Aachen University of Applied Sciences, Campus Jülich

Transcription

1 Aachen University of Applied Sciences, Campus Jülich Master of Science in Energy Systems Analysis on effects and limitations of cavitation in design and operation of Francis turbine Prepared by: Nirajan Khakurel Matriculation Number: Jülich, December, 2015 A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Energy System

2 II Declaration The work presented in this thesis is the sole work of the student alone. The literatures used for the thesis work have been referenced accordingly. This work has been carried out as a requirement for M.Sc. degree at FH Aachen and does not serve any other external purpose or company work. Jülich, 2015 Start of work: May 2015 End of work: December 2015 This master thesis was supervised by: Prof. Dr. rer. nat. Boris Neubauer, Energy Systems, FH Aachen Prof. Dr. techn. Dipl. -Ing. Stefan Bauschke, Energy Systems, FH Aachen

3 Acknowledgement III I owe my heartfelt gratitude to honorable Prof. Dr. rer. nat. Boris Neubauer for providing me opportunity to do my Master thesis under his supervision. Also my sincere thanks go to Prof. Dr. techn. Dipl. -Ing. Stefan Bauschke for being my one of my thesis examiner. I am grateful to my colleague Rajan Panthi for his valuable support to bring my thesis work successful. I shall not forget to thank my dear friend Simant, Aashish and Khum for helping on proof read and formatting my thesis document. At the end I express my friendly gratitude to my close friends Annika, Lucie, Alex for providing me always inspiration and motivation to make my thesis possible. Last, but of course, not the least, I am indebted to my grandparents, my parents and other family members for bearing my long absence at home with a smile and their immense support to pursue my degrees in Germany.

4 Table of Contents IV TABLE OF CONTENTS... IV LIST OF FIGURES... VI LIST OF TABLES... VII EXECUTIVE SUMMARY... VIII ABSTRACT... IX 1 INTRODUCTION BACKGROUND OBJECTIVE SCOPE METHODOLOGY FRANCIS TURBINES BRIEF INTRODUCTION WORKING PRINCIPLE OF FRANCIS TURBINE TYPES OF FRANCIS TURBINES CHARACTERISTIC OF CAVITATION ESSENCE OF CAVITATION CAVITATION AND BOILING Nucleation CATEGORIES OF CAVITATION Travelling bubble Cavitation Bubble Cavitation in the shear layer Attached bubbles Sheet cavitation Localised attached cavitation Localised Bubble cavitation Hub vortex Cavitation Tip Vortex cavitation Surface Cavitation Detached vortex cavitation Vaporous Cavitation Gaseous Cavitation Flow Cavitation... 13

5 Vibratory Cavitation FACTORS AFFECTING CAVITATION PHYSIOCHEMICAL EFFECTS OF CAVITATION V 4 HYDRODYNAMIC CAVITATION CAVITATION IN FRANCIS TURBINES FUNDAMENTALS OF CAVITATION IN FRANCIS TURBINE CLASSIFICATION OF CAVITATION Classification of Cavity Types of cavitation CAVITATION DETECTION AND PREVENTION Detection Techniques Prevention Experimental Analysis CAVITATION EFFECTS AND DAMAGES CAUSES OF CAVITATION CAVITATION INSPECTION AND REPAIR Frequency of Inspection and Repair Cavitation Repair Methods NUMERICAL ANALYSIS CONCLUSION AND DISCUSSION REFERENCES:... 58

6 List of Figures VI List of Figures Fig 2. 1 Francis turbine overview [5] Fig 2. 2 Schematic view of radial flow Francis turbines [8] Fig 3. 1 Triple point Diagram [12]... 9 Fig 3. 2 Intermolecular Potential [14]...10 Fig 3. 3 Hydrodynamic cavitation according to their characteristics and their interactions on the container walls [11]...14 Fig 5. 1 Kaplan Turbine Schematic [31] Fig 5. 2 Francis Turbine Schematic [32] Fig 5. 3 Schematic view Francis runner, draft tube and downstream reservoir [38] Fig 5. 4 Operating range of Francis turbine [30] Fig 5. 5 Vectors in Francis kinematic [30] Fig 5. 6 The growth of liquid vapor in liquid nitrogen [24] Fig 5.7 Travelling bubble cavities [24] Fig 5. 8 Attached cavitation [24] Fig 5. 9 Cavitation transition: bubbly flow left to fully developed attached cavitation right [24] Fig Cloud Cavitation [24] Fig Vortex Cavitation [24] Fig Main types of cavitation in Francis turbines [30] Fig Von Karman vortex occurring location in Francis turbine [30] Fig Cavitation location and sensor positioning in Francis turbine [30] Fig Experimental setup to monitor Francis Model test rig [54] Fig Variation of turbines efficiency with respect to cavitation number σ [29] Fig Hill chart showing the regions where cavitation occurs in Francis Turbine [57] Fig Outline of measuring positions [58] Fig Experimental setup for high speed visualization of inter blade vortices [48] Fig Entire installation of the instrumented guide vane, boroscope, and LED light source [48] Fig Coalesced effects of cavitation and silt erosion [41]

7 List of Tables VII List of Tables Table 3. 1 Physiochemical effects of cavitation...15

8 Executive Summary VIII Executive Summary Water or any other liquids have a unique property to change its state from liquid to gas or gas to liquid under specific conditions. Such phenomena can be seen every day, for e.g. boiling of water, or hairsprays or body sprays, streams, carbonated water. A specific case when water changes it liquid phase to vapor phase due to drop in pressure is known as cavitation. This phenomenon is very likely to occur in Hydro machineries such as pumps, turbines or ships propeller where the pressure fluctuations occur through the flow. This simple phase changing phenomenon can be very devastating which might reduce the efficiency and may also damages the surface of the hydro machines. So it is very important to know how, where and why such cavitation occur in different types of hydro machines. This Master thesis mainly deals with reasons and effects of cavitation in specific type of hydraulic machine which is called as Francis Turbines.

9 Abstract IX Abstract Hydroelectricity is one of the most suitable, efficient and nature friendly conventional source of energy. Around 20% of the total worldwide electricity consumption results from hydropower. The efficiency of hydropower basically depends on design conditions like types of turbine used, size of turbines, total head and flow rate, runner blade number and its angle. Every turbine unit is designed for an effective operation at its highest efficiency level with optimum values for head, flow rate and turbine speed. However, in this state, the dynamic behavior of flow becomes unstable with high fluctuations in pressure. So there is a higher possibility of cavitation to occur. Hence, it becomes necessary to find out innovative solutions in order to avoid cavitation and its damages, thus designing hydraulic machines at maximum efficiency level. Cavitation is an unavoidable problem in hydraulic turbines. Cavitation depletes the performance of the machines. It also induces structural and fluid borne vibrations and causes damages on the guide vane and runner of the turbines. Cavitation results in formation of micro-jets in the flow of stream. If these micro-jets strike on the runner surface or the tip or on the casing, the impulsion of the jet results in the pitting of the metallic surfaces. Turbine operating at off design conditions such as part load, deep part load or over load situations, has higher tendency to create more cavities in the flow. Francis turbines are designed to be operated over large range of operations and this research encompasses the limitations and effects of cavitation on Francis turbine. This work has been conducted as a theoretical research on different types of cavitation, their causes, locations, as well as the impacts, effects and detections processes. Different books, journals and research papers published under cavitation topic were studied and reviewed to acquire the knowledge and information about cavitation. Mathematically cavitation can be interpreted by dimensionless number, also known as a Thoma factor (σ). There are many mathematical models developed which simplifies flow dynamic and predicts the damages and effects of cavitation, but none of them till date has been able to replicate an accurate result. A detailed description of cavitation, its types, effects and causes are explained in the upcoming chapters.

