. T., 2004, "Study to determine the costs of implementation of SHP in Brazil", Brazilian Dams Committee, IV Brazilian Symposium on Small and Medium Hydroelectric Power Plants, Porto de Galinhas, PE.

[8] Canales, F. A., Beluco, A., 2008, "Parametric cost curves for Mini Hydropower Plants in Nicaragua". Brazilian Dams Committee, VI Brazilian Symposium on Small and Medium Hydroelectric Power Plants, Belo Horizonte, MG.

[9] Domínio Engenharia, 2008, “Hydrological Studies – Lajeado SHP”, Technical Report, Itajubá, MG.

[10] Domínio Engenharia, 2008, “Commissioning and Feasibility Study - Lajeado SPH”, Technical Report, Itajubá, MG.


EVALUATION OF HYDROELECTRIC, WIND AND SOLAR POTENTIAL: A CASE

STUDY OF EXISTING PLANTS1Filho,Wilson Pereira Barbosa; 2Silva, Lívia Maria Leite da; 3Silva, Nathan Vinícius Martins da;

4Oliveira, Karina Aleixo Benetti de; 5Abreu, Anna Luisa de Oliveira; 6Swiatovy, Gabriel Hepp

1Civil Engineer at PUC Minas, Lawyer at University Salgado de Oliveira, MSc. in Environmental Management and Audit at European University Miguel de Cervantes, PhD student of Program Nuclear Science and Techniques of Department of Nuclear Engineering at UFMG. Environmental Analyst of State Foundation of the Environment (FEAM). Professor of Energy Engineering degree course at the PUC Minas. Curriculum Lattes: http://lattes.cnpq.br/4241912943857821.2Energy Engineer and Master in Electrical Engineering from the Pontifical Catholic University of Minas Gerais. Researcher at the State Foundation of the Environment - FEAM. Curriculum Lattes: http://lattes.cnpq.br/6661724494856451.3Environmental Engineering student at Centro Universitário Newton Paiva. Intern at State Foundation for the Environment in Minas Gerais – FEAM. Lattes resume: http://lattes.cnpq.br/9519876602254143.4Student of Energy Engineering at Pontifical Catholic University of Minas Gerais - PUC Minas. Doing internship at the State Foundation of the Environment - FEAM. Conducting Voluntary Scientific Initiation with the State Foundation of the Environment - FEAM.5Student of Energy Engineering at Pontifical Catholic University of Minas Gerais - PUC Minas. Conducting Voluntary Scientific Initiation with the State Foundation of the Environment - FEAM.6Student of Energy Engineering at Pontifical Catholic University of Minas Gerais - PUC Minas. Conducting Voluntary Scientific Initiation with the State Foundation of the Environment - FEAM.

ABSTRACT

The current scenario of electricity generation in Brazil shows a matrix strongly supported by hydroelectricity. Despite being considered a clean source, strong dependence on power from a single source reduces the security of supply and reliability of a system. This was evident in the middle of 2014, when a serious water crisis was installed in the country, which affected drastically the level of reservoirs, requiring the activation of thermal plants to meet demand, causing economic losses to society given the more onerous character of this last type of generation. In this way, this article points to the insertion of renewable sources, namely, solar and wind, as an alternative for the diversification of the national energy matrix and consequent increase of the reliability of the current generation model. A case study was carried out to evaluate the wind and solar potential in two localities where there are hydroelectric plants already functioning, the Emborcação power plant and the small hydroelectric plant of Cachoeira do Brumado, located in the State of Minas Gerais, Brazil, in order to evaluate the potential of combined use of these sources, verifying their gains in terms of seasonal stability of generation. The study was based on the analysis of historical wind speed and solar radiation data recorded in the regions that were the object of study. The achieved results show significant gains in terms of increased energy availability and stabilization of the annual generation. Therefore, it is considered feasible for the state of Minas Gerais to adopt complementary generation models based on the analyzed sources, which may reduce the use of thermal plants during the drought season, which may result in a decrease of carbon emissions rates, given the cleaner generation characteristics of the analyzed sources.

KEYWORDS: Energy, renewable sources, regulatory bases, energy scenario.

1. INTRODUCTION

In the modern world, several human activities have been causing damage to the environment and natural resources. In this sense, segments linked, among others, to the civil society and the academia have sought to draw attention to the urgent need for changes in existing productive models. One of these models is the generation of energy based on fossil sources, which is at the base of the development of the current society [1] and also characterizes one of the main causes of the high emission rates of Greenhouse Gases (GHG) in the terrestrial atmosphere, one of the main damages that civilization has implied to the planet. In this way, we have sought alternatives that can meet the current needs of society by observing the conservation of resources and care for the environment. In this context, renewable energy sources appear, which may play a relevant role in meeting the demands for electricity and have GHG emission levels along their production chain, much lower than those found in sources of fossil origin [2].

According to the National Electric Energy Agency [3], the Brazilian energy matrix is represented by hydroelectricity (64.87%), thermoelectricity (26.97%), thermonuclear generation (1.31%), wind generation (8%) and solar (0.02%). It is observed,

therefore, that the generation of national electricity is strongly supported in hydroelectricity. This guarantees the country less GHG emission indices when compared to other countries that have their generation based on fossil sources, however, hydroelectricity is a resource linked to the country's rainfall regime, which has a stochastic character and seasonal variability. In this way, meeting the demand has always faced the challenge of stabilizing generation during the dry period of the year.

This situation becomes even more difficult in times of rainfall. As a coping strategy, there is a need to diversify the energy supply, where, within the context of environmental concern previously mentioned, the use of renewable sources becomes an increasingly interesting alternative. It is known that Brazil is a country with ample availability of renewable resources.

In terms of wind energy, according to the "Atlas of Brazilian Wind Potential" [4], the wind potential in Brazil reaches 143,000 MW, not including in this calculation offshore potential, and considering only heights up to 50 m. In Brazil, The Wind Atlas of Minas Gerais, completed in May 2010 by Energy Company of Minas Gerais (CEMIG), estimated the seasonal wind potential in the state, in three different dimensions, and the results indicate a potential of 10.6 GW, 24.7 GW and 39.0 GW, at heights of 50 m, 75 m and 100 m, respectively [5].



In Brazil, the wind regime tends to reach higher velocities in periods that coincide with low rainfall, which opens space for wind operation in a complementary way to hydroelectric dams that contributes to preserving reservoir water in drought periods [4].

In the case of solar energy, despite the different climatic characteristics observed in Brazil, it can be noticed that the annual average of global irradiation shows good uniformity, with annual averages relatively high in all of the country, varying from 4.25 kWh/m².day to 6.5 kWh/m².day. The values of global solar irradiation in any region of the brazilian territory (1500-2500 kWh/m²) are higher than in most European Union countries, such as Germany (900-1250 kWh/m²), France (900-1650 kWh/m²) and Spain (1200-1850 kWh/m²), where projects using solar resources, some with strong government incentives, are widely disseminated [6].

In this sense, the present work shows and evaluates the complementarity of hydraulic generation with wind and solar sources as a strategy for the seasonal stabilization of energy supply. Wind and solar resources were evaluated from two localities where two hydroelectric plants are located in operation in the State of Minas Gerais, Brazil, in order to determine the annual generation profile obtained through the joint use of these three sources.

The plants analyzed were the Emborcação Hydroelectric Plant and the Small Hydroelectric Plant of Cachoeira do Brumado. The wind and solar generation were evaluated by means of the theoretical power plant design, carried out through historical series of wind velocities and values of solar radiation recorded in the regions of interest. The results allowed relevant discussions about the characteristics of each source and the strategic role that each one can play in meeting the demands for electricity.

2. MATERIALS AND METHODS

2.1. Characterization of study areas

The plants analyzed are located in the State of Minas Gerias, Brazil. The Emborcação plant is located in the Paranaíba river basin, on the river of the same name, between the States of Minas Gerais and Goiás, more specific in the cities of Catalão (Goiás) and Araguari (Minas Gerais) at the coordinates 47°59'13" W and 18°27'05" S. It has a reservoir with an area of approximately 476 km² and an installed capacity of 1.192 MW.

