Jan 21, 2016 - Figure 20 Sediment erosion in Guide vanes at Panauti Hydropower ...... Study of Upper Tamakoshi Hydroelectric Project," Journal of Water, ...
KATHMANDU UNIVERSITY SCHOOL OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING DISERTATION ON
SEDIMENT EROSION AND ITS EFFECT ON GUIDE VANES OF FRANCIS TURBINE In Partial Fulfillment of the Requirements for the M.S. by Research in Mechanical Engineering
Ravi Koirala
March, 2017
© 2017 Ravi Koirala
AUTHORIZATION I hereby declare that I am the sole author of the thesis. I authorize the Kathmandu University to lend this thesis to other institutions or individuals for the purpose of scholarly research. I further authorize the Kathmandu University to reproduce the thesis by photocopying or by other means, in total or in part, at the request of other institutions or individuals for the purpose of scholarly research.
___________________________________________ Ravi Koirala
March, 2017
PREFACE This thesis has been prepared based on two years joint research work, partly at Turbine Testing Lab, Department of Mechanical Engineering, Kathmandu University, Nepal and State Key Laboratory of Hydroscience and Engineering, Department of Thermal Engineering, Tsinghua University, Beijing, China. Dr. Hari Prasad Neopane and Dr. Baoshan Zhu were my supervisors during the period. This study focuses on sediment erosion in guide vanes of Francis turbine. It was funded by Turbine Testing Lab Research Fund jointly with Grant number 51179090 of National Science Foundation of China and Tsinghua University. The study was segmented into three parts; 6 months at KU, 1 year at THU and last 6 months back in KU. During the period five peer-reviewed journal papers and 1 conference paper were prepared. Stay at KU was primarily focused on course works and experiments, were as stay at THU was focused on course work, computational analysis and experimental design. Pursing research degree is both painful and enjoyable experience. It’s like climbing a high peak where steps are full of bitterness, hardships, frustration, encouragement and trust. When I found myself at the top enjoying the beauty, I realize it is in fact a team work that got me here. My sincere gratitude towards everyone, for moral and technical help, support and guidance. I sincerely express my gratitude towards my professor and friends in China for helping me feel homely.
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ACKNOWLEDGMENTS This thesis owes its existence to the help, support and inspiration of several people and institutions. My sincere acknowledgement with deep sense of gratitude towards my enthusiastic supervisors Dr. Hari Prasad Neopane and Dr. Baoshan Zhu, for the continuous guidance, support, inspiration and encouragement. I express my gratefulness towards Turbine Testing Lab, Department of Mechanical Engineering, Kathmandu University, Nepal and State Key Laboratory of Hydroscience and Engineering, Department of Thermal Engineering, Tsinghua University, China for supporting this work academically and financially. My profound gratitude to Prof. Bhola Thapa, Dr. Biraj Singh Thapa and Mr. Sailesh Chitrakar for the encouragement and sharing their experiences regarding accelerated testing, laboratory estimation and guide vane erosion. Special mention goes to Mr. Wang Hongbiao, Mr. Lui Linhai, Mr. Ma Zhe and Mr. Rao Cong for going far beyond call of duty. I have very fond memories from China because you guys were there. I am indebted to Dr. Lekhendra Tripathee (Post –doctoral Scholar, CAS) and Mrs. Prakriti Sharma (PhD Scholar, CAS) for being with me in hardest time at China, made me feel at home. I am appreciative to Mr. Edgar Cando, Mr. Santo Sahed, Mr. Abbas Haider, Mr. Wang Tabiao; my fellows around THU, for wonderful tea and dinner times. My gratefulness towards Mr. Oblique Shrestha, fellow researcher at TTL, for his continuous encouragement and support during my activities. To Mr. Nirmal Acharya and Mr. Aatma Ram Kayastha for sharing my responsibilities during rush hours of work.
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Mr. Bishnu Prasad Aryal deserves special acknowledgement for helping with installation of my rig and running of experiment. Amish Ratna Sthapit, Vipassana Paudel, Sandeep Adhikari, Anil Sapkota, Santosh G.C., Nitish Sapkota, Rijju Sigdel and Antivirus Colony members deserve special mention for all the support during this work. I owe a lot to Ms. Maneesha Rayamajhee for regular encouragement and faith that I will come up with something better. The last word of acknowledgement I have saved for my father, mother, brother and Eliza for being with me and supporting me in what I wanted to be.
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TABLE OF CONTENTS
PREFACE …................................................................................................................... i ACKNOWLEDGMENTS .............................................................................................. ii TABLE OF CONTENTS .............................................................................................. iv LIST OF FIGURES ....................................................................................................... vi LIST OF TABLES ........................................................................................................ ix ABSTRACT………………………………………………………………………….. x BIOGRAPHICAL SKETCH ........................................................................................ xii LIST OF ABBREVIATIONS ..................................................................................... xiv LIST OF SYMBOLS ................................................................................................... xvi Chapter 1. Introduction ................................................................................................. 1 1.1.
Background ...................................................................................................... 1
1.2.
Rationale .......................................................................................................... 3
1.3.
Research gap .................................................................................................... 5
1.4.
Research question ............................................................................................ 5
1.5.
Objectives ........................................................................................................ 5
1.6.
Scope ................................................................................................................ 6
1.7.
Methodology .................................................................................................... 6
Chapter 2. Literature Review ........................................................................................ 8 Chapter 3. Field Study ................................................................................................ 22 Chapter 4. Computational Study ................................................................................ 30 4.1.
Effect of Clearance gap on Performance of Francis turbine .......................... 30
4.2.
Selection of Guide Vane Profile for Erosion Handling ................................. 33
Chapter 5. Experimental Study ................................................................................... 36 5.1.
Effect of Guide Vane erosion on Flow around it ........................................... 36
5.2.
Selection Guide Vane Profile for Erosion Handling ..................................... 39
Chapter 6. Result and Discussion ............................................................................... 42 6.1.
Effect of Guide Vanes Erosion ...................................................................... 42
6.2.
Selection of Guide Vane Profile for erosion Handling .................................. 51 iv
Chapter 7. Conclusion And Recommendation ........................................................... 57 References ……………............................................................................................... 60 APPENDIX – A: Associated Publications ................................................................... 66 APPENDIX – B: Design and Development of 3 Guide Vane Cascade System .......... 67 APPENDIX – C: Callibration and Uncertainity Analysis ............................................ 70 APPENDIX – D: Design of Guide Vanes for Francis turbine ..................................... 72
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LIST OF FIGURES Figure 1 Global proportion of undeveloped hydropower and annual sediment load deposition ....................................................................................................................... 2 Figure 2 Cross Section View of Francis turbine ............................................................ 3 Figure 3 Cross flow through Guide Vanes of Francis turbine........................................ 4 Figure 4 Losses in Francis turbine.................................................................................. 4 Figure 5 Work flow and methodology implemented ..................................................... 7 Figure 6 Guide Vane construction .................................................................................. 8 Figure 7 Flow phenomena in Francis turbine ................................................................ 9 Figure 8 Location of guide vane based on sediment handling ..................................... 10 Figure 9 Selection of number of guide vanes ............................................................... 11 Figure 10 Wakes in flow passing cylinder ................................................................... 12 Figure 11 Velocity wake profile at guide vane outlet .................................................. 13 Figure 12 One Guide Vane Casade study of flow and phenomena of leakage flow .... 14 Figure 13 Vibration amplitude of various hydrofoil trailing edges .............................. 15 Figure 14 Vorticity evolution during the shedding cycle in truncated and oblique trailing edges ............................................................................................................................. 16 Figure 15 Normalized mean and standard deviation of the stream wise velocity ........ 16 Figure 16 Cross flow and flow stagnation around shaft hole in Clearance gap ........... 18 Figure 17 Possible facilities for guide vanes erosion test............................................. 20 Figure 18 Facilities for measurement of effect of erosion ........................................... 21 Figure 19 Sediment erosion in Guide Vanes of Francis turbine .................................. 22 Figure 20 Sediment erosion in Guide vanes at Panauti Hydropower Plant ................. 23 Figure 21 Sediment erosion in Guide Vanes and facing plate at Jhimruk Hydropower Center ........................................................................................................................... 24 Figure 22 Sediment Erosion in Guide vanes at Middle Marsyangdi HPP ................... 25 Figure 23 Erosion in guide vanes and facing plates at Sunkoshi Hydropower Plant ... 27 Figure 24 Sediment erosion in guide vanes at Kaligandaki-A Hydropower Plant....... 28 Figure 25 Sediment erosion in Guide Vanes at Bhilangana Hydropower Plant, India 28
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Figure 26 Hexahedral mesh of guide vane made in ICEM and Runner made in Turbogrid ...................................................................................................................................... 31 Figure 27 Computational domain ................................................................................. 32 Figure 28 Thickness depletion in the facing plate ........................................................ 33 Figure 29 Guide Vane profiles for analysis .................................................................. 34 Figure 30 Computational Domain ................................................................................ 35 Figure 31 Particle number independency test .............................................................. 35 Figure 32 3GV cascade development methodology ..................................................... 37 Figure 33 Computational Model for wall refinement................................................... 37 Figure 34 Cu and Cm plot of analytical, turbine simulation & Cascade calculation ..... 38 Figure 35 Test setup ..................................................................................................... 38 Figure 36 Mineral Composition of Sediment Sample .................................................. 39 Figure 37 Rotating Disc Apparatus Optimized for erosion test in guide vane ............. 41 Figure 38 Rotating Disc Setup flow description and sample ....................................... 41 Figure 39 Comparison between Empirical and Computational result .......................... 43 Figure 40 Variation in hydraulic performance with clearance gap .............................. 44 Figure 41 Guide vane measurement position ............................................................... 45 Figure 42 Velocity profile over the gap from button to top at leading edge ................ 45 Figure 43 Velocity Profile over the gap from button to top at Trailing edge ............... 46 Figure 44 Surface plots at the Leading Edge, Trailing edge and Radial view in the gap ...................................................................................................................................... 48 Figure 45 Weight loss Vs Sediment Passed ................................................................. 49 Figure 46 Observation of erosion on Aluminum GV ................................................... 50 Figure 47 Observation of change in surface texture on MS GV .................................. 50 Figure 48 Pressure change with quantity of sediment passed ...................................... 51 Figure 49 ERD Vs Op for different guide vane profiles ................................................ 52 Figure 50 ΔP Vs Op for different guide vane profiles ................................................. 52 Figure 51 Experimental observation of erosion pattern on guide vane ........................ 53 Figure 52 % Weight loss at various guide vane positions in different profiles measured at 3 different time intervals........................................................................................... 54
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Figure 53 η Vs Guide Vane opening for different profiles .......................................... 55 Figure 54 Guide Vane torque Vs Guide Vane opening for different profiles .............. 55 Figure 55 Inlet Velocity triangle at BEP ...................................................................... 56 Figure 56 Cm1 vs Op with various guide vane profiles ................................................. 56 Figure 57 Cu1 vs Op at various guide vane profiles ...................................................... 56 Figure 58 C1 vs Op at various guide vane profiles........................................................ 56 Figure 59 W1 vs Op at various guide vane profiles ...................................................... 56
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LIST OF TABLES Table 1 Mesh Description ............................................................................................ 30 Table 2 Boundary Condition ........................................................................................ 35 Table 3 Mesh Information ............................................................................................ 35
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ABSTRACT This thesis has been prepared based on two years research work of Masters by research at Turbine Testing Lab, Kathmandu University and State Key Laboratory of Hydroscience and Engineering, Tsinghua University. Sediment erosion has been a crucial issue for hydropower development in Himalayas and Andes valley. Large sediment concentration with higher percentage of quartz in water, originating from these regions affects the exposed mechanical components of installed hydel projects. This phenomenon of sediment effect on exposed turbine component is Sediment Erosion. In Francis turbine, Spiral Casing, Stay Vanes, Guide Vanes, facing plates, covers, runner and draft tube are found to have been affected by it. This study has been focused on Sediment Erosion in Guide Vanes of Francis turbine and its effect on flow around it. Guide vanes are stationary component in Francis turbine that performs periodic movement though a pivoted support, in response to the change in flow or load. In order to allow this movement, small gaps are provided at top and bottom of vanes, called clearance gap. They are internally lined with replaceable or metal claded linings called facing plates. These vanes are externally controlled through pneumatic, hydraulic or electric actuator that responds to the change. Each vane is linked to each other through linkage mechanism, such that equal angular change occurs during actuation. Operational point of turbine is determined by this movement, which regulates amount and direction of flow to runner. In Francis turbine, pressure decreases with decreasing radius i.e. highest pressure at spiral casing inlet and lowest at runner outlet. In guide vanes, at the region where flow strikes, has high pressure whereas the point perpendicular to it has lower pressure hence have pressure and suction side. This results into cross flow i.e. secondary leakage flow x
through clearance gaps. In presence of sediment flowing with highly accelerating water at guide vane passage, erosion increases these gaps inducing leakage losses. Computational study showed significant loss in efficiency with increasing gaps. Field observation has reported these increments in entire Francis turbine, operating in sediment laden flow. This gap increment is due to erosion on both facing plates and guide vanes. In addition to it, significant erosion on leading and trailing edge and faces were also observed. Erosion increases surface roughness and ultimately increases the pressure resulted from friction. Erosion in these vanes was found to be reduced by suitable selection of vane profile.
