Dr. S.M. Maingi ..... Ct. Cv d. Dr. Dp di dj do. E. F f g. H. Hatm. Cross-sectional
area of a water jet ..... between the runner and the tail race (Hothersall, 2004).
PERFORMANCE OF A MODIFIED VEHICLE DRIVE SYSTEM IN GENERATING HYDROPOWER
BY MURIITHI JAMES MUCHIRA B.Sc. (Mechanical Engineering), University of Nairobi I56/7283/2002
A THESIS SUBMITTED IN PARTIAL FULFILMENT FOR THE DEGREE OF MASTER OF SCIENCE IN RENEWABLE ENERGY TECHNOLOGY, KENYATTA UNIVERSITY
APRIL 2011
ii DECLARATION
This thesis is my original work and has not been presented for a degree in any other University or any other award.
Date Muriithi James Muchira
We confirm that the candidate under our supervision carried out the work reported in this thesis.
Date Dr. Thomas F. N. Thoruwa Department of Energy Engineering Kenyatta University
Date Prof. F. Makau Luti Department of Mechanical and Manufacturing Engineering University of Nairobi
Date Dr. S.M. Maingi Department of Water Engineering Kenyatta University
iii
DEDICATION
I would like to dedicate this thesis to my dear wife, Purity Waithira Muriithi and my daughters Caroline Wanja and Evaline Wairimu for their unconditional love, encouragement and great sacrifices for the success of this research work.
iv ACKNOWLEDGEMENT
I would like to thank my supervisors, Dr. Thomas N. Thoruwa, Dr. S. M. Maingi and Prof. F. Makau Luti for their keen interest, invaluable advices and guidance, patience, understanding and encouragement and also for their able and diligent supervision while undertaking this research.
I would like to acknowledge and thank the Government of Kenya for supporting my work throughout the course and particularly for offering me a scholarship to enable me go through the Masters of Science degree program.
I would also like to thank the Ministry of Energy for giving financial support for the civil works materials used in the construction of the testing site in the field and the Thima community in Kirinyaga for their offer of semi-skilled labour during the construction process of the testing site.
I would also like to thank all the staff of Engineering and Technology School for all their support at various stages of the research study. Special thanks to John Maina,George Kamau, Francis Gathungu, Peter Kimani, Patrick Njoka, and Aggrey Adagala for their advice and support in the construction of the research project. Also to be acknowledged areMr. Joseph Kanyiri and Mr. Muigai Mwaura of the Science workshops, Kenyatta University and Mr. James Kuria of the Mechanical Engineering Workshops, University of Nairobi for their support and advice during the construction of the experimented project.
I am also grateful to my colleagues Mr. Elias Ako and Mr. Simon Mwangi for their company and constant support and suggestions to make this project a success.
v
I cannot forget to thank my wife and children for their understanding, encouragement and prayers when the problems seemed overburdening and their untiring efforts and sacrifices, which have helped me come this far.
Lastly, I would like to thank the Almighty God for his favour, provision, love, protection and His mercy and Grace that has always been sufficient all through my studies.
vi TABLE OF CONTENTS CONTENTS
PAGE
Declaration
ii
Dedication
iii
Acknowledgement
iv
Table of Contents
vi
List of Tables
xi
List of Figures
xiii
Nomenclature
xv
Abbreviations and Acronyms
xix
Abstract
xx
1.
CHAPTER ONE: INTRODUCTION
1
1.1
Background of the Study
1
1.2
Problem Statement
3
1.3
Justification
3
1.4
Objectives
4
1.5
Research Hypothesis
4
1.6
Scope
4
2.
CHAPTER TWO: LITERATURE REVIEW
5
2.1
Micro Hydro Power
5
3.
CHAPTER THREE: BASIC THEORY
10
3.1
Introduction
10
3.2
Hydroelectric Power
10
vii 3.3
Hydraulic Turbines
11
3.4
Performance of Hydraulic Turbines
15
3.4.1
15
Mechanical Efficiency
3.4.1.1 Net Head and Power Input to Hydraulic Turbine
15
3.4.1.2 Losses in a Turbine
19
3.4. 1.3 Power Output from a Turbine and Efficiency
23
3.4.2
27
Specific Speed
3.5
Pumps as Turbines
28
3.6
Vehicle Axle-Propeller Shaft System
29
3.7
Vehicle Final Drive as a Turbine
31
4.
CHAPTER FOUR: METHODOLOGY
35
4.1.
Introduction
35
4.2
Experimental Hydropower System Components
35
4.2.1
Testing Site
35
4.2.2
Intake
38
4.2.3
Penstock
39
4.2.4
Power House
41
4.2.5
Turbine
42
4.2.6
Tail Race
42
4.3
Design Parameters and System Construction
42
4.3.1. Vehicle Axle Propeller Shaft as a turbine
43
4.3.2
Final Drive of a vehicle
44
4.3.3
The Runner Buckets
45
4.3.4
Nozzle and Turbine Casing
46
4.3.5
Mounting Frame
49
viii 4.3.6
Installation of the test turbine
51
4.4
Cost of Vehicle Axle as a Turbine
52
4.5
Turbine Testing
52
4.5.1
Method
52
4.5.2
Brake Power Method
53
4.5.3
Electrical Method
56
4.5.4
Measurement of Test Parameters
58
4.5.4.1 Site Head
58
4.5.4.2 Discharge
59
4.5.4.2.1 Flow Measuring Weir
59
4.5.4.2.2 Container Method Flow Measurement
61
4.5.4.3 Turbine Loads and Speeds
62
4.5.4.4 Voltage, Current and Frequency
63
4.6.
Calibration of Testing Equipments
64
4.7
Testing Site Development cost
65
4.8
Transmission System
66
5.0
CHAPTER FIVE: RESULTS AND DISCUSSION
68
5.1.
Introduction
68
5.2.
Gross Head
69
5.3
Discharge
69
5.4.
Test Turbine Hydraulic Power input, Power Output and Efficiency
70
5.5.
Turbine Output Characteristics
71
5.5.1
71
Turbine Output characteristics at Changing Flow rates
ix 5.5.1.1.
Part Flow Efficiency
71
5.5.1.2.
Loaded Speed against Power Output
72
5.5.1.3. Speed versus Efficiency at Changing Flow Rate
74
5.5.2. Turbine Output Characteristics at Constant Flow Rate
75
5.5.2.1 Loaded Speed against Power output
75
5.5.2.2 Loaded Speed against Efficiency
76
5.5.3. Specific Speed, Ns
77
5.5.4. Loaded to a Generator
78
5.6.
Cost per kW Turbine Output
81
5.7.
Financial Evaluation
81
5.7.1
Introduction
81
5.7.2
Life Cycle Costing of Experimental System
82
5.7.3
Comparison of Capital Costs
82
5.7.4
Comparison of the ALCC and the LEC of the two systems
84
5.7.5
Environmental Benefits of Small hydropower Schemes
85
5.8.
Error Analysis
85
5.8.1
Data Error
86
5.8.2
Error due to approximations
86
5.8.3
Standard Deviation (Variance)
86
5.8.3
Plotting of curves
86
6.
CHAPTER 6: CONCLUSIONS AND RECOMMENDATIONS
87
6.1
Conclusions
87
6.2.
Recommendation for Further Work
90
x 7.
REFERENCES
91
8.
APPENDICES
97
Appendix A
Sample Raw Data for Various Experiments
97
Appendix B
Design parameters and calculations for the turbine
107
Appendix C
Test Site Developments Costs
114
Appendix D
Life Cycle Costing
116
Appendix E
Cost data for Life Cycle Costing
119
xi LIST OF TABLES TABLE
TITLE
Table 2.1
Classification of hydropower by size
Table 2.2
Costs of turbines in units of USD 1,000 excluding alternator and drive
Table 2.3
PAGE 5
8
Cost of cross-flow and single jet pelton microturbines in units of US $ 1,000 excluding alternator and drive
8
Table 3.1
Variation of Vapour Pressure Head with temperature
20
Table 3.2
Typical efficiencies of small turbines
25
Table 3.3
Specific speed range for different turbines
28
Table.4.1
Geographical coordinates of the test site
37
Table 4.2
Cost of turbine materials and components
52
Table 4.3
Projects costs excluding the turbine
66
Table 5.1
Head measurement readings as taken using a dumpy level
69
Table 5.2
Results of the discharge using the weir and container methods
69
Table 5.3
Performance of the vehicle-axle propeller shaft as a turbine
70
Table 5.4
Manufacturer‟s ratings of the synchronous generator
78
Table 5.5
Voltage V, Current I and Frequency f with power fed to ballast load of 4 cooking coils of 1100 W each
Table 5.6
Voltage V, Current I and Frequency f with power fed to ballast load of 2 cooking coils of 1100 W each
Table 5.7
79
79
Life cycle comparisons between the vehicle axle propeller shaft as a turbine for power generation and a diesel generator
83
Table 5.8
Carbon dioxide production by various energy sources
85
Table A-1
Sample Data Sheet for discharges – container method
98
xii Table A-2
Sample Data Sheet for discharges –weir method
100
Table A-3
Sample Data Sheet for penstock losses and hydraulic power
102
Table A-4
Sample Data Sheet for turbine brake loading
103
Table A-5
Sample Data Sheet for turbine power output computation
104
Table A-6
Sample Data Sheet for test turbine power input, power output and part load efficiency
Table A-7
Sample Data Sheet for electrical method with ballast load 4 cooking coils of 1100 W each
Table A-8
105
105
Sample Data Sheet for electrical method with ballast load 2 cooking coils of 1100 W each
106
Table B-1
Characteristics of different turbines
108
Table B-2
Typical values of Cc and Cv
108
Table B6-1
Values of bending moment Cm and torsional moment Ct factors
113
Table C-1
Intake, penstock and power house development costs
115
Table E-1
Retail prices of diesel in Kenya
119
Table E-2
Load factors
121
Table E-3
Technical data for LCC Comparison between a vehicle axle propeller shaft as a turbine and diesel generator
122
Table E-4
Present Worth of major service costs
123
Table E-5
Present worth of operation, minor service and fuel costs
123
xiii LIST OF FIGURES FIGURE
TITLE
PAGE
Fig. 3.1
Layout of a typical micro-hydropower scheme
11
Fig. 3.2
Turbine Applications ranges for outputs of one Megawatt and below
14
Fig 3.3
The Moody Chart for wall friction losses in pipes
16
Fig 3.4
Net head definition
19
Fig.3.5
Part flow efficiencies of various turbines
25
Fig. 3.6
Part load efficiencies of small water turbines
26
Fig.3.7
Simple method transmitting the drive from the propeller shaft to the back axle by means of a pinion and crown wheel
30
Fig. 3.8
Arrangement of bevel gear and differential in the real axle
31
Fig. 3.9
The bucket dimensions
33
Fig. 4.1
Map of Kenya showing Thima pico hydropower test site
36
Fig. 4.2
Geographical location of the Thima pico hydro project test site
37
Fig. 4.3
Philips Fall on Rutui river
38
Fig.4.4
Intake of the test site
39
Fig.4.5
Layout plan of the test site and the penstock longitudinal profile
40
Fig. 4.6
Lay out plan of the power house
41
Fig. 4.7
Vehicle axle propeller shaft installed at the end of the Penstock
42
Fig. 4.8
Vehicle axle propeller shaft being modified to a water turbine
43
Fig. 4.9
Motor vehicle rear axle
44
Fig. 4.10
Wheel rim and runner bucket
45
Fig. 4.11
Buckets being blazed on the groove of a vehicle wheel rim
46
Fig.4.12
Turbine casing and nozzle assemblies
47
Fig. 4.13
Turbine nozzle being fabricated
48
xiv Fig. 4.14
Turbine casing being fabricated
48
Fig. 4.15
Setting a 5 mm clearance between runner and nozzle
49
Fig. 4.16
Turbine mounting frame
50
Fig. 4.17
Vehicle axle propeller shaft as a turbine being aligned with the penstock system
51
Fig. 4.18
Brake load test rig
54
Fig. 4.19
Head measurement using a surveyor‟s dumpy level
58
Fig. 4.20
Rectangular discharge/flow measuring weir
59
Fig.4.21
Flow measurement using the container method
62
Fig.4.22
Vehicle axle propeller shaft as turbine being tested using the brake load method the brake method
Fig. 4.23
63
Vehicle axle propeller shaft as turbine being tested using the electrical method
64
Fig.4.24
Calibrating the weighing balance
65
Fig. 4.25
Electricity distribution network for the Thima community pico hydro power scheme
67
Fig. 5.1
Part Flow efficiency curve
72
Fig. 5.2
Turbine runner loaded speed against turbine power output at changing flow
73
Fig. 5.3
Turbine runner loaded speed against turbine efficiency at changing flow
74
Fig. 5.4
Turbine runner loaded speed against turbine power output at constant flow
75
Fig. 5.5
Turbine runner loaded speed against turbine efficiency at constant flow
77
Fig. 5.6
Turbine and generator system
80
Fig. B6-1
Mechanical power transmission shaft from the differential system to the pulley
110
xv
NOMENCLATURE Symbol
Description
Unit
A
Cross-sectional area of a water jet
m2
B
Width of tail race channel
m
b
Width of Weir
m
C
Hazen-Williams coefficient
None
C
Capacitance
µF
Cc
Contraction coefficient
None
Cd
Coefficient of discharge
None
Cm
Shock factor
None
Ct
Fatigue factor
None
Cv
Coefficient of kinetic energy loss
None
d
Diameter of pipe
m
Dr
Diameter of runner
m
Dp
Diameter of pulley
m
di
Diameter internal
m
dj
Diameter of water jet
m
do
Diameter outside
m
E
Energy per unit weight
W/kg
F
Flow Friction factor
None
f
Frequency
Hz
g
Acceleration due to gravity, 9.81
m/s2
H
Gross head
m
Hatm
Atmospheric pressure head
m
xvi HI
Total head across impeller
m
Hmin
Minimum pressure head
m
Hn
Net head
m
Hs
Turbine setting head
m
Hv
Vapour pressure head
m
Hwc
Height of weir crest above the channel bed
m
h
Depth of water above weir crest
m
hwc
Head of water above weir crest
m
hc
Head loss in turbine casing
m
hi
Head loss in impeller
m
ht
Head loss due to turbulence
m
hw
Head loss due to wall friction
m
i
Annual interest rate
%
I
Electric current
Amps
K
Head loss coefficient: intakes, bends, contractions, valves
None
k
Blade skin coefficient
None
α
Kinetic energy correction factor
None
L
Length of Pipe
m
Lp
Length of Pipe
m
M
Moment
NM
N
Speed of runner
Revs/minute
Nb
Number of buckets
None
Nc
Critical speed of a propeller shaft
Revs/minute
Nj
Number of water jets
None
Ns
Specific speed
None
xvii η
Efficiency
%
θ
Water jet deflection angle
Degrees
Ø
Diameter
mm
σT
Thomas cavitation coefficient
None
ρ
Density of water
kg/m3
p
Pressure of water
m
P
Power
kW
p.c.d
Pitch circle diameter
m
Pi
Turbine power input
kW
Pm
Mechanical power losses
kW
Po
Turbine power output
kW
Q
Water flow rate
m3/s
Qi
Volumetric flow through impeller
m3/s
q
Volumetric flow leakage past the impeller
m3/s
R
Radius
m
S
Spring balance reading on the slack side of a pulley
N
Suts
Ultimate tensile strength of steel
MN/m2
Sy
Yield strength of steel
MN/m2
t
Time
s
Ve
Water velocity
m/s
Vo
Voltage
Volts
ω
Angular Velocity
Rads/sec
T
Torque
N-m
Te
Temperature
0
tp
Permissible stress of steel
MN/m2
C
xviii u
Runner peripheral velocity
m/s
V
Average water velocity
m/s
Va
Velocity of approach
m/s
Vjet
Velocity of water jet
m/s
W
Power
Watts
Ws
Spring balance reading on the tight side of running pulley
N
φ
Phase angle
degrees
xix ABBREVIATIONS AND ACRONYMS ALCC
Annualized Life Cycle Cost
ASME
America Society of Mechanical Engineers
A
Amphere
BP
Brake Power
CBSK
Central Bureau of Statistics of Kenya
Esha
European small hydropower association
FCE
FinnConsult Consulting Engineers
Kg
Kiloogram
Ksh
Kenya Shillings
kW
Kilowat
kWh
Kilowatt hour
LEC
Levelized Energy Cost
LCC
Life Cycle Cost
MHP
Micro Hydro Power
MN
Mega Newton
MW
Megawatt
PAAT
Propeller Axle As Turbine
PAT
Pump As Turbine
p.c.d
Pitch Circle Diameter
rpm
Revolution Per Minute
SD
Standard Deviation
$
Dollar
USD
United States Dollar
V
Volt
W
Watt
xx
ABSTRACT
Micro hydropower generated electricity can function as an effective tool for rural development. One of the barriers to smooth implementation of community/village micro hydropower schemes in the country is lack of appropriate hydraulic turbines, thus making the site specific costs of micro hydropower rather high, hence not easily affordable by the rural communities. The purpose of the study was to investigate the use of a vehicle live axlepropeller shaft system to replace conventional turbines for micro hydropower generation. There are axle-propeller shafts of many vehicles that have fallen into disuse and are commonly found in many motor vehicle scrap yards. New ones are also entering the Kenyan market with the small vehicles (saloon cars; station wagons; panel Vans, Pick-ups, lorries/trucks, buses/coaches and minibuses/matatus) comprising the biggest percentage, for example in the year 2008, out of 121,831 newly registered vehicles 65,556 (53.8%) belongs to this category. The study was carried out mainly to investigate and establish the performance of the live rear vehicle axle-propeller shaft as a micro hydropower electricity generation system with the objective of lowering the unit cost of hydropower generation in small water streams. This was done by modifying a vehicle axle propeller shaft system by fixing designed buckets on the wheel rim to take the role of a turbine runner and replacing the propeller shaft right from the rear universal joint with a solid bright steel shaft where mechanical power is generated and tapped. A wheel rim/turbine casing with a nozzle for creating a water jet was fabricated and together with a mounting frame for the axle formed a complete Vehicle Propeller-Axle as a Turbine (PAAT). A jet of water from the nozzle strikes the buckets and the kinetic energy is converted into rotating shaft power by the wheel rim and the rear axle. The power is transmitted through the differential box with an accompanying speed increase to the rear universal joint where a shaft is fixed for eventual mechanical power take off. The power can be used to drive mechanical equipments or an alternator to generate electricity. The performance of the propeller-Axle as a turbine was tested at a community hydropower site in Kirinyaga, constructed for this purpose. The tests were conducted to determine the power output and efficiency under a constant head and different discharges. The final result of the study was a low cost vehicle axle-propeller shaft system operating as a turbine (cost of USD 274.4), generating 1.18 kW of shaft power at an optimum flow rate of0.0238 m3/s at a gross head of 21.874 m and at an optimum loaded runner speed of 500 rpm. The specific speed of the modified vehicle system as a hydraulic turbine was 12. The energy cost from a hydropower scheme using a vehicle axle-propeller shaft as a turbine is 10 times cheaper than that of a similar scheme using a diesel generator as its source of power. These research findings are an important contribution to providing a solution to increasing use of micro hydropower for rural electrification by making the technology available and affordable to individual and communities in the rural areas. Vehicle drive systems are available as dumped materials in most metal scrap yards and car garages scattered across the country and they are an environmental hazard as there are no vehicle parts re-cycling facilities in the country.