10 Introduction 1 1 Introduction 1.1 Background This literature research project, ''Cavitation in Francis Turbines'', is a master thesis work conducted at the department of Energy Technology, University of Applied Sciences Aachen. As the formation of cavitation is a phenomenon of fluids, it may exist and occur when the fluids are subjected to dynamic conditions. So it is clear that cavitation occurs in all types of hydraulic machines for e.g. water turbines, water pumps, ships propeller, valves, rivers, streams etc [1]. This project concentrates on cavitation that occurs in Francis Turbines where the fluid dynamic conditions are most favorable to form cavities in water flow. This document creates a platform for the researchers and the students for the scientific study of cavitation, its effects and impacts in reaction type Francis Turbines. It has been found that scientific inquiry about cavitation began in the early 20 th century, initiated by Lord Rayleigh, M.S. Plesset and has continued with extensive work by C.E. Brennen. Historically, cavitation noise and damages were considered on the basis of collapse of individual bubbles. Since 1997 new concepts have been developed to study about the effects of flow on a single cavitation event. Recently it has been revealed that the interaction between bubbles is more dominant than individual bubble collapse [2]. At present, many research institutes like Electric Power Research Institute (EPRI), California USA, Laboratory for Hydraulic Machines, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland, Alternate Hydro Energy Centre, Indian Institute of Technology, India worldwide employs hundreds of researchers and scientists who work on cavitation of hydraulic turbines. These institutes provide laboratory where the cavitation phenomena can be tested in a cavitation tunnel or on the scaled model of a turbine unit. This experiment requires advance and high-tech monitoring equipments which includes different types of transducers like pressure sensors, accelerometer, motion sensors and acoustic sensors. High speed cameras and boroscope embedded guide vanes can also be used in order to observe visual information of cavitation flow. F. Avellan, M. Farhat, X. Escaler, M. Dular and F.G. Hammitt are the renowned names of the current pioneer researchers. Few of them are engaged in their research work on cavitation in the above mentioned institutes.

11 Introduction 2 Modern computational techniques like FEM, BEM and DRM have made it possible to transform complex 3D flow model of cavitating flow stream onto simplified 2D flow model. Then the simplified 2D flow model can be solved and discrete values of flow parameter (i.e. pressure, velocity, density) can assessed onto respective nodes on the model [3]. 1.2 Objective The major objective of this master thesis is to provide an overview about the theory and experiences linked to cavitation in Francis turbines. As cavitation has a direct impact on the efficiency and the life time of the turbines, it is very important to conduct research about the causes of cavitation. These may include the definition, types and the occurring conditions for cavitation. Furthermore the aim of research is to find out any possible way to stop the cavitation or at least reduce its impact. The initial chapters 2 and 3 present an overview of basic type of hydraulic turbines and essence of cavitation respectively. This provides a base to know further characteristics of cavitation in Francis turbines. The next step has been aimed to define and explain the fundamentals of cavitation in Francis turbines (chapters 4 and 5). These chapters provide detailed explanation about the types of cavitation found in Francis turbines. It explains the detection and prevention techniques for cavitation which are quite significant for the systematic monitoring and inspection of turbine during operation. An accurate and reliable detection technique predicts the failure on right time and can save the turbines to suffer from significant damages due to cavitation in form of time and money. The last part of the thesis work includes the cavitation inspection and repair methods. The objective of this part is to provide the information that even cavitation cannot be stopped completely, but the impact of damages can be reduced by using routines inspection followed by required maintenance and remedy. Besides this, the thesis work aims to provide a brief introduction about numerical model which can be solve cavitation erosion damage. In general the objective of the whole work is to highlights the specific or general effects of cavitation and its possible detection and prevention techniques.

12 Introduction Scope This thesis work comprises of very useful and important information about the cavitation and its effects. In case of hydropower generation cavitation can be compared as cancer. As cancer, cavitation also has many causes, forms and occurrence. At the initial phase, the small size cavitation pit can be repair easily but very difficult to detect or diagnose. As the pit size are increased cure is very difficult meanwhile can be detected easily. The severe damages due to cancer in human life accounts financial loss, organ loss and finally death of the person. In other hand cavitation also accounts financial loss in terms of performance and repair, runner fitting and edge modification can be compared to organ loss or finally replacement of new turbine. This master thesis work creates a platform for the researchers and the students for the scientific study of cavitation and its effects and impacts in reaction type Francis turbines. Cavitation is one of the biggest and unavoidable problems for all types of water turbines. So it is very essential that research and experiment has to be conducted to know the unpredictable behavior of cavitation. This result has to be structured in written form so that this information can be shared. This master thesis serves other researchers or students, as source of information on cavitation. This document includes basic definition along with detailed information on types of cavitation, exact locations where cavitation occurs and the possible way to predict and detect cavitation. 1.4 Methodology This research work has been carried to find out in details about the main reasons that lead to cavitation in Francis turbines. It also deals to find out the effects cavitation in details in hydro machines. This project is solely based on literature review. No practical experiment has been conducted to precede the research. Different books, journals and research paper published under cavitation topic are studied and reviewed to acquire the knowledge and information on cavitation. The acquired information has been studied, analyzed and compared. From this analysis and comparisons, the root causes and effects of cavitation has been concluded in brief. Also the research deals with the monitoring and detecting the cavitation in case of Francis turbines along with the materials that can be used to reduce the cavitation impacts. Sources including books from the library and information found on

13 Introduction 4 the internet websites were carefully studied and reviewed for a better understanding and explanation of cavitation. The references have been cited accordingly Although much experimental research already has been conducted by various scientist and researchers, it is still difficult to detect and monitor cavitation and its effects because of the technical difficulties as well as due to the complexity of the subject.

14 Francis Turbines 5 2 Francis Turbines 2.1 Brief Introduction A Francis turbine is a rotary engine that converts the inertia of flow of water into useful mechanical work by turning the shaft. Francis turbine was first developed during the end of 19 th century. Nowadays they are most widely used machines to generate electricity. Water can be stored in dams or the current of flowing river can be used to drive the turbines. With the increase in the level of water, the potential energy of the water also increases. So by increasing the level of the water in the dam, the output work of turbine unit can be increased. The output of the turbine can also be increased by increasing the flow rate of water flowing through the turbine. While letting stored or runoff water to flow through the turbine, power from water's potential and kinetic energy can be transferred into mechanical energy via the turbine [4]. A schematic view of Francis turbine can be seen in Fig 2.1 and Working principle of Francis turbine Fig 2. 1 Francis turbine overview [5]

15 Francis Turbines 6 Francis turbines are reaction type water turbine. The main part of Francis turbines are inlet guide vanes and rotating blades. Depending upon the design, inlet guide vanes can be classified as fixed and adjustable guide vanes. The fixed guide vanes are known as stay vanes and adjustable are known as wicket gates. The rotating blades are known as runner blades. All these blades are mounted into closed spiral casing known as volute. Water enters tangentially through the stay vanes which guides into runner blades. The narrow passages created by stay vanes and wicket gates result in large tangential velocity of water. This increase in velocity creates momentum which is exchanged between fluid and the runner blades. This causes the runner to rotate and there exist large pressure drop. Khurana et al. [6] stated that cavitation occurs due to drop in local fluid pressure. Water flows tangentially into the turbine and exits the turbine axially. Water pressure decreases as it passes through the turbine imparting reaction on the turbine blades which propels the turbine. Reaction turbines utilize pressure energy of water where the major part of pressure drop occurs in the turbine itself, unlike the impulse turbine where complete pressure drops after the nozzle. The turbine passage (casing) is completely filled by the water flow during the operation [4]. Normally this type of turbine is suitable for medium or low head type of power plants. Y.A. Cengel and J. M. Cimbala [1] informed in their book that Francis turbine was first designed and developed in 1940s by James B. Francis. They also described overall or gross head (H gross ) of turbine as a difference between the surface elevation of water at highest elevation point (z A ) and the surface of the water at tail race (z E ). In an ideal case i.e. without any losses in the system, maximum amount of power that turbine can develop would be given by Where, ρ = density of the water [kg/m 3 ] g = gravity [m/s 2 ] H gross = gross of the [m] V = volumetric flow rate [m 3 /s]