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BIOGRAPHICAL SKETCH Ravi Koirala is a Masters in Mechanical Engineering by Research student at Department of Mechanical Engineering, Kathmandu University. His Masters work is a part of international collaboration between Tsinghua University, Beijing, China and Kathmandu University, Dhulikhel, Nepal. He has been working in the area of Design, Analysis and Manufacturing of Francis turbine for last 3 years. He is also a Researcher at Turbine Testing Lab, Nepal.
xii
Dedicated to my Parents
xiii
LIST OF ABBREVIATIONS TW
Tera Watt
CFD
Computational Fluid Dynamics
PIV
Particle Image Velocimetry
BEP
Best Efficiency Point
LDA
Laser Doppler Annemometry
NACA
National Advisory Committee for Aeronautics
TRPIV
Time Resolved Particle Image Velocimetry
kW
Kilo Watt
MW
Mega Watt
TTL
Turbine Testing Lab
NTNU
Norwegian University of Science and Technology
WPL
Water Power Laboratory
PPM
Parts Per Million
GV
Guide Vanes
ERP
Erosion Resistance Probe
3D
Three Dimensional
KG-A
Kaligandaki –A Hydropower Project
3-GV
3 Guide Vane
ATM
Automatic Topology Mesh
RAM
Random Access Memory
LPS
Liter Per Second
GUI
Graphical User Interface
RDA
Rotating Disc Apparatus
ANSYS
Analysis System
RMS
Root Mean Square
KETEP
Korea Institute of Energy Technology Evaluation and Planning
PS
Pressure Side
SS
Suction Side xiv
IEC
International Electro technical Commission
LE
Leading Edge
SF
Scale Factor
xv
LIST OF SYMBOLS H
Head
Q
Flow
V
Flow Velocity
A
Analytical Value
T
Turbine Value
C
Cascade Value
Ngv
Number of Guide Vanes
T
Guide vane Torque
D1
Inlet Diameter
D2
Outlet Diameter
E
Total Energy
Cm
Meridional component of flow
Cu
Tangential component of flow
Ω
Speed number
Q*&*
Reduced flow and speed
αo
Full load Guide vane opening
r1&r2
Inlet and outlet radius of runner
Rsc
Radius of spiral casing spiral
rsvi&rsvo
Radius of stay vanes inlet& outlet
rgvi&rgvo
Radius of guide vane inlet and outlet
ro
Radius of guide vane shaft
Re
Reynolds Number
ΔP
Pressure difference in
Δh
Pressure difference
l/s
Ratio of length to width
µ
Flow coefficient
UP
Particle Velocity xvi
FD
Drag Force
FR
Force due to domain rotation
FP
Pressure gradient force
FBA
Basset force
K1
Model constant
ϒ
Impact angle
QL
Leakage Flow Rate
p
Guide vane profile
α
Guide vane angle
Sp
Sediment property
P1, P2, P3
Position 1, 2 and 3
ERD
Erosion Rate Density
ΔC
Clearance gap
U1
Tangential velocity at Inlet
C1
Swirl Velocity at Inlet
Cu1
Tangential velocity at Inlet
Cm1
Meridional velocity at Inlet
W1
Relative velocity at Inlet
η
Efficiency
Op
Percentage Guide Vane Opening
gverosion
Guide vane erosion
B1
Inlet Height
Cu
Tangential Velocity Component
xvii
CHAPTER 1.
INTRODUCTION
1.1.Background It has been a global initiative to utilize renewable technology for fulfilling current energy demand. Hydropower has been considered as one of the most flexible and consistent renewable energy source fulfilling both base and peak energy demand, utilizing the energy of naturally moving water. Its production cost consistency, low operation and maintenance cost, environmental acceptability, economic viability and constant cost makes it to be more reliable perpetual energy source. With global installed capacity of 1036 GW, it fulfills 16% of energy demand, which is 85% of total renewable energy generated. [1] Among two third of the undeveloped projects most of them lies in Asia and South America, where, to fulfill increasing energy demand, new projects are being conceived. From Figure 1, Asia and South America has larger global potential of hydropower development along with the problems, invited by sediment flowing with water. Hence, with larger opportunities lie greater challenges [2]. Problems from suspended sediment are one of the major technical challenges for hydropower as its mechanical impact reduces performance and life of the exposed components. Prior to development of new projects, identification of existing problems, its causes, severity and research approach on mitigation are important associated issues. This ascertains consistent or enhanced generation in more economical way.
1
Figure 1 Global proportion of undeveloped hydropower and annual sediment load deposition [1] [2] Francis turbines are reaction machinery with wide operational range, specific hydraulic characters, relatively higher speed and compact unit. The topographical land forms of most of the undeveloped regions are projected to have this turbine in future projects. Hence, have larger opportunities of future Research and Development. Being the only hydropower research institution in Nepal, Turbine Testing Lab, Kathmandu University hosted a NORAD funded project in developing erosion resistant runner based upon design optimization. The project ended in the year 2014 with the design computationally compared for erosion resistivity. The relative velocity at the outlet was reduced to reduce erosion, with minute compromise in the efficiency. [3] This work is a continuation of R&D of TTL in developing erosion resistant Francis turbine. It is an important perspective to include design optimization for sediment handling in case of guide vane as well. The erosion at the hub, shroud, tip and symmetric section limits the proper functioning of the guide vanes resulting the deterioration of performance at overall operation scenario. Leakage flow, secondary flows around the profile, wakes, vortex etc. are some of the major issues related with the guide vane erosion. Particularly they result into erosion due to Turbulence, secondary flow, Leakage flow and acceleration in the vicinity of the Guide Vanes. 2
1.2.Rationale Guide Vanes in Francis turbine performs periodic movement through pivoted support in response to the change in load and flow of turbine. In order to allow this movement, small clearance gaps (Figure 2) are allowed.
Figure 2 Cross Section View of Francis turbine [4] In a Francis turbine, internal pressure decreases with decreasing radius of the region. From Figure 3, point 1 has higher pressure compared to point 2, which forces water to cross the vane from gaps, to reach point 2.This secondary flow is leakage and cross flow through the gaps. This flow energy remains un-utilized and disturbs the main flow stream. It has been considered a major part of internal losses. Brekke [5], 1988 in Figure 4, illustrates losses at different regions from inlet to outlet of a High Head Francis Turbine. The possible total loss in a high head Francis turbine is around 5%–6%, during the operation in BEP. With minimum dry gap, losses of around 1.5% occur through leakage. In presence of sediment flowing with water, due to erosion these gaps are further increased. In addition to it, wall roughness increases, affecting life and performance of Francis turbine.
3
Figure 3 Cross flow through Guide Vanes of Francis turbine
Figure 4 Losses in Francis turbine
4
1.3.Research gap i. Trend of erosion in Guide Vanes of Francis turbine Past activities were found to be absent in describing qualitative and quantitative specialized trend of erosion in guide vanes and vicinity of Francis turbine. ii. Effect of erosion on flow around guide vanes of Francis turbine Post erosion phenomena in terms of simplified clearance gap has been discussed from late 80s to present days but actual effect of erosion has not been explored yet. iii. Selection of Guide Vane profile for erosion handling The research gap lies in forwarding possible design modification attempt for minimizing erosion in guide vanes of Francis turbine. 1.4.Research question i. What is the trend of erosion in Guide Vanes operating in Sediment Laden Flow? This refers to qualitative and quantitative trend of erosion in guide vanes of Francis turbine operating in the hydropower originating from Himalayan River. ii. What are the effects of erosion on flow around guide vanes? This refers to post erosion effect on flow around guide vanes of Francis turbine. iii. How can erosion be minimized with design modification? This refers to erosion reduction through design modification of guide vane profile. 1.5.Objectives i. To observe sediment erosion in Guide Vanes of Francis turbine. ii. To investigate the erosion and its effect on flow in the eroded guide vane at different clearance gaps. iii. To propose a design of guide vane in order to minimize the sediment erosion.
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1.6.Scope This work is limited to study in guide vanes of Francis turbine. The major focus is on Sediment erosion in Guide Vanes of Francis turbine, effect of clearance gap on performance of Francis turbine, effect of erosion on flow around guide vanes and selection of guide vane for erosion handling. 1.7.Methodology This work was performed in four phases, study of flow around guide vanes of Francis turbine, Study of erosion in Guide Vanes of Francis turbine, Effect of erosion on flow around vanes and possible majors for solution through design modification. An approach on problem identification, effect analysis and solution has been forwarded. Following activities were performed with described method and outcome in it: i. Background study Background of this research is focused on guide vanes, its construction, systems, flow around it and profiles of vanes. These prospects were examined based on literatures available. After which, flow phenomena, estimation method, guide vane system and activities in it along with possible research gaps were identified. ii. Sediment erosion problem in guide vane of Francis turbine Sediment erosion in guide vanes of Francis turbine has not been specifically explored hence collection of data from scattered literatures and field observation were major methods for this activity. After which, quantitative and qualitative erosion on guide vanes of Francis turbine has been identified. iii. Effect of Erosion Estimation of effect of erosion is the prime activity of this work. Post erosion phenomena in guide vanes have been studied based on field observation, computational analysis and experimental investigation. Effect of clearance gap on performance of Francis turbine and effect of erosion on flow around vanes were found. 6
iv. Possible solution From preceding study of this work, erosion in guide vane, it emergence and effect has been identified. Based on computational and experimental study, modifications were done to select suitable hydrofoil to handle erosion.
Figure 5 Work flow and methodology implemented
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CHAPTER 2.
LITERATURE REVIEW
2.1. Design and Construction Guide vanes are symmetric or unsymmetrical hydrofoils, attached with shaft to direct water into runner. The joints with shaft has fillet for smooth flow, as shown in Figure 6. Shaft bears guide vane load though Hub and shroud edges, which passes through upper and lower facing plates and eventually bolted at covers with plain bearing or bushings. Thus attached shafts are connected to each other through linkage mechanism and are operated manually, pneumatically, oil control system or servo mechanisms. Position of vane rotational axis is determined based on CFD calculations and laboratory testing. The net torque experienced during operation may cause fast opening eventually hitting the runner inlet or rapid closing of the vanes. Hence, selection processes ensure zero torque at low guide vane opening. Usually for Micro Hydro applications, axis position is set at two third of the vane length (from outlet) [6].
Figure 6 Guide Vane construction [7] Guide vanes or wicket gates consists of numbers of vanes, pivoted in between the facing plate, which directs and regulates water into the runner. Moreover, through movable pivoted mechanism, it conveys tangential velocity and angular momentum to runner, bearing radial part of turbine flow. Flow at guide vane outlet is not affected by runner vanes; hence guide vanes are designed based on free vortex flow theory. The longer the vanes, better is the directing however this increases losses. Figure 7 shows variation in pressure and kinetic energy inside Francis turbine from guide vane inlet to runner outlet. 8
Francis turbines are designed at Best Efficiency Point [BEP] but are operated in varying operating conditions (to meet demand). Operational angle of guide vane is a function of turbine speed and flow, hence sensing either of these instantaneous changes, control mechanism responds. Speed number (Equation (1)) is a dimensionless parameter collectively representing the speed and flow at BEP hence the opening range of vane is described in Equation (2) as [6]; Ω = 𝜔∗ ∗ √𝑄 ∗
( 1)
Where the maximum angle (αo) of vanes at full load is given by; 𝛼𝑜 = 4 ∗ (−4 ∗ Ω2 + 13 ∗ Ω + 1)
(2)
Figure 7 Flow phenomena in Francis turbine [6] Neopane, 2011 in his doctoral thesis discussed an additional technical factor of interrelationship between particle swirl at suction side and guide vane opening. In operational ranges, relation between velocity ratio and guide vane opening should be maintained, such that particle exit with water (no secondary circulation of particles). 9
Figure 8 represents interrelationship between guide vanes opening with respect to particle size at different runner diameter [8]. It was calculated based on the author’s experiment in a swirling flow test rig at Water Power Laboratory-Norwegian University of Science and Technology [WPL-NTNU].It is an additional limiting criterion for defining guide vane opening of turbines, operating in sediment laden water. Guide vane angle should be larger in larger turbines where water flows with larger particle size.
Figure 8 Location of guide vane based on sediment handling [8] Number of guide vanes should be different from runner vanes to prevent resonance by blade passing frequencies [9].Selection of the number is performed based on noninteger division value of number of guide vanes by runner vanes. Figure 9is the empirical description on trends of selection of number of guide vanes based on speed number which was summarized by NTNU, Norway based on implementation practice and experiences.
10
Number of Guide Vanes
30
28
26
24
22
20
18
16 0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
Speed Number
Figure 9 Selection of number of guide vanes [6] Vane height is shorter for a low specific speed turbine, hence runner inlet flow circulation is maintained with larger curvature diameter (Larger than runner inlet diameter). General diameter range is (Equations 3); 𝑟𝑔𝑣 = (1.15 𝑡𝑜 1.26) ∗ 𝑟1 For high specific speed turbines; (Equation 4) 𝑟𝑔𝑣 = 1.16 ∗ 𝑟1
For low Specific speed turbines; (Equation 5) 𝑟𝑔𝑣 = (1.18 𝑡𝑜 1.2) ∗ 𝑟1
( 3)
( 4)
( 5)
High flow velocity at narrow cascade, causes serious abrasion on these surfaces. Hence curvature diameter for turbine operating in sediment laden water are made larger compared to the conventional design [10]. This increases passage size and thus reduces velocity. For operation in sediment laden flows, (Equation 6) 𝑟𝑔𝑣 > 1.2 ∗ 𝑟1
11
( 6)
2.2. Flow around guide vanes At guide vane flow enters from stay vanes and exits to runner. This exiting flow, swirl and acceleration are governed through periodic movement of guide vane foil, along pivoted support. Leading and trailing edge of Hydrofoil profile, clearance gap, shaft and angle are the major physical factors associated with this flow. Presence of shaft in high velocity water generates wake whose intensity is dependent on Reynolds number. In Francis turbine, these turbulent wake results into drag causing loss of hydraulic energy. Figure 10is the radial view for flow passing the bluff body. From 1 to 6 the wake gradually increases with Reynolds number. This in addition increases turbulent energy and number of eddies. [11] [12] [13] 1
𝑅𝑒 < 5
2
5 − 15 ≤ 𝑅𝑒 < 40
3 4
40 ≤ 𝑅𝑒 < 90 150 ≤ 𝑅𝑒 < 300 300 ≤ 𝑅𝑒 < 3𝑥105
5
3𝑥105 ≤ 𝑅𝑒 < 3.5𝑥106
6
3.5𝑥106 ≤ 𝑅𝑒 < ∞
Figure 10 Wakes in flow passing cylinder [11] Qian [14], during his Doctoral thesis, performed experimental study for measurement of unsteady flow at the stator of Francis Turbine using PIV experiment and miniature piezo-resistive pressure sensors. It was performed for light overload, BEP and Partial Load conditions with Q11/Q11n = 1.08, 1, 0.75 at 10 different phase positions. At BEP, in inter guide vane channel, small recirculation were found but no evident unsteady flow were reported. The flow at exit of the stator was strongly non uniform with higher velocity fluctuation at part load conditions. It was found that the best flow guide is at Best Efficiency Point and light overload points. The variation in power demand is achieved by opening or closing GV, this does not allow the BEP operation and results into formation of secondary vortex formation and destruction [15]. 12
Antonsen [16] in his PhD work performed experimental and numerical study of the unsteady flow due to guide vane and possibility of achieving uniform pressure at runner inlet. From the experiment, wake developed and their natures were studied. It was found that the guide vane passing wakes can be described through classical wake theory. Wake induced in the flow will change flow direction at inlet, causing alteration in inlet angle. This change in inlet angle varies the angle of attack causing increased induction of wake and resulting dynamic loading on runner vanes. Hence selection of suitable profile can assist in achieving uniform pressure around the guide vanes and hence increases stability of runner. Figure 11 is the velocity wake plot at guide vane outlet.
