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Design of high efficiency pelton turbine for micro hydropower
 

Design of high efficiency pelton turbine for micro hydropower

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    Design of high efficiency pelton turbine for micro hydropower Design of high efficiency pelton turbine for micro hydropower Document Transcript

    • INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING International Journal of & TECHNOLOGY (IJEET) (IJEET), ISSN 0976 – Electrical Engineering and Technology 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEMEISSN 0976 – 6545(Print)ISSN 0976 – 6553(Online)Volume 4, Issue 1, January- February (2013), pp. 171-183 IJEET© IAEME: www.iaeme.com/ijeet.aspJournal Impact Factor (2012): 3.2031 (Calculated by GISI) ©IAEMEwww.jifactor.com DESIGN OF HIGH EFFICIENCY PELTON TURBINE FOR MICRO- HYDROPOWER PLANT Bilal Abdullah Nasir1 1 Hawijah Technical Institute, Kirkuk, Iraq ABSTRACT The Pelton turbine was performed in high head and low water flow, in establishment of micro-hydro electric power plant, due to its simple construction and ease of manufacturing. To obtain a Pelton hydraulic turbine with maximum efficiency during various operating conditions, the turbine parameters must be included in the design procedure. In this paper all design parameters were calculated at maximum efficiency. These parameters included turbine power, turbine torque, runner diameter, runner length, runner speed, bucket dimensions, number of buckets, nozzle dimension and turbine specific speed. Keywords:Pelton turbine, maximum efficiency, designparameters,micro-hydro power plant. 1. INTRODUCTION Hydraulic turbine can be defined as a rotary machine, which uses the potential and kinetic energy of water and converts it into useful mechanical energy. According to the way of energy transfer, there are two types of hydraulic turbines namely impulse turbines and reaction turbines. In impulse turbines water coming out of the nozzle at the end of the penstock is made to strike a series of buckets fitted on the periphery of the runner. The runner revolves freely in air and the casing is not important in impulse turbine. In a reaction turbine, water enters all around the periphery of runner and the runner remains full of water every time. The water leaves from the runner is discharged into the tailrace with a different pressure. Therefor casing is necessary for reaction turbines [1].Pelton turbine is an impulse turbine. The runner of the Pelton turbine consists of double hemispherical cups fitted on its periphery as shown in figure (1). 171
    • International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – Engineering6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME January Figure (1) The runner ofthePelton turbine The jet strikes these cups (buckets) at the central dividing edge of the front edge. Thecentral dividing edge is also called as splitter. The water jet strikes edge of the splittersymmetrically and equally distributed into the two halves of hemispherical bucket.Theoretically, if the buckets are exactly hemispherical, it will deflect the jet through 180°. ,Then the velocity of the water jet leaving the bucket would be opposite in direction to thevelocity of jet entering. Practically, this can not be achieved because the jet le leaving thebucket strikes the back