The Cachoeira do Brumado plant is located in the Paraíba do Sul river basin, on the Peixe river, in the city of Lima Duarte (MG), at the coordinates 43º53'19" W and 21º51'10" S. It has a reservoir with an area of approximately 0,0075 km² and an installed capacity of 2,340 MW.

Figure 1 illustrates the location of the power plants and Figure 2 shows their satellite images.

[Figure 1: Location of the plants analyzed in relation to Brazil (left) And Minas Gerais (right).]

[Figure 2: Satellite image of the Emborcação (up) and Cachoeira do Brumado (below) plants.]

2.2. Stages of the methodology

[Figure 3: Methodological flowchart.]

Characterization of the plants analyzed

Determination of hydraulic

generation profile

Survey of historical hydraulic generation

data

Determination of the solar generation profile: sizing of the

plant

Survey of the solar radiation data of the analyzed localities

Determination of conversion

technology (module) and technical specifications

Determination of the number of modules

used and their conversion efficiency

Determination of the monthly energy generated by the

plant in MWh

Determination of the Wind power

generation profile: sizing of the plant

Survey of wind velocity data in the analyzed localities

Data extrapolation: 10 m to 120 m

Replacement of velocity values not recorded by mean

values

Calculation of the monthly Weibull

distribution for each locality

Determination of conversion

technology (wind turbine) and survey of its power curve

Determination of the number of turbines

used

Determination of the monthly energy generated by the

plant in MWh


The methodology used was characterized by the collection of data related to the plants analyzed and the determination of an annual generation curve for the hydraulic, wind and solar sources for each of the plants. The determination of the hydraulic generation was carried out by means of the survey of the historical series of generation of the plants in question, through contact with the responsible owners or organizations. The seasonal water potential was considered as the monthly average of the historical generation raised. The solar generation was determined through the design of a theoretical plant using solar radiation data recorded for the latitude and longitude values of the plants and made available by the Reference Center for Solar and Wind Energy Sérgio Brito (CRESESB) [7].

Wind generation was determined through the design of a theoretical plant, using historical series of wind speeds recorded and made available by the National Institute of Meteorology (INMET) [8].

For sizing of wind and solar generation it was considered that each of the theoretical plants would have 100% of the installed power of the hydroelectric plant. It should be emphasized that this consideration does not take into account the economic viability of wind and solar power plants of the aforementioned size, since this is not the scope of this work. It is only a premise used for the seasonal evaluation of resources.

Figure 3 presents the steps of the methodology used that is described in detail in the next section.

3. THEORIES / CALCULATIONS

3.1. Calculations of seasonal energy generation: Wind energy

The wind potential was calculated from historical measurement series recorded by the INMET measuring stations located in the vicinity of the hydroelectric plants analyzed. With the latitude and longitude data of the plants, it was identified, through Google Earth, the closest station to each hydroelectric plant and, consequently, of the wind power plants. For the Cachoeira do Brumado plant, the Juiz de Fora station was used, and, in the case of the Emborcação plant, the Uberlândia station. The data provided by INMET are wind velocity values in m/s recorded hour per hour during the day, from 2008 to 2013. The figures provided presented, however, two inconsistencies for the purpose used here:

• The occurrence of unmeasured values;• The fact that the measurements were carried out at 10m,

inadequate height to the energy use.

In this way, it was first determined that the last year of measurements would be used for the sizing, and the values of speeds not recorded in that year were replaced by the average values recorded on the same day and hour of previous years. For the calculation of the wind speed for a height of 120 meters, suitable for the energy use, was used the Hellmann Law, given by Equation 1 [9-11]:

(1)

Where Vz is the velocity for height z; z is the height to be extrapolated; Vr is the velocity measured at the reference height; Zr is the reference height; n is the soil roughness coefficient [4]. A soil roughness coefficient of 0,20 (mean roughness class) was used, since it was considered that the characteristics of the areas where the hydroelectric plants are located are close to forests, live fences and shrubs.

[Table 1]: Roughness coefficients [12]. Land Type Coefficient

Lake, ocean and smooth soil 0,10

Florests 0,15

Fences and shrubs 0,20

Small towns with few trees and shrubs 0,25

Large cities with high buildings 0,30

Wind speeds and directions show well-defined seasonal trends within their stochastic character. Therefore, in order to determine the annual energy production, a probabilistic distribution must be analyzed that can represent, as accurately as possible, the behavior of the wind regime in a region.

The Weibull distribution, (ν), given by Equation 2, is classified as the most adequate to describe the wind regime of a place and represent the monthly frequencies of its velocity [12].

(2)

Where ν is the wind speed recorded in m/s; c is the scaling factor in m/s and k is the (dimensionless) form factor. The scale factor "c" is related to the average local wind speed. On the other hand, the form factor "k" is related to the wind velocity variance around the mean velocity. The scale factor can be estimated by means of Equation 3:

(3)

According to Freitas and Volpato [13] many mathematical methods can be used to estimate the parameters of the Weibull distribution, including least squares analysis for an observed distribution, methods of average wind speeds and quartiles, correlation method of "k" with the mean velocity. Still in accordance with these authors, the present work used the least squares analysis to determine the parameter "k".

This method makes an adjustment of this by minimizing the square sum of the differences between the estimated value for the probability distribution and the observed data. The observed values and the monthly probability distributions found for each plant are presented in Appendices A and B. The next step is characterized by the specification of the equipment considered in the design. The chosen wind turbine was the Enercon E-126 EP4 with rotor diameter of 127 m and power of 4,200 kW.

Figure 4 shows the power curve of this wind turbine [14].

[Figure 4: Power curve of the wind turbine.]

The number of turbines used by the plant is characterized by the ratio of turbine power to installed power at the plant. Finally, the monthly generation can be determined by means of Equation 4:


(4)

Where GMEE is the average monthly generation of wind energy; v is the wind speed in m/s; W(v) is the Weibull distribution for each wind speed; P(v) is the power generated by the turbine for each wind speed; 720 is the number of hours considered in the month; n is the number of turbines [15].

3.2. Calculations of seasonal energy generation: Photovoltaic energy

The potential of solar generation was obtained from information provided by CRESESB, which allows the consulting of data of average monthly solar radiation in kWh /m2.day from the geographical coordinates (latitude and longitude) of the desired places. For the sizing of the solar generation the data of solar radiation in the horizontal plane for the latitudes of the analyzed plants were considered.

Note that the radiation values for the horizontal plane are lower than those observed for the radiation in the inclined plane (whose inclination angle can be considered equal to the latitude of the place, in order to optimize the performance of the systems), however, it was decided to use them, adopting a scenario of pessimistic design. In terms of conversion technology, the Canadian MAXPOWER CS6X of 325 W [16] photovoltaic module was adopted. The total number of modules used is characterized by the ratio between the installed power of the plant and the nominal power of the module used. The estimated generation curve was obtained by means of Equation 5.

GMES = RS × AM × η × d (5)

Where GMES is the average monthly generation of solar energy; RS are the average daily solar radiation values in the analyzed locations (in kWh/m2.day); AM is the estimated total area of modules, obtained by multiplying the number of modules of the plant with the area of each module; η is the conversion efficiency of solar energy into electric energy obtained by the technology, in this case, 17% [16], and d is the number of days in the month.

4. RESULTS

[Figure 5: Evaluation of resources for the Emborcação plant.Source: INMET (2014) and CRESESB (2017).]

Figure 5 and Figure 6 show the results obtained in terms of the evaluations of the renewable resources in the locations of the plants under study. The mean monthly values of wind speed and annual daily mean values of solar radiation are presented. The wind velocity data were obtained from the Uberlândia (MG) measuring station for the Emborcação plant and the Juiz de Fora (MG) station for the Cachoeira do Brumado plant and are

related to the years 2008 to 2013. It can be seen that, in the case of Emborcação, the wind velocity values range from 2 to 4,5 m/s. The values of solar radiation vary between 4,22 to 5,44 kWh/m².day (horizontal plane). In the case of Cachoeira do Brumado, wind velocity values range from 3,5 to 6 m/s. The values of solar radiation vary between 3,11 to 5,03 kWh/m².day (horizontal plane).