xxi
CHAPTER ONE INTRODUCTION
1.1
Background
Hydropower is the energy contained in flowing water in rivers and streams as it descends towards sea level. This power can be converted into mechanical and/or electrical energy and its potential in a river or stream is determined by the amount of flow (Q) and the available head (H).
The hydroelectric power potential in Kenya is about 6000 MW (30 000 GWh/year). Half of this potential is located in small rivers where harnessing for national grid connection is hampered by the small nature of the rivers and the rugged topography that characterize the country‟s terrain (World Bank Staff Appraisal, 1988).
The total electricity generation installedcapacity in Kenya by end of June 2009 was 1331 MW of which hydropower‟s share was 737.3 MW with an effective capacity of 723.1 MW. The total hydropower generation for 2007/2008 was 3488.6 GWh. The bulk of this power was generated from the large hydro dams: Tana – 14.4 MW, Wanjii – 7.4 MW, Kaburu – 94.2 MW, Gitaru – 225 MW, Kindaruma – 40 MW, Masinga – 40 MW Kiambere – 144 MW, Turkwel – 106 MW, SonduMiriu – 60 MW and the small hydropower stations of Gogo – 2.0 MW, Sociani –0.4 MW, MESCO – 0.38 MW and Sagana–2.0 MW (KenGen, 2008)
For the numerous small rivers and streams in the country, decentralized micro hydropower installations is the best way to exploit their hydropower potential. This is due to their small
xxii potential (less than 100 kW) which renders them fall outside the “least cost power development plan”. Implementation of Rural Electrification Programs has been very slow and time consuming process, no matter the efforts and financial input (Sanier and Mohanty, 1992). For example, in the USA it took half a century to complete the electrification of the rural areas. Kenya has been no exception. Currently, about 3.8 % of rural households have access to electricity as compared to 46% for urban households (Kamweti-KamFor, 2002). This figure can be increased by using decentralized electricity generation from micro hydro, wind, solar and diesel generator sets.
These generating plants can be economically applied to serve
consumers with power in the rural areas. Of all these sources, micro hydro power has been found to produce electricity cheaply than all other competing sources (Walkade, 1986; Chullakesa, 1992)
In hydroelectric engineering, turbines and generators occupy key positions and they form a considerable part of the total project cost. Civil costs are site specific. For small schemes, pico and micro sizes (Table 2.1), to bring down the costs and to make the technology easily and readily available, standard pumps and induction motors, which are cheap and easily available have been used instead of the conventional turbines and generators (Smith, 1995; William, 1995). However, for Kenya, they are still imported. On the other hand, automobiles are mass-produced and are part of today‟s world life. Their main work is to provide motive power. The automobile of today is a result of the accumulation of many years of research and development. It is a highly sophisticated machine involving numerous efficient and dependable mechanical and electrical devices. Once out of use, they are dumped in various scrap yards. They waste space and are an environmental hazard (Giri, 1979).Therefore, in this study the use of a vehicle drive dive system (Vehicle Axle Propeller Shaft (VAP)) to operate as a micro turbine for power generation was undertaken.
xxiii
1.2
Problem Statement
The problem of high costsrural electrification by grid and the importance of rural electrification for growth of national economy calls for another approach – decentralized electric generation.
Micro hydropower is a cheaper and viable alternative. However,
exploitation of MHP demands the use of micro turbines, which are currently imported, as there is no established local manufacturing capacity in Kenya. They are expensive, long delivery time, not easy to install and spare parts not easily available. Even if local capacity is established, unless batch produced they will tendto be expensive. Pumps can also be used as turbines, but they are also imported. No study that has explored the use of home-grown technologies to lower down the costs and ensure their serviceability. The task of this study was to develop an alternative and appropriate MHP turbine using locally available materials and resources in Kenya. The technology can be used by individual farmers, rural communities and small commercial enterprises for harnessing MHP in small streams and rivers for their own benefit.
1.3
Justification
Rural electrification using grid connection is expensive and the alternative source of MHP is the cheapest known way of producing power for rural areas (Walkade, 1986). There are several small rivers and streams in large portions of the country. If their energy can be exploited cheaply and easily, the standard of living of rural population would be improved. This can only be achieved through home-grown solutions to the technology barrier.
xxiv
1.4
Objectives
The general objective of this study is toreduce the cost of unit power generation in micro hydro-electric power plants by developing a low cost device for converting the kinetic energy in the water to mechanical power.
The specific objectives of the study were to: (i)
Modify a vehicle drive system to operate as aturbine for micro hydropower generation;
(ii)
Determine performance characteristics of the turbine;
(iii)
Determine the comparison in terms of cost per kW of shaft power and
(iv)
Carry out an economic analysis of the modified vehicle drive system as a microhydropower turbine.
1.5
Research Hypothesis
There have been many researches about hydraulic turbines all geared towards cheaper power generation. However, their affordability and availability to rural communities has been far from over. The problem can further be improved through exploration and adoption of home grown solutions with one of them being the use of a modified vehicle drive system as a hydraulic turbine.
1.6
Scope
xxv The main focus was the vehicle live axle – propeller shaft system operating as turbine. The study investigated its operation as a water turbine for power generation at Philip fall on Rutui river in Thima Village, Kirinyaga district, about 130 Km to the north-east of Nairobi.
CHAPTER TWO LITERATURE REVIEW 2.1
Micro Hydro Power
There is no universal definition of small-scale plants and different countries and organizations have different classifications. The common definition of micro hydro power plant is one with an installed capacity of less than 100 kW and Mini hydro between 100 – 500 kW (Monition, et al.,1984; Harvey, 1993; Khennas and Barnett, 2000). It has been estimated that 26% (Manwell, 1988) of all global technically developable sites have capacities less than 1000 kW. The potential output depends on available head and water flow rate and also on a result of optimization process based economic and technical parameters (Shanker and Krause, 1992).A more precise definition of the classification of hydropower by size is given in Table 2.1.
Table 2.1
Classification of hydropower by size
Classification
Size & Application
Large hydro
More than 100 MW and usually feeding to a large electricity grid
Medium hydro
15 – 100 MW usually feeding to a grid
Mini hydro
Above 100 KW but below 1 MW either stand alone schemes or more often feeding into the grid.
Micro hydro
Ranging from 5 kW for battery charging or food processing applications
xxvi up to 100 kW, usually provided power for a small community or rural industry in remote areas away from the grid. Pico hydro
Ranging from a few watts to 5 kW for battery charging and providing power to a community.
Source: Fraenkel et al., 1991 Several factors influence the feasibility of MHP plant site. These include: (i) the available head, (ii) the flow rate and its distribution through a hydrological year, (iii) the potential electricity demand in the area, (iv)the distance between the plant site, the grid supply and the load centre and, (v) the existing infrastructure (Kaberere, 1999).
MHP has a number of advantages over fossil based and large-scale hydro including: (i) simple technology, (ii) decentralization of MHP sites concedes with dispersed nature of population, (iii) most sites are near load center, (iv) short implementation periods, (v) no environmental damage as they are mostly run-off the river schemes and, (vi) have village participation (Kaberere, 1999).
However, they have some obstacles to their viable implementation. These include (i) high capital cost per installed kW, average US $ 3,000 (ii) effects of seasonal river flow variations (iii) attitudes/policy of lending agencies (iv) lack of good hydrological data (Kaberere, 1999).
The estimated MHP potential of identified sites (>50 kW) in Kenya totals to 22,394 kW (Njau - 1976; Bank, et al., 1978; FCE, 1981). Of this only 2,087 kW has been harnessed. There are other numerous sites excluded due to the remote location by then, proximity to grid and their small outputs (Hv) orσT> σ.
Another method to control the occurrence of cavitationis given by (Esha, 2004)
Ns equal or less than 0.686σ0.5882
Where Ns is the specific speed of the turbine.
(3.17)
xliii In hydropower plants, cavitation is thus prevented by submerging turbines to a low level, that calls for costly excavation works.
Cavitation is a major problem in reaction turbines like the Francis and Kaplan. It has also been noted that local cavitation can occur on Pelton buckets if the inlet edge is not properly designed or if the laboratory tested shape has not been fully respected during manufacture (Esha, 2004).
Cavitation can also occur as a result of a liquid containing dissolved air or other gases. The gas or air bubbles are released in the same manner as vapour bubbles (Douglas et al., 1983). It is thus imperative to design intakes of hydropower plants well such that they don‟t allow air into the penstock system.
Without considering loss of efficiency due to cavitation, the energy balance in kW in a turbine (Douglas et al., 1983) is given by
Fluid power input=Mechanical losses+Impeller Losses+Casing Losses+leakage losses (3.18)
The fluid power output in equation format is given as
ρgQHn = Pm + ρg(hiQi) + hcQ + H1q) + Pshaft power output (Douglas et al., 1983)
Where
(3.19)
xliv Q is the water flow rate in m3/s, Hn the net head, Pm the mechanical power losses in kW, hi the head loss in the impeller in m, Qi the volumetric flow rate through the impeller in m3/s, hc the head loss in the turbine casing in m, HI the total head loss across impeller in m,q the volumetric flow leakage past the impeller, ρ the density of fluid in Kg/m3 and g the acceleration due to gravity in m/s2 (Douglas et al., 1983).
Mechanical losses are due to the bearings and sealing gland, impeller losses are due to loss of head across the impeller, casing losses are due to friction and separation in the casing, while leakage losses are due to flow leakage across the impeller.
3.4.1.3
Power Output from a Turbine and Efficiency
The efficiency of the turbine is given by the expression
η=
Power output from shaft= Fluid Power input
P gHnQ
(3.20)
The power output, shaft power is given by the expression (Douglas etal., 1983)
Po= ωT
(3.21)
Where ω and T are the angular speed and developed torque respectively.
For impulse turbines, like the Pelton, energy transfer to the turbineis given by (Douglas etal., 1983)
E = (u/g)(V1-u)(1-kcosθ)
(3.22)
xlv Where V1 the absolute velocity of the jet and, u is the peripheral velocity of the runner, k is the blade skin coefficient and θ is the jet deflection angle (Rajput, 1998).
Theoretically, the maximum energy transfer occurs when the velocity of the runner is half the velocity of the jet of water at inlet (Douglas et al., 1983)
Emax = V12/4g (1-kcosθ)
(3.23)
The power input can theoretically be given by the power of the jet which is given by the expression
Pjet = ρAV13 =ρ(Πd2/8)V13
(3.24)
(Rajput, 1998)
Where ρ is the density of water, A is the jet cross-sectional area, d the diameter of the jet and V1 is the velocity of the jet. The velocity of the jet is determined by
V1 = Cv(2gHn)1/2
(3.25)
(Douglas et al., 1983; Rajput 1998)
Where Cv is the coefficient of kinetic energy loss with values between 0.98and 0.99.
The maximum theoretical efficiency is thus given by
ηmax = (1-kcosθ)/2
(3.26)
xlvi The expression is valid when speed of the runner is constant. From experimentation, it has been found that the maximum efficiency occurs when the jet deflection angle is 1650to avoid interference between the oncoming and outgoing jets. The speed ratio of the runner to the water jet velocity is 0.46 (Douglas et al., 1983). Figure 3.5 when used with Table 3.2 indicates the typical efficiency guaranteed by manufacturers for several types of turbines.