of succeeding bucket and the overall efficiency would decrease. Inpractice, the angular deflection of the jet in the bucket is limited to about 165° 165°→170°. Theamount of water discharges from the nozzle is regulated by a needle valve provided inside the needlenozzle as shown in figure (2).Figure (2) The nozzle and deflector of the Pelton turbine: (a) the nozzle spear and deflector. (b) The nozzle components. A deflector is used to control the turbine speed. One or more water jets (nozzles) canbe provided with the Pelton turbine depending on the water flow rate and the nozzle capacity. 172
    • International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEMEThe Pelton turbines have been given increasing interest by the research community withinmultiple fields. This is due to the increasing demand for energy on a global basis in additionto the growing focus on meeting the increasing demand by utilizing renewable energyresources. An increase in efficiency in the order 0.1 % would lead to large increase inelectrical power production.Innovation within energy business is kept a close corporate secret and all research done on aturbine designed by commercial companies is confidential. Thus the deferent researchcommunities have no common practical case with which they can cooperate within theirdistinctive fields [2]. The literature on Pelton turbine design available is scarce at best due tothe competitive nature of the industry and the resulting secrecy surrounding design methodsand innovations. In the last decade a lot of papers about numerical and experimental analysisand design of Pelton turbines have been published. A water jet from Pelton turbine injectorwas analyzed experimentally and numerically by Barkinson in reference [3]. The influence ofjet velocity and jet quality on turbine efficiency were investigated by Vesely and Staubli inreferences [4,5]. A bucket simulation using three adjacent buckets was shown by Mack andMoser in reference [6]. Unsteady analysis of a Pelton runner with mechanical simulation waspresented by Parkinson in reference [7]. A numerical analysis of water flow in a two jetsPelton turbine with horizontal axis was presented by Jost in reference [8]. A modification inthe bucket design of Pelton turbine is suggested by SurajYadav in reference [9] to increasethe efficiency of the Pelton turbine. The effect of runner to jet speed ratio on the Peltonturbine efficiency is tested experimentally by Bryan in reference [10]. In this paper acomplete design procedure of a Pelton turbine, based on analytical and empirical calculationof the turbine parameters. The design steps was presented by Matlab Simulink computerprogram. The designed Pelton turbine was used in micro-hydro electric power plant tooperate at maximum efficiency.2. DESIGN STEPS OF THE PELTON TURBINE The design procedure of the Pelton turbine which is used in micro-hydro powergeneration can be systematic as follow:1. Preparing the site data of power plantThis involves the calculations and measuring the net head and the water flow rate.‫ܪ‬௡ ൌ ‫ܪ‬௚ െ ‫ܪ‬௧௟a. Calculation of the net head (Hn): (1)Where Hg = the gross head which is the vertical distance between water surface level at theintake and at the turbine.Htl = total head losses due to the open channel, trash rack, intake, penstock and gate or valve.These losses approximately equal to 6% of gross head.b. Calculation of the water flow rate (Q):The water flow rate can be calculated by measuring the river or stream flow velocity (Vr) in(m.s-1) and its cross-sectional area (Ar) in (m2), then:ܳ ൌ ܸ ‫ܣ כ‬௥ ௥ ሺ݉ଷ . ‫ି ݏ‬ଵ ሻ (2) 173