[Figure 6: Evaluation of the resources for the Cachoeira do Brumado plant. Source: INMET (2014) and CRESESB (2017).]

Figure 7 and Figure 8 present the estimated generation profiles for the two plants under analysis. In the case of the Emborcação plant, the dimensioned solar generation is able to supply, annually, about 54% of the hydraulic energy produced.

Wind power is capable of supplying about 10% of this value. For the Cachoeira do Brumado plant, solar generation is able to respond annually to 37% of the hydropower, and the wind power source accounts for 40% of that value.

[Figure 7: Estimated generation profiles for the Emborcação plant.]

[Figure 8: Estimated generation profiles for the Cachoeira do Brumado plant.]


Other important results to be presented are the Capacity Factor of the plants and the area occupied by each one, as shown in Figure 9 and Figure 10. The estimation of the area occupied by the wind turbines was performed as proposed by Garbe, Mello and Tomaselli [17]. Where the authors point out that, in general, a safe distance for the installation of turbines is of the order of 10 times the diameter "D", if installed downstream, and 5 times "D" if installed next to in relation to the prevailing wind.

It is important to note that the values of the Capacity Factors were determined according to the dimensioning done for the wind source and the solar source. For the hidraulic plants, were used the data measured used in the sizing of generation. In the case of the solar photovoltaic source, the losses which such plants are subject were not considered such as: losses by mutual shadowing between rows, soiling losses, mismatch losses, losses by elevation of temperature, etc.

[Figure 9: FC and estimated occupied areas for the Emborcação plant.]

[Figure 10: FC and estimated occupied areas for the Cachoeira do Brumado plant.]

4. CONCLUSIONS

The present work carried out a case study of two existing plants in Minas Gerais, Brazil – Emborcação e Cachoeira do Brumado – evaluating based on their generation profiles, their seasoned complementarity with wind and solar sources. It was observed that the availability of the hydraulic and wind resources has inverse behaviors throughout the year, characterizing a final profile with complementary characteristics. The generation

based on the solar source has lower values of variability, however, presented significant values of generation.

The wind and solar sources have as characteristic their intermittent character. The utilization of large-scale power plants based on these sources requires investments in expanding storage capacities. In the case of hybrid generation (solar + wind + hydropower) it is necessary to analyze the capacity of hydroelectricity in accommodating these plants. However, this was not the objective of this work that sought to realize a evaluation of the potential energy, i.e. of the resources availability

5. BIBLIOGRAPHY

[1] World Wind Energy Association (WWEA). “Wind energy 2050 on the shape of near 100% re grid”. 2015.

[2] Intergovernmental Panel on Climate Change (IPCC). “Renewable energy sources and climate change mitigation”, Cambridge University Press, New York. 2012.

[3] National Electric Energy Agency (ANEEL). "Generation Information Bank: Generation Capacity of Brazil". 2017.

[4] Amarante, O. A. C., Zack, M. B. J., SÁ, A. L. "Atlas of Brazilian Wind Potential". MME, Brasília. 2001.

[5] Energy Company of Minas Gerais (CEMIG). "Wind Atlas of Minas Gerais". Belo Horizonte, Minas Gerais, pp. 43-56, 2010.

[6] Pereira, E. B. P.; Martins, F. R.; Abreu, S. L. De; Ruther, R. "Brazilian Atlas of Solar Energy". 2006.

[7] Reference Center for Solar and Wind Energy Sérgio Brito (CRESESB). "Solar Potential - SunData". 2017.

[8] National Institute of Meteorology (INMET). "Meteorological Data". CD-Room. 2014.

[9] Ðurisic, Z; Mikulovic, J. "A model for vertical wind speed data extrapolation for improving wind resource assessment using WAsP." Renewable Energy. V 41. p 407 and 411. 2012.

[10] Gualtieri, G; Sauro, S. "Comparing methods to calculate atmospheric stability-dependent wind speed profiles: A case study on coastal location". Renewable Energy. V 36. p. 2189 - 2204. 2011.

[11] Gualtieri, G.; Secci, S. "Methods to extrapolate wind resource to the turbine hub height based on power law: A 1-h wind speed vs. Weibull distribution extrapolation comparison.”Renewable Energy. V 43. p. 183-200. 2012.

[12] Sansigolo, C. A. Distributions of Probability of Speed and Wind Power. Brazilian Journal of Meteorology. V.20, n.2, 207-214, 2005.

[13] Freitas, T. C.; Volpato, D. C. R. "Methodology to evaluate the viability of windfarm - cases study". Proceedings of ECOS 2016 - the 29th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems. Slovenia. 2016.

[14] Enercon. "Enercon E-126 EP4: Overview of technical details". 2017.

[15] Traveler, G. P; Camacho, J.R.; Andrade, D.A. Estimation of obtaining energy from the wind in a given area. Federal University of Uberlândia.2014.

[16] Canadian Solar. "PV Module Product Datasheet - Maxpower CS6X-315 | 320 | 325P". 2016.

[17] Garbe, E. A.; Mello, R. de; Tomaselli, I. "Conceptual Project and Analysis of Economic Viability of Wind Power Generation Unit in Lagoa dos Patos -RS". Brazilian Journal of Energy. Vol 20. nº 1. 2014.


6. APPENDICES

A. Monthly histograms and distributions of Weibull elaborated for the Emborcação power plant.


B. Monthly histograms and distributions of Weibull elaborated for the Cachoeira do Brumado power plant


Prediction of Pressure Pulsation in Francis Turbines Using Rans Solution:

An Applied Study of Effects of the Turbulence Models, Mesh, Domain

Extension and Multiphase Flow 1Marra, João M.; 2Gramani, Liliana M.; 3Zubeldia, Luiz F.; 4Kaviski, Eloy

1Department of Maintenance Engineering, Itaipu Binacional, Iguassu Falls, 85856-970, Brazil, [email protected]; Tel: (+55 45)3520-2690; Fax: (+55 45)3520-38352. Department of Mathematics, Federal University of Parana - UFPR, Curitiba, 81531-990, Brazil, [email protected]. Center for Advanced Studies in Dam Safety – FPTI, Iguassu Falls, 85.867-900, Brazil, [email protected]. Department of Hydraulic, Federal University of Parana – UFPR, Curitiba, 81531-990, Brazil, [email protected]

ABSTRACT

The present work shows a comparison between turbulence models, computational meshes, and domains extension, as regards its ability to numerically modeling the flow in a Francis turbine operating in part load and full load conditions. The main objective of this study is to evaluate the influence of these parameters at prediction of the amplitude and frequency of pressure pulsations in 3D flow in the turbine hydraulic system in any operative condition, when using RANS solution for single-phase incompressible model for the ruler equations of the flow or two-phase compressible model to consider the effects of the occurrence of cavitation on the flow. In this study were used the SST, k-ε and k-ω turbulence models with three different mesh densities and two extensions of the domain. The configuration of mesh and turbulence model whose results best adhered to available data was used to simulate two-phase flow and entire domain. The study was applied to the ITAIPU turbines and results obtained in each simulation were compared with data available for the operating conditions considered.

KEYWORDS: Francis turbine, Turbulence models, CFD, numerical simulation.

1. INTRODUCTION

As further a hydraulic turbine operates out of its designing conditions, worst is the flow at the turbine and greater is the possibility of hydraulic instability phenomena, mainly in turbines with fixed blades runners, as Francis.

Such changes in its operating condition cause pressure fluctuations with damage potential to the physical integrity of the turbine, generating unit and even civil facilities from the powerhouse to the dam.

One cause of this damage is due to the development of vortices at the runner outlet which induces pressure fluctuations which propagate throughout the hydraulic circuit [1], which may cause dynamic interactions which cause hydraulic instabilities and resonance in the turbine’s hydraulic circuit.