Fig. 3.5: Part flow efficiencies of various turbines (Esha, 2004) Table 3.2: Typical efficiencies of small turbines (Esha, 2004) Turbine type Kaplan single regulated
Best Efficiency 0.91
Kaplan double regulated
0.93
Francis
0.94
Pelton n nozzles
0.90
Pelton 1 nozzle
0.89
Turgo
0.89
xlvii With the exception of Kaplan turbine, part load efficiencies for pelton and turgo wheels are generally better than reaction turbines. Depending on the type of turbine, the optimum efficiency does not occur at maximum flow but at part load flows of between 0.7 – 0.9. (Hothersall, 2004).This is attributed to deviation of flow from nominal discharge that makes the turbine‟s hydraulic efficiency deviate accordingly. This makes the design discharge different from the best efficiency discharge (Esha, 2004). Figure 3.6 shows part load efficiencies of small turbines within the optimum range.
Fig. 3.6: Part load efficiencies of small water turbines (Hothersall, 2004)
Efficiencies of simple small hydraulic turbines range typically between 60 and 75 percent while for very small turbines of less than several kW, the efficiencies are even less due considerable efficiency losses at the edges (Harvey, 1994). Efficiencies ofun-conventional turbinesare also low.These are the water wheel, water current turbine and the hydram with efficiencies being 0.2-0.60, 0.15-0.40 and 0.50-0.65, respectively (IT, 1994).
xlviii 3.4.2
Specific Speed
Another parameter which can be used to compare turbines is the specific speed which is defined as
Ns = (NP1/2)/ (Hn5/4)
(3.27)
(Dandekar and Sharma, 1979; Douglas, etal., 1983)
Where Nsis the specific speed, N rotational speed of the runner in rpm, P the turbine power output in kW, and Hnthe net head in m.
Clearly specific speed is not dimensionless. It is however the degenerate form of the nondimensional ratio.
NP1/2/ρ1/2(gHn)5/4
(3.28)
(Dandekar and Sharma 1979; Douglas et al., 1983)
With the ρ and g terms omitted as they are sensibly the same for all turbines encountered in practice, the term „specific speed‟ is then neither dimensionless („specific‟) nor a speed. It is better regarded as a „shape factor‟ and it is its ability to describe the shape of a turbine design independently of turbine size that makes specific speed useful to the turbine designer (Massey, 1989). Table 3.3 gives specific speed ranges of different types of turbines.
xlix Table 3.3: Specific speed range for different turbines
Turbine Type 1 –Jet Pelton 2 – Jet Pelton 3 – Jet Pelton 4 – Jet Pelton 6 – Jet Pelton Turgo Cross-flow Francis Kaplan Propeller
3.5
Specific Speed 10 – 35 10 – 45 10 – 55 10 – 70 10 – 80 20 – 80 20 – 90 70 – 500 350 – 1100 600 – 900
Pumps as Turbines
Reverse-running pumps have found various applications as turbines in industrial environments and in stand-alone or grind linked hydropower, especially in developed countries on account of the much larger size of their market, availability, lower cost and easier maintenance as compared to conventional turbines. The only difference between a pump-as-turbine (PAT) and a conventional turbine is the PAT lack of a flow control devicenecessitating it to have constancy in its operating conditions with the load variations being met by an electronic load controller (Altorre-Frenk et al., 1996).
There is also lack of performance information on pumps when in turbine mode. Performanceprediction methods of a pump in turbine-mode based on the geometry of the machine or the pump-mode performance or both have been proposed. One of the prediction methods that was shown to give better results than many others required as input data the pump-mode best efficiency point (BEP) flow Q in m3/s, net head Hn in m and the efficiency η for some given speed ω (Alatorre-Frenk et al.,1996). The turbine-mode BEP (head, flow and efficiency) for the same rotating speed is given by the equations 3.29, 3.30 and 3.31.
l HPAT =1.21Hpηp0.8[1+(0.6+InNsp)2]0.3
(3.29)
QPAT = 1.21Qpηp0.6
(3.30) 0.25
ηPAT = 0.95ηp0.7[1 + (0.5 + InNsp)2)]
(3.31)
(Alatorre-Frenk et al., 1996)
Equations 3.29 and 3.30 shows that, to operate at peak efficiency and at the same speed, the head and flow in turbine mode are much large (20 to 60 per cent) than in pump mode.
3.6
Vehicle Axle-Propeller Shaft System
In a vehicle, the source of power is the fuel that can be either gasoline/dieselor lately biofuels and electric. The fuel in chemical form is burned with the right amount of air in an enclosed cylinder with the final output being shaft power. This power is then transmitted to the wheels for the vehicle to be mobile. The power transmission system in sequence comprises of a clutch system, a gearbox system and the final drive system.
The final drive system which is the one used in this study comprises of the propeller shaft, the rear axle with wheels at the two ends and the differential. The propeller shaft transmits the drive from the main or output shaft of the gearbox to the rear axle through the differentiating mechanism. The differentiatingmechanism divides the drive by use of bevel gears and at the same time makes a speed reduction in addition to making it possible for the individual variation of rotation of either wheel, while still maintaining the drive. Because of this, the real wheels cannot be fixed to the same axle shaft as shown in Figure 3.7.Each must be mounted on a separate shaft (Abbey, 1959)
li
Fig 3.7: Simple method transmitting the drive from the propeller shaft to the back axle by means of a pinion and crown wheel. (Abbey, 1959)
The problem of maintaining the drive from the propeller shaft to each axle shaft but allowing independent motion between the shafts is solved by the use of a differential gear as shown in Figure 3.8.
The differential bevel-gears reduces the speed from the propeller shaft by a ratio of 3:1 to 5:1 for passenger vehicles and 5:1 to 11:1 for trucks. Propeller shafts of road vehicles are sufficiently long and operate in general at high speed and to avoid any whirling effects they are made tubular and also well balanced. Their critical speed varies directly as the diameter of the tube and inversely as the square of the length as given by the following equation Nc = 1,890,000 (do2 + di2)/L2 (Giri, 1979)
(3.32)
lii
Fig 3.8: Arrangement of bevel gear and differential in the real axle (Abbey, 1959)
3.7
Vehicle Final Drive as a Turbine
The final drive of a vehicle when operated in reverse can perform the role of a hydraulic turbine. This requires modification. The wheels need to be turned by an external force and the power transmitted through the differentiating mechanism to the propeller shaft where it can be tapped. This is achieved by introducing water buckets on the wheel rim that can convert kinetic energy in a water jet into shaft power. As the propeller shaft is tubular, this is substituted with a solid shaft where power is tapped either using a direct coupling if the speed matched that of the alternator or pulley/belt drive system for any speed step up/down.One of the advantages of the final drive system of a vehicle is that it is well-engineered and tested technology, which can operate for long periods and also offers a speed step-up mechanism when run in reverse. The recommended practical speed range of water turbines for 1500 RPM alternator drives is 400-1500 RPM (Giri, 1979; Harvey, 1993)
liii When operating as a turbine, the two wheel rims needs to turn together to avoid slip in the differential. To achieve this, the two shafts are welded on the crown wheel. As the turbine will operate in between a water wheel and pelton turbine, the number of blades/buckets is determined by the following equation used for pelton wheels (Harvey, 1993)
Nb = ((Dr/dj) x 0.5) + 14
(3.33)
(Harvey, 1993) Where Dr and djare determined by the equations given in the Appendix B3. The profile and shape of a pelton bucket has evolved for maximum efficiency through experience and theoretical modelling over many years and is normally split into two halves so that a central area does not act as a dead spot incapable of deflecting water away from the incoming jet. A cut away notch is made on the lower lip to allow the following bucket to move further into place before interfering with the jet which is still propelling the earlier bucket (Harvey, 1993)
IfL is the width/length of the bucket, B the width of the bucket, T the depth of the bucket as shown in Figure 3.9 and D the diameter of the runner, then for optimal performance
L/d = 2 to 3; B/d = 3 to 4; D/d = 11 to 16; T/d =0.8 to 11.2; Notch width = 1.1d + 5 mm (Rajput, 1998)
liv
Fig. 3.9: The bucket dimensions (Source: Rajput, 1998)
For most pelton bucket designs, maximum flow rates are based on a maximum nozzle size of 12% of the runner pitch circle diameter. If this is exceeded, it will result in a significant drop in efficiency. Hence, for a selected pitch circle diameter runner and head, the maximum flow rate is given by the following equation
Qmax = 0.05 x p.c.d2 x ( Hnet)1/2
(3.34)
(Maher and Smith, 2001)
Where p.c.d is the pitch circle diameter of the runner and Hnet is the net head.
The expected speed of the runner (pelton) is also given by expression
Nr = 38 x (Hnet)1/2/Dr (Harvey, 1993)
Where Dr is the diameter of the runner.
(3.35)
lv The relationship between the speeds of the runner (axle shaft speed) and the propeller shaft is determined by the gear ratio of the bevel-gear and is found by dividing the number of teeth on the drive gear by the number of teeth on the pinion. This gives the speed step-up/reduction ratio (Giri, 1979).
lvi CHAPTER FOUR METHODOLOGY 4.2.
Introduction
This chapter describes the methodology used in carrying out series of experiments. The experimental components are described and their design and construction details given. The design and construction of a hydropower testing site: intake, penstock, power house and a tail raceis given.
4.2
Experimental Hydropower System Components
The experimental system used in this study consists of a complete hydropower plant comprising of an intake, a penstock, a power house, a turbine and a tail race (Fig 4.5). Other than a conventional turbine, the final drive of a vehicle system is modified to operate as a hydro turbine. The flow through the turbine is regulated using a gate valve and installed before entry to the turbine and is determined using a constructed rectangular weir across the tail race channel just before joining the river. A full description of the components is given below:
4.2.1
Testing Site
The testing site was constructed on Philip Falls on River Rutui, Thima village in Kirinyaga district in CentralProvince of Kenya, about 130 kilometres North East of Nairobi.Figure 4.1 shows the site location on a map of Kenya.
The geographical coordinates of the site as taken using a Geographical Positioning System (GPS) Germin 12 Model are given on Table 4.1. On the map the site is between Embu and Nyeri Towns.
lvii
lviii Table4.1: Geographical coordinates of the test site Units
Intake
Power House
Latitude
Degrees, minutes and seconds
000 27‟ 36.0‟‟ S
000 27‟ 38.8‟‟ S
Longitude
Degrees, minutes and seconds
0370 15‟ 35.0‟‟ E
0370 15‟ 35.2‟‟ E
Elevation
M
1725
1705
Figure 4.2 shows the location of the site on a topographical map of f liner scale of 1:50,000
Fig. 4.2: Geographical location of the test site, Thima pico hydro project
lix The site has an existing small hydropower power plant generating about 2.2 kW. The topography of the site is characterised by a very steep valley. The river flows gently up to the intake and then drops through the Philip falls to a deeper V-valley. After the fall, the river then flows again gently without sizeable increase in head. Figure 4.3 shows the Philip fall, existing power house and the extension of the power house (test house) on the side of the river.
Fig. 4.3: Philip Fall on Rutui River. Near the base of the fall is the Power House (existing and the extended test house)
4.2.2
Intake
This was temporary a run off-the-river intake. The pipe inlet fitted was with a screen for sieving trash. The inlet to the pipe was then positioned 0.60 m below the water surface to
lx prevent air being drawn into the pipe as a result of vortex formation on the surface if the pipe is closer to the water surface (Harvey, 1993). The air bubbles reduces power output of the turbine and also induces turbine vibrations (Douglaset al, 1983). Figure 4.4 shows a photograph of the intake.
Fig. 4.4: Intake of the test site
4.2.3
Penstock
A 0.160 m (6 inch pipe) diameter PVC pipe running from the existing intake to the secondary power house, a total distance of 86.5 m was used.A reducer of 1 m length to change the diameter from 0.160 m to 0.100 mwas incorporated between the PVC pipe and a Ø0.100 m gate valve that controls water flow to the turbine.Two 450 bends are located at 45.15 m and 63.6 m from the intake. The gross head of the site between the water surface level at the intake and the turbine horizontal axis was 21.874 m while the total length of the PVC
lxi penstock was 86.5 m. Figure 4.5 shows the layout plan of the testing site and the penstock longitudinal profile.
Fig. 4.5: Layout plan of the test site and the penstock longitudinal profile
lxii 4.2.4
Power House
The power house was an extension of the existing power house and constructed using masonry stones on the side of the river with its dimensions being length 2.5 m and width 1.8 m. Entrance to the new power house was located on the partitioning wall between the two power houses. The tail race channel from existing power traversed underneath the floor of the new power house. Water from the test turbine flows and joins the tail race channel underneath the floor. Figure 4.6 shows the configuration of the power house.
Fig. 4.6: Layout plan of the power house
lxiii 4.2.5
Turbine
The test turbine is the Vehicle Axle Propeller Shaft. Buckets are fitted on the wheel rim and a pulley at the end of the propeller shaft for tapping the mechanical/shaft power. Figure 4.7 shows the test turbine installed at the end of the penstock.
Fig. 4.7: Vehicle axle propeller shaft installed at the end of the penstock.
4.2.6
Tail Race
The tail race channel conveys the water from the turbine back to the river. The existing tail race, a concrete channel measuring 0.47 m width and 0.275 m depth and 1.5 m length has a slope of 1: 8.5.
4.4 Design Parameters and System Construction The system was designed using standard procedures for hydropower systems (Harvey, 1993). It included use of the equations in appendix B2 to B6 for determining the runner diameter,
lxiv design of the buckets and their number, nozzle and the transmission shaft to replace the propeller shaft.The vehicle axle-propeller shaft system was coupled to the generation system.
4.3.1. Vehicle Axle Propeller Shaft as a turbine The rear vehicle axle-propeller shaft was modified to operate as a turbine. Most of the modifications and fabrications were done at Energy Engineering Department and Science Workshops of Kenyatta University. The vehicle axle model with a universal joint together with the wheel rims was purchased from a metal scrap yard. The propeller shaft was replaced by a solid bright steel shaft which was machined to the appropriate diameter of 25 mm at the Mechanical Engineering and Manufacturing Workshops of the University of Nairobi. Since a propeller shaft is normally splined so as to lock with the universal join, the shaft was also splined in a workshop in the city.Figure 4.8 shows a vehicle axle-propeller shaft being modified at Kenyatta University workshops to operate as a water turbine.
Fig. 4.8: Vehicle axle propeller shaft being modified to a water turbine
lxv 4.3.2
Drive System of a Small Toyota Vehicle
Thedrive of a vehicle system was purchased from the vehicle scrap yards as a whole unit comprising of two live half-axles and the wheel rims size 14 (360 mm) diameter, the differentiating mechanism and the rear universal joint. Figure 4.9shows the various features and dimensions of the final drive of a 1500 cc Toyota vehicle model.
A 25 mm diameter shaft made from bright steel replaced the propeller shaft. One end was splined so as to slide and lock with the universal joint while the other end, a key way was made where a 219 mm pulley is located. The diameter of the shaft was determined by the power to be transmitted with a safety marginof greater than 2.5 and the distance between the bearings being 300 mm (Appendix B6 for technical details).
Fig. 4.9: Motor vehicle rear axle
lxvi 4.3.3
The Runner Buckets
The buckets of the runner were made using galvanized iron sheet metal 3mm thick according to the design parameters for buckets (Rajput, 1998).
The maximum flow rate was
determined using equation 3.31 and found to be 0.03 m3/s giving jet diameter of 42 mm (design calculations Appendix B4).