    • International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME2. Calculation of the turbine input power (Pti)ܲ௧௜ ൌ ߩ ‫ܥ כ ݃ כ‬௡ ‫ܪ כ‬௡ ‫ܳ כ‬௧ ሺܹܽ‫ ݐݐ‬ሻ ଶThe electrical input power to the turbine in (Watt) can be calculated as: (3)3. Calculation of the turbine speed (N)The correlation between the specific speed (Ns) and the net head (Hn) is given for the Pelton ඥ݊௝turbine as [11]:ܰ௦ ൌ 85.49 ‫כ‬ ൘ ଴.ଶସଷ ‫ܪ‬௡ (4) ܳ݊௝ ൌ ௧ൗܳWhere nj = number of turbine nozzles (jets), and can be calculated as: ௡ (5)Where Qt = water flow capacity of each nozzle (m3.s-1). ‫ܪ‬௡ ହൗThen the turbine speed in (r.p.m) can be calculated as [11]:ܰ ൌ ܰ௦ ‫כ‬ ൘ ସ ඥܲ௧௜ (6)4. Calculation of the runner circle diameter (Dr)ܸ ൌ ‫ܥ‬௡ ‫ כ‬ඥ2 ‫ܪ כ ݃ כ‬௡ (m.s )The water jet through nozzle has a velocity (Vj) in (m.s-1) can be calculated as [11]: ௝ -1 (7) ߨܰ‫ܦ‬௥The runner tangential velocity (Vtr) in (m.s-1) can be calculated as:ܸ௧௥ ൌ ‫ܴ כ ݓ‬௥ ൌ 60 (m.s-1) (8)Also the runner tangential velocity can be given as [11]:ܸ௧௥ ൌ ‫ܸ כ ݔ‬௝ (m.s-1) (9)Where x = ratio of runner tangential velocity to nozzle or jet velocity. 60 ‫ݔ כ‬‫ܦ‬௥ ൌ ‫ܸכ‬From equations (8) and (9): ߨܰ ௝ (10)At maximum efficiency the ratio of (x) between (0.46) to (0.47).Then the runner diameter at maximum efficiency can be calculated from equations (7) and ඥ‫ܪ‬௡൘(10) as:‫ܦ‬௥ ൌ 38.6 ‫כ‬ ܰ (11) 174
    • International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEMEThe required diameter must be greater than this calculated value due to inconsistencies in themanufacture of the buckets and the need to have a minimum distance of safety between thenozzle and the Pelton runner.If the turbine is free to rotate under no-load speed (run-away speed), the runner tangentialspeed should be equal to the jet speed as: ‫ܦ‬௥ൗ ߨܰ௥ ‫ܦ‬௥ܸ௧௥ ൌ ‫כ ݓ‬ 2 ൌ 60 ൌ ܸ௝Or 60 ‫ܸ כ‬ܰ௥ ൌ ௝ ൘ሺߨ ‫ ܦ כ‬ሻ ௥ (r.p.m) (12)The run-away speed (Nr) is independent on the water flow rate.5. Calculation of nozzle dimensions [11]: ܳ௡ ൌ ܸ ‫ܣ כ‬௝The water flow rate through each nozzle (Qn) can be calculated as: ௝ (m3.s-1) (13) ‫ܦ‬ଶ‫ܣ‬௝ ൌ ߨ ‫ כ‬௝ ൘The nozzle area (Aj) can be calculated as: 4 (m2) (14) 4 ‫ܳ כ‬௧Then from equations (13) and (14) the nozzle diameter (Dj) can be calculated as: ‫ܦ‬௝ ൌ ඨ ൘ ‫ ܸ כ ݊ כ‬ሻ (m) ሺߨ ௝ ௝ (15) ሺ‫ ܦ‬െ ‫ܦ‬௝ ሻ ‫ܮ‬௡ ൌ ௣௡ ൘The nozzle length can be calculated as [11]: tan ሺߚሻ (m) (16) ‫ܦ‬௣௧ ‫ܦ‬௣௡ ൌ ൘ ݊ ඥ ௝ (m) (17)The nozzle exits have to be located as close to the Pelton runner as possible to prevent the jetfrom diverging the designed diameter. The distance between the nozzle and runner should be5% of the runner circle diameter, plus an extra (3) mm clearance to account for emergencydeflectors as:ܺ௡௥ ൌ 0.05 ‫ܦ כ‬௥ ൅ ‫ܦ‬௧ (m) (18) 175