Figure 11 Velocity wake profile at guide vane outlet [16] Thapa et. al. [17] studied, flow around guide vanes of High Head Francis turbine, though 1 guide vane cascade system using Particle Image Velocimetry (PIV) in a symmetric NACA profile. Figure 12 (i) is velocity contour plot. The flow velocity distribution and point of stagnation at leading edge and wall can be visualized. In addition to it, unbalance trailing edge flow can also be observed. The existence of pressure difference along sides of profile can also be seen. From energy conversion diagram in Figure 7, meridional velocity increases towards decreasing radius, according to the continuity law and Bernoulli’s theorem, pressure energy must therefore decrease toward decreasing radius. Due to this energy conversion, 13
guide vane will have high and low pressure side. In Figure 12(ii), pressure at 1 must be higher than 2 since it is at larger radius. Hence, 1 and 2 are at Pressure and suction side of the guide vane. This pressure difference between 1 and 2 pulls water to point 2 giving rise to leakage flow across the facing plate. This leakage flow disturbs main flow in the guide vane channel, which also causes swirl flow at the distinct region of clearance gap. Thus generated leakage flow never enters the runner channel and leaves the energy unutilized, which eventually reduces the efficiency and bears major part of total loss in Francis turbines. In off design conditions, non-uniform velocity field at guide vane inlet is further amplified, increasing pressure difference which accelerates leakage flow. Antonsen et. al. [18] discussed small guide vane openings as the reason for major efficiency loss due to clearance gap because of higher pressure drop. At closed guide vanes the entire energy is converted to pressure energy and this pressure energy decreases with increasing guide vane opening. At the gap, directed flow deviates from the main stream and crosses guide vane axially, resulting cross flow which disturbs the main flow at suction side. Thapa et. al. during his study of flow around guide vane explored the effect of 2mm clearance gap on flow. Figure 12 (iii) shows the velocity contour plot in the middle span of 2 mm gap. Flow stagnation around shaft and cross flow vortex induced in the gap was observed.
(i)
(ii)
(iii)
Figure 12 One Guide Vane Casade study of flow and phenomena of leakage flow [17] Donaldson in 1959 [19], studied flow induced vibration frequency and amplitude and wake dynamic at different trailing edge geometry in a Francis turbine. It was found trailing edge geometry is strong function, governing turbine instability. Significant reduction in vibration with 30o oblique cut of blunt trailing edge was found. Figure 13is 14
the experimental plot showing relative amplitude at different flow velocity for various trailing edge geometry.
Figure 13 Vibration amplitude of various hydrofoil trailing edges [19] Zobeiri et. al. [20] studied flow effect on NACA 009 stainless steel hydrofoils with truncated and oblique b = 30otrailingedge of same sizes in high speed cavitation tunnel, with test section of 150 x 150 x 750 mm, maximum inlet velocity of 50 m/s and maximum static pressure of 16 bar. In vanes, shedding frequency increases with velocity except, at 12 and 14 m/s in truncated and 13 to 15 m/s in oblique vanes. In the oblique geometry the lower region of detachment for the cavitation vortices shifts upward colliding with each other in the passage resulting into the redistribution of the vortices, Figure 14. As a result the resultant vibration originated from the flow is lesser in oblique trailing edge compared to the truncated one. Figure 15 shows the normalized mean and standard deviation of the stream wise velocity for the two different trailing edge geometry under lock in condition where unsymmetrical thickness of the wake at downstream of the oblique trailing edge was observed.
15
Figure 14 Vorticity evolution during the shedding cycle in truncated and oblique trailing edges [20]
Figure 15 Normalized mean and standard deviation of the stream wise velocity [20] Further optimization to minimize trailing edge effect has been felt hence researches are also performed in this direction. Lewis et. al. [21] studied over a design modification approach to reduce resultant oscillation cause vortex trailing edge. Internal water blowing through trailing edge can eliminate Von Karman’s vortices at downstream. Sand in water does not make its new path rater causes severity following the path of water. Above we examined the path of water around guide vane, with which severity 16
occurs which has been examined. Section 4 of this work describes the nature of erosion in the guide vane and its periphery based upon the field observation. Zhao et. al. [22] studied flow phenomena through the gap between two perpendicularly arranged flat plates. This study showed proportional relation between clearance gap, pressure difference and leakage flow. A simplified test setup was used to develop empirical relation for leakage flow rate (as a function of area of gap and pressure difference across it). This relation can be used for leakage flow approximation to ascertain the vulnerability of operation. 𝑄 = 𝐴𝜇√2𝑔∆ℎ
( 7)
Flow coefficient for incompressible flow was derived to be Equation 8. 1 𝜇2
𝑙
= 0.0011 (𝑠) + 1.609
( 8)
Koirala et. al. [23] 2016 studied guide vane clearance gap erosion phenomenon, based on computational estimation and field observations. Clearance gap erosion induces at pressure side of gap which eventually spreads inside, further eroding the surfaces. Fine sediment particles are more responsible for this kind of erosion since the gap sizes are smaller. Field observation showed, clearance gap increases with operational time, with which cross flow vortex and eventual losses increases. Figure 16 (i) shows the computational result with cross flow through gap. Eide et. al. [24] [25], performed analytical and numerical study on sensitivity of clearance gap caused by mechanical deflection in head cover at Pressurized conditions. A computational model with guide vane clearance gap of 0.25 mm, 1 mm, 2 mm and 4 mm that could possibly occur during the deflection was considered for the study. The resultant of pressure drop from pressure side to suction side in decreasing radius caused inevitable induction of cross flow. Pressure from inlet to outlet of the guide vane increases, also the amount of cross flow. At the inlet, leakage flow in radial direction was observed due to insufficient pressure for flow blockage. The guide vane shaft forms 17
pressure and velocity stagnation around it as shown in Figure 16 (ii) as radial boundary vector plot in flow cascade.
(i)
Stagnation of flow around guide vane shaft
(ii)
Figure 16 Cross flow and flow stagnation around shaft hole in Clearance gap [23] [24] In addition to gap erosion; erosion on foil surfaces, leading and trailing edges has considerable effect on flow around vanes. The surface erosion causes friction drag on the flow resulting flow stream vortex and high friction losses. Figure 14 explains the effect of trailing edge geometry on flow passing guide vanes. Trailing edge tip erosion changes its shape, further increasing oscillatory problem, as flow passing it reaches the vaneless space of rotor stator region. These operational phenomena are serious issues related with high head Francis turbine that are yet to be explored. Development of logical test facility and study of above mentioned features are important prospects for future Research and Development. In order to fulfill these research gaps, rigorous study in laboratory facility is important. A laboratory test rig with the facility of estimation of effect of erosion needs to be developed. Section 6 of this paper further more elaborates on possible concept of test facility development. 2.3. Estimation and Observation of Erosion in Guide Vanes Experimental study of effect of erosion on guide vanes is a destructive process, focused on estimating the effect on base materials, coatings and profiles. Additionally, it is the only method to approximate effect on performance due to erosion. It can be done either by field testing at actual operating condition or through laboratory replication with accelerated test. Estimation of effect at actual condition is often qualitative, which takes longer time and is difficult to summarize the effect, hence laboratory testing has been 18
prioritized. Laboratory estimation can be done either by particle, specimen or both in motion, where relative velocity is important. [26] Estimation of erosion is laboratory condition allows examination by varying several independent parameters to observe changes in variable parameter. Usually observations are performed through accelerated test in laboratory facility/ rigs. Guide vanes are associated component of Francis turbine and estimation of erosion on it (at laboratory condition) requires flow similarity in vanes. Both comparative and absolute studies on design are possible. Below we present some of the relevant past practices implemented for estimation of erosion. Pugsley et al. [27] compared wear response of WC-Co with standard material in a slurry erosion environment using suction at nozzle to mix eroding particles into working fluid inside test chamber. Thapa, 2004 [26] and Paudel, 2013 [28] performed, experiment using high velocity jet. This is considered as one of the most widely used methodology for estimation of material resistivity on the specimen. Usually a flat plate specimen is clamped in a jig and sediment laden water through jet hits the specimen to perform the experiment. Sediment particles were separately retrieved to minimize effect on pump. Bajracharya et. al., 2006 [29]used another type of jet type rig with the facility to use the water in loop. The sediment isolation through inclined settlement is its major feature. These concepts simplify test system, since sediment management is a crucial issue in these erosion tests. Rotating Disc Apparatus are rotating type test setup, originally designed for estimating material loss through erosion and erosion cavitation combined effects [30] [31]. It was latter modified by Rajkarnikar et. al. [32] to compare erosion handling of Francis runner blades(Figure 17(a)) and by Shrestha et. al. [33] to estimate erosion on cross flow turbine runner vanes. Maintaining leading edge tip velocity during guide vane rotation inside RDA, estimation of material loss on designs can be performed. It can facilitate in multiple design comparison and observation. One of the most appropriate methods for erosion study is using a guide vane cascade system, which maintains flow similarity with prototype turbine. Antosen [16] in his 19
work used 5 guide vane cascade system for flow phenomena study (Figure 17 (b)). Thapa et. al. [34] proposed design of 1 guide vane and 3 guide vane cascade. The flow similarity was maintained based on the computational study (Figure 17 (c)). This preserves the actual operational essence in the experiment environment and provide with more close results.
(a)
(b)
(c)
Figure 17 Possible facilities for guide vanes erosion test [32, 16, 34] Estimation of sediment erosion and post erosion effect on flow are two major research gaps in the field. The effects of sand on design are usually measured with material or thickness loss. Overall material loss can be estimated with weighing machines of high precision [35] but localization of the erosion cannot be predicted via it. Erosion Resistance Probe (ERP) [36] can be used for laboratory and field measurement of erosion thickness (Figure 18 (a)). ER measures with linearized resistance signal at localized region, which is proportional to the metal loss or thickness depleted. Thickness measurement through gauge is another option to estimate the loss. Guangjie et. al. [37] used MINITEST-1100 (Figure 18 (b)) during field observation to estimate thickness loss in Francis runner vanes. Rai et. al. [38] used an innovative and more reliable technique for erosion estimation using 3D scanner (Figure 18 (c)). Eroded specimens were 3D scanned and compared for the volume loss. His application can be further used with 3D modeling of the scanned surface, mesh generation and further more computational study for estimating post erosion phenomena on flow. The method of Antosen and Thapa (Figure 18 (d)) with LDV and PIV on eroded profile may give more reliable result on erosion loss and post erosion phenomena.
20
(a)
(b)
(c)
(d)
Figure 18 Facilities for measurement of effect of erosion [36, 37, 38, 34]
21
CHAPTER 3.
FIELD STUDY
At guide vane cascade highest acceleration occurs that results into higher amount of erosion resulted from sediment particles of different sizes. Theoretically four kinds of erosion are more prominent in guide vanes; Turbulence erosion, Leakage Flow erosion, Secondary flow erosion and acceleration erosion. Turbulence erosion is caused at outlet of guide vanes due to high velocity of fine sediments. Secondary flow erosion occurs at the cornets between facing plates and guide vanes due to horse shoe vortex. Leakage flow erosion is often caused by fine sediment particle at the guide vane clearance gaps. Acceleration erosion are caused due to rotation of water in front of runner. Figure 19 shows erosion mechanism in guide vanes of Francis turbine. So far earlier work lacks data and nature on guide vanes erosion of Francis turbine. This work fulfills the gap to some extent. During this course of this study, author visited power plants and took the relevant data, presenting the current operational scenario of guide vane in sediment laden water.
Figure 19 Sediment erosion in Guide Vanes of Francis turbine [39]
22
Panauti Hydropower Plant, Nepal At Panauti Hydro Power (3x800 kW), author inspected the erosion after the disassembly, on an operation of approximately 8000 hours, for rehabilitation and overhauling. Major erosion was observed at outlet which blunted trailing edge. The pressure and suction side had increased roughness. Comparative study of overhauled and the old guide vanes were performed and found to be weight loss of 625-892 grams in guide vanes, with the original weight around 6.5 kg. Figure 20 shows the guide vane erosion at Panauti Hydropower Plant, Nepal.
(ii)
(i)
(iii)
(iv)
Figure 20 Sediment erosion in Guide vanes at Panauti Hydropower Plant Sunkoshi Hydropower Plant, Nepal At Sunkoshi Hydropower Plant (3x3.3 MW), the turbine units were dismantled for inspection of effect of earthquake. It was observed that the surfaces of the guide vanes were eroded visualizing the drag path of sediment as shown in the Figure 23A (ii). High roughness was observed. At leading and trailing edge comparatively higher erosion with chipping effect on vanes were observed (Figure 23 A (iii,iv)). This in-turn increases hydraulic losses due to friction and induces guide vane wakes. No traces of erosion were seen on the upper and lower ends of guide vanes. Small traces of wear were found 23
in the facing plate in the region around shaft because of the recirculation of flow and direct impact on the bluff body (Figure 23 C (i)). Apart from the guide vane, the regions with internal facing plate bolts were found to have effect of sediment cavitation combined effect (Figure 23 C (ii)). Jhimruk Hydropower Plant, Nepal At Jhimruk Hydropower Center (3x4 MW), sediment monitoring systems are installed at river intake, end of settling basin and end of Headrace tunnel. In between 1994 – 1997, the highest concentration of the sediment was recorded to be 57,094 PPM however, 90% of the time it was recorded below 5000 PPM [40]. Higher amount of quartz content was found in the samples smaller than 0.09 mm. After 4000 hours of operation in 1994, guide vanes and facing plate were in un-repairable conditions even through the plant operated only for 1/4thtime in monsoon. Most of the damages were observed in outlet edges and bottom. Vortex erosion at the facing plates on different guide vanes openings with maximum effect on neutral position was observed. In 2001, during the inspection major erosion in the shaft and faces of guide vanes were observed with grooves of 4 mm depth and 11.5 mm width [26].