To better understand the complex flow in a Francis turbine and evaluate disturbances which occur throughout the hydraulic circuit due to pressure fluctuations can be used the Computational Fluid Dynamics (CFD). For this, knowledge of inherent peculiarities to the application of this technique is extremely important for obtaining satisfactory results. In this work were conducted studies with variation of system’s range (domain),spatial discretization (mesh) and turbulence models (SST, k-ε e k-ω) in solving the governing equations of three-dimensional turbulent flow, aiming to evaluate the adopted numerical solution ability of reproducing the hydraulic system behavior as pressure pulsation and associated frequencies to draft tube vortex cores.

Nevertheless, as states [2], 'many dynamics problems occurring in hydraulic machines can only be properly understood if their interaction with the fluid column in the waterways of the plant is taken into account,' which is related to the properties of inertia, compressibility, and dissipation of the system.

Three-dimensional geometric modeling of the entire hydraulic system and numerical simulations were performed using applications of CAD and CFD available at Center for Advanced Studies on Safety of Dams – CEASB considering as an object of study the turbines of Itaipu Hydroelectric Powerplant, which one has a rated power of 14,000 MW generated by 20 Francis turbines of 700 MW.

2. GOVERNING EQUATIONS AND NUMERICAL SOLUTION

Navier-Stokes equations have full capacity to describe the behavior of turbulent flows without needing of additional terms. However, as quoted in [3], its analytical solution for general cases is still open and, to meet the need of knowing the behavior of fluids in its countless applications, several numeric methods have been developed.

According to [4], one of the most successful methods is the Finite Volumes Method, which discretizes differential equations by a conservation balance of each property, e.g., the mass flow for each volume element.

However, turbulent flows of realistic high Reynolds numbers presents a wide range of spatial and temporal turbulence scales which generally involves spatial scales much smaller than the smallest finite volume of a mesh still viable to use. To allow that effects of turbulence be analyzed, a large amount of research in CFD has focused on developing of turbulence models conforming to [5].

Regarding the numerical solution of the Navier-Stokes equations, is common sense in the scientific world that its direct solution (DNS) is only computationally viable for more simplified systems. Given the inherent difficulty of a solution of these equations for real systems, as the flow in the hydraulic system



of a turbine Francis, the most widely used alternative is using the Reynolds Averaged Navier-Stokes (RANS) equations. However, due to the required modeling of original equation terms, such procedure represents a filter in the system dynamic response, as demonstrated by [6], limiting its application in assessing the dynamic flow behavior. RANS solution modality and other types of solutions of the Navier-Stokes equations will be briefly discussed in the next section, aiming only characterize them.

2.1. Turbulence models

The numerical methods that model the turbulence are grouped into the following three categories:a) Reynolds Averaged Navier-Stokes (RANS) is a method

which solves the mean flow and models the effects that all turbulence scales have over the mean flow. ([5]).

b) Large Eddy Simulation (LES) is an intermediary methodology that solves the large turbulence scales, which carry most of the energy and models the smaller scales. ([7]).

c) Direct Numerical Simulation (DNS) is able to solve the mean flow and all speed fluctuations due to turbulence. This method is extremely costly in terms of computational resources, so it is not used by the industry to solve flows. ([8]).

Among these methods, in line with [9] the RANS modeling is preferentially adopted for engineering cases, as it significantly reduces the required computational effort. In this method, the variables in a turbulent flow, e.g., flow velocity, are decomposed in an average term and fluctuating term, as shown in Equation (1).

(1)

The substitution of the average values in the original transport equations for single-phase fluid results in Reynolds Averaged Equations given below in index notation, in which the bar indicates the average values, ρ the specific mass, p the pressure, tij the stress tensor, SM the sum of the body forces per unit of volume. x and t are respectively the spatial and temporal variables.

(2)

(3)

Equation (2) is the continuity equation and the Equation (3) is the conservation of momentum equation, in which appears an additional term, the Reynolds stresses, This term represents correlations between the floating speeds and it is one more unknown in the system, according to [9]. To close the equations system it's necessary a model for the Reynolds tensor.

The eddy viscosity hypothesis, proposed by Boussinesq in 1877, establishes that the Reynolds tensor is proportional to the mean velocity gradient, mathematically analogous to the stress and strain tensor in a Newtonian fluid. Thus it is given by:

(4)

Where34 is the eddy viscosity and kis the kinetic energy per unit of mass, like in [10].

When applying the hypothesis to Reynolds Averaged Equation for the momentum is obtained the following:

(5)

Where µef is the effective viscosity composed by molecular (µ) and eddy (µt) viscosity, such that:

(6)

Eddy viscosity models are distinguished by the manner in which they prescribe the eddy viscosity and eddy diffusivity.([10]).

2.1.1. The k-ε model

The model k-ε is based on the eddy viscosity hypothesis, as reported in [10]. In this model, the following expression relates the eddy viscosity µt to the specific turbulent kinetic energy (k) and specific turbulence eddy dissipation rate (ε), where Cµ = 0,09 is a constant, and ρ the specific mass:

(7)

The transport equations for the turbulent kinetic energy (Equation 8) and eddy dissipation rate (Equation 9) give the values of k and ε:

(8)

(9)

where Cε1 = 1,44, Cε2 = 1,92, σk = 1,0 and σε = 1,3 are constants. The term Pk is the production of turbulence due to viscous forces modeled by the following expression:

(10)

2.1.2. The k-ωmodel

According to the same [10], the k-ω model offers as an advantage treatment for calculating low Reynolds numbers near to the wall. Its formulation does not involve nonlinear damping functions as in the k-ε model and is generally more accurate and robust.

In this model, it is assumed that the turbulent kinetic energy and the turbulent frequency are related to eddy viscosity by the expression

(11)

Two transport equations are solved, one for the turbulent kinetic energy (Equation 12) and another for the turbulent frequency (Equation 13):

(12)

(13)

where the specific mass, ρ , and the mean velocity vector, U, are treated as known quantities and Pk is the is the turbulence production rate given by Equation (10).

The model constants are given by β' = 0.09, α = 5/9, β = 0.075, σk = 2 e σw = 2. The Reynolds Stress, (eq), is an unknown given by Equation (4).


2.1.3. Model Shear Stress Transport (SST)

In the free flow region far from the wall, the results obtained with the k-ε model are few influenced by the boundary conditions, however, near to the wall performance is not satisfactory for boundary layers with adverse pressure gradients as in agreement with F. R. Menter (1992a) apud [8]. To solve this deficiency, a hybrid model was suggested applying a transformation of the k-ε model for the k-ω model in regions near the wall and the k-ε model in completely turbulent regions far from the wall as reported by Menter (1992a, b, 1994, 1997) apud [8].

A complete formulation of the SST model, given below, is extracted from [11].

(14)

(15)

where the blending function F1 is defined by:

(16)

WhereM is the distance to the closest wall and

(17)

The value of A2 is equal to zero when far from the wall, thus defining the use of k-ε model and becomes unitary when inside the boundary layer indicating the use of the k-ω model.

The eddy viscosity is defined by:

(18)

where S is the invariant measure of the deformation rate F2, and is a second blending function defined by:

(19)

A turbulent energy production limiter is used for SST model to prevent the buildup of turbulence in stagnant regions:

(20)

All constants are calculated from a combination of constants corresponding to the k-ε model (F=0) and the k-ω model (F=1) by the general expression

(21)

Whereα corresponds to one of the constants to be calculated. The constants for this model are:

2.2. Two-phase flow

The occurrence of cavitation in the turbine flow requires two-phase flow treatment for better represent the flow phenomena. Considering a homogeneous mixing model, in which both phases share the same pressure and velocity

fields, it is sufficient to solve one equation for each the field, instead of solving it for each phase of field. However, apart the continuity equation and of the moment, it is necessary an additional transport equation coupled those, forming thus a set of nine governing flow equations in the considered control volume element for the case of three-dimensional flow, more the restriction that the pressure in all phases be equal to the average pressure of the mixture.