16 Francis Turbines Types of Francis turbines Through various books it can be deduced that there are different types of Francis turbines. Logan [7] has defined that there exist basic two types of Francis turbines according to the flow of water, in his book Handbook of Turbomachinery. Radial flow Francis Turbines: In this type of Francis turbine, water enters radially. This means the flow at entry is tangential to the runner. Fig 2.2 shows a schematic view of radial flow Francis turbines. The water enters through guide vanes and then directed to runner blade. This type of design normally has less efficiency as compared to mixed or axial flow type. Normally they are designed for small - medium scale hydropower plants. Fig 2. 2 Schematic view of radial flow Francis turbines [8] Mixed Flow Francis Turbines: In this type of turbine, the flow is directed in an angle between radial and axial. As per requirement a mixed flow Francis can be designed as reversible machine which can be used as pump. Turbines designed for radial flow normally has lesser flow rate than turbines that are designed for axial flow. Hence, the turbine speed increases and the increment in the shaft output power is achieved.

17 Characteristic of Cavitation 8 3 Characteristic of Cavitation 3.1 Essence of cavitation The word cavity comes from Latin word cavitas which means space or hollow space [9]. In fluid mechanics, it is a particular phenomenon that happens inside liquids when the pressure field changes. This drop in pressure makes the liquid less dense. If further decrease in pressure below the liquid's vapor pressure, results in the formation of voids which are filled by vapor along with dissolved gasses. When the compressive force acts on these voids, they explode. Cavitation occurs only in liquid but not in gas because gases have no surface tension. In cavitation liquid state changes to gas which is also seen in boiling of liquid. But reasons for phase change are totally different. Boiling occurs when the local temperature in the liquid increases, in the other hand, cavitation occurs when local pressure in liquid drops. As discussed above, cavitation appears in processes where local pressure field changes. However, cavitation also occurs generally in three processes involving interaction with liquids [10]; 1. Hydrodynamic Process: Cavitation normally occurs in flowing liquids where some external influences causes fall in static pressure. Those influences can be constrictions like in valves, curves or bends and also as a result of motion of solid object in liquids. e.g. Water Turbines, Ship Propellers. 2. Process involving ultrasound: The influence of earthquakes or other source of vibration on the bottom surface or walls of the container. 3. Process that supply large energy to small volume in liquids: Processes like laser beams or stream of protons passing through the liquids can also bear cavitation. The protons collision results in increase of the internal energy of the liquid to a critical limit where phase change occurs. During this phase change, dissolved gases released turn into bubble cavities.

18 Characteristic of Cavitation 9 The research basically deals with the hydrodynamic cavitation which is further discussed in chapters 4 and Cavitation and Boiling It is important to know the liquid-gas-liquid phase change process before understanding cavitation and boiling phenomenon. Fig 3. 1 Triple point Diagram [12] Fig 3.1 shows triple point diagram for water. Triple point is the point in the phase diagram where there exits all three phases i.e., solid, liquid and gases. It can be clearly understood, from the diagram, liquid state can be changed either by lowering the pressure or increasing the temperature. So varying pressure and temperature may lead to phase changes. These changes in pressure and temperature creates tensile stress which breaks the intermolecular forces in liquids, hence the phase changes to vapor. Frenkel [13] has illustrated potential tensile strength by means of simple calculation. The potential energy associated with the intermolecular forces (Φ) changes with respect to distance between two molecules(s) as shown in the Fig 3.2.

19 Characteristic of Cavitation 10 Fig 3. 2 Intermolecular Potential [14] Points x 0 is the equilibrium point which has value of typically m. The attractive force (F) between molecules is given by equation 3.1. At x 1, which is typically % bigger than x 0, F is maximum. This results in liquids volume to increase up to one third of its original volume. When the subjected tensile stress in the liquid equals or is greater than the corresponding attractive force at x 1, the liquid molecules break apart, because for any x greater than x 1, the attractive force is not enough to neutralize tensile stress. Compressibility moduli (κ) normally has a value in the range of to kg/ms 2. Therefore, typical pressure (tensile stress) that ruptures liquid is around the value of -3*10 9 to - 3*10 10 kg/m s 2 (3*10 4 to 10 5 atmospheres). When liquid's pressure (p) decreases at a constant temperature below saturated vapor pressure (p v ), the resulting difference in pressure value (p v- p), if equal or greater than the tensile strength of the liquid, the liquid will rupture. This rupture results in phase change of the liquid to vapor phase. It results in formation of bubbles filled by vapor or dissolved gas. This process of liquid rupture by decreasing pressure at constant temperature is also known as cavitation. In contrary to cavitation, if liquid at constant pressure subjected to increase to the level above its saturation temperature, the temperature difference acts as tensile stress, hence results in

20 Characteristic of Cavitation 11 rupture of liquid. The process of rupturing of liquid by increasing its temperature at constant pressure is called boiling Nucleation X. F. Peng et al. [15] stated in his research that phase instability in liquids causes nucleation. Washio [16] explained that liquid inherently holds some defects in its homogeneous structure. If the liquid pressure is reduced below the vapor pressure, then they expand to form cavities. These defects are called as cavitation nuclei ; they act as nuclei from which cavitation initiates. Skripov [17] has mentioned that nucleation can be categorized into two types. Homogeneous nucleation, where thermal motion in the liquids creates temporary microscopic voids that creates the nuclei which ruptures the liquid and grow into macroscopic bubbles. Heterogeneous nucleation happens, for example in practical engineering, where nuclei formation occurs at the boundary between liquid or solid wall, or at the boundary between liquid and dissolved particles in the liquid. Some other hypothetical models have been proposed which classifies nuclei in different types, which are published as books and research papers. Among them, Knapp et al. [18] has categorized and explained three different types of nuclei: microscopic voids with a size of molecule temporarily formed in the liquid by random thermal fluctuations gases that present in crevices of hydrophobic solids, Harvey et al. [19], and free gas bubbles with organic skins on their boundaries, Fox and Herzfeld [20]. 3.3 Categories of Cavitation Different scientific papers published worldwide classify different characteristic forms of cavitation. As there are always diverse conditions for cavitation, it is difficult to develop single mode of cavitation classification. According to Franc and Michel [21], there are 8 basic types of cavitation: Travelling bubble cavitation This type of cavitation appears in the form of bubbles, which moves along the solid body. When the bubbles reach the vicinity of low pressure point, it becomes visible.