The buckets aremade to follow the groove cross-section of the wheel rim as shown in Figure 4.10
Fig. 4.10: Wheel rim and runner bucket
lxvii The number of buckets were determined using equation 3.33 and were 18. They were blaze welded across the groove of the wheel rim. Figure 4.11 shows the buckets being blazed on the groove of the wheel rim.
Fig. 4.11: Buckets being blazed on the groove of the vehicle wheel rim
4.3.4
Nozzle and Turbine Casing
A conical nozzle was fabricated for creating the water jet. The diameter of the jet is given by the equation below
dj = (Cd0.5 x 0.54 x Qmax0.5)/Hn0.5
(4.1)
(Maher, 2001) where Cd is the coefficient of discharge = 0.98, Qmax is maximum discharge through the nozzle = 0.03 m3/s and Hn is the net head (20 m for this study). The jet diameter was 44.7 mm. For a tapered nozzle the coefficient of kinetic energy loss is 0.98 thus giving an effective jet diameter of 43.8 mm.
lxviii The nozzle was designed using the jet diameter of 42 mm and penstock diameter before entry to the turbine of 106 mm (4 inches). Ideally the taper of a nozzle cone is 140 (Maher, 2001). The nozzle needs a steel plate for it to be fixed to the turbine casing (See Appendix B5).
The turbine casing was constructed in such a manner that it aligns the runner buckets with the nozzle and the rest of the penstock and also the rear axle system. It was in two parts, the lower and the upper parts which can be separated in case of maintenance. Figure 4.12 shows the design of the turbine casing, the nozzle and base plate welded to the 106 mm Galvanized Iron pipe in such away that an optimum distance of 5 mm was left between the end of nozzle and the runner buckets.
Fig. 4.12: Turbine casing and nozzle
lxix Fabrication of the components was done at the Energy and Engineering Workshops, Kenyatta University. Figure 4.13 shows fabrication of the nozzlewhile Figure 4.14 shows fabrication of the turbine casing and Figure 4.15 aligning the turbine runner, turbine casing and the nozzle so as to ensure a clearance of 5 mm between the runner and nozzle.
Fig. 4.13: Turbine nozzle being fabricated
Fig. 4.14: Turbine casing being fabricated
lxx
Fig. 4.15: Setting a 5 mm clearance between runner and nozzle
4.3.5
Mounting Frame
The mounting flame supports the vehicle axle as a hydro turbine system and was constructed using 50 mm by 50 mm (2 inch) x 3.2 mm (1/8 inch) thickness angle line bars. The width of the frame was guided by the location of the two brackets on the axle, one on each side of the differential casing, that are used to bolt the vehicle body while the length was guided by the location of the two plummer block bearings and the shaft pulley such that the distance between the bearings was 300 mm and pulley to the bearing and additional 100mm so as to have a design safety factor of greater than 2.5.The height of the mounting frame was guided by the pitch circle diameter (p.c.d) of the runner and the horizontal axis of the water jet such that when the vehicle axle was placed on its right position on top of the mounting frame, the p.c.d of the runner and the water jet axis were each 100mm from the base of the frame. The design also allowed a 50mm clearance between the floor and the penstock inlet to the turbine casing for any maintenance purposes.The two plummer block spherical ball bearings allows
lxxi the shaft to rotate freely with a low coefficient of friction and at the same time hold the shaft in the correct position against any forces imposed on the shaft (Figure 4.16 and Appendix B Figure B6-1).
Holes of 8 mm diameter were drilled on appropriate locations of the frame where the vehicle axle and bearings will be bolted while 12 mm holes were incorporated for anchoring the frame to the foundation with bolts. Figure 4.16 shows the mounting frame being fabricated at the Science workshops, Kenyatta University.
Fig. 4.16: Turbine mounting frame.
lxxii 4.3.6 Installation of the test turbine The runner of the prototype vehicle axle propeller shaft as turbine underwent a balance test in normal petroleum outlet station equipped with the necessary equipments to avoid any vibrations which might be created by weight imbalance as a result of adding the water buckets. Mass weights were added where required to rectify any detected imbalance.The transmission fluid in the differential system was emptied and replaced with fresh one. The turbine was then installed in the power house and connected to the penstock. Measures were taken to align the turbine runner and the penstock. Figure 4.17 shows the turbine installation and alignment with the penstock system.
Fig. 4.17: Vehicle axle propeller shaft as turbine being aligned with the penstock system
lxxiii 4.4
Cost of Vehicle Axle as a Turbine
The construction of the vehicle axle as a hydro turbine system involved the components listed in Table 4.2.
Table 4.2: Cost of turbine materials and components (Ksh), 1 US $ = 78 Kshs in 2005) Component
Quantity
Unity Cost
Cost (Ksh)
Rear vehicle axle with two wheel rims
1
6,000
6,000
Universal joint
1
1,000
1,000
Spherical ball bearings in plummer block
2
1,500
3,000
Steel shaft Ø25mm length 500mm
1
1,300
1,300
2
600
1,200
Galvanized iron sheet metal 4ft x 4ft x 1
700
700
1,500
1,500
1 set
600
600
Pulley Ø220 mm
1
1,000
1,000
Paint
2 litres
300
600
Labour
Lot
inclusive of splining 50mm x 50mm x 3.2 mm Angle bars
2mm for the buckets Mild steel sheet metal for the turbine 1 casing 4 ft x 4ft x 1.5 mm Nozzle – GI pipe Ø100 mm, Length 250 mm, GI cone, 6mm steel plate
Total
4,500 21,400 (US$ 274.4)
4.5
Turbine Testing
4.5.1
Method
The hydraulic power (hp) of a turbine is the power available at the turbine inlet. The power that is available at the turbine shaft is called the shaft power or brake power (b.p.) of the turbine.
lxxiv The difference between hydraulic power and the brake power is the sum of the power that is lost in mechanical and fluid frictions during transmission.The mechanical efficiency which indicates this aspect of turbine performance is defined as the ratio of the brake power and the hydraulic power (Somandaram, 1975; Stone, 1999).
The brake power was determined using the friction method that employs use of a belt or the turbine can be made to run generator whose output power can be determined (Somandaram, 1975; Stone, 1999)
4.5.2
Brake Power Method
The brake power of an engine or hydraulic turbine is tested using the friction method which employs use of a belt or a rope or alternatively an electric dynamometer (Somandaram, 1975; Stone, 1999). The action of all power absorbing devices used for testing results in converting the rotational tendency of the shaft into a tangential force acting at some established distance from the centre of the rotation. The belt methodwas used in this study.
On the pulley side of the mounting frame, a rigid stand was erected using 50 mm steel square tubes and a 6 mm steel metal cross bar was used for testing of the turbine using the friction method as shown in Figure 4.18 where: 1. Pulley. 2. Asbestos belt. 3. Tensioning bolt. 4. Turbine mounting frame. 5. Test stand for hanging the spring balances. A. Spring balance on the slack side
lxxv B. Spring balance on the tension side S1. Spring balance for hanging counter weights.
3
A
B
Fig. 4.18: Brake load test rig (dimensions in mm)
lxxvi An asbestos belt of thickness 6 mm, embraced half of the pulley with two spring balances A and B on each side of the belt were hung from the rigid steel cross bar using hooks welded on threaded bolts. The load on the pulley was increased by increasing the tension on the belt and this was done by altering the spring balance reading using the bolts.
When the pulley turned towards spring balance A, the spring balance indicated the tension on the slack side of the belt. The other spring balance B indicated the tension on the tight side of the belt.
Given: W = Spring balance reading on the tight side of the belt in Newtons. S = Spring balance reading on the slack side of the belt in Newtons. Dp = Diameter of pulley. tb = Thickness of belt.
Then the nett or effective tangential force on the pulley against which the turbine acts is
F = Ws – S
(4.2)
(Somandaram, 1975; Stone, 1999)
Where N is the net effective force in Newtons.
Considering this net load to be acting along the centre line of the belt, the effective braking torque T in Newtons metre is given by
lxxvii T = (Ws – S) (Dp + tb)/2
(4.3)
(Somandaram, 1975; Stone, 1999) The brake power in watts is hence given by
B.P = (Ws – S)((Dp + tb)/2) x (2ΠN/60)
(4.4)
(Somandaram, 1975; Stone, 1999)
where N is the pulley speed in revolutions per minute.
4.5.3
Electrical Method
The second method for measuring hydraulic power of the turbine was the electrical method. The method involved coupling the turbine to a 2 kW electrical generator using two SPB Vbelts with each belt with a power transmission capacity of 10 kW.
The performance
characteristics of the generator as indicated on the manufacturer‟s plate was
Power output
2 kW
Voltage
230 volts
Current
8.7 Amps
Frequency
50 Hz
Synchronous Speed
1500 rpm.
Using equation 3.32, the theoretical operating loaded speed of the hydro turbine runner was expected to be 500 rpm. The differential system steps up the speed of the axle linked to the runner by a ratio of 2 to a 1000 rpm. The speed was transmitted to the propeller/power transmission shaft via the universal joint to the pulley fixed at the end of the shaft where the
lxxviii SPB V-belts coupled it to the pulley on the generator. Figure 4.12 shows the coupling configuration.
The diameter of the pulley at the end of the power transmission shaft was 219 mm. For the generator to be operated at its synchronous speed of 1500 rpm, a smaller pulley of diameter 146 mm, sized with the inverse of the speed step ratio of 1.5 (1000 rpm to 1500 rpm) was used.
Electrical cables of 6 mm2 linked the generator power output to a ballast load comprising of 4 cooking coils of 1100 W each and later the ballast load was changed to 2 cooking coils of the same rating.
The system was started by opening the gating valve to allow water flow impart energy into the runner buckets and in return the hydro turbine driving the generator. The electricity generated by the generator was dissipated through the cooking coils.
A power measurement cramp multi-meter was used to measure current, voltage and frequency of the generated power by cramping the device on the live cable of the electrical connections between the generator output and the ballast load. Various readings were obtained by increasing the flow from zero to the maximum at the same intervals used for testing the turbine using the friction belt method.
The expression in equation 4.5 gives the power output from a generator Pgen = I x V x Cosφ (Havey, 1993; Smith, 1995)
(4.5)
lxxix Where I is the current, V the voltage and φ the phase angle or power factor.
4.5.4
Measurement of Test Parameters
4.5.4.1 Site Head The gross head between the water surface level at the intake and the horizontal axis of the turbine was measured using a dumpy level (Tilting Level) Model - LEICA NA720 ART. No.641982 and made in Singaporewith an accuracy of 1 mm and was 21.874 m. Figure 4.19 shows head measurements using the dumpy level.
Fig. 4.19: Head measurement using a surveyor‟s dumpy level Model-LEICA NA720 ART No. 641982.
lxxx The same head when measured several times with an altimeter was 20 metres.The accuracy of an altimeter is 1 metre hence when readings are taken between two positions (intake and turbine axis) the error was plus or minus two metres. An altimeter measures atmospheric pressure and the pressure changes by 9 mm head for every 100 metres change in elevation (Harvey, 1993).
4.5.4.2
Discharge
4.5.4.2.1
Flow Measuring Weir
Discharge through the turbine was measured by use of a standard wooden rectangular weir constructed across the tail race (Holland, 1983). Figure 4.20 shows the various parameters of the weir.
Fig. 4.20: Rectangular discharge/flow measuring weir (Holland1983)
The parameters are: Width of the tail race channel, B
0.48 m
lxxxi Width of the weir, b
0.40 m
Height of the weir crest above the channel bed, P
0.10 m
Depth of water above the weir crest
hm
Using Francis equation for a rectangular weir that wasnot drownedand with two end contractions and with no velocity of approach, the discharge over the weir is given as follows:
Q = 2/3 x Cd x (b -0.2h) x (2g)1/2 h3/2
(4.6)
(Rajput, 1998)
Where Cd is the coefficient of discharge.
The coefficient of discharge for this kind of weir is 0.623. With g = 9.81 m/s2, the discharge is (Rajput, 1998)
Q = 1.84 (b - 0.2h)h3/2
(4.7)
(Rajput, 1998)
With a velocity of approach Va, the discharge over the weir becomes
Q = 1.84 b ((h + ha)3/2 – ha3/2)
(4.8)
(Rajput, 1998)
Where ha is the additional head due the velocity of approach and acting on water flowing over the weir. The additional head is determined by the expression
lxxxii ha = Va2/(2g)
(4.9)
(Rajput, 1988)
The velocity of approach Va, is the surface velocity V corrected with a factor of 0.85 (Harvey, 1993)
For each test speed, the height of the water above the weir crest was taken using a standard measuring ruler, above a nail head located 0.42 m upstream the weir. The head of the nail was on the same level as the crest of the weir.The approach velocity was measured using the float method. The time taken for a floating leaf to cover a distance of 1.5 m length between the weir and a point upstream was measured using stopwatches from the School of Engineering, Kenyatta University and the speed computed. For every test flow, the speed test was done five times and the average approach velocity computed (Holland, 1983; Harvey 1993; Rajput, 1998).
4.5.4.2.2
Container Method Flow Measurement
The method was incorporated in this study for cross checking the flow discharges obtained using the weir method. A gutter sheet of metal is placed in the channel after the weir and all flow directed toan oil drum whose dimensions are known, diameter - 567 mm and depth - 390 mm as shown in Figure 4.21. The time taken to fill the drum was taken with a laboratorystop watchand the flow rate then determined. For each test flow, five runs were done for comparison and repeatability. The averages were computed as recommended by Holland (1983) and Harvey (1993).
lxxxiii
Fig. 4.21: Flow measurement using the container method.The method is used accurately for flow rates of up to 20 litres per second (Holland, 1983, Harvey, 1993).
4.5.4.3 Turbine Loads and Speeds The Vehicle-Axle-Propeller as Turbine (VAPT) was tested to determine its performance at various flows. The flow was varied using the gate valve. At each steady flow, the parameters reading were taken: Speed of the pulley, Spring balances readings W and S, height of water above the weir lip h, breadth of weir, time (t) taken for a float to cover a certain length L of the tail face. For each test, five runs were done for comparison and repeatability. The averages were computed.
The speed of the turbine was measured using a mechanical tachometer model K 4538 made in England by Smiths London NW2 with accuracy of 20 rpm while spring balances SALTER Model of Englandwere usedwith accuracy of 0.2 kg to measure the tangential pulls on the turbine. Figure 4.22 shows the turbine speed being measured with the mechanical tachometer.
lxxxiv
Fig. 4.22: Vehicle axle propeller shaft as water turbine being tested using the brake power method
4.5.4.4 Voltage, Current and Frequency The turbine was coupled to a single phase electrical generator using V-belts as shown in Figure 4.23. The power from the generator was fed to a dummy load (ballast load). The flow was varied to the test discharge flows using the gate valve. A power multi-meter model from the micro-hydropower centre of Nottingham Trent University in the United Kingdom and given to the community was used to measure the generated voltage, current and frequency. At each stead flow, parameters of current, voltage, frequency, speed of generator and power factor were measured.
The first test was done with the electrical power produced by the generator being dissipated to a ballast load of 4 cooking coils of 1100 W and second test to a ballast load with 2 coils of 1100 W each.
lxxxv
Fig. 4.23: Vehicle axle propeller shaft as a water turbine being tested using the electrical method
4.6.
Calibration of Testing Equipments
The weighing balances model of UK and of accuracy of 0.2 kg for measuring the torque forces were calibrated using a known weight as shown in Figure 4.24.