The additional transport equation can be obtained by conservation volume law which expresses the sum of partial fractions of the phases volumes should be equal to the unity. According to this law, a compressible viscous fluid mixture formed of liquid and a β vapor volume fraction, the density ρm of the mixture is given by Equation (22), where subscripts c and l refer respectively to the cavitation and liquid phase, as quoted by [1].

(22)

Replacing this conservation condition at the continuity equation the additional transport equation (25) can be obtained, forming a set of coupled equations to the mass and momentum conservation of the compressible two-phase mixture, where the subscripts m were omitted for variables ρ,U

_, p at Reynolds

Averaged Equations (23), (24) and (25), and the cavitation volume β is an additional variable of the system:

(23)

(24)

(25)

The term Scl is a source term relative to the mass flow rate of the vapor phase per unit volume, considering condensation and vaporization processes, which were modeled by Rayleigh-Plesset equation.

3. LOW FREQUENCY PHENOMENA IN SWIRLING FLOW

This section aims to present the origin of low-frequency phenomena that happens when a Francis turbine operates out of its optimum flow conditions. This section discusses also the limitation of the satisfactory representation of hydraulic system behavior at these operatives’ conditions through RANS numerical solution of governing equations of three-dimensional flows using the turbulence models indicated in the previous section.

In its simplest form, the flow in a Francis turbine can be represented by a one-dimensional model. Euler equation for hydraulic machines relates the power absorbed by the turbine only with the fluid inlet and outlet conditions in its runner. According to Equation (22) in order to have an optimum efficiency, the fluid must enter in the turbine runner without shock with its blades, being tangential to them, and exiting axially (UV2 = 0), as happen when the turbine flow rate Q = Qot. However, as the Francis turbines have a fixed blades runner and rotate at a constant synchronous speed, whenever the flow in the turbine get away from their optimum conditions the speeds at inlet and outlet may no longer meet the ideal


condition, which normally occurs to meet the required power generation adjustment to its demands, as charge dispatches usually practiced.

(22)

Due to operation outside of optimum conditions, the speed at the outlet is no longer fully axial, giving rise to tangencies components which swirl the fluid, generating the well-known vortices cores at the draft tube. These components cause fluctuations in pressure and can produce significant oscillation in the electrical power, as mentioned by [2]. This author also mentions that vortices core depends on the distribution of the speed field at runner outlet, the geometry of draft tube and the dynamic response of the hydraulic circuit as a whole.

Such behavior can be seen in Figure 1 by the speed triangle at the outlet of the turbine blades for different flow rate, Q, in the turbine. In part load (Q < Qot) and overload (Q > Qot) the tangential component UV2, is responsible for the rotational effect on the fluid. In ideal condition (Q = Qot) the flow exits axially and this effect does not occur.

When the boundary conditions allow the occurrence of the water vapor phase, the vortex core is configured as an underpressure in the core region of the fluid flow. Under these conditions, they become visually clear in a transparent draft tube, like the used in scale models of turbine testing laboratories, as illustrated in Figure 1.

These vortices act as an exciter source that dynamically interacts with the hydraulic system through a forced oscillation process or a hydraulic instability mechanism. At part load condition the vortex moves like a spiral with precessional movement and acts like a forced vibration with a characteristic frequency. If this frequency coincides with a natural frequency of the system there is a hydraulic resonance situation. At full load condition, the vortex can pulse radially at eigenvalue frequency of the system, configuring a self-excited phenomenon that produces oscillation even without a forcing source, as explained by [2]. Due to the influence of the compliance of the vortex in this phenomenon is essential to adopt a model that considers the occurrence of cavitation in the flow.

[Figure 1: Vortex core (Adapted from [1]).]

Although the intensity of the rotational component a, in the fluid has singular importance in pressure fluctuation, other factors such as cavitation, depending on its intensity, also influence this process. The explanation for the effect of cavitation in the pressure pulsation in the draft tube is due to the dynamic gain provided by the resonance with the draft tube fluid system natural frequency, as indicated in [12].

To finalize this section, it is observed that single-phase solution of the governing equations (2) and (3) does not allow

the appearance of the cavitation, excluding the evaluation of its influence on the hydraulic system behavior. Other limiting factors in the proposed mathematical model are not considering the effects of elasticity and viscoelasticity throughout the whole hydraulic boundary surface and mitigation system of pressure fluctuations by atmospheric aeration or compressed air injection in the turbine.

4. GEOMETRICAL MODELING OF THE HYDRAULIC SYSTEM

The hydraulic system considered as object of study was the existing at Francis turbines of Itaipu Hydroelectric Power Plant, equipped with 20 vertical generating units with the following nominal values for its turbines:• Shaft power: 715 MW• Net head: 112.9 mca• Rotation: 91.6 RPM

The hydraulic system of Itaipu turbine is illustrated in the following figure:

[Figure 2: Hydraulic system of Itaipu turbines - Vertical section - [13].]

The geometrical models used for developing this study were developed based on design's bidimensional technical drawings of the turbine and of the hydraulic system and on some measurements made on site. The models of the set Spiral Case, Pre-distributor first two geometrical models ones were dev developed by [14] and the last one by [15]. Besides these components were also molded geometries of part of the Reservoir, Water Intake, and Penstock.

4.1. Modeling of stationary domains

4.1.1. Set Spiral Case, Pre-distributor and Distributor

[Figure 3: Geometric model of the set Spiral Case, Pre-distributor and Distributor - [14].]


The geometrical models of the set Spiral Case, Pre-distributor, and Distributor, for the operating conditions contemplated in this work were developed by [14]. The opening of the distributor is different for each condition and its value is given by the smallest distance between two blades of the Distributor.

4.1.2. Draft Tube

The three-dimensional model of the Draft Tube used in this study was developed by [15]. In order to avoid recirculating problems in the outlet region of the draft tube, was introduced an extension to ward off the exit boundary condition, thus making the numerical solution process more stable.

[Figure 4: Geometric model of Draft Tube -[15].]

4.1.3. Resevoir, Water Intake and Penstock

In order to allow evaluation of the influence that presence of components upstream of the spiral case has on simulation results, the geometric modeling of the components was made, as illustrated in Figure 5.

[Figure 5: Geometric model of reservoir, water intake and penstock (Adapted from [13]).]

4.2. Modeling of the rotating domain: the Turbine Runner

The geometric model of the Turbine Runner was developed by [14]. Due to the lack of blade's profile's drawings, was necessary a field survey in order to get points on the blade. The nominal value of the runner outlet diameter is 8.1 m.

[Figure 6: Geometric model of the Turbine Runner -[14].]

5. BOUNDARY CONDITIONS AND MEASUREMENTS

Aiming more robust results, the boundary conditions chosen were the mass flow at the inlet and the static pressure at the outlet of the domain. For the domain without the penstock, the inlet boundary condition corresponds to the flow (or speed) at spiral case inlet and the outlet condition corresponds to the static pressure at draft tube outlet. For these conditions, the total pressure is an implicit result of the solution.

In order to have an appreciation of the numerical solution of measurements that was developed for two turbine operating points tested in scale model and prototype, being one for operation with discharge below design point and another with discharge above design point, of which there are images of the vortex core at draft tube of scale model, as in [16]. In unitary values, the simulated operating points are:• Part load: n11 = 65.9 RPM; Q11 = 0.580 m3/s• Overload: n11 = 68.9 RPM; Q11 = 0.995 m3/s

The location of these points on the unitary hill chart of a scale model of the turbine and the image of the respective vortex core are shown in Figure 7.

[Figure 7: Simulated point and respective vortex cores - [16].]

Based on the scale model data [16] and measurements made on hydraulic stability tests of turbines of the units U04 [17] and U11 [18] the values considered to evaluate the adherence of numerical simulations are presented in Table 1.

[Table 1]: Operating parameters and measurements in prototype.