21 Characteristic of Cavitation Bubble Cavitation in the shear layer Bubble cavitation in the shear layer can be seen when liquid jet is subjected into a liquid filled container. It can also be seen when liquid jet is introduced on the edge of boundary layer separation Attached bubbles It is also termed as sheet cavitation. In case of axis symmetric body, this is also termed as ring cavitation. The bubbles are formed on the surface body of submerged solid and then they are detached by the flow Sheet cavitation It can be seen in laminar cavitation at an advanced stage. Normally, it appears as a cavity filled with homogeneous mixture of vapor with glossy surface Localised attached cavitation It is also described as localized sheet cavitation. It is linked with local roughness of the surface. It appears as attached cavities Localised bubble cavitation This type of cavitation occurs as a continuous stream of bubbles forming in specific places on the surface of solid body. It is also associated with the pitted nature of the surface Hub vortex cavitation This type of cavitation occurs in the cores of vortices spiraling away from the flow around the obstacle Tip vortex cavitation This type of cavitation occurs in the core of vortices flowing from the load bearing surfaces.

22 Characteristic of Cavitation 13 Furthermore Bagienski [22] has mentioned that Arzumanov's two major types of cavitation cloud: Surface cavitation As it is clear from the name, surface cavitation appears on the surface of streamlined bodies and they remain attached to the surface. This occurs due to formation of a resistance point. It can be found in pipelines, valves restrictions etc. This cavitation is dependent on the geometry and the flow parameters. It can take on many different forms like bubbles, sheet or laminar or attached sheet cavitation Detached vortex cavitation This type of cavitation appears along the axis of the stream and carried out with the flow. It also develops from cavitation nuclei found in crevices, on the boundary surfaces restricting flow and also in the wake. It can also be seen in high speed turbulent wake from orifices and also at the point where many streams from different directions meet Also J. Ozonek indicated that according to Polish Standard [23], cavitation has been classified into following forms: Vaporous cavitation When the liquid pressure drops to the critical value at constant temperature, then the liquid evaporates forming bubbles. These bubbles are vapor filled and grow very quickly Gaseous cavitation This type of cavitation can be seen in supersaturated liquid state where this dissolved gases diffuse. In this case, the diffused gases are diffused into vapor filled bubbles which are already present in the liquid. The typical characteristic of this cavitation is the bubbles grow and collapse very slowly than vaporous cavitation Flow cavitation This is also known as hydrodynamic cavitation. In case of flowing liquid, static pressure may fall due to flow conditions or external or geometrical factors. This pressure drop leads to the formation of cavitation which is called Hydrodynamic cavitation. Mostly it can be seen in constricted flow channels, curvatures and deviations from the plane of streamlined body. Fig 3.3 below shows different forms of hydrodynamic cavitation.

23 Characteristic of Cavitation 14 Fig 3. 3 Hydrodynamic cavitation according to their characteristics and their interactions on the container walls [11] Vibratory cavitation It is also called Acoustic cavitation. Pressure pulsations within the liquid induce vibratory cavitation. Pressure pulsation occurs due to dispersion of acoustic waves due to the impact, due to vibrations of surface enclosing the liquid, or due to vibration of body submerged in liquid. The separation of liquid molecules and formation of bubbles occur during rarefaction half cycle and their collapse occurs during compression half cycle. 3.4 Factors affecting cavitation As described by Brennen [24], cavitation occurs due to various factors which include not only the thermal properties of liquids but also due to the presence of gaseous impurities dissolved in liquids. Gogate [25] has also defined similar explanation that cavitation occur due to impurities present in the submerged solid bodies. The cavitation nuclei appear in the form of gaseousvapor micro bubbles which are essential for cavitation. These nuclei actually reduce the

24 Characteristic of Cavitation 15 capability of the liquid to transfer tensile stress which leads to cavitation. Large number of possible potential cavitation nuclei may be found in liquids in form of primary additives and pollutants. 3.5 Physiochemical effects of cavitation Effects of cavitation can be divided into mechanical and physiochemical effects. These effects can be observed due to changes in the cavitation bubbles from its formation till implosion. Table 3.1 illustrates these effects in brief. With the implosion of the bubbles, primary shockwave is produced. The pressure amplitude of this wave is around 240 MPa and molecular speed up to 1700 m/s. Secondary waves are also generated with pressure limit up to 70 GPa. This shockwaves sometimes emits short bursts of light. This phenomenon is called as Sonoluminescence [26]. Physical and Chemical 1 Changes in thermodynamic properties of liquid (changes in pressure and temperature) Mechanical Cavitation noise 2 Sonochemical processes Throttling the flow induced by the formation of vapor 3 Sonoluminiscence Strong vibrations in the cavitation zones of the device 4 Cavitation corrosion Wear and metal loss Table 3. 1 Physiochemical effects of cavitation

25 Hydrodynamic Cavitation 16 4 Hydrodynamic Cavitation A brief discussion about this type of cavitation can be found in chapter 3.3. As our interest of topic is cavitation in Francis turbine, it is necessary to explain about hydrodynamic cavitation. Description of various forms of hydrodynamic cavitation as shown in Fig. 3.3 are as follows: Laminar and Wall cavitation caverns a thin layer on the surface of the emerged body on the way of flow. Slotted cavitation are formed in between two moving parts. e.g. between stator and rotor blades. Traced cavitation are seen around the region where there exist influence of the boundary layer separation. Fog cavitation is formed when liquid flow through a constriction or under the influence of body submerged in water. Dash cavitation forms shape of a cloud at the sharp edge of circumnavigate body. Swirled cavitation clouds takes the shape of diverse spatially located braids. Though hydrodynamic cavitation has several forms, overall effects of the process can be seen as changes in thermodynamic properties. It also throttles the flow due to formation of bubbles. They produce loud ultrasonic cavitation noise and strong vibration in the devices. May be sonoluminescence can be seen during collapsing of bubbles that leads to cavitation corrosion or pitting. Dular and Delgosha [27] described cavitation as a phenomenon which is characterized by vaporization and condensation in high-speed liquid flows. It is a recurring process in industrial configurations, where rotating machinery, injectors, and other hydraulic devices are involved. It's consequences are effects like vibrations, increase of hydrodynamic drag, changes in the flow hydrodynamics, noise, erosion, light effects such as sonoluminescence, and also thermal effects.

26 Hydrodynamic Cavitation 17 In similar way, Knapp et al. [28] also described cavitation as the thermodynamic situation when a liquid reaches a state where vapor cavities are created. Further reduction of local dynamic-pressure below the vapor pressure, results in cavities to grows into bubbles, at constant temperature. In a flowing liquid, these cavities move rapidly to high pressure where bubbles stop and reverse their growth, collapsing implosively and disappearing. The violent process of cavity collapse takes place in a very short time of about several nanoseconds and results in the emission of large amplitude shock-waves. Kumar and Saini [29] explained and elaborate one of the most serious of issue of cavitation in fields of hydro turbines. They mention according to the Bernoulli s equation, the pressure fall, if the velocity of flow increases. In case when the pressure at any part of turbine falls below vapor pressure, the liquid boils and large number of small bubbles of vapors are formed. The vapor pressure is defined as the pressure at which liquid is vaporized at a given temperature and it depends upon the temperature and net pressure head of the liquid. They further explain that stream of water cuts short of its path which give rise to eddies and vortices containing voids or bubbles. These bubbles are formed at low pressure region and flow along with stream towards higher pressure region where the vapors condense and the bubbles suddenly collapse or implode. This result in the formation of a cavity and the surrounding streams of liquid coming from all directions collide at the center of the cavity. This increase pressure at that point up to very high level whose magnitude may be as high as 7000 atm. This process occur several thousand times a second. This causes pitting on the metallic surface of turbine and its devices, and the material then suffers fatigue failure, added by corrosion. Some parts of turbine such as runner blades may borne permanent damages by this process. The phenomenon which manifests itself in the pitting of the metallic surfaces of turbine parts is known as cavitation because of the formation of cavities.