Using a 25.4 Kg (56 lb) weight, reading on spring balance 1 (S1) on the left (S1) read 25.2 kg and the spring balance on the right (S2) read 25.4 kg. Spring balance 1 had an error of 0.8% while spring balance 2 had no error. The error in spring balance 1 was considered not significant to affect the results.
Two laboratory stop watches of Hanhart Felix model with accuracy of 0.2 seconds were used for time measurements were from Kenyatta University while the mechanical tachometer was
lxxxvi used to measure the turbine speeds was from University of Nairobi. The instruments are used for experimental and research work in the respective universities and hence were taken to have minimal errors and appropriate for this study without further calibration.
Fig.4.24: Weighing balances being calibrated
4.7
Testing Site Development Costs
The costs for the site excluding the turbine and transmission system are as summarized in Table 4.2.A detailed breakdown is given in Appendix C.
lxxxvii Table 4.3: Projects costs excluding the turbine Component
Cost (Ksh)
Civil works (intake, PVC penstock and accessories
125,675
and power house) Alternator and Control
57,000
Labour (20%)
36,400
Total
219,075 (US$ 2,738.4)
Cost up to Production of Mechanical power
115,975 (US$ 1,466.9)
(Ksh125,675 less KSh 9,700 for the electrical components)
4.8
Transmission System
The transmission system, comprising of 20,000 metres of 6.0 mm2 and 2.0 mm2 of insulated copper cables for the transmission and service lines respectively and 271 poles was in place before the research work, having been constructed in 2002 at a cost of Ksh372,300 (Thima Community, 2002). Figure 4.25 shows the distribution network of the scheme.
lxxxviii
Fig.4.25: Electricity distribution network for the Thima community pico hydropower scheme. Source: Maher, 2002
lxxxix CHAPTER FIVE RESULTS AND DISCUSSION 5.1.
Introduction
The data collected during the experiments were: Spring balance readings, pulley speed, head of water above the weir lip, breadth of the weir, time (T) taken for a float to cover a certain length L of the tail race, time also taken to fill the oil drum. Other constant parameters taken were: The gross hydraulic head, the total length of the penstock, the bends on the penstock, the speed increase ratio of the differential mechanism and the weir breadth. Detailed information appears in Appendix A.
Data collected in the electrical method are: current, voltage, frequency, power factor, running speed of the pulley as well as the flow ratemeasurements using the weir and container methods.
The power input to the turbine at various discharges and loaded speeds was computed using equation 3.4 where the net head was determined by computing the hydraulic losses using equation 3.5 and deducting them from the gross head of 21.874 m. The power output from turbine at various discharges and loaded speeds was determined using equation 4.4 and the efficiencies determined as a ratio of the power output to the power input. At each set flow rate, the power output increases with the load to a maximum value and the falls as the load is increased. The computed maximum power output values were plotted against the discharges and an efficiency curve of the turbine obtained.The specific speed was computed using equation 3.23 and the cost of the turbine per installed kW was computed as a ratio of the cost of the turbine to the maximum power output of the turbine. These results were analysed and discussed in detail in the subsequent sections. Samples of the raw data are presented in Appendix A.
xc
5.2.
Gross Head
The measurements taken by dumpy level are shown in Table 5.1
Table 5.1: Head measurement readings as taken using a dumpy level Back site (m)
2.558
Foresight (m)
1.757
0.001
0.133
0.260
0.413
4.101
4.924
4.900
4.863
4.468
3.740
Gross head = Total foresight – total back sight = 26.996 – 5.122 = 21.874 m.
5.3
Discharge
The discharge through the test turbine at various test speeds for both the weir and container methods are given in Table 5.2. Table 5.2: Results of discharge rates using the weir and container methods Discharge (m3/s)
Unloaded Speed of Propeller Shaft Pulley (rpm)
Weir Method
Container Method
0
0.0055
0.0050
200
0.0105
0.0108
400
0.0134
0.0124
600
0.0148
0.0146
800
0.0163
0.0164
1000
0.0194
0.0189
1200
0.0200
0.0199
1400
0.0208
0.0213
1600
0.0238
0.0261
1700
0.0256
-----
1810
Speed too high for any readings to be taken as the turbine was
xci unstable.
Comparison of discharge measurements using the weir and container method shows that, flow measurements of up to 0.0200 m3/s for the two methods compares very well but beyond this, the container method becomes unreliable due to splashing and too much error in the timing.
5.4.
Test Turbine Hydraulic Power input, Power Output and Efficiency
The power output and efficiency of the turbine at optimal loading are shown on Table 5.3
Table 5.3: Performance of the vehicle-axle propeller shaft as a turbine Discharge, Part Flow
Propeller Shaft Pulley Power
Power
Efficiency
Q
speed (rpm)
Input
Output
(%)
Q/Qmax
(m3/s)
Unloaded
loaded
(Watts)
(Watts)
0.0148
0.58
600
375
3001.1
180.73
6.02
0.0163
0.64
800
600
3295.8
366.13
11.11
0.0194
0.76
1000
600
3892.2
393.17
10.10
0.0200
0.78
1200
800
4007.4
553.82
13.82
0.0208
0.81
1400
800
4160.8
735.96
17.69
0.0238
0.93
1600
1000
4720.3
1178.83
24.97
0.0256
1.0
1700
800
5051
1021.65
20.23
The efficiency increases from zero at no flow to a maximum of 25% at a part-flow of 0.93 and drops to 20 % at full flow. This behaviour compares well with the conventional turbines as they have similar performance curves.
xcii
5.5.
Turbine Output Characteristics
5.5.1
Turbine Output characteristics at Changing Flow rates
5.5.1.1 Part Flow Efficiency From Table 5.3, a graph of efficiencyagainst part flow of the turbine was plotted as shown in Figure 5.1
It can be observed that a decrease in flow from the optimum level of 0.93 is accompanied by a sharp decrease in efficiency, showing the turbine has a poor performance part-flow characteristic.
The efficiency of the turbine increases with increase in the discharge/flow up to a maximum of 25 % at a part flow of 0.993, after which the efficiency drop with further increase in the flow. At maximum flow (Q/Qmax. = 1), the efficiency is 20%.
The trend conforms with the
conventional pelton turbines as shown in figure 3.5 where a large 1 nozzle pelton turbine has its maximum efficiency of 99% at a part flow of 0.85. Further increase in the flow is also accompanied by a drop in efficiency. This behaviour in poor part-flow performance is exhibited by the Propeller and Kaplan turbines as indicated in Figure 3.5.
The turbine, starts producing some power, at a part-flow level of 0.22, equivalent to 0.0055 m3/s, which is also the flow required to make the turbine runner start rotating.
xciii
Fig. 5.1: Part Flow efficiency curve
5.5.1.2
Power Output against Loaded Speed
The average power output of the turbinewas plotted against loaded speed of the turbine runner generating the graph in Figure 5.2. The runner speed was varied by varying the flow.
xciv
w
(rpm)
Fig. 5.2: Turbine power outputagainstturbine runner loaded speed at changing flow
It can be seen from Figure 5.2 that the turbine power output increases with increase in speed up to a maximum power output of 1200 W at an average speed of 500 rpm. Further increase in speed is accompanied by a decrease in power output.
The 500 rpm is then the optimum loaded speed for optimum power output.
xcv 5.5.1.3.
Efficiency versus Speed at Changing Flow Rate
The efficiencywhen plotted against loaded speed of the turbine runner at changing flow rate yields the graph in Figure 5.3. Similar to power versus speed graph at changing flow rate, the efficiency increases with increase of the loaded speed of the turbine runner to a maximum of 25 % at loaded speed of 500 rpm and then deceases with further increase in the loaded speed.
%
Fig. 5.3: Turbine efficiency against turbine runner loaded speed at changing flow
xcvi 5.5.2. Turbine Output Characteristics at Constant Flow Rate 5.5.2.1 Power Output against Loaded Speed At the optimum constant flow rate of 0.0238 m3/s (part-flow, Q/Qmax. = 0.93), the turbine was subjected to varying brake loads. A graph ofaverage power output of the turbine versus the average loaded speed is given in Figure 5.4. It can be observed that a decrease in the loaded speed from the optimum of 500 rpm to 400 rpm (20%) is accompanied by a decrease of 12.2 % in the power output from 1180 W to 1036 W and an increase in the loaded speed from the optimal speed of 500 rpm to 600 rpm (20%) is accompanied by a decrease in power output of 13.6 % from 1180 W to 1020 W.
w
Fig. 5.4: Turbine power output against turbine runner loaded speed at constant flow.
xcvii The power output behaviour of the turbine with changing loaded speedsat constant flow rate is good and is important when governing the system as a result changing with time of the consumer loads. When the system is overloaded with consumer loads, the speed of the turbine decreases and switching off consumer loads leads to increase in the speed of the turbine. The turbine performance should not be affected drastically by the phenomenon.
5.5.2.2 Efficiency against Loaded Speed A graph of efficiencyversus loaded speed at the optimal constant flow rate of 0.0238 m3/s is given in Figure 5.5. Similar to the power outputversus speed graph at constant flow rate, when the loaded speed of the turbine deceases from the optimum 500 rpm to 400 rpm (20% decrease), average efficiency decreases by 13.6 % from 25 % to 21.6 % and when the loaded speedincreases from the optimal 500 rpm to 600 rpm (20% increase), the average efficiency decreases by 12.2 % from 25 % to 21.95%.
The phenomena of changing turbine load speeds at constant flow rate is as a result of varying consumer loads with time.
xcviii
Fig. 5.5: Turbine efficiencyagainst turbine runner loaded speed at constant flow
5.5.3. Specific Speed, Ns The maximum average power output of the turbine is 1200 W (1.2 kW) developed at an average loaded speed of the turbine of 500 rpm under a net head of 21.051 m.
xcix Using equation 3.26, the specific speed Ns is 12. The specific speed is within the range of single jet Pelton turbines of 10 – 35 as given in Table 3.3 indicating that the designed VehicleAxle Propeller Shaft as turbine is in the family of Pelton turbines.
5.5.4. Loaded to a Generator The average values of the generated voltage, current and frequency when a synchronous generator of ratings given in Table 5.4 was connected to the pulley on the propeller shaft of the turbine using two SPB V-belts are shown in Figure 5.6. Detailed data is given in Appendix A
Table 5.4: Manufacturer‟s ratings of the synchronous generator Parameter
Rating
County of Origin
China
Power
2 KW
Voltage
230 Volts
Current
8.7 Amps
Frequency
50 Hz
Power Factor
1.0
Phase
Single Phase
Speed
1500 rpm
According to the data in table 5.6, the generator ran at its factory rating (Synchronous) of voltage – 230 V and frequency – 50 Hz when the flow through the prime mover (turbine) was 0.0238 m3/s. The synchronous speed of the generator at the mentioned rating is 1500 rpm. The flow related to this performance corresponds with flow of the optimal performance of the turbine.
c Table5.5: Voltage V, Current I and Frequency f with power fed to ballast load of 4 cooking coils of 1100 W each. Discharge,
Part Load
Voltage V,
Current, I
Frequency, f
Calculated Power
Q(m3/s)
Flow, Q/Qmax.
(Volts)
(Amps)
(Hz)
(W)
0
0
0
0
0
0
0.0105
0.41
32.4
0.48
16.4
15.6
0.0134
0.52
68.6
1.24
21.6
85.1
0.0148
0.59
84.4
1.43
24.4
120.7
0.0163
0.64
97.2
1.81
27
175.9
0.0194
0.76
113.4
2.13
29.6
241.5
0.0208
0.81
134
2.55
32.8
341.7
0.0238
0.93
149.6
2.91
35.8
435.3
0.0256
1.00
188.4
3.69
43
695.2
Table 5.6: Voltage V, Current I and Frequency f with power fed to ballast load of 2 cooking coils of 1100 W each. Discharge,
Part Load
Voltage V
Current, I
Frequency, f
Calculated Power
Q (m3/s)
Flow, Q/Qmax (Volts)
(Amps)
(Hz)
(W)
0
0
0
0
0
0
0.0105
0.41
28
0.23
16
6.4
0.0134
0.52
81.5
0.68
26.6
55.4
0.0148
0.59
112.5
1.03
31.4
115.9
0.0163
0.64
131.3
1.22
34.6
160.2
0.0194
0.76
159.5
1.51
38.8
240.8
0.0208
0.81
175.3
1.68
41.6
294.5
0.0238
0.93
229.3
2.21
50
505.8
0.0256
1.00
260.2
2.50
55
650.5
ci The synchronous speed of the generator is 1500 rpm. The diameter of the pulley of the generator was 0.146 m while that of the propeller shaft (driver pulley) was 0.219 m, giving a step up ratio of 1.5.
The speed of the propeller shaft pulley was then 1000 rpm and
correspondingly with a step down ratio of 2 in the differential system of the vehicle axle, the speed of the turbine runner was 500 rpm.
The performance of the generator at its
manufacturer‟s rating synchronized with the optimal performance (optimal power output) of the designed Vehicle-Axle Propeller Shaft as a Turbine. Figure 5.6 shows the arrangement of the turbine, pulleys, power belts and the generator.
2 kW AC Ge ne ra tor
2 SPB V-B e lt Pulle y s
Sha ft pulle y Ø 2 1 9 m m optim um loa de d s pe e d 1 0 0 0 rpm
Ge ne ra tor pulle y Ø 1 4 6 m m optim um loa de d s pe e d 1 5 0 0 rpm
Powe r tra ns m is s ion s ha ft
Wa te r je t
D iffe re ntia l s y s te m s pe e d ra tio a x le : powe r tra ns m is s ion s ha ft 1 :2
W he e l rim runne r with buc k e ts optim um s pe e d 5 0 0 rpm
Fig. 5.6: Turbine and generator system
cii 5.6.
Cost per kW Turbine Output
The cost of the Vehicle Axle-Propeller Shaft as Turbine was Ksh 21,400 (274.4 USD). The prevailing average exchange rate in the year 2005, the year of fabrication, was 1 US Dollar = Kshs 78).
The power output of the test turbine was 1.18 kW giving the cost per kW of the turbine as USD 232.5 per KW. Compared with the costs per kW of other types of turbines as given in Table 2.2 and Table 2.3, the Vehicle Axle-Propeller Shaft has the lowest value.
The installation costs up to the production of shaft/mechanical power were Ksh 115,975 (USD 1,486.9).
The cost per installed Shaft power is then USD 1,260.0. In micro hydropower
installations, the average cost per installed shaft/mechanical power is USD 1,000 (Khennas and Barnett, 2000). The hydropower installation with a vehicle axle-propeller shaft as turbine has a slightly higher installation cost because of the low efficiency. A low efficiency value calls for large volumes of water to be delivered to the turbine for the same power output, implying large diameter penstock, henceadditional cost.
5.7.
Financial Evaluation
5.7.1
Introduction
Economic and financial considerations are important factors for consideration when examining and evaluating the viability of investment in renewable energy projects. Life cycle costing (LCC) was considered to be one of the most complete approaches to economic appraisal (Harvey, 1994). In the method, the initial costs and all future costs of the entire operational life of the renewable energy project are considered. Detailed description of the LCC methodology is given in Appendix D.
ciii 5.7.2
Life Cycle Costing of the Experimental System
The Life cycle costing of the whole experimental system was computed. The payback period, Net present value and internal rate of return were computed. The values were compared with a competing alternative source of energy that is a 3 kW (4.6 kVA) diesel generator (Harvey, 1993).