(i)
(ii)
(iii)
Figure 21 Sediment erosion in Guide Vanes and facing plate at Jhimruk Hydropower Center [26] Bhilangana Hydropower Plant, India At Bhilangana Hydropower (3x8 MW), in Utarakhand, India, it started operation from the year 2012. In the first year of operation turbine were operated without coating. Soon in next one year severe damages were observed in all exposed turbine components, including guide vanes, by then unit 1 was operated for 4,288 hours, unit 2 for 4,467 24
hours and unit 3 was operated for 2,879 hours. For 79.1% time the turbines were operated in the sediment concentration ranging from 0 – 500 PPM. During monsoon, when concentration reaches higher than 2000 PPM, the plant was shut down. The turbine were coated with HPHVOF coating in 2013 and again by the next 5,528 hours, the guide vanes of unit 1 were replaced due to serious erosion in the shafts, bushing and guide vane surfaces. In all the units guide vane erosion was common on the lower side in the direction of water flow, faces and at lower bolting arrangement. Consecutively, the turbines were overhauled 2 times by 2014. The amount of sediment passing through all the units of the turbines were monitored and it was found that between 2012-2013 15265.5 Tons , 16129.24 Tons and 15622.8 Tons silt passed through unit 1, 2 and 3 respectively. Whereas, in the year 2013-2014, 23003.9 Ton, 26028.7 and 17850.23 Ton sediment passed through unit 1, 2 and 3 respectively, despite of the 50% operation in monsoon. Figure 25 shows the damages around guide vane in the plant. Middle Marsyangdi Power Plant, Nepal At 69 MW Marsyangdi Power Plant, they have sediment monitoring unit for constant monitoring at headworks and turbines. During 1991-1998, the suspended sediment passing through headworks was approximately 16.7 million tons. The highest concentration was observed to be 15164 mg/ltr [41]. The sediment sample from the plant was analyzed and found to have 60% Quartz [42]. After 70,000 hours, significant erosion was recorded in the guide vanes of the Francis turbines. The clearance gaps between the facing plate and Guide Vane was recorded to have increased from 0.3 mm to 1.6 mm.
Before Maintenance
After Maintenance
Figure 22 Sediment Erosion in Guide vanes at Middle Marsyangdi HPP 25
Kaligandaki – A Hydropower Plant, Nepal At Kaligandaki – A (3x48 MW) Hydropower project, it was found to be highly vulnerable to erosion. The guide vane faces, leading edge, trailing edge, clearance gaps, facing plate, internal bolting holes and almost all the parts associated with the guide vane were eroded. The sediment samples from the desilting basin and the Downstream were analyzed at sediment lab, TTL and it was found that higher percentage of sediment were in the range between 300 µm and 600 µm. In the Figure 24 (iii), A+C is the clearance gap at the inlet region and B+D is the clearance gap in the outlet region. From the observation after an operation of 8500 hours it was found that the clearance gap increased to 1.8 mm at the inlet region and outlet region. Similarly after 16500 hours of operation, this gap at inlet increased to 4.5 mm and 6 mm at the outlet. The alternate increment in erosion pattern was observed in the guide vanes as shown in Figure 24 (iv). Erosion at the clearance gaps are induced by the leakage flow during the initial operation with 0.3 mm gap. As described in the section 3, the inlet region has less pressure hence lower cross flow and lesser erosion whereas this increases with the decreasing radius resulting into higher clearance gap at the outlet after an operation of 16500 hours. The erosion at the guide vane shafts, surfaces and trailing edges are other major erosions in the plant (Figure 24 (i, ii)). Due to higher erosion the tip gap at the full closing of guide vane reached to 4 mm resulting into the higher amount of tip losses. This may have caused during the operation at lower angles. [43]
26
A.ii
A.i
A.iii
A.iv
B.
C.ii
C.i Figure 23 Erosion in guide vanes and facing plates at Sunkoshi Hydropower Plant
27
(i)
(ii)
(iv)
(iii)
(v)
Figure 24 Sediment erosion in guide vanes at Kaligandaki-A Hydropower Plant
Figure 25 Sediment erosion in Guide Vanes at Bhilangana Hydropower Plant, India From the observations it was found that the leading edge, trailing edge, clearance gaps and faces of the guide vanes are vulnerable to the erosion. The adjacent component 28
facing plates were found to have severe erosion, especially at shaft hole, vane clearance gap and internal flat bolt holes. Figure 20 (ii) and Figure 23 (iii) shows the erosion at the outlet of the guide vanes, they are due to the turbulence erosion caused by the high velocity fine grain particles. Erosion at the corners like the one in the Figure 24 C (ii) and at the Marsyangdi Hydropower plant are due to the secondary flow horse shoe vortex caused by fine and medium sized particles. Figure 24 (i) shows erosion at the clearance gaps due to the leakage flow and are called leakage erosion. Figure 25 has the erosion caused by velocity stagnation and axial transformation of vortex formed at point of stagnation. Impact of both finer particles and larger particle are seen. Most of the severe erosion in guide vanes is due to the fine grain particle [44]. Guide Vane erosion is strongly dependent on guide vane profiles. Dahl [45] performed, computational analysis of Francis turbine with different guide vane profiles (Set of symmetric and unsymmetrical profiles). The result showed significant change in Erosion Rate Density by varying guide vane profiles. Quantitative study with experimental observation should be performed to identify the pattern.
29
CHAPTER 4.
COMPUTATIONAL STUDY
4.1.Effect of Clearance gap on Performance of Francis turbine 4.1.1. Computational Model This analysis used the geometry of model Francis turbine scaled based on IEC 60193, optimized for sediment handling by Turbine Testing Lab (TTL), Kathmandu University [46]. It was developed in reference to Jhimruk Hydropower Center (JHPC), Nepal. Separate domains for Spiral Casing, Stay Vanes, Guide Vanes, Runner and Draft tube were defined. This project is a continuation of earlier research activity performed by TTL with a vision of developing an erosion resistant Francis Turbine. Computational Domain The meshes were generated considering 5% convergence criteria in Grid Independent Analysis with an interval of 1.5 times mesh size. ICEM (a powerful meshing software) and Turbogrid meshing features of ANSYS (Analysis System software) 14 available at State Key Laboratory of Hydroscience and Engineering, Tsinghua University, China were used. Blades and Stay vanes were meshed using ATM optimized features of Turbogrid, whereas Spiral Casing, guide vanes and Draft tube were meshed using manual block refinement in ICEM to generate structural mesh. The flow cascade consists of 17 runner vanes, 24 guide vanes and 24 stay vanes. A single 3 Dimensional guide vane flow cascade was developed to generate high quality mesh. Stay vanes, guide vanes and runner vanes were transformed in CFX-pre. Table 1 presents mesh details of the components. Table 1 Mesh Description Domain Spiral Casing Stay vane Guide Vane Blade Vane Draft Tube
Total Nodes 850,831 2,460,240 2,616,936 1,196,800 319,235
Unit Nodes Min Angle 850,831 81 102,510 81 109,039 22 70,400 38 319,235 80 30
y+ 830 41 220 61 316
In contradiction with the practice, this computational approach implemented the practical design of guide vane with shaft, fillets and clearance. Seven different guide vane domains with clearance gaps of 0, 0.5, 1, 1.5, 2, 2.5 and 3 mm were prepared. The selection of gaps was based on the site observation, prototype to model relation and computational result in Figure5 shows hex dominant mesh in guide vanes and the runner.
Guide Vane Section Mesh
Turbo grid Mesh in Blades
Figure 26 Hexahedral mesh of guide vane made in ICEM and Runner made in Turbogrid Preprocessing Mass flow inlet of 227 kg/s and pressure outlet to atmospheric pressure was used as boundary conditions, since this has been found to be robust with fluid flow simulation. Rests of the boundaries were defined as interfaces and no slip walls. Frozen rotor interface was selected between the stator and rotor. Turbulence was simulated using Shear Stress Transport Turbulence model, due to its robustness in predicting both near and away wall boundary flows. Figure 27 shows the boundary condition in flow passages. The RMS for solution convergence has been selected at 10-4. All computations were performed in a cluster computer with eight CPUs of Intel 5645, 2.4GHz processor, 96 GB RAM and 2 TB storage.
31
Spiral Casing Stay Vanes Guide Vanes
Draft Tube Outlet
Runner Vanes Inlet
Figure 27 Computational domain 4.1.2. Clearance Gap Approximation Thickness depletion analysis through CFD was performed in the prototype design of the turbine. Guide Vane and its periphery were observed. The designed clearance gap has been used for analysis purposes. At Jhimruk Hydropower Center, a higher concentration of sand has been found in the range from 0 to 90 µm with a higher percentage of quartz, hence, considering the effect of sand size of 30 µm and shape factor 1, this analysis was performed [47]. At best efficiency point, the maximum erosion at leading edge of guide vane was observed. The study priority was given to erosion in clearance gaps and was found to be distributed over gap regions in both the leading and trailing edges and in facing plates. CFD analysis gives Erosion Rate Density (ERD). With some additional processing, thickness depletion was computed. Equation (9) was used to calculate the loss of thickness. ℎ𝑒 =
ERD ∗ 𝑇𝑖𝑚𝑒 𝜌𝑚
(9)
Where he is the eroded height, ERD is the erosion rate density, Time is the time of operation and ρm is the density of material. 32
The observational time of about 1 year, i.e., around approximately 7000 hr has been considered, variable area is cancelled in equation terms and density of turbine material is 7850 kg/m3, hence eroded depth was calculated. The erosion model of Tabakoff and Grant was used since it was defined for Steel-Sand interaction. Figure 28 is the result with around 3 mm loss in the facing plate and a similar amount of loss in the guide vane edges. Suction side Pressure side
Guide Vane Clearance Gap
Facing Plate Figure 28 Thickness depletion in the facing plate In 2001, at Nepal Hydro and Electric Company, Butwal, when the turbine from JHPC was observed in an operation of around 4212 hr, facing plate depth was found to be around 4 mm and the height of the guide vane was also decreased [26]. In this further computation, the 0.46 times scaled IEC standard model has been considered with simplified gap spaces of up to 3 mm in an interval of 0.5mm to observe the effect. 4.2.Selection of Guide Vane Profile for Erosion Handling This study uses four digit NACA hydrofoils for guide vane. Here, hydrofoils with chamber percentage of 0% and 40% and maximum camber of 0%, 1%, 2% and 4% were used to select best profile for erosion handling. Computational and experimental studies were performed on the profiles shown in Figure 29. 33
These profiles were generated with GUI based MATLAB interface developed for plotting guide vanes of different profiles at different angles for Francis turbine.
NACA 0012
NACA 1412
NACA 2412
NACA 4412
Figure 29 Guide Vane profiles for analysis Computational Method Computational analysis for sediment erosion in guide vanes of Francis turbine with commercial CFD software Analysis System (ANSYS) allows single periodic passage flow of SV, GV and RV with rotational periodicity (Figure 30). Geometry considered for this study is an earlier research of Turbine Testing Lab, Kathmandu University which was generated for erosion handling in runner vanes [46]. Mass flow inlet of 92.92 kg/s and outlet pressure of 1 atm, used for proper convergence of result. Inlet swirl was defined with cylindrical coordinate system (Table 2). Runner rotates at 1000 rpm in clockwise direction and defined to have frozen rotor interface with the stator. Reynold’s Average NavierStoke’s Equation with Shear Stress Turbulence model was used to simulate turbulence flow within the turbine. Particle size ranging from 200-300 µm with flow rate of 0.5 kg/sec were inserted for the calculation. The range of particle and its flow rate were selected based on field observation. Interaction of the particle with no slip walls were defined with parallel (0.8) and perpendicular (1.0) restitution coefficients. Computational method of Neopane has been adopted for this calculation [8]. All meshes were developed using, Turbogrid from coordinate files extracted through design tool. Two major sensitivity parameters were considered; y+ value and injected number of particles. Figure 31is the plot for particle number independency test. 34
Table 2 Boundary Condition Inlet Flow Direction (0, 0.509701, 0.860352) Convergence Criteria 10-5 RMS size (a, r, t)
Figure 30 Computational Domain 1.6E-06
ERD[Kg.m-2.s-1]
1.2E-06
8.0E-07
4.0E-07
0.0E+00 0
4000
8000
12000
16000
20000
Number of Particles
Figure 31 Particle number independency test Table 3 Mesh Information Component Stay Vanes Runner Vanes Guide Vanes
Node Size 102,510 170,400 109,039 – 110,516
35
Min angle 81 38 20-31
y+ 41 28 32-37
CHAPTER 5.