    • International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEMEThe distance between nozzle and bucket taking into account the minimum clearance betweenthe nozzle and buckets was given as: ܺ௡௕ ൌ 0.625 ‫ܦ כ‬௥ (m) (19)The required distance was bigger than the calculated above, due to inconsistencies in themanufacture of buckets and the need to have a minimum distance of safety between thenozzle and Pelton runner.6. Calculation of bucket dimensions [11]The bucket axial width can be calculated as:‫ܤ‬௪ ൌ 3.4 ‫ܦ כ‬௝ (m) (20)The bucket radial length can be calculated as:‫ܤ‬௟ ൌ 3 ‫ܦ כ‬௝ (m) (21)The bucket depth can be calculated as:‫ܤ‬ௗ ൌ 1.2 ‫ܦ כ‬௝ (m) (22)The number of buckets in each runner must be determined so that no water particle was lostwhile minimizing the risks of detrimental interactions between the out flowing water particles ‫ܦ‬݊௕ ൌ 15 ൅ ௥൘ ‫ ܦ כ‬ሻand adjacent buckets. It can be calculated as: ሺ2 ௝ (23)The length of the moment arm of bucket can be calculated as:‫ܮ‬௔௕ ൌ 0.195 ‫ܦ כ‬௥ (m) (24)The runner size was determined by its diameter, and its shaper was determined by the numberof buckets. The runner shaft was sized to mount directly on the generator shaft. The flingerseal was also necessary to seal the whole through which the generator shaft enters the turbinebox. The radius of bucket center of mass to center of runner was given as:ܴ௕௥ ൌ 0.47 ‫ܦ כ‬௥ (m) (25)The bucket volume was given as:ܸ௕ ൌ 0.0063 ‫ܦ כ‬௥ ଷ (m3) (26) 176
    • International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEMEThe mass of bucket can be calculated as:‫ܯ‬௕ ൌ ߩ௠ ‫ܸ כ‬௕ (Kg) (27)7. Penstock design [11]The penstock was the piping that brings the water from the river or stream to the point whereit begins to be directed to the turbine. Penstock material was made of high pressure such asPVC, chosen for its availability, affordability and low friction loss characteristics. The PVCwas susceptible to mechanical damage from ultraviolet radiation. If the piping was weakenedin any way, due to the high pressure in the penstock in any surge event, failure was a definitepossibility. To prevent this, the PVC piping would be founded in concrete along its entirelength. At the bottom of penstock, before the entrance to the turbine house, a valve would beinstalled. This valve would allow the penstock to be emptied for turbine maintenance.The thickness of penstock was chosen by determining the potential water hummer effect. Awater hummer effect was a surge pressure that occurs when the nozzles in turbine becomeplugged and the flow in penstock was suddenly stopped. The thickness of penstock (tb) can becalculated by the following relations; ‫ܦ‬௣௧ ൅ 508‫ݐ‬௣ ൌ ቈቆ ቇ ൅ 1.2቉ ‫ି01 כ‬ଷ 400 (m) (28) ଶ ‫ܮ‬‫ܦ‬௣௧ ൌ 2.69 ‫ כ‬ሺ݊௣ ‫ܳ כ‬௧ ‫ כ‬௣௧൘‫ ܪ‬ሻ଴.ଵ଼଻ହ ଶ ௚ (m) (29)‫ܪ‬௦ ൌ ܸ ‫ܸ∆ כ‬ൗ݃The surge pressure (Hs) in (m) can be calculated as: ௪ (m) (30) 1ܸ ൌ ௪ ඩ 1 ‫ܦ‬௣௧ ߩ௪ ‫ כ‬ሺ‫ ܭ‬൅ ‫ ݐ כ ܯ‬ሻ (m.s-1) (31) ௪௠ ௣ ௣ ܳ∆ܸ ൌ ݊௝ ‫ܣ כ‬௣ (m.s-1) (32)The safety factor to mitigate the water hummer effect in the design of micro-hydro electric ‫ݐ‬௣௘ ‫ݐ כ‬௦௣power plant was given as [13, 14]:ܵ. ‫ ܨ‬ൌ ሺ൐ 2.5ሻ 5 ‫01 כ‬ଷ ‫ܦ כ‬௣௧ ‫ܪ כ‬௧ (33)‫ܪ‬௧ ൌ ሺ‫ܪ‬௚ ൅ ‫ܪ‬௦ ሻ (m) (34) 177
    • International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME8. Deflector design [15, 16]An emergency deflector system must be installed to protect the generator in case a loadcircuit failure, and the generator rotates at over speed.The force in each deflector can be calculated as:‫ܨ‬ௗ ൌ ߩ௪ ‫ܳ כ‬௡ ‫ܸ כ‬௝ (Newton) (35)The required force in each deflector was given as:‫ܨ‬ௗ௥ ൌ ‫ܨ‬ௗ ‫݂ .