Parameters Partload Fullload

Distributor’s opening [%] 49.3 88.8

Net Head [mca] 126.8 116.0

Flow Rate [m3/s] 434.2 712,4

Efficiency [%] 90.7 92.7

Power [MW] 488.8 748,6

Pressure oscillation at draft tube [kPap/p] – Model Transposition

65 19

Pressure oscillation at spiral case [kPap/p] – Model Transposition

22 16

Main frequency of the pressure oscillation [Hz] - Model Transposition

0.38 1.60

Pressure oscillation at draft tube [kPap/p] – Prototype 56 (U04) 43 (U11)

Pressure oscillation at spiral case [kPap/p] – Prototype 35(U04) 47 (U11)

Main frequency of the pressure oscillation [Hz] - Prototype

0.42/(U04)

1.10 (U11)


6. NUMERICAL ANALYSIS

6.1. Computational mesh

In order to evaluate the influence, the spatial discretization has on the results were tested three meshes with a different number of elements for each one of the two evaluated operating conditions. Table 2 shows the total number of elements of the respective meshes utilized for each simulated condition and also shows the number of elements of the meshes per component of the turbine's domain.

[Table 2]: Number of elements of the mesh for each simulated condition.

PartLoad Fullload

Component Mesh1 Mesh2 Mesh3 Mesh1 Mesh2 Mesh3

Spiral Case 1593308 3123673 5356802 1547968 3174044 5226729

Runner 1904397 2593739 3298709 1991912 2510822 3338452

Draft Tube 867022 1652722 4399713 867030 1652722 4398676

Total 4364727 7370134 13055224 4406910 7337588 12963857

A viewing surface of the Mesh 3 is shown in Figure 8, on what the virtual prolongation of the draft tube shown in Figure 4 is partially represented.

[Figure 8: Computationalmesh M3.]

6.2. Temporal discretization, computational resources and simulation times

In order to enhance the convergence of simulations, it was decided to divide them into two stages. The first stage of simulation has the function of providing a good initial condition for the following stage. For this stage was utilized varied time steps, as shown in Table 3, and the first order advection scheme (upwind), which convergence is easier.

[Table 3]: Time steps used in simulations.

Operation Condition

Time Steps [s]

Initialstage Final stage

Part load 20 x 0.01;20 x 0.1; 20 x 0.01; 40 x 0,00181 1440 x 0.00181

Full load 30 x 0.01;30 x 0.1; 30 x 0.01; 30 x 0,00181 1080 x 0.00181

For the second simulation, stage was utilized the second-order advection scheme and constant time step equivalent to the period that runner takes to rotate one degree. The simulated time for Part Load condition is equivalent to approximately 7,8 runner revolutions and the time for the Full load is equivalent to 8,6 revolutions.

The convergence criterion adopted for all simulations was 1x10-5 to the RMS value of residues.

The computational resources used were a computer with Intel® Xeon® E5-1650 CPU of 3.2GHz processor of which was

utilized ten cores, 16GB of RAM and 64-bit operating system. The simulation times are shown in Table 4:

[Table 4]: Simulation time [h]. PartLoad Fullload

Turbulence Model

Mesh1 Mesh2 Mesh3 Mesh1 Mesh2 Mesh3

SST 18.9 29.2 48.3 11.0 14.3 29

k-ε 17.7 27.8 47.6 9.8 11.7 28.4

k-ω 17.4 27.0 43.1 8.7 13.7 25.9

7. RESULTS

Flow in a Francis turbine operating at Part Load or in Full load produces its characteristics vortex hydraulic phenomena in the flow in the draft tube at the turbine runner outlet, as previously mentioned. All these phenomena produce pressure pulsation with a determined amplitude and frequency, being the amplitude strongly dependent on dynamic interaction with the entire hydraulic system involved in the flow. Monitor points in the numerical simulation were inserted at spiral case inlet and at draft tube inlet for acquiring these values at each simulated time step.

The results related to incompressible single-phase simulations are presented at items 7.1 to 7.3. The results related to compressible two-phase simulations are presented at item 7.4.

7.1. Core vortices prediction

[Figure 9: Part Load vortex for each simulated configuration (P = 300 kPa).]


The main flow characteristic in part load and full load is vortices formation at the draft tube with a characteristic geometry for each condition, with volume and length dependents of the turbine suction head, that is, of Thoma coefficient, σ.

At the part load condition, all considered turbulence models and meshes were able of reproducing the vortex characteristic shape, but without reaching the expected water vapor pressure for the considered suction head corresponding to σ=0.17. However, the isopressure surfaces indicated in Figure 9, corresponding to the pressure of the suction head considered (300kPa) for this condition, shows a vortex core at turbine output with similar characteristics to the one observed on scale model test, as available in [16]. Below this value, lower is the pressure, the isopressure surfaces obtained at this simulation becomes ever more deformed and divergent of the results of the scale model test.

For full load condition, the considered turbulence models and meshes were successful in reproducing the characteristic geometry of the vortex of this operative condition and also in reaching the vapor pressure expected for the considered suction head corresponding to σ=0.132, but with very small volume for coarser mesh M1. The effects of turbulence models and mesh refinement can be compared by images shown Figure 10 for isopressure surfaces of 130kPa, wherein the configuration with SST model and mesh M3 presented aspects more adherent to the data available in [16] to this operative condition.

[Figure 10: Full load vortices for each simulated configuration (P = 130 kPa).]

The vortex volume variation with the reference pressure for isopressure surfaces of 130kPa and vapor pressure (3.2kPa) can

be seen in Figure 11 for configuration of mesh and turbulence model M3-SST, where the blue core refers to vapor pressure.

[Figure 11: Full load vortices – Volume comparison (P = 130 kPa e P=3.2 kPa).]

7.2. Pressure pulsation

The frequency and amplitude of pressure fluctuation due to vortex core presence in numerical simulations were obtained by applying Fast Fourier Transform to temporal values obtained with virtual monitor probe at the spiral case and draft tube.

For part load condition, the virtual monitor probe of pressure at draft tube recorded the frequency of 0.33Hz for all simulated configurations of turbulence models and meshes considered, against 0.38 Hz for the transposition from scale model and 0.42 Hz for the prototype measurement. As pressure fluctuations caused by vortex propagate to upstream and downstream, disregarding dynamic gains or nonlinearities, as expected, pressure fluctuation at monitor points of spiral casing should register the same frequency of draft tube, but with smaller amplitude. This happened for all configurations except for the frequency at the configurations M2 k-ε e M2 k-ω, whose obtained value was 0.16 Hz, as indicated in Table 5.

Depending on configuration, the value peak to peak of the pressure pulsation amplitude varied from 34 kPa to 44 kPa in draft tube and 12,9kPa to 17,5kPa on spiral casing. Considering the average value of the pulsations found in the simulations, there was a deviation for less of about 36% relative to the reduced model and for the prototype 30% at draft tube and 58% at the spiral casing. Additional simulation of the part load with mesh M3-SST for longer simulation of 10,73s resulted at 50,6 kPa p/p in the draft tube and 24,7kPa p/p in the spiral casing, reducing the respective deviations for about -22% and 12% compared to values from scale model and 10% and 29% for the measurements at prototype. The simulation with two-phase model could also contribute to reducing these deviations since the cavitation effect on the response of the suction tube to the excitation of the vortex would be better represented, but this simulation was not performed.

[Table 5]: Power, pressure pulsation and frequency for part load condition.

ParameterM1 M1 M1 M2 M2 M2 M3 M3 M3

SST k-ε k-ω SST k-ε k-ω SST k-ε k-ω

N [MW] 485.7 480.8 484.8 490.4 483.2 491.4 487.3 480.1 487.5

ΔH [kPap/p] (Draf Tube)

40.0 43.9 42.4 35.8 34.7 35.2 36.5 41.7 41.5

f [Hz] (Draft Tube)

0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33

ΔH [kPap/p] (Spiral Case)

13.8 14.7 14.7 12.3 12.9 13.5 15.6 16.9 17.5

f [Hz] (Spiral Case)

0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33


Another parameter that also indicated adherence of the simulation results on part load to those provided by the scale model are the value of the generated power, whose expected value for part load conditions is 488.8MW at the simulated point. Regarding the ability to represent this parameter, k-ε model had the worst result at all meshes and SST model the best. However, SST and k-ω results present adherent results for the more refined mesh M3.