EXPERIMENTAL STUDY
5.1.Effect of Guide Vane erosion on Flow around it Earlier attempts focused on simplified approach for effect of increased clearance gap prediction. In contrast to it, here an additional attempt of effect of friction due to increased roughness after erosion will be studied. Erosion estimation is a destructive process, involving a test setup with agent and specimen. In a test rig either specimen or agent for both is moving, relative velocity between them is important. Laboratory estimation of erosion in hydraulic turbine is estimated with sand as agent, water as flow medium and turbine component as specimen. Sediment shape and mineral content is an absolute uncontrollable factor, whereas size can be segregated to a narrow range. This result into limitations associated with repeatability and redundancy of sediment erosion estimation [26]. This experiment is associated with erosion estimation and observation of its effect on guide vanes of Francis turbine. A simplified 3GV setup was developed to erode and observe the effect. Computational approach was used to study the flow similarity and structural rigidity. 5.1.1. Design and Development of 3GV Cascade Design methodology of Thapa et al. [34] was adopted to develop experimental setup. This setup has 3GV with flow equivalent to 4 passages. This kind of configuration is suitable to overcome wall effect on flow field of mid guide vane. Figure 32 shows the design concept of the 3GV rig developed for this study. Walls on the test setup were determined based on free vortex theory, further refined with computational analysis to match the tangential and normal velocity component at outlet of vanes (Figure 33). The prime concept for this setup is matching velocity triangle to ensure flow similarity with model turbine, although the effect of rotating runner vanes on guide vanes has been neglected. 36
Parameter Prototype Model Unit H 201.5 35 m Q 2.35 0.17 m3/sec SF 1 0.42 Ngv
24
24
Ω
0.32
0.32
D2
544
228.1
mm
D1
864
362.88
mm
B1
92
39
mm
Figure 32 3GV cascade development methodology
Figure 33 Computational Model for wall refinement The Cartesian velocity components u, v and the angle θ are explained in Figure 34. The terms Cu and Cm are the tangential and meridional components of the velocity, which are analogous to the real turbine. Cu component is responsible for work done and power 37
produced by the turbine, whereas Cm component is responsible for directing the flow downstream. 𝐶𝑚 = −(𝑢. 𝑐𝑜𝑠𝜃 + 𝑣. 𝑠𝑖𝑛𝜃)
(10)
𝐶𝑢 = (𝑢. 𝑠𝑖𝑛𝜃 − 𝑣. 𝑐𝑜𝑠𝜃)
(11)
Figure 34 is the plot for Cu and Cm obtained from analytical calculation, turbine simulation and cascade simulations. Cu-T and Cm-T were calculated from an earlier analysis in Koirala et. al.
Figure 34 Cu and Cm plot of analytical, turbine simulation & Cascade calculation Pressure
Sediment
Tank
Hooper
Sump Tank (a)
3GV Setup
Pump (b)
Figure 35 Test setup 38
5.1.2. Sediment Characterization Sediment samples were collected from Sunkoshi River for this study. Sieve with shaker was used to segregate particle of size ranging from 200-300 µm. Mineral composition analysis was performed at Sediment Lab, TTL-KU. Particle count method with Radial Trinocular Stereo Zoom Microscope having head of 0.7x – 4.5x with Trinocular Camera was used to summarize mineral composition. Quartz content in the sample is over 55% whereas around 25% is Feldspar (Figure 36). These sediment particles were fed from sediment hoper in the rig.
Figure 36 Mineral Composition of Sediment Sample 5.2.Selection Guide Vane Profile for Erosion Handling 5.2.1. Experimental Method In an erosion test rig, either the specimen or agent or both should be in motion, the relative velocity between them is important [26]. Rotating Disc Apparatus [RDA] is one of the accepted ways for simulating erosion phenomena in hydraulic turbines. It was originally developed to study erosion cavitation combined effect on turbine materials, with the need modifications were done for design tests. Rajkarnikar et. al. [32] used it for erosion comparison in reference and optimized design of Francis runner vanes and 39
Shrestha et. al. [33] used it to study erosion in Cross Flow runner vanes. Figure 37 shows the experimental setup of Rotating Disc Apparatus modified to perform erosion test in Guide Vanes of Francis Turbine. Through vane tip velocity of 6 m/s, on a disc of 250 mm diameter, rotating at 458 rpm, flow velocity was comprehended. The arrangement of profile on disc is based on Figure 37 (a). Experiments were performed at 3 GV angles; P1, P2 and P3 as shown in Figure 37 (b). Figure 37 (c) (d) and Figure 38 (a) shows the arrangement and construction in RDA. Particles were manually traced and visualized (Figure 38 (b)) to ensure expected particle swirl around vanes. Test samples were coated with epoxy based spay to visualize location of erosion (Figure 38). Baffles were installed at the circumference of drum to ensure stagnation of sediment and water. Physical description regarding the rig is described in Shrestha et. al. [33]. Additional computational analysis with rotating domain of drum ensured velocity, flow and swirl in the setup for accelerated testing with Aluminum GV. Experiment was performed with sediment size ranging from 150 µm to 300 µm. On each operational cycle, concentration of 66.67 gm/ltr was maintained.
40
Test Vane
Flow
Disc
Direction
Turbine Center
SS
PS
(a) Rotation
P1
(a)
(b) Drive
Electric Motor
P2 P3
Guide Vane
(b)
Test Drum Rotating Disc
(c)
Inside Drum
(d)
(c)
Figure 37 Rotating Disc Apparatus
Figure 38 Rotating Disc
Optimized for erosion test in guide vane
Setup flow description and sample
41
CHAPTER 6.
RESULT AND DISCUSSION
6.1.Effect of Guide Vanes Erosion Based on the observation of erosion through field study and literature survey, location of erosion has been identified. Majorly erosion on clearance gaps, faces, leading edge and trailing edges were observed. The effect of these erosion is another essential research prospect. This section describes it in two parts; Part – I: Effect of Clearance gap on performance of Francis turbine Part – II: Effect of Guide Vane erosion on Flow around it 6.1.1. Effect of Clearance gap on Performance of Francis turbine i. Leakage Flow Rate Leakage flow through varying clearance gap using computational and empirical relation was calculated. Zhao et al. [22], through a series of experiments and computational study in a simplified setup, developed an empirical relation (Equation (12)) for estimating the leakage flow rate. It was derived from the Bernoulli and continuity equation predicting the orifice flow in the gap. The flow region, clearance gaps and flow characteristics in experimental setup justifies the flow similarity. 𝑄𝐿 = 𝐴𝜇√2𝑔Δℎ
(12)
Where A is the cross sectional area, Δh is the pressure difference in terms of water head and µ is the coefficient of flow. Equation (13) was developed based on the regression of the experimental data obtained for various clearance gap and flow conditions. Hence, the flow coefficient was calculated using Equation (13) which is a function of the ratio of clearance length and gap; 1 𝑙 = 0.0011 ( ) + 1.6097 2 𝜇 𝑠 Where, l/s is the ratio of clearance length and gap.
42
(13)
A user defined surface feature in commercial CFD post processing, with four points coordinate defined by .csv (Comma Separated Valued) data file was used to define a finite surface along the camber line in the gap. At this surface, average leakage flow rate across the gap was calculated. Pressure measured across the vane was used in the empirical relation for flow rate (Equation (10)). Figure 39 shows a matching relationship between empirical and computational results obtained from the analysis. In a cascade with 9.45 LPS, flow leakage flow from 0.4 to 1.7 LPS was calculated. Maximum deviation of 17% was found in 1.5 mm gap whereas the rest of the results were below 10%.
Figure 39 Comparison between Empirical and Computational result ii. Hydraulic Performance Figure 40 shows relative hydraulic performance of the turbine at varying clearance gaps. A comparative chart between relative efficiency loss, relative energy drop and relative pressure drop has been presented. The total pressure and kinetic energy at Guide Vane outlet, mechanical efficiency of the turbine and average pressure in the Spiral Casing were observed. All the differences were computed in reference to the obtained values at 0 mm clearance gap. It has been found that, with increase in clearance, gaps losses increases. The proportion of the efficiency drop has been found to be sharply changing with a significant amount of losses. Around 3% efficiency loss, for increase in gap by 43
1% of Passage height is observed. This is similar to the observation by Brekke [5]. Spiral casing pressure was found to drop by 2% with every 1 mm increase in the gap. This can be a major reason behind the problem in pneumatic flow control systems for flow regulation since, during inspection; external mechanical failures were not found. These proportions and trends in the energy change is the result of un-utilized leaked cross flow through gaps.
Figure 40 Variation in hydraulic performance with clearance gap iii. Nature of Leakage Flow So far, literature has been concerned with the trending velocity profile in the gaps between the two surfaces compared to the flat plate flow. However, the flow nature at the gap varies in upper and lower regions due to the presence of edge of guide vane in one side and the flat facing plate on the other side. Figure 41 shows the location of plane for velocity observation.
44
Figure 41 Guide vane measurement position The study was performed considering a percentage region for common comparison of the phenomena. Figure 42 shows velocity distribution over a gap between facing plate and guide vanes at leading edge, where 0 refers to the region near the guide vane edge and 100 refers to the region near the facing plate edge. It was found that the velocity profile is different from general flat plate flow. The magnitude of velocity near the facing plate boundary was found to be higher compared to near guide vanes. This may be due to the continuous flow at the upper region and interrupted flow at the lower region because of the sudden projection of guide vanes geometry. With increasing clearance gap, velocity is found to be decreasing, as defined by continuity equation for the orifice flow. The stiffness in the graph decreases with the increase in the gap since, with larger gaps, flow tends to behave like in a continuous flat plate system. 12
V [m/sec]
10
8
0.5 mm 1 mm 1.5 mm 2 mm 2.5 mm
6
4 0
20
40
% ΔC
60
80
100
Figure 42 Velocity profile over the gap from button to top at leading edge 45
Figure 43 shows the graphical representation of the velocity distribution in the trailing edge. Unlike the leading edge, the velocity distribution seems to be close in all the cases, although the decreasing pattern with increasing gap is similar. The stiffness pattern is also similar to the leading edge. The magnitude of the velocity distribution is higher compared to the leading edge because of the high acceleration with decreasing radius. 17
V [m/sec]
14
11
8 0.5 mm 1 mm 1.5 mm 2 mm 2.5 mm 3 mm
5
2 0
20
40
60
80
100
%ΔC
Figure 43 Velocity Profile over the gap from button to top at Trailing edge Figure 44 is the surface streamline plot of flow in leading edge, trailing edge and radial gap view at various clearance gaps. Based on general observation, leakage flow through clearance gap can be divided as upstream, passage and downstream. It has been observed that flow at the leading edge of the guide vane has large turbulence and accumulation at the upstream region. With larger gap, higher flow affected regions were observed, because of the substantial pressure variation across the vanes. At the trailing edge, along with flow accumulation upstream, an unsteady turbulence vortex was observed downstream. This leakage flow vortex has high turbulent intensities which may result dynamic operational issues. The smaller the gap, the more intense is the vortex, which eventually gets fade because of the change in leakage flow velocity. This turbulent vortex is formed due to flow rolling during interaction of leakage flow 46
with primary flow, while detaching from guide vane tip [48]. The leading edge downstream is found to have fade turbulence since the leakage induced turbulence vortex is largely dependent on the thickness of the guide vane [49]. Apart from this, the radial flow surface plot shows that the flow direction deviation is larger in the trailing edge compared to the leading edge. At the radial region in the gap, a sudden change in the flow direction around gap was observed, due to leakage cross flow. This change in direction is highly intense at the trailing edge compared to the leading edge, resulting higher cross flow across the vanes. During the radial flow, the shaft acts as a cylindrical bluff body, the flow across which forms curl and wake, resulting another secondary flow in the turbine [50]. Gap (mm)
Leading Edge
Trailing Edge
Flow Direction
0.5
1
1.5
47
Radial view
2
2.5
3
Figure 44 Surface plots at the Leading Edge, Trailing edge and Radial view in the gap 6.1.2. Effect of Erosion on Flow around Guide Vanes The prime objective of this study was to identify the effect of sediment erosion on flow around guide vane of Francis turbine. In a simplified 3GV test setup, sample vanes were inserted and tested for the erosion and later the same vane was used for change in cross sectional pressure at three predetermined points. The inlet condition through a 50 mm pipe was set at 105 Pa pressure and 6 LPS flow. Observations were made at constant pressure and flow condition with GV positioned at BEP. i. Erosion in Guide Vanes of Francis turbine Sediment Erosion in Guide Vane of Francis turbine was studied with 3GV test setup. Detachable mild steel shaft system GV was made up of Aluminum (Light weight sample 48
for high accuracy weight measurement). Sediment was fed to the system through a hoper installed in the middle of the delivery pipe at an average rate of 7.8 gm/sec, which make the average concentration to be 1300 PPM. An Aluminum GV was installed in between two mild steel vanes in order to observe the effect of erosion due to mid vane. Figure 45 shows the erosion in mid guide vane after each interval of sediment passed through the system. Total of 21 kg sand were passed and found to have lost about 322.3 mg of weight.
% Cumulative Weight Loss
0.8
0.6
0.4
0.2
0
3
6
9 12 15 Weight of Sediment passed [Kg]
18
21
Figure 45 Weight loss Vs Sediment Passed Author would like to share his experience on vane testing during this work. Primarily all the vanes were of mild steel, numerous experiments were conducted but no significant loss in material weight were found. But changes in surface texture were observable. For adaptability with the objective of this work, author re-developed the setup with Aluminum Guide Vane. Figure 46 and Figure 47 shows the observation of erosion on both the Sample Vanes. MS vanes were also included here, because the author finds it to be more relevant in terms of location of erosion. In addition to it, this strengthens qualitative data on location of erosion on Aluminum vanes. Most of the erosion were observed at leading edge, in addition to it erosion on trailing edge and at trailing edge tip region of clearance gap were observed. 49
(c)
(a)
(b)
(d)
Figure 46 Observation of erosion on Aluminum GV
(c)
(a)
(b)
(d)
Figure 47 Observation of change in surface texture on MS GV ii. Effect of Erosion on Pressure at 3 points Pressure was monitored at three different points in the cascade as described in Figure 48 using Omega PX 480A-100GV pressure transducers. Manufacturer’s calibration sheet was used for this purpose. Data logging was performed in computer through an acquisition interface Graphtec GL500A. Figure 48 shows the increasing change in pressure with increasing mass of sediment passed through the cascade. It was found that, at pressure side of the vane maximum amount of changes occurs whereas minimum loss occurs at suction side. Considerable change of up to 2.5 % was found at outlet of vane. This change increases with increasing erosion. Increase in pressure of the flow passing vane is resulted from the flow friction induced from surface roughness caused by erosion. Random uncertainties of mean were calculated for each of the cases and 50
were found to be in the range of 0.076% to 0.121 %, where maximum uncertainty was at P3. 10
P1 % Pressure Change
8
P2 P3
6
4
2
0 3
9 15 Sediment Passed [kg]
21
Figure 48 Pressure change with quantity of sediment passed 6.2.Selection of Guide Vane Profile for erosion Handling i. Computational Results Primarily, selection of profile was based on erosion handling; Erosion Rate Density. In addition to it, pressure difference between pressure and suction side were also noted to ascertain minimum cross flow. Figure 49 is a plot of ERD against %Op of GV at same inlet condition. The asymmetric profile NACA 4412 is found to have minimum ERD hence better erosion handling from computational perspective.