ܵ כ‬ (Newton) (36)The torque acting on the deflector arm was given as:ܶௗ ൌ ‫ܨ‬ௗ௥ ‫ܴ כ‬ௗ (N.m) (37)The required torque acting on the deflector arm was given as:ܶௗ௥ ൌ ܶௗ ‫ܨ כ‬௖ (N.m) (38)9. Calculation of maximum turbine efficiency [12]The turbine efficiency generally affected by three factors:i.) Hydraulic losses or power losses those occur due to flow irregularity within the bucket.ii.)Windage losses which occur because of resistance in the air to the moving bucket.iii.) Mechanical losses in the system used to transmit the power from the turbine to the generator. If the turbine was mounted directly to the generator, there were no mechanical losses in the turbine. ߩ௪ ‫ܳ כ‬௧ ‫ ܸ כ‬ଶThe input power to the turbine can be calculated as:ܲ௧௜ ൌ ௝ 2 (W) (39)The power output developed by the turbine was given as:ܲ௧௢ ൌ ߩ௪ ‫ܳ כ‬௧ ‫ܸ כ‬௧௥ ‫ כ‬ሾሺܸ െ ܸ௧௥ ሻሺ1 ൅ ߰ ‫ כ‬cosሺ߶ሻሻሿ ௝ (W) (40)Then the turbine hydraulic efficiency can be calculated as: ܲ௧௢ 2 ‫ܸ כ‬௧௥ ‫ כ‬ሺܸ െ ܸ௧௥ ሻሺ1 ൅ ߰ ‫ כ‬cosሺ߶ሻሻߟ௧௛ ൌ ൌ ௝ ܲ௧௜ ܸଶ ௝ (41)߶ ൌ 180° െ ߠߠ ൌ 160° ՜ 170° (42) 178
    • International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME݀ሺߟ௧௛ ሻFor maximum hydraulic turbine efficiency: ൘ ݀ሺܸ௧௥ ሻ ൌ 0Or ܸ௧௥ ൌ 0.5 ‫ܸ כ‬ (43) ௝Then the maximum hydraulic efficiency was given as: ሾ1 ൅ ߰ ‫ כ‬cosሺ߶ሻሿߟ௧௛ሺ௠௔௫.ሻ ൌ 2 (44)The turbine windage efficiency was given as: ‫ܭ‬ௗ ‫ߩ כ‬௔ ‫ܣ כ‬௕ ‫ ݔ כ‬ଷߟ௧௪ ൌ 1 െ ߩ௪ ‫ܣ כ‬௝ (45)Then the total turbine efficiency was given as:ߟ௧ ൌ ߟ௧௛ ‫ߟ כ‬௧௪ ‫ߟ כ‬௧௠ (46)If the turbine was mounted directly to the generator the mechanical losses can be neglectedand the mechanical efficiency (ηtm) equal to unity.The torque developed by the turbine can be calculated as: ܲ௧௢ ܶ௧ ൌ ൌ ܳ௧ ‫ܦ כ‬௥ ‫ כ‬ሺܸ െ ܸ௧௥ ሻ ‫ݓ‬ ௝ (N.m) (47)3. RESULTS The design calculations of the Pelton turbine were implemented by a Matlab Simulinkcomputer program. Table (1) shows the design parameters of the Pelton turbine with constantflow rate (Q = 0.1 m3.s-1) and variable gross head of the plant site (Hg= 50 → 140 m), whiletable (2) shows the same turbine parameters at constant head (Hg = 50, 60 m) with variablewater flow rate (Q = 0.1→ 0.4 m3.s-1) of the site. Figure (3) shows the variation of runner tonozzle diameter ratio with specific speed at different values of water flow rate, while figure(4) shows the variation of the same ratio with the nozzle length.From these results, the turbine maximum efficiency was found to be 97% constant. In case ofvariable head, all the design parameters were varied with head except of number of runnerbuckets and runner diameter, while in a variable flow rate all the design parameters wereconstant except of turbine power, specific speed and nozzle length. 179
    • International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME Dr/Dj 10 9.5 9 Runner/Nozzle Diameter Ratio 8.5 8 7.5 7 6.5 3 3 3 3 Q=0.1m /s Q=0.2m /s Q=0.3m /s Q=0.4m /s 6 5.5 5 20 30 40 50 60 70 80 Specific Speed NsFigure (3) Variation of runner to nozzle diameter ratio with specific speed at different values of water flow rate. Dr/Dj 10 9.5 9 8.5 Runner/Nozzle Diameter Ratio 8 7.5 7 6.5 3 3 3 3 Q=0.4 m /s Q=0.3 m /s Q=0.2 m /s Q=0.1 m /s 6 5.5 5 180 200 220 240 260 280 300 Nozzle Length Ln (mm) Figure (4)Variation of runner to nozzle diameter ratio with nozzle length at different values of water flow rate.Table (1) design parameters of the Pelton turbine at maximum efficiency and constant flow rate (Qt =0. 1 m3.s-1) Pto ηt Tt N Dj Vtr Vj LnHg (m) Ns Dr(m) nb (Kw) (%) (N.m) (r.p.m) (m) (m) (m) (m) 50 43 96.9 660 620 33.5 0.43 0.065 13.9 29.8 0.27 19 60 51.5 96.9 722 680 32 0.43 0.062 15.2 32.5 0.26 19 70 60 96.9 779 735 31 0.43 0.060 16.4 35.2 0.25 19 80 68.5 96.9 832 787 30 0.43 0.058 17.5 37.5 0.25 19 90 77.2 96.9 882 835 29 0.43 0.056 18.6 40 0.24 19 100 85.8 96.9 930 881 28.3 0.43 0.055 19.6 42 0.24 19 110 94.3 96.9 974 925 27.7 0.42 0.053 20.6 44 0.24 19 120 103 96.9 1016 967 27 0.42 0.052 21.5 46 0.233 19 130 111.5 96.9 1057 1007 26.6 0.42 0.051 22.4 48 0.230 19 140 120 96.9 1097 1045 26 0.42 0.050 23.2 50 0.228 19 180