For full load condition, none of the configurations of simulation was able to reproduce the vortex dynamics, resulting in an almost static pressure field, therefore, without pressure pulsation, in disagreement to what is observed in the prototype at the operating point considered. Additionally, also it was performed a single-phase simulation with the complete domain at full load. The mesh used was M3 and the turbulence model was SST. This configuration also resulted in a static field of pressure.

The obtaining of null pressure fluctuation in full load may be related to the fact that on ITAIPU turbines such fluctuation is due to a hydraulic instability phenomenon. At this situation, the single-phase model used for governing equations does not allow the existence of water vapor at the central vortex core, as well as does not consider the elastic and viscoelastic effects of the fluid and the entire hydraulic contour, respectively considered as incompressible and ideally rigid.

Notwithstanding, the values obtained for the turbine power were reasonable, presenting a deviation from 2.6% to 3.5% compared to the value of 748,6MW predicted by the scale model transposed to prototype. The better results for this parameter was found with mesh M1, while the M2 and M3 meshes presented worst results for all turbulence models, except for configuration M2/ k-ε. Table 6 shows the values of power obtained and respective deviation for the full load simulations.

[Table 6]: Power and deviation for full load condition at the simulated configurations.

ParameterM1 M1 M1 M2 M2 M2 M3 M3 M3

SST k-ε k-ω SST k-ε k-ω SST k-ε k-ω

N [MW] 768.5 769.4 767.4 777.9 768.2 775.5 775.9 775.4 773.9

Deviation [%] 2.7 2.8 2.5 3.9 2.6 3.6 3.7 3.6 3.4

7.3 Pressure and velocity fields

Figure 12 displays the streamlines for part load and full load condition. In part load, streamlines allow to distinguish the swirling effect of flow at the same direction of runner’s rotation and the flow disequilibrium in the right and left draft tube channels due to tangential component of absolute speed a,at the same direction of rotation. In full load, is observed a symmetrical concentration of flow at the periphery of the draft tube conical section and elbow, but without disequilibrium of flow in channels.

[Figure 12: Streamlines for M3 SST - Part load (left) and full load (right).]

Figure 13 shows vertical sections of pressure and velocity fields in turbine domain at part load condition.

The image corresponding to the pressure field allows visualization of different areas along the pressure transition from spiral case to draft tube, as well as the region corresponding to the spiraled vortex of the part load. The image corresponding to velocity field allows observing the velocity transition between the spiral case and the draft tube, denoting the lack of symmetry of velocity field at draft tube due to the presence of the spiraled vortex.

[Figure 13: Pressure (left) and velocity (right) fields for M1 SST – Part load.]

Figure 14 shows vertical sections of the pressure and velocity fields in turbine domain at full load condition. The image corresponding to the pressure field allows visualization of different areas along the pressure transition from spiral case to draft tube, as well as the region corresponding to the oblong shaped vortex core for the full load. The image corresponding to velocity field allows observing the velocity transition between the spiral case and the draft tube, denoting the almost-symmetry of velocity field at the conical initial stretch of draft tube due to the presence of symmetrical vortex core.

[Figure 14: Pressure (left) and velocity (right) for M3 SST – Full loadConsidering the topographical difference between the level of downstream and the center of the.]

Considering the topographical difference between the level of downstream and the center of the spiral case inlet section and disregarding the head loss in this stretch, the expected pressure in the spiral case is 1325 kPa.

Therefore, is observed a deviation of approximately +368 kPa on the expected pressure value for part load condition and of approximately +198 kPa for full load condition. This difference is probably due to an insufficient spatial discretization, which is directly influencing the integration process of viscous friction in solving governing equations.

7.4. Two-phase simulations

The implementation of the two-phase simulations were mainly motivated by the fact that RANS incompressible single-


phase simulations had not captured the vortex dynamics in full load condition, as seen at the prototype turbine used as an object of study at this work and whose origin is attributed to a known process of hydraulic instability due to the self-excited phenomenon mentioned in section 3. So, to evaluate the contribution of the hydraulic system and cavitation in the behavior of the pressure pulsations, compressible two-phase simulations were performed at two domains: Partial - from the inlet of the spiral case up to the outlet of the draft tube; Total- from the surface of upstream reservoir up to the outlet of the draft tube. A display of the surface mesh the entire domain and its elements numbers are shown in Figure 15.

[Figure 15: Entire hydraulic system – Total Domain.]

Considering the very long time for processing the two-phase simulations using the computational resources used in the single-phase simulations, the two-phase simulations were performed at a cluster of 8 servers with Intel® Xeon® E5-2697 CPU of 2.7 GHz processor and 64 logics cores, 20GB of RAM/Server and 64-bit operating system Linux.

According to recommendations of [10], two-phase simulations were performed at two stages for both domains considered. At the first stage, the cavitation model is set unable and this converged preliminary solution will provide the initial condition for the second stage of the simulation, to be performed with the cavitation model activated. Due to the greater complexity of the equations to be solved for this case, was adopted a milder convergence criterion of 1x10-4. However, the RMS value of the residues was lower than 1x10-5 at the second stage of the solution. The mesh used was M3 presented at Table 2 and turbulence model was SST. All others configurations mentioned for single-phase were kept at the two-phase simulations. The total simulated time was 10.2s, corresponding to 15.5 revolutions of the turbine. The variation of time steps and time of simulation are shown in Table 7.

[Table 7]: Time steps and time simulation in full load two-phase simulations.

DomainTime Steps [s]

Time Simulation

[h]

Initialstage Final stage Total

Parcial30 x 0.01;30 x 0.1; 30 x 0.01; 30

x 0,001813600 x 0.00181 119

Total30 x 0.01;30 x 0.1; 30 x 0.01; 30

x 0,001813600 x 0.00181 204

The values peak-to-peak of the pressure pulsation and respective frequency obtained at two-phase simulations for both domains considered are shown in Table 8. In contrast with single-phase simulation, the virtual monitoring probes at Spiral Case and Draft Tube registered pressure pulsations at two-phase simulations.The values were calculated by Fast Fourier Transform of the time variation of the pressure at Spiral Casing and Draft Tube from 4 to 10.2 seconds of time simulation,

which corresponds to an already range stabilized of the final stage of the simulation. The reference values of the model and prototype were taken from existing time pressure records, considering the maximum value peak-to-peak.

The pressure pulsation in the prototype was not adherent to the results obtained from the scale model, as shown in Table 8. Possibly this is due to an interaction with the hydraulic system in the prototype turbine, leading to a lack of dynamic similarity with the test rig and possible effect of hydraulic instability at considered Full Load operation point. For this reason, the turbines of ITAIPU were preventively provided with an axial atmospheric aeration system to smooth full load operation of its turbines, as explained at [19].

[Table 8]: Pressure pulsation and frequency for two-phase full load simulations.

ParameterModel

Prototype Measurements

Domain Simulated

Test Rig U11 Partial Total

ΔH [kPap/p] (Draft Tube) 19 43 50.0 58.0

ΔH [kPap/p] (Spiral Case) 16 47 79.0 62.0

f [Hz] 1.6 1.10 0.32 1.14

With respect to the results of pressure pulsation obtained at the simulations, the maximum peak-to-peak values greatly exceeded the reference value of the prototype, as illustrated by the graphs of Figure 16 for the case of Total Domain. However, considering the value peak-to-peak of the FFT at the interval of 4.0 s 10.2 s they presented less deviation in the amplitude with relation to the measurements on the prototype, as shown in Table 8. Nevertheless, Partial Domain simulation not adequately represented the frequency of pressure pulsations on the prototype, since the value obtained was 0.32 Hz and measured value in the prototype was 1.10 Hz. Meantime, it should be noted some positive aspects related to results of two-phase simulations, mainly considering that prototype measurements present characteristics that it operates near a hydraulic instability point well controlled by an atmospheric aeration system of the turbine, not included in the numerical simulations of the flow. At prototype, a similar damped pressure pulsation to Figure 16 appears every 12s at the operating point in reference.