The LCC of the two systems were computed and compared for a village electrification situation as shown in Table 5.7. Cost data for the analysis is given in Appendix E.
5.7.3
Comparison of Capital Costs
The total capital cost for the vehicle axle-propeller shaft as a turbine comprises of the planning and engineering; civil works for the intake, power house and tail race channel; piping and steel fittings for the penstock; machinery comprising of the turbine, generator and control system; and the transmission line. The total capital cost was Ksh 612,775.
The diesel generator has to produce and supply power continuously at variable loads like the hydro system, hence has to be prime diesel generator. The smallest diesel generator in the market for comparison with the hydro-turbine was a 5.8 kVA (4.6 kW) gen-set. The capital costs comprised of planning and engineering; civil works for the power house where the diesel generator will be located (same as for the hydro-turbine); machinery comprising of the prime diesel generator and accessories; and the transmission line (same as for the hydro-turbine). The total capital cost was Ksh 1,128,175
civ Table 5.7: Life Cycle Cost comparisons between the vehicle axle-propeller shaft as a micro turbine for power generation and a diesel generator Investment (Ksh) Description Vehicle axle propeller shaft as a turbine
Diesel generator 4.6 KW
Planning/Engineering
36,400
23,200
Civil works
82,675
82,675
Machinery
88,100
650,000
Piping, steel components
33,300
-------
Transmission line
372,300
372,300
Total Capital Cost
612,775
1,128,175
Equipments
Annual of expenditures Calculative life cycles (years) Civil components
20
Equipments
20
20
Transmission line
20
20
Operation Costs
358,531
358,531
Minor service
38,841
194,204
Major service
8,551
34,196
---------
9,025,682
Total Present Values
405,923
9,612,613
Total Life Cycle Cost
1,018,698
10,740,788
136,382
1,437,972
9,920
27,200
31.25
330.40
Present Values of futures costs
Fuel
Annualized Life Cycle Cost Total Electricity generated per year (kWh/year) Levelized Energy Cost (LEC) (KSh/KWh) at r=12%, LF =44% for hydro and 16% for diesel generator
cv The capital costs do not include operations and maintenance costs over the lifetime of the system. It does also take into considerations of the energy available from the systems. Another important factor
5.7.4
Comparison of the ALCC and the LEC of the Two Systems
The Annualized Life Cycle Cost (ALCC) and the Levelized Energy Cost (LEC) takes into account the amount of energy generated from the systems and are therefore utilized to give a more intelligent expression of the cost of the renewable energy system. A load factor of 44 % and 16 % for the hydro-turbine and diesel generator respectively was used to take into account of the useful energy. These were obtained from a survey done on the community households as given in Appendix E, Table E-2.
The vehicle axle-propeller shaft as turbine had the lowest ALCC of Ksh 136,382 compared to Ksh 1, 347,972. The high ALCC for the diesel generator can mainly be attributed to the high cost of the fuel for running the engine. The engine consumes 2.0 litres of diesel fuel per hour at 75% load factor. The average price of diesel in Kenya during the period of 27th November to 10th December 2009 was Ksh 72.60 per litre. This is given in Appendix E, Table E-1.
It can be seen in Table 4.4 that the scheme using the vehicle axle-propeller shaft as a turbine for the power generation had the lowest Levelized Energy Cost (LCC) of Ksh 31.25 (USD 0.40) per kWh compared to the one using the diesel generator which had Ksh 330.40 (USD 4.24) per kWh. The big difference is attributable to high cost of the prime diesel generator and its high operation and maintenance costs.
cvi A community hydropower scheme using a vehicle axle-propeller shaft as turbine for power generation is about 10 times cheaper that a similar one using a diesel generator as the source of power.
5.7.5
Environment Benefits of Micro Hydropower Schemes
Micro hydro can contribute significantly to the reduction of Green House Gases (GHGs) emissions that cause global warming or climate change. Table5.8 shows a comparative analysis of production of carbon dioxide by various energy sources.
Table 5.8: Carbon dioxide production by various energy sources (Doig, 2007) Electricity production sources Coal Oil Gas Geothermal Wind turbines Photovoltaic Small Hydro Large Hydro Biomass
Tonnes of Carbon Dioxide/GWh 851-1362 733 367-561 57 9 59-71 5 32 14
It has been shown that where appropriate micro hydropower is the cost effective option for minimum carbon dioxide emissions where new investment in generating capacity is required. When the environmental benefits are then included, the vehicle axle-propeller shaft as turbine for power generation then becomes more than 10 times cheaper that a similar one using a diesel generator as the source of power.
5. 8.
Error Analysis
In the course of undertaking the study, a number of errors could have arisen as aresult accuracy in the data, rounding-off of the measurements and results as well as approximations.
cvii 5.8.1
Data Error
A lot of data that included the spring balance readings, speed of the pulley, weir measurements, time, gross hydraulic head of the site, penstock length, etc. was taken. Each of the individual data could have had some accuracy errors that could have affected the final results. At high speeds of the turbine runner, some vibrations also set in and the spring balance readings on the tension side were approximated.
5.8.2
Error due to Approximations
The power outputs of the modified vehicle system as turbine at various part flows were obtained using the power output equation 3.4. As the data was rounded-off to two decimal places, the resulting arithmetical operations introduced further errors to the final results.
5.8.3
Standard Deviation (Variance)
Each test was done five times for repeatability. The data size was small. However, the standard deviation or variance of the data was computed using the normal standard deviation equation of large size sample data.
5.8.4
Plotting of the Curves
Average single values were used in the plotting of the curves and the best fit curve determined. This can also have some errors.
cviii
CHAPTER SIX
CONCLUSIONS AND RECOMMENDATIONS
6.1
Conclusions
A Vehicle Axle-Propeller Shaft was procured from the metal scrap yards in Nairobi, redesigned and constructed using standard procedures for hydropower systems to operate as a turbine for micro hydropower generation in Kenya at the Energy Engineering and Science Workshops in Kenyatta University.It was tested at a site constructed on Philips Falls on Rutui River, Thima Village in Kirinyaga district.
In this work, the main objective was to reduce the cost of unit power generation in micro hydroelectric power plants by coming up with a low cost device for converting the kinetic energy in the water to mechanical power. A vehicle live axle-propeller shaft system of a small vehicle was used in this study. The rim of the wheel was fitted with designed buckets, and water from an intake at the test site was conveyed to the buckets via a 0.160 m diameter PVC penstock over a gross hydraulic head of 21.784 m. A designed tapered nozzle at the end of the penstock converted the kinetic energy into jet energy that was then converted to rotational kinetic energy by the buckets and finally to shaft/mechanical power by the shaft. A 2 kW synchronousgenerator was used to convert the mechanical power to electricity.
The speed of the turbine as measured at the propeller end pulley was increased from zero to the maximum at intervals of 200 rpm by increasing the flow through the turbine. This calibrated
cix the water levels of water above the flow measuring weir crest, hence the flows and was used for any further measurements.
In the fabrication/modification of the vehicle live axle-propeller shaft to operate as a turbine, all the costs were documented, so as to know the total cost to be used in determining the cost per kW of the prototype turbine and also for the benefits of individuals/communities who might require it for their own power generation.
The main conclusions arrived at are the following: 1.
The maximum power output of the Vehicle Axle-Propeller Shaft as a Turbine was 1.180 kW.
2.
Optimum efficiency of the test turbine was 25%.
3.
The optimum flow rate was 0.0238 m3/s with the maximum flow rate being 0.0256 m3/s.
4.
The optimum loaded speed of the test turbine (propeller shaft speed) was 1000 rpm. With a step-down ratio of 2:1 (Propeller shaft to Axle) in the differential system, the corresponding optimal speed of the turbine runner (wheel) shaft end was 500 rpm.
5.
The runner away speed of the test turbine at the propeller shaft end was 1800 rpm corresponding to 900 rpm of the turbine runner. The runner away speed was then 180 %. This is a typical figure of most water turbine. The runner speed of a cross flow turbine is about 185%.
6.
The part-flow efficiency of the test turbine was poor. The optimum part-flow ratio (Q/Qmax) was 0.93 that is typical of most water turbines. However, when the flow was reduced below the optimum value, the efficiency drops suddenly by 45% from
cx the maximum of 25% to 13.8% with only the part-flow ratio changing only by 16% from 0.93 to 0.78. The efficiency then drops gradually to zero. 7.
The turbine performance under constant flow rate was good. A decrease of 20% of the loaded speed from the optimal 500 rpm is accompanied by a power decrease of 12.2 % in the optimal power output of 1180 W and an increase of the loaded speed by 20 % is accompanied by a decrease of 13.6% in the optimal power output. The trend is the same but reversed in the average efficiency characteristic. Change of loaded speed at constant flow rate is brought about by changing with time of consumer loads.
8.
The specific speed of the turbine was 12 placing it in the family of single jet Pelton turbines.
9.
The cost per kW of shaft power was USD 274.4. It is a very low cost turbine and hence affordable by majority of individuals and communities in Kenya.
10.
The energy cost from hydropower scheme using a vehicle axle-propeller shaft as turbine for power generation is 10 times cheaper than that of a similar scheme using a diesel generator as the source of power.
From the results obtained and discussed in this study, it can be concluded that a Vehicle Axle-Propeller Shaft can be re-designed and modified to operate as a water turbine for power generation. These systems are available in almost all car repair garages, metal scrap yards and dump yards and if not available for free as they are environmental hazards, they can be sold very cheaply to any prospecting buyer. As the cost of power continues to rise in Kenya, the cheapness of the systems makes them affordable to many individuals and communities located remotely from national grid network or those interested in their own power generation.
cxi 6.2.
Recommendation for Further Work and Policy
The results obtained in this work can further be improved and complemented with the following research suggestions: 1.
Use of a heavy metal hub bolted to the wheel rim to increase the mass of the runner hence the torque and the power output.
2.
Incorporate a jet split ridge at the centre of the bucket to avoid a dead centre in the runner bucket.
3.
Change the configuration of the runner.
4.
Explore the occurrence of maximum efficiency of a turbine at a part-flow less than unit (less than the design flow).
5.
Policy changes to allow communities to distribute generated electrical power among its members.
cxii 7.
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cxviii
8.
APPENDICES
APPENDIX A
SAMPLE DATA SHEETS FOR VARIOUS EXPERIMENTS.
119
Table A1: Sample Data sheet for discharges – container method Turbine speed (rpm) Inertia
200
400
600
800
Time taken to fill drum (S) Timer 1 Timer 2 19.8 19.8 19.6 19.4 19.2 19.2 19.8 19.6 19.4 19.8 9.0 9.0 9.2 9.2 9.0 9.0 9.2 9.2 9.2 9.2 8.0 8.0 8.2 8.2 7.6 7.8 8.0 7.8 7.8 7.8 7.0 6.8 6.6 6.6 7.0 6.2 6.8 6.8 6.8 6.8 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0
Discharge (m3/s)
19.6
Standard deviation, σ 0.26
9.1
0.11
0.0108
7.9
0.18
0.0124
6.7
0.25
0.0146
6.0
0
0.0164
Average time (s)
0.005
120 Turbine speed (rpm) 1000
Time taken to fill drum (S) Average time (s) Timer 1 Timer 2 5.2 5.0 5.2 5.0 5.0 5.6 5.0 5.4 5.0 5.4 5.4 1200 5.0 5.0 4.9 5.0 5.0 5.0 4.8 5.0 5.0 5.0 4.8 1400 4.6 4.2 4.6 4.6 4.6 4.8 4.8 4.2 4.2 4.6 4.6 1600 3.8 3.8 3.8 3.8 3.8 4.0 3.8 3.8 3.6 3.8 3.6 1810 Turbine unstable with vibrations Drum diameter d – 0.567m, drum height h – 0.390m, Volume – 0.0985m3