27 18 5 Cavitation in Francis Turbines Cavitation found in hydro turbines falls under hydrodynamic or flow cavitation. Escaler et al [30] mentioned that Cavitation plays an important role in reaction water turbines such as Kaplan, Francis and Pumps than in case of impulse turbines. The main difference between Kaplan and Francis turbines is the design of the runner. The other machine components like penstock, spiral casing, stay vanes, guide vanes, draft tube, shaft, alternator and bearings are very similar in general design considerations. In Fig 5.1, a schematic view of a Kaplan turbine and a cross section of a Francis runner with its downstream reservoir shown in Fig 5.2 and Fig 5.3. The runner design has a clear influence on the cavitation phenomenon. The machine setting level and the operation at off-design conditions also have important influence in inception and development of cavitation. Fig 5. 1 Kaplan Turbine Schematic [31]

28 19 Fig 5. 2 Francis Turbine Schematic [32] Francis turbines are most widely used turbine types in the field of hydro electricity production. That's why many scientific research works are already carried out by Khurana et al [6], Escalar et al. [30], Lipez and Jost [33], Katz [34], Yamamoto et al. [35], which basically deals with reasons for cavitation, their types and occurrence, detection and prediction and possible method to avoid and prevent cavitation in Francis turbines. In this chapter, now we specifically discuss about the cavitation that happens in Francis turbines. The places of occurrence of cavitation, their types and forms, the overall and local effects of cavitation as well as detection and prevention techniques shall be discussed in this chapter. As Francis turbine is most widely used hydro turbine worldwide, it is significant to study the effects and their consequences which might occur during operation of this type of turbine. Khurana et al. [6] also specifies that cavitation is a problem for reaction turbine and it negatively affects turbine's performance. So study of cavitation in Francis turbines is very important in field of water energy sector which is directly linked with industrial sectors in regions where water is the major source of electricity generation.

29 Fundamentals of cavitation in Francis turbine It is obvious till now that cavitation are happening in every type of hydro turbines. But it is found in several literatures, in Francis turbines, their occurrence and effect is very enormous. Banshee [36] has informed through his book that only reaction turbines are subjected to cavitation. In Francis turbines cavitation generally may occur at the outlet of the runner or at the inlet of the draft tube. At these both regions, pressure is reduced considerably below the vapor pressure. Thoma cavitation factor (σ) is a dimensionless number suggested by Prof. D. Thoma which can be use to determine the region where the cavitation process occurs. Mathematically it is written as Where, H b = Barometric pressure head of water [m] H atm = Atmospheric pressure head of water [m] H s = Suction pressure at the outlet of reaction turbine / or height of turbine runner above the water tail race H v = Vapor pressure of water [m] H = Net head on the turbine [m] [m] According to Belahadji [37], International Electrotechnical Commission (ICE) defines the Thoma factor as plant cavitation number σ p as, Where, E is the specific energy and NPSE is the net positive suction specific energy of the turbine. NPSE can be calculate mathematically as: Where, p I = suction pressure [m]

30 21 ρ = density of water [kg/m 3 ] g = gravity [m/s 2 ] Z I = suction section height [m] Z ref = reference section height [m] C I = suction mean velocity [m/s] p v = vapor pressure [m] H s = machine setting level [m] p a = down-stream free surface pressure [m] Fig 5. 3 Schematic view Francis runner, draft tube and downstream reservoir [38] It can be seen in Fig 5.3 that suction pressure is the downstream pressure after draft tube and H s can be taken as the difference between reference section height and suction section height. Similarly, Arndt et al. [39], Dular [40], Gohil and Saini [41] and several other scientists and researchers also have discussed about the cavitation factor in the similar way. It is seen from the cavitation factor that turbine level setting has significance role on the cavitation. Besides, cavitation also effects other design parameters like volumetric flow rate, selection of materials for turbine runner, pitch angle, shaft rpm etc.

31 22 Avellan [42] found out that design, operation and refurbishment of turbines are strongly related to cavitation development in the flow, which mostly occur at runner or impeller and may also be found at stationary parts of the system. Fig 5.4 shows the range of operating range of Francis turbine and Fig 5.5 shows the vectors quantities associated in case of Francis turbines. Fig 5. 4 Operating range of Francis turbine [30]

32 23 Where, Fig 5. 5 Vectors in Francis kinematic [30] ѱ, is pressure or head coefficient given by, φ, is flow coefficient and is given by, β is guide vane angle [ ] α, is the incidence angle [ ] C 1, C2 absolute fluid velocity (inlet and outlet respectively) [m/s] W 1, W2 relative fluid velocity (inlet and outlet respectively) [m/s] U 1, U2 fluid tangential velocity (inlet and outlet) [m/s] R is runner diameter [m] Pressure coefficient (ѱ) and flow coefficient (φ) usually determine the operating point of turbine. The coefficient with sub index ѱ and φ indicates best efficiency or design point. Flow rate normally is controlled by opening the guide vane angle, which regulates the net powers output as well. Variance in head and flow rate has a direct influence on the kinematics of the flow through the runner that determines the tendency to promote cavitation. So it is necessary to choose suitable operating point where cavitation occurrence can at least be optimized. If, in case, head is increased for a given guide vane angle, β; the absolute fluid velocity C 1 will grow and the incidence angle, α will have

33 24 positive value. Normally this incidence angle has very small value close to zero for the design condition. And, when, machine operates at maximum head available or at head higher than the design head i.e. ѱ/ ѱ >> 1, then it is possible that attached cavitation occurs at suction side of the turbine blades. This naturally also changes the magnitude of velocity at outlet, so cavitation phenomenon can also be seen at pressure side. Readers requiring an overall vision of hydraulic turbines and power generation may refer to Cengel and Cimbala [1], Dandekar and Sharma [4] and Wright [43]. 5.2 Classification of cavitation Many scientists have studied the types of cavitation. In chapter 3.3 it is already discussed about general forms of cavitation, this chapter mainly focuses on the type of cavitation found in Francis turbines. Basically, cavitation types are classified according to the form of cavities formed and also on the flow conditions, types and flow turbulence. These cavities have different forms named as travelling bubbles, attached cavities or cavitating vortices as mentioned and elaborated by Hammit [44] and Arndt [38] Classification of cavity Travelling bubbles Bubbles are formed around a body in low pressure regions of the flow. Bubbles emerge from the micron sized nuclei. These bubbles travel with the flow. When they reach high pressure region, adverse pressure is exerted and they implode. These bubbles are strongly influenced by air content in the liquid. The erosive power of the implosion is relatively weak. Brennen [24] has proposed that an individual bubble can be modeled by assuming that the bubble remains spherical in an infinite liquid. Rayleigh-Plesset equation is also valid to approximate the bubble growth and solved to find the radius of the bubble, denoted by R B (t) in the equation 5.6.