51
1.6E-07 4412 2412 1412 OO12
ERD [kg.m-2.s-1]
1.2E-07
8.0E-08
4.0E-08
0.0E+00 20
40
60
80
100
Op [%]
Figure 49 ERD vs Op for different guide vane profiles Figure 50 is the plot for Pressure difference between pressure and suction side and guide vane openings. ΔP has higher variations among the profile at low opening and tends to be similar at higher openings. Possibly because of higher pressure difference at part openings most of the clearance gap erosion were observed at this condition. With NACA 4412, pressure difference were also found to be minimum, so as the cross flow and hence the clearance gap erosion. 25 4412 2412 1412 OO12
ΔP [MPa]
20
15
10
5
0 20
40
60
80
Op [%]
Figure 50 ΔP vs Op for different guide vane profiles 52
100
ii. Experimental results Experimental activities showed that, the trend in erosion pattern is similar in profile cases but the severity varies. From Figure 51, at P1 and P2, LE erosion is towards SS whereas at P3 it is towards PS. Higher erosion in SS at P1 and PS at P2 and P3. LE
SS
PS
P1
P2
P3
Figure 51 Experimental observation of erosion pattern on guide vane Figure 52 is the plot for % weight loss in GV obtained through RDA experiment in contrast to the computational analysis. Figure 52 (a) (b) and (c) are the comparative plot at different operational time in four different profiles at different angular positions. Erosion in NACA 4412 is comparatively lower than other three although, it has little difference with NACA 0012 in the case of P2. At P3 erosion in all the cases are higher and at this condition NACA 4412 has comparatively higher erosion behavior.
53
30 mins 60 mins 90 mins
% Weight loss
1.2
1.3
30 mins 60 mins 90 mins
1.04
% Weight loss
1.6
0.78
0.8
0.52
0.4
0.26 0
0 NACA0012
NACA2412 NACA1412 Profiles
NACA4412
(a) Mid Position (P2)
NACA0012 NACA2412 NACA1412 NACA4412 Profiles
(b) Toward Closing (P1)
% Weight loss
1.2
30 mins 60 mins 90 mins
0.8
0.4
0 NACA0012
NACA2412 NACA1412 Profiles
NACA4412
(c) Toward Opening (P3) Figure 52 % Weight loss at various guide vane positions in different profiles measured at 3 different time intervals iii. Optimization effect on Performance In addition to geometric shape and design properties of runner vanes, performance of turbine is significantly related to flow striking the blades’ leading edge. Property of flow at this point is a strong function of guide vane positioning and profiles. In addition to erosion handling, performance of turbine is primary criteria for selection of guide vanes. Figure 53 shows the plot of turbine efficiency at different guide vane opening for different profiles. The efficiency of turbine is optimum at 60 % opening for all guide vane profiles. With asymmetric profile NACA 4412 selected based on erosion handling, part load performance is higher compared to other profiles whereas full load efficiency is relatively lower. 54
100
η [%]
75
50 4412 2412 1412 OO12
25 20
40
60 Op [%]
80
100
Figure 53 η vs Guide Vane opening for different profiles In addition to efficiency, GV torque is another general design and selection criteria ensuring actuation and control through pivoted support. This ascertains mechanical strength and functionality of the system. 0 20
40
60
-2000
80
100 4412 2412 1412 OO12
T [N.m]
-4000 -6000 -8000
-10000
Op [%]
Figure 54 Guide Vane torque vs Guide Vane opening for different profiles With guide vane profile and its angular variation there is change in Design case of the turbine resulting drastic variation in performance. The variation is mark able at low vane opening and is almost consistent at larger openings for same flow condition. Cm1, Cu1, C1 and W1 has similar kind of variation pattern and graphical stiffness. At around BEP i.e. 60% opening, in all profiles flow tends to be similar. Figure 55 is the design case description of runner vanes. Figure 56, Figure 57, Figure 58 and Figure 59 are the plots 55
of meridian, tangential, absolute and relative component of velocity with respect to guide vane openings. Design Case U1 44.013 C1 43.744 Cu1 43.115 Cm1 7.389 W1 7.443 Figure 55 Inlet Velocity triangle at BEP
Figure 56 Cm1 vs Op with various guide vane profiles
Figure 57 Cu1 vs Op at various guide vane profiles
Figure 58 C1 vs Op at various guide vane profiles
Figure 59 W1 vs Op at various guide vane profiles
56
CHAPTER 7.
CONCLUSION AND RECOMMENDATION
Sediment erosion in guide vanes of Francis turbine is a crucial technical challenge for turbines operating in sediment laden water. This research is a part of long term plan of TTL-KU in developing erosion resistant Francis turbine. It is focused on sediment erosion in Guide Vanes of Francis turbine and its effect on flow around it. In course of this study, author focused on 5 majors associated with guide vanes of Francis turbine; Flow around guide vanes of Francis turbine, field observation of erosion in guide vanes of Francis turbine, Effect of clearance gap on performance of Francis turbine, Effect of overall erosion on flow around guide vanes and selection of vane profile for erosion handling. Guide vane operates best at BEP, where wake in flow passing it, is dependent on guide vane profile and trailing edge geometry. Pressure stagnation occurs around guide vane shaft. The pressure difference between two sides induces leakage flow, whose rate is dependent on operational angle of guide vanes. In presence of sand, at initial stages, particle follows the path of water. Slowly impacts initiates through, side, leading edge, clearance gap and trailing edge erosions. This erosion amplifies cross flow, leakage flows, tip leakage and friction losses in the flow passing guide vanes. All the observed turbines had internal flat bolt system for connecting facing plate to the head cover and bottom cover. Most of the erosion in facing plate was found to be initiated in this region. In addition to it, peripheries of holes for guide vane in facing plate were also found to be damaged. Hence, additional factors like pressure difference between guide vane pressure and suction side in entire operational range, trailing and leading edge geometry, guide vane profile, minimum surface alteration in flow channel, external bolting mechanism for facing plates and special coating around the shaft holes (since stagnation of pressure and impact of sediment both act to result sediment cavitation combined effect) are to be considered for minimizing erosion in turbines operating in sediment laden water.
57
Field study at KG-A showed that, higher concentration of sediment is in the range of 300-600 µm with high amount of quartz. This sediment load is increasing annually. In addition, hardness of quartz is higher than GV material which results into more significant erosion. At clearance gap larger losses (up to 10 mm) were found in trailing edge compared to leading one. Guide Vane angle is a strong function of localization and severity of erosion. In summary the erosion phenomenon in guide vanes of Francis turbine, with flow from spiral casing outlet is found to be dependent on Sediment Property (Ps), Guide Vane material (Pm), Velocity of particle (Vp) and Guide Vane Angle (αo). Model turbine simulation was performed to estimate the effect of increasing clearance gap on performance of Francis turbine. It was observed that, leakage flow rate increases with increasing clearance gap which consequently increases hydraulic losses and relative efficiency loss in the turbine. About 3% of efficiency loss with increase in gap by 1% of passage height were observed. Similarly, spiral casing pressure was found to drop by 2% with every 1 mm increase in the gap. The velocity profiles in gaps of trailing region were found to be higher compared to leading side. This shows, velocity in the region near guide vane is lower compared to the facing plate because of obstruction in the developed flow. The cross flow velocity decreases with increasing gaps. Using experimental setup of 3GV Cascade system, effect of erosion on flow around vane has been studied. It was found that with increasing erosion friction increases which ultimately increases pressure around vane and at GV outlet. After 21 kg sand passed to Aluminum guide vane 0.6 % of weight loss was observed. This consequently increases the outlet pressure of guide vane by about 2%. Finally, computational study was performed on different sets of GV profile to identify the best possible design. This study was aided by RDA experiments. It was found that with unsymmetrical vanes better erosion handling and better performance can be achieved.
58
In continuation of this activity, future R&D should focus on detail estimation of erosion and effect. For this purpose, enough amount of sediment will be required. The author would also like to propose an additional idea that can help in further study of this process which involves erosion from RDA and effect prediction in 3GV cascade. Additionally, unsteady analysis in the cases with increasing gaps like Paper 3 can further help in the study of vortex transfer from clearance gap to runner inlet. Erosion handling with combination of two modified designs, further optimization with design modification continuing from this point are some of the other associated issues along with consideration of rotational effect on flow around eroded guide vane.
59
REFERENCES [1] O. Edenhofer, R.P. Madruga, and Y. Sokona, "Renewable Energy Sources and Climate Change Mitigation: Special Report of the Intergovernmetnal Panel on Climate Change," New York, ISBN 978-1-107-60710-1, 2011. [2] P.H. Gleick, "Water in Crisis," New York, 1993. [3] Biraj Singh Thapa, "Design of Francis turbine to minimize effect of sediment erosion," Dhulikhel, Masters Thesis 2012. [4] Ravi Koirala, Sailesh Chitrakar, Amod Panthee, Hari Prasad Neopane, and Bhola Thapa, "Implementation of Computer Aided Engineering for Francis turbine development in Nepal," Journal of Manufacturing Engineering, 2015. [5] Hermod Brekke, "The influence of the Guide Vane Clearance Gap on Efficiency and Scale Effect," in Proceedings of IAHR Symposium on Progress within Large and High Specific Energy Units, Trondheim, Norway, 1990. [6] NTNU Lecture Note, "Design of Guide Vanes in Francis turbines," Trondheim, Lecture Notes 2012. [7] Shenyang Research Institute of Foundary. (2012, February) Stainless Steel Casting. [Online]. http://www.foundrysuppliers.com/suppliers/product?id=132875750197410183 [8] H. P. Neopane, "Sediment Erosion in Hydro Turbines," Trondheim, Doctoral Thesis 2010. [9] B. Nennemann, T.C. Vu, and M. Farhat, "CFD Presiction of unsteady wicket gate - runner interaction in Francis turbines: A new standard hydraulic design procedure," in Hydro 2005, Villach , 2005. [10] E. Cabrera, V. Espert, and F. Martinez, Eds., Hydraulic Machinery and Cavitation.: Kluwer Academic Publishers, 1996, vol. I. [11] (2012) Turbulent Cylindrical Wakes. [Online]. http://electron6.phys.utk.edu/101/CH6/Turbulent%20wakes.htm.
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[12] S. Yagmur, S. Dogan, M.H. Aksoy, E. Canli, and M. Ozgoren, "Experimental and Numerical Investigation of Flow Structures around Cylindrical Bluff Bodies," in EPJ Web of Conferences, vol. 92, Český Krumlov, Czech Republic, 2015. [13] J.H. Lienhard , "Synopsis of Lift, Drag and Vortex frequency data for rigid circular
cylinders,"
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http://www.uh.edu/engines/vortexcylinders.pdf [14] R. Qian, "Flow Field Measurement in a Stator of a Hydraulic Turbine," Quebec, PhD Thesis 2008. [15] C. Trivedi, B. Gandhi, and C.J. Michel, "Effect of transients on Francis turbine runner life: a review," Journal of Hydraulic Research, pp. 1 - 12, 2013. [16] Ø. Antonsen, "Unsteady flow in wicket gate and runner with focus on static and dynamic load on runner," Trondheim, PhD Thesis 2007. [17] B.S. Thapa, O.G. Dahlaug, and B. Thapa, "Flow Field measurement in a guide vane cascade of a High Head Francis turbine," in Int. Conf. On Water Resources and Hydropower Development in Asia, vol. 6, Vientiane, Lao PDR, 2016. [18] Ø. Antonsen and T.K. Nielsen, "CFD simulations of Von Karman Vortex shedding ," in 22nd IAHR Symposium, Stockholm, 2004. [19] R.M. Donaldson, "Hydraulic Turbine Runner Vibration," Journal of Engineering and Power, vol. 78, pp. 1141-1147, 1956. [20] A. Zobeiri, P. Ausoni, F. Avellan, and M. Farhat, "How oblique trailing edge of a hydrofoil reduces the vortex-induced vibration," Journal of Fluids and Structures , vol. 32, pp. 78-89, 2012. [21] B.J. Lewis, J.M. Cimbala, and A.M. Wouden, "Wicket gate trailing-edge blowing: A method for improving off-design hydroturbine performance by adjusting the runner inlet swirl angle," in IAHR Symposium on Hydraulic Machinery and Systems, vol. 27 , 2014.