Standard deviation, σ 0.24
Discharge (m3/s)
0.11
0.0199
0.26
0.0213
0.12
0.0261
0.0189
121
Table A2: Sample Data sheet for discharges – weir method
Propeller shaft speed, Np (rpm)
Head above weir crest, h (m)
Time taken (s)
Average time (s)
Standard deviation σ
Average velocity of approach, V (m/s)
Average velocity head, h (m)
Average Discharge (m3/s)
0 Inertia
Turbine runner speed, Nr (rpm) 0 0
0 0.03
0 2.4
0 0.07
0 0.503
0 0.013
0 0.055
200
100
0.05
2.4
0.10
0.503
0.013
0.0105
400
200
0.06
2.4
0.10
0.503
0.013
0.0134
600
300
0.065
2.5
0.09
0.483
0.012
0.0148
800
400
0.07
0 2.4 2.3 2.3 2.4 2.4 2.3 2.5 2.3 2.4 2.5 2.3 2.5 2.3 2.4 2.5 2.4 2.6 2.5 2.5 2.4 2.5 2.4 2.6 2.6 2.5
2.5
0.09
0.483
122 Propeller shaft speed, Np (rpm)
Head above weir crest, h (m)
Time taken (s)
Average time (s)
Standard deviation σ
Average velocity of approach, V (m/s)
Average velocity head, h (m)
Average Discharge (m3/s)
1000
Turbine runner speed, Nr (rpm) 500
0.08
2.6
0.38
0.464
0.11
0.194
1200
600
0.082
2.6
0.10
0.464
0.11
0.0200
1400
700
0.85
2.7
0.30
0.447
0.01
0.0208
1600
800
0.095
3.0
0.26
0.402
0.008
0.0238
1700
850
0.10
2.0 3.0 2.4 2.8 2.6 2.6 2.4 2.6 2.6 2.6 3.0 2.2 2.8 2.6 2.8 3.2 3.4 2.8 3.0 2.8 3.1 2.9 3.0 3.2 2.9
3.0
0.13
0.402
0.008
0.0256
123 Table A3: Sample Data sheet for penstock losses and hydraulic power Np (rpm) 0 200 400 600 800 1000 1200 1400 1600 1700 Kc Kent Kbend, 45o Kbend, 20o Kgate valve Lpenstock Hg Cv
Nr (rpm) 0 100 200 300 400 500 600 700 800 850 0.26 0.80 0.45 0.36 0.20 86.50 m 21.874 m 0.98
Q (m3/s) 0.0055 0.0105 0.0134 0.0148 0.0163 0.0194 0.0200 0.0208 0.0238 0.0256
f 0.023 0.0195 0.0190 0.0185 0.0180 0.0178 0.0175 0.0170 0.0165 0.0160
V (m3/s) 0.2790 0.522 0.666 0.736 0.811 0.965 0.995 1.035 1.184 1.273
hf (m) 0.046 0.142 0.225 0.267 0.316 0.442 0.462 0.485 0.617 0.694
ht (m) 0.011 0.040 0.065 0.080 0.097 0.137 0.145 0.157 0.206 0.238
hf+ht (m) 0.057 0.182 0.290 0.347 0.413 0.579 0.607 0.642 0.823 0.932
Hn (m) 21.817 21.692 21.584 21.527 21.461 21.295 21.267 21.232 21.051 20.942
Ph (W) 1177.1 2234.4 2837.3 3125.5 3431.7 4052.7 4172.6 4332.3 4914.9 5259.3
Pjet (W) 1130.5 2145.9 2724.9 3001.7 3295.8 3892.2 4007.4 4160.8 4720.3 5051.0
124 Table 4: Sample Data sheet for turbine brake load testing Head of water above Weir Crest, hwc (m)
Av. Approach Velocity, V (m/s)
Discharge (m3/s)
Propeller Shaft Pulley, Un loaded speed, (rpm)
Propeller Shaft Pulley, Loaded Speed (rpm)
0.065
0.0483
0.015
600
0.070
0.0483
0.016
800
0.08
0.464
0.019
1000
0.082
0.464
0.200
1200
0.085
0.447
0.021
1400
0.095
0.402
0.024
1600
0.100
0.402
0.026
1700
400 375 300 600 400 300 800 600 400 1000 800 600 400 1200 1000 800 600 400 1400 1200 1000 800 1600 1400 1200 1000 800 600
Test 1 (Kg)
Test 2 (Kg)
Test 3 (Kg)
Test 4 (kg)
Test 5 (Kg)
Ave. (Kg)
Standard deviation
σ
S1 3.50 4.25 5.00 3.40 4.75 6.00 2.75 5.00 7.00 5.50 7.50 9.00 10.50 5.00 5.50 8.50 11.50 13.00 5.00 7.75 11.00 12.75 3.00 5.00 6.50 9.50 14.00 17.50
S2 0.25 0.25 0.50 0.25 0.75 1.00 0.25 1.00 1.50 0.50 1.50 2.00 2.00 0.50 0.75 1.75 2.75 3.00 0.00 1.00 2.00 3.00 0.00 0.75 1.00 2.00 3.50 4.75
S1 3.00 4.50 5.25 6.50 8.00 7.50 3.75 6.50 8.00 4.40 6.20 8.00 10.00 4.50 6.00 9.00 11.50 13.50 5.50 8.25 11.25 13.25 3.50 5.50 7.00 10.00 14.50 18.00
S2 0.00 0.25 0.50 0.60 1.00 0.80 0.00 0.40 0.80 0.00 0.40 1.10 1.40 0.50 0.75 1.20 2.40 2.75 0.00 1.00 2.00 3.00 0.00 0.50 1.00 3.00 3.50 4.75
S1 3.60 4.25 5.50 6.75 8.00 8.50 4.25 5.75 7.75 4.50 6.50 7.75 9.50 4.75 7.00 9.50 10.50 12.50 5.25 8.50 12.00 14.00 4.00 5.50 6.75 10.25 14.25 17.50
S2 0.4 0.5 0.75 0.5 0.75 1.00 0.00 0.25 0.75 0.00 0.50 0.80 1.00 0.25 0.75 1.00 1.25 1.75 0.00 1.00 1.50 2.00 0.00 0.50 1.00 2.50 2.75 4.00
S1 3.25 4.60 5.00 6.00 7.50 8.50 4.00 6.75 8.50 4.50 6.40 6.00 10.50 5.00 6.50 9.75 12.50 13.50 6.00 8.75 12.50 13.50 4.50 5.75 7.50 9.75 14.50 17.00
S2 0.00 0.25 0.25 0.50 0.50 0.75 0.00 0.50 1.00 0.00 0.25 1.00 1.50 0.50 1.00 1.50 2.50 3.00 0.00 1.00 1.50 2.00 0.25 0.50 1.00 1.75 2.50 3.00
S1 3.80 5.00 6.00 6.00 7.75 8.75 4.50 7.00 8.25 5.00 6.50 8.00 10.75 5.25 7.00 10.00 11.50 14.00 6.50 8.25 12.25 14.50 4.50 6.50 8.00 10.00 13.25 17.25
S2 0.00 0.25 1.00 0.40 0.50 1.00 0.00 0.50 1.00 0.25 0.50 1.00 1.50 0.50 1.00 1.50 2.00 3.00 0.50 0.75 1.00 1.50 0.50 1.00 1.50 1.75 2.00 3.50
S1 3.43 4.52 5.35 5.75 7.2 7.85 3.85 6.20 7.90 4.78 6.62 7.75 10.25 4.90 6.40 9.35 11.50 13.50 5.65 8.30 11.80 13.6 3.90 5.65 7.15 9.90 14.1 17.45
S2 0.13 0.30 0.60 0.45 0.7 0.91 0.05 0.53 1.01 0.47 0.63 1.18 1.48 0.45 0.85 1.39 2.18 2.70 0.10 0.95 1.60 2.81 0.15 0.65 1.10 2.20 2.85 4.00
S1 0.311 0.31 0.42 1.32 1.39 1.14 0.68 0.82 0.58 0.15 0.51 1.09 0.50 0.29 0.65 0.60 0.71 0.61 0.60 0.37 0.65 0.68 0.65 0.55 0.60 0.29 0.52 0.37
S2 0.19 0.11 0.29 0.13 0.21 0.12 0.11 0.28 0.30 0.22 0.50 0.47 0.36 0.11 0.14 0.29 0.59 0.54 0.22 0.11 0.42 0.88 0.22 0.22 0.22 0.54 0.65 0.77
125 Table A5: Sample Data sheet for test turbine, power input, power output and part flow efficiency Discharge Q (m3/s)
Propeller Shaft Pulley Speed, rpm Unloaded Loaded
0.0148
600
0.0163
800
0.0194
1000
0.0200
1200
0.0208
1400
0.0238
1600
0.0256
1700
400 375 300 600 400 300 800 600 400 1000 800 600 400 1200 1000 800 600 400 1400 1200 1000 800 1600 1400 1200 1000 800 600
Test 1 S1-S2 (Kg) 3.25 4.00 4.50 3.15 4.00 5.00 2.50 4.00 5.50 5.00 6.00 7.00 8.50 4.50 4.75 6.75 8.75 10.00 5.00 6.75 9.00 9.75 3.00 4.25 5.50 7.50 10.50 12.75
Power (W) 150.24 173.36 156.02 218.43 184.91 173.36 231.14 277.37 254.56 577.86 554.74 485.40 392.94 624.09 548.96 624.09 606.75 462.29 808.00 936.13 1040.14 901.46 554.74 687.65 762.77 866.79 970.80 884.12
Test 2 S1-S2 (Kg) 3.00 4.25 4.75 5.90 7.00 6.70 3.75 6.10 7.20 4.40 5.80 6.90 8.60 4.00 5.25 7.80 9.10 10.75 5.50 7.25 9.25 10.25 3.50 5.00 6.00 7.00 11.00 13.25
Power (W) 138.69 184.19 164.69 409.12 323.60 232.30 346.71 422.99 332.85 508.51 536.25 478.47 397.57 554.74 606.75 721.17 631.02 496.96 889.90 1005.47 1069.03 947.68 647.20 809.00 832.11 809.00 1017.03 918.79
Test 3 S1-S2 (Kg) 3.20 3.75 4.75 6.25 7.25 7.50 4.25 5.50 7.00 4.50 6.00 6.95 8.50 4.50 6.25 8.50 9.25 10.75 5.25 7.50 10.50 12.00 4.00 5.00 5.75 7.75 11.50 13.50
Power (W) 147.93 162.52 164.69 433.39 335.17 260.04 392.94 381.39 323.60 520.07 554.74 481.93 392.94 624.09 722.32 785.89 641.42 496.96 849.45 1040.14 1213.50 1109.48 739.66 809.00 797.44 895.68 1063.26 936.13
Test 4 S1-S2 (Kg) 3.25 4.35 4.75 5.50 7.00 7.75 4.00 6.25 7.50 4.50 6.15 7.00 9.00 4.50 5.50 8.25 10.00 10.50 6.00 7.75 11.00 11.50 4.25 5.25 6.50 8.00 11.00 14.00
Power (W) 150.24 188.53 164.69 381.39 323.60 268.70 369.83 433.39 346.71 520.07 568.61 485.40 416.06 624.09 635.64 762.77 693.43 486.40 970.80 1074.81 1271.28 1063.26 785.89 849.45 901.46 924.57 1017.03 970.80
Test 5 S1-S2 (Kg) 3.80 4.50 5.00 5.60 6.25 7.75 4.50 6.50 7.25 4.75 6.00 7.00 9.25 4.75 6.00 8.50 9.50 11.00 6.00 7.50 11.25 12.50 4.00 5.50 6.50 8.25 11.25 12.75
Power (W) 175.67 195.03 173.36 388.32 288.93 268.70 416.06 450.73 335.16 548.96 554.74 485.40 427.61 658.76 693.43 785.89 658.76 508.51 970.80 1040.14 1300.18 1155.71 739.66 889.90 901.46 953.46 1040.14 953.46
Av. Power (W)
Standard Deviation
152.55 180.73 164.69 366.13 291.24 240.62 351.34 393.17 318.58 535.09 553.82 483.32 405.42 617.15 641.42 735.96 646.28 490.22 897.79 1019.34 1178.83 1035.52 693.43 809.00 839.05 889.90 1021.65 932.66
27.54 12.88 6.13 85.02 61.92 40.46 71.99 69.59 36.72 28.19 11.51 3.10 15.64 37.98 68.98 67.89 32.40 17.46 72.67 52.58 121.23 107.67 92.56 75.68 62.02 55.57 34.31 33.35
σ
126 Table A6: Sample Data sheet for test turbine power input, power output and part flow efficiency Discharge, Q (m3/s)
Q/Qmax
0.0148 0.0163 0.0194 0.0200 0.0208 0.0238 0.0256
0.58 0.64 0.76 0.78 0.81 0.93 1.00
Propeller shaft pulley speed (rpm) Unloaded Loaded 600 800 1000 1200 1400 1600 1700
375 600 600 800 800 1000 800
Turbine running speed (rpm) 187.5 300 300 400 400 500 400
Average turbine power input (W) 3001.7 3295.8 3892.2 4007.4 4160.8 4720.3 5051.0
Average turbine power output (W) 180.73 366.13 393.17 553.82 735.96 1178.83 1021.65
Part-flow efficiency (%) 6.02 11.11 10.10 13.82 17.69 24.97 20.23
Table A7: Sample Data sheet for electrical method with ballast load of 4 cooking coils of 1100W each hweir Q Test 1 Test 2 Test 3 Test 4 Test 5 (m) (m3/s) V I f V I F V I f V I f V I f 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.050 0.0105 30 0.40 16 29 0.43 16 32 0.48 17 35 0.50 16 36 0.60 17 0.060 0.0134 50 0.88 19 74 1.30 23 59 1.04 21 75 1.44 21 85 1.55 24 0.065 0.0148 65 1.17 22 82 1.53 24 76 1.36 23 98 1.51 26 101 1.58 27 0.070 0.0163 75 1.40 24 99 1.82 27 99 1.85 27 101 1.88 28 112 2.10 29 0.080 0.0194 107 1.98 29 108 2.00 29 114 2.17 30 118 2.24 30 120 2.28 30 0.085 0.0208 123 2.32 31 126 2.38 32 140 2.65 34 138 2.68 32 143 2.72 35 0.095 0.0238 164 3.15 38 141 2.76 34 150 2.85 36 142 2.90 35 151 2.90 36 1.000 0.0256 185 3.65 43 188 3.64 43 190 3.67 43 189 3.74 43 190 3.76 43 Power factor – 1.0, Driver pulley diameter – 0.219m, Driven pulley diameter – 0.146m, V – Voltage in volts, I – Current in Amps, f – frequency in Hz
V 0 32.4 68.6 88.4 97.2 113.0 134.0 150.0 188.0
Average I 0 0.48 1.24 1.43 1.81 2.13 2.55 2.91 3.69
f 0 16.4 21.6 24.4 27.0 29.6 32.8 35.8 43.0
127 Table A8: Sample Data sheet foe electrical method with ballast load of 2 cooking coils of 1100W each
hwc Q Test 1 Test 2 Test 3 Test 4 Test 5 (m) (m3/s) V I f V I F V I f V I f V I f 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.050 0.0105 0.3 0 0 39 0.01 20 0.9 0.40 16 62 0.50 23 38 0.23 21 0.060 0.0134 51.5 0.30 22 84 0.72 27 85 0.74 27 79 0.67 26 108 0.98 31 0.065 0.0148 93.5 0.79 28 101 0.92 30 110 1.00 31 127 1.18 34 131 1.24 34 0.070 0.0163 117 1.04 32 132 1.23 35 127 1.18 34 134 1.26 35 147 1.38 37 0.080 0.0194 149 1.40 37 155 1.48 38 160 1.50 39 156 1.48 38 178 1.71 42 0.085 0.0208 162 1.53 39 166 1.58 40 171 1.67 42 183 1.75 42 194 1.88 45 0.095 0.0238 225 2.14 49 227 2.18 50 236 2.28 51 232 2.26 50 227 2.20 50 1.000 0.0256 254 2.45 55 260 2.51 55 261 2.52 55 262 2.54 55 264 2.50 55 Power factor – 1.0, Driver pulley diameter – 0.219m, Driven pulley diameter – 0.146m, V – Voltage in volts, I – Current in Amps, f – frequency in Hz
V 0 28.0 81.5 113.0 131.0 160.0 175.0 229.0 260.0
Average I 0 0.23 0.68 1.03 1.22 1.51 1.68 2.21 2.50
f 0 16.0 26.6 31.4 34.6 38.8 41.6 50.0 55.0
APPENDIX B
DESIGN PARAMETERS AND CALCULATIONS FOR THE EXPERIMENTAL TURBINE
cxxix B1.
Performance characteristics of some turbines
Table B1: Characteristics of different turbines Type
Head (m)
Water wheel Pelton
0.5-5
and 30-800
Flow (l/s)
Power
Efficiency
Design
(KW)
(%)
>40
0.3-10
20-60
Very simple
2-10,000
1-10,000
80-99
Complex
Simple
Turgo M.P.P.U
3-30
20-100
2-14
About 50
Cross-flow
2-200
10-5,000
5-500
60-83
Francis
4-500
100-30,000
5-2,000,000
75-99
Complex
Propeller
1-30
300-100,000
100-50,000
90-99
Complex
0
0.5-4 m/s
0.2-15
15-40
Simple
>1
0.1-20
0.1-2.5
50-65
Simple
and Kaplan Water current Hydrams
Source: The Power guide: An international catalogue of small-scale energy equipments, Published by IT publications, 1994. 1SBN 1 85339 192 1
B2.
Values of Contraction Coefficient Cc and Coefficient of Kinetic Energy Loss Cv
Table B2: Typical values of Cc and Cv Type of orifice
Cc
Cv
Sharp edged plate orifice
0.61
0.98
Tapered nozzle
1.00
0.98
Spear valved nozzles
Almost closed
0.92
Damaged, worn nozzle Profiled nozzle Mid-position
(Harvey, 1993)
0.7-0.8 0.98
0.97 0.97
cxxx
B3.
Determination of runner diameter Dr and jet size dj
Dr = Cv x 38 H0.5/ Nr
where Cv is coefficient of kinetic energy loss or velocity loss due to
edge turbulence effects in orifices. dj= Cd0.5 x 0.54 x Q0.5/(H0.25 x Nj) where Nj is the number of jets and Cd is coefficient of discharge and is a product of velocity loss (Cv) and contraction coefficient (flow area reduction effects) Cc.
B4:
Design of the buckets
The chosen p.c.d.for the runner is 365mm Maximum Flow = 0.05 x p.c.d2 x (Hnet)1/2 = 0.05 x 0.3652 x 201/2 = 0.0298 m3/s = 30 l/s Jet diameter = 0.981/2 x 0.54 x 0.0301/2/(200.25x1) = 0.0438 m; set at 42 mm Bucket Notch width = djet + 5mm = 47mm Notch depth = 0.5 x notch width = 21 mm Max. bucket width = 3 x 43 = 141mm. For practical purpose dictated by the rim the width will be 76mm Bucket depth = 0.25 x 76 mm = 19mm
B5:
Design of the Nozzle
The diameter of the nozzle is determined using equation the in appendix B5 for the jet djet = 0.980.5 x 0.54 x 0.030.5/(200.25) = 0.0438 m; set at 42 mm dnozzle = 42mm as Cv = 1 for tapered nozzle The taper angle is 14o. For it to be fitted to a 100 mm pipe, its length then is 125 mm.
cxxxi B6.