34 25 But to solve the equation 5.6, bubble pressure p B (t) and infinite domain pressure p (t) should be known. It can be assumed that the bubble collapsing implosion starts at the maximum radius R 0, and then the collapse time (Rayleigh time) τ, time taken for the bubble radius to become zero, can be calculated by solving equation 5.7. The collapsing of bubbles emits high pressure pulses and noises where the radii of the bubble tend to zero. The theoretical work of Rayleigh on an imploding spherical cavity is also useful to calculate the potential of emission process. But, it only gives approximate results because the viscosity and surface tension effects are neglected, and it is assumed that the bubble contains vapor only. Other assumptions, such as the bubbles remain spherical and that they are isolated, also limit the accurate results. But in reality the bubbles characteristics vary far from the assumed theory, which is realized especially in boundary regions. So, still lots of experimental work should be done to characterize the exact dynamics and acoustics behavior of bubbles interaction in real flows. Depending upon the pressure, it takes about milliseconds for the bubble to reach maximum radius which can be seen in Fig 5.6. Fig 5. 6 The growth of liquid vapor in liquid nitrogen [24]

35 26 Fig 5.7 Travelling bubble cavities [24] Fig 5.7 shows dense travelling bubble cavitation on the hydrofoil surface. The incidence angle, γ, is set to zero, cavitation number, σ = 0.3 and velocity of 13.7 m/s. Flow is from left to right and the leading edge of the foil is just to the left of white glare patch on the surface Attached cavitation Cavitation structures form when the region of separated flow fills with vapor. Adverse to travelling bubble cavities, attached cavities form when the incidence angle is greater than about 10 or less than about -2. It occurs as a single vapor-filled separation zone as illustrated in Fig 5.8. Travelling bubble in case of bluff bodies may be transited into single vapor filled attached cavity wake when the cavitation number is reduced. As shown in Fig 5.9, bubble cavities can be seen for sphere body (left) before transition into fully developed or attached cavities. This is very common and complex type of cavities fall under large scale or macroscopic cavities. Depending on the hydrodynamic of flow and geometry of the submerged body, different forms or patterns of attached cavitation are seen: Sheet cavitation is characterized by thin stable cavities with smooth and transparent interface, Fig 5.9 (right). At the rear part, cavity closure shows weak pulsation due

36 27 to the shedding of small cavitation vortices. Normally, sheet cavitation represents a less risk of erosion and happens when body has smooth geometry and positive incidence angle. Fig 5. 8 Attached cavitation [24] Fig 5. 9 Cavitation transition: bubbly flow left to fully developed attached cavitation right [24] Cloud cavitation, shown in Fig 5.10, in contrary to sheet cavitation, shows strong unsteadiness and pulsation that induce significant fluctuation in cavity enclosure length and has wavy and turbulent cavity interface. It is known to be very aggressive form of cavitation which has very high erosive power as compared to bubble or sheet cavitation. This type of cavitation may cause serious damages in turbines blades and components.

37 28 Fig Cloud Cavitation [24] Vortex Cavitation Flow regions with very concentrated and fast vortices can develop cavitation in their central cores where liquid local pressure is very low. If the tips of these vapor filled vortices come to contact with a solid surface, then the whole cavity collapses or implosion takes place which exerts compressive thrust on the solid surface. This phenomenon has high erosive potential. This type of cavitation develops if vortex shedding occurs at the trailing edge of a hydrofoil and if pressure is low enough. This type of cavitation, shown in Fig 5.11, is normally seen in the swirling flow in draft tube of Francis turbines and can be found at the tips of the blades of propeller or runner. Fig Vortex Cavitation [24]

38 Types of cavitation Li [45] has described different types of cavitation in details. Different type of cavitation can be occurred in Francis turbine and their corresponding location, see Fig 5.12 and According to him, main types of cavitation seen in Francis turbines are as follows: Leading edge cavitation Fig 5.12 (1) shows leading edge cavitation. It can be found on the suction side of the runner blades and appears like attached cavity. This type of cavitation occurs when turbines are operated at a higher head than the machine design head (ѱ/ ѱ > 1) when the incidence angle is positive and deviated from design value very largely. It can also happen at the pressure side while operates at lower than design head (ѱ/ ѱ <1) when the incidence angle is negative. The unstable stage of this type of cavitation is very aggressive which tends to deeply erode the blades and provoke pressure fluctuations [46] Travelling bubble cavitation It has the form of separated bubbles attached to the blade suction side near the mid chord next to the trailing edge. Normally this cavitation occurs at low cavitation number. Their formation grows as the load increases and reaches maximum as machines operate at maximum load where the flow is also maximum (φ/φ >> 1). It is very severe and noisy type of cavitation and reduces machine efficiency by significant amount. It may also provoke erosion in cases when the bubble collapses on the blades. This type of cavitation is very sensitive to the content of cavitation nuclei and to the value of the cavitation or Thoma number Draft tube swirl Fig 5.12 (3) shows the formation of typical draft tube swirl cavitation in Francis turbines. It forms behind the runner cone in the centre of the draft tube. The volume depends on cavitation number (σ p ) and appears only at part load operation (φ/φ <1) and also at overload (φ/φ >1) because of the residual circumferential velocity component of the flow after the runner. This vortex rotates in the direction of the runner at part load and at overload operation the direction is reversed. At part load operation from 50% up to 80%,

39 30 the vortex core has a helical shape and its rotation is precession. The speed of the rotation is around 25-35% of the runner rotating speed. In this case, circumferential pressure pulsations are generated at this low frequency. If the precession frequency matches one of the free natural oscillation frequencies of the draft tube or penstock strong pressure, fluctuation may happen. This provokes large pressure pulsation in the draft tube causing strong vibrations on the turbine and even on the powerhouse Inter-blade vortex cavitation During part load operation, when φ/φ < 1 or at low flow regime, complex flow recirculation at the inlet of the runner can be seen which leads to the formation of vortex cavities attached to the hub and extending up to the blade to blade passage, see Fig 5.12(4). Fig Main types of cavitation in Francis turbines [30]

40 31 This type of turbine operation is considered as off design operation and is unavoidable, for instance the filling up the reservoir of a new hydro-power generation scheme. This is formed by secondary vortices present in the cascades between blades. These vortices are formed due to the variance in flow dynamics due incidence variation from the hub to the band. They can attach to the intersection of the blade inlet-edge with the crown or mid-way of the crown between the blades near to the suction side. If the runner surface collides with the tip of vortex cavities it results in erosion or pitting. They can also appear at very highhead operation ranges (ѱ/ ѱ >>1) because the cavitation number or Thoma number σ p is relatively low. In this case, they become unstable and cause strong vibrations. Zuo et al. [47] and Avellan et al. [48] has investigated more about inter-blade vortex modeling and pressure fluctuation Von Karman vortex cavitation Periodic vortex-shedding can occur at the trailing edge of blades and vanes. Severe pulsations and singing noise can be caused if a lock-in phenomenon occurs. As a result, the trailing edge might be damaged. The occurrence of lock-in, defined as the local synchronization between the vortex shedding frequency and the cross-flow structural vibration frequency [49]. Landry et al. [50], Decaix et al. [51] and Hočevar et al. [52] have studied about the dynamic behavior and modeling of vortex rope in draft tube of Francis turbines. For more detail about the subject, the listed authors can be referenced. Fig 5.13 shows location of the Von Karman vortex in Francis turbines. Fig Von Karman vortex occurring location in Francis turbine [30]

41 32 Whereas in some books like Li [45], cavitation in Francis turbine is also classified into following types: 1. Outlet edge cavitation: It is seen in form of small individual bubbles attached to the blade. This type of cavitation has strong dependence on submergence and has low noise level. 2. Inlet edge cavitation between blades: It is characterized by the formation of large bubbles between runner vanes. It emits high noise level which has broad band. It can be seen at the suction side of the blades where vortex or voids are formed on the lowest part of inlet edge and leads to severe pressure fluctuations. 3. Part load vortex cavitation: In this type a core vortex on turbine crown is formed, resulting in low frequency noise. It is very sensible to guide vane opening. 5.3 Cavitation detection and prevention As various forms and types of cavitation is discussed in previous chapter, it can be seen that cavitation behavior also changes according to the location where they occur. This happens due to different geometry present at different location of the turbines. There are different hydrodynamic conditions, for example, the gap between guide vanes and rotor has different hydrodynamic properties as compared to gap between successive rotors. The stream leaving the trailing edge and entering the draft tube has totally different geometrical pattern as compared to other location inside the Francis turbines. Fig 5.14 shows different type of cavitation occurring at different location. At the suction side of the runner, leading edge cavitation can be present in form of attached cavities. At the part of blade suction side which is near to the mid chord next to trailing edge, travelling bubble cavities can be found. Draft tube swirl can be found just below the runner cone in the center of draft tube. In the channels between the blades, the flow separation provoked due to the variation of incidence from hub to the band, secondary vortices can be formed. This is called as inter blades vortex cavitation. At the trailing edge of Francis a turbine periodic vortex shedding can occur which is technically also called Von Karman vortex cavitation.