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[22] W. Zhao, J.T. Billdal, T.K. Nielsen, and H. Brekke, "Study of the leakage flow through a clearance gap between two stationary walls," in 26th IAHR Symposium on Hydraulic Machinery and Systems, 2012. [23] R. Koirala, B. Zhu, and H.P. Neopane, "Effect of Guide Vane Clearance Gap on Francis Turbine Performance," Energies, vol. 9, no. 275, 2016. [24] S. Eide, "Numerical analysis of the head covers deflection and the leakage flow in the guide vanes of high head Francis turbines," Trondheim, PhD Thesis 2004. [25] S. Eide and H. Brekke, "Analysis of the Head Covers Deflections and the Leakage Flow in the Guide Vanes," in IAHR 2014, 2014. [26] B. Thapa, "Sediment Erosion in Hydraulic Machinery," Trondheim, Ph.D. Thesis 2004. [27] V.A. Pugsley and C. Allen, "Microstructure/ property relationships in the slurry erosion of tungsten carbide-cobalt," Wear, vol. 225-229, pp. 1017-1024, 1999. [28] L. Paudel, "Study on Sediment Characterization and its impact on Hydraulic turbine materials," Dhulikhel, Doctoral Thesis 2013. [29] T.R. Bajrachaya et al., "Correlation study on Sand Led Erosion of Buckets and Efficiency Losses in High Head Power Plants," in National Conference on Renewable Energy Technilogy for Rural Development, vol. 1, Kathmandu, 2006. [30] M. Bjordal, "Erosion and corrosion of ceramic-metallic coatings and stainless steel," Trondheim, Dr. Ing. Thesis 1995. [31] B. Thapa, P. Chaudhary , O.G. Dahlhaug, and P. Upadhyay, "Study of Combined Effect of Sand Erosion and Cavitation in Hydraulic Turbines," in International Conference
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http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.559.5462&rep=rep1 &type=pdf [32] B. Rajkarnikar, H.P. Neopane, and B.S. Thapa, "Development of rotating disc apparatus for test of sediment-induced erosion in Francis runner blades," Journal of Wear, vol. 306, pp. 119-125, 2013. 62
[33] O. Shrestha , N. Acharya , B. Thapa , H.P. Neopane, and Y.H. Lee , "Design and Development of Rotating Disk Apparatus to Test Sediment Erosion in Cross Flow turbine Runner Blades," in Proceedings of the International Symposium on Current Research in Hydraulic Turbines-VI, vol. 6, Dhulikhel, Nepal, 2016. [34] B.S. Thapa, C. Trivedi , and O.G. Dahlhaug, "Design and development of guide vane cascade for a low speed number Francis turbine," Journal of Hydrodynamics, no. Accepted for Publication, 2015, Through Researchgate. [35] Ravi Koirala et al., "Analysis of Sediment Samples and Erosion Potential: A Case Study of Upper Tamakoshi Hydroelectric Project," Journal of Water, Energy and Environment, no. 16, pp. 28 - 31, January 2015. [36] A. Subedi, "Sediment Monitoring. Testing of an Erosion Sensor," in International Conference on Small Hydropower, Kandy, 2007. [37] P. Guangjie, W. Zhengwei, X. Yexiang, and L. Yongyao, "Abrasion predictions for Francis turbines based on liquid - solid two - phase fluid simulations," Engineering Failure Analysis, vol. 33, pp. 327-225, 2013. [38] A.K. Rai, A. Kumar, and T. Staubli, "International Conference on Hydropower for Sustainable Development ," in International Conference on Hydropower for Sustainable Development, Dehradun, 2015, pp. 535-547. [39] Sailesh Chitrakar, Hari Prasad Neopane, and Ole Gunnar Dahlhaug, "Study of simultaneous effects of secondary flow and sediment erosion in Francis turbine," Renewable Energy, vol. 97, pp. 881-891, November 2016. [40] M.B. Bishwakarma, "Sediment exclusion optimization study, Jhimruk Hydropower Plant, Nepal," in Conference on Optimum use of run-off-river, Trondheim, 1999. [41] G.P. Kayastha, "Silting problems in hydro power plants in Nepal," in International Conference on Silting Problems in Hydro Power Plants, New Delhi, 1999, pp. 23 - 30.
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[42] C.S. Chaudhary, "Impact of high sediment on hydraulic equipment of Marsyangi hydropower Plant," in International seminar on sediment handling technique, Kathmandu, 1999. [43] Ravi Koirala, Bhola Thapa, Hari Prasad Neopane, Baoshan Zhu, and Balendra Chhetri, "Sediment Erosion in Guide Vanes of Francis turbine: A Case Study of Kaligandaki - A Hydropower Plant, Nepal," Wear , vol. 362-363, pp. 53-60, May 2016. [44] H. Brekke, Y.L. Wu, and B.Y. Cai, "Design of Hydraulic Machinery working in Sand Laden Water," in Abrasive Erosion and Corrosion of Hydraulic Machinery, C.G. Duan and V.Y. Karelin, Eds.: Imperical College Press, 2002, vol. 2, pp. 155-232. [45] G.A. Dahl, "Hydraulic design of a Francis turbine that will be influenced by sediment erosion," NTNU, Trondheim, Norway , Master Thesis 2014. [46] Biraj Singh Thapa, Bhola Thapa, and Ole Gunner Dahlhaug, "Current research in hydraulic turbines for handling Sediment Erosion," Journal of Energy , vol. 47, pp. 62-69, 2012. [47] S. Basnyat, "Monitoring sediment load and its abrasive effects in Jhimruk Hydropower Plant, Nepal," in In proceedings of the Optimum Use of Run-offRiver Conference, Trohdheim, Norway, 1999. [48] D. You, M. Wang, P. Moin, and R. Mittal, "Effects of tim-gap size on the tipleakage flow in a turbomachine cascade," Physics of Fluids, vol. 18, 2006. [49] G. Tang, "Measurement of the Tip-GapTurbulent Flow Structure in a Low-speed Compressor Cascade," Virginia Polytechnic Institute and State University, Blacksburg, USA, May, 2004. [50] Princeton University. (2015, October) Draft of Blunt Bodies and Streamlined Bodies. [Online]. https://www.princeton.edu/~asmits/Bicycle_web/blunt.html [51] H.H. Francke, K. Haugan, E. Kobro, J. Ramdal, and P.T.S. Storli, High Head Hydraulic Machinery. Trondheim: Water Power Laboratory, NTNU, 2009. 64
APPENDIX
65
APPENDIX – A: ASSOCIATED PUBLICATIONS 1. Koirala R., Thapa B., Neopane H.P., Zhu B. A review on flow and erosion in guide vanes of Francis turbine, Renewable and Sustainable Energy Reviews, November, 2016. (In Press) 2. Koirala R., Thapa B., Neopane H.P., Zhu B., Chhetry B., Sediment Erosion in Guide Vanes of Francis turbine: A Case study of Kaligandaki – A Hydropower Plant, Nepal, Wear. Vol. 362-363, pp. 53-60, May, 2016. 3. Koirala R., Zhu B., Neopane H.P., Effect of Guide Vane Clearance gap on Performance of Francis turbine, Energies, Vol. 9 (4), pp. 275, April, 2016. 4. Koirala R., Neopane H.P., Zhu B., Thapa B., Effect of erosion on Flow around Guide Vane of Francis turbine, Journal of Renewable Energy,2017. (Under Review) 5. Koirala R., Neopane H.P., Zhu, B., Shrestha O., Thapa B., Selection of Francis turbine Guide Vane profile for Erosion Handling, Journal of Renewable Energy, 2016. (Under Review)
66
APPENDIX – B: DESIGN AND DEVELOPMENT OF 3 GUIDE VANE CASCADE SYSTEM
Figure: CFD analysis of flow around 3 GV cascade system
67
(i)
(iii)
(ii)
(iv)
(v)
(vii) Figure: Developmental process of 3GV test rig 68
(vi)
Figure: Test Rig installed at Turbine Testing Lab, Nepal for the experimental process 69
APPENDIX – C: CALLIBRATION AND UNCERTAINITY ANALYSIS B.1. Pressure data uncertainty analysis Thapa in this Doctoral research simplified uncertainty analysis technique for pressure measurement applications. Below are the numerical relations associated with it. Mean Pressure 𝑁
̅= 𝑃
1 ∑ 𝑃𝑖 𝑁 𝑖=1
Standard deviation of Mean Pressure 𝑁
1 𝜎=√ ∑(𝑃𝑖 − 𝑃̅)2 𝑁−1 𝑖=1
Standard Error of Mean 𝛿 = ± (1.96.
𝜎 √𝑁
Percentage Random uncertainty of Mean 𝜀=±
𝛿 . 100 ̅𝑖 𝑃
70
)
B.2. Weir Calibration
No. 1 2 3 4 5 6 7 8 9 10 11
Time [sec] 2.1 2.1 2.02 2.1 2.22 2.29 2.05 1.9 2.01 1.9 1.81
Volume[Ltr] 14.8 14.5 14.28 15.25 16.25 17.38 14.38 14.76 15.32 16.16 13.44 Average
71
Height[cm] 34 31.2 33 33 33 33 33 33 33 33 33
V/T[LPS] 7.047619 6.904762 7.069307 7.261905 7.31982 7.58952 7.014634 7.768421 7.621891 8.505263 7.425414 7.412
APPENDIX – D: DESIGN OF GUIDE VANES FOR FRANCIS TURBINE During this master’s work a GUI based tool for design of guide vane was developed. Below is the description for it. B.1. Design of Guide Vanes Calculate diameter of guide vane outlet and breadth of the guide vane 𝐷𝐺𝑉𝑂 = 1.05 ∗ 𝐷1 𝐵𝐺𝑉𝑂 = 𝐺𝐵1 + 0.001 Calculate CuGVo and CmGVo; 𝑄𝑜 𝐶𝑚𝐺𝑉𝑜 = (𝐷𝐺𝑉𝑜 ∗ 𝐵𝐺𝑉𝑜 ∗ 𝜋) 𝐶𝑢𝐺𝑉𝑜 =
𝐶𝑢1 ∗ 𝐷1 𝐷𝐺𝑉𝑜
𝛼𝐺𝑉𝑜 = 𝑡𝑎𝑛−1 (
𝐶𝑚𝐺𝑉𝑜 ) 𝐶𝑢𝐺𝑉𝑜
Calculate initial axis diameter of Guide vanes 𝐷𝐺𝑉𝐴 = 𝐷1 ∗ (0.29 ∗ Ω + 1.07) Length of guide vane (𝜋 ∗ 𝐷𝐺𝑉𝐴 ) 𝐿𝐺𝑉𝑚𝑖𝑛 = 𝑍𝐺𝑉 𝐿𝐺𝑉 = 𝐿𝐺𝑉𝑚𝑖𝑛 ∗ 𝑓𝑐𝑜𝑣𝑒𝑟 Calculate the diameter of guide vane inlet 𝐷𝐺𝑉𝑜 2 𝐷𝐺𝑉𝑜 𝜋 2 𝐷𝐺𝑉𝑖 = 2 ∗ √(𝐿𝑔𝑣 ) + ( ) − 𝐿𝑔𝑣 ∗ ( ) ∗ cos ( − 𝛼𝐺𝑉𝑜 ) 2 2 2
Plot the desired shape of the profile
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B.2. Summary of Design tool for Guide Vane
Design tool summary This tool is named as GVKhoj and is developed to design guide vane for Francis turbines. The tool was developed using MATLAB GUI coding easing user interface. It is one of the outcomes of 1 year stay at State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing, China. It is capable of plotting both symmetric and unsymetric profiles that can be meshed in Turbogrid and used for processing in CFX turbo mode, with the output from Khoj (existing program at TTL). Inputs
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The program takes Head, Flow, Turbine Speed, Inlet diameter of turbine, Inlet height, Cu1, Number of guide vanes, overlapping factor and angle of vane as input parameters in the box provided. Outputs Maximum guide vane opening and profile plot for the turbine are the major outputs. Generated profiles will be exported in the form of .curve and .txt file format. Each outputs are separated with its file name in the form of YY-MM-DD-HH-MM-SS. B.3. MATAB GUI Code functionvarargout = GVKhoj(varargin) % GVKHOJ MATLAB code for GVKhoj.fig % GVKHOJ, by itself, creates a new GVKHOJ or raises the existing % singleton*. % H = GVKHOJ returns the handle to a new GVKHOJ or the handle to % the existing singleton*. % GVKHOJ('CALLBACK',hObject,eventData,handles,...) calls the local % function named CALLBACK in GVKHOJ.M with the given input arguments. % GVKHOJ('Property','Value',...) creates a new GVKHOJ or raises the % existing singleton*. Starting from the left, property value pairs are % applied to the GUI before GVKhoj_OpeningFcn gets called. An % unrecognized property name or invalid value makes property application % stop. All inputs are passed to GVKhoj_OpeningFcn via varargin. % *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one % instance to run (singleton)". % % See also: GUIDE, GUIDATA, GUIHANDLES % Edit the above text to modify the response to help GVKhoj % Last Modified by GUIDE v2.5 21-Jan-2016 13:34:37 % Begin initialization code - DO NOT EDIT gui_Singleton = 1; gui_State = struct('gui_Name', mfilename, ... 'gui_Singleton', gui_Singleton, ... 'gui_OpeningFcn', @GVKhoj_OpeningFcn, ... 'gui_OutputFcn', @GVKhoj_OutputFcn, ... 'gui_LayoutFcn', [] , ... 'gui_Callback', []); ifnargin&&ischar(varargin{1}) gui_State.gui_Callback = str2func(varargin{1}); end ifnargout [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
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else gui_mainfcn(gui_State, varargin{:}); end % End initialization code - DO NOT EDIT % --- Executes just before GVKhoj is made visible. functionGVKhoj_OpeningFcn(hObject, eventdata, handles, varargin) % This function has no output args, see OutputFcn. % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % varargin command line arguments to GVKhoj (see VARARGIN) % Choose default command line output for GVKhoj handles.output = hObject; % Update handles structure guidata(hObject, handles); % UIWAIT makes GVKhoj wait for user response (see UIRESUME) % uiwait(handles.figure1); % --- Outputs from this function are returned to the command line. functionvarargout = GVKhoj_OutputFcn(hObject, eventdata, handles) % varargout cell array for returning output args (see VARARGOUT); % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Get default command line output from handles structure varargout{1} = handles.output; functionhead_Callback(hObject, eventdata, handles) % hObject handle to head (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of head as text % str2double(get(hObject,'String')) returns contents of head as a double % --- Executes during object creation, after setting all properties. functionhead_CreateFcn(hObject, eventdata, handles) % hObject handle to head (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. ifispc&&isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end functionflow_Callback(hObject, eventdata, handles) % hObject handle to flow (see GCBO)