[Figure 16: Damping of the pressure pulsation at two-phase full load simulations - Total Domain.]

Pressure pulsations in the simulation with the entire domain in full load showed an average deviation of approximately 33,4% higher than the amplitude of reference in the prototype. Even so, in the author's opinion, a deviation of this magnitude could be considered an acceptable prediction to the pressure pulsations in hydraulic turbines in its design phase. In this simulation, the frequency of the pulsations was also well represented, as well as the occurrence of damping pulsations


observed in the prototype. Another positive factor for the CFD simulations was the detection of the gain in the amplitude of pressure pulsations in the spiral casing relative to the draft tube be of the same order as in the prototype and synchronously. This discrete gain is a symptom the prototype turbine operates with some interaction with the hydraulic system. However, at scale model test this phenomenon was not observed, signalizing the test rig did not operate with hydraulic instability. Possibly due to that the deviation of the results regarding the scale model test was very large, up 200%, evidencing the high risk of validating the prototype turbine pressure pulsation prediction at design stage based only on a model test.

The fact that the amplitude of recorded pressure pulsation in the spiral case have been higher and in sync with the pulsation in the draft tube indicates, as described by [20] and [1], the propagation of a permanent plane wave in the hydraulic circuit, confirming the need to take into account the cavitation modeling at simulations of self-excited oscillation phenomena, normally associated with the possibility of hydraulic instability.

The fact that the frequency of the pressure pulsations at simulations with Partial Domain presented no adherent results shows the dependence of this parameter with the hydroacoustic effects related to the compressibility of the cavitation vapor volume and to domain extension at acoustic wave propagation, better represented at Total Domain simulations.

The evolution of the volume and geometry of the vortex at the two-phase full load simulation is shown in Figure 17 in four pictures for each domain taken respectively in similar moments of the simulations. The vortexes presented are images rendered of the elements where the volumetric fraction of the vapor is higher than 75%. The vortex core is quite axisymmetric as expected, but its shape is not oblong comparatively to observations at scale model test. The volume and length of the vortex core at the simulations with entire domain was lower than that with Partial Domain.

[Figure 17: Full load vortices for two-phase simulation: a) Partial Domain (top); b) Total Domain (bottom).]

8. FINAL CONSIDERATIONS

All the used configurations of turbulence models and mesh satisfactorily represented the shape and frequency of part load vortex at single-phase simulations. However, it not allows reaching the expected vapor pressure at vortex core to the simulated operative point. However, on a broad way, the configuration M3-SST showed the best results. The pressure pulsation amplitude showed a maximum deviation of

22% to less on scale model and 29% relative to prototype. Furthermore, the CFD simulation showed a consistent pressure pulsation attenuation from draft tube to spiral case consistent with results of the model and prototype. The simulation with the two-phase model at part load wasn't performed, but probably could contribute to reducing these deviations, since the cavitation effect on the response of the suction tube to the excitation of the vortex would be better represented.

All the used configurations of turbulence models and mesh satisfactorily represented the vortex shape at full load condition at single-phase simulations and allowed to reach the expected vapor pressure at vortex core, but the configuration with better relative dimensional similarity with the vortex from scale model was M3-SST. The amplitude and frequency of the pressure pulsation were unsatisfactorily represented even considering the entire hydraulic domain since the simulation had not captured the vortex dynamics at this configuration. However, the simulation with two-phase model and the complete domain has captured the dynamics of the pressure pulsation observed at prototype as to the frequency and stability of the pressure pulsations, although operates close an instability point. The pressure pulsation amplitude showed a maximum deviation of 33% to greater than prototype records. Furthermore, the CFD simulation showed a discrete pressure pulsation gain from draft tube to spiral casing consistent with results of the model and prototype.

The comparison of results of CFD with scale model results transposed to prototype indicated an excessive deviation at full load condition, indicating a high risk of validating the prototype turbine pressure pulsation prediction at design stage based only on a model test when a resonance or instability cannot be discarded at the prototype.

A more realistic comparison at full load condition requires realizing a prototype test with the aeration system of the turbine inhibited or consider the air injection at the simulations, configuring a three-phase simulation, consuming greater computational effort to run the simulation. Other improvements would be consider the contribution of the fluctuation of boundary conditions of the inlet (flow) and outlet (pressure) and also the elasticity and viscoelasticity of the lateral walls of the boundary of the hydraulic system.

Nevertheless, the results obtained in these simulations signalize that RANS solution of the governing equations considering the presence of the cavitation at a two-phase compressible model and the entire extension of the hydraulic domain can present satisfactory results at the prediction of pressure pulsation of Francis turbines operating out of the optimum point.

Aiming to improve the results of the prediction of pressure pulsation, authors are developing a new study with a model of three-dimensional flow three-phase and/or with updating conditions through a one-dimensional model which considers the vortex dynamics and the flexibility and viscoelasticity of the walls of the hydraulic contour. To better comparison with prototype measurements, was developed a device that permits vary and/or inhibit the aeration atmospheric of the turbines during the test. The results of these complementary studies will be part of another article.

LIST OF SYMBOLS

Ui Velocity α Constant model k-w_Ul Average velocity component β Constant model k-w

ui Time dependent velocity component

σw Constant model k-w


t Time ~Pk Limiter SST turbulence model production

ρ Specific mass Scl Source term relative to mass flow rate of the vapor phase per unit volume

p Pressure F1 First merge function of the SST model

x Variable of space F2 Second merge function of the SST model

tij Stress tensor F

Δ Variation y Distance to the nearest wall in the SST model

SM Sum of the body force per unit volume

σk1 Constant model SST

eq Reynolds tensor σw1 Constant model SST

µ Dynamic viscosity α1 Constant model SST

µt Turbulent viscosity α2 Constant model SST

µef Effective viscosity σk2 Constant model SST

δij Kronecker delta function σw2 Constant model SST

k Turbulent kinetic energy β1 Constant model SST

ε specific turbulent dissipation rate β2 Constant model SST

Cµ Constant model k-ε σ Constant model SST

Cε1 Constant H Head of the turbine [mWc]

Cε2 Constant N Power

σk Constant m Mass flow

σε Constant

Pk Produced turbulence by viscous forces

w Turbulent frequency

β' Constant model k-w

9. ACKNOWLEDGMENTS

The present work only was possible due to the support of the Center for Advanced Studies on Safety of Dams – CEASB belonging to the Foundation Itaipu Technological Park – FPTI which especially we thank the availability of computer equipment and application necessary for this work.

10. REFERENCES

[1]Alligné, S.Forced and self-oscillations of hydraulic systems induced by cavitation vortex rope of francis turbines. PhD thesis, École Polytechnique Fédéral de Lausanne, Lausanne, Switzerland, 2011.

[2] Dörfler, P; Mirjam, S; Coutou, A. Flow Induced Pulsation and Vibrations in Hydroelectric Machinery: Engineers Guidebook for Planning, Design and Troubleshooting. Springer, London, 2013.

[3] Fox, R. W.; McDonald A. T.; Pritchard, P. J. Introduction to Fluid Mechanics. 7. ed. LTC, 2013.

[4] Maliska, C. R. Heat Transfer and Computational Fluid Mechanics. 2. ed. LTC, Rio de Janeiro, Brazil, 2004.

[5] ANSYS. Ansys CFX - Solver modeling guide- Release 15.0. Ansys Inc, 2013.

[6] Smagorinsk, J. General circulation experiments with the primitive equations. Monthly Weather Review, n. 91, p. 66, 1963.

1 American Journal of Hydropower, Water and Environment Systems, july 2016

published by ACTA Editora

Technical Papers - latiniahr.comlatiniahr.com/docs/journal_6.pdf · Marra, João M.; Gramani,...

Documents

Transcript of Technical Papers - latiniahr.comlatiniahr.com/docs/journal_6.pdf · Marra, João M.; Gramani,...