42 Detection techniques It is already discussed in previous chapters that cavitation is an unsteady phenomena that raises low frequency pressure oscillation as well as high frequency pressure pulsation. This pressure oscillation depends on the dynamics of cavities, for e.g. shape, type, location, while pressure pulsation is produced due to implosion of these cavities. This both phenomena emit vibrations and acoustic noise and are propagated through hydrodynamic and mechanical systems. Thus, by using suitable sensors which sense that vibratory and acoustic noise, cavitation phenomena in turbine can be observed or analyzed. Normally sensors like accelerometers, acoustic emission sensor are fixed on the external wall of the fixed components and dynamic pressure transducers are flush mounted to the wet wall. Fig Cavitation location and sensor positioning in Francis turbine [30] Fig 5.14 shows schematic view of the sensors mounted in case of Francis turbines. Thus, by measuring and analyzing those induced signal, cavitation in real machines can be detected. But it is not an easy task to detect cavitation because its type, behavior and location are different according to design and operating conditions of the turbine. As well as, the measured signals may also includes the noises coming from other excitation sources rather than cavitation. Therefore, it is rather important issue to select most adequate sensors and to position the sensors to improve detection accuracy. Escaler et al. [53] presented their work about complete measurement and recording set-up for an experimental test. In their experiment, vibrations are monitored by piezoelectric accelerometers with mounted natural frequency of 40 khz and also by acoustic emission

43 34 sensors which has resonance frequency of 200 khz. The dynamic pressures are measured by piezoelectric pressure sensors. A photoelectric tachometer probe was used to measure shaft rotation. The output signals of the transducers have been conditioned prior to their recording with a RACAL V-Store tape recorder. The vibrations are measured at the guide bearing has been measured at draft tube wall by flush mounted pressure sensors. Erosive cavitation activity can be detected by the study of high frequency content of the vibrations. To identify the type of cavitation, it is necessary to use specific signal processing techniques like the demodulation of band pass filtered signals. The results shall be improved with the use of synchronous time averaged signals. Joint time-frequency analysis is a promising tool that helps to detect the implosive forces produced by cavity collapse. Detection of other forms of cavitation that generate strong pressure fluctuations is relative easier because of their low frequency. Normally the vibrations and acoustic noises excited by cavitation process can be classified into following categories, Escalar [30]: 1. Structure and fluid borne noise: Ceccio and Abbot [54] have demonstrated that analysis of hydraulic noise is useful tools to investigate the feature of cavitation phenomena. Structure borne noise can be measured easily in turbine while fluid borne noise is rather difficult to measure because it is impossible to place pressure sensor in the runner. Also it has to be considered that cavitation noise cannot be measured directly because the signal strength is attenuated during their propagation. But still the spectral content of high frequencies and modulating frequencies can be used for cavitation detection. 2. Low frequency content: Cavitation vortices and unstable cavities with a large oscillating volume create turbulence in the main flow. That in turn creates strong pressure pulsations inside the hydraulic system. This can be observed in the draft tube swirl in certain flow conditions. This low frequency fluctuation can be detected by the use of flush mounted pressure transducers. If the intensity of the fluctuation is strong, the detection can also be made from structural vibrations. So, in this case, only the analysis of the frequency content of the pressure and vibration signals within a low frequency range is required.

44 35 Hočevar et al. [52], also presented his result on the experimental work performed to predict vortex dynamic of draft tube in a model Francis test rig. The experiment setup layout can be seen in Fig Fig Experimental setup to monitor Francis Model test rig [54] Fig 5.15 shows typical setup and sensor position to monitor cavitation vortex dynamic in the draft tube of Francis turbine. Twenty different operating points with different flow coefficients, pressure coefficient and cavitation number were selected. The operating points are set by varying guide vanes opening, the rotation speed and the pressure. Kistler piezoeletric pressure transducer, mounted directly into the wall of turbine draft tube, was used to measure the pressure. According to Liu et al. [55], during cavitation in turbines, the bubble implosion will produce numerous micro jet or shock waves on the runner blades and also on the flow passage walls. This micro jets and shockwaves form impact and vibration along with the acoustic emission (AE) signals. Normally, this signals high frequency ranging from 20 khz to 1 MHz and is spread through the hydraulic body and the mechanical system. By analyzing the AE signals, cavitation location and cavitation damages can be realized. LabVIEW software has been used to monitor and analyze AE signals on their research. The research was performed on 8000 kw Francis turbine where SR-150 M acoustic emission sensor was used to collect AE. PAI preamplifier was used to convert AE into standard electrical signals.

45 36 He and Shen [56] pointed out three common types of methods to detect cavitation in practice. a) Paint testing: In this method, related parts of fluid machines are painted and cavitation erosion is estimated by observing the removal of the paint. It can detect cavitation erosion directly and thus results can be considered more accurate. However, these methods are complicated because of difficulties in choosing the right paint and realizing online detection. b) Cavitation acoustic noise measurement: These methods, using audible sound, cavitation noise and so on, are indirect detection methods of cavitation erosion. However, the correlation between cavitation and cavitation erosion is complicated because they are not always of positive correlation, which makes that it is hard to use these methods to estimate cavitation erosion state accurately. c) Vibration test: This method is also an indirect detection, which estimates cavitation erosion state by examining the vibration state of fluid machines. However, the constituents of the vibration signals are quite complicated. It is very difficult to separate the vibration component being related to cavitation erosion from the collected vibration signals of fluid machines Prevention As already discussed in above chapters, cavitation detection is very complex and difficult task, in the same way its prevention is almost impossible. Kumar and Saini [29] have concluded that '' It is unavoidable to reduce cavitation completely, but can be reduced to a minimum acceptable level ''. They also emphasize that although changes in turbine's component design, choosing suitable operating conditions or coating high resistive materials on the blades still is not significant to prevent cavitation effects completely. Whereas they have suggested that if cavitation number or Thoma number (σ) is kept at a certain value which is greater than critical thoma number, σ c, and then the turbines operation can be cavitation free.