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% eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of flow as text % str2double(get(hObject,'String')) returns contents of flow as a double % --- Executes during object creation, after setting all properties. functionflow_CreateFcn(hObject, eventdata, handles) % hObject handle to flow (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. ifispc&&isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end % --- Executes on button press in Calc. functionCalc_Callback(hObject, eventdata, handles) % hObject handle to Calc (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) n1 = str2num(get(handles.head,'string')); n2 = str2num (get(handles.flow,'string')); p=997*9.81*n1*n2; pp = num2str(p); set(handles.power,'string',pp); % Turbine speed number tspeed=str2num(get(handles.speed,'string')); omega=(2*pi*tspeed)/60; rp=sqrt(2*9.81*n1); omega_red=omega/rp; flow_red=n2/rp; sp_num=omega_red*sqrt(flow_red); %Full Opening Angle of Guide Vane fopn=4*(-4*sp_num^2+13*sp_num+1); alpha0_1=num2str(fopn); set(handles.alpha0,'string',alpha0_1); %Guide Vane outlet diameter td_1=str2num(get(handles.d_1,'string')); d_gvo=1.05*td_1; d_gv2=num2str(d_gvo); set(handles.d_gvo,'string',d_gv2); %GV meridional flow b_gv=str2num(get(handles.b_1,'string')); cmgv=n2/(d_gvo*b_gv*pi); %Tangential Flow cu1=str2num(get(handles.c_u1,'string'));
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cugv=(cu1*td_1)/d_gvo; %Guide Vane angle alpha_gv=(atand(cmgv/cugv)); %Initial axis diameter dgva1=td_1*(0.29*sp_num+1.05); d_gva=num2str(dgva1); set(handles.d_gva,'string',d_gva); %Length of guide vane z_gv=str2num(get(handles.n_gv,'string')); lgvm=(pi*dgva1)/z_gv; kf=str2num(get(handles.cf,'string')); l_gv=lgvm*kf; lgv=num2str(l_gv); set(handles.l_gv,'string',lgv); %Guide Vane inlet diameter d_gvi=2*sqrt(l_gv^2+(d_gvo/2).^2-2*l_gv*(d_gvo/2)*cosd(alpha_gv+90)); dgvi=num2str(d_gvi); set(handles.d_gvi1,'string',dgvi); %Thickness of Profile thickness=0.16*lgvm; thi=thickness/2; th=str2num(get(handles.th,'string')); th1_cn=th/100; %NACA Generation seg=l_gv/(200); a=1; for a=1:200 xsym=a*seg; ysym=(thi/th1_cn)*(0.2969*sqrt((xsym/l_gv))-0.126*(xsym/l_gv)0.3516*(xsym/l_gv).^2+0.2843*(xsym/l_gv).^3-0.1015*(xsym/l_gv).^4); E1(a)=xsym; F1(a)=ysym+dgva1/2; G1(a)=-ysym+dgva1/2; a=a+1; end xad=0; yad=dgva1/2; E=[xad,E1]; F=[yad,F1]; G=[yad,G1]; %fstptx=[0]; %fstpty=[dgva1/2]; rot_ax_x=1/3*l_gv; rot_ax_y=dgva1/2;
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theta_rot=str2num(get(handles.angle,'string')); %NACA Plot %axes(handles.naca0015) %plot (E,F); %hold on; %plot(E,G); A_rot=(E-rot_ax_x)*cosd(theta_rot)-(F-rot_ax_y)*sind(theta_rot)+rot_ax_x; B_rot=(E-rot_ax_x)*sind(theta_rot)+(F-rot_ax_y)*cosd(theta_rot)+rot_ax_y; C_rot=(E-rot_ax_x)*cosd(theta_rot)-(G-rot_ax_y)*sind(theta_rot)+rot_ax_x; D_rot=(E-rot_ax_x)*sind(theta_rot)+(G-rot_ax_y)*cosd(theta_rot)+rot_ax_y; axes(handles.naca0015) plot (A_rot,B_rot); holdon; plot(C_rot,D_rot); grid %theta1_rot=360/z_gv; %A1_rot=(A_rot)*cosd(theta1_rot)-(B_rot)*sind(theta1_rot); %B1_rot=(A_rot)*sind(theta1_rot)+(B_rot)*cosd(theta1_rot); %C1_rot=(C_rot)*cosd(theta1_rot)-(D_rot)*sind(theta1_rot); %D1_rot=(C_rot)*sind(theta1_rot)+(D_rot)*cosd(theta1_rot); %plot (A1_rot,B1_rot); %plot(C1_rot,D1_rot); holdoff; ee=fliplr(C_rot); gg=fliplr(D_rot); naca0015=[A_rot' B_rot'; ee' gg'] %xyad=[0 0]; %naca0015ad1=[xyad;naca0015;xyad]; %naca0015ad2=[naca0015;xyad]; %naca0015_2=(naca0015;repmat(xyad,1,1)); %naca0015_3=(naca0015_2;repmat(xyad,402,1)); naca0015(201,:)=[]; %Deleting the 200th item %fid=fopen('b.txt','wt'); %fprintf(fid,'%6s\n',M); %fclose(fid); %for k=1:3 %str=sprintf('temp%d.txt',k); %fid=fopen(str,'wt'); %fprintf(fid,'%s\n',naca0015); % fclose(fid); %end filename0015=sprintf('naca0015_%s.txt',datestr(now,'dd-mmm-yyyy-HH-MM-SS')); save (filename0015,'-ascii','naca0015');
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c=1; taa=str2num(get(handles.taa,'string')); pa=str2num(get(handles.pa,'string')); uth=str2num(get(handles.uth,'string')); m=taa/100*c; p=pa/10*c; ta=uth/100*c; ns = 200; y = linspace(0,c,ns+1)'; zc_before = (m/(p^2))*(2*p*y - y.^2); zc_after = (m/(1-p)^2)*((1-2*p) + 2*p*y - y.^2); ddy_zc_before = -2*m*(y - p).*1/(p.^2); ddy_zc_after = -2*m*(y-p).*1/((p - 1).^2); zt_positive = (5*ta)*(0.2969*(y.^(1/2)) - 0.1260*(y) - 0.3516*(y.^2) + 0.2843*(y.^3) - 0.1015*(y.^4)); zt_negative = -(5*ta)*(0.2969*(y.^(1/2)) - 0.1260*(y) - 0.3516*(y.^2) + 0.2843*(y.^3) - 0.1015*(y.^4)); theta_before = atan(ddy_zc_before); theta_after = atan(ddy_zc_after); % determine location of maximum camber in terms of i i = 1; while y(i) < (p) %y(i) %i i = i + 1; end i=i-1; % input the nodal coordinates for j = 1:1:i position(:,j) = [y(j) zt_positive(j)*sin(theta_before(j)); zc_before(j) + zt_positive(j)*cos(theta_before(j)); 0]; end for k = (i+1):1:(ns+1) position(:,k) = [y(k) zt_positive(k)*sin(theta_after(k)); zc_after(k) + zt_positive(k)*cos(theta_after(k)); 0]; end for r = (ns+2):1:(ns+2+ns-i-1) position(:,r) = [y(2*ns-r+2) - zt_negative(2*ns-r+2)*sin(theta_after(2*ns-r+2)); zc_after(2*ns-r+2) + zt_negative(2*ns-r+2)*cos(theta_after(2*ns-r+2)); 0]; end for q = (ns+2+ns-i):1:(2*ns) position(:,q) = [y(2*ns-q+2) - zt_negative(2*ns-q+2)*sin(theta_before(2*ns-q+2)); zc_before(2*nsq+2) + zt_negative(2*ns-q+2)*cos(theta_before(2*ns-q+2)); 0]; end % set up the nodal coordinate arrays for s = 1:1:(2*ns) x(s) = position(1,s); v(s) = position(2,s); z(s) = position(3,s); end
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% set up the element connectivity array node_connect for t = 1:1:(2*ns-1) node_connect(1,t) = t; node_connect(2,t) = t+1; end node_connect(1,2*ns) = 2*ns; node_connect(2,2*ns) = 1; % Calculate total area for u = 1:1:(2*ns-1) dL(:,u) = (position(:,u+1) - position(:,u)); dA(:,u) = cross(position(:,u),dL(:,u)); end dL(:,2*ns) = (position(:,1) - position(:,2*ns)); dA(:,2*ns) = cross(position(:,2*ns),dL(:,2*ns)); dummy = sum(dA,2); Total_Area = abs((1/2)*dummy(3)) % Calculate centroid x_centroid(1) = 0; y_centroid(1) = 0; for u = 2:1:(2*ns) x_centroid(u) = (2/3)*(norm(position(:,u)))*position(1,u)/norm(position(:,u)); y_centroid(u) = (2/3)*(norm(position(:,u)))*position(2,u)/norm(position(:,u)); end X = sum(x_centroid.*abs((1/2)*dA(3,:)))/Total_Area Y = sum(y_centroid.*abs((1/2)*dA(3,:)))/Total_Area % plot the whole system for u = 1:1:(2*ns) node_1 (u) = node_connect(1,u); node_2 (u) = node_connect(2,u); yy = [x(node_1),x(node_2)]; zz = [v(node_1),v(node_2)]; xx = [z(node_1),z(node_2)]; yyr=yy*l_gv/c; xxr=xx*l_gv/c+dgva1/2; zzr=zz*l_gv/c+dgva1/2; %axes(handles.asymnaca) %plot(yyr,zzr) A2_rot=(yyr-rot_ax_x)*cosd(theta_rot)-(zzr-rot_ax_y)*sind(theta_rot)+rot_ax_x; B2_rot=(yyr-rot_ax_x)*sind(theta_rot)+(zzr-rot_ax_y)*cosd(theta_rot)+rot_ax_y; axes(handles.asymnaca) plot(A2_rot,B2_rot)%Negative profile of Asymetric Profile %plot(B2_rot,A2_rot) view([0 0 1]) grid
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nacauns=[A2_rot' B2_rot';A2_rot' B2_rot']; %Negative Profile of the Asymetric Vanes %nacauns=[B2_rot' A2_rot';B2_rot' A2_rot']; %filenameuns=sprintf('nacaunsym_%s.txt',datestr(now,'dd-mmm-yyyy-HH-MM-SS')); % save (filenameuns,'-ascii','nacauns'); %plot3(yyr,zzr,xxr,'-',X,Y,0,'+') holdon end filenameuns=sprintf('nacaunsym_%s.txt',datestr(now,'dd-mmm-yyyy-HH-MM-SS')); save (filenameuns,'-ascii','nacauns'); holdoff %A2_rot=(yyr-rot_ax_x)*cosd(theta_rot)-(zzr-rot_ax_y)*sind(theta_rot)+rot_ax_x; %B2_rot=(yyr-rot_ax_x)*sind(theta_rot)+(zzr-rot_ax_y)*cosd(theta_rot)+rot_ax_y; %C_rot=(E-rot_ax_x)*cosd(theta_rot)-(G-rot_ax_y)*sind(theta_rot)+rot_ax_x; %D_rot=(E-rot_ax_x)*sind(theta_rot)+(G-rot_ax_y)*cosd(theta_rot)+rot_ax_y; %axes(handles.asymnaca) % plot(A2_rot,B2_rot) % display the figure the way I want to %axis([0,1,-.5,.5]) %nacauns=[A2_rot B2_rot]; %filenameuns=sprintf('nacaunsym_%s.txt',datestr(now,'dd-mmm-yyyy-HH-MM-SS')); %save (filenameuns,'-ascii','nacauns'); %NACA 0015 Plot functionspeed_Callback(hObject, eventdata, handles) % hObject handle to speed (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of speed as text % str2double(get(hObject,'String')) returns contents of speed as a double % --- Executes during object creation, after setting all properties. functionspeed_CreateFcn(hObject, eventdata, handles) % hObject handle to speed (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. ifispc&&isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end function d_1_Callback(hObject, eventdata, handles)
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% hObject handle to d_1 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of d_1 as text % str2double(get(hObject,'String')) returns contents of d_1 as a double % --- Executes during object creation, after setting all properties. function d_1_CreateFcn(hObject, eventdata, handles) % hObject handle to d_1 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. ifispc&&isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end function b_1_Callback(hObject, eventdata, handles) % hObject handle to b_1 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of b_1 as text % str2double(get(hObject,'String')) returns contents of b_1 as a double % --- Executes during object creation, after setting all properties. function b_1_CreateFcn(hObject, eventdata, handles) % hObject handle to b_1 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. ifispc&&isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end function c_u1_Callback(hObject, eventdata, handles) % hObject handle to c_u1 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of c_u1 as text % str2double(get(hObject,'String')) returns contents of c_u1 as a double % --- Executes during object creation, after setting all properties. function c_u1_CreateFcn(hObject, eventdata, handles) % hObject handle to c_u1 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows.
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% See ISPC and COMPUTER. ifispc&&isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end functionn_gv_Callback(hObject, eventdata, handles) % hObject handle to n_gv (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of n_gv as text % str2double(get(hObject,'String')) returns contents of n_gv as a double % --- Executes during object creation, after setting all properties. functionn_gv_CreateFcn(hObject, eventdata, handles) % hObject handle to n_gv (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. ifispc&&isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end functioncf_Callback(hObject, eventdata, handles) % hObject handle to cf (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of cf as text % str2double(get(hObject,'String')) returns contents of cf as a double % --- Executes during object creation, after setting all properties. functioncf_CreateFcn(hObject, eventdata, handles) % hObject handle to cf (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. ifispc&&isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end functionangle_Callback(hObject, eventdata, handles) % hObject handle to angle (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of angle as text % str2double(get(hObject,'String')) returns contents of angle as a double % --- Executes during object creation, after setting all properties.
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functionangle_CreateFcn(hObject, eventdata, handles) % hObject handle to angle (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. ifispc&&isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end functionth_Callback(hObject, eventdata, handles) % hObject handle to th (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of th as text % str2double(get(hObject,'String')) returns contents of th as a double % --- Executes during object creation, after setting all properties. functionth_CreateFcn(hObject, eventdata, handles) % hObject handle to th (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. ifispc&&isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end functiontaa_Callback(hObject, eventdata, handles) % hObject handle to taa (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of taa as text % str2double(get(hObject,'String')) returns contents of taa as a double % --- Executes during object creation, after setting all properties. functiontaa_CreateFcn(hObject, eventdata, handles) % hObject handle to taa (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. ifispc&&isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end functionpa_Callback(hObject, eventdata, handles) % hObject handle to pa (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB
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% handles
structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of pa as text % str2double(get(hObject,'String')) returns contents of pa as a double % --- Executes during object creation, after setting all properties. functionpa_CreateFcn(hObject, eventdata, handles) % hObject handle to pa (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. ifispc&&isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end functionuth_Callback(hObject, eventdata, handles) % hObject handle to uth (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of uth as text % str2double(get(hObject,'String')) returns contents of uth as a double % --- Executes during object creation, after setting all properties. functionuth_CreateFcn(hObject, eventdata, handles) % hObject handle to uth (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. ifispc&&isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end
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