    • International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEMETable (2) design parameters of the Pelton turbine at maximum efficiency and constant gross head Qt Pto Tt ηt N Dj Vtr Vj LnHg(m) Ns Dr(m) nb (m3.s-1) (Kw) (N.m) (%) (r.p.m) (m) (m) (m) (m) 0.1 43 660 96.9 620 33.5 0.43 0.065 13.9 29.8 0.270 19 0.2 85.8 1320 96.9 620 47.4 0.43 0.065 13.9 29.8 0.240 19(50) 0.3 129 1980 96.9 620 58 0.43 0.065 13.9 29.8 0.220 19 0.4 171.5 2640 96.9 620 67.1 0.43 0.065 13.9 29.8 0.208 19 0.1 51.5 722 96.9 680 32 0.43 0.062 15.2 32.5 0.250 19 0.2 103 1444 96.9 680 45.4 0.43 0.062 15.2 32.6 0.230 19(60) 0.3 154.4 2167 96.9 680 55.6 0.43 0.062 15.2 32.6 0.210 19 0.4 206 2889 96.9 680 64.2 0.43 0.062 15.2 32.6 0.202 194. CONCLUSIONS The Pelton turbine is suitable for installing small hydro-electric power plants in case of highhead and low water flow rate. A complete design of such turbines has been presented in this paperbased on theoretical analysis and some empirical relations. The maximum turbine efficiency wasfound to be 97% constant for different values of head and water flow rate. The complete designparameters such as turbine power, turbine torque, turbine speed, runner dimensions andnozzledimensionsare determined at maximum turbine efficiency.Nomenclature Ab Peripheral area of penstock (m2) Aj Jet or nozzle cross-sectional area (m2) Ap penstock cross-sectional area (m2) Ar River or steam cross-sectional area (m2) Bd Bucket depth (m) Bl Bucket radial length (m) Nozzle (jet) discharge coefficient (≅ 0.98) Bw Bucket axial width (m) Cn Dj Jet or nozzle diameter (m) Dpn Diameter of penstock connected to the nozzle (m) Dpt Diameter of penstock connected to the turbine (m) Dr Runner (wheel) circle diameter (m) Friction factor acted upon by bearings (≅1.2) Dt Deflector thickness (m) Fc Fd Deflector force (N) Fdr Required deflector force (N) g Gravity acceleration constant (9.81 m.s-2) Hg Gross head (m) Hn Net head (m) Hs Surge head (m) Ht Total head (m) Htl Total head loss (m) Kd Drag coefficient Kwm Bulk water modulus (2.1*109 N.m-2) Lab Length of bucket moment arm (m) Ln Nozzle length (m) 181
    • International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME Lpt Length of penstock between intake and turbine (m) Mb Mass of bucket (Kg) Mp Modulus of penstock material (for PVC = 2.8*109 N.m-2) nb Number of buckets nj Number of turbine nozzles np Manning factor of penstock N Turbine (runner) speed (r.p.m) Nr Turbine run-away speed (r.p.m) Ns Turbine specific speed Pti Turbine input power (watt) Pto Turbine output power (watt) Qn Nozzle flow rate (m3.s-1) Qt turbine flow rate (m3.s-1) Rbr Radius of bucket center of mass to runner center (m) Rd Radius of deflector arm (m) Rr Radius of runner (m) S.F Safety factor to prevent water hummer effect (> 2.5) tp Thickness of penstock (m) tpe Effective thickness of penstock (m) tsp Tensile strength of penstock material (N.m-2) Td Deflector torque (N.m) Tdr Required deflector torque (N.m) Tt turbine torque (N.m) Vb Volume of bucket (m3) Vj Water jet velocity (m.s-1) Vr River velocity (m.s-1) Vtr Runner tangential velocity (m.s-1) Vw Pressure wave velocity (m.s-1) x Ratio of runner tangential velocity to jet velocity Xnb Distance between bucket and nozzle (m) Xnr Distance between nozzle and runner (m) V Change in velocity of penstock (m.s-1) ߚGreek symbols ߰ Bucket roughness coefficient (≅ 0.98) Nozzle tapper angle (degrees) ߠ ߩa Deflection angle between bucket and jet (160°→170°) ߩm Air density (1.23 Kg.m-3) ߩw Density of bucket material (Kg.m-3) ߱ Water density (1000 Kg.m-3) ߱r Runner velocity (radian.sec-1) ߟt Runner run-away velocity (radian.sec-1) ߟth Total turbine efficiency ߟtm Turbine hydraulic efficiency ߟtw Turbine mechanical efficiency Turbine windage efficiency 182
    • International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEMEREFERENCES[1]Atthanayake, I. U.: "Analytical study on flow through a Pelton turbine bucket using boundary layer theory", International Journal of Engineering and Technology (IJET), Vol. 9, No. 9, pp. 241-245, 2009.[2]Solimslie, B. W. and Dahlhaug, O. G.: "A reference Pelton turbine design", 6th, IAHR Symposium on Hydraulic Machinery and Systems, IOP Publishing, IOP Conf. Series: Earth and Environmental Science, 15, 2012.[3] Parkinson, E. and et al.: "Experimental and numerical investigation of free jet flow at a model nozzle of a Pelton turbine", Proceeding of the XXI IAHR Symposium on Hydro Machines and Systems, Switzerland, 2002.[4]Vesely, J. and Pochyly, F.: "Stability of the flow through Pelton turbine nozzles", Hydro- 2003, Dubrovnik, Croatia, 2003.[5]Staubli, T. and et al.: "Jet quality and Pelton efficiency", Proceeding of Hydro-2009, Lyon, France,2009.[6] Mack, R. and Moser, W.: "Numerical investigation of the flow in a Pelton turbine", Proceeding of the XXI IAHR Symposium on Hydro Machines and Systems, Switzerland, 2002.[7] Parkinson, E. and et al.: "Unsteady analysis of a Pelton runner with flow and mechanical simulations", Hydro-2005, Beljak, Austria, 2005.[8]Jost, D. and et al.: "Numerical prediction of Pelton turbine efficiency", 25th, IAHR Symposium on Hydraulic Machinery and Systems, IOP Conf. 12, 2010.[9]SurajYadav: "Some aspects of performance improvement of Pelton wheel turbine with reengineered blade and auxiliary attachments", International journal of Scientific and Engineering Research, Vol. 2, No. 9, September, pp. 1-4, 2011.[10] Bryan, R. C. and Sharp, K. V.: "Impulse turbine performance characteristics and their impact on Pico-hydro installation", Renewable Energy Journal, Elsevier, Vol. 50, pp. 959- 964, 2013.[11] Thake, J.: "The micro-hydro Pelton turbine manual, design, manufacture and installation for small-scale hydro power", ITDG Publishing, UK, 2000.[12] Fluid-machinery, chapter-2, Pelton turbine. Available from: htt:// Ptumech. Loremate.com / fluid-machinery / node / 12 / [accessed 12 / 1 / 2013].[13] Harvey, A. and et al.: "Micro-hydro design manual", ITDG Publishing, UK, 2005[14] Comunidad Nueva Alianza: "Micro-hydro electric design", Engineering Design Document, Producing by Xelateco, Endorsed by AIDG, Guatemala, July, 2006.[15] Carvill, J.: "Mechanical engineers data handbook", Butterworth-Heinmann, 1993.[16] Johnson, R. M. and et al.: "Pelton turbine deflector over speed control for a small power system", IEEE Transactions on Power Systems, Vol. 19, No. 2, pp. 1032-1037, 2004. 183