46 37 In case of Francis wheel, this critical Thoma number (σ c ) can be calculated as: where, N s = specific speed of turbines Fig Variation of turbines efficiency with respect to cavitation number σ [29] From Fig 5.16, it can be seen clearly that the turbine has best efficiency point when cavitation number σ, has smaller value than critical cavitation number σ c. Thus, to maintain cavitation free condition, the turbine should be operated below the best efficiency level. Also, from equation 5.1, we can see that by increasing the suction head H s, a corresponding decrease in σ. Further decrease in H s, brings the value of σ lower than σ c which leads to cavitation. So the suction head should not be larger than certain maximum value. In the same way from equation 5.8 we can see, the value of σ decrease as value N s is decreased. That's why, value of turbine specific speed (N s ) should be larger than certain minimum value. It can be seen clearly from Fig 5.17, that there is no point of operation where no cavitation occurs. During large head operation and part flow rate, leading edge cavitation occurs at suction side, inter blade vortex and draft swirl cavitation can be seen during low head

47 38 operation and part flow rate cavitation occurs on the leading edge at pressure side. Cavitation may also be seen in valve openings, expansion joints or any constriction on the way of flow which produce throttling effects. Fig Hill chart showing the regions where cavitation occurs in Francis Turbine [57] Theoretical solution to cavitation can be reducing the pressure gradually from inlet to outlet; it avoids a large pressure drop at the vena contracta. Vena contracta is the narrowest cross section in the flow stream. This point can be around the region like outlet of guide vanes, valves. Cavitation can be avoided entirely by maintaining the pressure above the vapor pressure, thereby stopping bubble formation and subsequent collapse. Another solution that can be used for lower levels of cavitation can be achieved by isolating bubbles away from the metal surfaces. This greatly reduces the amount of energy exerted on the exposed surfaces of a runner, guide vanes, valves and other accessories, reducing the fatigue effects on the surface [58]. So it can be concluded that, to avoid cavitation while operating, turbine's parameters should be maintained in such way that at any point of flow, the static pressure should not fall below the vapor pressure of the liquid. These cavitation controlling parameters are pressure head, flow rate and exit pressure of the liquid. The control parameters for cavitation free operation of hydraulic turbines can be obtained by conducting tests on model of the turbine under consideration. The parameters beyond which cavitation starts and turbine efficiency falls significantly should be avoided while operation of hydraulic

48 39 turbines. Flow separation at the exit of the turbine in the draft tube causes vibrations which can damage the draft tube. To dampen the vibration and stabilize the flow, air is injected in the draft tube. To totally avoid the flow separation and cavitation in the draft tube, it is submerged below the level of the water in tailrace. Draft tube against cavitation Also, cavitation can be controlled to some extent by connecting runner outlet to a conical shaped outlet which is called as draft tube. The design and selecting the dimension of draft tube is an important parameter to avoid cavitation. If, we apply Bernoulli's equation between outlet of the runner and discharge point of the draft tube by neglecting any head losses through the draft tube. Mathematically it can be expressed as: z 2 = z (Height of draft tube) z 3 = height of tail race which is referenced as datum line (=0) p 2 = pressure at the outlet of the runner p 3 = gauge pressure Since, draft tube is a diffuser V 3 is always less than V 2 which implies p 2 is always negative, thus, height of the draft tube is an important parameter to avoid cavitation [59] Experimental analysis Cavitation monitoring and prevention Escaler et al. [60], has explained his experiment on model of Francis turbine to monitor cavitation. Cavitation phenomena can be replicated in a model and can be visually observed in laboratory. But, the conditions of apparition and the intensity of their undesired effects cannot yet be scaled accurately to the corresponding prototype. Because of that, unexpected cavitation problems can arise during normal operation of the actual

49 40 Francis turbine. Application of adequate detection techniques which can be easily and effectively used in real hydropower plants; cavitation can be detected and prevented. The vibrations and pressures can be detected by the sensors and are useful for cavitation monitoring. However, much research in the field of cavitation monitoring has been already done, it is still necessary to investigate, under controlled conditions, the different types of cavitation that can appear in a Francis turbine. The results from these investigations are useful to identify and quantify in prototypes. Fig Outline of measuring positions [58] The experiment was carried out in Laboratory for Hydraulic Machines, Ecole Polytechnique Federal de Lausanne, LHM- EPFL, Switzerland. The test rig has maximum head of 100 m and maximum flow rate of 1.4 m 3 /s. The model was composed of 20 guide vanes and 19 runner blades which rotate with average speed of 874 rpm. The fundamental frequency (ff) of flow was Hz, blade passing frequency (fb) was Hz and guide vane passing frequency (fg) was Hz. Required sensors are placed as shown in Fig Two accelerometers, A1 and A2, were installed on the turbine guide bearing in radial and in axial direction respectively at angular distance of 180. Two dynamic

50 41 pressure sensors, P1 and P2, were mounted at 90º in the guide vane channels upstream the runner. And finally, two more dynamic pressure sensors, P3 and P4, were mounted at 180º on the draft tube. The signals from pressure transducer were low pass filtered below 20 khz and anti-aliased with a Chebychev filter. A LeCroy 6810 A/D converter was used to make simultaneous records with a sampling frequency of 50 khz per channel. The experiment was carried out under five different operating regimes and named as below: 1. Cavitation free [NO CAV] 2. Intermittent and weak outlet blade cavitation and overload rope [OUTLET] 3. Outlet cavitation and von Karman cavitation and overload rope [OUT_VK] 4. Strong bubble cavitation and overload rope [BUBBLE] 5. Pulsating inlet cavitation on extrados and part load rope [INLET] Methodology The methodology was analyzing the structure and fluid-borne noise generated during the final collapse of the vapor cavities in the form of bubbles, clouds or vortexes. The structure borne noise was measured with high frequency accelerometers mounted on the machine bearings and the fluid-borne noise was measured with dynamic pressure sensors flush mounted on the wetted surfaces of the turbine. As the pulsating behavior of bubble collapsing and high generation, frequencies above 10 khz up to several hundred khz is excited on the flow, when cavitation occurs. The vibration and pressure signals hence can be achieved by amplitude demodulation in the high frequency range. The signals are then analyzed on the frequency domain to identify most sensitive frequency bands. An increase on the amplitudes clearly indicates the presence of some form of cavitation. The raw time signals are filtered in such bands and amplitude demodulation is applied to identify the main frequency peaks. The synchronous peak frequency at the rotating frequency, the blade passing frequency and the guide vane frequency were clear indication of the type of cavitation.

51 42 According to many researchers and scientists, it can be concluded that, flow behavior of experimental model are different than that in prototype. Thus, it was confirmed that a particular turbine has its unique hydrodynamics and has strong influence in cavitation process. It's a difficult task to place sensors on the rotor blades, guide vanes to observe local hydrodynamic flow conditions. Even more to apply visualization technique at this location requires innovations, advanced techniques and large investment. For the purpose of understanding and revealing the characteristics and dynamical behavior of the cavitation, visualizations play a decisive role. So Escaler et al. [60], have conducted the first successful experiment which acquired visualization technique to perform case-study of the inter blade cavitation vortex developing inside blade to blade channel of Francis turbine. Both the onset and the dynamics of the inter-blade vortices were investigated for the first time using the presented visualization. Generally, high speed camera technique, would properly visualize the inter-blade cavitation vortices from the low pressure side of the turbine through the transparent diffuser cone with an inclined window as shown in Fig However, the visualization of the cavitation from the high pressure side of the turbine has not yet been successfully conducted, due to the complicated structure obstructing the visual access in the high pressure side. The specialty of this experiment was a fully developed sophisticated visualization technique which could visualize the blade channel through the guide vane. The test rig features a specially instrumented guide vane, a boroscope with a swivel prism covering the variable visual range, and a suitable power LED light. A special guide vane is equipped with a transparent acrylic glass window. The hollow guide vane is manufactured, and the transparent window which has the same surface profile as an original guide vane is attached. The window is perfectly sealed by an epoxy resin in order to isolate the embedded equipment from the pressurized water in the spiral case. The dimension of the instrumented guide vane is made completely same as the original one, and the surface of the guide vane and window is sufficiently polished and made smooth in order not to influence the flow and efficiency of the turbine. For the optical access to the blade channel a boroscope is mounted in the guide vane. Special type

52 43 Fig Experimental setup for high speed visualization of inter blade vortices [48] Fig Entire installation of the instrumented guide vane, boroscope, and LED light source [48]