Power Transmission Shaft Sizing
Fig. B6 – 1: Mechanical Power Transmission Shaft from the differential system to the pulley
Data Type of shaft material – bright mild steel (high strength) Yield Strength of the steel, Sy
= 300 N/mm2
Ultimate tensile strength of the steel, Suts.
= 550 N/mm2
Rotational speed at optimum power transmission = 1000 rpm
= 104.72 rads/s
Maximum hydraulic power of the site (100 % efficiency), to be transmitted by the shaft = 9. 81 x 0.03 x 20 =6 KW
= 6000 W
Pulley pitch diameter = 219 mm
= 0.219 m
Pulley
Calculations Torque at the pulley, T = 6000 W/ώ = 6000/104.72
= 57.3 NM
Force on the pulley, Torque/radius = 57.3/0.1095
= 523.3 N
cxxxii Moments Taking moments about A RB x 0.3 + (523.3 x 0.4)
=0
RB
= -697.73 N
Taking Moments about B RA x 0.3 – (523.3 x 0.1)
=0
RA
= 174.4 N
Moments at any point equals the sum of the forces to the left of the point multiplied by the distance from the left of the point.
Moment at A
=0
Moment at B = -174.4 x 0.3
= -52.32 NM
Moment at pulley C = -(174.4 x 0.4) + (697.73 x 0.1)
=0
Maximum bending moment is at B
= 52.32 NM
Sizing of shaft diameters The American Society of Mechanical Engineers (ASME) established a code method in 1927 for determining shaft diameters based on maximum-shear stress theory (Harvey, 1993)
The ASME code defines a permissible shear stress which is smaller of the following values
cxxxiii a)
tp
= 0.30Sy or
(B6 -1)
b)
tp
= 0.18Suts
(B6-2)
(Harvey, 1993)
For high quality steel Sy = 300 N/mm2 and Suts = 550 N/mm2 making a)
tp
= 90 N/mm2 and
b)
tp
= 99 N/mm2
The smaller value of the permissible stress is 90 N/mm2
ASME formulae for determining shaft diameters is
d = [5.1/tp{(CmM)2 + (CtT)2}0.5]0.33
(B6-3)
(Harvey, 1993) which can be re-written as
d3 = 5.1/tp{(CmM)2 + (CtT)2}0.5
(B6-4)
where M = maximum bending moment; T = torque on the shaft; Cm = shock factor and Ct = fatigue factor.
Cm and Ct values depends on the expected conditions of service of the shaft as given in Table B6 - 1
cxxxiv Table B6-1: Values of bending moment Cm and torsional moment factor Ct (Harvey, 1993) Shaft condition
Type of loading
Cm
Ct
Stationery shaft
Load applied gradually
1.0
1.0
Load applied suddenly
1.5 - 2.0
1.5 – 2.0
Load applied gradually
1.5
1.0
Steady load
1.5
1.0
Load applied suddenly, minor shocks
1.5 – 2.0
1.0 – 1.5
Load applied suddenly, heavy shocks
2.0 – 3.0
1.5 – 2.0
Rotating shaft
For belt drives, shaft is rotating and the load is considerably steady hence Cm= 1.5 and Ct = 1.0
d3 = 5.1/90{(1.5 x 52.32 x 103)2 + (1.0 x 57.3 x 103)2}0.5 d3 = 5506.414 d = 17.66 mm
A standard shaft of 25 mm (1”) was chosen and since increase in strength is approximately proportional to d to the power 3, the strength of the shaft is increased by 1.4163 or 2.8 times.
cxxxv
APPENDIX C TEST SITE DEVELOPMENTS COSTS
cxxxvi Table C1: Intake, Penstock and Power House Development Costs No.
DESCRIPTION
Building stones 6x9 –550 running ft B Cement C Building sand D Ballast ½ inch E Hardcore E Reinforcement bars Y10 F DPC G Iron sheets GI, G30, 3M H Nails Roofing Ordinary 2,3 and 4 inches J Timber 4 x 2 2x2 6x1 K Wooden door 6‟ x 3‟ Metal grill door L Wood window (1mx1m) Metal grill window M Binding wire R6 N Tie wire P PVC pipes Ø150mm C/B Q Copper cables 6.00 mm2 single core S PVC T-Junction Ø150mm T PVC 45o 150 mm bend U 24-30 gauge Metal screen filter V Control box X Cooking coils (elements) 1.1 KW each TOTAL A
QTY
UNIT Lorry
UNIT PRICE 9000
COST (Ksh) 13,500
1½ 20 1 3 1 6 3.5 14 2 4 100 55 100 1 1 1 1 1 2 10 100
Bag Lorry P/up Lorry No. M No. Kg Kg Ft Ft Ft No. No. No. No. No. Kg No. Lot
800 9000 1500 3,500 500 1,500 750 125 100 35 15 18 2,500 5,000 1,200 1,300 250 100 2,500 2,500
16,000 9,000 4,500 3,500 3,000 5,250 10,500 250 400 3,500 825 1,800 2,500 5,000 1,200 1,500 250 200 25,000 2,500
1 2 1
No. No. No.
3,000 2,400
3,000 4,800 500
1 8
No. No.
2,000 650
2,000 5,200
Items Q, V and X are for the electrical system.
125,675
cxxxvii APPEDINDIX D LIFE CYCLE COSTING
Life Cycle Costing and Discounting Methodology The Life Cycle Costs (LCC) is the sum of all costs associated with the initial purchase, installation, operation and maintenance of the system throughout its operational life. To make meaningful comparison, all future costs and benefits have to be discounted to their equivalent value in today‟s economy, called the present value or worth (PV). To achieve this, each future cost is multiplied with a discount factor, calculated from the discount rate. All calculations are done relative to the general inflation, so that all costs are expressed in today‟s money.
Calculation of Present Value There are two types of calculations used in LCC to express a future cost at its present value. These include:
(a) Single Payment This is applicable for a single future cost (Cr), payable in n year‟s time for example replacement cost of runner, the replacement value is given by:
PV = Cr.Pr
D-1
where Pr ={(1+r)/(1+d)}n with d being the discount rate, i the commodity specific inflation rate (above general inflation) and n the year of incurred cost. (b) Annual Payment
cxxxviii For a payment Ca occurring annually for a period of n years, the present value (PV) is given by
PV = Ca.Pa
D-2
where Pa = {((1+i)n-1)/(i(1+i)n)}
For each of the payments to be made during the life of the system, the present value can therefore be determined using the discount factors Pr and Pa. The sum of all present value of all costs gives the life cycle cost of the system.
Replacement Costs The lifetime of both the test turbine and the diesel generator was taken as 20 years which also the economic life time of the plant, so there were replacement costs for discounting to the present value.
Period of Analysis An analysis period of 20 years was chosen, which corresponds to the useful lifetime of the small hydropower systems (Holland, 1983; Harvey, 1993; Khennas and Barnet, 2000). A discount rare of 12% was chosen, as this is usually considered typical for energy projects for developing countries (Harvey, 1993; Khennas and Barnet, 2000).
Economic Indicators There are two ways that the LCC is commonly used to provide intelligible expression of system cost, namely;
cxxxix
(i)
(i)
Annualized Life Cycle Cost
(ii)
Levelized Energy Cost
Annualized Life Cycle Cost (ALCC)
The ALCC is the LCC expressed in terms of a constant per year. It‟s is the annual expenditure required to pay for the system over its lifetime and include the cost of repayments on borrowed capital
ALCC = LCC/(Pa) (n)
D-3
Where Pa is the annualization factor.
(ii) Levelized Energy Cost (LEC) This is the most useful figure for comparing energy technologies. It expresses the average cost of generating each useful unit during the lifetime of the system. For a system generating electricity, the LEC can be determined from the ALCC as follows:
LEC =
ALCC/(Electricity supplied per year (KWh/year))
D-4
cxl APPENDIX E: DATA FOR FINANCIAL EVALUATION Table E-1: Retail prices of diesel in Kenya (27 November – 10 December, 2009), Prices Collection through a survey by researcher. No. Town Station Price (Ksh 1 Nairobi Shell – Valley Road 75.90 2 Shell – Kenyatta Avenue 75.90 3 Total – Koinange Street 76.90 4 Kobil – Koinage Street 78.00 5 Shell – University Way 75.90 6 Shell – Langata Road 73.90 7 National Oil – Nairobi West 73.90 8 Shell – Lusaka Road 71.90 9 Total – Lusaka Road 71.90 10 Oilybia – Lusaka Road 71.90 11 Shell – Jogoo Road, City Stadium 70.90 12 Gulf – Jogoo Road 70.90 13 Petrol City – Jogoo Road 71.70 14 Kobil – Jogoo Road 74.50 15 Shell – Jogoo Road 69.90 16 Shell – Jogoo Road/Likoni Road Junction 70.90 17 Caltex –Jogoo, Buruburu Junction 70.90 18 Caltex – Outering Road, Donholm 69.50 19 Petrol City – Outering Road, Donholm 69.50 20 Kenol – Kangundo Road, Umoja 74.90 21 Petrol City – Kangundo Road, Umoja 68.50 22 Total – Kangundo Road, Umoja 70.90 23 Total - Outering Road/Kangundo Road junction 70.90 24 Kobil–Buruburu 74.90 25 Kobil – Lusaka Road 73.90 26 Shell – Mombasa Road, Nyayo Stadium 74.90 27 Kenol South C 77.90 28 Total - South C 74.90 29 Total - Mbagathi Road 73.90 30 Shell – Mbagathi Road 72.90 31 Shell – Thika Road, Ngara 73.90 32 Kobil – Thika Road, Ngara 72.80 33 Fuel Max – Thika Road, Ngara 72.80 34 Oilibya – Thika Road, Ngara 72.90 35 Total - Thika Road, Ruaraka 73.90 36 Total –Ngara 73.90 37 Kobil–Ngara 73.80 38 Petrol –Ngara 73.90 39 Oilibya – Ronald Ngara Street 72.90 40 Oilibya – Mombasa Road – Bellevue 77.90 41 Kobil – Mombasa Road – Bellevue 76.90 42 Gulf–Outering 70.50 43 Oilibya – Outering Road, Donholm 72.90
cxli No. 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89
Town
NakuruNairobi Road
Naivasha Nakuru
Station Shell Outering – Outering Ring Road, Tena Total – Kariobangi South National Oil – Haile Selassie Shell – Haile Selassie Kenol – Haile Selassie Road Total - Westland Oilibia– Westland Total – Westland Petrol – Westland Engen– Westland Total –Uthiru Shell – Uthiru Total – Uthiru/Kabete Triton – Uthiru/Kabete Kenol–Kabete Nuclear –Uthiru Uthiru Petrol Station Shell –Kinoo
Price (Ksh 72.90 72.90 71.90 73.90 74.80 72.90 74.90 72.90 72.90 71.90 71.90 72.90 72.90 72.90 72.80 70.90 71.90 73.90
Nodfall–Kinoo Kobil– Zambezi Oilibya– Zambezi National Oil Limuru Kenol–Limuru Kobil–Limuru Kobil–Kinale Kobil–Kinungi Total Kenol–Delamere Bismak Timex Caltex Triton Mogas Nobil Jetco National Oil Petrol Shell Gulf Energy Kenol National Oil Delta Total Shell Riva Hashi
71.90 72.90 69.90 69.50 72.40 72.40 72.90 72.90 72.90 73.90 71.90 70.90 71.40 71.90 70.90 70.90 70.90 71.40 70.90 71.90 70.90 72.80 69.90 69.50 71.40 70.90 70.50 71.30
cxlii No. Town 90 Karatina 91 92 93 94 95 96 Nanyuki 97 98 99 100 Isiolo 101 102 103 104 Eldoret 105 106 107 108 109 110 111 112 Kitale 113 114 115 116 117 118 Kapenguria 119 120 Kerugoya TOTAL Average price
Station National Oil Oilibya Caltex Mogas Kenol Total Total Caltex Shell Oilibya Total Caltex Shell Millennium Petrol Caltex Kenol Total Oilibya National Oil Kobil Triton Kenol Total Kobil Oilibya Caltex National Oil Caltex Oilibya Total
Price (Ksh 70.50 70.50 70.00 70.00 71.50 70.50 70.90 70.90 70.90 70.90 73.90 73.90 73.90 72.90 73.90 72.90 74.90 72.90 72.90 72.90 74.90 72.90 74.50 71.90 72.90 71.90 71.90 71.90 72.90 72.90 72.90 8709.2 72.60
Table E-2: Load factor. Use Lighting
No. lamps 1 2 3 3
of Rating (w) 8 8 8 8 4
No. of HHs
Hours/day
Wh/day
113 25 4 1 church 142
5 5 5 1 12
4520 400 96 24 6816 11,856
Radio Total Power Factor = 0.44 for turbine power and 0.16 for diesel generator
cxliii Table E-3: Technical data for LCC comparison between vehicle axle-propeller shaft as a turbine and a diesel generator. Description
Test Turbine
Diesel Gen-set (5.8 KVA)
Type of Technology
Hydraulicwater
Heavy duty Lister
turbine
diesel engine generator
Source
Local
Imported
Cost of System
219,075
650,000
3
Rating (kW)
3 kW
6.46
4
Mode of operation
Continuous
Continuous
5
Availability factor (%)
95
90
6
Operations (Ksh/year)
48,0000
48,000
7
Fuel consumption ( Litres/year)
8
Unit price of diesel (Ksh/litre
----------
72.60
9
Minor service Lubricants (Ksh/year)
5,200
26,000
10
Major service (Ksh every 2 years)
2,000
10,000
11
Load factor (%)
44
12
12
Energy generation (kWh)
4,211
12,059
13
Plant life (years)
20
20
1
2
16,644
Source: Diesel generator – Manufacturer‟s specifications and technical data (Lister Petter Ltd of England and from local dealer Rift Valley Machinery Services Ltd, Industrial Area, Nairobi).
cxliv Table E-4: Present worth of major service cost (done every 2 years for vehicle axle-propeller shaft as a turbine – Ksh 2,500and diesel generator - Ksh 10,000) Year
Discount Factor
Present Worth (PW) - Ksh Vehicle Axle
Diesel Generator
2
0.7972
1,993
7,972
4
0.6355
1,589
6,455
6
0.5066
1,267
5,066
8
0.4039
1,010
4,039
10
0.3220
805
3,220
12
0.2567
642
2,567
14
0.2046
512
2,046
16
0.1631
408
1,631
18
0.1300
325
1,300
8,551
34,196
Total
Table E-5: Present worth of operation, minor service and fuel costs (discount factor 7.4694) Technology
Annual Cost (Ksh)
Present Worth (Ksh)
Vehicle axle as turbine
48,000
358,531
Diesel generator
48,000
358,531
Minor
Vehicle axle as turbine
5,200
38,841
service
Diesel generator
26,000
194,204
Fuel
Vehicle axle as a turbine
------------
-----------
Diesel generator
1,208,354
9,025,682
Operator
